Auxiliary-Free Replica Shadows: Efficient Estimation of Multiple Nonlinear Quantum Properties

TL;DR

The paper introduces an auxiliary-free replica shadow framework that significantly improves the efficiency and accuracy of estimating multiple nonlinear quantum properties without auxiliary qubits or deep circuits, enabling practical use on near-term quantum devices.

Contribution

It proposes the AFRS framework that offers exponential accuracy improvements and allows simultaneous estimation of nonlinear properties without auxiliary qubits.

Findings

Exponential improvements in estimation accuracy over traditional shadow methods.

Ability to estimate multiple nonlinear properties simultaneously.

Implementation of a local-AFRS variant for constant-depth circuits.

Abstract

Efficient estimation of nonlinear properties is a significant yet challenging task from quantum information processing to many-body physics. Current methodologies often suffer from an exponential sampling cost or require auxiliary qubits and deep quantum circuits. To address these limitations, we propose an efficient auxiliary-free replica shadow (AFRS) framework, which leverages the power of the joint entangling operation on a few input replicas while integrating the mindset of shadow estimation. We rigorously prove that AFRS can offer exponential improvements in estimation accuracy compared with the conventional shadow method, and facilitate the simultaneous estimation of various nonlinear properties, unlike the destructive swap test. Additionally, we introduce an advanced local-AFRS variant tailored to estimating local observables with constant-depth quantum circuits, significantly simplifying the experimental implementation. Our work paves the way for efficient and practical estimation of nonlinear properties on near-term quantum devices.