  The Schrodinger equation describes how quantum states evolve according to the
Hamiltonian of the system. For physical systems, we have it that the
Hamiltonian must be a Hermitian operator to ensure unitary dynamics. For
anti-Hermitian Hamiltonians, the Schrodinger equation instead models the
evolution of quantum states in imaginary time. This process of imaginary time
evolution has been used successfully to calculate the ground state of a quantum
system. Although imaginary time evolution is non-unitary, the normalised
dynamics of this evolution can be simulated on a quantum computer using the
quantum imaginary time evolution (QITE) algorithm. In this paper, we broaden
the scope of QITE by removing its restriction to anti-Hermitian Hamiltonians,
which allows us to solve any partial differential equation (PDE) that is
equivalent to the Schrodinger equation with an arbitrary, non-Hermitian
Hamiltonian. An example of such a PDE is the famous Black-Scholes equation that
models the price of financial derivatives. We will demonstrate how our
generalised QITE methodology offers a feasible approach for real-world
applications by using it to price various European option contracts modelled
according to the Black-Scholes equation.
