High-Precision Observable Estimation with Single Qubit Quantum Memory

TL;DR

This paper introduces a new method for estimating multi-qubit observables using a single qubit quantum memory, significantly reducing the number of measurements needed and mitigating shot noise, especially beneficial for noisy quantum devices.

Contribution

The authors propose a novel observable estimation algorithm leveraging single qubit memory to lower measurement complexity and shot noise in multi-qubit systems.

Findings

Reduces measurement count scaling to N^{2/3} for N Pauli strings

Achieves lower shot noise compared to traditional methods

Efficient for noisy intermediate-scale quantum devices

Abstract

The estimation of multi-qubit observables is a key task in quantum information science. The standard approach is to decompose a multi-qubit observable into a weighted sum of Pauli strings. The observable can then be estimated from projective single qubit measurements according to the Pauli strings followed by a classical summation. As the number of Pauli strings in the decomposition increases, shot-noise drastically builds up, and the accuracy of such estimation can be considerably compromised. Access to a single qubit quantum memory, where measurement data may be stored and accumulated can circumvent the build-up of shot noise. Here, we describe a many-qubit observable estimation approach to achieve this with a much lower number of interactions between the multi-qubit device and the single qubit memory compared to previous approaches. Our algorithm offers a reduction in the required number of measurements for a given target variance that scales $N^{\frac{2}{3}}$ with the number of Pauli strings $N$ in the observable decomposition. The low number of interactions between the multi-qubit device and the memory is desirable for noisy intermediate-scale quantum devices.