Witnessing eigenstates for quantum simulation of Hamiltonian spectra

Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A.; Paesani, Stefano; Wiebe, Nathan; McClean, Jarrod R.; Morley-Short, Sam; Shadbolt, Peter J.; Bonneau, Damien; Silverstone, Joshua W.; Tew, David P.; Zhou, Xiaoqi; O’Brien, Jeremy L.; Thompson, Mark G.

doi:10.1126/sciadv.aap9646

Title: Witnessing eigenstates for quantum simulation of Hamiltonian spectra

Journal Article · 26 January 2018 · Science Advances

DOI: https://doi.org/10.1126/sciadv.aap9646 · OSTI ID:1494079

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Univ. of Bristol (United Kingdom). Quantum Engineering Technology Labs. H. H. Wills Physics Lab. Dept. of Electrical and Electronic Engineering
Microsoft Research, Redmond, WA (United States). Quantum Architectures and Computation Group
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Google Inc., Venice, CA (United States)
Univ. of Bristol (United Kingdom). Quantum Engineering Centre for Doctoral Training. Quantum Engineering Technology Labs. H. H. Wills Physics Lab. Dept. of Electrical and Electronic Engineering
Imperial College London (United Kingdom). Dept. of Physics
Univ. of Bristol (United Kingdom). School of Chemistry; Max Planck Inst. for Solid State Research, Stuttgart (Germany)
Sun Yat-Sen Univ., Guangzhou (China). State Key Lab. of Optoelectronic Materials and Technologies. School of Physics

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); LBNL Laboratory Directed Research and Development (LDRD) Program; Army Research Office (ARO) (United States); Royal Society (United Kingdom); Engineering and Physical Sciences Research Council (EPSRC) (United Kingdom); European Research Council (ERC); National Key Research and Development Program (China); National Young 1000 Talents Plan (China); Natural Science Foundation of Guangdong (China)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1494079

Journal Information:: Science Advances, Journal Name: Science Advances Journal Issue: 1 Vol. 4; ISSN 2375-2548

Publisher:: AAASCopyright Statement

Country of Publication:: United States

Language:: English

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Polarization entangled state measurement on a chip Sansoni, L.; Sciarrino, F.; Vallone, G. arXiv https://doi.org/10.48550/arxiv.1009.2426	text	January 2010
Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance Li, Zhaokai; Yung, Man-Hong; Chen, Hongwei arXiv https://doi.org/10.48550/arxiv.1106.0440	text	January 2011
Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation Babbush, Ryan; McClean, Jarrod; Wecker, Dave arXiv https://doi.org/10.48550/arxiv.1410.8159	text	January 2014
Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States McClean, Jarrod R.; Schwartz, Mollie E.; Carter, Jonathan arXiv https://doi.org/10.48550/arxiv.1603.05681	text	January 2016
A quantum Fredkin gate Patel, Raj B.; Ho, Joseph; Ferreyrol, Franck arXiv https://doi.org/10.48550/arxiv.1603.08086	text	January 2016
The Complexity of the Local Hamiltonian Problem Kempe, Julia; Kitaev, Alexei; Regev, Oded arXiv https://doi.org/10.48550/arxiv.quant-ph/0406180	text	January 2004
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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
Simulations of subatomic many-body physics on a quantum frequency processor Lu, Hsuan-Hao; Klco, Natalie; Lukens, Joseph M. Physical Review A, Vol. 100, Issue 1 https://doi.org/10.1103/physreva.100.012320	journal	July 2019
Quantum-classical hybrid algorithm using an error-mitigating N -representability condition to compute the Mott metal-insulator transition Smart, Scott E.; Mazziotti, David A. Physical Review A, Vol. 100, Issue 2 https://doi.org/10.1103/physreva.100.022517	journal	August 2019
Construction of Green's functions on a quantum computer: Quasiparticle spectra of molecules Kosugi, Taichi; Matsushita, Yu-ichiro Physical Review A, Vol. 101, Issue 1 https://doi.org/10.1103/physreva.101.012330	journal	January 2020
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
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
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
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
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
Subspace-search variational quantum eigensolver for excited states Nakanishi, Ken M.; Mitarai, Kosuke; Fujii, Keisuke Physical Review Research, Vol. 1, Issue 3 https://doi.org/10.1103/physrevresearch.1.033062	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
Low-Depth Quantum Simulation of Materials Babbush, Ryan; Wiebe, Nathan; McClean, Jarrod Physical Review X, Vol. 8, Issue 1 https://doi.org/10.1103/physrevx.8.011044	journal	March 2018
Quantum computational chemistry McArdle, Sam; Endo, Suguru; Aspuru-Guzik, Alán Reviews of Modern Physics, Vol. 92, Issue 1 https://doi.org/10.1103/revmodphys.92.015003	journal	March 2020
Multidimensional quantum entanglement with large-scale integrated optics Wang, Jianwei; Paesani, Stefano; Ding, Yunhong Science, Vol. 360, Issue 6386 https://doi.org/10.1126/science.aar7053	journal	March 2018
Photonic scheme of quantum phase estimation for quantum algorithms via cross-Kerr nonlinearities under decoherence effect Hong, Changho; Heo, Jino; Kang, Min-Sung Optics Express, Vol. 27, Issue 21 https://doi.org/10.1364/oe.27.031023	journal	January 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
Photonic quantum information processing: a review Flamini, Fulvio; Spagnolo, Nicolò; Sciarrino, Fabio arXiv https://doi.org/10.48550/arxiv.1803.02790	text	January 2018
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 Computation of Excited States Higgott, Oscar; Wang, Daochen; Brierley, Stephen arXiv https://doi.org/10.48550/arxiv.1805.08138	text	January 2018
Variational quantum algorithms for discovering Hamiltonian spectra Endo, Suguru; Jones, Tyson; McArdle, Sam arXiv https://doi.org/10.48550/arxiv.1806.05707	text	January 2018
Quantum computational chemistry McArdle, Sam; Endo, Suguru; Aspuru-Guzik, Alan arXiv https://doi.org/10.48550/arxiv.1808.10402	text	January 2018
Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments O'Brien, T. E.; Tarasinski, B.; Terhal, B. M. arXiv https://doi.org/10.48550/arxiv.1809.09697	text	January 2018
Simulations of Subatomic Many-Body Physics on a Quantum Frequency Processor Lu, Hsuan-Hao; Klco, Natalie; Lukens, Joseph M. arXiv https://doi.org/10.48550/arxiv.1810.03959	text	January 2018
Generation of non-classical light in a photon-number superposition Loredo, J. C.; Antón, C.; Reznychenko, B. arXiv https://doi.org/10.48550/arxiv.1810.05170	text	January 2018
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
Decoding quantum errors with subspace expansions McClean, Jarrod R.; Jiang, Zhang; Rubin, Nicholas C. arXiv https://doi.org/10.48550/arxiv.1903.05786	text	January 2019
Calculating energy derivatives for quantum chemistry on a quantum computer O'Brien, T. E.; Senjean, B.; Sagastizabal, R. arXiv https://doi.org/10.48550/arxiv.1905.03742	text	January 2019
High-dimensional quantum communication: benefits, progress, and future challenges Cozzolino, Daniele; Da Lio, Beatrice; Bacco, Davide arXiv https://doi.org/10.48550/arxiv.1910.07220	text	January 2019
Quantum-classical hybrid algorithm using an error-mitigating $N$-representability condition to compute the Mott metal-insulator transition Smart, Scott E.; Mazziotti, David A. arXiv https://doi.org/10.48550/arxiv.2004.07739	text	January 2020

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