Physical Realization of Harmonic Oscillator Quantum Computer

Algorithms are the key concept of computer science. The spectacular promise of quantum computers is to enable new algorithms which render feasible problems requiring exorbitant resources for their solution on a classical computer. The relationship between the energy eigenstates of a simple harmonic oscillator and quantum computation comes by taking a finite subset of these states to represent quantum bits. These quantum bits will have lifetimes determined by physical parameters such as the cavity quality factor, which can be made very large by increasing the reflectivity of the cavity walls. Moreover, unitary transforms can be applied by simply allowing the system to evolve in time. We begin by studying the system Hamiltonian, and then discuss how one might implement simple quantum logic gates.