We describe a simulation approach to study the functioning of Quantum Computer hardware. The latter is modeled by a collection of interacting spin-1/2 objects. The time evolution of this spin system maps one-to-one to a quantum program carried out by the Quantum Computer. Our simulation software consists of code that solves the time-dependent Schrödinger equation for a sequence of time-dependent Hamiltonians and a graphical user interface to program and control the solver. We present results of simulations on a 4-qubit Quantum Computer executing Grover’s database search algorithm.