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Increasing the distance of topological codes with time vortex defects

Quantum Science and Technology (arXiv overlay)

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Researchers Gilad Kishony and Erez Berg introduced "time vortices"—space-time defects in topological quantum error-correcting codes—to drastically reduce physical qubit requirements for fault tolerance. The technique modifies measurement sequences by adding spatially varying delays, creating defects where accumulated delay equals an integer multiple of the code’s period, enhancing error correction efficiency. Applied to the Floquet color code on a torus, the method optimizes vortex placement, asymptotically halving the qubits needed to achieve a given code distance compared to traditional approaches. Monte Carlo simulations with circuit-level noise show a 30-qubit vortexed code outperforms a 42-qubit vortex-free version, demonstrating superior error suppression with fewer resources. This advancement could accelerate practical quantum computing by lowering hardware demands while maintaining logical qubit reliability.

Increasing the distance of topological codes with time vortex defects

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AbstractWe propose modifying topological quantum error correcting codes by incorporating space-time defects, termed “time vortices,'' to reduce the number of physical qubits required to achieve a desired logical error rate. A time vortex is inserted by adding a spatially varying delay to the periodic measurement sequence defining the code such that the delay accumulated on a homologically non-trivial cycle is an integer multiple of the period. We analyze this construction within the framework of the Floquet color code and optimize the embedding of the code on a torus along with the choice of the number of time vortices inserted in each direction. Asymptotically, the vortexed code requires less than half the number of qubits as the vortex-free code to reach a given code distance. We benchmark the performance of the vortexed Floquet color code by Monte Carlo simulations with a circuit-level noise model and demonstrate that the smallest vortexed code (with $30$ qubits) outperforms the vortex-free code with $42$ qubits.► BibTeX data@article{Kishony2026increasingdistance, doi = {10.22331/q-2026-02-23-2006}, url = {https://doi.org/10.22331/q-2026-02-23-2006}, title = {Increasing the distance of topological codes with time vortex defects}, author = {Kishony, Gilad and Berg, Erez}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2006}, month = feb, year = {2026} }► References [1] Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill. Topological quantum memory. Journal of Mathematical Physics, 43 (9): 4452–4505, 09 2002. ISSN 0022-2488. 10.1063/1.1499754. URL https://doi.org/10.1063/1.1499754. https://doi.org/10.1063/1.1499754 [2] A.Yu. Kitaev. Fault-tolerant quantum computation by anyons. Annals of Physics, 303 (1): 2–30, 2003. ISSN 0003-4916. 10.1016/S0003-4916(02)00018-0. URL https://doi.org/10.1016/S0003-4916(02)00018-0. https://doi.org/10.1016/S0003-4916(02)00018-0 [3] Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A, 86: 032324, Sep 2012. 10.1103/PhysRevA.86.032324. URL https://doi.org/10.1103/PhysRevA.86.032324. https://doi.org/10.1103/PhysRevA.86.032324 [4] Keisuke Fujii. Quantum Computation with Topological Codes: From Qubit to Topological Fault-Tolerance, volume 8 of SpringerBriefs in Mathematical Physics. Springer Singapore, 2015. 10.1007/978-981-287-996-7. URL https://doi.org/10.1007/978-981-287-996-7. https://doi.org/10.1007/978-981-287-996-7 [5] Clarice Dias de Albuquerque, Eduardo Brandani da Silva, and Waldir Silva Soares Jr. Quantum Codes for Topological Quantum Computation. SpringerBriefs in Mathematics.

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Increasing the distance of topological codes with time vortex defects

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