Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

Wang, Samson; Czarnik, Piotr; Arrasmith, Andrew; Cerezo, M.; Cincio, Lukasz; Coles, Patrick J.

doi:10.22331/q-2024-03-14-1287

Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

Journal Article · Thu Mar 14 00:00:00 EDT 2024 · Quantum

DOI:https://doi.org/10.22331/q-2024-03-14-1287· OSTI ID:2350627

^[1]; ^[2]; ^[3]; ^[4]; ^[4]; Coles, Patrick J. ^[4]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Imperial College, London (United Kingdom)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Jagiellonian Univ., Krakow (Poland)
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;Quantum Science Center, Oak Ridge, TN 37931, USA
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Quantum Science Center (QSC)

Variational Quantum Algorithms (VQAs) are often viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs, e.g., by exponentially flattening the cost landscape and suppressing the magnitudes of cost gradients. Error Mitigation (EM) shows promise in reducing the impact of noise on near-term devices. Thus, it is natural to ask whether EM can improve the trainability of VQAs. In this work, we first show that, for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere. This class of strategies includes as special cases Zero Noise Extrapolation, Virtual Distillation, Probabilistic Error Cancellation, and Clifford Data Regression. Second, we perform analytical and numerical analysis of these EM protocols, and we find that some of them (e.g., Virtual Distillation) can make it harder to resolve cost function values compared to running no EM at all. As a positive result, we do find numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. Our results show that care should be taken in applying EM protocols as they can either worsen or not improve trainability. On the other hand, our positive results for CDR highlight the possibility of engineering error mitigation methods to improve trainability.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001; 20190659PRD4; 20210116DR; 20190065DR

OSTI ID:: 2350627

Report Number(s):: LA-UR-21-28574; TRN: US2411198

Journal Information:: Quantum, Vol. 8; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

References (99)

Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus Holmes, Zoë; Sharma, Kunal; Cerezo, M. PRX Quantum, Vol. 3, Issue 1 https://doi.org/10.1103/PRXQuantum.3.010313	journal	January 2022
Cost function dependent barren plateaus in shallow parametrized quantum circuits Cerezo, M.; Sone, Akira; Volkoff, Tyler Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-21728-w	journal	March 2021
Variational Quantum Simulation of General Processes Endo, Suguru; Sun, Jinzhao; Li, Ying Physical Review Letters, Vol. 125, Issue 1 https://doi.org/10.1103/PhysRevLett.125.010501	journal	June 2020
Higher order derivatives of quantum neural networks with barren plateaus Cerezo, M.; Coles, Patrick J. Quantum Science and Technology, Vol. 6, Issue 3 https://doi.org/10.1088/2058-9565/abf51a	journal	June 2021
Low-cost error mitigation by symmetry verification Bonet-Monroig, X.; Sagastizabal, R.; Singh, M. Physical Review A, Vol. 98, Issue 6 https://doi.org/10.1103/PhysRevA.98.062339	journal	December 2018
Circuit-centric quantum classifiers Schuld, Maria; Bocharov, Alex; Svore, Krysta M. Physical Review A, Vol. 101, Issue 3 https://doi.org/10.1103/PhysRevA.101.032308	journal	March 2020
Long-time simulations with high fidelity on quantum hardware Gibbs, Joe; Gili, Kaitlin; Holmes, Zoë arXiv https://doi.org/10.48550/arXiv.2102.04313	preprint	January 2021
Adaptive shot allocation for fast convergence in variational quantum algorithms Gu, Andi; Lowe, Angus; Dub, Pavel A. arXiv https://doi.org/10.48550/arXiv.2108.10434	text	January 2021
Variational-state quantum metrology Koczor, Bálint; Endo, Suguru; Jones, Tyson New Journal of Physics, Vol. 22, Issue 8 https://doi.org/10.1088/1367-2630/ab965e	journal	August 2020
A variational toolbox for quantum multi-parameter estimation Meyer, Johannes Jakob; Borregaard, Johannes; Eisert, Jens npj Quantum Information, Vol. 7, Issue 1 https://doi.org/10.1038/s41534-021-00425-y	journal	June 2021
Variational Quantum Linear Solver Bravo-Prieto, Carlos; LaRose, Ryan; Cerezo, M. Quantum, Vol. 7 https://doi.org/10.22331/q-2023-11-22-1188	journal	November 2023
Variational quantum state eigensolver Cerezo, M.; Sharma, Kunal; Arrasmith, Andrew npj Quantum Information, Vol. 8, Issue 1 https://doi.org/10.1038/s41534-022-00611-6	journal	September 2022
Variational consistent histories as a hybrid algorithm for quantum foundations Arrasmith, Andrew; Cincio, Lukasz; Sornborger, Andrew T. Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-11417-0	journal	July 2019
On contraction coefficients, partial orders and approximation of capacities for quantum channels Hirche, Christoph; Rouzé, Cambyse; Stilck França, Daniel Quantum, Vol. 6 https://doi.org/10.22331/q-2022-11-28-862	journal	November 2022
Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation Commeau, Benjamin; Cerezo, M.; Holmes, Zoë arXiv https://doi.org/10.48550/arXiv.2009.02559	preprint	January 2020
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
Non-trivial symmetries in quantum landscapes and their resilience to quantum noise Fontana, Enrico; Cerezo, M.; Arrasmith, Andrew Quantum, Vol. 6 https://doi.org/10.22331/q-2022-09-15-804	journal	September 2022
Efficient Variational Quantum Simulator Incorporating Active Error Minimization Li, Ying; Benjamin, Simon C. Physical Review X, Vol. 7, Issue 2 https://doi.org/10.1103/PhysRevX.7.021050	journal	June 2017
Training deep quantum neural networks Beer, Kerstin; Bondarenko, Dmytro; Farrelly, Terry Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-14454-2	journal	February 2020
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
An Adaptive Optimizer for Measurement-Frugal Variational Algorithms Kübler, Jonas M.; Arrasmith, Andrew; Cincio, Lukasz Quantum, Vol. 4 https://doi.org/10.22331/q-2020-05-11-263	journal	May 2020
Variational algorithms for linear algebra Xu, Xiaosi; Sun, Jinzhao; Endo, Suguru Science Bulletin https://doi.org/10.1016/j.scib.2021.06.023	journal	June 2021
Adaptive Variational Quantum Dynamics Simulations Yao, Yong-Xin; Gomes, Niladri; Zhang, Feng PRX Quantum, Vol. 2, Issue 3 https://doi.org/10.1103/PRXQuantum.2.030307	journal	July 2021
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
QVECTOR: an algorithm for device-tailored quantum error correction Johnson, Peter D.; Romero, Jonathan; Olson, Jonathan arXiv https://doi.org/10.48550/arXiv.1711.02249	preprint	January 2017
Practical Quantum Error Mitigation for Near-Future Applications Endo, Suguru; Benjamin, Simon C.; Li, Ying Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031027	journal	July 2018
Exponential Error Suppression for Near-Term Quantum Devices Koczor, Bálint Physical Review X, Vol. 11, Issue 3 https://doi.org/10.1103/PhysRevX.11.031057	journal	September 2021
Error mitigation with Clifford quantum-circuit data Czarnik, Piotr; Arrasmith, Andrew; Coles, Patrick J. Quantum, Vol. 5 https://doi.org/10.22331/q-2021-11-26-592	journal	November 2021
Noisy intermediate scale quantum simulation of time dependent Hamiltonians Lau, Jonathan Wei Zhong; Bharti, Kishor; Haug, Tobias arXiv https://doi.org/10.48550/arXiv.2101.07677	preprint	January 2021
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control Larocca, Martin; Czarnik, Piotr; Sharma, Kunal arXiv https://doi.org/10.48550/arXiv.2105.14377	text	January 2021
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
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
Barren plateaus in quantum neural network training landscapes McClean, Jarrod R.; Boixo, Sergio; Smelyanskiy, Vadim N. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-07090-4	journal	November 2018
Scalable error mitigation for noisy quantum circuits produces competitive expectation values Kim, Youngseok; Wood, Christopher J.; Yoder, Theodore J. Nature Physics https://doi.org/10.1038/s41567-022-01914-3	journal	February 2023
Simple mitigation of global depolarizing errors in quantum simulations Vovrosh, Joseph; Khosla, Kiran E.; Greenaway, Sean Physical Review E, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevE.104.035309	journal	September 2021
Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states McClean, Jarrod R.; Kimchi-Schwartz, Mollie E.; Carter, Jonathan Physical Review A, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevA.95.042308	journal	April 2017
Optimal resource cost for error mitigation Takagi, Ryuji Physical Review Research, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevResearch.3.033178	journal	August 2021
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
Classification with Quantum Neural Networks on Near Term Processors Farhi, Edward; Neven, Hartmut arXiv https://doi.org/10.48550/arXiv.1802.06002	preprint	January 2018
Classical-Quantum Noise Mitigation for NISQ Hardware Shaw, Andrew arXiv https://doi.org/10.48550/arXiv.2105.08701	preprint	January 2021
Extending quantum probabilistic error cancellation by noise scaling Mari, Andrea; Shammah, Nathan; Zeng, William J. Physical Review A, Vol. 104, Issue 5 https://doi.org/10.1103/PhysRevA.104.052607	journal	November 2021
Zero-noise extrapolation for quantum-gate error mitigation with identity insertions He, Andre; Nachman, Benjamin; de Jong, Wibe A. Physical Review A, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevA.102.012426	journal	July 2020
Variational quantum algorithms Cerezo, M.; Arrasmith, Andrew; Babbush, Ryan Nature Reviews Physics, Vol. 3, Issue 9 https://doi.org/10.1038/s42254-021-00348-9	journal	August 2021
A Simplex Method for Function Minimization Nelder, J. A.; Mead, R. The Computer Journal, Vol. 7, Issue 4 https://doi.org/10.1093/comjnl/7.4.308	journal	January 1965
Entanglement-Induced Barren Plateaus Ortiz Marrero, Carlos; Kieferová, Mária; Wiebe, Nathan PRX Quantum, Vol. 2, Issue 4 https://doi.org/10.1103/PRXQuantum.2.040316	journal	October 2021
Qubit-efficient exponential suppression of errors Czarnik, Piotr; Arrasmith, Andrew; Cincio, Lukasz arXiv https://doi.org/10.48550/arXiv.2102.06056	preprint	January 2021
Quantum autoencoders for efficient compression of quantum data Romero, Jonathan; Olson, Jonathan P.; Aspuru-Guzik, Alan Quantum Science and Technology, Vol. 2, Issue 4 https://doi.org/10.1088/2058-9565/aa8072	journal	August 2017
Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm Verdon, Guillaume; Marks, Jacob; Nanda, Sasha arXiv https://doi.org/10.48550/arXiv.1910.02071	preprint	January 2019
Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation Endo, Suguru; Cai, Zhenyu; Benjamin, Simon C. Journal of the Physical Society of Japan, Vol. 90, Issue 3 https://doi.org/10.7566/JPSJ.90.032001	journal	March 2021
An adaptive variational algorithm for exact molecular simulations on a quantum computer Grimsley, Harper R.; Economou, Sophia E.; Barnes, Edwin Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-10988-2	journal	July 2019
Barren Plateaus Preclude Learning Scramblers Holmes, Zoë; Arrasmith, Andrew; Yan, Bin Physical Review Letters, Vol. 126, Issue 19 https://doi.org/10.1103/PhysRevLett.126.190501	journal	May 2021
Error mitigation on a near-term quantum photonic device Su, Daiqin; Israel, Robert; Sharma, Kunal Quantum, Vol. 5 https://doi.org/10.22331/q-2021-05-04-452	journal	May 2021
Variational fast forwarding for quantum simulation beyond the coherence time Cîrstoiu, Cristina; Holmes, Zoë; Iosue, Joseph npj Quantum Information, Vol. 6, Issue 1 https://doi.org/10.1038/s41534-020-00302-0	journal	September 2020
Error Mitigation via Verified Phase Estimation O’Brien, Thomas E.; Polla, Stefano; Rubin, Nicholas C. PRX Quantum, Vol. 2, Issue 2 https://doi.org/10.1103/PRXQuantum.2.020317	journal	May 2021
Fundamental limits of quantum error mitigation Takagi, Ryuji; Endo, Suguru; Minagawa, Shintaro npj Quantum Information, Vol. 8, Issue 1 https://doi.org/10.1038/s41534-022-00618-z	journal	September 2022
Effect of barren plateaus on gradient-free optimization Arrasmith, Andrew; Cerezo, M.; Czarnik, Piotr Quantum, Vol. 5 https://doi.org/10.22331/q-2021-10-05-558	journal	October 2021
Noise-induced barren plateaus in variational quantum algorithms Wang, Samson; Fontana, Enrico; Cerezo, M. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-27045-6	journal	November 2021
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz Hadfield, Stuart; Wang, Zhihui; O'Gorman, Bryan Algorithms, Vol. 12, Issue 2 https://doi.org/10.3390/a12020034	journal	February 2019
Learning-Based Quantum Error Mitigation Strikis, Armands; Qin, Dayue; Chen, Yanzhu PRX Quantum, Vol. 2, Issue 4 https://doi.org/10.1103/PRXQuantum.2.040330	journal	November 2021
Measurement Error Mitigation for Variational Quantum Algorithms Barron, George S.; Wood, Christopher J. arXiv https://doi.org/10.48550/arXiv.2010.08520	preprint	January 2020
A variational eigenvalue solver on a photonic quantum processor Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5213	journal	July 2014
Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems Xiong, Yifeng; Chandra, Daryus; Ng, Soon Xin IEEE Access, Vol. 8 https://doi.org/10.1109/ACCESS.2020.3045016	journal	January 2020
Training Variational Quantum Algorithms Is NP-Hard Bittel, Lennart; Kliesch, Martin Physical Review Letters, Vol. 127, Issue 12 https://doi.org/10.1103/PhysRevLett.127.120502	journal	September 2021
Variational Quantum Generators: Generative Adversarial Quantum Machine Learning for Continuous Distributions Romero, Jonathan; Aspuru‐Guzik, Alán Advanced Quantum Technologies, Vol. 4, Issue 1 https://doi.org/10.1002/qute.202000003	journal	December 2020
A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation Powell, M. J. D. Advances in Optimization and Numerical Analysis https://doi.org/10.1007/978-94-015-8330-5_4	book	January 1994
Variational quantum algorithms for discovering Hamiltonian spectra Jones, Tyson; Endo, Suguru; McArdle, Sam Physical Review A, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevA.99.062304	journal	June 2019
Robust quantum compilation and circuit optimisation via energy minimisation Jones, Tyson; Benjamin, Simon C. Quantum, Vol. 6 https://doi.org/10.22331/q-2022-01-24-628	journal	January 2022
Variational Quantum Gate Optimization Heya, Kentaro; Suzuki, Yasunari; Nakamura, Yasunobu arXiv https://doi.org/10.48550/arXiv.1810.12745	preprint	January 2018
Variational Quantum Factoring Anschuetz, Eric; Olson, Jonathan; Aspuru-Guzik, Alán Quantum Technology and Optimization Problems https://doi.org/10.1007/978-3-030-14082-3_7	book	January 2019
Digital zero noise extrapolation for quantum error mitigation Giurgica-Tiron, Tudor; Hindy, Yousef; LaRose, Ryan 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) https://doi.org/10.1109/QCE49297.2020.00045	conference	October 2020
Hierarchical quantum classifiers Grant, Edward; Benedetti, Marcello; Cao, Shuxiang npj Quantum Information, Vol. 4, Issue 1 https://doi.org/10.1038/s41534-018-0116-9	journal	December 2018
Variational ansatz-based quantum simulation of imaginary time evolution McArdle, Sam; Jones, Tyson; Endo, Suguru npj Quantum Information, Vol. 5, Issue 1 https://doi.org/10.1038/s41534-019-0187-2	journal	September 2019
Unifying and benchmarking state-of-the-art quantum error mitigation techniques Bultrini, Daniel; Gordon, Max Hunter; Czarnik, Piotr Quantum, Vol. 7 https://doi.org/10.22331/q-2023-06-06-1034	journal	June 2023
Noise resilience of variational quantum compiling Sharma, Kunal; Khatri, Sumeet; Cerezo, M. New Journal of Physics, Vol. 22, Issue 4 https://doi.org/10.1088/1367-2630/ab784c	journal	April 2020
Subspace Variational Quantum Simulator Heya, Kentaro; Nakanishi, Ken M.; Mitarai, Kosuke arXiv https://doi.org/10.48550/arXiv.1904.08566	preprint	January 2019
The dominant eigenvector of a noisy quantum state Koczor, Bálint New Journal of Physics, Vol. 23, Issue 12 https://doi.org/10.1088/1367-2630/ac37ae	journal	December 2021
Limitations of optimization algorithms on noisy quantum devices Stilck França, Daniel; García-Patrón, Raul Nature Physics, Vol. 17, Issue 11 https://doi.org/10.1038/s41567-021-01356-3	journal	October 2021
Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers Huggins, William J.; McClean, Jarrod R.; Rubin, Nicholas C. npj Quantum Information, Vol. 7, Issue 1 https://doi.org/10.1038/s41534-020-00341-7	journal	February 2021
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions Lagarias, Jeffrey C.; Reeds, James A.; Wright, Margaret H. SIAM Journal on Optimization, Vol. 9, Issue 1 https://doi.org/10.1137/S1052623496303470	journal	January 1998
Entanglement devised barren plateau mitigation Patti, Taylor L.; Najafi, Khadijeh; Gao, Xun Physical Review Research, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevResearch.3.033090	journal	July 2021
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 convolutional neural networks Cong, Iris; Choi, Soonwon; Lukin, Mikhail D. Nature Physics, Vol. 15, Issue 12 https://doi.org/10.1038/s41567-019-0648-8	journal	August 2019
Qubit readout error mitigation with bit-flip averaging Smith, Alistair W. R.; Khosla, Kiran E.; Self, Chris N. Science Advances, Vol. 7, Issue 47 https://doi.org/10.1126/sciadv.abi8009	journal	November 2021
Unified approach to data-driven quantum error mitigation Lowe, Angus; Gordon, Max Hunter; Czarnik, Piotr Physical Review Research, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevResearch.3.033098	journal	July 2021
Machine Learning of Noise-Resilient Quantum Circuits Cincio, Lukasz; Rudinger, Kenneth; Sarovar, Mohan PRX Quantum, Vol. 2, Issue 1 https://doi.org/10.1103/PRXQuantum.2.010324	journal	February 2021
Experimental error mitigation using linear rescaling for variational quantum eigensolving with up to 20 qubits Rosenberg, Eliott; Ginsparg, Paul; McMahon, Peter L. Quantum Science and Technology https://doi.org/10.1088/2058-9565/ac3b37	journal	November 2021
Operator Sampling for Shot-frugal Optimization in Variational Algorithms Arrasmith, Andrew; Cincio, Lukasz; Somma, Rolando D. arXiv https://doi.org/10.48550/arXiv.2004.06252	preprint	January 2020
Training saturation in layerwise quantum approximate optimization Campos, E.; Rabinovich, D.; Akshay, V. Physical Review A, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevA.104.L030401	journal	September 2021
Characterizing local noise in QAOA circuits Marshall, Jeffrey; Wudarski, Filip; Hadfield, Stuart IOP SciNotes, Vol. 1, Issue 2 https://doi.org/10.1088/2633-1357/abb0d7	journal	August 2020
Variational quantum state diagonalization LaRose, Ryan; Tikku, Arkin; O’Neel-Judy, Étude npj Quantum Information, Vol. 5, Issue 1 https://doi.org/10.1038/s41534-019-0167-6	journal	June 2019
Virtual Distillation for Quantum Error Mitigation Huggins, William J.; McArdle, Sam; O’Brien, Thomas E. Physical Review X, Vol. 11, Issue 4 https://doi.org/10.1103/PhysRevX.11.041036	journal	November 2021
Quality, Speed, and Scale: three key attributes to measure the performance of near-term quantum computers Wack, Andrew; Paik, Hanhee; Javadi-Abhari, Ali arXiv https://doi.org/10.48550/arXiv.2110.14108	preprint	January 2021
A Quantum Approximate Optimization Algorithm Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam arXiv https://doi.org/10.48550/arXiv.1411.4028	preprint	January 2014
Quantum Algorithm Implementations for Beginners J., Abhijith; Adedoyin, Adetokunbo; Ambrosiano, John ACM Transactions on Quantum Computing, Vol. 3, Issue 4 https://doi.org/10.1145/3517340	journal	July 2022
Hybrid Quantum-Classical Approach to Correlated Materials Bauer, Bela; Wecker, Dave; Millis, Andrew J. Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031045	journal	September 2016
Quantum approximate optimization algorithm for MaxCut: A fermionic view Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang Physical Review A, Vol. 97, Issue 2 https://doi.org/10.1103/PhysRevA.97.022304	journal	February 2018
Effects of Quantum Noise on Quantum Approximate Optimization Algorithm Xue, Cheng; Chen, Zhao-Yun; Wu, Yu-Chun Chinese Physics Letters, Vol. 38, Issue 3 https://doi.org/10.1088/0256-307X/38/3/030302	journal	March 2021
Error mitigation extends the computational reach of a noisy quantum processor Kandala, Abhinav; Temme, Kristan; Córcoles, Antonio D. Nature, Vol. 567, Issue 7749 https://doi.org/10.1038/s41586-019-1040-7	journal	March 2019
Observation of separated dynamics of charge and spin in the Fermi-Hubbard model Arute, Frank; Arya, Kunal; Babbush, Ryan arXiv https://doi.org/10.48550/arXiv.2010.07965	preprint	January 2020

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