Quantum Bit and Square Well in Quantum Computation

Abstract

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. Quantum computation is based on transformation of quantum states. Quantum bits are two-level quantum systems, and as the simplest elementary building blocks for a quantum computer, they provide a convenient labeling for pairs of states and their physical realizations. This paper shows how a single quantum bit can be represented by the two lowest levels in a square well potential, and how simple perturbations of the potential can effect computational operations on the quantum bit. The controlling system is just another quantum system, and it couples to the one we are trying to do quantum computation. These problems lead to decoherence.