Decoherence Limits to Quantum Factoring

Abstract

Soon after the idea of quantum computation became an active part of current research through the seminal work of Shor on factorization [1], decoherence was recognised as a major problem that cannot be ignored, at least when one is interested in practical applications including especially the factorization of large numbers [2,3]. In this paper we present fundamental limits imposed by spontaneous emission on the size of the numbers that can be factorized on a quantum computer. We also include the use of error correction methods in our estimates and show that this does not substantially change our pessimistic predictions of the maximum size of factorizable numbers on a quantum computer.