Abstract: A system and method for solving general classes of difficult financial calculations such as capital calculations and pricing calculations on a quantum computer are disclosed. In some embodiments, the disclosed method reduces financial problems to problems in # P. In some embodiments, the method includes constructing a quantum circuit whose ground states are comprised of solutions to an associated NP problem that the problem in # P is counting, and then using a quantum annealing process to find one of those ground states, if it exists. For the gross estimate of the size of the solution set of the NP problem, which the # P problem is counting, the method includes finding one solution that achieves a specific random hash value, applying a correction formula, and amplifying the result using a k-fold iterated hash function, in which the number of bits of the hash value increases linearly with each iteration.