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arXiv:2401.09393

Élivágar: Efficient Quantum Circuit Search for Classification

Sashwat Anagolum, Narges Alavisamani, Poulami Das, Moinuddin K. Qureshi, Kessler, Eric, Yunong Shi

Published Jan 17, 2024• 1 citation
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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.

DOI
10.48550/arxiv.2401.09393

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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 such circuits, 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.
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Quantum Machine Learning (QML) utilizes the principles of quantum computations to improve the performance of learning by the use of parameterized quantum circuits and variational algorithms. But despite the qubit number, circuit depth, and patterns of entanglement, creating the optimal quantum circuit architectures for particular machine learning applications remains an important problem. Fixed circuits, or classical Neural Architecture Search (NAS), are not enough to transfer knowledge to other tasks and/or to search the quantum search space efficiently. In this context, this paper presents an Adaptive Quantum Circuit Architecture Search (AQ CAS) framework that dynamically generates and optimizes quantum circuit architectures using a hybrid search algorithm that integrates reinforcement learning, evolutionary operators, and evaluation without gradient. AQ CAS involves a task-specific feedback mechanism to eliminate those candidates that perform poorly and concentrate the search on those candidates with good performance. The framework is evaluated on benchmark data sets such as Iris, synthetic classical ML tasks, and hybrid quantum-classical tasks, and compared to fixed circuits, existing quantum NAS methods, and classical machine learning models. Experimental results indicate that AQ CAS can achieve higher accuracy for the task, using fewer qubits, fewer layers, and less training time, which further shows the need for adaptivity and task specialization. These results inform us about efficient hybrid classical-quantum pipelines, and give a glimpse of the directions that adaptive architecture search might take in enabling scalable and practical QML deployment.
Quantum architecture search (QAS) has emerged to automate the design of high-performance quantum circuits under specific tasks and hardware constraints. We propose a noise-aware quantum architecture search (NA-QAS) framework based on variational quantum circuit design. By incorporating a noise model into the training of parameterized quantum circuits (PQCs) , the proposed framework identifies the noise-robust architectures. We introduce a hybrid Hamiltonian ε\varepsilonε -greedy strategy to optimize evaluation costs and circumvent local optima. Furthermore, an enhanced variable-depth NSGA-II algorithm is employed to navigate the vast search space, enabling an automated trade-off between architectural expressibility and quantum hardware overhead. The effectiveness of the framework is validated through binary classification and iris multi-classification tasks under a noisy condition. Compared to existing approaches, our framework can search for quantum architectures with superior performance and greater resource efficiency under a noisy condition.
Unsupervised representation learning presents new opportunities for advancing Quantum Architecture Search (QAS) on Noisy Intermediate-Scale Quantum (NISQ) devices. QAS is designed to optimize quantum circuits for Variational Quantum Algorithms (VQAs). Most QAS algorithms tightly couple the search space and search algorithm, typically requiring the evaluation of numerous quantum circuits, resulting in high computational costs and limiting scalability to larger quantum circuits. Predictor-based QAS algorithms mitigate this issue by estimating circuit performance based on structure or embedding. However, these methods often demand time-intensive labeling to optimize gate parameters across many circuits, which is crucial for training accurate predictors. Inspired by the classical neural architecture search algorithm A r c h 2 v e c , we investigate the potential of unsupervised representation learning for QAS without relying on predictors. Our framework decouples unsupervised architecture representation learning from the search process, enabling the learned representations to be applied across various downstream tasks. Additionally, it integrates an improved quantum circuit graph encoding scheme, addressing the limitations of existing representations and enhancing search efficiency. This predictor-free approach removes the need for large labeled datasets. During the search, we employ REINFORCE and Bayesian Optimization to explore the latent representation space and compare their performance against baseline methods. We further validate our approach by executing the best-discovered MaxCut circuits on IBM's ibm_sherbrooke quantum processor, confirming that the architectures retain optimal performance even under real hardware noise. Our results demonstrate that the framework efficiently identifies high-performing quantum circuits with fewer search iterations.
Quantum computing leverages quantum mechanics to address computational problems in ways that differ fundamentally from classical approaches. While current quantum hardware remains error-prone and limited in scale, Variational Quantum Circuits offer a noise-resilient framework suitable for today's devices. The performance of these circuits strongly depends on the underlying architecture of their parameterized quantum components. Identifying efficient, hardware-compatible quantum circuit architectures -- known as Quantum Architecture Search (QAS) -- is therefore essential. Manual QAS is complex and error-prone, motivating efforts to automate it. Among various automated strategies, Reinforcement Learning (RL) remains underexplored, particularly in Quantum Machine Learning contexts. This work introduces RL-QAS, a framework that applies RL to discover effective circuit architectures for classification tasks. We evaluate RL-QAS using the Iris and binary MNIST datasets. The agent autonomously discovers low-complexity circuit designs that achieve high test accuracy. Our results show that RL is a viable approach for automated architecture search in quantum machine learning. However, applying RL-QAS to more complex tasks will require further refinement of the search strategy and performance evaluation mechanisms.