Fundamental thresholds of realistic quantum error correction circuits from classical spin models

Vodola, Davide; Rispler, Manuel; Kim, Seyong; Müller, Markus

doi:10.48550/arxiv.2104.04847

Cited by 3 publications

(3 citation statements)

References 53 publications

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“…For uncorrelated disorder, outstanding properties of the system in the special subspace have been found useful in applications in many fields including statistical inference [37,, quantum error correction [39,[82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98], quantum Hall effect [99], and localization [100,101]. The present result may stimulate further developments in these fields in addition to the spin glass theory itself.…”

Section: Discussionmentioning

confidence: 59%

Analyticity of the energy in an Ising spin glass with correlated disorder

Nishimori

2022

J. Phys. A: Math. Theor.

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The average energy of the Ising spin glass is known to have no singularity along a special line in the phase diagram although there exists a critical point on the line. This result on the model with uncorrelated disorder is generalized to the case with correlated disorder. For a class of correlations in disorder that suppress frustration, we show that the average energy in a subspace of the phase diagram is expressed as the expectation value of a local gauge variable of the Z2 gauge Higgs model, from which we prove that the average energy has no singularity although the subspace is likely to have a phase transition on it. Though it is diﬃcult to obtain an explicit expression of the energy in contrast to the case of uncorrelated disorder, an exact closed-form expression of a physical quantity related to the energy is derived in three dimensions using a duality relation. Identities and inequalities are proved for the speciﬁc heat and correlation functions.

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Section: Discussionmentioning

confidence: 59%

Analyticity of the energy in an Ising spin glass with correlated disorder

Nishimori

2022

J. Phys. A: Math. Theor.

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“…For uncorrelated disorder, outstanding properties of the system in the special subspace have been found useful in applications in many fields including statistical inference [36,, quantum error correction [38,[81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97], quantum Hall effect [98], and localization [99,100]. The present result may stimulate further developments in these fields in addition to the spin glass theory itself.…”

Section: Discussionmentioning

confidence: 70%

Analyticity of the energy in an Ising spin glass with correlated disorder

Nishimori

2021

Preprint

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The average energy of the Ising spin glass is known to have no singularity along a special line in the phase diagram although there exists a critical point on the line. This result on the model with uncorrelated disorder is generalized to the case with correlated disorder. For a class of correlations in disorder that suppress frustration, we show that the average energy in a subspace of the phase diagram is expressed as the expectation value of a local gauge variable of the Z2 gauge Higgs model, from which we prove that the average energy has no singularity although the subspace is likely to have a phase transition on it. This is a generalization of the result for uncorrelated disorder. Though it is difficult to obtain an explicit expression of the energy in contrast to the case of uncorrelated disorder, an exact closed-form expression of a physical quantity related to the energy is derived in three dimensions using a duality relation. Identities and inequalities are proved for the specific heat and correlation functions.

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“…We address the problem by a combination of theoretical analyses and numerical simulations. Using a statistical-mechanical mapping method [6] that has previously produced error thresholds for codes beyond those for which it was initially conceived [25][26][27][28][29][30][31][32], we derive two statistical models related to Pauli errors of the X-cube model, in the formulation of classical spin variables that are suited for simulations. The numerical simulation of statistical models in three dimensions with randomness is generally challenging, and the required resources are even higher for our models as they possess lower-dimensional subsystem symmetries rather than a more conventional global symmetry.…”

mentioning

confidence: 99%

Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry

Song¹,

Schönmeier-Kromer²,

Liu³

et al. 2021

Preprint

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Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for quantum error correcting codes based on fracton models. By mapping the error-correction process for bit-flip and phase-flip noises into novel statistical models with Ising variables and random multi-body couplings, we obtain models that exhibit an unconventional subsystem symmetry instead of a more usual global symmetry. We perform large-scale parallel tempering Monte Carlo simulations to obtain disorder-temperature phase diagrams, which are then used to predict optimal error thresholds for the corresponding fracton code. Remarkably, we found that the X-cube fracton code displays a minimum error threshold (7.5%) that is much higher than 3D topological codes such as the toric code (3.3%), or the color code (1.9%). This result, together with the predicted absence of glass order at the Nishimori line, shows great potential for fracton phases to be used as quantum memory platforms.

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Fundamental thresholds of realistic quantum error correction circuits from classical spin models

Cited by 3 publications

References 53 publications

Analyticity of the energy in an Ising spin glass with correlated disorder

Analyticity of the energy in an Ising spin glass with correlated disorder

Analyticity of the energy in an Ising spin glass with correlated disorder

Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry

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