Analytic asymptotic performance of topological codes

Fowler, Austin G.

doi:10.1103/physreva.87.040301

Cited by 20 publications

(26 citation statements)

References 43 publications

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“…[64][65][66]. In our case, one can find that this function provides a good fit to our numerical data.…”

Section: Appendix F: the Error Model And Charge Tunnelling Errorssupporting

confidence: 73%

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems

2016

Phys. Rev. Lett.

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Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g. superconducting circuits or quantum dots, is studied in this paper. Errors caused by topologically unprotected quantum systems need to be corrected with error correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer, and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about a thousand normal qubits.

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“…[64][65][66]. In our case, one can find that this function provides a good fit to our numerical data.…”

Section: Appendix F: the Error Model And Charge Tunnelling Errorssupporting

confidence: 73%

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems

2016

Phys. Rev. Lett.

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“…This can be translated to a lower bound on the decay rate α, although the bound is not expected to be tight. A different version of the method, proposed by Fowler [20], enables exact computation of P L in the asymptotic regime of small error rates p. In this regime the dominant contribution to P L comes from minimum-weight uncorrectable errors that span d/2 physical locations [47]. Accordingly, if the limit p → 0 is taken for a fixed code distance d, one can use an asymptotic formula P L = A d p d/2 , where A d is a constant coefficient.…”

Section: Introductionmentioning

confidence: 99%

Simulation of rare events in quantum error correction

Bravyi¹,

Vargo²

2013

Phys. Rev. A

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We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the splitting method widely used in Monte Carlo simulations of rare events and Bennett's acceptance ratio method for estimating the free energy difference between two canonical ensembles. To illustrate the power of these methods in the context of error correction, we calculate the logical error probability $P_L$ for the 2D surface code on a square lattice with a pair of holes for all code distances $d\le 20$ and all error rates $p$ below the fault-tolerance threshold. Our numerical results confirm the expected exponential decay $P_L\sim \exp{[-\alpha(p)d]}$ and provide a simple fitting formula for the decay rate $\alpha(p)$. Both noiseless and noisy syndrome readout circuits are considered.Comment: 16 pages, 11 figures. Version 3: added a new referenc

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“…For simplicity, our simulations are run with a periodic north-south boundary condition, which suffices for threshold comparison [41]. However for completeness, we summarize the decoder on lattices with boundary, along with our modifications to account for asymmetric error rates.…”

Section: Asymmetrically-weighted Union-find Decodingmentioning

confidence: 99%

2D Compass Codes

Miller

Newman

et al. 2019

Phys. Rev. X

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The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We explore threshold behavior in this broad class of local codes by trading locality for asymmetry and gauge degrees of freedom for stabilizer syndrome information. We analyze these codes with asymmetric and spatially inhomogeneous Pauli noise in the code capacity and phenomenological models. In these idealized settings, we observe considerably higher thresholds against asymmetric noise. At the circuit level, these codes inherit the bare-ancilla fault-tolerance of the Bacon-Shor code. arXiv:1809.01193v2 [quant-ph]

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Analytic asymptotic performance of topological codes

Cited by 20 publications

References 43 publications

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems

Simulation of rare events in quantum error correction

2D Compass Codes

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