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

Willers Yang, Jason Chadwick, Mariesa H. Teo, Joshua Viszlai, Fred Chong

TL;DR

RASCqL demonstrates a concrete path forward for qLDPC codes as CISQ compute modules, extending their practical utility in fault-tolerant quantum computing architectures at space-time costs comparable to state-of-the-art transversal surface-code architectures.

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.

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

TL;DR

RASCqL demonstrates a concrete path forward for qLDPC codes as CISQ compute modules, extending their practical utility in fault-tolerant quantum computing architectures at space-time costs comparable to state-of-the-art transversal surface-code architectures.

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 to footprint reduction under realistic physical error rates of to , 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.
Paper Structure (51 sections, 14 theorems, 34 equations, 20 figures, 3 tables)

This paper contains 51 sections, 14 theorems, 34 equations, 20 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Logical Layer: Quantum Error Correcting Codes
  4. The surface code
  5. qLDPC codes
  6. Magic State Distillation
  7. Physical Layer: Reconfigurable Atom Arrays
  8. Functional Layer: Quantum Algorithms
  9. Factoring
  10. Quantum Chemistry
  11. Full Stack Fault-Tolerant Quantum Architectures
  12. RASCqL Architecture
  13. CQLU Design
  14. PReP Design
  15. RNAA Implementation
  16. ...and 36 more sections

Key Result

Theorem 1

Let us be given a $[n,k,d]$ code $\mathcal{C}(G,H)$ and $\mathcal{G} = \{g_1,...,g_m\} \leq \mathbb{GL}_{k}(\mathbb{F}_2)$. There exists a family of $[n'\leq nm,k,d'\leq dm]$ codes $\mathcal{C}_{\mathcal{G}}(G_{\mathcal{G}},H_{\mathcal{G}})$ such that $\mathcal{C}\cong\mathcal{C}_\mathcal{G}$, $\mat

Figures (20)

  • Figure 1: Top: RASCqL exhibits high circuit-level threshold, high encoding rate, and space-time efficient ISA for algorithms. Bottom: space-time volume comparison of RASCqL adder against baselines.
  • Figure 2: A three-stack view of FTQC. The surface code implements an efficient logical layer due to its hardware compatibility and RISC ISA, but suffers from large qubit overhead. qLDPC codes may reduce footprint, but require long-range interactions and have comparatively limited logical primitives. RASCqL achieves efficient in-block computation by co-designing qLDPC codes with CISQ compilations with key functional subroutines and reconfigurable neutral atom-array implementations.
  • Figure 3: Quantum error correcting codes. a) $[[9,1,3]]$ surface codes with 2D planar syndrome checks. b) $[[98, 18, 4]]$ qLDPC code with non-local syndrome checks and improved encoding rate. c) Fault tolerant logical instructions of a surface code: (from left to right) arbitrary Pauli Product measurements, parallel transversal CNOTs, and addressable single qubit Clifford gates. d) Fault tolerant logical instructions of qLDPC codes: particular Pauli Product measurements given by a universal adapter, global transversal CNOTs, and automorphism Clifford gates given by code symmetries.
  • Figure 4: Abstract overview of the factoring algorithm. It can be implemented using repeated applications of quantum adders and quantum look-up tables, with a QFT.
  • Figure 5: RASCqL Overview. Input algorithms supported by key subroutines are implemented using Complex Quantum Logic Units (CQLU) in tailored qLDPC codes and Predictive Resource-state Preparation (PReP) optimized using CQLU complex instructions. Logical primitives are then compiled down to parallel physical instructions on reconfigurable neutral atom arrays to obtain realistic estimations for logical performance and space-time cost.
  • ...and 15 more figures

Theorems & Definitions (31)

  • Theorem 1: Code Automorphism Expansion
  • Theorem 2: qLDPC with Virtual Instruction
  • Definition 1: Binary vector space
  • Definition 2: Hilbert space
  • Definition 3: Binary Linear Code
  • Definition 4: CSS Code
  • Definition 5: Hypergraph Product (HGP) Code
  • Definition 6: Automorphisms in Classical Codes
  • proof
  • proof
  • ...and 21 more