Quantum Coding Transitions in the Presence of Boundary Dissipation

• URL: http://arxiv.org/abs/2304.02664v1
• Date: Wed, 5 Apr 2023 18:00:08 GMT
• Title: Quantum Coding Transitions in the Presence of Boundary Dissipation
• Authors: Izabella Lovas, Utkarsh Agrawal, and Sagar Vijay
• Abstract summary: We study the fate of quantum information in a one-dimensional qudit chain. unitary evolution in the presence of boundary dissipation allows this information to remain partially protected. For strong enough dissipation, this information is completely lost to the dissipative environment.
• Score: 0.3441021278275805
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate phase transitions in the encoding of quantum information in a quantum many-body system due to the competing effects of unitary scrambling and boundary dissipation. Specifically, we study the fate of quantum information in a one-dimensional qudit chain, subject to local unitary quantum circuit evolution in the presence of depolarizating noise at the boundary. If the qudit chain initially contains a finite amount of locally-accessible quantum information, unitary evolution in the presence of boundary dissipation allows this information to remain partially protected when the dissipation is sufficiently weak, and up to time-scales growing linearly in system size $L$. In contrast, for strong enough dissipation, this information is completely lost to the dissipative environment. We analytically investigate this ``quantum coding transition" by considering dynamics involving Haar-random, local unitary gates, and confirm our predictions in numerical simulations of Clifford quantum circuits. We demonstrate that scrambling the quantum information in the qudit chain with a unitary circuit of depth $ \mathcal{O}(\log L)$ before the onset of dissipation can perfectly protect the information until late times. The nature of the coding transition changes when the dynamics extend for times much longer than $L$. We further show that at weak dissipation, it is possible to code at a finite rate, i.e. a fraction of the many-body Hilbert space of the qudit chain can be used to encode quantum information.

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