Collective decoherence of the superpositional entangled states in the quantum Shor algorithm
G. P. Berman, D. I. Kamenev, V. I. Tsifrinovich · Physical Review A · 2005
We consider collective decoherence for the quantum Shor algorithm. A quantum computer which interacts with its environment is modeled by a spin-$1∕2$ chain interacting with harmonic oscillators at a given temperature. We calculate the nondiagonal matrix elements of the density matrix which are important for implementation of the quantum Shor algorithm, and study the decay rate and the Lamb phase shift for these elements. It is shown that the probability of superdecoherence in the quantum Shor algorithm is extremely small. The conditions for preserving quantum entanglement are formulated.