Breakdown of surface-code error correction due to coupling to a bosonic bath

Hutter, Adrian; Loss, Daniel

doi:10.1103/physreva.89.042334

Cited by 21 publications

(28 citation statements)

References 27 publications

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“…These errors can be corrected in future cycles of error-correction, provided the remaining noise is of a form that a decoder can correct. In general, however, one must worry that large correlated errors can be introduced that adversarially corrupt encoded information 45 46 47 48 49 50 . Such errors may occur in the gauge color code if, for instance, we mistakenly predict two stabilizer defects of the same color that are separated by a large distance.…”

Section: Resultsmentioning

confidence: 99%

Fault-tolerant error correction with the gauge color code

2016

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The constituent parts of a quantum computer are inherently vulnerable to errors. To this end, we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a universal set of computational operations with the minimal cost in quantum resources remains an important and ongoing challenge. One proposal of significant recent interest is the gauge color code. Notably, this code may offer a reduced resource cost over other well-studied fault-tolerant architectures by using a new method, known as gauge fixing, for performing the non-Clifford operations that are essential for universal quantum computation. Here we examine the gauge color code when it is subject to noise. Specifically, we make use of single-shot error correction to develop a simple decoding algorithm for the gauge color code, and we numerically analyse its performance. Remarkably, we find threshold error rates comparable to those of other leading proposals. Our results thus provide the first steps of a comparative study between the gauge color code and other promising computational architectures.

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Section: Resultsmentioning

confidence: 99%

Fault-tolerant error correction with the gauge color code

2016

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“…Each L n (t) for echo in case of both single-and two-qubit coherences, can be calculated according to Eqs. (12)(13)(14)(15)(16), with Hamiltonian of the environment consisting only of the Zeeman splitting of considered nucleus. When transverse couplings to the qubit are negligible, as in our case, when the whole system is in magnetic field B >100 mT, non-interacting bath of nuclei does not give any contribution to decoherence, i.e., L n (t) = 1.…”

Section: Calculation Of Two-qubit Decoherencementioning

confidence: 99%

“…For the calculation of each L kl (t), we need to consider qubit(s) interacting with a pair of nuclei k and l and now the Hamiltonian of the environment, as in procedure described in Eqs. (12)(13)(14)(15)(16) contains not only Zeeman splittings of each of the nuclei, but also coupling between them. In this paper, we shall use the dipolar interaction as described in Eq.…”

Section: Calculation Of Two-qubit Decoherencementioning

confidence: 99%

Decoherence of two entangled spin qubits coupled to an interacting sparse nuclear spin bath: Application to nitrogen vacancy centers

Kwiatkowski

Cywiński

2018

Phys. Rev. B

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We consider pure dephasing of Bell states of electron spin qubits interacting with a sparse bath of nuclear spins. Using the newly developed two-qubit generalization of cluster correlation expansion method, we calculate the spin echo decay of |Ψ and |Φ states for various interqubit distances. Comparing the results with calculations in which dephasing of each qubit is treated independently, we identify signatures of influence of common part of the bath on the two qubits. At large interqubit distances, this common part consists of many nuclei weakly coupled to both qubits, so that decoherence caused by it can be modeled by considering multiple uncorrelated sources of noise (clusters of nuclei), each of them weakly affecting the qubits. Consequently, the resulting genuinely two-qubit contribution to decoherence can be described as being caused by classical Gaussian noise. On the other hand, for small interqubit distances the common part of the environment contains clusters of spins that are strongly coupled to both qubits, and their contribution to two-qubit dephasing has visibly non-Gaussian character. We show that one van easily obtain information about non-Gaussianity of environmental noise affecting the qubits from the comparison of dephasing of |Ψ and |Φ Bell states. Numerical results are obtained for two nitrogen vacancy centers interacting with a bath of 13 C nuclei of natural concentration, for which we obtain that Gaussian description of correlated part of environmental noise starts to hold for centers separated by about 3 nm. arXiv:1806.06845v2 [cond-mat.mes-hall]

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“…Let the latent probability (correlation) of an error-induced in pairwise with the center and one of four qubits be 0 ≤ p (m * ,n * ),(m,n) ≡ p * 1 ≤ 1/2. In this case, the error probability of the center qubit in subset (N sub1 = 5) is given by the following [13]:…”

Section: Semi-classical Description Of Nonlinear Local Correlated Errorsmentioning

confidence: 99%

Introduction to Semi-Classical Analysis for Digital Errors of Qubit in Quantum Processor

Hirota

2021

Entropy

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In recent years, remarkable progress has been achieved in the development of quantum computers. For further development, it is important to clarify properties of errors by quantum noise and environment noise. However, when the system scale of quantum processors is expanded, it has been pointed out that a new type of quantum error, such as nonlinear error, appears. It is not clear how to handle such new effects in information theory. First of all, one should make the characteristics of the error probability of qubits clear as communication channel error models in information theory. The purpose of this paper is to survey the progress for modeling the quantum noise effects that information theorists are likely to face in the future, to cope with such nontrivial errors mentioned above. This paper explains a channel error model to represent strange properties of error probability due to new quantum noise. By this model, specific examples on the features of error probability caused by, for example, quantum recurrence effects, collective relaxation, and external force, are given. As a result, it is possible to understand the meaning of strange features of error probability that do not exist in classical information theory without going through complex physical phenomena.

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Breakdown of surface-code error correction due to coupling to a bosonic bath

Cited by 21 publications

References 27 publications

Fault-tolerant error correction with the gauge color code

Fault-tolerant error correction with the gauge color code

Decoherence of two entangled spin qubits coupled to an interacting sparse nuclear spin bath: Application to nitrogen vacancy centers

Introduction to Semi-Classical Analysis for Digital Errors of Qubit in Quantum Processor

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