Representing Quantum States with Neural Networks, Poster 48

Representing and manipulating a quantum state is a challenging problem for classical computers. This is due to the fact that the amount of memory needed to store a state of n quantum particles classically grows on the order of... [ view full abstract ]

Representing and manipulating a quantum state is a challenging problem for classical computers. This is due to the fact that the amount of memory needed to store a state of n quantum particles classically grows on the order of O(2^n). The exponential requirement for state representations means that for large systems, classical computers very quickly run out of memory. This paper explores using neural networks to represent or approximate quantum states using only a polynomial number of parameters, thus solving the memory issue. The network will be trained using the energy of the system as the cost function. By minimizing the cost, or energy, the network will approximately represent the ground state of the quantum system. Restricted Boltzmann Machine neural networks have been demonstrated to be able to represent quantum states; the main focus of this project is to study how efficiently a deep, fully connected, neural network can represent a quantum state in comparison with a Restricted Boltzmann Machine.