Harnessing symmetry-protected topological order for quantum memories

M Goihl,N Walk,N Tarantino,J Eisert

doi:10.1103/physrevresearch.2.013120

M Goihl, N Walk + Show 2 more

Open Access

https://doi.org/10.1103/physrevresearch.2.013120

Copy DOI

Abstract

Spin chains with symmetry-protected edge modes are promising candidates to realize intrinsically robust physical qubits that can be used for the storage and processing of quantum information. In any experimental realization of such physical systems, weak perturbations in the form of induced interactions and disorder are unavoidable and can be detrimental to the stored information. At the same time, the latter may in fact be beneficial; for instance by deliberately inducing disorder which causes the system to localize. In this work, we explore the potential of using an $XZX$ cluster Hamiltonian to encode quantum information into the local edge modes and comprehensively investigate the influence of both many-body interactions and disorder on their stability over time, adding substance to the narrative that many-body localization may stabilize quantum information. We recover the edge state at each time step, allowing us to reconstruct the quantum channel that captures the locally constrained out of equilibrium time evolution. With this representation in hand, we analyze how well classical and quantum information are preserved over time as a function of disorder and interactions. We find that the performance of the edge qubits varies dramatically between disorder realizations. Whereas some show a smooth decoherence over time, a sizeable fraction are rapidly rendered unusable as memories. We also find that the stability of the classical information -- a precursor for the usefulness of the chain as a quantum memory -- depends strongly on the direction in which the bit is encoded. When employing the chain as a genuine quantum memory, encoded qubits are most faithfully recovered for low interaction and high disorder.

Highlights

The prospect of highly controllable quantum simulators [1,2,3,4] allows for the simulation of complex Hamiltonians, potentially realizing exotic phases of matter
Simple instances of these exist in one-dimensional spin chains, where one finds symmetry-protected topological phases (SPTs) which host emergent edge zero modes that enforce approximate degeneracies in the spectrum and define edge states which are dynamically decoupled from the bulk [8,9,10,11,12]
Largely unclear how stable information encoded into these systems will be when the system is perturbed away from its solvable point by spurious interactions and disorder, both of which are omnipresent in realistic experimental realizations

Summary

Introduction

The prospect of highly controllable quantum simulators [1,2,3,4] allows for the simulation of complex Hamiltonians, potentially realizing exotic phases of matter. A celebrated class of such phases is topological phases of matter, which offer the promise of robust encodings of quantum information with a reduced need for active error correction [5,6,7] Simple instances of these exist in one-dimensional spin chains, where one finds symmetry-protected topological phases (SPTs) which host emergent edge zero modes that enforce approximate degeneracies in the spectrum and define edge states which are dynamically decoupled from the bulk [8,9,10,11,12].

Methods

Results

Conclusion