Spacetime-Efficient and Hardware-Compatible Complex Quantum Logic Units in qLDPC Codes

Abstract

Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computing due to their substantially reduced footprint. However, these gains can be diluted at utility scale if we cannot also realize space-time efficient logical operations for relevant quantum applications. We present RASCqL, a reaction-time-limited architecture for space-time efficient complex-instruction-set quantum computation with qLDPC logic. RASCqL supports key algorithmic subroutines such as quantum arithmetic and state preparation directly within co-designed qLDPC codes, achieving $2\times$ to $7\times$ reductions in qubit footprint while maintaining space-time volume comparable to state-of-the-art transversal surface-code architectures. Unlike prior approaches that aim for versatile logical instruction sets for arbitrary circuits, RASCqL adopts an application-tailored code modification that embeds specific complex Clifford transformations useful for common subroutines as virtually implementable operations arising from code automorphisms. RASCqL further leverages parallel physical operations available in reconfigurable neutral-atom arrays to enable fast QEC cycles and high-fidelity transversal operations. At the cost of increased design complexity and specialization, RASCqL can improve end-to-end resource estimates for applications such as factoring and quantum chemistry simulation in both footprint and space-time volume under realistic physical error rates of approximately $2\times10^{-3}$ to $5\times10^{-4}$, without requiring additional hardware capabilities. These results demonstrate that qLDPC codes can serve as complex quantum logic units for useful quantum algorithms, extending their practical utility in fault-tolerant quantum computing architectures.