Ansatz-Agnostic Exponential Resource Saving in Variational Quantum Algorithms Using Shallow Shadows

TL;DR

This paper introduces a protocol using shallow shadows to significantly reduce quantum resource requirements in variational quantum algorithms, applicable to a wide range of shallow ansatzes and observables.

Contribution

The authors develop a shallow shadow-based protocol that achieves exponential resource savings for nearly any shallow ansatz, broadening the applicability of resource-efficient VQAs.

Findings

Orders of magnitude improvement over standard VQA models

Applicable to variational quantum state preparation and circuit synthesis

Works with low Frobenius norm observables

Abstract

Variational Quantum Algorithms (VQA) have been identified as a promising candidate for the demonstration of near-term quantum advantage in solving optimization tasks in chemical simulation, quantum information, and machine learning. The standard model of training requires a significant amount of quantum resources, which led us to use classical shadows to devise an alternative that consumes exponentially fewer quantum resources. However, the approach only works when the observables are local and the ansatz is the shallow Alternating Layered Ansatz (ALA), thus severely limiting its potential in solving problems such as quantum state preparation, where the ideal state might not be approximable with an ALA. In this work, we present a protocol based on shallow shadows that achieves similar levels of savings for almost any shallow ansatz studied in the literature, when combined with observables of low Frobenius norm. We show that two important applications in quantum information for which VQAs can be a powerful option, namely variational quantum state preparation and variational quantum circuit synthesis, are compatible with our protocol. We also experimentally demonstrate orders of magnitude improvement in comparison to the standard VQA model.