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arXiv:2408.13211 · Quantum Information Processing

Optimal quantum circuit design via unitary neural networks

M. Zomorodi, Hadis Amini, M. Abbaszadeh, J. Sohrabi, Vahid Salari, Paweł Pławiak

Published Apr 27, 2026• 1 citation
arXivHTMLPDF
DOI
10.1007/s11128-026-05170-9

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Quantum algorithms operate on quantum states through unitary transformations in high dimensional complex Hilbert space. In this work, we propose a machine learning approach to create the quantum circuit using a single-layer complex-valued neural network. The input and ouput quantum states are provided to the network, which is trained to approximate the output state of a given quantum algorithm. To ensure that the fundamental property of unitarity is preserved throughout the training process, we employ optimization in Stiefel Manifold.
This paper presents an adaptive quantum circuit design framework leveraging a neural network to automate the process of circuit creation. Traditional quantum circuit design is often a laborious and iterative process, relying heavily on expert knowledge and trial-and-error. We introduce a novel system that utilizes a trained neural network to automatically generate quantum circuits with optimized properties, aiming to significantly reduce manual effort and accelerate quantum algorithm development. The framework employs a multi-stage training process, beginning with a pre-trained model and iteratively refining it based on a defined set of performance metrics. The core mechanism centers on the neural network's ability to learn the optimal circuit parameters to maximize desired properties such as fidelity, coherence, and connectivity. This approach promises to provide a more efficient and scalable method for quantum circuit design.
Abstract Despite the pursuit of quantum advantages in various applications, the power of quantum computers in executing neural network has mostly remained unknown, primarily due to a missing tool that effectively designs a neural network suitable for quantum circuit. Here, we present a neural network and quantum circuit co-design framework, namely QuantumFlow, to address the issue. In QuantumFlow, we represent data as unitary matrices to exploit quantum power by encoding n = 2k inputs into k qubits and representing data as random variables to seamlessly connect layers without measurement. Coupled with a novel algorithm, the cost complexity of the unitary matrices-based neural computation can be reduced from O(n) in classical computing to O(polylog(n)) in quantum computing. Results show that on MNIST dataset, QuantumFlow can achieve an accuracy of 94.09% with a cost reduction of 10.85 × against the classical computer. All these results demonstrate the potential for QuantumFlow to achieve the quantum advantage.