  The possible effect of environment on the efficiency of a quantum algorithm
is considered explicitely. It is illustrated through the example of Shor's
prime factorization algorithm that this effect may be disastrous. The influence
of environment on quantum computation is probed on the basis of its analogy to
the problem of wave function collapse in quantum measurement.Techniques from
the Hepp-Colemen approach and its generalization are used to deal with
decoherence problems in quantum computation including dynamic mechanism of
decoherence, quantum error avoiding tricks and calculation of decoherence time.
