Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

Ha, Yunsoo; Shashaani, Sara; Menickelly, Matt

doi:10.1287/ijoc.2024.0575

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

Journal Article · Wed Nov 27 00:00:00 EST 2024 · INFORMS Journal on Computing

DOI:https://doi.org/10.1287/ijoc.2024.0575· OSTI ID:2588218

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National Renewable Energy Laboratory (NREL), Golden, CO (United States)
North Carolina State University, Raleigh, NC (United States)
Argonne National Laboratory (ANL), Argonne, IL (United States)

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 2588218

Journal Information:: INFORMS Journal on Computing, Journal Name: INFORMS Journal on Computing Journal Issue: 1 Vol. 37; ISSN 1526-5528; ISSN 1091-9856

Publisher:: Institute for Operations Research and the Management Sciences (INFORMS)Copyright Statement

Country of Publication:: United States

Language:: English

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