Guang Hao Low, William J. Huggins, Dominic W. Berry, Tanuj Khattar, Alec F. White, Nicholas C. Rubin, Ryan Babbush (Jun 01 2026).
Abstract: We present a quantum code implementable on a regular
2D hex grid with an estimated encoding rate up to
4.5× 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
2d2 data and measurement qubits per patch. Assuming a
1μs surface code cycle time and a
10μs 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
89k 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× space and
6.6× spacetime improvement, respectively, over our previous state-of-the-art minimum-Toffoli resource estimates (Phys. Rev. X 15, 041016).
