Method for Identifying a Valid Energy State

A computing apparatus for identifying an excited energy state of a system of interacting electrons, comprising:

• a classical computer;
• and
• a quantum computer comprising a set of qubits, the quantum computer configured to apply a first quantum circuit the first quantum circuit defined by a generator function parameterised by a set of parameters, θ, wherein applying the first quantum circuit to a set of qubits in an initial state generates a state of the system represented by a wavefunction, Ψ, and to apply a second quantum circuit defined by a discriminator function parameterised by a set of parameters, ϕ, wherein applying the second quantum circuit to the set of qubits in a state of the system represented by a wavefunction, Ψ provides an output representing an extent of overlap of the wavefunction Ψ with the wavefunction Ψn−1 of each of the n known valid states of the system, wherein each of the n known valid states of the system are parametrised by a set of values θn−1 for the set of parameters, θ;
• wherein the computing apparatus is configured to optimise the values of the set of parameters θ to substantially minimise the energy of the state generated by the first quantum circuit represented by the wavefunction Ψ, and to substantially minimise the extent of overlap of the state generated by the first quantum circuit represented by the wavefunction Ψ and each of the n known valid states of the system represented by respective wavefunction Ψn−1;
• and
• cooperatively, to train the discriminator function by optimising the value of the set of parameters ϕ to train the discriminator function to discriminate between the wavefunction of the state generated by the first quantum circuit and the wavefunction Ψn−1 representing each of the n valid states of the system;
• wherein the optimised values of the set of parameters θ correspond to a set of values θn parametrising the generator function defining the first quantum circuit for generating an n+1th valid energy state of the system represented by wavefunction, Ψn, which is an excited energy state of the system of interacting electrons.