A Denser Planar Surface Code

• URL: http://arxiv.org/abs/2605.30455v1
• Date: Thu, 28 May 2026 18:27:34 GMT
• Title: A Denser Planar Surface Code
• Abstract summary: We present a quantum code implementable on a regular $2$D hex grid with an estimated encoding rate up to $4.5times$ of that of a rotated surface code patch.<n>We demonstrate a space-efficient architecture for computing on densely packed logical qubits.
• Score: 0.7669816560862509
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a quantum code implementable on a regular $2$D hex grid with an estimated encoding rate up to $4.5\times$ of that of a rotated surface code patch using circuit-level noise in a one- and two-qubit $10^{-3}$ error uniform depolarizing model. Our approach is based on yoking a dense packing of surface code twist defects, enabled by new stabilizer measurement cycles with an optimal four layers of nearest-neighbor two-qubit gates, almost no distance-reducing hook errors, and efficient decoding. We demonstrate a space-efficient architecture for computing on densely packed logical qubits, including new padding-free lattice surgery protocols in an optimal bounding box of $2d^2$ data and measurement qubits per patch. Assuming a $1μ$s surface code cycle time and a $10μ$s reaction time, these developments enable chemically accurate ground state phase estimation of a broad class of `utility-scale' electronic structure simulation problems such as the $108$ spin-orbital FeMoco-based nitrogen fixation catalyst in under a month with $89$k noisy superconducting qubits. We elucidate a Pareto frontier of space-time trade-offs and find a minimum physical quantum volume of $1.3$ mega-qubit-hours. These correspond to a $36\times$ space and $6.6\times$ spacetime improvement, respectively, over our previous state-of-the-art minimum-Toffoli resource estimates (Phys. Rev. X 15, 041016).

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