Two Layers, No Swaps: Biplanar SPOQC Architecture Improves Runtime of Fermi-Hubbard Simulation

TL;DR

This paper proposes a biplanar SPOQC architecture for simulating the 2D Fermi-Hubbard model, reducing runtime by eliminating fermionic swaps and optimizing circuit depth, with detailed noise and error analysis.

Contribution

It introduces a novel biplanar architecture that improves simulation efficiency by co-designing the hardware and algorithm, reducing circuit depth and error sources.

Findings

Reduced Trotter step depth from 6 to 4t_synth + 90 logical timesteps.

Estimated 2-hour runtime for an 8x8 lattice with 1.35 million qubits.

Rotation synthesis failure probability becomes a scalability bottleneck.

Abstract

We estimate the cost of simulating the two-dimensional Fermi-Hubbard model on a biplanar spin-optical quantum computing (SPOQC) architecture. Qubits are encoded in the honeycomb Floquet code, and we use a circuit-level noise model with explicit timings for each native physical operation. We benchmark lattice surgery and magic state preparation within each plane, and transversal CNOT gates between corresponding logical qubits across planes. We compile a plaquette-based Trotterization of the time evolution operator, mapping the two spin sectors of the Fermi-Hubbard model onto two physical planes. This architectural co-design eliminates fermionic swap operations and reduces the depth of each Trotter step to $4t_{\mathrm{synth}} + 90$ logical timesteps, where $t_\mathrm{synth}$ is the logical timestep cost of arbitrary-angle rotations, compared to $6t_\mathrm{synth} + 354$ in prior single-plane compilations. All error sources - algorithmic (Trotter), logical noise, magic state infidelity, and rotation synthesis - are treated jointly within a single 1% diamond norm budget. For an $L\times L$ lattice with hopping amplitude $t$ and on-site interaction strength $U$, setting $L=8$ and $U/t=8$, we estimate a total runtime of approximately $2$ hours using $1.35\times 10^6$ physical qubits. We find that fallback-based rotation synthesis methods become a scalability bottleneck: the probability that all $L^2$ parallel rotations succeed on the first attempt vanishes exponentially with system size, causing the failure branch to dominate the expected runtime already at moderate $L$.