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001038568 005__ 20250131215342.0
001038568 0247_ $$2arXiv$$aarXiv:2311.14338
001038568 037__ $$aFZJ-2025-01551
001038568 088__ $$2arXiv$$aarXiv:2311.14338
001038568 1001_ $$0P:(DE-Juel1)184680$$aBotzung, Thomas$$b0
001038568 245__ $$aRobustness and measurement-induced percolation of the surface code
001038568 260__ $$c2025
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001038568 3367_ $$2ORCID$$aWORKING_PAPER
001038568 3367_ $$028$$2EndNote$$aElectronic Article
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001038568 3367_ $$2BibTeX$$aARTICLE
001038568 3367_ $$2DataCite$$aOutput Types/Working Paper
001038568 500__ $$a18 pages, 11 figures
001038568 520__ $$aWe examine the robustness of a logical qubit in the planar surface code subject to 'measurement-errors', i.e., to local Pauli measurements at known positions. This yields a measurement-only dynamics, which is driven by the competition between local Pauli measurements and stabilizer measurements. The setup differs from the conventional surface code for which errors are caused by decoherence and their positions are unknown. Yet, our setting allows us to examine the dynamics of the encoded logical qubit by using a combination of analytical arguments based on percolation theory and numerical simulations. Firstly, we show that for a single round of Pauli measurements only, the threshold corresponding to the irreversible loss of the logical qubit depends only on the rate of $ \hat X$- and $\hat Z$-measurements, and that this loss of logical quantum information is equivalent to the bond percolation transition in a 2D square lattice. Local $\hat Y$-measurements, which affect both $X$ and $Z$ stabilizers, erase the logical qubit only if all physical qubits along one of the diagonals are measured, and are thus negligible at large code distance. Secondly, we examine the dynamics in the code by considering the interplay between rounds of Pauli measurements and rounds of stabilizer measurements. Focusing on the lifetime of the logical qubit, we obtain a rich phase diagram featuring different dynamical regimes. We argue that the loss of the logical qubit in this setting can still be understood by percolation theory and underpin our arguments with numerical simulations.
001038568 536__ $$0G:(DE-HGF)POF4-5221$$a5221 - Advanced Solid-State Qubits and Qubit Systems (POF4-522)$$cPOF4-522$$fPOF IV$$x0
001038568 588__ $$aDataset connected to arXivarXiv
001038568 7001_ $$0P:(DE-HGF)0$$aBuchhold, Michael$$b1
001038568 7001_ $$0P:(DE-HGF)0$$aDiehl, Sebastian$$b2
001038568 7001_ $$0P:(DE-Juel1)179396$$aMüller, Markus$$b3$$eCorresponding author$$ufzj
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001038568 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)179396$$aForschungszentrum Jülich$$b3$$kFZJ
001038568 9131_ $$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
001038568 9141_ $$y2025
001038568 920__ $$lyes
001038568 9201_ $$0I:(DE-Juel1)PGI-2-20110106$$kPGI-2$$lTheoretische Nanoelektronik$$x0
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