ConiQ: Enabling Concatenated Quantum Error Correction on Neutral Atom Arrays

2025-08-07

AI Summary

To address the twin bottlenecks—non-addressable logical gates and poor hardware compatibility—of hypercube hierarchical quantum error-correcting codes on neutral-atom platforms, this work proposes a hierarchical compilation framework. It introduces Automorphism-assisted Hierarchical Addressing (AHA) to enable addressable logical CNOT gates, employs Virtual Atom Intermediate Representation (VAIR) to abstract long-range interactions, and integrates hardware-aware optimization tailored to neutral-atom arrays. The framework supports layer-wise spatiotemporal overhead optimization, significantly improving compilation efficiency and physical feasibility. Experimental results demonstrate that the full pipeline reduces spatiotemporal overhead by up to 2000× and accelerates compilation by up to 10⁶× over baseline methods. Ablation studies show that AHA alone contributes up to a 20× reduction in overhead. This work provides critical enabling technology for practical fault-tolerant quantum computation on neutral-atom hardware.

Technology Category

• Machine Learning: Hardware-aware ML
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Recent progress on concatenated codes, especially many-hypercube codes, achieves unprecedented space efficiency. Yet two critical challenges persist in practice. First, these codes lack efficient implementations of addressable logical gates. Second, the required high degree of parallelism and long-range interactions pose significant challenges for current hardware platforms. In this paper, we propose an efficient compilation approach for concatenated codes, specifically many-hypercube codes, targeted at neutral atom arrays, which provide the necessary parallelism and long-range interactions. Our approach builds on two key innovations. First, we introduce Automorphism-assisted Hierarchical Addressing (AHA) logical CNOT gates that significantly reduce spacetime overhead compared to conventional distillation-based methods. Second, we develop Virtual Atom Intermediate Representation (VAIR) that enables level-wise optimization and legalization. We implement these innovations in ConiQ, a hardware-aware quantum compiler designed to compile fault-tolerant quantum circuits for neutral atom arrays using many-hypercube codes. Our evaluation demonstrates that ConiQ achieves up to 2000x reduction in spacetime overhead and up to 10^6x reduction in compilation time compared to state-of-the-art compilers, with our AHA gates providing an additional overhead reduction of up to 20x. These results establish concatenated codes as a promising approach for fault-tolerant quantum computing in the near future.

Problem

• Lack efficient addressable logical gates for concatenated codes
• High parallelism and long-range interactions challenge current hardware
• Need optimized compilation for fault-tolerant quantum circuits

Innovation

• Automorphism-assisted Hierarchical Addressing CNOT gates
• Virtual Atom Intermediate Representation optimization
• Hardware-aware compiler for neutral atom arrays