Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors

Abstract

Topological quantum computing is based on the notion of braiding non-Abelian anyons, such as Majorana zero modes (MZMs), to perform gate operations. A crucial building block of these protocols is the adiabatic shuttling of MZMs through topological superconductors. Here, we consider the "piano key" approach, where MZMs are transported using local electric gates to tune sections ("keys") of a wire between topologically trivial and nontrivial phases. We numerically simulate this transport on a single wire and calculate the diabatic error corresponding to exciting the system. We find that this error is typically reduced when transport is facilitated by using multiple keys as one may expect from modeling each piano key press as an effective Landau-Zener process. However, further increasing the number of keys increases errors; thus, there exists a nontrivial optimal number of keys that minimizes the diabatic error given a fixed total shuttle time. As we show, this optimal number of keys can be explained by modeling each key press as an effective Landau-Zener process while paying careful attention to power-law corrections that arise due to the nonanalytic behavior of the time-dependent modulation of the chemical potential at the beginning and end of each key press.

14 pages, 6 figures; v2: updated to reflect referee comments, typos corrected, additional references included. Published version

References in corpus (29)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Scaling of Majorana Zero-Bias Conductance Peaks
• Zero-bias anomaly in a nanowire quantum dot coupled to superconductors
• A Majorana smoking gun for the superconductor-semiconductor hybrid topological system
• Distinguishing a Majorana zero mode using spin resolved measurements
• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Flux-induced topological superconductivity in full-shell nanowires
• Signature of a pair of Majorana zero modes in superconducting gold surface states
• Controlled length-dependent interaction of Majorana modes in Yu-Shiba-Rusinov chains
• Spin-polarized Yu-Shiba-Rusinov states in an iron based superconductor
• Shortcuts to nonabelian braiding
• Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor
• Optimal Control of Majorana Zero Modes
• Topological Quantum Computing Using Nanowire Devices
• Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies
• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
• $\text{Draiding}$ majoranas to dynamically engineer Hamiltonians
• Effects of decoherence on diabatic errors in Majorana braiding
• Dynamical approach to improving Majorana qubits and distinguishing them from trivial bound states
• Transport probe of nonadiabatic transition caused by Majorana moving

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• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Majorana braiding simulations with projective measurements
• Shuttling Majorana zero modes in disordered and noisy topological superconductors
• Transport and fusion of Majorana zero modes in the presence of nonadiabatic transitions
• Majorana edge modes in isolated wires
• Probing nontrivial fusion of Majorana zero modes via near-adiabatic coupling