Quantum Shadow Gradient Descent for Variational Quantum Algorithms
This addresses a critical bottleneck in training variational quantum circuits, such as quantum neural networks, by improving sample efficiency, though it is an incremental advancement building on shadow tomography.
The paper tackled the challenge of gradient estimation in variational quantum algorithms, which is hindered by quantum features like state collapse, by introducing quantum shadow gradient descent (QSGD) that uses a single sample per iteration to estimate all gradient components, achieving a significantly faster convergence rate than existing methods under locality conditions.
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.