Barnes, JP; Warren, WS, *Decoherence and programmable quantum computation*,
Physical Review A - Atomic, Molecular, and Optical Physics, vol. 60 no. 6
(1999),
pp. 4363-4374 .
**Abstract:**

*When coherent states of the electromagnetic field are used to drive the evolution of a quantum computer, a decoherence results due to the back reaction from the qubits onto the fields. We show how to calculate this effect. No assumptions about the environment are necessary, so this represents a useful model to test the fidelity of quantum error correcting codes. We examine two cases of interest. First, the decoherence from the Walsh-Hadamard transformations in Grover's search algorithm is found [Phys. Rev. Lett. 79, 325 (1997)]. Interference effects, and decoherence-dependent phases, are present that could be useful in reducing the decoherence. Second, Shor's fault-tolerant controlled-NOT gate is examined, utilizing frequency-selective pulses [Proceedings, 35th Annual Symposium on Foundations of Computer Science (IEEE Press, New York, 1994), pp. 56-65]. This implementation is found not to be optimal in regards to fault-tolerant quantum computation.*