Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise

Barron, George S.; Gard, Bryan T.; Altman, Orien J.; Mayhall, Nicholas J.; Barnes, Edwin; Economou, Sophia E.

doi:10.1103/physrevapplied.16.034003

Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise

Journal Article · Wed Sep 01 04:00:00 EDT 2021 · Physical Review Applied

DOI:https://doi.org/10.1103/physrevapplied.16.034003· OSTI ID:1852932

^[1]; ^[2]; Altman, Orien J. ^[2]; Mayhall, Nicholas J. ^[2]; Barnes, Edwin ^[2]; Economou, Sophia E. ^[2]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); OSTI
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

One of the most promising applications of noisy intermediate-scale quantum computers is the simulation of molecular Hamiltonians using the variational quantum eigensolver (VQE). Here, we show that encoding symmetries of the simulated Hamiltonian in the VQE ansatz reduces both classical and quantum resources compared to other widely available ansatze. Through simulations of the H₂ molecule and of a Heisenberg model on a two-dimensional lattice, we verify that these improvements persist in the presence of noise. This is done using both real IBM devices and classical simulations. We also demonstrate how these techniques can be used to find molecular excited states of various symmetries using a noisy processor. We use error-mitigation techniques to further improve the quality of our results.

View Accepted Manuscript (DOE)

Research Organization:: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0019199; SC0019318

OSTI ID:: 1852932

Journal Information:: Physical Review Applied, Journal Name: Physical Review Applied Journal Issue: 3 Vol. 16; ISSN 2331-7019

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (54)

Fermionic Quantum Computation Bravyi, Sergey B.; Kitaev, Alexei Yu. Annals of Physics, Vol. 298, Issue 1 https://doi.org/10.1006/aphy.2002.6254	journal	May 2002
Lipschitzian optimization without the Lipschitz constant Jones, D. R.; Perttunen, C. D.; Stuckman, B. E. Journal of Optimization Theory and Applications, Vol. 79, Issue 1 https://doi.org/10.1007/bf00941892	journal	October 1993
Robust implementation of generative modeling with parametrized quantum circuits Leyton-Ortega, Vicente; Perdomo-Ortiz, Alejandro; Perdomo, Oscar Quantum Machine Intelligence, Vol. 3, Issue 1 https://doi.org/10.1007/s42484-021-00040-2	journal	May 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
Revising the measurement process in the variational quantum eigensolver: is it possible to reduce the number of separately measured operators? Izmaylov, Artur F.; Yen, Tzu-Ching; Ryabinkin, Ilya G. Chemical Science, Vol. 10, Issue 13 https://doi.org/10.1039/c8sc05592k	journal	January 2019
Experimental error mitigation via symmetry verification in a variational quantum eigensolver Sagastizabal, R.; Bonet-Monroig, X.; Singh, M. Physical Review A, Vol. 100, Issue 1 https://doi.org/10.1103/physreva.100.010302	journal	July 2019
Error mitigation for short-depth quantum circuits Temme, Kristan; Bravyi, Sergey; Gambetta, Jay M. arXiv https://doi.org/10.48550/arxiv.1612.02058	text	January 2016
Quantum Simulation of Electronic Structure with Linear Depth and Connectivity Kivlichan, Ian D.; McClean, Jarrod; Wiebe, Nathan arXiv https://doi.org/10.48550/arxiv.1711.04789	text	January 2017
Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers Klco, N.; Dumitrescu, E. F.; McCaskey, A. J. arXiv https://doi.org/10.48550/arxiv.1803.03326	text	January 2018
Variational quantum generators: Generative adversarial quantum machine learning for continuous distributions Romero, Jonathan; Aspuru-Guzik, Alan arXiv https://doi.org/10.48550/arxiv.1901.00848	preprint	January 2019
Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver Parrish, Robert M.; Hohenstein, Edward G.; McMahon, Peter L. arXiv https://doi.org/10.48550/arxiv.1901.01234	text	January 2019
Quantum Approximate Optimization of the Long-Range Ising Model with a Trapped-Ion Quantum Simulator Pagano, G.; Bapat, A.; Becker, P. arXiv https://doi.org/10.48550/arxiv.1906.02700	text	January 2019
Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States Bonet-Monroig, Xavier; Babbush, Ryan; O'Brien, Thomas E. arXiv https://doi.org/10.48550/arxiv.1908.05628	text	January 2019
Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms Sim, Sukin; Johnson, Peter D.; Aspuru‐Guzik, Alán Advanced Quantum Technologies, Vol. 2, Issue 12 https://doi.org/10.1002/qute.201900070	journal	October 2019
Lipschitzian optimization without the Lipschitz constant Jones, D. R.; Perttunen, C. D.; Stuckman, B. E. Journal of Optimization Theory and Applications, Vol. 79, Issue 1 https://doi.org/10.1007/BF00941892	journal	October 1993
�ber das Paulische �quivalenzverbot Jordan, P.; Wigner, E. Zeitschrift f�r Physik, Vol. 47, Issue 9-10 https://doi.org/10.1007/BF01331938	journal	September 1928
Simulating physics with computers Feynman, Richard P. International Journal of Theoretical Physics, Vol. 21, Issue 6-7 https://doi.org/10.1007/BF02650179	journal	June 1982
Accuracy and Resource Estimations for Quantum Chemistry on a Near-Term Quantum Computer Kühn, Michael; Zanker, Sebastian; Deglmann, Peter Journal of Chemical Theory and Computation, Vol. 15, Issue 9 https://doi.org/10.1021/acs.jctc.9b00236	journal	August 2019
Unitary Partitioning Approach to the Measurement Problem in the Variational Quantum Eigensolver Method Izmaylov, Artur F.; Yen, Tzu-Ching; Lang, Robert A. Journal of Chemical Theory and Computation, Vol. 16, Issue 1 https://doi.org/10.1021/acs.jctc.9b00791	journal	November 2019
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan Nature, Vol. 549, Issue 7671 https://doi.org/10.1038/nature23879	journal	September 2017
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
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
Soundness and completeness of quantum root-mean-square errors Ozawa, Masanao npj Quantum Information, Vol. 5, Issue 1 https://doi.org/10.1038/s41534-018-0113-z	journal	January 2019
Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm Gard, Bryan T.; Zhu, Linghua; Barron, George S. npj Quantum Information, Vol. 6, Issue 1 https://doi.org/10.1038/s41534-019-0240-1	journal	January 2020
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
Self-verifying variational quantum simulation of lattice models Kokail, C.; Maier, C.; van Bijnen, R. Nature, Vol. 569, Issue 7756 https://doi.org/10.1038/s41586-019-1177-4	journal	May 2019
Revising the measurement process in the variational quantum eigensolver: is it possible to reduce the number of separately measured operators? Izmaylov, Artur F.; Yen, Tzu-Ching; Ryabinkin, Ilya G. Chemical Science, Vol. 10, Issue 13 https://doi.org/10.1039/C8SC05592K	journal	January 2019
The Bravyi-Kitaev transformation for quantum computation of electronic structure Seeley, Jacob T.; Richard, Martin J.; Love, Peter J. The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4768229	journal	December 2012
The theory of variational hybrid quantum-classical algorithms McClean, Jarrod R.; Romero, Jonathan; Babbush, Ryan New Journal of Physics, Vol. 18, Issue 2 https://doi.org/10.1088/1367-2630/18/2/023023	journal	February 2016
Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer Moll, Nikolaj; Fuhrer, Andreas; Staar, Peter Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 29 https://doi.org/10.1088/1751-8113/49/29/295301	journal	June 2016
Quantum optimization using variational algorithms on near-term quantum devices Moll, Nikolaj; Barkoutsos, Panagiotis; Bishop, Lev S. Quantum Science and Technology, Vol. 3, Issue 3 https://doi.org/10.1088/2058-9565/aab822	journal	June 2018
Rigorous measurement error correction Geller, Michael R. Quantum Science and Technology, Vol. 5, Issue 3 https://doi.org/10.1088/2058-9565/ab9591	journal	June 2020
Experimental error mitigation via symmetry verification in a variational quantum eigensolver Sagastizabal, R.; Bonet-Monroig, X.; Singh, M. Physical Review A, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevA.100.010302	journal	July 2019
Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions Barkoutsos, Panagiotis Kl.; Gonthier, Jerome F.; Sokolov, Igor Physical Review A, Vol. 98, Issue 2 https://doi.org/10.1103/PhysRevA.98.022322	journal	August 2018
Quantum-classical computation of Schwinger model dynamics using quantum computers Klco, N.; Dumitrescu, E. F.; McCaskey, A. J. Physical Review A, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevA.98.032331	journal	September 2018
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
Mitigating algorithmic errors in a Hamiltonian simulation Endo, Suguru; Zhao, Qi; Li, Ying Physical Review A, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevA.99.012334	journal	January 2019
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
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
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
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
Quantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver Parrish, Robert M.; Hohenstein, Edward G.; McMahon, Peter L. Physical Review Letters, Vol. 122, Issue 23 https://doi.org/10.1103/PhysRevLett.122.230401	journal	June 2019
Superfast encodings for fermionic quantum simulation Setia, Kanav; Bravyi, Sergey; Mezzacapo, Antonio Physical Review Research, Vol. 1, Issue 3 https://doi.org/10.1103/PhysRevResearch.1.033033	journal	October 2019
Increasing the Representation Accuracy of Quantum Simulations of Chemistry without Extra Quantum Resources Takeshita, Tyler; Rubin, Nicholas C.; Jiang, Zhang Physical Review X, Vol. 10, Issue 1 https://doi.org/10.1103/PhysRevX.10.011004	journal	January 2020
Scalable Quantum Simulation of Molecular Energies O’Malley, P. J. J.; Babbush, R.; Kivlichan, I. D. Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031007	journal	July 2016
Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm Colless, J. I.; Ramasesh, V. V.; Dahlen, D. Physical Review X, Vol. 8, Issue 1 https://doi.org/10.1103/PhysRevX.8.011021	journal	February 2018
Multivariate stochastic approximation using a simultaneous perturbation gradient approximation Spall, J. C. IEEE Transactions on Automatic Control, Vol. 37, Issue 3 https://doi.org/10.1109/9.119632	journal	March 1992
Training of quantum circuits on a hybrid quantum computer Zhu, D.; Linke, N. M.; Benedetti, M. Science Advances, Vol. 5, Issue 10 https://doi.org/10.1126/sciadv.aaw9918	journal	October 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
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
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

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