Decoding the Projective Transverse Field Ising Model

TL;DR

This paper investigates the projective transverse field Ising model, revealing a finite error correction threshold that is distinct from the entanglement transition, highlighting its potential for quantum information protection.

Contribution

It introduces a novel analysis of the model's error correction capabilities, distinguishing between entanglement transitions and information retrievability thresholds.

Findings

Finite error correction threshold identified

Threshold differs from entanglement transition point

Quantum information can be protected without being retrievable

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.