Dephasing and leakage dynamics of noisy Majorana-based qubits: Topological versus Andreev

Abstract

Topological quantum computation encodes quantum information nonlocally by nucleating non-Abelian anyons separated by distances $L$, typically spanning the qubit device size. This nonlocality renders topological qubits exponentially immune to dephasing from all sources of classical noise with operator support local on the scale of $L$. We perform detailed analytical and numerical analyses of a time-domain Ramsey-type protocol for noisy Majorana-based qubits that is designed to validate this coveted topological protection in near-term devices such as the so-called `tetron' design. By assessing dependence of dephasing times on tunable parameters, e.g., magnetic field, our proposed protocol can clearly distinguish a bona fide Majorana qubit from one constructed from semilocal Andreev bound states, which can otherwise closely mimic the true topological scenario in local probes. In addition, we analyze leakage of the qubit out of its low-energy manifold due to classical-noise-induced generation of quasiparticle excitations; leakage limits the qubit lifetime when the bulk gap collapses, and hence our protocol further reveals the onset of a topological phase transition. This experiment requires measurement of two nearby Majorana modes for both initialization and readout---achievable, for example, by tunnel coupling to a nearby quantum dot---but no further Majorana manipulations, and thus constitutes an enticing pre-braiding experiment. Along the way, we address conceptual subtleties encountered when discussing dephasing and leakage in the context of Majorana qubits.

22 pages, 12 figures

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• Protocol to identify a topological superconducting phase in a three-terminal device
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• Braiding-based quantum control of a Majorana qubit built from quantum dots
• Detecting Majorana modes by readout of poisoning-induced parity flips
• Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits
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• Dephasing of Majorana qubits due to quasistatic disorder
• Dynamical approach to improving Majorana qubits and distinguishing them from trivial bound states
• Implementation of single-qubit gates via parametric modulation in the Majorana transmon
• Capacitance-based Fermion parity read-out and predicted Rabi oscillations in a Majorana nanowire
• Realization of the Non-endpoint Majorana Bound States in an Extended Kitaev Chain
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• Erasure conversion in Majorana qubits via local quasiparticle detection
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires
• Tight-Binding Energy-Phase Calculation for Topological Josephson Junction Nanowire Architecture
• Decoherence of Majorana zero modes mediated by gapless fermions