Quantum algorithm for evaluating operator size with Bell measurements

TL;DR

This paper introduces a quantum algorithm utilizing Bell measurements to directly evaluate operator size and its distribution, aiding the study of quantum chaos on noisy quantum computers.

Contribution

It proposes a novel quantum algorithm for direct measurement of operator size, including analysis of errors and noise mitigation strategies.

Findings

Saturation of operator size growth can result from quantum chaos or quantum noise.

Error mitigation effectively reduces noise influence, restoring system distinguishability.

The protocol enables investigation of quantum chaos on noisy quantum computers.

Abstract

Operator size growth describes the scrambling of operators in quantum dynamics and stands out as an essential physical concept for characterizing quantum chaos. Important as it is, a scheme for direct measuring operator size on a quantum computer is still absent. Here, we propose a quantum algorithm for direct measuring the operator size and its distribution based on Bell measurement. The algorithm is verified with spin chains and meanwhile, the effects of Trotterization error and quantum noise are analyzed. It is revealed that saturation of operator size growth can be due to quantum chaos itself or be a consequence of quantum noises, which make a distinction between quantum integrable and chaotic systems difficulty on noisy quantum processors. Nevertheless, it is found that the error mitigation will effectively reduce the influence of noise, so as to restore the distinguishability of quantum chaotic systems. Our work provides a feasible protocol for investigating quantum chaos on noisy quantum computers by measuring operator size growth.