A Generalized Quantum Inner Product and Applications to Financial Engineering

A Generalized Quantum Inner Product and Applications to Financial Engineering

A team at Wells Fargo and University of California has just released a paper on solving a central and difficult problem in Financial Engineering: Computing Weighted Sums.

Those familiar with expected values, value at risk, or derivative pricing will recognize the importance of such computations, but everyone can relate to calculating revenue by multiplying the quantity and price for each product, and adding up. That is a simple example of a weighted sum, and in fact Excel has a function called SUMPRODUCT for this calculation. Neural networks also rely on computing weighted sums of inputs. 

The paper generalizes this operation in a way the merge of two spreadsheets generalizes SUMPRODUCT, or inner joins allow to combine values in two database tables through a foreign key. For those mathematically inclined, the generalization is similar to the way Lebesgue integration generalizes Riemann integration, and in fact Lebesgue integrals can be computed using our method. The paper also includes efficient approximate and, for a small number of qubits, exact implementations of normal distributions and linear functions, which turn out to be sufficient for computing the expected value of any discrete function. (Constantin Gonciulea)

Quantum Computing happens to excel at calculating inner products, and therefore weighted sums.

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