1
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Bornet G, Emperauger G, Chen C, Machado F, Chern S, Leclerc L, Gély B, Chew YT, Barredo D, Lahaye T, Yao NY, Browaeys A. Enhancing a Many-Body Dipolar Rydberg Tweezer Array with Arbitrary Local Controls. PHYSICAL REVIEW LETTERS 2024; 132:263601. [PMID: 38996299 DOI: 10.1103/physrevlett.132.263601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Revised: 05/01/2024] [Accepted: 05/20/2024] [Indexed: 07/14/2024]
Abstract
We implement and characterize a protocol that enables arbitrary local controls in a dipolar atom array, where the degree of freedom is encoded in a pair of Rydberg states. Our approach relies on a combination of local addressing beams and global microwave fields. Using this method, we directly prepare two different types of three-atom entangled states, including a W state and a state exhibiting finite chirality. We verify the nature of the underlying entanglement by performing quantum state tomography. Finally, leveraging our ability to measure multibasis, multibody observables, we explore the adiabatic preparation of low-energy states in a frustrated geometry consisting of a pair of triangular plaquettes. By using local addressing to tune the symmetry of the initial state, we demonstrate the ability to prepare correlated states distinguished only by correlations of their chirality (a fundamentally six-body observable). Our protocol is generic, allowing for rotations on arbitrary sub-groups of atoms within the array at arbitrary times during the experiment; this extends the scope of capabilities for quantum simulations of the dipolar XY model.
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2
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Chan A, Shi Z, Dellantonio L, Dür W, Muschik CA. Measurement-Based Infused Circuits for Variational Quantum Eigensolvers. PHYSICAL REVIEW LETTERS 2024; 132:240601. [PMID: 38949342 DOI: 10.1103/physrevlett.132.240601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 04/10/2024] [Accepted: 05/15/2024] [Indexed: 07/02/2024]
Abstract
Variational quantum eigensolvers (VQEs) are successful algorithms for studying physical systems on quantum computers. Recently, they were extended to the measurement-based model of quantum computing, bringing resource graph states and their advantages into the realm of quantum simulation. In this Letter, we incorporate such ideas into traditional VQE circuits. This enables novel problem-informed designs and versatile implementations of many-body Hamiltonians. We showcase our approach on real superconducting quantum computers by performing VQE simulations of testbed systems including the perturbed planar code, Z_{2} lattice gauge theory, 1D quantum chromodynamics, and the LiH molecule.
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Affiliation(s)
| | | | - Luca Dellantonio
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
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3
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Fauseweh B. Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges. Nat Commun 2024; 15:2123. [PMID: 38459040 PMCID: PMC10923891 DOI: 10.1038/s41467-024-46402-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 02/14/2024] [Indexed: 03/10/2024] Open
Abstract
Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.
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Affiliation(s)
- Benedikt Fauseweh
- Institute for Software Technology, German Aerospace Center (DLR), Linder Höhe, 51147, Cologne, Germany.
- Department of Physics, TU Dortmund University, Otto-Hahn-Str. 4, 44227, Dortmund, Germany.
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4
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Petrova EV, Tiunov ES, Bañuls MC, Fedorov AK. Fractal States of the Schwinger Model. PHYSICAL REVIEW LETTERS 2024; 132:050401. [PMID: 38364163 DOI: 10.1103/physrevlett.132.050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Revised: 10/09/2023] [Accepted: 12/18/2023] [Indexed: 02/18/2024]
Abstract
The lattice Schwinger model, the discrete version of QED in 1+1 dimensions, is a well-studied test bench for lattice gauge theories. Here, we study the fractal properties of this model. We reveal the self-similarity of the ground state, which allows us to develop a recurrent procedure for finding the ground-state wave functions and predicting ground-state energies. We present the results of recurrently calculating ground-state wave functions using the fractal Ansatz and automized software package for fractal image processing. In certain parameter regimes, just a few terms are enough for our recurrent procedure to predict ground-state energies close to the exact ones for several hundreds of sites. Our findings pave the way to understanding the complexity of calculating many-body wave functions in terms of their fractal properties as well as finding new links between condensed matter and high-energy lattice models.
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Affiliation(s)
- Elena V Petrova
- Russian Quantum Center, Skolkovo, Moscow 121205, Russia
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Egor S Tiunov
- Russian Quantum Center, Skolkovo, Moscow 121205, Russia
- Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, UAE
| | - Mari Carmen Bañuls
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schllingstrasse 4, D-80799 München, Germany
| | - Aleksey K Fedorov
- Russian Quantum Center, Skolkovo, Moscow 121205, Russia
- National University of Science and Technology "MISIS," Moscow 119049, Russia
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5
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Pal S, Bhattacharya M, Lee SS, Chakraborty C. Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics. Mol Biotechnol 2024; 66:163-178. [PMID: 37244882 PMCID: PMC10224669 DOI: 10.1007/s12033-023-00765-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 05/04/2023] [Indexed: 05/29/2023]
Abstract
Modern biological science is trying to solve the fundamental complex problems of molecular biology, which include protein folding, drug discovery, simulation of macromolecular structure, genome assembly, and many more. Currently, quantum computing (QC), a rapidly emerging technology exploiting quantum mechanical phenomena, has developed to address current significant physical, chemical, biological issues, and complex questions. The present review discusses quantum computing technology and its status in solving molecular biology problems, especially in the next-generation computational biology scenario. First, the article explained the basic concept of quantum computing, the functioning of quantum systems where information is stored as qubits, and data storage capacity using quantum gates. Second, the review discussed quantum computing components, such as quantum hardware, quantum processors, and quantum annealing. At the same time, article also discussed quantum algorithms, such as the grover search algorithm and discrete and factorization algorithms. Furthermore, the article discussed the different applications of quantum computing to understand the next-generation biological problems, such as simulation and modeling of biological macromolecules, computational biology problems, data analysis in bioinformatics, protein folding, molecular biology problems, modeling of gene regulatory networks, drug discovery and development, mechano-biology, and RNA folding. Finally, the article represented different probable prospects of quantum computing in molecular biology.
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Affiliation(s)
- Soumen Pal
- School of Mechanical Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India
| | - Manojit Bhattacharya
- Department of Zoology, Fakir Mohan University, Vyasa Vihar, Balasore, Odisha, 756020, India
| | - Sang-Soo Lee
- Institute for Skeletal Aging & Orthopedic Surgery, Hallym University-Chuncheon Sacred Heart Hospital, Chuncheon, Gangwon-Do, 24252, Republic of Korea
| | - Chiranjib Chakraborty
- Department of Biotechnology, School of Life Science and Biotechnology, Adamas University, Kolkata, West Bengal, 700126, India.
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6
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Charles C, Gustafson EJ, Hardt E, Herren F, Hogan N, Lamm H, Starecheski S, Van de Water RS, Wagman ML. Simulating Z_{2} lattice gauge theory on a quantum computer. Phys Rev E 2024; 109:015307. [PMID: 38366518 DOI: 10.1103/physreve.109.015307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 12/21/2023] [Indexed: 02/18/2024]
Abstract
The utility of quantum computers for simulating lattice gauge theories is currently limited by the noisiness of the physical hardware. Various quantum error mitigation strategies exist to reduce the statistical and systematic uncertainties in quantum simulations via improved algorithms and analysis strategies. We perform quantum simulations of Z_{2} gauge theory with matter to study the efficacy and interplay of different error mitigation methods: readout error mitigation, randomized compiling, rescaling, and dynamical decoupling. We compute Minkowski correlation functions in this confining gauge theory and extract the mass of the lightest spin-1 state from fits to their time dependence. Quantum error mitigation extends the range of times over which our correlation function calculations are accurate by a factor of 6 and is therefore essential for obtaining reliable masses.
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Affiliation(s)
- Clement Charles
- Department of Physics, The University of the West Indies, St. Augustine Campus, Trinidad and Tobago
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Erik J Gustafson
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
- Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, California 94035, USA
- USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, California 94043, USA
| | - Elizabeth Hardt
- Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Florian Herren
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Norman Hogan
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Henry Lamm
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Sara Starecheski
- Department of Physics, Sarah Lawrence College, Bronxville, New York 10708, USA
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | | | - Michael L Wagman
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
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7
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Verdel R, Zhu GY, Heyl M. Dynamical Localization Transition of String Breaking in Quantum Spin Chains. PHYSICAL REVIEW LETTERS 2023; 131:230402. [PMID: 38134792 DOI: 10.1103/physrevlett.131.230402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2023] [Accepted: 11/09/2023] [Indexed: 12/24/2023]
Abstract
The fission of a string connecting two charges is an astounding phenomenon in confining gauge theories. The dynamics of this process have been studied intensively in recent years, with plenty of numerical results yielding a dichotomy: the confining string can decay relatively fast or persist up to extremely long times. Here, we put forward a dynamical localization transition as the mechanism underlying this dichotomy. To this end, we derive an effective string breaking description in the light-meson sector of a confined spin chain and show that the problem can be regarded as a dynamical localization transition in Fock space. Fast and suppressed string breaking dynamics are identified with delocalized and localized behavior, respectively. We then provide a further reduction of the dynamical string breaking problem onto a quantum impurity model, where the string is represented as an "impurity" immersed in a meson bath. It is shown that this model features a localization-delocalization transition, giving a general and simple physical basis to understand the qualitatively distinct string breaking regimes. These findings are directly relevant for a wider class of confining lattice models in any dimension and could be realized on present-day Rydberg quantum simulators.
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Affiliation(s)
- Roberto Verdel
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Guo-Yi Zhu
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany
| | - Markus Heyl
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany
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8
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Joshi MK, Kokail C, van Bijnen R, Kranzl F, Zache TV, Blatt R, Roos CF, Zoller P. Exploring large-scale entanglement in quantum simulation. Nature 2023; 624:539-544. [PMID: 38030731 DOI: 10.1038/s41586-023-06768-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 10/20/2023] [Indexed: 12/01/2023]
Abstract
Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science1. Here we perform experimental investigations of entanglement on the basis of the entanglement Hamiltonian (EH)2 as an effective description of the reduced density operator for large subsystems. We prepare ground and excited states of a one-dimensional XXZ Heisenberg chain on a 51-ion programmable quantum simulator3 and perform sample-efficient 'learning' of the EH for subsystems of up to 20 lattice sites4. Our experiments provide compelling evidence for a local structure of the EH. To our knowledge, this observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann5,6, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatially varying temperature profile as a signature of entanglement2. Our results also show the transition from area- to volume-law scaling7 of von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions.
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Affiliation(s)
- Manoj K Joshi
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
- University of Innsbruck, Institute for Experimental Physics, Innsbruck, Austria
| | - Christian Kokail
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
- University of Innsbruck, Institute for Theoretical Physics, Innsbruck, Austria
| | - Rick van Bijnen
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
- University of Innsbruck, Institute for Theoretical Physics, Innsbruck, Austria
| | - Florian Kranzl
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
- University of Innsbruck, Institute for Experimental Physics, Innsbruck, Austria
| | - Torsten V Zache
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
- University of Innsbruck, Institute for Theoretical Physics, Innsbruck, Austria
| | - Rainer Blatt
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
- University of Innsbruck, Institute for Experimental Physics, Innsbruck, Austria
| | - Christian F Roos
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
- University of Innsbruck, Institute for Experimental Physics, Innsbruck, Austria
| | - Peter Zoller
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria.
- University of Innsbruck, Institute for Theoretical Physics, Innsbruck, Austria.
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9
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Zhou H, Martin LS, Tyler M, Makarova O, Leitao N, Park H, Lukin MD. Robust Higher-Order Hamiltonian Engineering for Quantum Sensing with Strongly Interacting Systems. PHYSICAL REVIEW LETTERS 2023; 131:220803. [PMID: 38101374 DOI: 10.1103/physrevlett.131.220803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 10/18/2023] [Indexed: 12/17/2023]
Abstract
Dynamical decoupling techniques constitute an integral part of many quantum sensing platforms, often leading to orders-of-magnitude improvements in coherence time and sensitivity. Most ac sensing sequences involve a periodic echolike structure, in which the target signal is synchronized with the echo period. We show that for strongly interacting systems, this construction leads to a fundamental sensitivity limit associated with imperfect interaction decoupling. We present a simple physical picture demonstrating the origin of this limitation, and further formalize these considerations in terms of concise higher-order decoupling rules. We then show how these limitations can be surpassed by identifying a novel sequence building block, in which the signal period matches twice the echo period. Using these decoupling rules and the resulting sequence building block, we experimentally demonstrate significant improvements in dynamical decoupling timescales and magnetic field sensitivity, opening the door for new applications in quantum sensing and quantum many-body physics.
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Affiliation(s)
- Hengyun Zhou
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Leigh S Martin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Matthew Tyler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Oksana Makarova
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Nathaniel Leitao
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Hongkun Park
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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10
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Huang R, Tan X, Xu Q. Learning to Learn Variational Quantum Algorithm. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:8430-8440. [PMID: 35226607 DOI: 10.1109/tnnls.2022.3151127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Variational quantum algorithms (VQAs) use classical computers as the quantum outer loop optimizer and update the circuit parameters to obtain an approximate ground state. In this article, we present a meta-learning variational quantum algorithm (meta-VQA) by recurrent unit, which uses a technique called "meta-learner." Motivated by the hybrid quantum-classical algorithms, we train classical recurrent units to assist quantum computing, learning to find approximate optima in the parameter landscape. Here, aiming to reduce the sampling number more efficiently, we use the quantum stochastic gradient descent method and introduce the adaptive learning rate. Finally, we deploy on the TensorFlow Quantum processor within approximate quantum optimization for the Ising model and variational quantum eigensolver for molecular hydrogen (H2), lithium hydride (LiH), and helium hydride cation (HeH+). Our algorithm can be expanded to larger system sizes and problem instances, which have higher performance on near-term processors.
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11
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Zache TV, González-Cuadra D, Zoller P. Quantum and Classical Spin-Network Algorithms for q-Deformed Kogut-Susskind Gauge Theories. PHYSICAL REVIEW LETTERS 2023; 131:171902. [PMID: 37955498 DOI: 10.1103/physrevlett.131.171902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2023] [Revised: 08/10/2023] [Accepted: 09/25/2023] [Indexed: 11/14/2023]
Abstract
Treating the infinite-dimensional Hilbert space of non-Abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we employ q-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, this approach simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. This enables the development of both quantum as well as quantum-inspired classical spin-network algorithms for q-deformed gauge theories. To be explicit, we focus on SU(2)_{k} gauge theories with k∈N that are controlled by the deformation parameter q=e^{2πi/(k+2)}, a root of unity, and converge to the standard SU(2) Kogut-Susskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational ground-state simulations in 2D, providing first evidence that the continuum limit can be reached with k=O(10). Finally, we develop a scalable quantum algorithm for Trotterized real-time evolution by analytically diagonalizing the SU(2)_{k} plaquette interactions. Our work gives a new perspective for the application of tensor network methods to high-energy physics and paves the way for quantum simulations of non-Abelian gauge theories far from equilibrium where no other methods are currently available.
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Affiliation(s)
- Torsten V Zache
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Daniel González-Cuadra
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Peter Zoller
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
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12
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Fukushima O, Hamazaki R. Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry. PHYSICAL REVIEW LETTERS 2023; 131:131602. [PMID: 37832011 DOI: 10.1103/physrevlett.131.131602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Revised: 09/04/2023] [Accepted: 09/06/2023] [Indexed: 10/15/2023]
Abstract
We elucidate how the presence of higher-form symmetries affects the dynamics of thermalization in isolated quantum systems. Under reasonable assumptions, we analytically show that a p-form symmetry in a (d+1)-dimensional quantum field theory leads to the breakdown of the eigenstate thermalization hypothesis for many nontrivial (d-p)-dimensional observables. For discrete higher-form (i.e., p≥1) symmetry, this indicates the absence of thermalization for observables that are nonlocal but much smaller than the whole system size without any local conserved quantities. We numerically demonstrate this argument for the (2+1)-dimensional Z_{2} lattice gauge theory. While local observables such as the plaquette operator thermalize even for mixed symmetry sectors, the nonlocal observable exciting a magnetic dipole instead relaxes to the generalized Gibbs ensemble that takes account of the Z_{2} one-form symmetry.
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Affiliation(s)
- Osamu Fukushima
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Ryusuke Hamazaki
- Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR), RIKEN iTHEMS, Wako, Saitama 351-0198, Japan
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13
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Tabares C, Muñoz de Las Heras A, Tagliacozzo L, Porras D, González-Tudela A. Variational Quantum Simulators Based on Waveguide QED. PHYSICAL REVIEW LETTERS 2023; 131:073602. [PMID: 37656849 DOI: 10.1103/physrevlett.131.073602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Revised: 04/28/2023] [Accepted: 07/03/2023] [Indexed: 09/03/2023]
Abstract
Waveguide QED simulators are analog quantum simulators made by quantum emitters interacting with one-dimensional photonic band gap materials. One of their remarkable features is that they can be used to engineer tunable-range emitter interactions. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms for certain problems. In particular, we illustrate their power in creating wave function Ansätze that capture accurately the ground state of quantum critical spin models (XXZ and Ising) with fewer gates and optimization parameters than other variational Ansätze based on nearest-neighbor or infinite-range entangling gates. Finally, we study the potential advantages of these waveguide Ansätze in the presence of noise. Overall, these results evidence the potential of using the interaction range as a variational parameter and place waveguide QED simulators as a promising platform for variational quantum algorithms.
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Affiliation(s)
- C Tabares
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - A Muñoz de Las Heras
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - L Tagliacozzo
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - D Porras
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - A González-Tudela
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
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14
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Wang HY, Zhang WY, Yao Z, Liu Y, Zhu ZH, Zheng YG, Wang XK, Zhai H, Yuan ZS, Pan JW. Interrelated Thermalization and Quantum Criticality in a Lattice Gauge Simulator. PHYSICAL REVIEW LETTERS 2023; 131:050401. [PMID: 37595229 DOI: 10.1103/physrevlett.131.050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Accepted: 06/22/2023] [Indexed: 08/20/2023]
Abstract
Gauge theory and thermalization are both topics of essential importance for modern quantum science and technology. The recently realized atomic quantum simulator for lattice gauge theories provides a unique opportunity for studying thermalization in gauge theory, in which theoretical studies have shown that quantum thermalization can signal the quantum phase transition. Nevertheless, the experimental study remains a challenge to accurately determine the critical point and controllably explore the thermalization dynamics due to the lack of techniques for locally manipulating and detecting matter and gauge fields. We report an experimental investigation of the quantum criticality in the lattice gauge theory from both equilibrium and nonequilibrium thermalization perspectives, with the help of the single-site addressing and atom-number-resolved detection capabilities. We accurately determine the quantum critical point and observe that the Néel state thermalizes only in the critical regime. This result manifests the interplay between quantum many-body scars, quantum criticality, and symmetry breaking.
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Affiliation(s)
- Han-Yi Wang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
| | - Wei-Yong Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
| | - Zhiyuan Yao
- Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou Center for Theoretical Physics, and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Ying Liu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
| | - Zi-Hang Zhu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
| | - Yong-Guang Zheng
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
| | - Xuan-Kai Wang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
| | - Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Hefei National Laboratory, Hefei 230088, China
| | - Zhen-Sheng Yuan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, Hefei 230088, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, Hefei 230088, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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15
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Torlai G, Wood CJ, Acharya A, Carleo G, Carrasquilla J, Aolita L. Quantum process tomography with unsupervised learning and tensor networks. Nat Commun 2023; 14:2858. [PMID: 37208324 DOI: 10.1038/s41467-023-38332-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 04/26/2023] [Indexed: 05/21/2023] Open
Abstract
The impressive pace of advance of quantum technology calls for robust and scalable techniques for the characterization and validation of quantum hardware. Quantum process tomography, the reconstruction of an unknown quantum channel from measurement data, remains the quintessential primitive to completely characterize quantum devices. However, due to the exponential scaling of the required data and classical post-processing, its range of applicability is typically restricted to one- and two-qubit gates. Here, we present a technique for performing quantum process tomography that addresses these issues by combining a tensor network representation of the channel with a data-driven optimization inspired by unsupervised machine learning. We demonstrate our technique through synthetically generated data for ideal one- and two-dimensional random quantum circuits of up to 10 qubits, and a noisy 5-qubit circuit, reaching process fidelities above 0.99 using several orders of magnitude fewer (single-qubit) measurement shots than traditional tomographic techniques. Our results go far beyond state-of-the-art, providing a practical and timely tool for benchmarking quantum circuits in current and near-term quantum computers.
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Affiliation(s)
- Giacomo Torlai
- AWS Center for Quantum Computing, Pasadena, CA, USA.
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY, 10010, USA.
| | | | - Atithi Acharya
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY, 10010, USA
- Physics and Astronomy Department, Rutgers University, Piscataway, NJ, 08854, USA
| | - Giuseppe Carleo
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY, 10010, USA
- Institute of Physics, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland
| | | | - Leandro Aolita
- Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, UAE
- Instituto de Física, Federal University of Rio de Janeiro, 21941-972, P. O. Box 68528, Rio de Janeiro, Brazil
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16
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Trahan CJ, Loveland M, Davis N, Ellison E. A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods. ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25040580. [PMID: 37190367 PMCID: PMC10137608 DOI: 10.3390/e25040580] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Revised: 03/21/2023] [Accepted: 03/22/2023] [Indexed: 05/17/2023]
Abstract
Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations.
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Affiliation(s)
- Corey Jason Trahan
- Information and Technology Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180, USA
| | - Mark Loveland
- Information and Technology Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180, USA
| | - Noah Davis
- Applied Research Laboratories, The University of Texas at Austin, Austin, TX 78713, USA
| | - Elizabeth Ellison
- Information and Technology Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS 39180, USA
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17
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Astrakharchik GE, Ardila LAP, Jachymski K, Negretti A. Many-body bound states and induced interactions of charged impurities in a bosonic bath. Nat Commun 2023; 14:1647. [PMID: 36964151 PMCID: PMC10039032 DOI: 10.1038/s41467-023-37153-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Accepted: 03/03/2023] [Indexed: 03/26/2023] Open
Abstract
Induced interactions and bound states of charge carriers immersed in a quantum medium are crucial for the investigation of quantum transport. Ultracold atom-ion systems can provide a convenient platform for studying this problem. Here, we investigate the static properties of one and two ionic impurities in a bosonic bath using quantum Monte Carlo methods. We identify three bipolaronic regimes depending on the strength of the atom-ion potential and the number of its two-body bound states: a perturbative regime resembling the situation of a pair of neutral impurities, a non-perturbative regime that loses the quasi-particle character of the former, and a many-body bound state regime that can arise only in the presence of a bound state in the two-body potential. We further reveal strong bath-induced interactions between the two ionic polarons. Our findings show that numerical simulations are indispensable for describing highly correlated impurity models.
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Affiliation(s)
- Grigory E Astrakharchik
- Department de Física, Universitat Politécnica de Catalunya, Campus Nord B4-B5, E-08034, Barcelona, Spain.
- Departament de Física Quàntica i Astrofísica, Facultat de Física, Universitat de Barcelona, E-08028, Barcelona, Spain.
- Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Martí i Franquès 1, E-08028, Barcelona, Spain.
| | - Luis A Peña Ardila
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167, Hannover, Germany.
| | - Krzysztof Jachymski
- Faculty of Physics, University of Warsaw, Pasteura 5, PL-02093, Warsaw, Poland
| | - Antonio Negretti
- Zentrum für Optische Quantentechnologien, Fachbereich Physik, Luruper Chaussee 149, D-22761, Hamburg, Germany
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18
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González-Cuadra D, Zache TV, Carrasco J, Kraus B, Zoller P. Hardware Efficient Quantum Simulation of Non-Abelian Gauge Theories with Qudits on Rydberg Platforms. PHYSICAL REVIEW LETTERS 2022; 129:160501. [PMID: 36306768 DOI: 10.1103/physrevlett.129.160501] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Revised: 07/12/2022] [Accepted: 09/27/2022] [Indexed: 05/02/2023]
Abstract
Non-Abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. Here we take an approach where gauge fields, discretized in spacetime, are represented by qudits and are time evolved in Trotter steps with multiqudit quantum gates. This maps naturally and hardware efficiently to an architecture based on Rydberg tweezer arrays, where long-lived internal atomic states represent qudits, and the required quantum gates are performed as holonomic operations supported by a Rydberg blockade mechanism. We illustrate our proposal for a minimal digitization of SU(2) gauge fields, demonstrating a significant reduction in circuit depth and gate errors in comparison to a traditional qubit-based approach, which puts simulations of non-Abelian gauge theories within reach of NISQ devices.
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Affiliation(s)
- Daniel González-Cuadra
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Torsten V Zache
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Jose Carrasco
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - Barbara Kraus
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - Peter Zoller
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
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19
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Xie XD, Guo X, Xing H, Xue ZY, Zhang DB, Zhu SL. Variational thermal quantum simulation of the lattice Schwinger model. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.054509] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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20
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Lan Z, Liang W. Amplitude Reordering Accelerates the Adaptive Variational Quantum Eigensolver Algorithms. J Chem Theory Comput 2022; 18:5267-5275. [PMID: 35971280 DOI: 10.1021/acs.jctc.2c00403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The variational quantum eigensolver (VQE) algorithm can simulate the chemical systems such as molecules in the noisy-intermediate-scale quantum devices and shows promising applications in quantum chemistry simulations. The accuracy and computational cost of the VQE simulations are determined by the underlying ansatz. Therefore, the most important issue is to generate a compact and accurate ansatz, which requires a shallower parametric quantum circuit and can achieve an acceptable accuracy. The newly developed adaptive algorithms (AAs) such as the adaptive derivative-assembled pseudo-Trotter VQE (ADAPT-VQE) can solve this issue via generating compact and accurate ansatzes. However, these AAs show very low computational efficiency because they require a large number of additional measurements. Here we propose an amplitude reordering (AR) strategy to accelerate the promising but expensive AAs by adding operators in a "batched" fashion in a way that their order is still quasi-optimal. We first introduce the AR method into ADAPT-VQE and build the AR-ADAPT-VQE algorithm. We then endow the energy-sorting VQE (ES-VQE) algorithm with the adaptive feature and introduce the AR into AES-VQE to form the AR-AES-VQE algorithm. To demonstrate the performance of these algorithms, we calculate the dissociation curves of three small molecules, LiH, linear BeH2, and linear H6, by using (AR-)ADAPT-VQE and (AR-)AES-VQE algorithms. It is found that all of the AR-equipped AAs (AR-AAs) can significantly reduce the number of iterations and subsequently accelerate the calculations with a speedup of up to more than ten times without the obvious loss of accuracy. The final ansatz generated by the AR-AAs not only avoids extra circuit depth but also maintains the computational accuracy; sometimes the AR-AAs even outperforms their original counterparts.
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Affiliation(s)
- Zhihao Lan
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, Fujian Province, Peoples' Republic of China
| | - WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, Fujian Province, Peoples' Republic of China
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21
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Frölian A, Chisholm CS, Neri E, Cabrera CR, Ramos R, Celi A, Tarruell L. Realizing a 1D topological gauge theory in an optically dressed BEC. Nature 2022; 608:293-297. [PMID: 35948710 DOI: 10.1038/s41586-022-04943-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 06/07/2022] [Indexed: 11/09/2022]
Abstract
Topological gauge theories describe the low-energy properties of certain strongly correlated quantum systems through effective weakly interacting models1,2. A prime example is the Chern-Simons theory of fractional quantum Hall states, where anyonic excitations emerge from the coupling between weakly interacting matter particles and a density-dependent gauge field3. Although in traditional solid-state platforms such gauge theories are only convenient theoretical constructions, engineered quantum systems enable their direct implementation and provide a fertile playground to investigate their phenomenology without the need for strong interactions4. Here, we report the quantum simulation of a topological gauge theory by realizing a one-dimensional reduction of the Chern-Simons theory (the chiral BF theory5-7) in a Bose-Einstein condensate. Using the local conservation laws of the theory, we eliminate the gauge degrees of freedom in favour of chiral matter interactions8-11, which we engineer by synthesizing optically dressed atomic states with momentum-dependent scattering properties. This allows us to reveal the key properties of the chiral BF theory: the formation of chiral solitons and the emergence of an electric field generated by the system itself. Our results expand the scope of quantum simulation to topological gauge theories and open a route to the implementation of analogous gauge theories in higher dimensions12.
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Affiliation(s)
- Anika Frölian
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain
| | - Craig S Chisholm
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain
| | - Elettra Neri
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain
| | - Cesar R Cabrera
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain.,Institut für Laserphysik, Universität Hamburg, Hamburg, Germany
| | - Ramón Ramos
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain
| | - Alessio Celi
- Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, Spain.
| | - Leticia Tarruell
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain. .,ICREA - Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain.
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22
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Kirmani A, Bull K, Hou CY, Saravanan V, Saeed SM, Papić Z, Rahmani A, Ghaemi P. Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers. PHYSICAL REVIEW LETTERS 2022; 129:056801. [PMID: 35960588 DOI: 10.1103/physrevlett.129.056801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2021] [Revised: 05/27/2022] [Accepted: 07/04/2022] [Indexed: 06/15/2023]
Abstract
Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the nonperturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that captures the geometric properties and graviton dynamics of fractional quantum Hall states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimally compiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimal-control-based variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.
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Affiliation(s)
- Ammar Kirmani
- Department of Physics and Astronomy, Western Washington University, Bellingham, Washington 98225, USA
- Physics Department, City College of the City University of New York, New York, New York 10031, USA
| | - Kieran Bull
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Chang-Yu Hou
- Schlumberger-Doll Research, Cambridge, Massachusetts 02139, USA
| | - Vedika Saravanan
- Department of Electrical Engineering, City College of the City University of New York, New York, New York 10031, USA
| | - Samah Mohamed Saeed
- Department of Electrical Engineering, City College of the City University of New York, New York, New York 10031, USA
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Armin Rahmani
- Department of Physics and Astronomy and Advanced Materials Science and Engineering Center, Western Washington University, Bellingham, Washington 98225, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Pouyan Ghaemi
- Physics Department, City College of the City University of New York, New York, New York 10031, USA
- Graduate Center of the City University of New York, New York, New York 10016, USA
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23
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Zhou ZY, Su GX, Halimeh JC, Ott R, Sun H, Hauke P, Yang B, Yuan ZS, Berges J, Pan JW. Thermalization dynamics of a gauge theory on a quantum simulator. Science 2022; 377:311-314. [DOI: 10.1126/science.abl6277] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Gauge theories form the foundation of modern physics, with applications ranging from elementary particle physics and early-universe cosmology to condensed matter systems. We perform quantum simulations of the unitary dynamics of a U(1) symmetric gauge field theory and demonstrate emergent irreversible behavior. The highly constrained gauge theory dynamics are encoded in a one-dimensional Bose-Hubbard simulator, which couples fermionic matter fields through dynamical gauge fields. We investigated global quantum quenches and the equilibration to a steady state well approximated by a thermal ensemble. Our work may enable the investigation of elusive phenomena, such as Schwinger pair production and string breaking, and paves the way for simulating more complex, higher-dimensional gauge theories on quantum synthetic matter devices.
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Affiliation(s)
- Zhao-Yu Zhou
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- School of Physics, University of Science and Technology of China, Hefei 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Guo-Xian Su
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- School of Physics, University of Science and Technology of China, Hefei 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jad C. Halimeh
- INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy
| | - Robert Ott
- Institute for Theoretical Physics, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
| | - Hui Sun
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- School of Physics, University of Science and Technology of China, Hefei 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Philipp Hauke
- INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy
| | - Bing Yang
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- Institut für Experimentalphysik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Zhen-Sheng Yuan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- School of Physics, University of Science and Technology of China, Hefei 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jürgen Berges
- Institute for Theoretical Physics, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- School of Physics, University of Science and Technology of China, Hefei 230026, China
- Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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24
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Taher-Ghahramani F, Zheng F, Eisfeld A. Gaussian process regression for absorption spectra analysis of molecular dimers. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2022; 275:121091. [PMID: 35306303 DOI: 10.1016/j.saa.2022.121091] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2021] [Revised: 02/05/2022] [Accepted: 02/25/2022] [Indexed: 06/14/2023]
Abstract
A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning technique, where the parameters for the numerical calculations are chosen from Gaussian Process Regression (GPR). This approach does not only quickly converge to an optimal parameter set, but in addition provides information about the complete parameter space, which allows for example to identify extended parameter regions where numerical spectra are consistent with the experimental one. We consider as example dimers of organic molecules and aim at extracting in particular the interaction between the monomers, and their mutual orientation. We find that indeed the GPR gives reliable results which are in agreement with direct calculations of these parameters using quantum chemical methods.
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Affiliation(s)
- Farhad Taher-Ghahramani
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str 38, Dresden, Germany.
| | - Fulu Zheng
- Bremen Center for Computational Materials Science, University of Bremen, Am Fallturm 1, 28359 Bremen, Germany.
| | - Alexander Eisfeld
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str 38, Dresden, Germany.
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25
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Daley AJ, Bloch I, Kokail C, Flannigan S, Pearson N, Troyer M, Zoller P. Practical quantum advantage in quantum simulation. Nature 2022; 607:667-676. [PMID: 35896643 DOI: 10.1038/s41586-022-04940-6] [Citation(s) in RCA: 45] [Impact Index Per Article: 22.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 06/07/2022] [Indexed: 11/09/2022]
Abstract
The development of quantum computing across several technologies and platforms has reached the point of having an advantage over classical computers for an artificial problem, a point known as 'quantum advantage'. As a next step along the development of this technology, it is now important to discuss 'practical quantum advantage', the point at which quantum devices will solve problems of practical interest that are not tractable for traditional supercomputers. Many of the most promising short-term applications of quantum computers fall under the umbrella of quantum simulation: modelling the quantum properties of microscopic particles that are directly relevant to modern materials science, high-energy physics and quantum chemistry. This would impact several important real-world applications, such as developing materials for batteries, industrial catalysis or nitrogen fixing. Much as aerodynamics can be studied either through simulations on a digital computer or in a wind tunnel, quantum simulation can be performed not only on future fault-tolerant digital quantum computers but also already today through special-purpose analogue quantum simulators. Here we overview the state of the art and future perspectives for quantum simulation, arguing that a first practical quantum advantage already exists in the case of specialized applications of analogue devices, and that fully digital devices open a full range of applications but require further development of fault-tolerant hardware. Hybrid digital-analogue devices that exist today already promise substantial flexibility in near-term applications.
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Affiliation(s)
- Andrew J Daley
- Department of Physics and SUPA, University of Strathclyde, Glasgow, UK.
| | - Immanuel Bloch
- Max Planck Institute of Quantum Optics, Garching, Germany.,Ludwig Maximilians University, Munich, Germany.,Munich Center for Quantum Science and Technology, Munich, Germany
| | - Christian Kokail
- Universität Innsbruck, Innsbruck, Austria.,Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck, Austria
| | - Stuart Flannigan
- Department of Physics and SUPA, University of Strathclyde, Glasgow, UK
| | - Natalie Pearson
- Department of Physics and SUPA, University of Strathclyde, Glasgow, UK
| | | | - Peter Zoller
- Universität Innsbruck, Innsbruck, Austria.,Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck, Austria
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26
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Neural Error Mitigation of Near-Term Quantum Simulations. NAT MACH INTELL 2022. [DOI: 10.1038/s42256-022-00509-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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27
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Cai ML, Wu YK, Mei QX, Zhao WD, Jiang Y, Yao L, He L, Zhou ZC, Duan LM. Observation of supersymmetry and its spontaneous breaking in a trapped ion quantum simulator. Nat Commun 2022; 13:3412. [PMID: 35701410 PMCID: PMC9197856 DOI: 10.1038/s41467-022-31058-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2022] [Accepted: 05/23/2022] [Indexed: 11/09/2022] Open
Abstract
Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond the Standard Model, its direct experimental evidence in nature still remains to be discovered. Here we report experimental realization of a supersymmetric quantum mechanics (SUSY QM) model, a reduction of the SUSY quantum field theory for studying its fundamental properties, using a trapped ion quantum simulator. We demonstrate the energy degeneracy caused by SUSY in this model and the spontaneous SUSY breaking. By a partial quantum state tomography of the spin-phonon coupled system, we explicitly measure the supercharge of the degenerate ground states, which are superpositions of the bosonic and the fermionic states. Our work demonstrates the trapped-ion quantum simulator as an economic yet powerful platform to study versatile physics in a single well-controlled system.
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Affiliation(s)
- M-L Cai
- Center for Quantumf Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People's Republic of China.,HYQ Co., Ltd, 100176, Beijing, People's Republic of China
| | - Y-K Wu
- Center for Quantumf Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People's Republic of China
| | - Q-X Mei
- Center for Quantumf Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People's Republic of China
| | - W-D Zhao
- Center for Quantumf Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People's Republic of China
| | - Y Jiang
- Center for Quantumf Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People's Republic of China
| | - L Yao
- Center for Quantumf Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People's Republic of China.,HYQ Co., Ltd, 100176, Beijing, People's Republic of China
| | - L He
- Center for Quantumf Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People's Republic of China
| | - Z-C Zhou
- Center for Quantumf Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People's Republic of China.,Beijing Academy of Quantum Information Sciences, 100193, Beijing, People's Republic of China
| | - L-M Duan
- Center for Quantumf Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, People's Republic of China.
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28
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Jiang Y, Cai ML, Wu YK, Mei QX, Zhao WD, Chang XY, Yao L, He L, Zhou ZC, Duan LM. Quantum Simulation of the Two-Dimensional Weyl Equation in a Magnetic Field. PHYSICAL REVIEW LETTERS 2022; 128:200502. [PMID: 35657866 DOI: 10.1103/physrevlett.128.200502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 04/25/2022] [Indexed: 06/15/2023]
Abstract
Quantum simulation of 1D relativistic quantum mechanics has been achieved in well-controlled systems like trapped ions, but properties like spin dynamics and response to external magnetic fields that appear only in higher dimensions remain unexplored. Here we simulate the dynamics of a 2D Weyl particle. We show the linear dispersion relation of the free particle and the discrete Landau levels in a magnetic field, and we explicitly measure the spatial and spin dynamics from which the conservation of helicity and properties of antiparticles can be verified. Our work extends the application of an ion trap quantum simulator in particle physics with the additional spatial and spin degrees of freedom.
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Affiliation(s)
- Y Jiang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - M-L Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
- HYQ Co., Ltd., Beijing 100176, People's Republic of China
| | - Y-K Wu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Q-X Mei
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - W-D Zhao
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - X-Y Chang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - L Yao
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
- HYQ Co., Ltd., Beijing 100176, People's Republic of China
| | - L He
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Z-C Zhou
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - L-M Duan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
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29
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Ebadi S, Keesling A, Cain M, Wang TT, Levine H, Bluvstein D, Semeghini G, Omran A, Liu JG, Samajdar R, Luo XZ, Nash B, Gao X, Barak B, Farhi E, Sachdev S, Gemelke N, Zhou L, Choi S, Pichler H, Wang ST, Greiner M, Vuletic V, Lukin MD. Quantum optimization of maximum independent set using Rydberg atom arrays. Science 2022; 376:1209-1215. [PMID: 35511943 DOI: 10.1126/science.abo6587] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.
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Affiliation(s)
- S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - M Cain
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - J-G Liu
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - R Samajdar
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - X-Z Luo
- QuEra Computing Inc., Boston, MA 02135, USA.,Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada.,Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - B Nash
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - X Gao
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - B Barak
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - E Farhi
- Google Quantum AI, Venice, CA 90291, USA.,Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - S Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
| | - N Gemelke
- QuEra Computing Inc., Boston, MA 02135, USA
| | - L Zhou
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - S Choi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - H Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - S-T Wang
- QuEra Computing Inc., Boston, MA 02135, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | | | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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30
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Xu K, Zhang YR, Sun ZH, Li H, Song P, Xiang Z, Huang K, Li H, Shi YH, Chen CT, Song X, Zheng D, Nori F, Wang H, Fan H. Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits. PHYSICAL REVIEW LETTERS 2022; 128:150501. [PMID: 35499907 DOI: 10.1103/physrevlett.128.150501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 03/15/2022] [Indexed: 06/14/2023]
Abstract
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.
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Affiliation(s)
- Kai Xu
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yu-Ran Zhang
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
| | - Zheng-Hang Sun
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hekang Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Pengtao Song
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhongcheng Xiang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Kaixuan Huang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hao Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yun-Hao Shi
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Chi-Tong Chen
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xiaohui Song
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Dongning Zheng
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
- Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - H Wang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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31
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Large-S and Tensor-Network Methods for Strongly-Interacting Topological Insulators. Symmetry (Basel) 2022. [DOI: 10.3390/sym14040799] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we exploit these connections to study the strongly-interacting limit of certain lattice Hubbard models of topological insulators, which map onto four-Fermi quantum field theories with a Wilson-type discretisation and have been recently shown to be at reach of cold-atom quantum simulators based on synthetic spin-orbit coupling. We combine large-S and tensor-network techniques to explore the possible spontaneous symmetry-breaking phases that appear when the interactions of the topological insulators are sufficiently large. In particular, we show that varying the Wilson parameter r of the lattice discretisations leads to a novel Heisenberg–Ising compass model with critical lines that flow with the value of r.
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32
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Marciniak CD, Feldker T, Pogorelov I, Kaubruegger R, Vasilyev DV, van Bijnen R, Schindler P, Zoller P, Blatt R, Monz T. Optimal metrology with programmable quantum sensors. Nature 2022; 603:604-609. [PMID: 35322252 DOI: 10.1038/s41586-022-04435-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2021] [Accepted: 01/18/2022] [Indexed: 11/09/2022]
Abstract
Quantum sensors are an established technology that has created new opportunities for precision sensing across the breadth of science. Using entanglement for quantum enhancement will allow us to construct the next generation of sensors that can approach the fundamental limits of precision allowed by quantum physics. However, determining how state-of-the-art sensing platforms may be used to converge to these ultimate limits is an outstanding challenge. Here we merge concepts from the field of quantum information processing with metrology, and successfully implement experimentally a programmable quantum sensor operating close to the fundamental limits imposed by the laws of quantum mechanics. We achieve this by using low-depth, parametrized quantum circuits implementing optimal input states and measurement operators for a sensing task on a trapped-ion experiment. With 26 ions, we approach the fundamental sensing limit up to a factor of 1.45 ± 0.01, outperforming conventional spin-squeezing with a factor of 1.87 ± 0.03. Our approach reduces the number of averages to reach a given Allan deviation by a factor of 1.59 ± 0.06 compared with traditional methods not using entanglement-enabled protocols. We further perform on-device quantum-classical feedback optimization to 'self-calibrate' the programmable quantum sensor with comparable performance. This ability illustrates that this next generation of quantum sensor can be used without previous knowledge of the device or its noise environment.
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Affiliation(s)
| | | | | | - Raphael Kaubruegger
- Institute for Quantum Optics and Quantum Information, Innsbruck, Austria.,Center for Quantum Physics, Innsbruck, Austria
| | - Denis V Vasilyev
- Institute for Quantum Optics and Quantum Information, Innsbruck, Austria.,Center for Quantum Physics, Innsbruck, Austria
| | - Rick van Bijnen
- Institute for Quantum Optics and Quantum Information, Innsbruck, Austria.,Center for Quantum Physics, Innsbruck, Austria
| | | | - Peter Zoller
- Institute for Quantum Optics and Quantum Information, Innsbruck, Austria.,Center for Quantum Physics, Innsbruck, Austria
| | - Rainer Blatt
- Institut für Experimentalphysik, Innsbruck, Austria.,Institute for Quantum Optics and Quantum Information, Innsbruck, Austria
| | - Thomas Monz
- Institut für Experimentalphysik, Innsbruck, Austria. .,Alpine Quantum Technologies, Innsbruck, Austria.
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33
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Zohar E. Quantum simulation of lattice gauge theories in more than one space dimension-requirements, challenges and methods. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210069. [PMID: 34923840 PMCID: PMC8886423 DOI: 10.1098/rsta.2021.0069] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 08/18/2021] [Indexed: 05/17/2023]
Abstract
Over recent years, the relatively young field of quantum simulation of lattice gauge theories, aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. Nowadays, it is not only of interest to the quantum information and technology communities. It is also seen as a valid tool for tackling hard, non-perturbative gauge theory problems by particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments implementing such simulators are being reported, manifesting beautiful results, but mostly on [Formula: see text] dimensional physics. In this article, we review the essential ingredients and requirements of lattice gauge theories in more dimensions and discuss their meanings, the challenges they pose and how they could be dealt with, potentially aiming at the next steps of this field towards simulating challenging physical problems in analogue, or analogue-digital ways. This article is part of the theme issue 'Quantum technologies in particle physics'.
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Affiliation(s)
- Erez Zohar
- Racah Institute of Physics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel
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34
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Montangero S, Rico E, Silvi P. Loop-free tensor networks for high-energy physics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210065. [PMID: 34923837 DOI: 10.1098/rsta.2021.0065] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2021] [Accepted: 09/13/2021] [Indexed: 06/14/2023]
Abstract
This brief review introduces the reader to tensor network methods, a powerful theoretical and numerical paradigm spawning from condensed matter physics and quantum information science and increasingly exploited in different fields of research, from artificial intelligence to quantum chemistry. Here, we specialize our presentation on the application of loop-free tensor network methods to the study of high-energy physics problems and, in particular, to the study of lattice gauge theories where tensor networks can be applied in regimes where Monte Carlo methods are hindered by the sign problem. This article is part of the theme issue 'Quantum technologies in particle physics'.
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Affiliation(s)
- Simone Montangero
- Dipartimento di Fisica e Astronomia 'G. Galilei', Università di Padova, Padova 35131, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, Padova 35131, Italy
- Padua Quantum Technologies Research Center, Università degli Studi di Padova, Padova, 35131, Italy
| | - Enrique Rico
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, Bilbao 48080, Spain
- IKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, Bilbao 48009, Spain
| | - Pietro Silvi
- Center for Quantum Physics, and Institute for Experimental Physics, University of Innsbruck, Innsbruck 6020, Austria
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35
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Aidelsburger M, Barbiero L, Bermudez A, Chanda T, Dauphin A, González-Cuadra D, Grzybowski PR, Hands S, Jendrzejewski F, Jünemann J, Juzeliūnas G, Kasper V, Piga A, Ran SJ, Rizzi M, Sierra G, Tagliacozzo L, Tirrito E, Zache TV, Zakrzewski J, Zohar E, Lewenstein M. Cold atoms meet lattice gauge theory. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210064. [PMID: 34923836 PMCID: PMC8685612 DOI: 10.1098/rsta.2021.0064] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 08/23/2021] [Indexed: 05/17/2023]
Abstract
The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more 'accessible' and easier to manipulate for experimentalists, but this 'substitution' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or [Formula: see text] Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. This article is not a general review of the rapidly growing field-it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue 'Quantum technologies in particle physics'.
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Affiliation(s)
- Monika Aidelsburger
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich 80799, Germany
- Munich Center for Quantum Science and Technology (MCQST), München 80799, Germany
| | - Luca Barbiero
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino, I-10129 Torino, Italy
| | - Alejandro Bermudez
- Departamento de Física Teorica, Universidad Complutense, Madrid 28040, Spain
| | - Titas Chanda
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Kraków 30-348, Poland
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | - Alexandre Dauphin
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Daniel González-Cuadra
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Przemysław R. Grzybowski
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University in Poznań, Poznań, Poland
| | - Simon Hands
- Department of Physics, Faculty of Science and Engineering, Swansea University, Swansea SA28PP, UK
- Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
| | - Fred Jendrzejewski
- Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg 69120, Germany
| | - Johannes Jünemann
- Institut für Physik, Johannes Gutenberg-Universität, Mainz 55128, Germany
| | - Gediminas Juzeliūnas
- Institute of Theoretical Physics and Astronomy, Vilnius University, Vilnius 10257, Lithuania
| | - Valentin Kasper
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Angelo Piga
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- Departament of Chemical Engineering, Universitat Rovira I Virgili, 43007, Tarragona, Catalonia, Spain
| | - Shi-Ju Ran
- Department of Physics, Capital Normal University, Beijing 100048, People’s Republic of China
| | - Matteo Rizzi
- Forschungszentrum Jülich GmbH, Institute of Quantum Control, Peter Grünberg Institut (PGI-8), Jülich 52425, Germany
- Institute for Theoretical Physics, University of Cologne, Köln 50937, Germany
| | - Germán Sierra
- Instituto de Física Teórica, UAM/CSIC, Universidad Autònoma de Madrid, Madrid, Spain
| | - Luca Tagliacozzo
- Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Barcelona, Catalonia 08028, Spain
| | - Emanuele Tirrito
- International School for Advanced Studies (SISSA), Trieste 34136, Italy
| | - Torsten V. Zache
- Center for Quantum Physics, University of Innsbruck, Innsbruck 6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck 6020, Austria
| | - Jakub Zakrzewski
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Kraków 30-348, Poland
| | - Erez Zohar
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Maciej Lewenstein
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- ICREA, Passeig Lluis Companys 23, Barcelona 08010, Spain
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36
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Abstract
Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the (N) lattice spin models and the SU(N) lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.
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37
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Armon T, Ashkenazi S, García-Moreno G, González-Tudela A, Zohar E. Photon-Mediated Stroboscopic Quantum Simulation of a Z_{2} Lattice Gauge Theory. PHYSICAL REVIEW LETTERS 2021; 127:250501. [PMID: 35029424 DOI: 10.1103/physrevlett.127.250501] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 11/15/2021] [Indexed: 06/14/2023]
Abstract
Quantum simulation of lattice gauge theories, aiming at tackling nonperturbative particle and condensed matter physics, has recently received a lot of interest and attention, resulting in many theoretical proposals as well as several experimental implementations. One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear. In this Letter, we propose a method to obtain them based on a combination of stroboscopic optical atomic control and the nonlocal photon-mediated interactions appearing in nanophotonic or cavity QED setups. We illustrate the method for a Z_{2} lattice gauge theory. We also show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.
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Affiliation(s)
- Tsafrir Armon
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Shachar Ashkenazi
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Gerardo García-Moreno
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain, Departamento de Física Teórica and IPARCOS, Universidad Complutense de Madrid, 28040 Madrid, Spain, and Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada, Spain
| | | | - Erez Zohar
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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38
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Chan HHS, Fitzpatrick N, Segarra-Martí J, Bearpark MJ, Tew DP. Molecular excited state calculations with adaptive wavefunctions on a quantum eigensolver emulation: reducing circuit depth and separating spin states. Phys Chem Chem Phys 2021; 23:26438-26450. [PMID: 34806097 DOI: 10.1039/d1cp02227j] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Ab initio electronic excited state calculations are necessary for the quantitative study of photochemical reactions, but their accurate computation on classical computers is plagued by prohibitive resource scaling. The Variational Quantum Deflation (VQD) is an extension of the quantum-classical Variational Quantum Eigensolver (VQE) algorithm for calculating electronic excited state energies, and has the potential to address some of these scaling challenges using quantum computers. However, quantum computers available in the near term can only support a limited number of quantum circuit operations, so reducing the quantum computational cost in VQD methods is critical to their realisation. In this work, we investigate the use of adaptive quantum circuit growth (ADAPT-VQE) in excited state VQD calculations, a strategy that has been successful previously in reducing the resources required for ground state energy VQE calculations. We also invoke spin restrictions to separate the recovery of eigenstates with different spin symmetry to reduce the number of calculations and accumulation of errors in computing excited states. We created a quantum eigensolver emulation package - Quantum Eigensolver Building on Achievements of Both quantum computing and quantum chemistry (QEBAB) - for testing the proposed adaptive procedure against two existing VQD methods that use fixed-length quantum circuits: UCCGSD-VQD and k-UpCCGSD-VQD. For a lithium hydride test case we found that the spin-restricted adaptive growth variant of VQD uses the most compact circuits out of the tested methods by far, consistently recovers adequate electron correlation energy for different nuclear geometries and eigenstates while isolating the singlet and triplet manifold. This work is a further step towards developing techniques which improve the efficiency of hybrid quantum algorithms for excited state quantum chemistry, opening up the possibility of exploiting real quantum computers for electronic excited state calculations sooner than previously anticipated.
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Affiliation(s)
- Hans Hon Sang Chan
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK.
| | - Nathan Fitzpatrick
- Cambridge Quantum Computing Ltd, 9a Bridge Street, Cambridge CB2 1UB, UK
| | - Javier Segarra-Martí
- Instituto de Ciencia Molecular, Universitat de Valencia, PO Box 22085, Valencia, Spain
| | - Michael J Bearpark
- Department of Chemistry, Imperial College London, Molecular Sciences Research Hub, White City Campus, 82 Wood Lane, London, W12 0BZ, UK
| | - David P Tew
- Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
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39
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Xu X, Sun J, Endo S, Li Y, Benjamin SC, Yuan X. Variational algorithms for linear algebra. Sci Bull (Beijing) 2021; 66:2181-2188. [PMID: 36654109 DOI: 10.1016/j.scib.2021.06.023] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Revised: 05/18/2021] [Accepted: 06/21/2021] [Indexed: 01/20/2023]
Abstract
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices. We show that the solutions of linear systems of equations and matrix-vector multiplications can be translated as the ground states of the constructed Hamiltonians. Based on the variational quantum algorithms, we introduce Hamiltonian morphing together with an adaptive ansätz for efficiently finding the ground state, and show the solution verification. Our algorithms are especially suitable for linear algebra problems with sparse matrices, and have wide applications in machine learning and optimisation problems. The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation. We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations. We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.
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Affiliation(s)
- Xiaosi Xu
- Center on Frontiers of Computing Studies, Department of Computer Science, Peking University, Beijing 100871, China; Department of Materials, University of Oxford, Oxford OX1 3PH, UK
| | - Jinzhao Sun
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Suguru Endo
- Department of Materials, University of Oxford, Oxford OX1 3PH, UK
| | - Ying Li
- Graduate School of China Academy of Engineering Physics, Beijing 100193, China
| | - Simon C Benjamin
- Department of Materials, University of Oxford, Oxford OX1 3PH, UK
| | - Xiao Yuan
- Center on Frontiers of Computing Studies, Department of Computer Science, Peking University, Beijing 100871, China; Department of Materials, University of Oxford, Oxford OX1 3PH, UK.
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40
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Zhang T, Sun J, Fang XX, Zhang XM, Yuan X, Lu H. Experimental Quantum State Measurement with Classical Shadows. PHYSICAL REVIEW LETTERS 2021; 127:200501. [PMID: 34860036 DOI: 10.1103/physrevlett.127.200501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)NPAHAX1745-247310.1038/s41567-020-0932-7], a thrifty scheme showed how to project the quantum state into classical shadows and simultaneously predict M different functions of a state with only O(log_{2}M) measurements, independent of the system size and saturating the information-theoretical limit. Here, we experimentally explore the feasibility of the scheme in the realistic scenario with a finite number of measurements and noisy operations. We prepare a four-qubit GHZ state and show how to estimate expectation values of multiple observables and Hamiltonians. We compare the measurement strategies with uniform, biased, and derandomized classical shadows to conventional ones that sequentially measure each state function exploiting either importance sampling or observable grouping. We next demonstrate the estimation of nonlinear functions using classical shadows and analyze the entanglement of the prepared quantum state. Our experiment verifies the efficacy of exploiting (derandomized) classical shadows and sheds light on efficient quantum computing with noisy intermediate-scale quantum hardware.
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Affiliation(s)
- Ting Zhang
- School of Physics, Shandong University, Jinan 250100, China
| | - Jinzhao Sun
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Xiao-Xu Fang
- School of Physics, Shandong University, Jinan 250100, China
| | - Xiao-Ming Zhang
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
- Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China
| | - Xiao Yuan
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
| | - He Lu
- School of Physics, Shandong University, Jinan 250100, China
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41
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Atas YY, Zhang J, Lewis R, Jahanpour A, Haase JF, Muschik CA. SU(2) hadrons on a quantum computer via a variational approach. Nat Commun 2021; 12:6499. [PMID: 34764262 PMCID: PMC8586147 DOI: 10.1038/s41467-021-26825-4] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 10/13/2021] [Indexed: 11/24/2022] Open
Abstract
Quantum computers have the potential to create important new opportunities for ongoing essential research on gauge theories. They can provide simulations that are unattainable on classical computers such as sign-problem afflicted models or time evolutions. In this work, we variationally prepare the low-lying eigenstates of a non-Abelian gauge theory with dynamically coupled matter on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a hybrid resource-efficient approach by combining classical and quantum computing, that not only allows the study of an SU(2) gauge theory with dynamical matter fields on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.
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Affiliation(s)
- Yasar Y Atas
- Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1.
- Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1.
| | - Jinglei Zhang
- Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1.
- Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1.
| | - Randy Lewis
- Department of Physics and Astronomy, York University, Toronto, ON, Canada, M3J 1P3
| | - Amin Jahanpour
- Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1
- Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1
| | - Jan F Haase
- Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1.
- Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1.
- Institut für Theoretische Physik und IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069, Ulm, Germany.
| | - Christine A Muschik
- Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1
- Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1
- Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada, N2L 2Y5
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42
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Kokail C, Sundar B, Zache TV, Elben A, Vermersch B, Dalmonte M, van Bijnen R, Zoller P. Quantum Variational Learning of the Entanglement Hamiltonian. PHYSICAL REVIEW LETTERS 2021; 127:170501. [PMID: 34739272 DOI: 10.1103/physrevlett.127.170501] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Revised: 08/20/2021] [Accepted: 09/01/2021] [Indexed: 06/13/2023]
Abstract
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.
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Affiliation(s)
- Christian Kokail
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Bhuvanesh Sundar
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- JILA, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Torsten V Zache
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Andreas Elben
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Benoît Vermersch
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
| | - Marcello Dalmonte
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea 265, 34136 Trieste, Italy
| | - Rick van Bijnen
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Peter Zoller
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
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43
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Ott R, Zache TV, Jendrzejewski F, Berges J. Scalable Cold-Atom Quantum Simulator for Two-Dimensional QED. PHYSICAL REVIEW LETTERS 2021; 127:130504. [PMID: 34623868 DOI: 10.1103/physrevlett.127.130504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 08/06/2021] [Indexed: 06/13/2023]
Abstract
We propose a scalable analog quantum simulator for quantum electrodynamics in two spatial dimensions. The setup for the U(1) lattice gauge field theory employs interspecies spin-changing collisions in an ultracold atomic mixture trapped in an optical lattice. We engineer spatial plaquette terms for magnetic fields, thus solving a major obstacle toward experimental realizations of realistic gauge theories in higher dimensions. We apply our approach to the pure gauge theory of compact QED and discuss how the phenomenon of confinement of electric charges can be described by the quantum simulator.
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Affiliation(s)
- R Ott
- Institut für Theoretische Physik, Heidelberg University, Philosophenweg 16, 69120 Heidelberg, Germany
| | - T V Zache
- Institut für Theoretische Physik, Heidelberg University, Philosophenweg 16, 69120 Heidelberg, Germany
- Center for Quantum Physics, University of Innsbruck, 6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - F Jendrzejewski
- Kirchhoff Institute for Physics, Heidelberg University, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - J Berges
- Institut für Theoretische Physik, Heidelberg University, Philosophenweg 16, 69120 Heidelberg, Germany
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44
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Kirby WM, Love PJ. Variational Quantum Eigensolvers for Sparse Hamiltonians. PHYSICAL REVIEW LETTERS 2021; 127:110503. [PMID: 34558958 DOI: 10.1103/physrevlett.127.110503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Revised: 05/24/2021] [Accepted: 07/14/2021] [Indexed: 06/13/2023]
Abstract
Hybrid quantum-classical variational algorithms such as the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) are promising applications for noisy, intermediate-scale quantum computers. Both VQE and QAOA variationally extremize the expectation value of a Hamiltonian. All work to date on VQE and QAOA has been limited to Pauli representations of Hamiltonians. However, many cases exist in which a sparse representation of the Hamiltonian is known but there is no efficient Pauli representation. We extend VQE to general sparse Hamiltonians. We provide a decomposition of a fermionic second-quantized Hamiltonian into a number of one-sparse, self-inverse, Hermitian terms linear in the number of ladder operator monomials in the second-quantized representation. We provide a decomposition of a general d-sparse Hamiltonian into O(d^{2}) such terms. In both cases, a single sample of any term can be obtained using two ansatz state preparations and at most six oracle queries. The number of samples required to estimate the expectation value to precision ε scales as ε^{-2} as for Pauli-based VQE. This widens the domain of applicability of VQE to systems whose Hamiltonian and other observables are most efficiently described in terms of sparse matrices.
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Affiliation(s)
- William M Kirby
- Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA
| | - Peter J Love
- Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA
- Computational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA
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45
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Bolens A, Heyl M. Reinforcement Learning for Digital Quantum Simulation. PHYSICAL REVIEW LETTERS 2021; 127:110502. [PMID: 34558930 DOI: 10.1103/physrevlett.127.110502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Revised: 05/09/2021] [Accepted: 07/22/2021] [Indexed: 06/13/2023]
Abstract
Digital quantum simulation on quantum computers provides the potential to simulate the unitary evolution of any many-body Hamiltonian with bounded spectrum by discretizing the time evolution operator through a sequence of elementary quantum gates. A fundamental challenge in this context originates from experimental imperfections, which critically limits the number of attainable gates within a reasonable accuracy and therefore the achievable system sizes and simulation times. In this work, we introduce a reinforcement learning algorithm to systematically build optimized quantum circuits for digital quantum simulation upon imposing a strong constraint on the number of quantum gates. With this we consistently obtain quantum circuits that reproduce physical observables with as little as three entangling gates for long times and large system sizes up to 16 qubits. As concrete examples we apply our formalism to a long-range Ising chain and the lattice Schwinger model. Our method demonstrates that digital quantum simulation on noisy intermediate scale quantum devices can be pushed to much larger scale within the current experimental technology by a suitable engineering of quantum circuits using reinforcement learning.
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Affiliation(s)
- Adrien Bolens
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Markus Heyl
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
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46
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Gluza M, Eisert J. Recovering Quantum Correlations in Optical Lattices from Interaction Quenches. PHYSICAL REVIEW LETTERS 2021; 127:090503. [PMID: 34506183 DOI: 10.1103/physrevlett.127.090503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 03/29/2021] [Accepted: 07/13/2021] [Indexed: 06/13/2023]
Abstract
Quantum simulations with ultracold atoms in optical lattices open up an exciting path toward understanding strongly interacting quantum systems. Atom gas microscopes are crucial for this as they offer single-site density resolution, unparalleled in other quantum many-body systems. However, currently a direct measurement of local coherent currents is out of reach. In this Letter, we show how to achieve that by measuring densities that are altered in response to quenches to noninteracting dynamics, e.g., after tilting the optical lattice. For this, we establish a data analysis method solving the closed set of equations relating tunneling currents and atom number dynamics, allowing us to reliably recover the full covariance matrix, including off-diagonal terms representing coherent currents. The signal processing builds upon semidefinite optimization, providing bona fide covariance matrices optimally matching the observed data. We demonstrate how the obtained information about noncommuting observables allows one to quantify entanglement at finite temperature, which opens up the possibility to study quantum correlations in quantum simulations going beyond classical capabilities.
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Affiliation(s)
- Marek Gluza
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
| | - Jens Eisert
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
- Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
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47
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Huang HY, Kueng R, Preskill J. Efficient Estimation of Pauli Observables by Derandomization. PHYSICAL REVIEW LETTERS 2021; 127:030503. [PMID: 34328776 DOI: 10.1103/physrevlett.127.030503] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements by fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any L low-weight Pauli observables, a deterministic measurement on only of order log(L) copies of a quantum state suffices. In some cases, for example, when some of the Pauli observables have high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.
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Affiliation(s)
- Hsin-Yuan Huang
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
- Department of Computing and Mathematical Sciences, Caltech, Pasadena, California 91125, USA
| | - Richard Kueng
- Institute for Integrated Circuits, Johannes Kepler University Linz, A-4040, Austria
| | - John Preskill
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
- Department of Computing and Mathematical Sciences, Caltech, Pasadena, California 91125, USA
- Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, California 91125, USA
- AWS Center for Quantum Computing, Pasadena, California 91125, USA
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48
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Bravo-Prieto C. Quantum autoencoders with enhanced data encoding. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/ac0616] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
We present the enhanced feature quantum autoencoder, or EF-QAE, a variational quantum algorithm capable of compressing quantum states of different models with higher fidelity. The key idea of the algorithm is to define a parameterized quantum circuit that depends upon adjustable parameters and a feature vector that characterizes such a model. We assess the validity of the method in simulations by compressing ground states of the Ising model and classical handwritten digits. The results show that EF-QAE improves the performance compared to the standard quantum autoencoder using the same amount of quantum resources, but at the expense of additional classical optimization. Therefore, EF-QAE makes the task of compressing quantum information better suited to be implemented in near-term quantum devices.
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49
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Magnifico G, Felser T, Silvi P, Montangero S. Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks. Nat Commun 2021; 12:3600. [PMID: 34127658 PMCID: PMC8203653 DOI: 10.1038/s41467-021-23646-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 05/07/2021] [Indexed: 02/05/2023] Open
Abstract
Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are still debated, especially at finite charge density, mostly due to the sign-problem affecting Monte Carlo numerical simulations. Here, we report the Tensor Network simulation of a three dimensional lattice gauge theory in the Hamiltonian formulation including dynamical matter: Using this sign-problem-free method, we simulate the ground states of a compact Quantum Electrodynamics at zero and finite charge densities, and address fundamental questions such as the characterization of collective phases of the model, the presence of a confining phase at large gauge coupling, and the study of charge-screening effects.
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Affiliation(s)
- Giuseppe Magnifico
- Dipartimento di Fisica e Astronomia G. Galilei, Università di Padova, Padova, Italy.
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, Padova, Italy.
| | - Timo Felser
- Dipartimento di Fisica e Astronomia G. Galilei, Università di Padova, Padova, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, Padova, Italy
- Theoretische Physik, Universität des Saarlandes, Saarbrücken, Germany
| | - Pietro Silvi
- Center for Quantum Physics, Institute for Experimental Physics, University of Innsbruck, Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
| | - Simone Montangero
- Dipartimento di Fisica e Astronomia G. Galilei, Università di Padova, Padova, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, Padova, Italy
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50
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Ferguson RR, Dellantonio L, Balushi AA, Jansen K, Dür W, Muschik CA. Measurement-Based Variational Quantum Eigensolver. PHYSICAL REVIEW LETTERS 2021; 126:220501. [PMID: 34152185 DOI: 10.1103/physrevlett.126.220501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Revised: 03/08/2021] [Accepted: 03/09/2021] [Indexed: 06/13/2023]
Abstract
Variational quantum eigensolvers (VQEs) combine classical optimization with efficient cost function evaluations on quantum computers. We propose a new approach to VQEs using the principles of measurement-based quantum computation. This strategy uses entangled resource states and local measurements. We present two measurement-based VQE schemes. The first introduces a new approach for constructing variational families. The second provides a translation of circuit- to measurement-based schemes. Both schemes offer problem-specific advantages in terms of the required resources and coherence times.
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Affiliation(s)
- R R Ferguson
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada
| | - L Dellantonio
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada
| | - A Al Balushi
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada
| | - K Jansen
- NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
| | - W Dür
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
| | - C A Muschik
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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