Quantum stochastic optimization

Matt Menickelly, Yunsoo Ha, Matthew Otten

Variational quantum algorithms, which have risen to prominence in the noisy intermediate-scale quantum setting, require the implementation of a stochastic optimizer on classical hardware. To date, most research has employed algorithms based on the stochastic gradient iteration as the stochastic classical optimizer. In this work we propose instead using stochastic optimization algorithms that yield stochastic processes emulating the dynamics of classical deterministic algorithms. This approach results in methods with theoretically superior worst-case iteration complexities, at the expense of greater per-iteration sample (shot) complexities. We investigate this trade-off both theoretically and empirically and conclude that preferences for a choice of stochastic optimizer should explicitly depend on a function of both latency and shot execution times.

Günter Mahler A, Volker A. Weberruß

Jincheng Zhang

Quantum-Inspired Stochastic Differential Equation (Q-SDE) Optimization addresses the challenges of optimizing complex, stochastic systems by integrating quantum-inspired stochastic differential equation modeling. This research presents a novel optimization algorithm, the Q-SDE-based method, designed to effectively handle highly non-linear, stochastic optimization problems characterized by significant noise. We develop a framework that utilizes the inherent stochasticity of Q-SDEs, coupled with differential equation principles, to provide a robust and adaptive approach to finding optimal solutions. The core mechanism involves a dynamic adjustment of the Q-SDE's parameters to minimize the error function across a wider range of solutions, mitigating the impact of noise and enhancing the algorithm's performance in challenging scenarios. This work demonstrates the effectiveness of this approach through extensive numerical simulations and comparisons with established optimization techniques, highlighting its potential for significant improvements in the optimization of stochastic systems.

Günter Mahler A, Volker A. Weberruß

Stanley Gudder

Lech S. Papiez

Classical mechanics is formulated as a kind of deterministic optimal control. The simplest, from the optimal control point of view, stochastic generalization of classical mechanisms is submitted. The connections between stochastic mechanics and quantum mechanics are shown, thanks to the stochastic optimal control method.