ConiQ: Enabling Concatenated Quantum Error Correction on Neutral Atom Arrays

TL;DR

ConiQ is a quantum compiler that enables efficient concatenated quantum error correction on neutral atom arrays, significantly reducing overhead and compilation time through innovative addressing and gate techniques.

Contribution

The paper introduces AHA logical CNOT gates and VAIR for optimized compilation of concatenated codes on neutral atom platforms, advancing fault-tolerant quantum computing.

Findings

Achieves up to 2000x reduction in spacetime overhead

Reduces compilation time by up to 10^6x

Provides a scalable approach for fault-tolerant quantum circuits

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.