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.
Highlights
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
Quantum computers are expected to dramatically outperform classical computers, so far quantum advantages have only been shown in a limited number of applications, from the prime factorization1 and sampling the output of random quantum circuits2 to the most recent breakthroughs on Boson Sampling3
We will demonstrate that quantum computers can achieve potential quantum advantage on neural network computation, a very common task in the prevalence of artificial intelligence (AI)
Summary
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. The first direction is to map the existing neural networks designed for classical computers to quantum circuits; for instance, recent works map McCulloch-Pitts (MCP) neurons onto quantum circuits. Such an approach has difficulties in consistently mapping the trained model to quantum circuits. It needs a large number of qubits to realize the multiplication of real numbers. To overcome this problem, some existing works assume binary representation (i.e., “−1” and “+1”) of activation, which cannot well represent data as seen in modern machine learning applications. To enable deep learning, batch normalization is a key step in a deep neural network to improve the training speed, model performance, and stability; directly conducting normalization on the output qubit is difficult
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