A duplication-free quantum neural network for universal approximation

Different from the concept of universal computation, the universality of a quantum neural network focuses on the ability to approximate arbitrary functions and is an important guarantee for effectiveness. However, conventional approaches of constructing a universal quantum neural network may result in a huge quantum register that is challenging to implement due to noise on a near-term device. To address this, we propose a simple design of a duplication-free quantum neural network whose universality can be rigorously proven. Specifically, instead of using multiple duplicates of the quantum register, our method relies on a single quantum register combined with multiple activation functions to create nonlinearity and achieve universality. Accordingly, our proposal requires significantly fewer qubits with shallower circuits, and hence substantially reduces the resource overhead and the noise effect. In addition, simulations demonstrate that our universality design is able to achieve a better learning accuracy in the presence of noise, illustrating a great potential in solving larger-scale learning problems on near-term devices.