Transversal STAR architecture for megaquop-scale quantum simulation with neutral atoms Part 1.

Recent progress in quantum error correction anticipates an early era of fault-tolerant quantum computers, with millions of reliable quantum operations, but the cost of preparing low-noise magic states remains challenging. The proposed partially-fault-tolerant STAR architecture attempted to address this challenge by using post-selection to prepare low-noise, small-angle magic. Its envisioned physical implementation, however, assumes fixed qubit connectivity, resulting in implementation costs closer to fully-fault-tolerant approaches. Here, we propose the transversal STAR architecture and co-design it with neutral-atom quantum hardware, deriving significant savings in logical layout, time, and space. Through circuit-level simulations, we derive the logical noise model for surface-code-based transversal gadgets and verify their composability. At its limit, the transversal STAR can efficiently simulate local Hamiltonians with a total simulation volume >600. Achieving this limit requires 10,000 physical qubits at a physical error rate of 10-3. This is equivalent to a fully-fault-tolerant computation requiring 106-107 T gates. Finally, we extend the transversal STAR architecture to high-rate quantum codes, demonstrating how a limited set of highly parallel transversal Clifford gates and generalized small-angle magic injection can be utilized for local Hamiltonian simulation, thus substantially reducing the physical resources necessary for megaquop-scale quantum simulation.