A Co-Design Framework of Neural Networks and Quantum Circuits Towards Quantum Advantage

Despite the pursuit of quantum advantages in various applications, the power of quantum computers in neural network computations has mostly remained unknown, primarily due to a missing link that effectively designs a neural network model suitable for quantum circuit implementation. In this article, we present the co-design framework, namely QuantumFlow, to provide such a missing link. QuantumFlow consists of novel quantum-friendly neural networks (QF-Nets), a mapping tool (QF-Map) to generate the quantum circuit (QF-Circ) for QF-Nets, and an execution engine (QF-FB). We discover that, in order to make full use of the strength of quantum representation, it is best to represent data in a neural network as either random variables or numbers in unitary matrices, such that they can be directly operated by the basic quantum logical gates. Based on these data representations, we propose two quantum friendly neural networks, QF-pNet and QF-hNet in QuantumFlow. QF-pNet using random variables has better flexibility, and can seamlessly connect two layers without measurement with more qbits and logical gates than QF-hNet. On the other hand, QF-hNet with unitary matrices can encode 2^k data into k qbits, and a novel algorithm can guarantee the cost complexity to be O(k^2). Compared to the cost of O(2^k)in classical computing, QF-hNet demonstrates the quantum advantages. Evaluation results show that QF-pNet and QF-hNet can achieve 97.10% and 98.27% accuracy, respectively. Results further show that for input sizes of neural computation grow from 16 to 2,048, the cost reduction of QuantumFlow increased from 2.4x to 64x. Furthermore, on MNIST dataset, QF-hNet can achieve accuracy of 94.09%, while the cost reduction against the classical computer reaches 10.85x. To the best of our knowledge, QuantumFlow is the first work to demonstrate the potential quantum advantage on neural network computation.