Lifetime of topological quantum memories in thermal environment

Al-Shimary, Abbas; Wootton, James R.; Pachos, Jiannis K.

doi:10.1088/1367-2630/15/2/025027

Cited by 12 publications

(14 citation statements)

References 22 publications

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“…This demonstrates the important effect that the chosen lattice will have on coherence time, as expanded upon in Al-Shimary, Wootton, and Pachos (2013). Although this focuses primarily on thermal noise, its main purpose is to optimize the lattice in the case in which noise is biased toward certain kinds of errors, specifically, either bit flip or dephasing noise.…”

Section: Coherent Noise Suppressionmentioning

confidence: 90%

Quantum memories at finite temperature

et al. 2016

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To use quantum systems for technological applications one first needs to preserve their coherence for macroscopic time scales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum memory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of no-go theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. The state-of-the-art developments in this field are reviewed in an informative and pedagogical way. The main principles of self-correcting quantum memories are given and several milestone examples from the literature of two-, three-and higher-dimensional quantum memories are analyzed.

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Section: Coherent Noise Suppressionmentioning

confidence: 90%

Quantum memories at finite temperature

et al. 2016

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“…Previous work using related methods focused on the high-temperature scaling of decoherence times [30][31][32][33] ; here we focus on the dynamics at low temperatures. We find a low-temperature regime that is well described by thermal relaxation dominated by quasiparticle pairs undergoing topologically nontrivial random walks.…”

Section: Introductionmentioning

confidence: 99%

Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low-temperature regime

et al. 2014

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We present an analysis of the relaxation dynamics of finite-size topological qubits in contact with a thermal bath. Using a continuous-time Monte Carlo method, we explicitly compute the low-temperature nonequilibrium dynamics of the toric code on finite lattices. In contrast to the size-independent bound predicted for the toric code in the thermodynamic limit, we identify a lowtemperature regime on finite lattices below a size-dependent crossover temperature with nontrivial finite-size and temperature scaling of the relaxation time. We demonstrate how this nontrivial finite-size scaling is governed by the scaling of topologically nontrivial two-dimensional classical random walks. The transition out of this low-temperature regime defines a dynamical finite-size crossover temperature that scales inversely with the log of the system size, in agreement with a crossover temperature defined from equilibrium properties. We find that both the finite-size and finite-temperature scaling are stronger in the low-temperature regime than above the crossover temperature. Since this finite-temperature scaling competes with the scaling of the robustness to unitary perturbations, this analysis may elucidate the scaling of memory lifetimes of possible physical realizations of topological qubits.

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“…These thresholds are best compared with those for an equivalent code based on Z 2 anyons, and so with only a single qubit on each vertex. For independent bit and phase flips, the thresholds forX 1 andZ 1 are p c ≈ 16.4% and p c ≈ 6.7%, respectively [64,65]. When the hexagonal and triangular plaquettes are decoded separately, these correspond to thresholds of p c ≈ 24.6% and p c ≈ 10.5% for depolarizing noise.…”

Section: B Without Defectsmentioning

confidence: 99%

Parafermions in a Kagome Lattice of Qubits for Topological Quantum Computation

2015

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Engineering complex non-Abelian anyon models with simple physical systems is crucial for topological quantum computation. Unfortunately, the simplest systems are typically restricted to Majorana zero modes (Ising anyons). Here we go beyond this barrier, showing that the Z4 parafermion model of non-Abelian anyons can be realized on a qubit lattice. Our system additionally contains the Abelian D(Z4) anyons as low-energetic excitations. We show that braiding of these parafermions with each other and with the D(Z4) anyons allows the entire d = 4 Clifford group to be generated. The error correction problem for our model is also studied in detail, guaranteeing fault-tolerance of the topological operations. Crucially, since the non-Abelian anyons are engineered through defect lines rather than as excitations, non-Abelian error correction is not required. Instead the error correction problem is performed on the underlying Abelian model, allowing high noise thresholds to be realized.

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Lifetime of topological quantum memories in thermal environment

Cited by 12 publications

References 22 publications

Quantum memories at finite temperature

Quantum memories at finite temperature

Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low-temperature regime

Parafermions in a Kagome Lattice of Qubits for Topological Quantum Computation

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