Circuit optimization of qubit IC-POVMs for shadow estimation

TL;DR

This paper improves the implementation of qubit IC-POVMs for shadow estimation by reducing CNOT gate counts using a dimension dilation framework, enhancing practicality and noise resilience in quantum measurements.

Contribution

It introduces a method to implement single-qubit IC-POVMs with at most 2 CNOTs and SIC-POVMs with only 1 CNOT, along with an efficient compilation algorithm.

Findings

Single-qubit IC-POVMs require at most 2 CNOT gates.

SIC-POVMs can be implemented with only 1 CNOT gate.

Optimized circuits show noise-resilient performance in shadow estimation.

Abstract

Extracting information from quantum systems is crucial in quantum physics and information processing. Methods based on randomized measurements, like shadow estimation, show advantages in effectively achieving such tasks. However, randomized measurements require the application of random unitary evolution, which unavoidably necessitates frequent adjustments to the experimental setup or circuit parameters, posing challenges for practical implementations. To address these limitations, positive operator-valued measurements (POVMs) have been integrated to realize real-time single-setting shadow estimation. In this work, we advance the POVM-based shadow estimation by reducing the CNOT gate count for the implementation circuits of informationally complete POVMs (IC-POVMs), in particular, the symmetric IC-POVMs (SIC-POVMs), through the dimension dilation framework. We show that any single-qubit minimal IC-POVM can be implemented using at most 2 CNOT gates, while an SIC-POVM can be implemented with only 1 CNOT gate. In particular, we provide a concise form of the compilation circuit of any SIC-POVM along with an efficient algorithm for the determination of gate parameters. Moreover, we apply the optimized circuit compilation to shadow estimation, showcasing its noise-resilient performance and highlighting the flexibility in compiling various SIC-POVMs. Our work paves the way for the practical applications of qubit IC-POVMs on quantum platforms.