![]() Both the challenge and objective are to find a suitable quantum circuit for a given feature map that is expressive and trainable 33. Two key factors must be considered when using PQCs for machine learning: the method of data encoding (feature map) 32, 33 and the choice of a quantum circuit 34, 35, 36. The QCNN belongs to the class of hybrid quantum-classical algorithms, in which a quantum computer executes the circuit, and a classical computer optimises its parameters. We use the QCNN as a basis and illustrate search space design and architecture search with NAS for PQCs. In this work, we formalise these design patterns by providing a hierarchical representation for quantum circuits. 5 use the multiscale entanglement renormalisation ansatz (MERA) as an instance of their proposed QCNN and discuss generalisations for quantum analogues of convolution and pooling operations. 27 use hierarchical architectures based on tensor networks to classify classical and quantum data. Similar patterns also appear in quantum circuit designs 5, 27, 28, 29, 30, 31. Cell-based representations are popular because they can capture repeated motifs and modular design patterns, which are often seen in successful hand-crafted architectures. Different cells are then stacked to form a complete architecture. Usually, a set of primitive operations, such as convolutions or pooling, are combined into a cell to capture some design motif (compute graph). Search space design often involves encoding architectures using a cell-based representation. The search space defines the set of possible architectures that a search algorithm can consider, and carefully designed search spaces help improve search efficiency and reduce computational complexity 26. NAS consist of three main categories: search space, search strategy and performance estimation strategy 22. ![]() NAS has already produced state-of-the-art deep-learning models with automatically designed architectures 21, 23, 24, 25. Naturally, the next step is learning network architecture, which Neural Architecture Search (NAS) aims to achieve 22. ![]() AlexNet 20 demonstrated this and marked the shift in focus from feature design to architecture design 21. Its main characteristic, learning features from raw data, eliminates the need for manual feature design by experts 19. Deep learning has been widely successful in recent years with applications spanning from content filtering and product recommendations to aided medical diagnosis and scientific research. Research at this intersection has been fruitful, yielding deep-learning solutions for quantum many-body problems 9, 10, 11, 12, quantum-inspired insights for deep learning 13, 14, 15 and equivalences between them 16, 17, 18. It has been implemented experimentally 8 and combines techniques from Quantum Error Correction (QEC), Tensor Networks (TNs) and deep learning. 5 stands out for its shallow circuit depth, absence of barren plateaus 6, and good generalisation capabilities 7. Among various parameterised quantum circuit (PQC) models, the Quantum Convolutional Neural Network (QCNN) introduced in ref. Machine learning using trainable quantum circuits provides promising applications for quantum computing 1, 2, 3, 4. Finally, we implement the framework as an open-source Python package to enable dynamic circuit creation and facilitate circuit search space design for NAS. Furthermore, we employ a genetic algorithm to perform Quantum Phase Recognition (QPR) as an example of architecture search with our representation. We use this framework to justify the importance of circuit architecture in quantum machine learning by generating a family of Quantum Convolutional Neural Networks (QCNNs) and evaluating them on a music genre classification dataset, GTZAN. We propose a framework for representing quantum circuit architectures using techniques from NAS, which enables search space design and architecture search. Neural Architecture Search (NAS) attempts to automate neural network design through learning network architecture and achieves state-of-the-art performance. These tend to be hierarchical, modular and exhibit repeating patterns. Quantum circuit algorithms often require architectural design choices analogous to those made in constructing neural and tensor networks.
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