Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits

TL;DR

This paper studies how errors affect quantum information in encoding-decoding circuits, revealing a phase transition from error protection to vulnerability as errors increase, with implications for quantum technology robustness.

Contribution

It analytically demonstrates a phase transition in error resilience in quantum circuits, linking it to entropy and multifractal features, advancing understanding of quantum information stability.

Findings

Identifies a phase transition from error-protecting to error-vulnerable regimes.

Links the transition to Rnyi entropy changes and multifractal behavior.

Provides an analytical framework for understanding dynamical critical phenomena in quantum systems.

Abstract

Understanding how errors deteriorate the information encoded in a many-body quantum system is a fundamental problem with practical implications for quantum technologies. Here, we investigate a class of encoding-decoding random circuits subject to local coherent and incoherent errors. We analytically demonstrate the existence of a phase transition from an error-protecting phase to an error-vulnerable phase occurring when the error strength is increased. This transition is accompanied by R\'enyi entropy transitions and by onset of multifractal features in the system. Our results provide a new perspective on storing and processing quantum information, while the introduced framework enables an analytic understanding of a dynamical critical phenomenon in a many-body system.