RASCqL: Reaction-time-limited Architecture for Space-time-efficient Complex qLDPC Logic

Abstract: Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computing (FTQC) due to their substantially reduced footprint, but these gains can be diluted at utility scale if we cannot also realize a space-time-efficient instruction-set architecture (ISA) for relevant quantum applications. We present RASCqL, a Reaction-time-limited Architecture for Space-time-efficient Complex qLDPC Logic, introducing a complex-instruction-set quantum computer (CISQ) that supports key algorithmic subroutines such as quantum arithmetic, table lookups, and magic-state distillation directly in co-designed qLDPC codes. Unlike prior constructions for qLDPC logic that aim at versatile ISAs amenable to diverse circuits, RASCqL adopts an application-tailored code-modification scheme that embeds specific complex Clifford instructions useful for functional subroutines as virtually implementable matrix automorphisms. RASCqL further leverages parallel physical operations in reconfigurable neutral-atom array platforms to achieve fast QEC cycles and high-fidelity transversal operations. At the cost of increased design complexity, RASCqL implements key algorithmic subroutines at space-time costs comparable to state-of-the-art transversal surface-code architectures while achieving up to $2\times$ to $7\times$ footprint reduction under realistic physical error rates of $2 \times 10^{-3}$ to $5 \times 10^{-4}$, without additional hardware complexity. RASCqL thus demonstrates a concrete path forward for qLDPC codes as CISQ compute modules, extending their practical utility in fault-tolerant quantum computing architectures.