  This paper proposes a method of quantum Monte Carlo integration that retains
the full quadratic quantum advantage, without requiring any arithmetic or
quantum phase estimation to be performed on the quantum computer. No previous
proposal for quantum Monte Carlo integration has achieved all of these at once.
The heart of the proposed method is a Fourier series decomposition of the sum
that approximates the expectation in Monte Carlo integration, with each
component then estimated individually using quantum amplitude estimation. The
main result is presented as theoretical statement of asymptotic advantage, and
numerical results are also included to illustrate the practical benefits of the
proposed method. The method presented in this paper is the subject of a patent
application [Quantum Computing System and Method: Patent application
GB2102902.0 and SE2130060-3].
