River Lane Research Ltd.

A method for determining an energy level of a physical system using a quantum computer, wherein the energy level of the physical system is described by the summation of a plurality of summands. The method comprises performing an energy estimation routine which comprises preparing an ansatz trial state, and estimating an expectation value of each summand respectively. The estimating comprises constructing, based on the arrangement of quantum gates, an initial quantum circuit to operate on the ansatz trial state and further comprises performing a summand expectation value determination sub-routine a plurality of times in an iterative process. The energy estimation routine further comprises summing the expectation value estimates of each summand to determine an estimate for the trial state energy. The method further comprises determining the energy level of the physical system by applying an optimisation procedure to the energy estimation routine.

- Claim 1. A method for determining an energy level of a physical system using a quantum computer controlled by a classical computer, the energy level of the physical system being described by the summation of a plurality of summandsthe method comprising performing an energy estimation routine comprising: preparing, by the quantum computer, an ansatz trial state using an arrangement of quantum gates, the ansatz trial state having a trial state energy dependent on a trial state variable, estimating an expectation value of each summand respectively, the estimating comprising constructing, by the quantum computer based on the arrangement of quantum gates, an initial quantum circuit to operate on the ansatz trial state and performing, by the quantum computer, a summand expectation value determination sub-routine a plurality of times in an iterative processthe energy estimation routine further comprising summing, by the quantum computer or the classical computer, the expectation value estimates of each summand to determine an estimate for the trial state energythe method further comprising determining the energy level of the physical system by applying an optimisation procedure to the energy estimation routine, the optimisation procedure comprising iteratively updating, by the classical computer or the quantum computer, the trial state variable and performing the energy estimation routine a plurality of times to determine a respective trial state energy for each of a plurality of different ansatz trial states.
- Claim 19. A computer readable medium comprising computer-executable instructions which, when executed by a quantum processor, cause the processor to: prepare an ansatz trial state using an arrangement of quantum gates, the ansatz trial state having a trial state energy dependent on a trial state variable, estimate an expectation value of each summand respectively, the estimating comprising constructing, based on the arrangement of quantum gates, an initial quantum circuit to operate on the ansatz trial state and performing a summand expectation value determination sub-routine a plurality of times in an iterative process.