Quantum artificial neural networks with applications

• A new type of neural networks has been proposed, named a quantum artificial neural network (QANN).
• A QANN is presented as a system of interconnected ”quantum neurons” simulated on quantum computers.
• The ability of approximation of a QANN has been proved by a universal approximation theorem (UAT).
• The UAT implies that a QANN may be a potential computing tool for dealing with quantum information.

Since simulations of classical artificial neural networks (CANNs) run on classical computers, the massive parallel processing speed advantage of a neural network is lost. A quantum computer is a computation device that makes direct use of quantum–mechanical phenomena while large-scale quantum computers will be able to solve certain problems much quicker than any classical computer using the best currently known algorithms. Combining the advantages of quantum computers and the idea of CANNs, we propose in this paper a new type of neural networks, named a quantum artificial neural network (QANN), which is presented as a system of interconnected “quantum neurons” which can compute quantum states from input-quantum states by feeding information through the network and can be simulated on quantum computers. To show the ability of approximation of a QANN, we prove a universal approximation theorem (UAT) which reads every continuous mapping that transforms n quantum states as a non-normalized quantum state can be uniformly approximated by a QANN. The UAT implies that QANNs would suggest a potential computing tool for dealing with quantum information. For instance, we prove that the state of a quantum system driven by a time-dependent Hamiltonian can be approximated uniformly by a QANN. This provides a possible way for finding approximate solution to a Schrödinger equation with a time-dependent Hamiltonian.