Quantum memories with zero-energy Majorana modes and experimental constraints

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.

18 pages, 7 figures. Updated to published version

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Cited by in corpus (12)

• Braiding Majorana zero modes using quantum dots
• Enhancing correlation times for edge spins through dissipation
• The Uhlmann connection in fermionic systems undergoing phase transitions
• Strong zero modes in a class of generalised Ising spin ladders with plaquette interactions
• Modeling noise and error correction for Majorana-based quantum computing
• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• Phonon-induced Majorana Qubit Relaxation in Tunnel-Coupled Two-Island Topological Superconductors
• A Model for Topological p-wave Superconducting Wires with Disorder and Interactions
• Majorana Zero Modes in Fermionic Wires coupled by Aharonov-Bohm Cages
• Erasure conversion in Majorana qubits via local quasiparticle detection
• Dynamical Phase Error in Interacting Topological Quantum Memories
• Memory-Critical Dynamical Buildup of Phonon-Dressed Majorana Fermions