1
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Quiroz G, Pokharel B, Boen J, Tewala L, Tripathi V, Williams D, Wu LA, Titum P, Schultz K, Lidar D. Dynamically generated decoherence-free subspaces and subsystems on superconducting qubits. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:097601. [PMID: 39059436 DOI: 10.1088/1361-6633/ad6805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Accepted: 07/15/2024] [Indexed: 07/28/2024]
Abstract
Decoherence-free subspaces and subsystems (DFS) preserve quantum information by encoding it into symmetry-protected states unaffected by decoherence. An inherent DFS of a given experimental system may not exist; however, through the use of dynamical decoupling (DD), one can induce symmetries that support DFSs. Here, we provide the first experimental demonstration of DD-generated decoherence-free subsystem logical qubits. Utilizing IBM Quantum superconducting processors, we investigate two and three-qubit DFS codes comprising up to six and seven noninteracting logical qubits, respectively. Through a combination of DD and error detection, we show that DFS logical qubits can achieve up to a 23% improvement in state preservation fidelity over physical qubits subject to DD alone. This constitutes a beyond-breakeven fidelity improvement for DFS-encoded qubits. Our results showcase the potential utility of DFS codes as a pathway toward enhanced computational accuracy via logical encoding on quantum processors.
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Affiliation(s)
- Gregory Quiroz
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, United States of America
- William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD 21218, United States of America
| | - Bibek Pokharel
- Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, United States of America
- Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, CA 90089, United States of America
| | - Joseph Boen
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, United States of America
| | - Lina Tewala
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, United States of America
- Thomas C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD 21218, United States of America
| | - Vinay Tripathi
- Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, United States of America
- Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, CA 90089, United States of America
| | - Devon Williams
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, United States of America
- William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD 21218, United States of America
| | - Lian-Ao Wu
- Department of Theoretical Physics and History of Science, University of the Basque Country, Leioa 48008, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao 48011, Spain
- EHU Quantum Center, University of the Basque Country UPV/EHU, Leioa, Biscay 48940, Spain
| | - Paraj Titum
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, United States of America
| | - Kevin Schultz
- Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, United States of America
| | - Daniel Lidar
- Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, United States of America
- Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, CA 90089, United States of America
- Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, United States of America
- Department of Chemistry, University of Southern California, Los Angeles, CA 90089, United States of America
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2
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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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3
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Zeng X, Fan Y, Liu J, Li Z, Yang J. Quantum Neural Network Inspired Hardware Adaptable Ansatz for Efficient Quantum Simulation of Chemical Systems. J Chem Theory Comput 2023. [PMID: 38044845 DOI: 10.1021/acs.jctc.3c00527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2023]
Abstract
The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.
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Affiliation(s)
- Xiongzhi Zeng
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Yi Fan
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei 230026, China
| | - Jie Liu
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Zhenyu Li
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jinlong Yang
- Key Laboratory of Precision and Intelligent Chemistry, 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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4
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Parajuli P, Govindarajan A, Tian L. State preparation in a Jaynes-Cummings lattice with quantum optimal control. Sci Rep 2023; 13:19924. [PMID: 37963930 PMCID: PMC10645998 DOI: 10.1038/s41598-023-47002-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 11/07/2023] [Indexed: 11/16/2023] Open
Abstract
High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation.
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Affiliation(s)
- Prabin Parajuli
- School of Natural Sciences, University of California, Merced, California, 95343, USA
| | - Anuvetha Govindarajan
- School of Natural Sciences, University of California, Merced, California, 95343, USA
| | - Lin Tian
- School of Natural Sciences, University of California, Merced, California, 95343, USA.
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5
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Pérez-Obiol A, Romero AM, Menéndez J, Rios A, García-Sáez A, Juliá-Díaz B. Nuclear shell-model simulation in digital quantum computers. Sci Rep 2023; 13:12291. [PMID: 37516795 PMCID: PMC10387092 DOI: 10.1038/s41598-023-39263-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 07/22/2023] [Indexed: 07/31/2023] Open
Abstract
The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum circuit design strategy to find nuclear ground states by exploiting an adaptive variational quantum eigensolver algorithm. Our circuit implementation is in excellent agreement with classical shell-model simulations for a dozen of light and medium-mass nuclei, including neon and calcium isotopes. We quantify the circuit depth, width and number of gates to encode realistic shell-model wavefunctions. Our strategy also addresses explicitly energy measurements and the required number of circuits to perform them. Our simulated circuits approach the benchmark results exponentially with a polynomial scaling in quantum resources for each nucleus. This work paves the way for quantum computing shell-model studies across the nuclear chart and our quantum resource quantification may be used in configuration-interaction calculations of other fermionic systems.
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Affiliation(s)
- A Pérez-Obiol
- Barcelona Supercomputing Center, 08034, Barcelona, Spain.
| | - A M Romero
- Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), c. Martí i Franqués, 1, 08028, Barcelona, Spain.
- Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Martí i Franqués, 1, 08028, Barcelona, Spain.
| | - J Menéndez
- Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), c. Martí i Franqués, 1, 08028, Barcelona, Spain
- Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Martí i Franqués, 1, 08028, Barcelona, Spain
| | - A Rios
- Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), c. Martí i Franqués, 1, 08028, Barcelona, Spain
- Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Martí i Franqués, 1, 08028, Barcelona, Spain
| | - A García-Sáez
- Barcelona Supercomputing Center, 08034, Barcelona, Spain
- Qilimanjaro Quantum Tech, 08007, Barcelona, Spain
| | - B Juliá-Díaz
- Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), c. Martí i Franqués, 1, 08028, Barcelona, Spain
- Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Martí i Franqués, 1, 08028, Barcelona, Spain
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6
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Kim Y, Eddins A, Anand S, Wei KX, van den Berg E, Rosenblatt S, Nayfeh H, Wu Y, Zaletel M, Temme K, Kandala A. Evidence for the utility of quantum computing before fault tolerance. Nature 2023; 618:500-505. [PMID: 37316724 PMCID: PMC10266970 DOI: 10.1038/s41586-023-06096-3] [Citation(s) in RCA: 46] [Impact Index Per Article: 46.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 04/18/2023] [Indexed: 06/16/2023]
Abstract
Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods2,3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications4,5.
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Affiliation(s)
- Youngseok Kim
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA.
| | - Andrew Eddins
- IBM Quantum, IBM Research - Cambridge, Cambridge, MA, USA.
| | - Sajant Anand
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA
| | - Ken Xuan Wei
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Ewout van den Berg
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Sami Rosenblatt
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Hasan Nayfeh
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Yantao Wu
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA
- RIKEN iTHEMS, Wako, Japan
| | - Michael Zaletel
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Kristan Temme
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Abhinav Kandala
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA.
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7
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Qi Y, Feng Y, Wu J, Sun Z, Bai M, Wang C, Wang H, Zhan X, Zhang J, Liu J, Chen J. An Efficient and Robust Partial Differential Equation Solver by Flash-Based Computing in Memory. MICROMACHINES 2023; 14:mi14050901. [PMID: 37241525 DOI: 10.3390/mi14050901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Revised: 04/17/2023] [Accepted: 04/20/2023] [Indexed: 05/28/2023]
Abstract
Flash memory-based computing-in-memory (CIM) architectures have gained popularity due to their remarkable performance in various computation tasks of data processing, including machine learning, neuron networks, and scientific calculations. Especially in the partial differential equation (PDE) solver that has been widely utilized in scientific calculations, high accuracy, processing speed, and low power consumption are the key requirements. This work proposes a novel flash memory-based PDE solver to implement PDE with high accuracy, low power consumption, and fast iterative convergence. Moreover, considering the increasing current noise in nanoscale devices, we investigate the robustness against the noise in the proposed PDE solver. The results show that the noise tolerance limit of the solver can reach more than five times that of the conventional Jacobi CIM solver. Overall, the proposed flash memory-based PDE solver offers a promising solution for scientific calculations that require high accuracy, low power consumption, and good noise immunity, which could help to develop flash-based general computing.
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Affiliation(s)
- Yueran Qi
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | - Yang Feng
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | - Jixuan Wu
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | - Zhaohui Sun
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | - Maoying Bai
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | - Chengcheng Wang
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | - Hai Wang
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | - Xuepeng Zhan
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
| | | | - Jing Liu
- Key Laboratory of Microelectronic Devices and Integrated Technology, Institute of Microelectronics of Chinese Academy of Sciences, Beijing 100029, China
| | - Jiezhi Chen
- School of Information Science and Engineering, Shandong University, Qingdao 266237, China
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8
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Grossi M, Kiss O, De Luca F, Zollo C, Gremese I, Mandarino A. Finite-size criticality in fully connected spin models on superconducting quantum hardware. Phys Rev E 2023; 107:024113. [PMID: 36932510 DOI: 10.1103/physreve.107.024113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Accepted: 01/17/2023] [Indexed: 02/12/2023]
Abstract
The emergence of a collective behavior in a many-body system is responsible for the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different approaches to study quantum phase transitions. In this work, we exploit the new resources offered by quantum algorithms to detect the quantum critical behavior of fully connected spin-1/2 models. We define a suitable Hamiltonian depending on an internal anisotropy parameter γ that allows us to examine three paradigmatic examples of spin models, whose lattice is a fully connected graph. We propose a method based on variational algorithms run on superconducting transmon qubits to detect the critical behavior for systems of finite size. We evaluate the energy gap between the first excited state and the ground state, the magnetization along the easy axis of the system, and the spin-spin correlations. We finally report a discussion about the feasibility of scaling such approach on a real quantum device for a system having a dimension such that classical simulations start requiring significant resources.
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Affiliation(s)
- Michele Grossi
- European Organization for Nuclear Research (CERN), 1211 Geneva, Switzerland
| | - Oriel Kiss
- European Organization for Nuclear Research (CERN), 1211 Geneva, Switzerland.,Department of Particle and Nuclear Physics, University of Geneva, 1211 Geneva, Switzerland
| | | | - Carlo Zollo
- Department of Physics, University of Trieste, 34127 Trieste, Italy
| | - Ian Gremese
- Department of Physics, University of Trieste, 34127 Trieste, Italy
| | - Antonio Mandarino
- International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-309 Gdańsk, Poland
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9
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Zhang ZJ, Sun J, Yuan X, Yung MH. Low-Depth Hamiltonian Simulation by an Adaptive Product Formula. PHYSICAL REVIEW LETTERS 2023; 130:040601. [PMID: 36763426 DOI: 10.1103/physrevlett.130.040601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Revised: 01/17/2022] [Accepted: 11/16/2022] [Indexed: 06/18/2023]
Abstract
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep quantum circuit that is beyond the capability of near-term noisy quantum devices. Here, focusing on the time evolution of a fixed input quantum state, we propose an adaptive approach to construct a low-depth time evolution circuit. By introducing a measurable quantifier that characterizes the simulation error, we use an adaptive strategy to learn the shallow quantum circuit that minimizes that error. We numerically test the adaptive method with electronic Hamiltonians of the H_{2}O and H_{4} molecules, and the transverse field Ising model with random coefficients. Compared to the first-order Suzuki-Trotter product formula, our method can significantly reduce the circuit depth (specifically the number of two-qubit gates) by around two orders while maintaining the simulation accuracy. We show applications of the method in simulating many-body dynamics and solving energy spectra with the quantum Krylov algorithm. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
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Affiliation(s)
- Zi-Jian Zhang
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
| | - Jinzhao Sun
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Xiao Yuan
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
| | - Man-Hong Yung
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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10
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Tammaro A, Galli DE, Rice JE, Motta M. N-Electron Valence Perturbation Theory with Reference Wave Functions from Quantum Computing: Application to the Relative Stability of Hydroxide Anion and Hydroxyl Radical. J Phys Chem A 2023; 127:817-827. [PMID: 36638358 DOI: 10.1021/acs.jpca.2c07653] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
Quantum simulations of the hydroxide anion and hydroxyl radical are reported, employing variational quantum algorithms for near-term quantum devices. The energy of each species is calculated along the dissociation curve, to obtain information about the stability of the molecular species being investigated. It is shown that simulations restricted to valence spaces incorrectly predict the hydroxyl radical to be more stable than the hydroxide anion. Inclusion of dynamical electron correlation from nonvalence orbitals is demonstrated, through the integration of the variational quantum eigensolver and quantum subspace expansion methods in the workflow of N-electron valence perturbation theory, and shown to correctly predict the hydroxide anion to be more stable than the hydroxyl radical, provided that basis sets with diffuse orbitals are also employed. Finally, we calculate the electron affinity of the hydroxyl radical using an aug-cc-pVQZ basis on IBM's quantum devices.
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Affiliation(s)
- Alessandro Tammaro
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, via Celoria 16, I-20133Milano, Italy
| | - Davide E Galli
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, via Celoria 16, I-20133Milano, Italy
| | - Julia E Rice
- IBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, California95120, United States
| | - Mario Motta
- IBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, California95120, United States
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11
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Cordier BA, Sawaya NPD, Guerreschi GG, McWeeney SK. Biology and medicine in the landscape of quantum advantages. J R Soc Interface 2022; 19:20220541. [PMID: 36448288 PMCID: PMC9709576 DOI: 10.1098/rsif.2022.0541] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Accepted: 11/04/2022] [Indexed: 12/03/2022] Open
Abstract
Quantum computing holds substantial potential for applications in biology and medicine, spanning from the simulation of biomolecules to machine learning methods for subtyping cancers on the basis of clinical features. This potential is encapsulated by the concept of a quantum advantage, which is contingent on a reduction in the consumption of a computational resource, such as time, space or data. Here, we distill the concept of a quantum advantage into a simple framework to aid researchers in biology and medicine pursuing the development of quantum applications. We then apply this framework to a wide variety of computational problems relevant to these domains in an effort to (i) assess the potential of practical advantages in specific application areas and (ii) identify gaps that may be addressed with novel quantum approaches. In doing so, we provide an extensive survey of the intersection of biology and medicine with the current landscape of quantum algorithms and their potential advantages. While we endeavour to identify specific computational problems that may admit practical advantages throughout this work, the rapid pace of change in the fields of quantum computing, classical algorithms and biological research implies that this intersection will remain highly dynamic for the foreseeable future.
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Affiliation(s)
- Benjamin A. Cordier
- Department of Medical Informatics and Clinical Epidemiology, Oregon Health and Science University, Portland, OR 97202, USA
| | | | | | - Shannon K. McWeeney
- Department of Medical Informatics and Clinical Epidemiology, Oregon Health and Science University, Portland, OR 97202, USA
- Knight Cancer Institute, Oregon Health and Science University, Portland, OR 97202, USA
- Oregon Clinical and Translational Research Institute, Oregon Health and Science University, Portland, OR 97202, USA
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12
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Ghamari D, Hauke P, Covino R, Faccioli P. Sampling rare conformational transitions with a quantum computer. Sci Rep 2022; 12:16336. [PMID: 36175529 PMCID: PMC9522734 DOI: 10.1038/s41598-022-20032-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Accepted: 09/07/2022] [Indexed: 11/09/2022] Open
Abstract
Structural rearrangements play a central role in the organization and function of complex biomolecular systems. In principle, Molecular Dynamics (MD) simulations enable us to investigate these thermally activated processes with an atomic level of resolution. In practice, an exponentially large fraction of computational resources must be invested to simulate thermal fluctuations in metastable states. Path sampling methods focus the computational power on sampling the rare transitions between states. One of their outstanding limitations is to efficiently generate paths that visit significantly different regions of the conformational space. To overcome this issue, we introduce a new algorithm for MD simulations that integrates machine learning and quantum computing. First, using functional integral methods, we derive a rigorous low-resolution spatially coarse-grained representation of the system's dynamics, based on a small set of molecular configurations explored with machine learning. Then, we use a quantum annealer to sample the transition paths of this low-resolution theory. We provide a proof-of-concept application by simulating a benchmark conformational transition with all-atom resolution on the D-Wave quantum computer. By exploiting the unique features of quantum annealing, we generate uncorrelated trajectories at every iteration, thus addressing one of the challenges of path sampling. Once larger quantum machines will be available, the interplay between quantum and classical resources may emerge as a new paradigm of high-performance scientific computing. In this work, we provide a platform to implement this integrated scheme in the field of molecular simulations.
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Affiliation(s)
- Danial Ghamari
- Department of Physics, University of Trento, Via Sommarive 14, Trento, 38123, Italy.,INFN-TIFPA, Via Sommarive 14, Trento, 38123, Italy
| | - Philipp Hauke
- INO-CNR BEC Center & Department of Physics, University of Trento, Via Sommarive 14, Trento, 38123, Italy
| | - Roberto Covino
- Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße 1, Frankfurt am Main, 60438, Germany.
| | - Pietro Faccioli
- Department of Physics, University of Trento, Via Sommarive 14, Trento, 38123, Italy. .,INFN-TIFPA, Via Sommarive 14, Trento, 38123, Italy.
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13
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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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14
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Quantum Error Correction: Noise-Adapted Techniques and Applications. J Indian Inst Sci 2022. [DOI: 10.1007/s41745-022-00332-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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15
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Gopinath N, Shyry SP. Enhancing the cloud security using side channel attack free QKD with entangled fuzzy logic. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-220398] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
As technology advances, it becomes easier to share large amounts of data over the internet. Cloud computing is one of the technologies that allows for easy data sharing over the internet. It is critical to provide security for this data when they are being shared across the internet. The security of data saved in cloud storage, as well as data transport and transmitting a key required to encrypt data between two parties, has been a source of concern for the industry, as a result of the growing use of cloud services in recent years. Collective attacks are significantly more powerful than individual strikes, according to our research. Despite the fact that additional research works were studied in the previous literature review, there are some study concerns for not correcting third-party data hacking. Therefore, this paper focuses on the design of Secured Quantum Key Distribution (SQKD) with Fuzzy logic to improve the security of the shared key. Quantum Key Distribution, Post Quantum Key Distribution, and the EPR Proto-col are technologies that increase the security of data sharing. We have incorporated the Secured Quantum Key Distribution (SQKD) with Fuzzy logic in our proposed work to improve the security of the shared key. The proposed systems include some additional characteristics in addition to the existing approaches. The proposed model uses shifting algorithms and the fuzzification procedure to assure the security of the secret key in the Fuzzification of Quantum Key approach. The experimental results states that the mean value of security losses in SFQ is 1.8306051, and the mean value of QKD is 14.6448416, with standard deviations of 1.7329 and 13.863 for SFQ and QKD, respectively.
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Affiliation(s)
- N. Gopinath
- School of Computing, Sathyabama Institute of Science and Technology, Chennai, India; Sri Manakula Vinayagar Engineering College, Pudhucherry, India
| | - S. Prayla Shyry
- Faculty of Computer Science and Engineering, Sathyabama Institute of Scienceand Technology, Chennai, India
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16
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Yoshikawa T, Takanashi T, Nakai H. Quantum Algorithm of the Divide-and-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver. J Chem Theory Comput 2022; 18:5360-5373. [PMID: 35926142 DOI: 10.1021/acs.jctc.2c00602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-and-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.
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Affiliation(s)
- Takeshi Yoshikawa
- Faculty of Pharmaceutical Sciences, Toho University, 2-2-1 Miyama, Funabashi, Chiba 274-8510, Japan.,Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Tomoya Takanashi
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.,Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.,Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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17
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Sajjan M, Li J, Selvarajan R, Sureshbabu SH, Kale SS, Gupta R, Singh V, Kais S. Quantum machine learning for chemistry and physics. Chem Soc Rev 2022; 51:6475-6573. [PMID: 35849066 DOI: 10.1039/d2cs00203e] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.
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Affiliation(s)
- Manas Sajjan
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Junxu Li
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA
| | - Raja Selvarajan
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA
| | - Shree Hari Sureshbabu
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN-47907, USA
| | - Sumit Suresh Kale
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Rishabh Gupta
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Vinit Singh
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Sabre Kais
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA.,Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN-47907, USA
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18
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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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19
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Motta M, Rice JE. Emerging quantum computing algorithms for quantum chemistry. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1580] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research‐Almaden San Jose California USA
| | - Julia E. Rice
- IBM Quantum, IBM Research‐Almaden San Jose California USA
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20
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Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers. Symmetry (Basel) 2022. [DOI: 10.3390/sym14030624] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.
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21
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Geller MR, Arrasmith A, Holmes Z, Yan B, Coles PJ, Sornborger A. Quantum simulation of operator spreading in the chaotic Ising model. Phys Rev E 2022; 105:035302. [PMID: 35428080 DOI: 10.1103/physreve.105.035302] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 02/28/2022] [Indexed: 06/14/2023]
Abstract
There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here we use an IBM Q processor, quantum error mitigation, and weaved Trotter simulation to study high-resolution operator spreading in a four-spin Ising model as a function of space, time, and integrability. Reaching four spins while retaining high circuit fidelity is made possible by the use of a physically motivated fixed-node variant of the OTOC, allowing scrambling to be estimated without overhead. We find clear signatures of a ballistic operator spreading in a chaotic regime, as well as operator localization in an integrable regime. The techniques developed and demonstrated here open up the possibility of using cloud-based quantum computers to study and visualize scrambling phenomena, as well as quantum information dynamics more generally.
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Affiliation(s)
- Michael R Geller
- Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
| | - Andrew Arrasmith
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Zoë Holmes
- Information Sciences, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Bin Yan
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Patrick J Coles
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Andrew Sornborger
- Information Sciences, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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22
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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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23
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Zhu Q, Cao S, Chen F, Chen MC, Chen X, Chung TH, Deng H, Du Y, Fan D, Gong M, Guo C, Guo C, Guo S, Han L, Hong L, Huang HL, Huo YH, Li L, Li N, Li S, Li Y, Liang F, Lin C, Lin J, Qian H, Qiao D, Rong H, Su H, Sun L, Wang L, Wang S, Wu D, Wu Y, Xu Y, Yan K, Yang W, Yang Y, Ye Y, Yin J, Ying C, Yu J, Zha C, Zhang C, Zhang H, Zhang K, Zhang Y, Zhao H, Zhao Y, Zhou L, Lu CY, Peng CZ, Zhu X, Pan JW. Quantum computational advantage via 60-qubit 24-cycle random circuit sampling. Sci Bull (Beijing) 2022; 67:240-245. [DOI: 10.1016/j.scib.2021.10.017] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Revised: 10/18/2021] [Accepted: 10/19/2021] [Indexed: 11/29/2022]
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24
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Urbanek M, Nachman B, Pascuzzi VR, He A, Bauer CW, de Jong WA. Mitigating Depolarizing Noise on Quantum Computers with Noise-Estimation Circuits. PHYSICAL REVIEW LETTERS 2021; 127:270502. [PMID: 35061411 DOI: 10.1103/physrevlett.127.270502] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Accepted: 11/18/2021] [Indexed: 06/14/2023]
Abstract
A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We present a method to mitigate the depolarizing noise by first estimating its rate with a noise-estimation circuit and then correcting the output of the target circuit using the estimated rate. The method is experimentally validated on a simulation of the Heisenberg model. We find that our approach in combination with readout-error correction, randomized compiling, and zero-noise extrapolation produces close to exact results even for circuits containing hundreds of CNOT gates. We also show analytically that zero-noise extrapolation is improved when it is applied to the output of our method.
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Affiliation(s)
- Miroslav Urbanek
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Benjamin Nachman
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Vincent R Pascuzzi
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Andre He
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Christian W Bauer
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Wibe A de Jong
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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25
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Bauer CW, Nachman B, Freytsis M. Simulating Collider Physics on Quantum Computers Using Effective Field Theories. PHYSICAL REVIEW LETTERS 2021; 127:212001. [PMID: 34860088 DOI: 10.1103/physrevlett.127.212001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2021] [Accepted: 10/12/2021] [Indexed: 06/13/2023]
Abstract
Simulating the full dynamics of a quantum field theory over a wide range of energies requires exceptionally large quantum computing resources. Yet for many observables in particle physics, perturbative techniques are sufficient to accurately model all but a constrained range of energies within the validity of the theory. We demonstrate that effective field theories (EFTs) provide an efficient mechanism to separate the high energy dynamics that is easily calculated by traditional perturbation theory from the dynamics at low energy and show how quantum algorithms can be used to simulate the dynamics of the low energy EFT from first principles. As an explicit example we calculate the expectation values of vacuum-to-vacuum and vacuum-to-one-particle transitions in the presence of a time-ordered product of two Wilson lines in scalar field theory, an object closely related to those arising in EFTs of the standard model of particle physics. Calculations are performed using simulations of a quantum computer as well as measurements using the IBMQ Manhattan machine.
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Affiliation(s)
- Christian W Bauer
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Benjamin Nachman
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Marat Freytsis
- NHETC, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA and Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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26
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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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27
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Vovrosh J, Khosla KE, Greenaway S, Self C, Kim MS, Knolle J. Simple mitigation of global depolarizing errors in quantum simulations. Phys Rev E 2021; 104:035309. [PMID: 34654120 DOI: 10.1103/physreve.104.035309] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2021] [Accepted: 09/03/2021] [Indexed: 11/07/2022]
Abstract
To get the best possible results from current quantum devices error mitigation is essential. In this work we present a simple but effective error mitigation technique based on the assumption that noise in a deep quantum circuit is well described by global depolarizing error channels. By measuring the errors directly on the device, we use an error model ansatz to infer error-free results from noisy data. We highlight the effectiveness of our mitigation via two examples of recent interest in quantum many-body physics: entanglement measurements and real-time dynamics of confinement in quantum spin chains. Our technique enables us to get quantitative results from the IBM quantum computers showing signatures of confinement, i.e., we are able to extract the meson masses of the confined excitations which were previously out of reach. Additionally, we show the applicability of this mitigation protocol in a wider setting with numerical simulations of more general tasks using a realistic error model. Our protocol is device-independent, simply implementable, and leads to large improvements in results if the global errors are well described by depolarization.
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Affiliation(s)
- Joseph Vovrosh
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Kiran E Khosla
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Sean Greenaway
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Christopher Self
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - M S Kim
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Johannes Knolle
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.,Department of Physics TQM, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
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28
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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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29
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Geller MR. Conditionally Rigorous Mitigation of Multiqubit Measurement Errors. PHYSICAL REVIEW LETTERS 2021; 127:090502. [PMID: 34506180 DOI: 10.1103/physrevlett.127.090502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2020] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
Several techniques have been recently introduced to mitigate errors in near-term quantum computers without the overhead required by quantum error correcting codes. While most of the focus has been on gate errors, measurement errors are significantly larger than gate errors on some platforms. A widely used transition matrix error mitigation (TMEM) technique uses measured transition probabilities between initial and final classical states to correct subsequently measured data. However from a rigorous perspective, the noisy measurement should be calibrated with perfectly prepared initial states, and the presence of any state-preparation error corrupts the resulting mitigation. Here we develop a measurement error mitigation technique, a conditionally rigorous TMEM, that is not sensitive to state-preparation errors and thus avoids this limitation. We demonstrate the importance of the technique for high-precision measurement and for quantum foundations experiments by measuring Mermin polynomials on IBM Q superconducting qubits. An extension of the technique allows one to correct for both state-preparation and measurement (SPAM) errors in expectation values as well; we illustrate this by giving a protocol for fully SPAM-corrected quantum process tomography.
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Affiliation(s)
- Michael R Geller
- Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
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30
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Micheletti C, Hauke P, Faccioli P. Polymer Physics by Quantum Computing. PHYSICAL REVIEW LETTERS 2021; 127:080501. [PMID: 34477421 DOI: 10.1103/physrevlett.127.080501] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Revised: 06/21/2021] [Accepted: 07/06/2021] [Indexed: 06/13/2023]
Abstract
Sampling equilibrium ensembles of dense polymer mixtures is a paradigmatically hard problem in computational physics, even in lattice-based models. Here, we develop a formalism based on interacting binary tensors that allows for tackling this problem using quantum annealing machines. Our approach is general in that properties such as self-avoidance, branching, and looping can all be specified in terms of quadratic interactions of the tensors. Microstates' realizations of different lattice polymer ensembles are then seamlessly generated by solving suitable discrete energy-minimization problems. This approach enables us to capitalize on the strengths of quantum annealing machines, as we demonstrate by sampling polymer mixtures from low to high densities, using the D-Wave quantum annealer. Our systematic approach offers a promising avenue to harness the rapid development of quantum machines for sampling discrete models of filamentous soft-matter systems.
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Affiliation(s)
- Cristian Micheletti
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, I-34136 Trieste, Italy
| | - Philipp Hauke
- Physics Department of Trento University and INO-CNR BEC Center, Via Sommarive 14, I-38123 Povo (Trento), Italy
| | - Pietro Faccioli
- Physics Department of Trento University and INFN-TIFPA, Via Sommarive 14, I-38123 Povo (Trento), Italy
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31
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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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32
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Russo AE, Rudinger KM, Morrison BCA, Baczewski AD. Evaluating Energy Differences on a Quantum Computer with Robust Phase Estimation. PHYSICAL REVIEW LETTERS 2021; 126:210501. [PMID: 34114854 DOI: 10.1103/physrevlett.126.210501] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Revised: 03/17/2021] [Accepted: 03/22/2021] [Indexed: 06/12/2023]
Abstract
We adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a single auxiliary qubit. As a proof of concept, we calculate the energies of the ground state and low-lying electronic excitations of a hydrogen molecule in a minimal basis on a cloud quantum computer. The denominative robustness of our approach is then quantified in terms of a high tolerance to coherent errors in the state preparation and measurement. Conceptually, we note that all quantum phase estimation algorithms ultimately evaluate eigenvalue differences.
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Affiliation(s)
- A E Russo
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - K M Rudinger
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - B C A Morrison
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
- Center for Quantum Information and Control (CQuIC), Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - A D Baczewski
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
- Center for Quantum Information and Control (CQuIC), Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
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33
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Kreshchuk M, Jia S, Kirby WM, Goldstein G, Vary JP, Love PJ. Light-Front Field Theory on Current Quantum Computers. ENTROPY (BASEL, SWITZERLAND) 2021; 23:597. [PMID: 34066258 PMCID: PMC8152011 DOI: 10.3390/e23050597] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Revised: 04/29/2021] [Accepted: 05/05/2021] [Indexed: 11/16/2022]
Abstract
We present a quantum algorithm for simulation of quantum field theory in the light-front formulation and demonstrate how existing quantum devices can be used to study the structure of bound states in relativistic nuclear physics. Specifically, we apply the Variational Quantum Eigensolver algorithm to find the ground state of the light-front Hamiltonian obtained within the Basis Light-Front Quantization (BLFQ) framework. The BLFQ formulation of quantum field theory allows one to readily import techniques developed for digital quantum simulation of quantum chemistry. This provides a method that can be scaled up to simulation of full, relativistic quantum field theories in the quantum advantage regime. As an illustration, we calculate the mass, mass radius, decay constant, electromagnetic form factor, and charge radius of the pion on the IBM Vigo chip. This is the first time that the light-front approach to quantum field theory has been used to enable simulation of a real physical system on a quantum computer.
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Affiliation(s)
- Michael Kreshchuk
- Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA; (M.K.); (W.M.K.); (G.G.)
| | - Shaoyang Jia
- Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA; (S.J.); (J.P.V.)
- Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA
| | - William M. Kirby
- Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA; (M.K.); (W.M.K.); (G.G.)
| | - Gary Goldstein
- Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA; (M.K.); (W.M.K.); (G.G.)
| | - James P. Vary
- Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA; (S.J.); (J.P.V.)
| | - Peter J. Love
- Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA; (M.K.); (W.M.K.); (G.G.)
- Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973, USA
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34
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Rice JE, Gujarati TP, Motta M, Takeshita TY, Lee E, Latone JA, Garcia JM. Quantum computation of dominant products in lithium-sulfur batteries. J Chem Phys 2021; 154:134115. [PMID: 33832277 DOI: 10.1063/5.0044068] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Quantum chemistry simulations of some industrially relevant molecules are reported, employing variational quantum algorithms for near-term quantum devices. The energies and dipole moments are calculated along the dissociation curves for lithium hydride (LiH), hydrogen sulfide, lithium hydrogen sulfide, and lithium sulfide. In all cases, we focus on the breaking of a single bond to obtain information about the stability of the molecular species being investigated. We calculate energies and a variety of electrostatic properties of these molecules using classical simulators of quantum devices, with up to 21 qubits for lithium sulfide. Moreover, we calculate the ground-state energy and dipole moment along the dissociation pathway of LiH using IBM quantum devices. This is the first example, to the best of our knowledge, of dipole moment calculations being performed on quantum hardware.
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Affiliation(s)
- Julia E Rice
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
| | - Tanvi P Gujarati
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
| | - Mario Motta
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
| | - Tyler Y Takeshita
- Mercedes Benz Research and Development North America, Sunnyvale, California 94085, USA
| | - Eunseok Lee
- Mercedes Benz Research and Development North America, Sunnyvale, California 94085, USA
| | - Joseph A Latone
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
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35
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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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36
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Arrazola JM, Bergholm V, Brádler K, Bromley TR, Collins MJ, Dhand I, Fumagalli A, Gerrits T, Goussev A, Helt LG, Hundal J, Isacsson T, Israel RB, Izaac J, Jahangiri S, Janik R, Killoran N, Kumar SP, Lavoie J, Lita AE, Mahler DH, Menotti M, Morrison B, Nam SW, Neuhaus L, Qi HY, Quesada N, Repingon A, Sabapathy KK, Schuld M, Su D, Swinarton J, Száva A, Tan K, Tan P, Vaidya VD, Vernon Z, Zabaneh Z, Zhang Y. Quantum circuits with many photons on a programmable nanophotonic chip. Nature 2021; 591:54-60. [PMID: 33658692 PMCID: PMC11008968 DOI: 10.1038/s41586-021-03202-1] [Citation(s) in RCA: 84] [Impact Index Per Article: 28.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2020] [Accepted: 01/04/2021] [Indexed: 01/31/2023]
Abstract
Growing interest in quantum computing for practical applications has led to a surge in the availability of programmable machines for executing quantum algorithms1,2. Present-day photonic quantum computers3-7 have been limited either to non-deterministic operation, low photon numbers and rates, or fixed random gate sequences. Here we introduce a full-stack hardware-software system for executing many-photon quantum circuit operations using integrated nanophotonics: a programmable chip, operating at room temperature and interfaced with a fully automated control system. The system enables remote users to execute quantum algorithms that require up to eight modes of strongly squeezed vacuum initialized as two-mode squeezed states in single temporal modes, a fully general and programmable four-mode interferometer, and photon number-resolving readout on all outputs. Detection of multi-photon events with photon numbers and rates exceeding any previous programmable quantum optical demonstration is made possible by strong squeezing and high sampling rates. We verify the non-classicality of the device output, and use the platform to carry out proof-of-principle demonstrations of three quantum algorithms: Gaussian boson sampling, molecular vibronic spectra and graph similarity8. These demonstrations validate the platform as a launchpad for scaling photonic technologies for quantum information processing.
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Affiliation(s)
| | | | | | | | | | - I Dhand
- Xanadu, Toronto, Ontario, Canada
| | | | - T Gerrits
- National Institute of Standards and Technology, Boulder, CO, USA
| | | | - L G Helt
- Xanadu, Toronto, Ontario, Canada
| | - J Hundal
- Xanadu, Toronto, Ontario, Canada
| | | | | | - J Izaac
- Xanadu, Toronto, Ontario, Canada
| | | | - R Janik
- Xanadu, Toronto, Ontario, Canada
| | | | | | - J Lavoie
- Xanadu, Toronto, Ontario, Canada
| | - A E Lita
- National Institute of Standards and Technology, Boulder, CO, USA
| | | | | | | | - S W Nam
- National Institute of Standards and Technology, Boulder, CO, USA
| | | | - H Y Qi
- Xanadu, Toronto, Ontario, Canada
| | | | | | | | - M Schuld
- Xanadu, Toronto, Ontario, Canada
| | - D Su
- Xanadu, Toronto, Ontario, Canada
| | | | - A Száva
- Xanadu, Toronto, Ontario, Canada
| | - K Tan
- Xanadu, Toronto, Ontario, Canada
| | - P Tan
- Xanadu, Toronto, Ontario, Canada
| | | | - Z Vernon
- Xanadu, Toronto, Ontario, Canada.
| | | | - Y Zhang
- Xanadu, Toronto, Ontario, Canada
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37
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Nachman B, Provasoli D, de Jong WA, Bauer CW. Quantum Algorithm for High Energy Physics Simulations. PHYSICAL REVIEW LETTERS 2021; 126:062001. [PMID: 33635685 DOI: 10.1103/physrevlett.126.062001] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2020] [Revised: 12/02/2020] [Accepted: 12/17/2020] [Indexed: 06/12/2023]
Abstract
Simulating quantum field theories is a flagship application of quantum computing. However, calculating experimentally relevant high energy scattering amplitudes entirely on a quantum computer is prohibitively difficult. It is well known that such high energy scattering processes can be factored into pieces that can be computed using well established perturbative techniques, and pieces which currently have to be simulated using classical Markov chain algorithms. These classical Markov chain simulation approaches work well to capture many of the salient features, but cannot capture all quantum effects. To exploit quantum resources in the most efficient way, we introduce a new paradigm for quantum algorithms in field theories. This approach uses quantum computers only for those parts of the problem which are not computable using existing techniques. In particular, we develop a polynomial time quantum final state shower that accurately models the effects of intermediate spin states similar to those present in high energy electroweak showers with a global evolution variable. The algorithm is explicitly demonstrated for a simplified quantum field theory on a quantum computer.
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Affiliation(s)
- Benjamin Nachman
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Davide Provasoli
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Wibe A de Jong
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Christian W Bauer
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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38
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Lacroix D. Symmetry-Assisted Preparation of Entangled Many-Body States on a Quantum Computer. PHYSICAL REVIEW LETTERS 2020; 125:230502. [PMID: 33337171 DOI: 10.1103/physrevlett.125.230502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Revised: 09/08/2020] [Accepted: 10/27/2020] [Indexed: 06/12/2023]
Abstract
Starting from the quantum-phase-estimate (QPE) algorithm, a method is proposed to construct entangled states that describe correlated many-body systems on quantum computers. Using operators for which the discrete set of eigenvalues is known, the QPE approach is followed by measurements that serve as projectors on the entangled states. These states can then be used as inputs for further quantum or hybrid quantum-classical processing. When the operator is associated with a symmetry of the Hamiltonian, the approach can be seen as a quantum-computer formulation of symmetry breaking followed by symmetry restoration. The method, called discrete spectra assisted, is applied to superfluid systems. By using the blocking technique adapted to qubits, the full spectra of a pairing Hamiltonian is obtained.
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Affiliation(s)
- Denis Lacroix
- Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
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39
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Urbanek M, Camps D, Van Beeumen R, de Jong WA. Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion. J Chem Theory Comput 2020; 16:5425-5431. [PMID: 32822184 DOI: 10.1021/acs.jctc.0c00447] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
Simulating chemical systems on quantum computers has been limited to a few electrons in a minimal basis. We demonstrate experimentally that the virtual quantum subspace expansion (Takeshita, T.; Phys. Rev. X 2020, 10, 011004, 10.1103/PhysRevX.10.011004) can achieve full basis accuracy for hydrogen and lithium dimers, comparable to simulations requiring 20 or more qubits. We developed an approach to minimize the impact of experimental noise on the stability of the generalized eigenvalue problem, a crucial component of the quantum algorithm. In addition, we were able to obtain an accurate potential energy curve for the nitrogen dimer in a quantum simulation on a classical computer.
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Affiliation(s)
- Miroslav Urbanek
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Daan Camps
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Roel Van Beeumen
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Wibe A de Jong
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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40
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McClean JR, Jiang Z, Rubin NC, Babbush R, Neven H. Decoding quantum errors with subspace expansions. Nat Commun 2020; 11:636. [PMID: 32005804 PMCID: PMC6994666 DOI: 10.1038/s41467-020-14341-w] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Accepted: 12/16/2019] [Indexed: 11/29/2022] Open
Abstract
With rapid developments in quantum hardware comes a push towards the first practical applications. While fully fault-tolerant quantum computers are not yet realized, there may exist intermediate forms of error correction that enable practical applications. In this work, we consider the idea of post-processing error decoders using existing quantum codes, which mitigate errors on logical qubits using post-processing without explicit syndrome measurements or additional qubits beyond the encoding overhead. This greatly simplifies the experimental exploration of quantum codes on real, near-term devices, removing the need for locality of syndromes or fast feed-forward. We develop the theory of the method and demonstrate it on an example with the perfect [[5, 1, 3]] code, which exhibits a pseudo-threshold of p ≈ 0.50 under a single qubit depolarizing channel applied to all qubits. We also provide a demonstration of improved performance on an unencoded hydrogen molecule. Fault-tolerant quantum computation is still far, but there could be ways in which quantum error correction could improve currently available devices. Here, the authors show how to exploit existing quantum codes through only post-processing and random measurements in order to mitigate errors in NISQ devices.
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Affiliation(s)
| | - Zhang Jiang
- Google Inc., 340 Main Street, Venice, CA, 90291, USA
| | | | - Ryan Babbush
- Google Inc., 340 Main Street, Venice, CA, 90291, USA
| | - Hartmut Neven
- Google Inc., 340 Main Street, Venice, CA, 90291, USA
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41
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Cerasoli FT, Sherbert K, Sławińska J, Buongiorno Nardelli M. Quantum computation of silicon electronic band structure. Phys Chem Chem Phys 2020; 22:21816-21822. [DOI: 10.1039/d0cp04008h] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present minimal depth circuits implementing the variational quantum eigensolver algorithm and successfully use it to compute the band structure of silicon on a quantum machine for the first time.
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Affiliation(s)
| | - Kyle Sherbert
- Department of Physics
- University of North Texas
- Denton
- USA
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42
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Kirby WM, Love PJ. Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers. PHYSICAL REVIEW LETTERS 2019; 123:200501. [PMID: 31809115 DOI: 10.1103/physrevlett.123.200501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Revised: 09/23/2019] [Indexed: 06/10/2023]
Abstract
Contextuality is an indicator of nonclassicality, and a resource for various quantum procedures. In this Letter, we use contextuality to evaluate the variational quantum eigensolver (VQE), one of the most promising tools for near-term quantum simulation. We present an efficiently computable test to determine whether or not the objective function for a VQE procedure is contextual. We apply this test to evaluate the contextuality of experimental implementations of VQE, and determine that several, but not all, fail this test of quantumness.
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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
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43
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Cao Y, Romero J, Olson JP, Degroote M, Johnson PD, Kieferová M, Kivlichan ID, Menke T, Peropadre B, Sawaya NPD, Sim S, Veis L, Aspuru-Guzik A. Quantum Chemistry in the Age of Quantum Computing. Chem Rev 2019; 119:10856-10915. [PMID: 31469277 DOI: 10.1021/acs.chemrev.8b00803] [Citation(s) in RCA: 283] [Impact Index Per Article: 56.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.
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Affiliation(s)
- Yudong Cao
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan Romero
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Jonathan P Olson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Matthias Degroote
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada
| | - Peter D Johnson
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Mária Kieferová
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Physics and Astronomy , Macquarie University , Sydney , NSW 2109 , Australia.,Institute for Quantum Computing and Department of Physics and Astronomy , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada
| | - Ian D Kivlichan
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States
| | - Tim Menke
- Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States.,Research Laboratory of Electronics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States.,Department of Physics , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Borja Peropadre
- Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Nicolas P D Sawaya
- Intel Laboratories , Intel Corporation , Santa Clara , California 95054 United States
| | - Sukin Sim
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry , Academy of Sciences of the Czech Republic v.v.i. , Doleǰskova 3 , 18223 Prague 8, Czech Republic
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology , Harvard University , Cambridge , Massachusetts 02138 , United States.,Zapata Computing Inc. , Cambridge , Massachusetts 02139 , United States.,Department of Chemistry , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Department of Computer Science , University of Toronto , Toronto , Ontario M5G 1Z8 , Canada.,Canadian Institute for Advanced Research , Toronto , Ontario M5G 1Z8 , Canada.,Vector Institute for Artificial Intelligence , Toronto , Ontario M5S 1M1 , Canada
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44
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Lamm H, Lawrence S, Yamauchi Y. General methods for digital quantum simulation of gauge theories. Int J Clin Exp Med 2019. [DOI: 10.1103/physrevd.100.034518] [Citation(s) in RCA: 57] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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45
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Zhang T, Li C, Evangelista FA. Improving the Efficiency of the Multireference Driven Similarity Renormalization Group via Sequential Transformation, Density Fitting, and the Noninteracting Virtual Orbital Approximation. J Chem Theory Comput 2019; 15:4399-4414. [PMID: 31268704 DOI: 10.1021/acs.jctc.9b00353] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This study examines several techniques to improve the efficiency of the linearized multireference driven similarity renormalization group truncated to one- and two-body operators [MR-LDSRG(2)]. We propose a sequential MR-LDSRG(2) [sq-MR-LDSRG(2)] scheme, in which one-body substitutions are folded exactly into the Hamiltonian. This new approach is combined with density fitting (DF) to reduce the storage cost of two-electron integrals. To further avoid storage of large four-index intermediates, we propose a noninteracting virtual orbital (NIVO) approximation of the Baker-Campbell-Hausdorff series that neglects commutators terms with three and four virtual indices. The NIVO approximation reduces the computational prefactor of the MR-LDSRG(2), bringing it closer to that of coupled cluster with singles and doubles (CCSD). We test the effect of the DF and NIVO approximations on the MR-LDSRG(2) and sq-MR-LDSRG(2) methods by computing properties of eight diatomic molecules. The diatomic constants obtained by DF-sq-MR-LDSRG(2)+NIVO are found to be as accurate as those from the original MR-LDSRG(2) and coupled cluster theory with singles, doubles, and perturbative triples. Finally, we demonstrate that the DF-sq-MR-LDSRG(2)+NIVO scheme can be applied to chemical systems with more than 550 basis functions by computing the automerization energy of cyclobutadiene with a quintuple-ζ basis set. The predicted automerization energy is found to be similar to the value computed with Mukherjee's state-specific multireference coupled cluster theory with singles and doubles.
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Affiliation(s)
- Tianyuan Zhang
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation , Emory University , Atlanta , Georgia 30322 , United States
| | - Chenyang Li
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation , Emory University , Atlanta , Georgia 30322 , United States
| | - Francesco A Evangelista
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation , Emory University , Atlanta , Georgia 30322 , United States
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46
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McArdle S, Mayorov A, Shan X, Benjamin S, Yuan X. Digital quantum simulation of molecular vibrations. Chem Sci 2019; 10:5725-5735. [PMID: 31293758 PMCID: PMC6568047 DOI: 10.1039/c9sc01313j] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2019] [Accepted: 04/23/2019] [Indexed: 01/30/2023] Open
Abstract
Molecular vibrations underpin important phenomena such as spectral properties, energy transfer, and molecular bonding. However, obtaining a detailed understanding of the vibrational structure of even small molecules is computationally expensive. While several algorithms exist for efficiently solving the electronic structure problem on a quantum computer, there has been comparatively little attention devoted to solving the vibrational structure problem with quantum hardware. In this work, we discuss the use of quantum algorithms for investigating both the static and dynamic vibrational properties of molecules. We introduce a physically motivated unitary vibrational coupled cluster ansatz, which also makes our method accessible to noisy, near-term quantum hardware. We numerically test our proposals for the water and sulfur dioxide molecules.
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Affiliation(s)
- Sam McArdle
- Department of Materials , University of Oxford , Parks Road , Oxford OX1 3PH , UK .
| | - Alexander Mayorov
- Department of Materials , University of Oxford , Parks Road , Oxford OX1 3PH , UK .
- Department of Chemistry , University of Cambridge , Lensfield Road , Cambridge CB2 1EW , UK
| | - Xiao Shan
- Physical and Theoretical Chemical Laboratory , University of Oxford , South Parks Road , Oxford OX1 3QZ , UK
| | - Simon Benjamin
- Department of Materials , University of Oxford , Parks Road , Oxford OX1 3PH , UK .
| | - Xiao Yuan
- Department of Materials , University of Oxford , Parks Road , Oxford OX1 3PH , UK .
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47
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Kokail C, Maier C, van Bijnen R, Brydges T, Joshi MK, Jurcevic P, Muschik CA, Silvi P, Blatt R, Roos CF, Zoller P. Self-verifying variational quantum simulation of lattice models. Nature 2019; 569:355-360. [DOI: 10.1038/s41586-019-1177-4] [Citation(s) in RCA: 264] [Impact Index Per Article: 52.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2018] [Accepted: 03/21/2019] [Indexed: 11/09/2022]
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Li Y, Hu J, Zhang X, Song Z, Yung M. Variational Quantum Simulation for Quantum Chemistry. ADVANCED THEORY AND SIMULATIONS 2019. [DOI: 10.1002/adts.201800182] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Yifan Li
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
| | - Jiaqi Hu
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
| | - Xiao‐Ming Zhang
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
- Department of PhysicsCity University of Hong KongTat Chee Avenue Kowloon Hong Kong SAR 999077 China
| | - Zhigang Song
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
- Department of EngineeringUniversity of CambridgeJJ Thomson Avenue CB3 0FA Cambridge United Kingdom
| | - Man‐Hong Yung
- Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055 China
- Shenzhen Key Laboratory of Quantum Science and EngineeringSouthern University of Science and TechnologyShenzhen 518055 China
- Central Research InstituteHuawei TechnologiesShenzhen 518129 China
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49
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McCaskey A, Dumitrescu E, Chen M, Lyakh D, Humble T. Validating quantum-classical programming models with tensor network simulations. PLoS One 2018; 13:e0206704. [PMID: 30532151 PMCID: PMC6287780 DOI: 10.1371/journal.pone.0206704] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Accepted: 10/15/2018] [Indexed: 11/24/2022] Open
Abstract
The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to understanding the utility of the hybrid computational model. In this paper, we demonstrate a newly developed quantum circuit simulator based on tensor network theory that enables intermediate-scale verification and validation of hybrid quantum-classical computing frameworks and programming models. We present our tensor-network quantum virtual machine (TNQVM) simulator which stores a multi-qubit wavefunction in a compressed (factorized) form as a matrix product state, thus enabling single-node simulations of larger qubit registers, as compared to brute-force state-vector simulators. Our simulator is designed to be extensible in both the tensor network form and the classical hardware used to run the simulation (multicore, GPU, distributed). The extensibility of the TNQVM simulator with respect to the simulation hardware type is achieved via a pluggable interface for different numerical backends (e.g., ITensor and ExaTENSOR numerical libraries). We demonstrate the utility of our TNQVM quantum circuit simulator through the verification of randomized quantum circuits and the variational quantum eigensolver algorithm, both expressed within the eXtreme-scale ACCelerator (XACC) programming model.
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Affiliation(s)
- Alexander McCaskey
- Quantum Computing Institute, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America
- Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America
| | - Eugene Dumitrescu
- Quantum Computing Institute, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America
| | - Mengsu Chen
- Department of Physics, Virginia Tech, Blacksburg, Virginia, 24060, United States of America
| | - Dmitry Lyakh
- Quantum Computing Institute, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America
- National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America
| | - Travis Humble
- Quantum Computing Institute, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States of America
- Bredesen Center for Interdisciplinary Research, University of Tennessee, Knoxville, Tennessee 37996, United States of America
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50
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Barren plateaus in quantum neural network training landscapes. Nat Commun 2018; 9:4812. [PMID: 30446662 PMCID: PMC6240101 DOI: 10.1038/s41467-018-07090-4] [Citation(s) in RCA: 140] [Impact Index Per Article: 23.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2018] [Accepted: 10/09/2018] [Indexed: 11/09/2022] Open
Abstract
Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum simulation, optimization, and machine learning. Due to its simplicity and hardware efficiency, random circuits are often proposed as initial guesses for exploring the space of quantum states. We show that the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. Specifically, we show that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. We argue that this is related to the 2-design characteristic of random circuits, and that solutions to this problem must be studied.
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