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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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2
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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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3
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Davoudi Z, Mueller N, Powers C. Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States. PHYSICAL REVIEW LETTERS 2023; 131:081901. [PMID: 37683176 DOI: 10.1103/physrevlett.131.081901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 02/27/2023] [Accepted: 06/01/2023] [Indexed: 09/10/2023]
Abstract
The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.
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Affiliation(s)
- Zohreh Davoudi
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Niklas Mueller
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Connor Powers
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
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4
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Illa M, Savage MJ. Multi-Neutrino Entanglement and Correlations in Dense Neutrino Systems. PHYSICAL REVIEW LETTERS 2023; 130:221003. [PMID: 37327435 DOI: 10.1103/physrevlett.130.221003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Revised: 04/27/2023] [Accepted: 04/28/2023] [Indexed: 06/18/2023]
Abstract
The time evolution of multi-neutrino entanglement and correlations are studied in two-flavor collective neutrino oscillations, relevant for dense neutrino environments, building upon previous works. Specifically, simulations performed of systems with up to 12 neutrinos using Quantinuum's H1-1 20 qubit trapped-ion quantum computer are used to compute n-tangles, and two- and three-body correlations, probing beyond mean-field descriptions. n-tangle rescalings are found to converge for large system sizes, signaling the presence of genuine multi-neutrino entanglement.
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Affiliation(s)
- Marc Illa
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, Washington 98195, USA
| | - Martin J Savage
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, Washington 98195, USA
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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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6
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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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7
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de Jong WA, Lee K, Mulligan J, Płoskoń M, Ringer F, Yao X. Quantum simulation of nonequilibrium dynamics and thermalization in the Schwinger model. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.054508] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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8
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Carena M, Lamm H, Li YY, Liu W. Improved Hamiltonians for Quantum Simulations of Gauge Theories. PHYSICAL REVIEW LETTERS 2022; 129:051601. [PMID: 35960555 DOI: 10.1103/physrevlett.129.051601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 05/08/2022] [Accepted: 07/08/2022] [Indexed: 06/15/2023]
Abstract
Quantum simulations of lattice gauge theories for the foreseeable future will be hampered by limited resources. The historical success of improved lattice actions in classical simulations strongly suggests that Hamiltonians with improved discretization errors will reduce quantum resources, i.e., require ≳2^{d} fewer qubits in quantum simulations for lattices with d-spatial dimensions. In this work, we consider O(a^{2})-improved Hamiltonians for pure gauge theories and design the corresponding quantum circuits for its real-time evolution in terms of primitive gates. An explicit demonstration for Z_{2} gauge theory is presented including exploratory tests using the ibm_perth device.
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Affiliation(s)
- Marcela Carena
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
- Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
- Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637, USA
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Henry Lamm
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Ying-Ying Li
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Wanqiang Liu
- Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
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9
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Caspar S, Singh H. From Asymptotic Freedom to θ Vacua: Qubit Embeddings of the O(3) Nonlinear σ Model. PHYSICAL REVIEW LETTERS 2022; 129:022003. [PMID: 35867463 DOI: 10.1103/physrevlett.129.022003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2022] [Accepted: 06/13/2022] [Indexed: 06/15/2023]
Abstract
Conventional lattice formulations of θ vacua in the 1+1-dimensional O(3) nonlinear sigma model suffer from a sign problem. Here, we construct the first sign-problem-free regularization for arbitrary θ. Using efficient lattice Monte Carlo algorithms, we demonstrate how a Hamiltonian model of spin-1/2 degrees of freedom on a two-dimensional spatial lattice reproduces both the infrared sector for arbitrary θ, as well as the ultraviolet physics of asymptotic freedom. Furthermore, as a model of qubits on a two-dimensional square lattice with only nearest-neighbor interactions, it is naturally suited for studying the physics of θ vacua and asymptotic freedom on near-term quantum devices. Our construction generalizes to θ vacua in all CP(N-1) models, solving a long-standing sign problem.
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Affiliation(s)
- Stephan Caspar
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, Washington 98195-1550, USA
| | - Hersh Singh
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, Washington 98195-1550, USA
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Klco N, Roggero A, Savage MJ. Standard model physics and the digital quantum revolution: thoughts about the interface. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:064301. [PMID: 35213853 DOI: 10.1088/1361-6633/ac58a4] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2021] [Accepted: 02/25/2022] [Indexed: 06/14/2023]
Abstract
Advances in isolating, controlling and entangling quantum systems are transforming what was once a curious feature of quantum mechanics into a vehicle for disruptive scientific and technological progress. Pursuing the vision articulated by Feynman, a concerted effort across many areas of research and development is introducing prototypical digital quantum devices into the computing ecosystem available to domain scientists. Through interactions with these early quantum devices, the abstract vision of exploring classically-intractable quantum systems is evolving toward becoming a tangible reality. Beyond catalyzing these technological advances, entanglement is enabling parallel progress as a diagnostic for quantum correlations and as an organizational tool, both guiding improved understanding of quantum many-body systems and quantum field theories defining and emerging from the standard model. From the perspective of three domain science theorists, this article compilesthoughts about the interfaceon entanglement, complexity, and quantum simulation in an effort to contextualize recent NISQ-era progress with the scientific objectives of nuclear and high-energy physics.
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Affiliation(s)
- Natalie Klco
- Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena CA 91125, United States of America
| | - Alessandro Roggero
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195, United States of America
| | - Martin J Savage
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195, United States of America
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Abstract
We characterize for the first time the performances of IBM quantum chips as quantum batteries, specifically addressing the single-qubit Armonk processor. By exploiting the Pulse access enabled to some of the IBM Quantum processors via the Qiskit package, we investigate the advantages and limitations of different profiles for classical drives used to charge these miniaturized batteries, establishing the optimal compromise between charging time and stored energy. Moreover, we consider the role played by various possible initial conditions on the functioning of the quantum batteries. As the main result of our analysis, we observe that unavoidable errors occurring in the initialization phase of the qubit, which can be detrimental for quantum computing applications, only marginally affect energy transfer and storage. This can lead counter-intuitively to improvements of the performances. This is a strong indication of the fact that IBM quantum devices are already in the proper range of parameters to be considered as good and stable quantum batteries comparable to state-of-the-art devices recently discussed in the literature.
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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: 10] [Impact Index Per Article: 5.0] [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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13
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Wiese UJ. From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of gauge theories. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210068. [PMID: 34923839 DOI: 10.1098/rsta.2021.0068] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2021] [Accepted: 08/18/2021] [Indexed: 06/14/2023]
Abstract
Quantum link models provide an extension of Wilson's lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson's parallel transporters, quantum links are intrinsically quantum degrees of freedom. In D-theory, these discrete variables undergo dimensional reduction, thus giving rise to asymptotically free theories. In this way [Formula: see text] [Formula: see text] models emerge by dimensional reduction from [Formula: see text] [Formula: see text] quantum spin ladders, the [Formula: see text] confining [Formula: see text] gauge theory emerges from the Abelian Coulomb phase of a [Formula: see text] quantum link model, and [Formula: see text] QCD arises from a non-Abelian Coulomb phase of a [Formula: see text] [Formula: see text] quantum link model, with chiral quarks arising naturally as domain wall fermions. Thanks to their finite-dimensional Hilbert space and their economical mechanism of reaching the continuum limit by dimensional reduction, quantum link models provide a resource efficient framework for the quantum simulation and computation of gauge theories. This article is part of the theme issue 'Quantum technologies in particle physics'.
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Affiliation(s)
- Uwe-Jens Wiese
- Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
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14
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Funcke L, Hartung T, Jansen K, Kühn S, Schneider M, Stornati P, Wang X. Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210062. [PMID: 34923847 DOI: 10.1098/rsta.2021.0062] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2021] [Accepted: 10/04/2021] [Indexed: 06/14/2023]
Abstract
We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high-energy physics and beyond on noisy intermediate-scale quantum (NISQ) devices. The first method is the dimensional expressivity analysis of quantum circuits, which allows for constructing minimal but maximally expressive quantum circuits. The second method is an efficient mitigation of readout errors on quantum devices. Both methods can lead to significant improvements in quantum simulations, e.g. when variational quantum eigensolvers are used. This article is part of the theme issue 'Quantum technologies in particle physics'.
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Affiliation(s)
- L Funcke
- Center for Theoretical Physics, Co-Design Center for Quantum Advantage, and NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5
| | - T Hartung
- Department of Mathematical Sciences, University of Bath, 4 West, Claverton Down, Bath BA2 7AY, UK
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, 2121 Nicosia, Cyprus
| | - K Jansen
- NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
| | - S Kühn
- Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, 2121 Nicosia, Cyprus
| | - M Schneider
- NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
- Institut für Physik, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin, Germany
| | - P Stornati
- NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
- Institut für Physik, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin, Germany
| | - X Wang
- School of Physics, Peking University, 5 Yiheyuan Rd, Haidian District, Beijing 100871, People's Republic of China
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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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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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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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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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Bhattacharya T, Buser AJ, Chandrasekharan S, Gupta R, Singh H. Qubit Regularization of Asymptotic Freedom. PHYSICAL REVIEW LETTERS 2021; 126:172001. [PMID: 33988408 DOI: 10.1103/physrevlett.126.172001] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 03/22/2021] [Indexed: 06/12/2023]
Abstract
We provide strong evidence that the asymptotically free (1+1)-dimensional nonlinear O(3) sigma model can be regularized using a quantum lattice Hamiltonian, referred to as the "Heisenberg comb," that acts on a Hilbert space with only two qubits per spatial lattice site. The Heisenberg comb consists of a spin-half antiferromagnetic Heisenberg chain coupled antiferromagnetically to a second local spin-half particle at every lattice site. Using a world-line Monte Carlo method, we show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200000 in lattice units and argue how the continuum limit could emerge. We provide a quantum circuit description of the time evolution of the model and argue that near-term quantum computers may suffice to demonstrate asymptotic freedom.
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Affiliation(s)
| | - Alexander J Buser
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91106, USA
| | | | - Rajan Gupta
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Hersh Singh
- Department of Physics, Box 90305, Duke University, Durham, North Carolina 27708, USA
- Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195-1550, USA
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Guan W, Perdue G, Pesah A, Schuld M, Terashi K, Vallecorsa S, Vlimant JR. Quantum machine learning in high energy physics. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abc17d] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Machine learning has been used in high energy physics (HEP) for a long time, primarily at the analysis level with supervised classification. Quantum computing was postulated in the early 1980s as way to perform computations that would not be tractable with a classical computer. With the advent of noisy intermediate-scale quantum computing devices, more quantum algorithms are being developed with the aim at exploiting the capacity of the hardware for machine learning applications. An interesting question is whether there are ways to apply quantum machine learning to HEP. This paper reviews the first generation of ideas that use quantum machine learning on problems in HEP and provide an outlook on future applications.
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Wu W, Zhang T, Chen PX. Quantum computing and simulation with trapped ions: On the path to the future. FUNDAMENTAL RESEARCH 2021. [DOI: 10.1016/j.fmre.2020.12.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
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