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Paper 1
Dense packing of the surface code: code deformation procedures and hook-error-avoiding gate scheduling
Kohei Fujiu, Shota Nagayama, Shin Nishio, Hideaki Kawaguchi, Takahiko Satoh
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2511.06758
- arXiv
- 2511.06758
The surface code is one of the leading quantum error correction codes for realizing large-scale fault-tolerant quantum computing (FTQC). One major challenge in realizing surface-code-based FTQC is the extremely large number of qubits required. To mitigate this problem, fusing multiple codewords of the surface code into a densely packed configuration has been proposed. It is known that by using dense packing, the number of physical qubits required per logical qubit can be reduced to approximately three-fourths compared to simply placing surface-code patches side by side. Despite its potential, concrete deformation procedures and quantitative error-rate analyses have remained largely unexplored. In this work, we present a detailed code-deformation procedure that transforms multiple standard surface code patches into a densely packed, connected configuration, along with a conceptual microarchitecture to utilize this dense packing. We also propose a CNOT gate-scheduling for stabilizer measurement circuits that suppresses hook errors in the densely packed surface code. We performed circuit-level Monte Carlo noise simulation of densely packed surface codes using this gate scheduling. The numerical results demonstrate that as the code distance of the densely packed surface code increases and the physical error rate decreases, the logical error rate of the densely packed surface code becomes lower than that of the standard surface code. Furthermore, we find that only when employing hook-error-avoiding syndrome extraction can the densely packed surface code achieve a lower logical error rate than the standard surface code, while simultaneously reducing the space overhead.
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Spatial inversion symmetry breaking of vortex current in biased-ladder superfluid
Weijie Huang, Yao Yao
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2307.15889
- arXiv
- 2307.15889
We investigate the quench dynamics of interacting bosons on a two-leg ladder in presence of a uniform Abelian gauge field. The model hosts a variety of emergent quantum phases, and we focus on the superfluid biased-ladder phase breaking the $Z_{2}$ symmetry of two legs. We observe an asymmetric spreading of vortex current and particle density, i.e., the current behaves particle-like on the right and wave-like on the left, indicating spontaneous breaking of the spatial inversion symmetry. By decreasing the repulsion strength, it is found the particle-like current is more robust than the wave-like one. The evolution of entanglement entropy manifests logarithmic growth with time suggesting many-body localization matters.
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