Fast and Parallel High-Rate STAR Architecture for Megaquop Quantum Simulation

Fault-tolerant quantum simulation is approaching a phase where encoding overhead, logical Clifford operations, magic-state preparation, and rotation synthesis must be optimized together for efficient implementation. Space-Time efficient Analog Rotation (STAR) architectures reduce two of these costs by preparing small-angle rotation magic states directly, and the transversal STAR variant further lowers the Clifford overhead. Existing concrete implementations, however, largely inherit the low O\(1/d²\) encoding rate of the surface code, while high-rate codes have not yet been integrated into comparably explicit architectures. Here, we introduce a high-rate STAR architecture for local lattice Hamiltonian simulation based on a symmetry-driven co-design of the algorithm, QEC code, and neutral-atom hardware. Translation symmetries of the target lattice determine the choice of bicycle chain codes, a tunable family of self-dual bivariate bicycle codes that natively implement Clifford gates required for lattice simulation. Disjoint logical representatives allow STAR injections to be performed in parallel on all k logical qubits in a code block, amortizing resource state preparation and enabling practical post-selection rates. On neutral-atom platform, the same translation symmetry compiles the key logical operations into low-depth, hardware-native acousto-optic-deflector shifts. End-to-end estimates show that an 8 times 8 transverse-field Ising simulation to T^* approx 8 (zJ)^-1 requires 2240 physical qubits and sim 200 s per shot, a sim 5.5times space reduction relative to a surface code STAR baseline at comparable speed; for Fermi-Hubbard dynamics to T^* approx 4 (zt)^-1, the corresponding estimates are sim 6300 physical qubits and sim 200 s per shot. These results provide a concrete route toward early fault-tolerant quantum simulation with high-rate codes.