001038537 001__ 1038537
001038537 005__ 20250131215341.0
001038537 0247_ $$2arXiv$$aarXiv:2412.14004
001038537 037__ $$aFZJ-2025-01522
001038537 088__ $$2arXiv$$aarXiv:2412.14004
001038537 1001_ $$0P:(DE-Juel1)187504$$aRispler, Manuel$$b0$$ufzj
001038537 245__ $$aThe random coupled-plaquette gauge model and the surface code under circuit-level noise
001038537 260__ $$c2025
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001038537 3367_ $$2ORCID$$aWORKING_PAPER
001038537 3367_ $$028$$2EndNote$$aElectronic Article
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001038537 3367_ $$2BibTeX$$aARTICLE
001038537 3367_ $$2DataCite$$aOutput Types/Working Paper
001038537 520__ $$aWe map the decoding problem of the surface code under depolarizing and syndrome noise to a disordered spin model, which we call the random coupled-plaquette gauge model (RCPGM). By coupling X- and Z-syndrome volumes, this model allows us to optimally account for genuine Y-errors in the surface code in a setting with noisy measurements. Using Parallel Tempering Monte Carlo simulations, we determine the code's fundamental error threshold. Firstly, for the phenomenological noise setting we determine a threshold of $6\%$ under uniform depolarizing and syndrome noise. This is a substantial improvement compared to results obtained via the previously known 'uncoupled' random plaquette gauge model (RPGM) in the identical setting, where marginalizing Y-errors leads to a threshold of $4.3\%$. Secondly, we tackle the circuit-level noise scenario, where we use a reduction technique to find effective asymmetric depolarizing and syndrome noise rates to feed into the RCPGM mapping. Despite this reduction technique breaking up some of the correlations contained in the intricacies of circuit-level noise, we find an improvement exceeding that for the phenomenological case. We report a threshold of up to $1.4\%$, to be compared to $0.7\%$ under the identical noise model when marginalizing the Y-errors and mapping to the anisotropic RPGM. These results enlarge the landscape of statistical mechanical mappings for quantum error correction. In particular they provide an underpinning for the broadly held belief that accounting for Y-errors is a major bottleneck in improving surface code decoders. This is highly encouraging for leading efficient practical decoder development, where heuristically accounting for Y-error correlations has seen recent developments such as belief-matching. This suggests that there is further room for improvement of the surface code for fault-tolerant quantum computation.
001038537 536__ $$0G:(DE-HGF)POF4-5221$$a5221 - Advanced Solid-State Qubits and Qubit Systems (POF4-522)$$cPOF4-522$$fPOF IV$$x0
001038537 588__ $$aDataset connected to arXivarXiv
001038537 7001_ $$0P:(DE-HGF)0$$aVodola, Davide$$b1
001038537 7001_ $$0P:(DE-Juel1)204218$$aMüller, Markus$$b2$$eCorresponding author$$ufzj
001038537 7001_ $$0P:(DE-HGF)0$$aKim, Seyong$$b3
001038537 909CO $$ooai:juser.fz-juelich.de:1038537$$pVDB
001038537 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)187504$$aForschungszentrum Jülich$$b0$$kFZJ
001038537 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)204218$$aForschungszentrum Jülich$$b2$$kFZJ
001038537 9131_ $$0G:(DE-HGF)POF4-522$$1G:(DE-HGF)POF4-520$$2G:(DE-HGF)POF4-500$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$9G:(DE-HGF)POF4-5221$$aDE-HGF$$bKey Technologies$$lNatural, Artificial and Cognitive Information Processing$$vQuantum Computing$$x0
001038537 9141_ $$y2025
001038537 920__ $$lyes
001038537 9201_ $$0I:(DE-Juel1)PGI-2-20110106$$kPGI-2$$lTheoretische Nanoelektronik$$x0
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001038537 980__ $$aVDB
001038537 980__ $$aI:(DE-Juel1)PGI-2-20110106
001038537 980__ $$aUNRESTRICTED