Decoherence and programmable quantum computation

When coherent states of the electromagnetic field are used to drive the evo lution of a quantum computer, a decoherence results due to the back reactio n from the qubits onto the fields. We show how to calculate this effect. No assumptions about the environment are necessary, so this represents a usef ul model to test the fidelity of quantum error correcting codes. We examine two cases of interest. First, the decoherence from the Walsh-Hadamard tran sformations in Grover's search algorithm is found [Phys. Rev. Lett. 79, 325 (1997)]. Interference effects, and decoherence-dependent phases, are prese nt that could be useful in reducing the decoherence. Second, Shor's fault-t olerant controlled-Nor gate is examined, utilizing frequency-selective puls es [Proceedings, 35th Annual Symposium on Foundations of Computer Science ( IEEE Press, New York, 1994), pp. 56-65]. This implementation is found not t o be optimal in regards to fault-tolerant quantum computation. [S1050-2947( 99)07212-1].