Scalable probes of measurement-induced criticality

TL;DR

This paper introduces a local entropy-based order parameter for measurement-induced phase transitions, enabling scalable and efficient detection on quantum platforms, with potential applications in quantum computing and fault tolerance.

Contribution

The authors propose a new local order parameter based on a reference qubit's entropy, and demonstrate its effectiveness in identifying measurement-induced criticality in a classically simulable quantum circuit.

Findings

The order parameter successfully detects phase transitions in the model.

The concept of a 'decoding light cone' shows local and measurable nature.

Critical exponents for the transition are estimated.

Abstract

We uncover a local order parameter for measurement-induced phase transitions: the average entropy of a single reference qubit initially entangled with the system. Using this order parameter, we identify scalable probes of measurement-induced criticality (MIC) that are immediately applicable to advanced quantum computing platforms. We test our proposal on a 1+1 dimensional stabilizer circuit model that can be classically simulated in polynomial time. We introduce the concept of a "decoding light cone" to establish the local and efficiently measurable nature of this probe. We also estimate bulk and surface critical exponents for the transition. Developing scalable probes of MIC in more general models may be a useful application of noisy-intermediate scale quantum (NISQ) devices, as well as point to more efficient realizations of fault-tolerant quantum computation.