A Denser Planar Surface Code

We present a quantum code implementable on a regular 2D hex grid with an estimated encoding rate up to 4.5times 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 36times space and 6.6times spacetime improvement, respectively, over our previous state-of-the-art minimum-Toffoli resource estimates (Phys. Rev. X 15, 041016).