Casey Duckering

We present a low-overhead architecture that supports the layout and resource estimation of large-scale fault-tolerant quantum algorithms. Utilizing recent advances in fault tolerance with transversal gate operations, this architecture achieves a run time speed-up on the order of the code distance d, which we find directly translates to run time improvements of large-scale quantum algorithms. Our architecture consists of functional building blocks of key algorithmic subroutines, including magic state factories, quantum arithmetic units, and quantum look-up tables. These building blocks are implemented using efficient transversal operations, and we design space-time-efficient versions of them that minimize interaction distance, thereby reducing atom move times and minimizing the volume for correlated decoding. We further propose models to estimate their logical error performance. We perform resource estimation for a large-scale implementation of Shor's factoring algorithm, one of the prototypical benchmarks for large-scale quantum algorithms, on dynamically reconfigurable neutral atom arrays, finding that 2048-bit RSA factoring can be executed with 19 million qubits in 5.6 days, for 1 ms QEC cycle times. This represents close to 50x speed-up of the run-time compared to existing estimates with similar assumptions, with no increase in space footprint, achieving a genuine reduction of the space-time volume required for error-corrected quantum computation, and bringing the runtime of large-scale algorithms on emerging platforms into a practical regime.