Operator Sampling for Shot-frugal Optimization in Variational Algorithms

TL;DR

This paper introduces Rosalin, a new optimizer that reduces measurement shots in variational quantum algorithms by random operator sampling, improving efficiency and performance in quantum chemistry simulations.

Contribution

The paper presents Rosalin, an innovative optimizer that combines weighted operator sampling with adaptive shot allocation to enhance variational quantum algorithm efficiency.

Findings

Rosalin outperforms other optimizers in finding molecular ground states.

Weighted sampling effectively reduces measurement shots needed.

Robust performance observed with and without quantum hardware noise.

Abstract

Quantum chemistry is a near-term application for quantum computers. This application may be facilitated by variational quantum-classical algorithms (VQCAs), although a concern for VQCAs is the large number of measurements needed for convergence, especially for chemical accuracy. Here we introduce a strategy for reducing the number of measurements (i.e., shots) by randomly sampling operators $h_i$ from the overall Hamiltonian $H = \sum_i c_i h_i$. In particular, we employ weighted sampling, which is important when the $c_i$'s are highly non-uniform, as is typical in chemistry. We integrate this strategy with an adaptive optimizer developed recently by our group to construct an improved optimizer called Rosalin (Random Operator Sampling for Adaptive Learning with Individual Number of shots). Rosalin implements stochastic gradient descent while adapting the shot noise for each partial derivative and randomly assigning the shots amongst the $h_i$ according to a weighted distribution. We implement this and other optimizers to find the ground states of molecules H$_2$, LiH, and BeH$_2$, without and with quantum hardware noise, and Rosalin outperforms other optimizers in most cases.