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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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Paper 2

Simulation of quantum computation with magic states via Jordan-Wigner transformations

Michael Zurel, Lawrence Z. Cohen, Robert Raussendorf

Year

2023

Journal

arXiv preprint

DOI

arXiv:2307.16034

arXiv

2307.16034

Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the magic state model. It is based on generalized Jordan-Wigner transformations, and it has a close connection to the probability representation of universal quantum computation based on the $Λ$ polytopes. For each number of qubits, it defines a polytope contained in the $Λ$ polytope with some shared vertices. It leads to an efficient classical simulation algorithm for magic state quantum circuits for which the input state is positively represented, and it outperforms previous representations in terms of the states that can be positively represented.

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