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<p>Quantum error correction<sup><CitationRef AdditionalCitationIDS="CR2 CR3" CitationID="CR1">1</CitationRef>–<CitationRef CitationID="CR4">4</CitationRef></sup> is essential for bridging the gap between the error rates of physical devices and the extremely low error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors<sup><CitationRef AdditionalCitationIDS="CR6 CR7" CitationID="CR5">5</CitationRef>–<CitationRef CitationID="CR8">8</CitationRef></sup> have focused primarily on the surface code<sup><CitationRef CitationID="CR9">9</CitationRef></sup>, which offers a high error threshold but poses limitations for logical operations. The colour code<sup><CitationRef CitationID="CR10">10</CitationRef></sup> enables more efficient logic, but it requires more complex stabilizer measurements and decoding. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and realizations of colour codes<sup><CitationRef AdditionalCitationIDS="CR12 CR13 CR14 CR15 CR16 CR17 CR18" CitationID="CR11">11</CitationRef>–<CitationRef CitationID="CR19">19</CitationRef></sup> have not addressed performance scaling with code size on any platform. Here we present a comprehensive demonstration of the colour code on a superconducting processor<sup><CitationRef CitationID="CR8">8</CitationRef></sup>. Scaling the code distance from three to five suppresses logical errors by a factor of <i>Λ</i><sub>3/5</sub> = 1.56(4). Simulations indicate this performance is below the threshold of the colour code, and the colour code may become more efficient than the surface code following modest device improvements. We test transversal Clifford gates with logical randomized benchmarking<sup><CitationRef CitationID="CR20">20</CitationRef></sup> and inject magic states<sup><CitationRef CitationID="CR21">21</CitationRef></sup>, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection. Finally, we teleport logical states between colour codes using lattice surgery<sup><CitationRef CitationID="CR22">22</CitationRef></sup>. This work establishes the colour code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.</p>

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Scaling and logic in the colour code on a superconducting quantum processor

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月26日

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  • N. Lacroix,
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摘要

Quantum error correction1–4 is essential for bridging the gap between the error rates of physical devices and the extremely low error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting processors5–8 have focused primarily on the surface code9, which offers a high error threshold but poses limitations for logical operations. The colour code10 enables more efficient logic, but it requires more complex stabilizer measurements and decoding. Measuring these stabilizers in planar architectures such as superconducting qubits is challenging, and realizations of colour codes11–19 have not addressed performance scaling with code size on any platform. Here we present a comprehensive demonstration of the colour code on a superconducting processor8. Scaling the code distance from three to five suppresses logical errors by a factor of Λ3/5 = 1.56(4). Simulations indicate this performance is below the threshold of the colour code, and the colour code may become more efficient than the surface code following modest device improvements. We test transversal Clifford gates with logical randomized benchmarking20 and inject magic states21, a key resource for universal computation, achieving fidelities exceeding 99% with post-selection. Finally, we teleport logical states between colour codes using lattice surgery22. This work establishes the colour code as a compelling research direction to realize fault-tolerant quantum computation on superconducting processors in the near future.