Transversal architecture for megaquop-scale quantum simulation with neutral atoms

Quantum computing experiments have made remarkable progress in demonstrating key components of quantum error correction, a prerequisite for scalable quantum computation. While we anticipate the arrival of early fault-tolerant quantum hardware capable of a million reliable quantum operations, the cost of preparing low-noise `magic resource states' presents a formidable challenge. The recently proposed partially-fault-tolerant architecture based on a space-time efficient analog rotation (STAR) approach attempts to address this challenge by using post-selection to prepare low-noise, small-angle magic states. Its proposed physical implementation, however, assumes fixed qubit connectivity, resulting in implementation costs closer to leading 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 overhead. Through circuit-level simulations, we derive the logical noise model for surface-code-based transversal STAR gadgets and verify their composability. At its limit, the transversal STAR architecture can efficiently simulate local Hamiltonians with a total simulation volume exceeding 600. Achieving this limit would require approximately 10,000 physical qubits at a physical error rate of $10^{-3}$. This is equivalent to a fully-fault-tolerant computation requiring over $10^6$-$10^7$ $T$ 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 effective quantum simulation. We anticipate that the co-designed transversal STAR architecture could substantially reduce the physical resources necessary for early-fault-tolerant quantum simulation at the megaquop scale.