  Ideal quantum algorithms usually assume that quantum computing is performed
continuously by a sequence of unitary transformations. However, there always
exist idle finite time intervals between consecutive operations in a realistic
quantum computing process. During these delays, coherent "errors" will
accumulate from the dynamical phases of the superposed wave functions. Here we
explore the sensitivity of Shor's quantum factoring algorithm to such errors.
Our results clearly show a severe sensitivity of Shor's factorization algorithm
to the presence of delay times between successive unitary transformations.
Specifically, in the presence of these {\it coherent "errors"}, the probability
of obtaining the correct answer decreases exponentially with the number of
qubits of the work register. A particularly simple phase-matching approach is
proposed in this paper to {\it avoid} or suppress these {\it coherent errors}
when using Shor's algorithm to factorize integers. The robustness of this
phase-matching condition is evaluated analytically or numerically for the
factorization of several integers: $4, 15, 21$, and 33.

Quantum Physics