A Generalized Quantum Inner Product and Applications to Financial Engineering

Understand

In this paper we present a canonical quantum computing method to estimate the weighted sum w(k)f(k) of the values taken by a discrete function f and real weights w(k).

• The canonical aspect of the method comes from relying on a single linear function encoded in the amplitudes of a quantum state, and using register entangling to encode the function f.
• We further expand this framework by mapping function values to hashes in order to estimate weighted sums w(k)h(f(k)) of hashed function values with real hashes h.
• This generalization allows the computation of restricted weighted sums such as value at risk, comparators, as well as Lebesgue integrals and partial moments of statistical distributions.