Quantum Circuit Cutting for Classical Shadows

TL;DR

This paper introduces a divide-and-conquer circuit cutting method combined with classical shadow tomography to efficiently estimate quantum observable expectations, especially for large, complex circuits, reducing resource requirements.

Contribution

It develops a novel circuit cutting approach for classical shadows, deriving formulas for predictions from circuit fragments and analyzing sample complexity for factorized observables.

Findings

Outperforms traditional shadow tomography for high-weight observables

Provides a general formula for predictions from circuit fragments

Demonstrates sample complexity advantages in numerical simulations

Abstract

Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be executed more robustly using fewer quantum resources. We introduce a divide-and-conquer circuit cutting method for estimating the expectation values of observables using classical shadows. We derive a general formula for making predictions using the classical shadows of circuit fragments from arbitrarily cut circuits, and provide the sample complexity analysis for the case when observables factorize across fragments. Then, we numerically show that our divide-and-conquer method outperforms traditional uncut shadow tomography when estimating high-weight observables that act non-trivially on many qubits, and discuss the mechanisms for this advantage.