Abstract

When quantum computers interact with environment they experience decoherence. The simplest situation is a quantum register constructed from a group of quantum bits, i.e., qubits. This register is then used to store binary-coded information. In quantum computers the superposition state of the register has a crucial role, but unfortunately it is very vulnerable to decoherence effects. We have studied the case where the decoherence appears as fluctuations in the phases of the probability amplitudes for the qubits [1], We show that due to the decoherence the superposition decays as exp[-p(L) t], where t is time and p(L) is some polynomial of the number of qubits in the register. Therefore the time to perform, for instance, Peter Shor’s factorisation algorithm [2] scales exponentially with L. Thus the advantage of this quantum algorithm over the classical factorisation algorithms is lost.

© 1996 Optical Society of America