High-Precision Fidelity Estimation with Common Randomized Measurements

TL;DR

This paper presents a resource-efficient protocol for high-precision fidelity estimation of multiqubit quantum states using common randomized measurements and shadow estimation, significantly reducing the number of circuits needed.

Contribution

It introduces a novel fidelity estimation method combining common randomized measurements with shadow estimation, requiring fewer circuits and being effective under practical noise conditions.

Findings

Requires only 1/ε circuits for high-precision estimation

Constant number of circuits needed under certain noise models

Outperforms standard shadow estimation methods

Abstract

Efficient fidelity estimation of multiqubit quantum states is crucial to many applications in quantum information processing. However, to estimate the infidelity $\epsilon$ with multiplicative precision, conventional estimation protocols require (order) $1/\epsilon^2$ different circuits in addition to $1/\epsilon^2$ samples, which is quite resource-intensive for high-precision fidelity estimation. Here we introduce an efficient estimation protocol by virtue of common randomized measurements (CRM) integrated with shadow estimation based on the Clifford group, which only requires $1/\epsilon $ circuits. Moreover, in many scenarios of practical interest, in the presence of depolarizing or Pauli noise for example, our protocol only requires a constant number of circuits, irrespective of the infidelity $\epsilon$ and the qubit number. For large and intermediate quantum systems, quite often one circuit is already sufficient. In the course of study, we clarify the performance of CRM shadow estimation based on the Clifford group and 4-designs and highlight its advantages over standard and thrifty shadow estimation.