An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States

A central problem of quantum physics, be it fundamental quantum physics or applications for quantum technology, is the ground state problem. It can be defined as finding a state vector |Ψ that minimises the expected value of the Hamiltonian Ĥ that represents the energetic interactions between the different parts that make up a quantum physical system. It is well-known that the difficulty of solving the ground state problem for a physical system arises from the exponential growth of the Hilbert space with respect to the number of the system components and their dimension. Therefore, techniques such as exact diagonalisation of Ĥ quickly render insufficient to find the ground state, and other approximate methods have to be used. Interestingly, other central problems of quantum physics such as finding the evolution of a quantum system can be cast into the ground state problem, as demonstrated by the Feynman-Kitaev formalism [24]. An immediate implication of using this formalism is that the computational tools historically developed for solving the ground state problem can be used to find the dynamics of a physical system. Broadly speaking, the Feynman-Kitaev formalism appends a clock as an auxilliary subsystem of the main physical system, i.e. the Hilbert space H of the whole system is H = P C, where P is the Hilbert space of the main physical system and C is the Hilbert space of the clock.