Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits

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 Rényi 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.

Revised version, incoherent and site-dependent errors included, 4+14 pages, comments welcome!

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• Critical properties of the measurement-induced transition in random quantum circuits
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