Decoding the Projective Transverse Field Ising Model

Abstract

The competition between non-commuting projective measurements in discrete quantum circuits can give rise to entanglement transitions. It separates a regime where initially stored quantum information survives the time evolution from a regime where the measurements destroy the quantum information. Here we study one such system - the projective transverse field Ising model - with a focus on its capabilities as a quantum error correction code. The idea is to interpret one type of measurement as an error and the other type as a syndrome measurement. We demonstrate that there is a finite threshold below which quantum information encoded in an initially entangled state can be retrieved reliably. In particular, we implement the maximum likelihood decoder to demonstrate that the error correction threshold is distinct from the entanglement transition. This implies that there is a finite regime where quantum information is protected by the projective dynamics, but cannot be retrieved by using syndrome measurements.

arXiv comment18 pages, 9 figures

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Cited by in corpus (8)

• Majorana Loop Models for Measurement-Only Quantum Circuits
• Boundary transfer matrix spectrum of measurement-induced transitions
• Steering-induced phase transition in measurement-only quantum circuits
• Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Disappearance of measurement-induced phase transition in a quantum spin system for large sizes