Feedback-based quantum algorithms for ground state preparation

Larsen, James B.; Grace, Matthew D.; Baczewski, Andrew D.; Magann, Alicia B.

doi:10.1103/PhysRevResearch.6.033336

Feedback-based quantum algorithms for ground state preparation

Journal Article · Wed Sep 25 04:00:00 EDT 2024 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.6.033336· OSTI ID:2473490

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The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one class of ground state algorithms that has received significant attention in recent years. These algorithms utilize a hybrid quantum-classical computing framework to prepare ground states on quantum computers. However, this requires solving a classical optimization problem that can become prohibitively expensive in high dimensions. Here, we develop formulations of feedback-based quantum algorithms for ground state preparation that can be used to address this challenge for two broad classes of Hamiltonians: Fermi-Hubbard Hamiltonians, and molecular Hamiltonians represented in second quantization. Feedback-based quantum algorithms are optimization-free; in place of classical optimization, quantum circuit parameters are set according to a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. A variety of numerical illustrations are provided that analyze the convergence and robustness of feedback-based quantum algorithms for these problem classes.

Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE

Grant/Contract Number:: NA0003525

OSTI ID:: 2473490

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 3 Vol. 6; ISSN 2643-1564; ISSN PPRHAI

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (71)

An implicit Lyapunov control for finite‐dimensional closed quantum systems Zhao, Shouwei; Lin, Hai; Sun, Jitao International Journal of Robust and Nonlinear Control, Vol. 22, Issue 11 https://doi.org/10.1002/rnc.1748	journal	May 2011
Beweis des Adiabatensatzes Born, M.; Fock, V. Zeitschrift f�r Physik, Vol. 51, Issue 3-4 https://doi.org/10.1007/BF01343193	journal	March 1928
Layerwise learning for quantum neural networks Skolik, Andrea; McClean, Jarrod R.; Mohseni, Masoud Quantum Machine Intelligence, Vol. 3, Issue 1 https://doi.org/10.1007/s42484-020-00036-4	journal	January 2021
The one-dimensional Hubbard model: a reminiscence Lieb, Elliott H.; Wu, F. Y. Physica A: Statistical Mechanics and its Applications, Vol. 321, Issue 1-2 https://doi.org/10.1016/S0378-4371(02)01785-5	journal	April 2003
Lyapunov control of bilinear Schrödinger equations Mirrahimi, Mazyar; Rouchon, Pierre; Turinici, Gabriel Automatica, Vol. 41, Issue 11 https://doi.org/10.1016/j.automatica.2005.05.018	journal	November 2005
Lyapunov control methods of closed quantum systems Kuang, Sen; Cong, Shuang Automatica, Vol. 44, Issue 1 https://doi.org/10.1016/j.automatica.2007.05.013	journal	January 2008
Rapid Lyapunov control of finite-dimensional quantum systems Kuang, Sen; Dong, Daoyi; Petersen, Ian R. Automatica, Vol. 81 https://doi.org/10.1016/j.automatica.2017.02.041	journal	July 2017
Measurement-Based Control for Minimizing Energy Functions in Quantum Systems Clausen, Henrik Glavind; Rahman, Salahuddin Abdul; Karabacak, Özkan IFAC-PapersOnLine, Vol. 56, Issue 2 https://doi.org/10.1016/j.ifacol.2023.10.111	journal	January 2023
Implicit Lyapunov control of finite dimensional Schrödinger equations Beauchard, Karine; Coron, Jean Michel; Mirrahimi, Mazyar Systems & Control Letters, Vol. 56, Issue 5 https://doi.org/10.1016/j.sysconle.2006.10.024	journal	May 2007
Quantum Chemistry in the Age of Quantum Computing Cao, Yudong; Romero, Jonathan; Olson, Jonathan P. Chemical Reviews, Vol. 119, Issue 19 https://doi.org/10.1021/acs.chemrev.8b00803	journal	August 2019
A cold-atom Fermi–Hubbard antiferromagnet Mazurenko, Anton; Chiu, Christie S.; Ji, Geoffrey Nature, Vol. 545, Issue 7655 https://doi.org/10.1038/nature22362	journal	May 2017
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
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
Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer Stanisic, Stasja; Bosse, Jan Lukas; Gambetta, Filippo Maria Nature Communications, Vol. 13, Issue 1 https://doi.org/10.1038/s41467-022-33335-4	journal	October 2022
Gate-free state preparation for fast variational quantum eigensolver simulations Meitei, Oinam Romesh; Gard, Bryan T.; Barron, George S. npj Quantum Information, Vol. 7, Issue 1 https://doi.org/10.1038/s41534-021-00493-0	journal	October 2021
Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution Motta, Mario; Sun, Chong; Tan, Adrian T. K. Nature Physics, Vol. 16, Issue 2 https://doi.org/10.1038/s41567-019-0704-4	journal	November 2019
Variational quantum unsampling on a quantum photonic processor Carolan, Jacques; Mohseni, Masoud; Olson, Jonathan P. Nature Physics, Vol. 16, Issue 3 https://doi.org/10.1038/s41567-019-0747-6	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
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
Faster ground state preparation and high-precision ground energy estimation with fewer qubits Ge, Yimin; Tura, Jordi; Cirac, J. Ignacio Journal of Mathematical Physics, Vol. 60, Issue 2 https://doi.org/10.1063/1.5027484	journal	February 2019
Measurement optimization in the variational quantum eigensolver using a minimum clique cover Verteletskyi, Vladyslav; Yen, Tzu-Ching; Izmaylov, Artur F. The Journal of Chemical Physics, Vol. 152, Issue 12 https://doi.org/10.1063/1.5141458	journal	March 2020
Elucidating reaction mechanisms on quantum computers Reiher, Markus; Wiebe, Nathan; Svore, Krysta M. Proceedings of the National Academy of Sciences, Vol. 114, Issue 29 https://doi.org/10.1073/pnas.1619152114	journal	July 2017
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
Variational quantum eigensolver for SU(N) fermions Consiglio, Mirko; Chetcuti, Wayne J.; Bravo-Prieto, Carlos Journal of Physics A: Mathematical and Theoretical, Vol. 55, Issue 26 https://doi.org/10.1088/1751-8121/ac7016	journal	June 2022
OpenFermion: the electronic structure package for quantum computers McClean, Jarrod R.; Rubin, Nicholas C.; Sung, Kevin J. Quantum Science and Technology, Vol. 5, Issue 3 https://doi.org/10.1088/2058-9565/ab8ebc	journal	June 2020
Classical and Quantum Computation Kitaev, A.; Shen, A.; Vyalyi, M. https://doi.org/10.1090/gsm/047	book	January 2002
Electron correlations in narrow energy bands Hubbard, J. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 276, Issue 1365, p. 238-257 https://doi.org/10.1098/rspa.1963.0204	journal	November 1963
From Pulses to Circuits and Back Again: A Quantum Optimal Control Perspective on Variational Quantum Algorithms Magann, Alicia B.; Arenz, Christian; Grace, Matthew D. PRX Quantum, Vol. 2, Issue 1 https://doi.org/10.1103/PRXQuantum.2.010101	journal	January 2021
Abrupt transitions in variational quantum circuit training Campos, Ernesto; Nasrallah, Aly; Biamonte, Jacob Physical Review A, Vol. 103, Issue 3 https://doi.org/10.1103/PhysRevA.103.032607	journal	March 2021
Resource estimate for quantum many-body ground-state preparation on a quantum computer Lemieux, Jessica; Duclos-Cianci, Guillaume; Sénéchal, David Physical Review A, Vol. 103, Issue 5 https://doi.org/10.1103/PhysRevA.103.052408	journal	May 2021
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
Lyapunov-control-inspired strategies for quantum combinatorial optimization Magann, Alicia B.; Rudinger, Kenneth M.; Grace, Matthew D. Physical Review A, Vol. 106, Issue 6 https://doi.org/10.1103/PhysRevA.106.062414	journal	December 2022
Optimizing quantum circuits with Riemannian gradient flow Wiersema, Roeland; Killoran, Nathan Physical Review A, Vol. 107, Issue 6 https://doi.org/10.1103/PhysRevA.107.062421	journal	June 2023
Quantifying T -gate-count improvements for ground-state-energy estimation with near-optimal state preparation Pathak, S.; Russo, A. E.; Seritan, S. K. Physical Review A, Vol. 107, Issue 4 https://doi.org/10.1103/PhysRevA.107.L040601	journal	April 2023
Necessary condition for the quantum adiabatic approximation Boixo, S.; Somma, R. D. Physical Review A, Vol. 81, Issue 3 https://doi.org/10.1103/PhysRevA.81.032308	journal	March 2010
Progress towards practical quantum variational algorithms Wecker, Dave; Hastings, Matthew B.; Troyer, Matthias Physical Review A, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevA.92.042303	journal	October 2015
Quantum Algorithms to Simulate Many-Body Physics of Correlated Fermions Jiang, Zhang; Sung, Kevin J.; Kechedzhi, Kostyantyn Physical Review Applied, Vol. 9, Issue 4 https://doi.org/10.1103/PhysRevApplied.9.044036	journal	April 2018
Strategies for solving the Fermi-Hubbard model on near-term quantum computers Cade, Chris; Mineh, Lana; Montanaro, Ashley Physical Review B, Vol. 102, Issue 23 https://doi.org/10.1103/PhysRevB.102.235122	journal	December 2020
Two-dimensional Hubbard model: Numerical simulation study Hirsch, J. E. Physical Review B, Vol. 31, Issue 7 https://doi.org/10.1103/PhysRevB.31.4403	journal	April 1985
Sufficient condition for absence of the sign problem in the fermionic quantum Monte Carlo algorithm Wu, Congjun; Zhang, Shou-Cheng Physical Review B, Vol. 71, Issue 15 https://doi.org/10.1103/PhysRevB.71.155115	journal	April 2005
Preparing Ground States of Quantum Many-Body Systems on a Quantum Computer Poulin, David; Wocjan, Pawel Physical Review Letters, Vol. 102, Issue 13 https://doi.org/10.1103/PhysRevLett.102.130503	journal	April 2009
Equation of State of the Two-Dimensional Hubbard Model Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H. Physical Review Letters, Vol. 116, Issue 17 https://doi.org/10.1103/PhysRevLett.116.175301	journal	April 2016
Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems Brady, Lucas T.; Baldwin, Christopher L.; Bapat, Aniruddha Physical Review Letters, Vol. 126, Issue 7 https://doi.org/10.1103/PhysRevLett.126.070505	journal	February 2021
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
Feedback-Based Quantum Optimization Magann, Alicia B.; Rudinger, Kenneth M.; Grace, Matthew D. Physical Review Letters, Vol. 129, Issue 25 https://doi.org/10.1103/PhysRevLett.129.250502	journal	December 2022
Quantum-optimal-control-inspired ansatz for variational quantum algorithms Choquette, Alexandre; Di Paolo, Agustin; Barkoutsos, Panagiotis Kl. Physical Review Research, Vol. 3, Issue 2 https://doi.org/10.1103/PhysRevResearch.3.023092	journal	May 2021
Adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer Zhu, Linghua; Tang, Ho Lun; Barron, George S. Physical Review Research, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevResearch.4.033029	journal	July 2022
Measurements as a roadblock to near-term practical quantum advantage in chemistry: Resource analysis Gonthier, Jérôme F.; Radin, Maxwell D.; Buda, Corneliu Physical Review Research, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevResearch.4.033154	journal	August 2022
Quantum imaginary-time control for accelerating the ground-state preparation Chen, Yu-Cheng; Chen, Yu-Qin; Hu, Alice Physical Review Research, Vol. 5, Issue 2 https://doi.org/10.1103/PhysRevResearch.5.023087	journal	May 2023
Randomized adaptive quantum state preparation Magann, Alicia B.; Economou, Sophia E.; Arenz, Christian Physical Review Research, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevResearch.5.033227	journal	September 2023
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
Optimizing Variational Quantum Algorithms Using Pontryagin’s Minimum Principle Yang, Zhi-Cheng; Rahmani, Armin; Shabani, Alireza Physical Review X, Vol. 7, Issue 2 https://doi.org/10.1103/PhysRevX.7.021027	journal	May 2017
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
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator Hempel, Cornelius; Maier, Christine; Romero, Jonathan Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031022	journal	July 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
Noisy intermediate-scale quantum algorithms Bharti, Kishor; Cervera-Lierta, Alba; Kyaw, Thi Ha Reviews of Modern Physics, Vol. 94, Issue 1 https://doi.org/10.1103/RevModPhys.94.015004	journal	February 2022
Analysis of Lyapunov Method for Control of Quantum States Wang, Xiaoting; Schirmer, Sophie G. IEEE Transactions on Automatic Control, Vol. 55, Issue 10 https://doi.org/10.1109/TAC.2010.2043292	journal	October 2010
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem Farhi, E.; Goldstone, J.; Gutmann, S. Science, Vol. 292, Issue 5516 https://doi.org/10.1126/science.1057726	journal	April 2001
Simulated Quantum Computation of Molecular Energies Aspuru-Guzik, A. Science, Vol. 309, Issue 5741 https://doi.org/10.1126/science.1113479	journal	September 2005
Bad metallic transport in a cold atom Fermi-Hubbard system Brown, Peter T.; Mitra, Debayan; Guardado-Sanchez, Elmer Science, Vol. 363, Issue 6425 https://doi.org/10.1126/science.aat4134	journal	December 2018
Hartree-Fock on a superconducting qubit quantum computer Arute, Frank; Arya, Kunal; Babbush, Ryan Science, Vol. 369, Issue 6507 https://doi.org/10.1126/science.abb9811	journal	August 2020
The Complexity of the Local Hamiltonian Problem Kempe, Julia; Kitaev, Alexei; Regev, Oded SIAM Journal on Computing, Vol. 35, Issue 5 https://doi.org/10.1137/S0097539704445226	journal	January 2006
The Hubbard Model Arovas, Daniel P.; Berg, Erez; Kivelson, Steven A. Annual Review of Condensed Matter Physics, Vol. 13, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031620-102024	journal	November 2021
The Hubbard Model: A Computational Perspective Qin, Mingpu; Schäfer, Thomas; Andergassen, Sabine Annual Review of Condensed Matter Physics, Vol. 13, Issue 1 https://doi.org/10.1146/annurev-conmatphys-090921-033948	journal	November 2021
A Survey of Quantum Lyapunov Control Methods Cong, Shuang; Meng, Fangfang The Scientific World Journal, Vol. 2013 https://doi.org/10.1155/2013/967529	journal	January 2013
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
Near-optimal ground state preparation Lin, Lin; Tong, Yu Quantum, Vol. 4 https://doi.org/10.22331/q-2020-12-14-372	journal	December 2020
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control Larocca, Martin; Czarnik, Piotr; Sharma, Kunal Quantum, Vol. 6 https://doi.org/10.22331/q-2022-09-29-824	journal	September 2022
PANSATZ: pulse-based ansatz for variational quantum algorithms Meirom, Dekel; Frankel, Steven H. Frontiers in Quantum Science and Technology, Vol. 2 https://doi.org/10.3389/frqst.2023.1273581	journal	October 2023

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