  We propose a hybrid quantum-classical algorithm, originated from quantum
chemistry, to price European and Asian options in the Black-Scholes model. Our
approach is based on the equivalence between the pricing partial differential
equation and the Schrodinger equation in imaginary time. We devise a strategy
to build a shallow quantum circuit approximation to this equation, only
requiring few qubits. This constitutes a promising candidate for the
application of Quantum Computing techniques (with large number of qubits
affected by noise) in Quantitative Finance.
