The Nature and Correction of Diabatic Errors in Anyon Braiding

Knapp, Christina; Zaletel, Michael P.; Liu, Dong E.; Cheng, Meng; Bonderson, Parsa; Nayak, Chetan

doi:10.1103/physrevx.6.041003

Cited by 71 publications

(87 citation statements)

References 68 publications

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“…4, frequency estimates given in Ref. [59], and E C = 160 μeV (see Ref. [20]), we estimate ω ∼ 100 MHz.…”

supporting

confidence: 54%

A Roadmap for a Scalable Topological Quantum Computer

2017

Physics

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We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues:(1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological T junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

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“…4, frequency estimates given in Ref. [59], and E C = 160 μeV (see Ref. [20]), we estimate ω ∼ 100 MHz.…”

supporting

confidence: 54%

A Roadmap for a Scalable Topological Quantum Computer

2017

Physics

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“…A possible avenue for exploring parity effects would involve coupling the Majorana wire to a charge sensitive system, such as a quantum dot, a single electron transistor, or a scanning tunneling microscope(STM) tip 25,89,[98][99][100][101][102] . Other methods which have gained prominence in the Majorana mode context include coupling to microwave cavity, circuit quantum electrodynamics, cooper pair boxes and Transmon systems seem to show promise and have gained much attention, especially as they directly couple to the parity sectors arising from the Majorana modes 92,[103][104][105][106][107][108][109] . There have also been several proposals for realization of topological systems hosting Majorana modes in cold atomic systems [110][111][112] .…”

Section: Discussionmentioning

confidence: 99%

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Hegde¹,

Vishveshwara²

2016

Phys. Rev. B

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We study the decay and oscillations of Majorana fermion wavefunctions and ground state (GS) fermion parity in one-dimensional topological superconducting lattice systems. Using a Majorana transfer matrix method, we find that Majorana wavefunction properties are encoded in the associated Lyapunov exponent, which in turn is the sum of two independent components: a 'superconducting component' which characterizes the gap induced decay, and the 'normal component', which determines the oscillations and response to chemical potential configurations. The topological phase transition separating phases with and without Majorana end modes is seen to be a cancellation of these two components. We show that Majorana wavefunction oscillations are completely determined by an underlying non-superconducting tight-binding model and are solely responsible for GS fermion parity switches in finite-sized systems. These observations enable us to analytically chart out wavefunction oscillations, the resultant GS parity configuration as a function of parameter space in uniform wires, and special parity switch points where degenerate zero energy Majorana modes are restored in spite of finite size effects. For disordered wires, we find that band oscillations are completely washed out leading to a second localization length for the Majorana mode and the remnant oscillations are randomized as per Anderson localization physics in normal systems. Our transfer matrix method further allows us to i) reproduce known results on the scaling of mid-gap Majorana states and demonstrate the origin of its log-normal distribution, ii) identify contrasting behavior of disorder-dependent GS parity switches for the cases of even versus odd number of lattice sites, and iii) chart out the GS parity configuration and associated parity switch points as a function of disorder strength.

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“…For this lower bound on δ 0 , the adiabatic decoupling time scale

δ t = 2 ℏ / δ_{0}

in Figure would be on the order of 1 ns, and the total duration of the fusion process

t_{0} ≳ 10 ℏ / δ_{0} ≳ 10 ns

. These operation times are at the lower end of those considered in the context of braiding experiments . They are still well below quasiparticle poisoning times, which in ideal circumstances can be as large as

1 μ s

…”

Section: Resultsmentioning

confidence: 88%

Dynamical Signatures of Ground‐State Degeneracy to Discriminate against Andreev Levels in a Majorana Fusion Experiment

2019

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Detection of the fusion rule of Majora na zero‐modes is a near‐term milestone on the road to topological quantum computation. An obstacle is that the non‐deterministic fusion outcome of topological zero‐modes can be mimicked by the merging of non‐topological Andreev levels. To distinguish these two scenarios, the dynamical signatures of the ground‐state degeneracy that is the defining property of non‐Abelian anyons is searched for. By adiabatically traversing parameter space along two different pathways, one can identify ground‐state degeneracies from the breakdown of adiabaticity. It is shown that the approach can discriminate against accidental degeneracies of Andreev levels.

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The Nature and Correction of Diabatic Errors in Anyon Braiding

Cited by 71 publications

References 68 publications

A Roadmap for a Scalable Topological Quantum Computer

A Roadmap for a Scalable Topological Quantum Computer

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Dynamical Signatures of Ground‐State Degeneracy to Discriminate against Andreev Levels in a Majorana Fusion Experiment

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