Numerical and analytical research of the impact of decoherence on   quantum circuits
  Three different levels of noisy quantum schemes modeling are considered: vectors, density matrices and Choi-Jamiolkowski related states. The implementations for personal computers and supercomputers are described, and the corresponding results are shown. For the level of density matrices, we present the technique of the fixed rank approximation and show some analytical estimates of the fidelity level. 
Yu.I. Bogdanov, A.Yu. Chernyavskiy, B.I. Bantysh, V.F. Lukichev, A.A.   Orlikovsky, I.A. Semenihin, D.V.Fastovets, A.S. Holevo
quant-ph