Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays

TL;DR

This paper proposes a low-overhead, reconfigurable architecture for neutral atom quantum arrays that significantly accelerates large-scale fault-tolerant quantum algorithms like Shor's factoring, using efficient transversal operations and resource estimation.

Contribution

It introduces a novel architecture leveraging transversal gates and optimized building blocks for resource-efficient, large-scale fault-tolerant quantum computing with detailed resource and error performance models.

Findings

Achieves nearly 50x speed-up for 2048-bit RSA factoring.

Reduces atom move times and correlated decoding volume.

Supports large-scale quantum algorithms with minimal space overhead.

Abstract

Neutral atom arrays have recently emerged as a promising platform for fault-tolerant quantum computing. Based on these advances, including dynamically-reconfigurable connectivity and fast transversal operations, 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, 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 50$\times$ speed-up of the run-time compared to existing estimates with similar assumptions, with no increase in space footprint.