  Monte Carlo integration using quantum computers has been widely investigated,
including applications to concrete problems. It is known that quantum
algorithms based on quantum amplitude estimation (QAE) can compute an integral
with a smaller number of iterative calls of the quantum circuit which
calculates the integrand, than classical methods call the integrand subroutine.
However, the issues about the iterative operations in the integrand circuit
have not been discussed so much. That is, in the high-dimensional integration,
many random numbers are used for calculation of the integrand and in some cases
similar calculations are repeated to obtain one sample value of the integrand.
In this paper, we point out that we can reduce the number of such repeated
operations by a combination of the nested QAE and the use of pseudorandom
numbers (PRNs), if the integrand has the separable form with respect to
contributions from distinct random numbers. The use of PRNs, which the authors
originally proposed in the context of the quantum algorithm for Monte Carlo, is
the key factor also in this paper, since it enables parallel computation of the
separable terms in the integrand. Furthermore, we pick up one use case of this
method in finance, the credit portfolio risk measurement, and estimate to what
extent the complexity is reduced.
