<title>Toward a model for multi-qubit quantum memory</title>

Abstract

To a large extent, the power of a quantum computer comes from the possibility of operating on a number of quantum memories simultaneously. For example, if there are n linearly independent quantum states in each of N quantum memories, then the number of linearly independent quantum states is n N when they are taken together. This exponential increase is the basis of the present interest in quantum computing. In the context of quantum mechanics as described by the Schrödinger equation (which is a partial differential equation), the most explicit model of the quantum memory is one with two linearly independent quantum states described in terms of the Fermi pseudo-potential at one point. In this model, operations on the quantum memory are accomplished through scattering with both symmetrical and anti-symmetrical incident waves. As a first step toward operating on more than one quantum memory, this model is generalized in two directions. (1) With the Fermi pseudo-potential at one point retained, three linearly independent quantum states are used for the quantum memory. This model of the quantum memory requires three external connections.(2) With a more general potential, operations on the quantum memory with two states are accomplished through scattering with either symmetrical or anti-symmetrical incident waves. This second generalization is important because it is not practical to keep the number of external connections equal to the number of linearly independent quantum states.