Quantum Shadow Gradient Descent for Variational Quantum Algorithms

TL;DR

This paper introduces quantum shadow gradient descent (QSGD), a novel method that improves sample efficiency in variational quantum algorithms by estimating all gradient components from a single measurement, leading to faster convergence.

Contribution

The paper proposes QSGD, a new gradient estimation technique using shadow tomography, reducing sample requirements and enhancing convergence speed in quantum variational algorithms.

Findings

QSGD estimates all gradient components from one sample per iteration.

QSGD converges faster than traditional methods under locality conditions.

Numerical experiments confirm theoretical advantages of QSGD.

Abstract

Gradient-based optimizers have been proposed for training variational quantum circuits in settings such as quantum neural networks (QNNs). The task of gradient estimation, however, has proven to be challenging, primarily due to distinctive quantum features such as state collapse and measurement incompatibility. Conventional techniques, such as the parameter-shift rule, necessitate several fresh samples in each iteration to estimate the gradient due to the stochastic nature of state measurement. Owing to state collapse from measurement, the inability to reuse samples in subsequent iterations motivates a crucial inquiry into whether fundamentally more efficient approaches to sample utilization exist. In this paper, we affirm the feasibility of such efficiency enhancements through a novel procedure called quantum shadow gradient descent (QSGD), which uses a single sample per iteration to estimate all components of the gradient. Our approach is based on an adaptation of shadow tomography that significantly enhances sample efficiency. Through detailed theoretical analysis, we show that QSGD has a significantly faster convergence rate than existing methods under locality conditions. We present detailed numerical experiments supporting all of our theoretical claims.