Quantum memories with zero-energy Majorana modes and experimental constraints

TL;DR

This paper investigates the potential and limitations of using zero-energy Majorana modes for quantum memory under experimental constraints, analyzing recovery operations, noise effects, and the role of the energy gap.

Contribution

It characterizes the optimal recovery operations on Majorana modes and compares information retrieval capabilities under different noise models and system sizes.

Findings

Recovery on zero-modes alone can be ineffective against certain noise models.

Memory fidelity decays exponentially over time in thermal environments.

The Hamiltonian gap remains beneficial for information storage despite experimental limitations.

Abstract

In this work we address the problem of realizing a reliable quantum memory based on zero-energy Majorana modes in the presence of experimental constraints on the operations aimed at recovering the information. In particular, we characterize the best recovery operation acting only on the zero-energy Majorana modes and the memory fidelity that can be therewith achieved. In order to understand the effect of such restriction, we discuss two examples of noise models acting on the topological system and compare the amount of information that can be recovered by accessing either the whole system, or the zero-modes only, with particular attention to the scaling with the size of the system and the energy gap. We explicitly discuss the case of a thermal bosonic environment inducing a parity-preserving Markovian dynamics in which the introduced memory fidelity decays exponentially in time, independent from system size, thus showing the impossibility to retrieve the information by acting on the zero-modes only. We argue, however, that even in the presence of experimental limitations, the Hamiltonian gap is still beneficial to the storage of information.