An Adaptive Optimizer for Measurement-Frugal Variational Algorithms

Kubler, Jonas; Coles, Patrick Joseph; Arrasmith, Andrew Thomas; Cincio, Lukasz

doi:10.22331/q-2020-05-11-263

An Adaptive Optimizer for Measurement-Frugal Variational Algorithms

Journal Article · Mon May 11 00:00:00 EDT 2020 · Quantum

DOI:https://doi.org/10.22331/q-2020-05-11-263· OSTI ID:1659200

^[1]; ^[2]; ^[2]; ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Max Planck Inst. for Intelligent Systems, Tubingen (Germany)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Variational hybrid quantum-classical algorithms (VHQCAs) have the potential to be useful in the era of near-term quantum computing. However, recently there has been concern regarding the number of measurements needed for convergence of VHQCAs. Here, we address this concern by investigating the classical optimizer in VHQCAs. We introduce a novel optimizer called individual Coupled Adaptive Number of Shots (iCANS). This adaptive optimizer frugally selects the number of measurements (i.e., number of shots) both for a given iteration and for a given partial derivative in a stochastic gradient descent. We numerically simulate the performance of iCANS for the variational quantum eigensolver and for variational quantum compiling, with and without noise. In all cases, and especially in the noisy case, iCANS tends to out-perform state-of-the-art optimizers for VHQCAs. We therefore believe this adaptive optimizer will be useful for realistic VHQCA implementations, where the number of measurements is limited.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1659200

Report Number(s):: LA-UR--19-29383

Journal Information:: Quantum, Journal Name: Quantum Vol. 4; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

References (36)

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
Qiskit: An Open-source Framework for Quantum Computing Aleksandrowicz, Gadi; Alexander, Thomas; Barkoutsos, Panagiotis https://doi.org/10.5281/zenodo.2562111	software	January 2019
ImprovedSCF convergence acceleration Pulay, P. Journal of Computational Chemistry, Vol. 3, Issue 4 https://doi.org/10.1002/jcc.540030413	journal	January 1982
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
Measuring All Compatible Operators in One Series of Single-Qubit Measurements Using Unitary Transformations Yen, Tzu-Ching; Verteletskyi, Vladyslav; Izmaylov, Artur F. Journal of Chemical Theory and Computation, Vol. 16, Issue 4 https://doi.org/10.1021/acs.jctc.0c00008	journal	March 2020
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
Deep learning LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey Nature, Vol. 521, Issue 7553 https://doi.org/10.1038/nature14539	journal	May 2015
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
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
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
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
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
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
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
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
An efficient method for finding the minimum of a function of several variables without calculating derivatives Powell, M. J. D. The Computer Journal, Vol. 7, Issue 2 https://doi.org/10.1093/comjnl/7.2.155	journal	February 1964
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 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
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
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
Sequential minimal optimization for quantum-classical hybrid algorithms Nakanishi, Ken M.; Fujii, Keisuke; Todo, Synge Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043158	journal	October 2020
Variational quantum algorithm for nonequilibrium steady states Yoshioka, Nobuyuki; Nakagawa, Yuya O.; Mitarai, Kosuke Physical Review Research, Vol. 2, Issue 4 https://doi.org/10.1103/PhysRevResearch.2.043289	journal	November 2020
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
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
Implementation of the simultaneous perturbation algorithm for stochastic optimization Spall, J. C. IEEE Transactions on Aerospace and Electronic Systems, Vol. 34, Issue 3 https://doi.org/10.1109/7.705889	journal	July 1998
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
$O(N^3)$ Measurement Cost for Variational Quantum Eigensolver on Molecular Hamiltonians Gokhale, Pranav; Angiuli, Olivia; Ding, Yongshan IEEE Transactions on Quantum Engineering, Vol. 1 https://doi.org/10.1109/TQE.2020.3035814	journal	January 2020
Iterative Procedures for Nonlinear Integral Equations Anderson, Donald G. Journal of the ACM, Vol. 12, Issue 4 https://doi.org/10.1145/321296.321305	journal	October 1965
Variational Quantum Unsampling on a Programmable Nanophotonic Processor Carolan, Jacques; Mosheni, Masoud; Olson, Jonathan P. CLEO: QELS_Fundamental Science, Conference on Lasers and Electro-Optics https://doi.org/10.1364/CLEO_QELS.2019.FTh3A.3	conference	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
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
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
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
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
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

Cited By (4)

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
Microcanonical and finite temperature ab initio molecular dynamics simulations on quantum computers Sokolov, Igor O.; Barkoutsos, Panagiotis Kl.; Moeller, Lukas arXiv https://doi.org/10.48550/arxiv.2008.08144	text	January 2020
Fermionic partial tomography via classical shadows Zhao, Andrew; Rubin, Nicholas C.; Miyake, Akimasa arXiv https://doi.org/10.48550/arxiv.2010.16094	text	January 2020
A semi-agnostic ansatz with variable structure for quantum machine learning Bilkis, M.; Cerezo, M.; Verdon, Guillaume arXiv https://doi.org/10.48550/arxiv.2103.06712	preprint	January 2021

Similar Records

Resource frugal optimizer for quantum machine learning

Journal Article · Tue Aug 22 20:00:00 EDT 2023 · Quantum Science and Technology · OSTI ID:2228652

Latency considerations for stochastic optimizers in variational quantum algorithms

Journal Article · Wed Mar 15 20:00:00 EDT 2023 · Quantum · OSTI ID:1961875

Related Subjects

97 MATHEMATICS AND COMPUTING
Computer Science
Mathematics

An Adaptive Optimizer for Measurement-Frugal Variational Algorithms

Citation Formats

References (36)

Cited By (4)

Similar Records

Related Subjects