Application US20210042653

METHOD OF DETERMINING A STATE ENERGY
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US20210042653

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 summands; the method comprising performing an energy estimation routine comprising: (9) (4)

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 process;

the 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 energy;

the 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.

2. The method of claim 1, wherein each iteration of the summand expectation value determination sub-routine comprises constructing a new quantum circuit. (4) (0)

3. The method of claim 2, further comprising operating, by the quantum computer, the newly constructed quantum circuit on the ansatz trial state to obtain a measurement value associated with an estimate of the summand expectation value. (1) (0)

5. The method of claim 2, wherein the quantum computer has an associated coherence time, T, and the new quantum circuit in each iteration of the summand expectation value determination sub-routine is constructed based on the coherence time. (0)

6. The method of claim 2, wherein each iteration of the summand expectation value estimation sub-routine further comprises generating, by the quantum computer, a distribution based on the measurement value, and the iterative process comprises updating, by the quantum computer, the distribution with each iteration based on the mean and standard deviation of the distribution of the previous iteration. (1) (0)

9. The method of claim 2, wherein the energy level of a physical system is determined to a required accuracy ∈, and the new quantum circuit in each iteration of the summand expectation value subroutine is constructed based on the required accuracy, ∈. (1) (0)

8. The method of claim 1, wherein the summand expectation value determination sub-routine comprises: (0) (3)

11. The method of claim 1, wherein the energy level is determined to a required accuracy, ∈, and the summand expectation value determination sub-routine is repeated N times, wherein N is dependent on ∈. (0)

12. The method of claim 1, wherein the summand expectation value determination sub-routine is repeated N times, wherein N is based on a coherence time, T, associated with the quantum computer. (0)

13. The method of claim 1, wherein determining the energy level of the physical system comprises identifying the lowest determined trial state energy. (0)

14. The method of claim 1, wherein the trial state variable is updated so as to bring the trial state energy of the next ansatz trial state closer to the energy level of the physical system. (0)

15. The method of claim 1, wherein, on a first time the energy estimation routine is performed, the trial state is prepared using the Hamiltonian of the physical system and/or knowledge of the possible states which may be efficiently prepared using the quantum computer. (0)

16. The method of claim 1, wherein the optimisation procedure comprises repeating the energy estimation routine a plurality of times in an iterative process to determine the energy level of the physical system. (1) (0)

18. The method of claim 1, wherein each summand comprises an operator, optionally wherein the operator is a tensored Pauli matrix. (0)

19. A computer readable medium comprising computer-executable instructions which, when executed by a quantum processor, cause the processor to: (0) (2)

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Application US20210042653

METHOD OF DETERMINING A STATE ENERGY

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