Élivágar: Efficient Quantum Circuit Search for Classification

TL;DR

Élivágar tackles the challenge of efficiently discovering high-performance, noise-robust quantum circuits for QML on NISQ devices by moving beyond classically-inspired QCS pipelines. It introduces a topology-aware, data-embedding-aware, gradient-free search workflow that uses two cheap predictors—Clifford Noise Resilience (CNR) and Representational Capacity (RepCap)—to decouple noise-robustness from performance and enable early circuit pruning. The framework yields measurable gains, achieving an average $5.3\%$ increase in accuracy and up to $271\times$ speedups over state-of-the-art methods across nine benchmarks on real hardware, with speedups that grow with problem size. By directly targeting device topology, embedding optimization, and cost-effective evaluation, Élivágar offers a scalable, practical approach to QCS that can be integrated with existing QML workflows and is open-sourced to foster further research.

Abstract

Designing performant and noise-robust circuits for Quantum Machine Learning (QML) is challenging -- the design space scales exponentially with circuit size, and there are few well-supported guiding principles for QML circuit design. Although recent Quantum Circuit Search (QCS) methods attempt to search for performant QML circuits that are also robust to hardware noise, they directly adopt designs from classical Neural Architecture Search (NAS) that are misaligned with the unique constraints of quantum hardware, resulting in high search overheads and severe performance bottlenecks. We present Élivágar, a novel resource-efficient, noise-guided QCS framework. Élivágar innovates in all three major aspects of QCS -- search space, search algorithm and candidate evaluation strategy -- to address the design flaws in current classically-inspired QCS methods. Élivágar achieves hardware-efficiency and avoids an expensive circuit-mapping co-search via noise- and device topology-aware candidate generation. By introducing two cheap-to-compute predictors, Clifford noise resilience and Representational capacity, Élivágar decouples the evaluation of noise robustness and performance, enabling early rejection of low-fidelity circuits and reducing circuit evaluation costs. Due to its resource-efficiency, Élivágar can further search for data embeddings, significantly improving performance. Based on a comprehensive evaluation of Élivágar on 12 real quantum devices and 9 QML applications, Élivágar achieves 5.3% higher accuracy and a 271$\times$ speedup compared to state-of-the-art QCS methods.

Figures (11)

• Figure 1: Comparison of classical and quantum ML systems.
• Figure 2: QuantumNAS: A state-of-the-art QCS framework.
• Figure 3: (a) Circuit and device topology mismatch results in a large routing cost due to noisy SWAP gates. (b) Both circuits use the same trainable gates, but different data embeddings. Circuit 1 learns the target function $f(x)$ but Circuit 2 fails, highlighting the importance of suitable data embeddings for QML tasks. (c) QML circuits consist of data embedding gates, trainable gates, and measurement operations. QML training involves running circuits on a quantum device and tuning parameters using a classical optimizer.
• Figure 4: An overview of Élivágar.
• Figure 5: (a) A circuit and (b) a Clifford replica of the circuit. CNR is strongly correlated with circuit fidelity, as demonstrated using circuits run on (c) IBMQ-Kolkata and IBMQ-Guadeloupe, and a (d) noise model of Rigetti Aspen-M-2.