  The universality of a quantum neural network refers to its ability to
approximate arbitrary functions and is a theoretical guarantee for its
effectiveness. A non-universal neural network could fail in completing the
machine learning task. One proposal for universality is to encode the quantum
data into identical copies of a tensor product, but this will substantially
increase the system size and the circuit complexity. To address this problem,
we propose a simple design of a duplication-free quantum neural network whose
universality can be rigorously proved. Compared with other established
proposals, our model requires significantly fewer qubits and a shallower
circuit, substantially lowering the resource overhead for implementation. It is
also more robust against noise and easier to implement on a near-term device.
Simulations show that our model can solve a broad range of classical and
quantum learning problems, demonstrating its broad application potential.
