Quantum simulations of quantum many-body problems on quantum computers and their application to lattice gauge theories

First, methods for simulating quantum many-body problems on a quantum computers will be reviewed.As is well-known, the exact solution of quantum-many problems require time and space requirements on classical computers that scale as the exponential of the problem size.In comparison, on a quantum computer the same problem can be solved in polynomial time and space up to a given accuracy.These methods are applied to two specific problems, of simulating U(1) lattice gauge theory and SU(2) lattice gauge theory.It is shown that such problems may be efficiently implemented on a quantum computer.