Application US20200057957

Quantum Computer with Improved Quantum Optimization by Exploiting Marginal Data
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US20200057957

1. A quantum optimization method, comprising: (9) (2)

estimating, on a classical computer and for a quantum state, an expectation value of a Hamiltonian, expressible as a linear combination of observables, based on expectation values of the observables; and

transforming, on the classical computer, one or both of the Hamiltonian and the quantum state to reduce the expectation value of the Hamiltonian.

2. The quantum optimization method of claim 1, further comprising measuring the expectation value of each of the observables on a quantum computer by: (1) (2)

generating the quantum state on the quantum computer; and

measuring, on the quantum computer, said each of the observables for the quantum state.

3. The quantum optimization method of claim 2, wherein said generating the quantum state includes generating the quantum state with a parametrized quantum circuit programmable via one or more circuit parameters. (1) (0)

4. The quantum optimization method of claim 3, further comprising updating the one or more circuit parameters such that the parametrized quantum circuit outputs an updated quantum state that better approximates a ground state of the Hamiltonian. (1) (0)

5. The quantum optimization method of claim 4, further comprising repeating: (0) (6)

said generating the quantum state with the parametrized quantum circuit;

said measuring each of the observables for the quantum state;

said transforming one or both of the Hamiltonian and the quantum state;

updating the Hamiltonian based on said transforming; and

said updating the one or more circuit parameters;

until the one or more circuit parameters have converged.

6. The quantum optimization method of claim 1, wherein said transforming one or both of the Hamiltonian and the quantum state includes applying a unitary transformation to said one or both of the Hamiltonian and the quantum state. (0)

7. The quantum optimization method of claim 1, further comprising generating, on the classical computer, the expectation value of each of the observables. (1) (0)

8. The quantum optimization method of claim 7, further comprising updating, on the classical computer, a first representation of the quantum state based on the expectation value of the Hamiltonian to better approximate a ground state of the Hamiltonian. (1) (0)

9. The quantum optimization method of claim 8, further comprising repeating: (0) (4)

said generating the expectation value of each of the observables;

said transforming one or both of the Hamiltonian and the quantum state; and

said updating the first representation of the quantum state;

until the first representation of the quantum state has converged.

10. The quantum optimization method of claim 1, wherein: (0) (2)

11. The quantum optimization method of claim 1, wherein said transforming one or both of the Hamiltonian and the quantum state includes applying a fermionic transformation to said one or both of the Hamiltonian and the quantum state. (6) (0)

12. The quantum optimization method of claim 11, the fermionic transformation including rotations of active orbitals. (0)

13. The quantum optimization method of claim 11, the fermionic transformation including transformations out of an active space to incorporate at least one of a core orbital and a virtual orbital. (0)

14. The quantum optimization method of claim 11, the fermionic transformation including rotations that respect one or more of an open-shell spin symmetry, a closed-shell spin symmetry, and a geometric symmetry. (0)

15. The quantum optimization method of claim 11, further comprising implementing a quantum subspace expansion technique. (0)

16. The quantum optimization method of claim 11, further comprising implementing a marginal projection technique. (0)

17. The quantum optimization method of claim 11, further comprising obtaining any of the expectation values the observables via orbital frames. (0)

18. The quantum optimization method of claim 1, wherein said transforming one or both of the Hamiltonian and the quantum state includes applying a Majorana fermionic transformation to said one or both of the Hamiltonian and the quantum state. (2) (0)

21. The quantum optimization method of claim 1, wherein said transforming one or both of the Hamiltonian and the quantum state includes applying a spin transformation to said one or both of the Hamiltonian and the quantum state. (0)

22. The quantum optimization method of claim 1, wherein the Hamiltonian is an Ising Hamiltonian configured for solving a combinatorial optimization problem. (0)

23. The quantum optimization method of claim 1, wherein said transforming one or both of the Hamiltonian and the quantum state includes minimizing the expectation value of the Hamiltonian estimated for the quantum state. (1) (0)

25. A computing system configured for quantum optimization, comprising: (1) (4)

a processor;

a memory communicably coupled with the processor and storing machine-readable instructions that, when executed by the processor, control the computing system to:

estimate, for a quantum state, an expectation value of a Hamiltonian, expressible as a linear combination of observables, based on expectation values of the observables, and

transform one or both of the Hamiltonian and the quantum state to reduce the expectation value of the Hamiltonian estimated for the quantum state.

26. The computing system of claim 25, further comprising a quantum computer that is communicably coupled with the processor and configured to measure the expectation value of each of the observables. (0)

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Application US20200057957

Quantum Computer with Improved Quantum Optimization by Exploiting Marginal Data

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