1
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Mazzola G. Quantum computing for chemistry and physics applications from a Monte Carlo perspective. J Chem Phys 2024; 160:010901. [PMID: 38165101 DOI: 10.1063/5.0173591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 10/18/2023] [Indexed: 01/03/2024] Open
Abstract
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo solutions into quantum algorithms. These include refined energy estimators, parameter optimization, real and imaginary-time dynamics, and variational circuits. Conversely, we will review new ideas for utilizing quantum hardware to accelerate the sampling in statistical classical models, with applications in physics, chemistry, optimization, and machine learning. This review aims to be accessible to both communities and intends to foster further algorithmic developments at the intersection of quantum computing and Monte Carlo methods. Most of the works discussed in this Perspective have emerged within the last two years, indicating a rapidly growing interest in this promising area of research.
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Affiliation(s)
- Guglielmo Mazzola
- Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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2
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Silva TL, Taddei MM, Carrazza S, Aolita L. Fragmented imaginary-time evolution for early-stage quantum signal processors. Sci Rep 2023; 13:18258. [PMID: 37880355 PMCID: PMC10600201 DOI: 10.1038/s41598-023-45540-2] [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: 04/24/2023] [Accepted: 10/20/2023] [Indexed: 10/27/2023] Open
Abstract
Simulating quantum imaginary-time evolution (QITE) is a significant promise of quantum computation. However, the known algorithms are either probabilistic (repeat until success) with unpractically small success probabilities or coherent (quantum amplitude amplification) with circuit depths and ancillary-qubit numbers unrealistically large in the mid-term. Our main contribution is a new generation of deterministic, high-precision QITE algorithms that are significantly more amenable experimentally. A surprisingly simple idea is behind them: partitioning the evolution into a sequence of fragments that are run probabilistically. It causes a considerable reduction in wasted circuit depth every time a run fails. Remarkably, the resulting overall runtime is asymptotically better than in coherent approaches, and the hardware requirements are even milder than in probabilistic ones. Our findings are especially relevant for the early fault-tolerance stages of quantum hardware.
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Affiliation(s)
- Thais L Silva
- Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, UAE.
- Federal University of Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ, 21941-972, Brazil.
| | - Márcio M Taddei
- Federal University of Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ, 21941-972, Brazil
- ICFO - Institut de Ciencies Fotòniques, The Barcelona Institute of Science and Technology, 08860, Castelldefels, Barcelona, Spain
| | - Stefano Carrazza
- Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, UAE
- TIF Lab, Dipartimento di Fisica, Università degli Studi di Milano and INFN Sezione di Milano, Milan, Italy
| | - Leandro Aolita
- Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, UAE
- Federal University of Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ, 21941-972, Brazil
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3
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Tian J, Sun X, Du Y, Zhao S, Liu Q, Zhang K, Yi W, Huang W, Wang C, Wu X, Hsieh MH, Liu T, Yang W, Tao D. Recent Advances for Quantum Neural Networks in Generative Learning. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023; 45:12321-12340. [PMID: 37126624 DOI: 10.1109/tpami.2023.3272029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum variational autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relations and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.
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4
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Davoudi Z, Mueller N, Powers C. Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States. PHYSICAL REVIEW LETTERS 2023; 131:081901. [PMID: 37683176 DOI: 10.1103/physrevlett.131.081901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 02/27/2023] [Accepted: 06/01/2023] [Indexed: 09/10/2023]
Abstract
The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.
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Affiliation(s)
- Zohreh Davoudi
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Niklas Mueller
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Connor Powers
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
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5
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Liu Y, Meitei OR, Chin ZE, Dutt A, Tao M, Chuang IL, Van Voorhis T. Bootstrap Embedding on a Quantum Computer. J Chem Theory Comput 2023; 19:2230-2247. [PMID: 37001026 DOI: 10.1021/acs.jctc.3c00012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
Abstract
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.
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Affiliation(s)
- Yuan Liu
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Oinam R. Meitei
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Zachary E. Chin
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Arkopal Dutt
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Max Tao
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Isaac L. Chuang
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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6
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Exploring finite temperature properties of materials with quantum computers. Sci Rep 2023; 13:1986. [PMID: 36737662 PMCID: PMC9898567 DOI: 10.1038/s41598-023-28317-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2022] [Accepted: 01/17/2023] [Indexed: 02/05/2023] Open
Abstract
Thermal properties of nanomaterials are crucial to not only improving our fundamental understanding of condensed matter systems, but also to developing novel materials for applications spanning research and industry. Since quantum effects arise at the nano-scale, these systems are difficult to simulate on classical computers. Quantum computers can efficiently simulate quantum many-body systems, yet current quantum algorithms for calculating thermal properties of these systems incur significant computational costs in that they either prepare the full thermal state on the quantum computer, or they must sample a number of pure states from a distribution that grows with system size. Canonical thermal pure quantum (TPQ) states provide a promising path to estimating thermal properties of quantum materials as they neither require preparation of the full thermal state nor require a growing number of samples with system size. Here, we present an algorithm for preparing canonical TPQ states on quantum computers. We compare three different circuit implementations for the algorithm and demonstrate their capabilities in estimating thermal properties of quantum materials. Due to its increasing accuracy with system size and flexibility in implementation, we anticipate that this method will enable finite temperature explorations of relevant quantum materials on near-term quantum computers.
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7
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Umer MJ, Sharif MI. A Comprehensive Survey on Quantum Machine Learning and Possible Applications. INTERNATIONAL JOURNAL OF E-HEALTH AND MEDICAL COMMUNICATIONS 2022. [DOI: 10.4018/ijehmc.315730] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Machine learning is a branch of artificial intelligence that is being used at a large scale to solve science, engineering, and medical tasks. Quantum computing is an emerging technology that has a very high computational ability to solve complex problems. Classical machine learning with traditional systems has some limitations for problem-solving due to a large amount of data availability. Quantum machine learning has high performance and computational ability that can effectively be used to solve computation tasks. This study reviews the latest articles in quantum computing and quantum machine learning. Building blocks of quantum computing and different flavors of quantum algorithms are also discussed. The latest work in quantum neural networks is also presented. In the end, different possible applications of quantum computing are also discussed.
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8
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Sahimi M, Tahmasebi P. The Potential of Quantum Computing for Geoscience. Transp Porous Media 2022. [DOI: 10.1007/s11242-022-01855-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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9
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Wild DS, Sels D, Pichler H, Zanoci C, Lukin MD. Quantum Sampling Algorithms for Near-Term Devices. PHYSICAL REVIEW LETTERS 2021; 127:100504. [PMID: 34533337 DOI: 10.1103/physrevlett.127.100504] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2021] [Accepted: 07/21/2021] [Indexed: 06/13/2023]
Abstract
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of quantum algorithms that provide unbiased samples by preparing a state encoding the entire Gibbs distribution. We show that this approach leads to a speedup over a classical Markov chain algorithm for several examples, including the Ising model and sampling from weighted independent sets of two different graphs. Our approach connects computational complexity with phase transitions, providing a physical interpretation of quantum speedup. Moreover, it opens the door to exploring potentially useful sampling algorithms on near-term quantum devices, as the algorithm for sampling from independent sets on certain graphs can be naturally implemented using Rydberg atom arrays.
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Affiliation(s)
- Dominik S Wild
- Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany
| | - Dries Sels
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
- Department of Physics, New York University, New York, New York 10003, USA
| | - Hannes Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Cristian Zanoci
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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10
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Bauer B, Bravyi S, Motta M, Chan GKL. Quantum Algorithms for Quantum Chemistry and Quantum Materials Science. Chem Rev 2020; 120:12685-12717. [DOI: 10.1021/acs.chemrev.9b00829] [Citation(s) in RCA: 134] [Impact Index Per Article: 33.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Bela Bauer
- Microsoft Quantum, Station Q, University of California
, Santa Barbara, California 93106, United States
| | - Sergey Bravyi
- IBM Quantum, IBM T. J. Watson Research Center
, Yorktown Heights, New York 10598, United States
| | - Mario Motta
- IBM Quantum, IBM Research Almaden
, San Jose, California 95120, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology
, Pasadena, California 91125, United States
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11
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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: 273] [Impact Index Per Article: 54.6] [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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12
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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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13
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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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14
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Poulin D, Kitaev A, Steiger DS, Hastings MB, Troyer M. Quantum Algorithm for Spectral Measurement with a Lower Gate Count. PHYSICAL REVIEW LETTERS 2018; 121:010501. [PMID: 30028152 DOI: 10.1103/physrevlett.121.010501] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Indexed: 06/08/2023]
Abstract
We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by standard fault tolerant techniques. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice size required by other techniques.
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Affiliation(s)
- David Poulin
- Département de Physique & Institut Quantique, Université de Sherbrooke, J1K 2R1, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
| | - Alexei Kitaev
- California Institute of Technology, Pasadena, California 91125, USA
| | | | - Matthew B Hastings
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
- Quantum Architecture and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
| | - Matthias Troyer
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
- Quantum Architecture and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
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15
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Dunjko V, Briegel HJ. Machine learning & artificial intelligence in the quantum domain: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:074001. [PMID: 29504942 DOI: 10.1088/1361-6633/aab406] [Citation(s) in RCA: 112] [Impact Index Per Article: 18.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Quantum information technologies, on the one hand, and intelligent learning systems, on the other, are both emergent technologies that are likely to have a transformative impact on our society in the future. The respective underlying fields of basic research-quantum information versus machine learning (ML) and artificial intelligence (AI)-have their own specific questions and challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been probing the question of the extent to which these fields can indeed learn and benefit from each other. Quantum ML explores the interaction between quantum computing and ML, investigating how results and techniques from one field can be used to solve the problems of the other. Recently we have witnessed significant breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups for ML problems, critical in our 'big data' world. Conversely, ML already permeates many cutting-edge technologies and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical ML optimization used in quantum experiments, quantum enhancements have also been (theoretically) demonstrated for interactive learning tasks, highlighting the potential of quantum-enhanced learning agents. Finally, works exploring the use of AI for the very design of quantum experiments and for performing parts of genuine research autonomously, have reported their first successes. Beyond the topics of mutual enhancement-exploring what ML/AI can do for quantum physics and vice versa-researchers have also broached the fundamental issue of quantum generalizations of learning and AI concepts. This deals with questions of the very meaning of learning and intelligence in a world that is fully described by quantum mechanics. In this review, we describe the main ideas, recent developments and progress in a broad spectrum of research investigating ML and AI in the quantum domain.
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Affiliation(s)
- Vedran Dunjko
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck 6020, Austria. Max Planck Institute of Quantum Optics, Garching 85748, Germany
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16
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Lei C, Peng S, Ju C, Yung MH, Du J. Decoherence Control of Nitrogen-Vacancy Centers. Sci Rep 2017; 7:11937. [PMID: 28931932 PMCID: PMC5607330 DOI: 10.1038/s41598-017-12280-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2017] [Accepted: 08/11/2017] [Indexed: 11/08/2022] Open
Abstract
Quantum mechanical systems lose coherence through interacting with external environments-a process known as decoherence. Although decoherence is detrimental for most of the tasks in quantum information processing, a substantial degree of decoherence is crucial for boosting the efficiency of quantum processes, for example, in quantum biology and other open systems. The key to the success in simulating those open quantum systems is therefore the ability of controlling decoherence, instead of eliminating it. Motivated by simulating quantum open systems with Nitrogen-Vacancy centers, which has become an increasingly important platform for quantum information processing tasks, we developed a new set of steering pulse sequences for controlling various coherence times of Nitrogen-Vacancy centers; our method is based on a hybrid approach that exploits ingredients in both digital and analog quantum simulations to dynamically couple or decouple the system with the physical environment. Our numerical simulations, based on experimentally-feasible parameters, indicate that decoherence of Nitrogen-Vacancy centers can be controlled externally to a very large extend.
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Affiliation(s)
- Chao Lei
- Hefei National Laboratory for Physics Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China
- Department of Physics, The University of Texas at Austin, Austin, Texas, 78712, USA
| | - Shijie Peng
- Hefei National Laboratory for Physics Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Chenyong Ju
- Hefei National Laboratory for Physics Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China
| | - Man-Hong Yung
- Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, People's Republic of China.
| | - Jiangfeng Du
- Hefei National Laboratory for Physics Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China.
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China.
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17
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Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S. Quantum machine learning. Nature 2017; 549:195-202. [DOI: 10.1038/nature23474] [Citation(s) in RCA: 1159] [Impact Index Per Article: 165.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2017] [Accepted: 07/04/2017] [Indexed: 01/24/2023]
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18
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Ge Y, Molnár A, Cirac JI. Rapid Adiabatic Preparation of Injective Projected Entangled Pair States and Gibbs States. PHYSICAL REVIEW LETTERS 2016; 116:080503. [PMID: 26967402 DOI: 10.1103/physrevlett.116.080503] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Indexed: 06/05/2023]
Abstract
We propose a quantum algorithm for many-body state preparation. It is especially suited for injective projected entangled pair states and thermal states of local commuting Hamiltonians on a lattice. We show that for a uniform gap and sufficiently smooth paths, an adiabatic runtime and circuit depth of O(polylogN) can be achieved for O(N) spins. This is an almost exponential improvement over previous bounds. The total number of elementary gates scales as O(NpolylogN). This is also faster than the best known upper bound of O(N^{2}) on the mixing times of Monte Carlo Markov chain algorithms for sampling classical systems in thermal equilibrium.
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Affiliation(s)
- Yimin Ge
- Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany
| | - András Molnár
- Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany
| | - J Ignacio Cirac
- Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany
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Abstract
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.
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Affiliation(s)
- Ashley Montanaro
- Department of Computer Science , University of Bristol , Woodland Road, Bristol, UK
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20
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Peruzzo A, McClean J, Shadbolt P, Yung MH, Zhou XQ, Love PJ, Aspuru-Guzik A, O’Brien JL. A variational eigenvalue solver on a photonic quantum processor. Nat Commun 2014. [DOI: 10.1038/ncomms5213 (2014)] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023] Open
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21
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A variational eigenvalue solver on a photonic quantum processor. Nat Commun 2014; 5:4213. [PMID: 25055053 PMCID: PMC4124861 DOI: 10.1038/ncomms5213] [Citation(s) in RCA: 534] [Impact Index Per Article: 53.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2013] [Accepted: 05/27/2014] [Indexed: 01/13/2023] Open
Abstract
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansätze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry—calculating the ground-state molecular energy for He–H+. The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future. Quantum computers promise to efficiently solve problems that would be practically impossible with a normal computer. Peruzzo et al. develop a variational computation approach that uses any available quantum resources and, with a photonic quantum processing unit, find the ground-state molecular energy of He–H+.
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Yung MH, Whitfield JD, Boixo S, Tempel DG, Aspuru-Guzik A. Introduction to Quantum Algorithms for Physics and Chemistry. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118742631.ch03] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
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23
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Yung MH, Casanova J, Mezzacapo A, McClean J, Lamata L, Aspuru-Guzik A, Solano E. From transistor to trapped-ion computers for quantum chemistry. Sci Rep 2014; 4:3589. [PMID: 24395054 PMCID: PMC5378044 DOI: 10.1038/srep03589] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2013] [Accepted: 12/06/2013] [Indexed: 12/02/2022] Open
Abstract
Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology.
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Affiliation(s)
- M.-H. Yung
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, P. R. China
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge MA, 02138, USA
- These authors contributed equally to this work
| | - J. Casanova
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
- These authors contributed equally to this work
| | - A. Mezzacapo
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - J. McClean
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge MA, 02138, USA
| | - L. Lamata
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - A. Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge MA, 02138, USA
| | - E. Solano
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
- IKERBASQUE, Basque Foundation for Science, Alameda Urquijo 36, 48011 Bilbao, Spain
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24
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Zhang J, Yung MH, Laflamme R, Aspuru-Guzik A, Baugh J. Digital quantum simulation of the statistical mechanics of a frustrated magnet. Nat Commun 2012; 3:880. [PMID: 22673907 DOI: 10.1038/ncomms1860] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2012] [Accepted: 04/23/2012] [Indexed: 11/09/2022] Open
Abstract
Many problems of interest in physics, chemistry and computer science are equivalent to problems defined on systems of interacting spins. However, most such problems require computational resources that are out of reach with classical computers. A promising solution to overcome this challenge is quantum simulation. Several 'analogue' quantum simulations of interacting spin systems have been realized experimentally, where ground states were prepared using adiabatic techniques. Here we report a 'digital' quantum simulation of thermal states; a three-spin frustrated magnet was simulated using a nuclear magnetic resonance quantum information processor, and we were able to explore the phase diagram of the system at any simulated temperature and external field. These results help to identify the challenges for performing quantum simulations of physical systems at finite temperatures, and suggest methods that may be useful in simulating thermal open quantum systems.
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Affiliation(s)
- Jingfu Zhang
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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25
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Solving quantum ground-state problems with nuclear magnetic resonance. Sci Rep 2012; 1:88. [PMID: 22355607 PMCID: PMC3216574 DOI: 10.1038/srep00088] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2011] [Accepted: 08/17/2011] [Indexed: 11/27/2022] Open
Abstract
Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10−5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers
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