Optimizing the information extracted by a single qubit measurement

TL;DR

This paper improves the estimation of quantum expectation values by optimizing single-qubit measurement decompositions, demonstrating that reflection-based decompositions outperform simple Pauli decompositions, especially for fast-forwardable operators.

Contribution

It introduces an optimal reflection-based decomposition method for expectation value estimation in quantum systems, enhancing measurement efficiency.

Findings

Reflection decompositions are optimal for expectation value estimation.

Numerical results show a $N^{0.7}$ improvement over Pauli decompositions.

Optimizations benefit error mitigation in quantum computing.

Abstract

We consider a quantum computation that only extracts one bit of information per $N$-qubit quantum state preparation. This is relevant for error mitigation schemes where the remainder of the system is measured to detect errors. We optimize the estimation of the expectation value of an operator by its linear decomposition into bitwise-measurable terms. We prove that optimal decompositions must be in terms of reflections with eigenvalues $\pm1$. We find the optimal reflection decomposition of a fast-forwardable operator, and show a numerical improvement over a simple Pauli decomposition by a factor $N^{0.7}$