Efficient post-selection in light-cone correlations of monitored quantum circuits

TL;DR

This paper introduces an efficient method to compute post-selected light-cone correlations in monitored quantum circuits by relating rare measurement outcomes to typical ones in a different circuit, enabling better analysis of quantum dynamics.

Contribution

It establishes a novel rare-to-typical mapping for post-selected correlations in monitored quantum circuits, with specific conditions for brickwork XYZ gate circuits.

Findings

Efficient computation of post-selected correlations from averaged correlations.

Identification of conditions for rare-to-typical mapping in XYZ gate circuits.

Demonstration of a dynamical crossover in a model system.

Abstract

We consider how to target evolution conditioned on atypical measurement outcomes in monitored quantum circuits, i.e., the post-selection problem. We show that for a simple class of measurement schemes, post-selected light-cone dynamical correlation functions can be obtained efficiently from the averaged correlations of a different unitary circuit. This connects rare measurement outcomes in one circuit to typical outcomes in another one. We derive conditions for the existence of this rare-to-typical mapping in brickwork quantum circuits made of XYZ gates. We illustrate these general results with a model system that exhibits a dynamical crossover (a smoothed dynamical transition) in event statistics, and discuss extensions to more general dynamical correlations.