Noisy intermediate-scale quantum algorithms

Bharti, Kishor; Cervera-Lierta, Alba; Kyaw, Thi Ha; Haug, Tobias; Alperin-Lea, Sumner; Anand, Abhinav; Degroote, Matthias; Heimonen, Hermanni; Kottmann, Jakob S.; Menke, Tim; Mok, Wai-Keong; Sim, Sukin; Kwek, Leong-Chuan; Aspuru-Guzik, Alán

doi:10.1103/revmodphys.94.015004

Noisy intermediate-scale quantum algorithms

Journal Article · Mon Feb 14 23:00:00 EST 2022 · Reviews of Modern Physics

DOI:https://doi.org/10.1103/revmodphys.94.015004· OSTI ID:1980381

^[1]; ^[2]; ^[2]; ^[3]; Alperin-Lea, Sumner ^[2]; ^[2]; ^[2]; Heimonen, Hermanni ^[4]; ^[2]; Menke, Tim ^[5]; ^[4]; ^[6]; Kwek, Leong-Chuan ^[7]; Aspuru-Guzik, Alán ^[8]

National Univ. of Singapore (Singapore); OSTI
Univ. of Toronto, ON (Canada)
Imperial College, London (United Kingdom)
National Univ. of Singapore (Singapore)
Harvard Univ., Cambridge, MA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Harvard Univ., Cambridge, MA (United States)
National Univ. of Singapore (Singapore); MajuLab International Research Lab (Singapore); Nanyang Technological Univ. (Singapore)
Univ. of Toronto, ON (Canada); Vector Institute for Artificial Intelligence (Canada); Canadian Institute for Advanced Research (CIFAR), Toronto, ON (Canada)

A universal fault-tolerant quantum computer that can efficiently solve problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement toward realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e., qubits that are not error corrected, and therefore perform imperfect operations within a limited coherence time. In the search for achieving quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry, and combinatorial optimization. The overarching goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, a thorough summary of NISQ computational paradigms and algorithms is provided. The key structure of these algorithms and their limitations and advantages are discussed. Finally, a comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices is additionally provided.

View Accepted Manuscript (DOE)

Research Organization:: Emory Univ., Atlanta, GA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); US Department of the Navy, Office of Naval Research (ONR)

Grant/Contract Number:: SC0019374

OSTI ID:: 1980381

Journal Information:: Reviews of Modern Physics, Journal Name: Reviews of Modern Physics Journal Issue: 1 Vol. 94; ISSN 0034-6861

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Quantum generative adversarial networks Dallaire-Demers, Pierre-Luc; Killoran, Nathan Physical Review A, Vol. 98, Issue 1 https://doi.org/10.1103/PhysRevA.98.012324	journal	July 2018
Quantum circuit learning Mitarai, K.; Negoro, M.; Kitagawa, M. Physical Review A, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevA.98.032309	journal	September 2018
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Gaussian boson sampling using threshold detectors Quesada, Nicolás; Arrazola, Juan Miguel; Killoran, Nathan Physical Review A, Vol. 98, Issue 6 https://doi.org/10.1103/PhysRevA.98.062322	journal	December 2018
Differentiable learning of quantum circuit Born machines Liu, Jin-Guo; Wang, Lei Physical Review A, Vol. 98, Issue 6 https://doi.org/10.1103/PhysRevA.98.062324	journal	December 2018
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Experimental realization of quantum algorithms for a linear system inspired by adiabatic quantum computing Wen, Jingwei; Kong, Xiangyu; Wei, Shijie Physical Review A, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevA.99.012320	journal	January 2019
Quantum codes for quantum simulation of fermions on a square lattice of qubits Steudtner, Mark; Wehner, Stephanie Physical Review A, Vol. 99, Issue 2 https://doi.org/10.1103/PhysRevA.99.022308	journal	February 2019
Evaluating analytic gradients on quantum hardware Schuld, Maria; Bergholm, Ville; Gogolin, Christian Physical Review A, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevA.99.032331	journal	March 2019
Learning and inference on generative adversarial quantum circuits Zeng, Jinfeng; Wu, Yufeng; Liu, Jin-Guo Physical Review A, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevA.99.052306	journal	May 2019
Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states Elben, A.; Vermersch, B.; Roos, C. F. Physical Review A, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevA.99.052323	journal	May 2019
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Boosting Computational Power through Spatial Multiplexing in Quantum Reservoir Computing Nakajima, Kohei; Fujii, Keisuke; Negoro, Makoto Physical Review Applied, Vol. 11, Issue 3 https://doi.org/10.1103/PhysRevApplied.11.034021	journal	March 2019
Generalization of the Output of a Variational Quantum Eigensolver by Parameter Interpolation with a Low-depth Ansatz Mitarai, Kosuke; Yan, Tennin; Fujii, Keisuke Physical Review Applied, Vol. 11, Issue 4 https://doi.org/10.1103/PhysRevApplied.11.044087	journal	April 2019
Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer Ganzhorn, M.; Egger, D. J.; Barkoutsos, P. Physical Review Applied, Vol. 11, Issue 4 https://doi.org/10.1103/PhysRevApplied.11.044092	journal	April 2019
Readiness of Quantum Optimization Machines for Industrial Applications Perdomo-Ortiz, Alejandro; Feldman, Alexander; Ozaeta, Asier Physical Review Applied, Vol. 12, Issue 1 https://doi.org/10.1103/PhysRevApplied.12.014004	journal	July 2019
Phase-Modulated Entangling Gates Robust to Static and Time-Varying Errors Milne, Alistair R.; Edmunds, Claire L.; Hempel, Cornelius Physical Review Applied, Vol. 13, Issue 2 https://doi.org/10.1103/PhysRevApplied.13.024022	journal	February 2020
Resource Estimation for Quantum Variational Simulations of the Hubbard Model Cai, Zhenyu Physical Review Applied, Vol. 14, Issue 1 https://doi.org/10.1103/PhysRevApplied.14.014059	journal	July 2020
Applying the Quantum Approximate Optimization Algorithm to the Tail-Assignment Problem Vikstål, Pontus; Grönkvist, Mattias; Svensson, Marika Physical Review Applied, Vol. 14, Issue 3 https://doi.org/10.1103/PhysRevApplied.14.034009	journal	September 2020
Improved Success Probability with Greater Circuit Depth for the Quantum Approximate Optimization Algorithm Bengtsson, Andreas; Vikstål, Pontus; Warren, Christopher Physical Review Applied, Vol. 14, Issue 3 https://doi.org/10.1103/PhysRevApplied.14.034010	journal	September 2020
Demonstration of an All-Microwave Controlled-Phase Gate between Far-Detuned Qubits Krinner, S.; Kurpiers, P.; Royer, B. Physical Review Applied, Vol. 14, Issue 4 https://doi.org/10.1103/PhysRevApplied.14.044039	journal	October 2020
Quantum Computer-Aided Design: Digital Quantum Simulation of Quantum Processors Kyaw, Thi Ha; Menke, Tim; Sim, Sukin Physical Review Applied, Vol. 16, Issue 4 https://doi.org/10.1103/PhysRevApplied.16.044042	journal	October 2021
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Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning Fujii, Keisuke; Nakajima, Kohei Physical Review Applied, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevApplied.8.024030	journal	August 2017
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Towards simulation of the dynamics of materials on quantum computers Bassman, Lindsay; Liu, Kuang; Krishnamoorthy, Aravind Physical Review B, Vol. 101, Issue 18 https://doi.org/10.1103/PhysRevB.101.184305	journal	May 2020
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Self-learning Monte Carlo method Liu, Junwei; Qi, Yang; Meng, Zi Yang Physical Review B, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevB.95.041101	journal	January 2017
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Quantum computing for neutrino-nucleus scattering Roggero, Alessandro; Li, Andy C. Y.; Carlson, Joseph Physical Review D, Vol. 101, Issue 7 https://doi.org/10.1103/PhysRevD.101.074038	journal	April 2020
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Genetic Algorithms for Digital Quantum Simulations Las Heras, U.; Alvarez-Rodriguez, U.; Solano, E. Physical Review Letters, Vol. 116, Issue 23 https://doi.org/10.1103/PhysRevLett.116.230504	journal	June 2016
Quantum-Enhanced Machine Learning Dunjko, Vedran; Taylor, Jacob M.; Briegel, Hans J. Physical Review Letters, Vol. 117, Issue 13 https://doi.org/10.1103/PhysRevLett.117.130501	journal	September 2016
Hybrid Quantum-Classical Approach to Quantum Optimal Control Li, Jun; Yang, Xiaodong; Peng, Xinhua Physical Review Letters, Vol. 118, Issue 15 https://doi.org/10.1103/PhysRevLett.118.150503	journal	April 2017
Gaussian Boson Sampling Hamilton, Craig S.; Kruse, Regina; Sansoni, Linda Physical Review Letters, Vol. 119, Issue 17 https://doi.org/10.1103/PhysRevLett.119.170501	journal	October 2017
Error Mitigation for Short-Depth Quantum Circuits Temme, Kristan; Bravyi, Sergey; Gambetta, Jay M. Physical Review Letters, Vol. 119, Issue 18 https://doi.org/10.1103/PhysRevLett.119.180509	journal	November 2017
Quantum Simulation of Electronic Structure with Linear Depth and Connectivity Kivlichan, Ian D.; McClean, Jarrod; Wiebe, Nathan Physical Review Letters, Vol. 120, Issue 11 https://doi.org/10.1103/PhysRevLett.120.110501	journal	March 2018
Cloud Quantum Computing of an Atomic Nucleus Dumitrescu, E. F.; McCaskey, A. J.; Hagen, G. Physical Review Letters, Vol. 120, Issue 21 https://doi.org/10.1103/PhysRevLett.120.210501	journal	May 2018
Using Gaussian Boson Sampling to Find Dense Subgraphs Arrazola, Juan Miguel; Bromley, Thomas R. Physical Review Letters, Vol. 121, Issue 3 https://doi.org/10.1103/PhysRevLett.121.030503	journal	July 2018
Quantum Generative Adversarial Learning Lloyd, Seth; Weedbrook, Christian Physical Review Letters, Vol. 121, Issue 4 https://doi.org/10.1103/PhysRevLett.121.040502	journal	July 2018
Measurement of the Entanglement Spectrum of a Symmetry-Protected Topological State Using the IBM Quantum Computer Choo, Kenny; von Keyserlingk, Curt W.; Regnault, Nicolas Physical Review Letters, Vol. 121, Issue 8 https://doi.org/10.1103/PhysRevLett.121.086808	journal	August 2018
Demonstration of Fidelity Improvement Using Dynamical Decoupling with Superconducting Qubits Pokharel, Bibek; Anand, Namit; Fortman, Benjamin Physical Review Letters, Vol. 121, Issue 22 https://doi.org/10.1103/PhysRevLett.121.220502	journal	November 2018
Quantum Machine Learning in Feature Hilbert Spaces Schuld, Maria; Killoran, Nathan Physical Review Letters, Vol. 122, Issue 4 https://doi.org/10.1103/PhysRevLett.122.040504	journal	February 2019
Experimental Realization of a Quantum Autoencoder: The Compression of Qutrits via Machine Learning Pepper, Alex; Tischler, Nora; Pryde, Geoff J. Physical Review Letters, Vol. 122, Issue 6 https://doi.org/10.1103/PhysRevLett.122.060501	journal	February 2019
Accelerated Variational Quantum Eigensolver Wang, Daochen; Higgott, Oscar; Brierley, Stephen Physical Review Letters, Vol. 122, Issue 14 https://doi.org/10.1103/PhysRevLett.122.140504	journal	April 2019
Error-Mitigated Digital Quantum Simulation McArdle, Sam; Yuan, Xiao; Benjamin, Simon Physical Review Letters, Vol. 122, Issue 18 https://doi.org/10.1103/PhysRevLett.122.180501	journal	May 2019
Three-Qubit Randomized Benchmarking McKay, David C.; Sheldon, Sarah; Smolin, John A. Physical Review Letters, Vol. 122, Issue 20 https://doi.org/10.1103/PhysRevLett.122.200502	journal	May 2019
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Robust Self-Testing of Quantum Systems via Noncontextuality Inequalities Bharti, Kishor; Ray, Maharshi; Varvitsiotis, Antonios Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.250403	journal	June 2019
Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers Kirby, William M.; Love, Peter J. Physical Review Letters, Vol. 123, Issue 20 https://doi.org/10.1103/PhysRevLett.123.200501	journal	November 2019
Variational Spin-Squeezing Algorithms on Programmable Quantum Sensors Kaubruegger, Raphael; Silvi, Pietro; Kokail, Christian Physical Review Letters, Vol. 123, Issue 26 https://doi.org/10.1103/PhysRevLett.123.260505	journal	December 2019
Cross-Platform Verification of Intermediate Scale Quantum Devices Elben, Andreas; Vermersch, Benoît; van Bijnen, Rick Physical Review Letters, Vol. 124, Issue 1 https://doi.org/10.1103/PhysRevLett.124.010504	journal	January 2020
Accelerating Lattice Quantum Field Theory Calculations via Interpolator Optimization Using Noisy Intermediate-Scale Quantum Computing Avkhadiev, A.; Shanahan, P. E.; Young, R. D. Physical Review Letters, Vol. 124, Issue 8 https://doi.org/10.1103/PhysRevLett.124.080501	journal	February 2020
Reachability Deficits in Quantum Approximate Optimization Akshay, V.; Philathong, H.; Morales, M. E. S. Physical Review Letters, Vol. 124, Issue 9 https://doi.org/10.1103/PhysRevLett.124.090504	journal	March 2020
Regimes of Classical Simulability for Noisy Gaussian Boson Sampling Qi, Haoyu; Brod, Daniel J.; Quesada, Nicolás Physical Review Letters, Vol. 124, Issue 10 https://doi.org/10.1103/PhysRevLett.124.100502	journal	March 2020
Quantum Autoencoders to Denoise Quantum Data Bondarenko, Dmytro; Feldmann, Polina Physical Review Letters, Vol. 124, Issue 13 https://doi.org/10.1103/PhysRevLett.124.130502	journal	March 2020
Quantum Information Scrambling in a Trapped-Ion Quantum Simulator with Tunable Range Interactions Joshi, Manoj K.; Elben, Andreas; Vermersch, Benoît Physical Review Letters, Vol. 124, Issue 24 https://doi.org/10.1103/PhysRevLett.124.240505	journal	June 2020
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Efficient variational simulation of non-trivial quantum states Ho, Wen Wei; Hsieh, Timothy H. SciPost Physics, Vol. 6, Issue 3 https://doi.org/10.21468/SciPostPhys.6.3.029	journal	January 2019
Quantum Computing in the NISQ era and beyond Preskill, John Quantum, Vol. 2 https://doi.org/10.22331/q-2018-08-06-79	journal	August 2018
In situ upgrade of quantum simulators to universal computers Dive, Benjamin; Pitchford, Alexander; Mintert, Florian Quantum, Vol. 2 https://doi.org/10.22331/q-2018-08-08-80	journal	August 2018
Real Randomized Benchmarking Hashagen, A. K.; Flammia, S. T.; Gross, D. Quantum, Vol. 2 https://doi.org/10.22331/q-2018-08-22-85	journal	August 2018
Exact Ising model simulation on a quantum computer Cervera-Lierta, Alba Quantum, Vol. 2 https://doi.org/10.22331/q-2018-12-21-114	journal	December 2018
Strawberry Fields: A Software Platform for Photonic Quantum Computing Killoran, Nathan; Izaac, Josh; Quesada, Nicolás Quantum, Vol. 3 https://doi.org/10.22331/q-2019-03-11-129	journal	March 2019
Quantum-assisted quantum compiling Khatri, Sumeet; LaRose, Ryan; Poremba, Alexander Quantum, Vol. 3 https://doi.org/10.22331/q-2019-05-13-140	journal	May 2019
Variational Quantum Computation of Excited States Higgott, Oscar; Wang, Daochen; Brierley, Stephen Quantum, Vol. 3 https://doi.org/10.22331/q-2019-07-01-156	journal	July 2019
Theory of variational quantum simulation Yuan, Xiao; Endo, Suguru; Zhao, Qi Quantum, Vol. 3 https://doi.org/10.22331/q-2019-10-07-191	journal	October 2019
An initialization strategy for addressing barren plateaus in parametrized quantum circuits Grant, Edward; Wossnig, Leonard; Ostaszewski, Mateusz Quantum, Vol. 3 https://doi.org/10.22331/q-2019-12-09-214	journal	December 2019
Data re-uploading for a universal quantum classifier Pérez-Salinas, Adrián; Cervera-Lierta, Alba; Gil-Fuster, Elies Quantum, Vol. 4 https://doi.org/10.22331/q-2020-02-06-226	journal	February 2020
Two-Qubit Circuit Depth and the Monodromy Polytope Peterson, Eric C.; Crooks, Gavin E.; Smith, Robert S. Quantum, Vol. 4 https://doi.org/10.22331/q-2020-03-26-247	journal	March 2020
Variational Quantum Fidelity Estimation Cerezo, Marco; Poremba, Alexander; Cincio, Lukasz Quantum, Vol. 4 https://doi.org/10.22331/q-2020-03-26-248	journal	March 2020
Improving Variational Quantum Optimization using CVaR Barkoutsos, Panagiotis Kl.; Nannicini, Giacomo; Robert, Anton Quantum, Vol. 4 https://doi.org/10.22331/q-2020-04-20-256	journal	April 2020
How many qubits are needed for quantum computational supremacy? Dalzell, Alexander M.; Harrow, Aram W.; Koh, Dax Enshan Quantum, Vol. 4 https://doi.org/10.22331/q-2020-05-11-264	journal	May 2020
Quantum Natural Gradient Stokes, James; Izaac, Josh; Killoran, Nathan Quantum, Vol. 4 https://doi.org/10.22331/q-2020-05-25-269	journal	May 2020
Scaling of variational quantum circuit depth for condensed matter systems Bravo-Prieto, Carlos; Lumbreras-Zarapico, Josep; Tagliacozzo, Luca Quantum, Vol. 4 https://doi.org/10.22331/q-2020-05-28-272	journal	May 2020
Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning Jiang, Zhang; Kalev, Amir; Mruczkiewicz, Wojciech Quantum, Vol. 4 https://doi.org/10.22331/q-2020-06-04-276	journal	June 2020
Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus Duncan, Ross; Kissinger, Aleks; Perdrix, Simon Quantum, Vol. 4 https://doi.org/10.22331/q-2020-06-04-279	journal	June 2020
Stochastic gradient descent for hybrid quantum-classical optimization Sweke, Ryan; Wilde, Frederik; Meyer, Johannes Quantum, Vol. 4 https://doi.org/10.22331/q-2020-08-31-314	journal	August 2020
Accelerated variational algorithms for digital quantum simulation of many-body ground states Lyu, Chufan; Montenegro, Victor; Bayat, Abolfazl Quantum, Vol. 4 https://doi.org/10.22331/q-2020-09-16-324	journal	September 2020
A volumetric framework for quantum computer benchmarks Blume-Kohout, Robin; Young, Kevin C. Quantum, Vol. 4 https://doi.org/10.22331/q-2020-11-15-362	journal	November 2020
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An efficient quantum algorithm for the time evolution of parameterized circuits Barison, Stefano; Vicentini, Filippo; Carleo, Giuseppe Quantum, Vol. 5 https://doi.org/10.22331/q-2021-07-28-512	journal	July 2021
Fisher Information in Noisy Intermediate-Scale Quantum Applications Meyer, Johannes Jakob Quantum, Vol. 5 https://doi.org/10.22331/q-2021-09-09-539	journal	September 2021
Fisher Information: A Crucial Tool for NISQ Research Bharti, Kishor Quantum Views, Vol. 5 https://doi.org/10.22331/qv-2021-10-06-61	journal	October 2021
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Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control Watts, Paul; O'Connor, Maurice; Vala, Jiří Entropy, Vol. 15, Issue 12 https://doi.org/10.3390/e15061963	journal	May 2013
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A genetic-algorithm-based method to find unitary transformations for any desired quantum computation and application to a one-bit oracle decision problem Bang, Jeongho; Yoo, Seokwon Journal of the Korean Physical Society, Vol. 65, Issue 12 https://doi.org/10.3938/jkps.65.2001	journal	December 2014

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