Error generation and propagation in Majorana-based topological qubits
arXiv:1905.06923 · doi:10.1103/PhysRevB.100.134307
Abstract
We investigate dynamical evolution of a topological memory that consists of two p-wave superconducting wires separated by a non-topological junction, focusing on the primary errors (i.e., qubit-loss) and secondary errors (bit and phase-flip) that arise due to non-adiabaticity. On the question of qubit-loss we examine the system's response to both periodic boundary driving and deliberate shuttling of the Majorana bound states. In the former scenario we show how the frequency dependent rate of qubit-loss is strongly correlated with the local density of states at the edge of wire, a fact that can make systems with a larger gap more susceptible to high frequency noise. In the second scenario we confirm previous predictions concerning super-adiabaticity and critical velocity, but see no evidence that the coordinated movement of edge boundaries reduces qubit-loss. Our analysis on secondary bit flip errors shows that it is necessary that non-adiabaticity occurs in both wires and that inter-wire tunnelling be present for this error channel to be open. We also demonstrate how such processes can be minimised by disordering central regions of both wires. Finally we identify an error channel for phase flip errors, which can occur due to mismatches in the energies of states with bulk excitations. In the non-interacting system considered here this error systematically opposes the expected phase rotation due to finite size splitting in the qubit subspace.
arXiv comment13 pages, 13 figures
References in corpus (61)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Anyons in an exactly solved model and beyond
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Unpaired Majorana fermions in quantum wires
- Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- Helical liquids and Majorana bound states in quantum wires
- Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
- Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
- Non-Abelian statistics and topological quantum information processing in 1D wire networks
- Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
- Exponential Protection of Zero Modes in Majorana Islands
- Majorana bound states in a coupled quantum-dot hybrid-nanowire system
- Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
- Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
- Majorana fermions in chains of magnetic atoms on a superconductor
- Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
- Quantized Majorana conductance
- Milestones toward Majorana-based quantum computing
- Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling
- End states and subgap structure in proximity-coupled chains of magnetic adatoms
- Ballistic Majorana nanowire devices
- Probing Atomic Structure and Majorana Wavefunctions in Mono-Atomic Fe-chains on Superconducting Pb-Surface
- Majorana qubit decoherence by quasiparticle poisoning
- Majorana box qubits
- Majorana edge states in interacting one-dimensional systems
- Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
- Majorana fermions in superconducting nanowires without spin-orbit coupling
- Probability distribution of Majorana end-state energies in disordered wires
- Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling
- Majorana fermions in superconducting helical magnets
- Andreev reflection from non-centrosymmetric superconductors and Majorana bound state generation in half-metallic ferromagnets
- Failure of protection of Majorana based qubits against decoherence
- Topological superconductivity and Majorana fermions in half-metal / superconductor heterostructure
- Universal quantum computation on a semiconductor quantum wire network
- Decay rates for topological memories encoded with Majorana fermions
- Non-adiabatic Effects in the Braiding of Non-Abelian Anyons in Topological Superconductors
- Non-adiabatic processes in Majorana qubit systems
- Topological Protection of Majorana Qubits
- Dephasing of Majorana-based qubits
- How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
- Decoherence of Majorana qubits by noisy gates
- Exact Solution to Interacting Kitaev Chain at Symmetric Point
- Majorana braiding with thermal noise
- Quantum Computing with Majorana Fermion Codes
- Shortcuts to nonabelian braiding
- Boosting Majorana zero modes
- Optimal Control of Majorana Zero Modes
- Robustness of quantum memories based on Majorana zero modes
- Dynamics of Majorana-based qubits operated with an array of tunable gates
- Robustness of Majorana edge modes and topological order -- exact results for the symmetric interacting Kitaev chain with disorder
- Many-body Majorana operators and the equivalence of parity sectors
- Exact Zero Modes in Closed Systems of Interacting Fermions
- Dynamical formation and manipulation of Majorana fermions in driven quantum wires
- Multi-particle content of Majorana zero-modes in the interacting p-wave wire
- Lifetime of Majorana qubits in Rashba nanowires with non-uniform chemical potential
- Degeneracy lifting of Majorana bound states due to electron-phonon interactions
- Optimal diabatic dynamics of Majorana-based quantum gates
- Modeling noise and error correction for Majorana-based quantum computing
- Decoherence Patterns of Topological Qubits from Majorana Modes
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- Transport probe of nonadiabatic transition caused by Majorana moving
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- Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
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