001038535 001__ 1038535
001038535 005__ 20250131215341.0
001038535 0247_ $$2arXiv$$aarXiv:2412.16727
001038535 037__ $$aFZJ-2025-01520
001038535 088__ $$2arXiv$$aarXiv:2412.16727
001038535 1001_ $$0P:(DE-HGF)0$$aColmenarez, Luis$$b0
001038535 245__ $$aFundamental thresholds for computational and erasure errors via the coherent information
001038535 260__ $$c2025
001038535 3367_ $$0PUB:(DE-HGF)25$$2PUB:(DE-HGF)$$aPreprint$$bpreprint$$mpreprint$$s1738310894_12723
001038535 3367_ $$2ORCID$$aWORKING_PAPER
001038535 3367_ $$028$$2EndNote$$aElectronic Article
001038535 3367_ $$2DRIVER$$apreprint
001038535 3367_ $$2BibTeX$$aARTICLE
001038535 3367_ $$2DataCite$$aOutput Types/Working Paper
001038535 500__ $$a31 pages, 14 figures
001038535 520__ $$aQuantum error correcting (QEC) codes protect quantum information against environmental noise. Computational errors caused by the environment change the quantum state within the qubit subspace, whereas quantum erasures correspond to the loss of qubits at known positions. Correcting either type of error involves different correction mechanisms, which makes studying the interplay between erasure and computational errors particularly challenging. In this work, we propose a framework based on the coherent information (CI) of the mixed-state density operator associated to noisy QEC codes, for treating both types of errors together. We show how to rigorously derive different families of statistical mechanics mappings for generic stabilizer QEC codes in the presence of both types of errors. We observe that the erasure errors enter as a classical average over fully depolarizing channels. Further, we show that computing the CI for erasure errors only can be done efficiently upon sampling over erasure configurations. We then test our approach on the 2D toric and color codes and compute optimal thresholds for erasure errors only, finding a $50\%$ threshold for both codes. This strengthens the notion that both codes share the same optimal thresholds. When considering both computational and erasure errors, the CI of small-size codes yields thresholds in very accurate agreement with established results that have been obtained in the thermodynamic limit. We thereby further establish the CI as a practical tool for studying optimal thresholds under realistic noise and as a means for uncovering new relations between QEC codes and statistical physics models.
001038535 536__ $$0G:(DE-HGF)POF4-5221$$a5221 - Advanced Solid-State Qubits and Qubit Systems (POF4-522)$$cPOF4-522$$fPOF IV$$x0
001038535 588__ $$aDataset connected to arXivarXiv
001038535 7001_ $$0P:(DE-HGF)0$$aKim, Seyong$$b1
001038535 7001_ $$0P:(DE-Juel1)204218$$aMüller, Markus$$b2$$eCorresponding author$$ufzj
001038535 909CO $$ooai:juser.fz-juelich.de:1038535$$pVDB
001038535 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)204218$$aForschungszentrum Jülich$$b2$$kFZJ
001038535 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$$x0
001038535 9141_ $$y2025
001038535 920__ $$lyes
001038535 9201_ $$0I:(DE-Juel1)PGI-2-20110106$$kPGI-2$$lTheoretische Nanoelektronik$$x0
001038535 980__ $$apreprint
001038535 980__ $$aVDB
001038535 980__ $$aI:(DE-Juel1)PGI-2-20110106
001038535 980__ $$aUNRESTRICTED