Generic constructin of quantum circuits for nonunitary operations: linear-response functions of molecules

The logic gates on a quantum circuit are restricted to unitary ones. This restriction makes it difficult to develop quantum algorithms for various practical problems. For example, quantum chemistry often requires us to calculate the quantities given via nonunitary operators. In this study, we propose a scheme for the construction of a quantum circuit for an arbitrary nonunitary operator given as a linear combination of unitary operators. Depending on the outcome of a measurement on the ancillary qubits, the input state on which the nonunitary operator has acted will be obtained probabilistically. This appoarch enables us to calculate the one-particle Green's functions[1] and linear-response functions.[2]
[1] T. Kosugi and Y. Matsushita, Phys. Rev. A 101, 012330 (2020)
[2] T. Kosugi and Y. Matsushita, Physical Review Research 2, 033043 (2020)