Decoding the Projective Transverse Field Ising Model

• URL: http://arxiv.org/abs/2303.03081v2
• Date: Tue, 20 Jun 2023 17:48:09 GMT
• Title: Decoding the Projective Transverse Field Ising Model
• Authors: Felix Roser, Hans Peter B\"uchler, and Nicolai Lang
• Abstract summary: We study a projective transverse field Ising model with a focus on its capabilities as a quantum error correction code. We demonstrate that there is a finite threshold below which quantum information encoded in an initially entangled state can be retrieved reliably. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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