Application US20200226487

Measurement Reduction Via Orbital Frames Decompositions On Quantum Computers
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US20200226487

1. A method for using a measurement module to compute an expectation value of a first operator more efficiently than Pauli-based grouping, the first operator comprising a plurality of component operators, wherein at least one of the plurality of component operators is not a product of Pauli operators, the method comprising: (7) (1)

1) computing the expectation value of the first operator, comprising: (a) on a quantum computer, using the measurement module to make a quantum measurement of at least one of the plurality of component operators, to produce a plurality of measurement outcomes of the at least one of the plurality of component operators; and

(b) on a classical computer, computing the expectation value of the first operator by averaging at least some of the plurality of measurement outcomes.

2. The method of claim 1, further comprising, before (1), decomposing the first operator into a decomposition of the plurality of component operators. (4) (0)

7. The method of claim 1, wherein making the quantum measurement comprises, for each component operator, applying a corresponding orbital rotation. (0)

8. The method of claim 1, further comprising, on the classical computer, computing a plurality of component operator expectation values based on the plurality of measurement outcomes. (2) (0)

11. The method of claim 1, wherein averaging the at least some of the plurality of measurement outcomes comprises computing a weighted average of the at least some of the plurality of measurement outcomes. (0)

12. The method of claim 1, wherein the first operator comprises a Hamiltonian operator. (0)

13. The method of claim 1, wherein the first operator comprises a sum of a Hamiltonian operator and a penalty operator. (3) (0)

17. The method of claim 1, further comprising estimating excited state energies of the first operator. (0)

18. A system for using a measurement module to compute an expectation value of a first operator more efficiently than Pauli-based grouping, the first operator comprising a plurality of component operators, wherein at least one of the plurality of component operators is not a product of Pauli operators, the system comprising: (7) (2)

a quantum computer comprising the measurement module, wherein the measurement module is adapted to make a quantum measurement of at least one of the plurality of component operators, to produce a plurality of measurement outcomes of the at least one of the plurality of component operators; and

a classical computer comprising at least one processor and at least one non-transitory computer-readable medium comprising computer program instructions which, when executed by the at least one processor, cause the at least one processor to compute the expectation value of the operator by averaging at least some of the plurality of measurement outcomes.

19. The system of claim 18, wherein the computer program instructions further comprise computer program instructions which, when executed by the at least one processor, cause the at least one processor to decompose the first operator into a decomposition of the plurality of component operators. (4) (0)

24. The system of claim 18, wherein the measurement module further comprises means for applying a corresponding orbital rotation for each component operator. (0)

25. The system of claim 18, wherein the computer program instructions further comprise computer program instructions which, when executed by the at least one processor, cause the at least one processor to compute a plurality of component operator expectation values based on the plurality of measurement outcomes. (2) (0)

28. The system of claim 18, wherein averaging the at least some of the plurality of measurement outcomes comprises computing a weighted average of the at least some of the plurality of measurement outcomes. (0)

29. The system of claim 18, wherein the first operator comprises a Hamiltonian operator. (0)

30. The system of claim 18, wherein the first operator comprises a sum of a Hamiltonian operator and a penalty operator. (3) (0)

34. The system of claim 18, wherein the computer program instructions further comprise computer program instructions which, when executed by the at least one processor, cause the at least one processor to estimate excited state energies of the first operator. (0)

35. A method for computing an expectation value of a first operator more efficiently than Pauli-based grouping, the first operator comprising a plurality of component operators, wherein at least one of the plurality of component operators is not a product of Pauli operators, the method performed by a classical computer comprising at least one processor and at least one non-transitory computer-readable medium comprising computer program instructions executable by the at least one processor to perform the method, the method comprising: (2) (1)

38. A system for computing an expectation value of a first operator more efficiently than Pauli-based grouping, the first operator comprising a plurality of component operators, wherein at least one of the plurality of component operators is not a product of Pauli operators, the system comprising at least one non-transitory computer-readable medium comprising computer program instructions executable by at least one processor to perform a method, the method comprising: (1) (1)

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Application US20200226487

Measurement Reduction Via Orbital Frames Decompositions On Quantum Computers

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