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arXiv:2302.04422

Latency-aware adaptive shot allocation for run-time efficient variational quantum algorithms

Kosuke Ito

Published Feb 9, 2023• 1 citation
arXivHTMLPDF

Abstract

Efficient classical optimizers are crucial in practical implementations of Variational Quantum Algorithms (VQAs). In particular, to make Stochastic Gradient Descent (SGD) resource efficient, adaptive strategies have been proposed to determine the number of measurement shots used to estimate the gradient. However, existing strategies overlook the overhead that occurs in each iteration. In terms of wall-clock runtime, significant circuit-switching and communication latency can slow the optimization process when using a large number of iterations. In terms of economic cost when using cloud services, per-task prices can become significant. To address these issues, we present an adaptive strategy that balances the number of shots in each iteration to maximize expected gain per unit time or cost by explicitly taking into account the overhead. Our approach can be applied to not only to the simple SGD but also its variants, including Adam. Numerical simulations show that our adaptive shot strategy is actually efficient for Adam, outperforming many existing state-of-the-art adaptive shot optimizers. However, this is not the case for the simple SGD. When focusing on the number of shots as the resource, our adaptive-shots Adam with zero-overhead also outperforms existing optimizers.

DOI
10.48550/arxiv.2302.04422

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Efficient classical optimizers are crucial in practical implementations of Variational Quantum Algorithms (VQAs). In particular, to make Stochastic Gradient Descent (SGD) resource efficient, adaptive strategies have been proposed to determine the number of measurement shots used to estimate the gradient. However, existing strategies overlook the overhead that occurs in each iteration. In terms of wall-clock runtime, significant circuit-switching and communication latency can slow the optimization process when using a large number of iterations. In terms of economic cost when using cloud services, per-task prices can become significant. To address these issues, we present an adaptive strategy that balances the number of shots in each iteration to maximize expected gain per unit time or cost by explicitly taking into account the overhead. Our approach can be applied to not only to the simple SGD but also its variants, including Adam. Numerical simulations show that our adaptive shot strategy is actually efficient for Adam, outperforming many existing state-of-the-art adaptive shot optimizers. However, this is not the case for the simple SGD. When focusing on the number of shots as the resource, our adaptive-shots Adam with zero-overhead also outperforms existing optimizers.
Variational Quantum Algorithms (VQAs) are a promising approach for practical applications like chemistry and materials science on near-term quantum computers as they typically reduce quantum resource requirements. However, in order to implement VQAs, an efficient classical optimization strategy is required. Here we present a new stochastic gradient descent method using an adaptive number of shots at each step, called the global Coupled Adaptive Number of Shots (gCANS) method, which improves on prior art in both the number of iterations as well as the number of shots required. These improvements reduce both the time and money required to run VQAs on current cloud platforms. We analytically prove that in a convex setting gCANS achieves geometric convergence to the optimum. Further, we numerically investigate the performance of gCANS on some chemical configuration problems. We also consider finding the ground state for an Ising model with different numbers of spins to examine the scaling of the method. We find that for these problems, gCANS compares favorably to all of the other optimizers we consider.
Variational quantum algorithms (VQAs) have attracted remarkable interest over the past few years because of their potential computational advantages on near-term quantum devices. They leverage a hybrid approach that integrates classical and quantum computing resources to solve high-dimensional problems that are challenging for classical approaches alone. In the training process of variational circuits, constructing an accurate probability distribution for each epoch is not always necessary, creating opportunities to reduce computational costs through shot reduction. However, existing shot allocation methods that capitalize on this potential often lack adaptive feedback or are tied to specific classical optimizers, which limits their applicability to common VQAs and broader optimization techniques. Our observations indicate that the information entropy of a quantum circuit’s output distribution exhibits an approximately exponential relationship with the number of shots needed to achieve a target Hellinger distance. In this work, we propose a distribution-adaptive dynamic shot (DDS) framework that efficiently adjusts the number of shots per iteration in VQAs using the entropy distribution from the prior training epoch. Our results demonstrate that the DDS framework sustains inference accuracy while achieving an ∼ 50 % reduction in average shot count compared to fixed-shot training, and ∼ 60 % higher accuracy than recently proposed tiered shot allocation methods. Furthermore, in noisy simulations that reflect the error rates of actual IBM quantum systems, DDS achieves an ∼ 30 % reduction in the total number of shots compared to the fixed-shot method with minimal degradation in accuracy and offers ∼ 70 % higher computational accuracy than tiered shot allocation methods.
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.
We introduce SantaQlaus, a resource-efficient optimization algorithm tailored for variational quantum algorithms (VQAs), including applications in the variational quantum eigensolver (VQE) and quantum machine learning (QML). Classical optimization strategies for VQAs are often hindered by the complex landscapes of local minima and saddle points. Although some existing quantum-aware optimizers adaptively adjust the number of measurement shots, their primary focus is on maximizing gain per iteration rather than strategically utilizing quantum shot-noise (QSN) to address these challenges. Inspired by the classical Stochastic AnNealing Thermostats with Adaptive momentum (Santa) algorithm, SantaQlaus explicitly leverages inherent QSN for optimization. The algorithm dynamically adjusts the number of quantum measurement shots in an annealing framework: fewer shots are allocated during the early, high-temperature stages for efficient resource utilization and landscape exploration, while more shots are employed later for enhanced precision. Numerical simulations on VQE and QML demonstrate that SantaQlaus outperforms existing optimizers, particularly in mitigating the risks of converging to poor local optima, all while maintaining shot efficiency. This paves the way for efficient and robust training of quantum variational models.
Variational Quantum Algorithms (VQAs) have gained significant attention as a potential solution for various quantum computing applications in the near term. However, implementing these algorithms on quantum devices often necessitates a substantial number of measurements, resulting in time-consuming and resource-intensive processes. This paper presents a generalized framework for optimization algorithms aiming to reduce the number of shot evaluations in VQAs. The proposed framework combines an estimator and an optimizer. We investigate two specific case studies within this framework. In the first case, we pair a sample mean estimator with a simulated annealing optimizer, while in the second case, we combine a recursive estimator with a gradient descent optimizer. In both instances, we demonstrate that our proposed approach yields notable performance enhancements compared to conventional methods.
Abstract Optimizing parameterized quantum circuits is a key routine in using near-term quantum devices. However, the existing algorithms for such optimization require an excessive number of quantum-measurement shots for estimating expectation values of observables and repeating many iterations, whose cost has been a critical obstacle for practical use. We develop an efficient alternative optimization algorithm, stochastic gradient line Bayesian optimization (SGLBO), to address this problem. SGLBO reduces the measurement-shot cost by estimating an appropriate direction of updating circuit parameters based on stochastic gradient descent (SGD) and further utilizing Bayesian optimization (BO) to estimate the optimal step size for each iteration in SGD. In addition, we formulate an adaptive measurement-shot strategy and introduce a technique of suffix averaging to reduce the effect of statistical and hardware noise. Our numerical simulation demonstrates that the SGLBO augmented with these techniques can drastically reduce the measurement-shot cost, improve the accuracy, and make the optimization noise-robust.