A composite measurement scheme for efficient quantum observable estimation

TL;DR

This paper introduces a composite measurement scheme for quantum observable estimation that combines multiple measurement strategies with optimized shot distribution, demonstrating improved efficiency and trainability on molecular systems.

Contribution

It proposes a novel composite measurement approach, including the C-LBCS scheme, which outperforms existing methods and is efficiently trainable for large quantum systems.

Findings

C-LBCS outperforms previous state-of-the-art methods in molecular systems.

The scheme can be optimized with stochastic gradient descent.

It remains effective even with many observable terms.

Abstract

Estimation of the expectation value of observables is a key subroutine in quantum computing and is also the bottleneck of the performance of many near-term quantum algorithms. Many works have been proposed to reduce the number of measurements needed for this task and they provide different measurement schemes for generating the measurements to perform. In this paper, we propose a new approach, composite measurement scheme, which composes multiple measurement schemes by distributing shots to them with a trainable ratio. As an example of our method, we study the case where only Pauli measurements are allowed and propose Composite-LBCS (C-LBCS), a composite measurement scheme made by composing locally-biased classical shadows. We numerically demonstrate C-LBCS on molecular systems up to $\mathrm{CO}_2$ (30 qubits) and show that C-LBCS outperforms the previous state-of-the-art methods despite its simplicity. We also show that C-LBCS can be efficiently optimized by stochastic gradient descent and is trainable even when the observable contains a large number of terms. We believe our method opens up a reliable way toward efficient observable estimation on large quantum systems.