Application US20200160204

Hybrid Quantum-Classical Computer for Packing Bits into Qubits for Quantum Optimization Algorithms
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US20200160204

1. A method for reducing the number of qubits with which an operator is represented on a quantum computer, the method comprising: (5) (3)

(1) receiving, as input, at a classical computer, an N-qubit operator;

(2) decomposing, at the classical computer, the N-qubit operator as a linear combination of products of Majorana operators on 2N Majorana modes;

(3) forming, at the classical computer, a second operator, representable on M qubits, based on a linear transformation of the Majorana operators of the N-qubit operator, wherein the linear transformation is from R{circumflex over ( )}(2N) to R{circumflex over ( )}(2M), wherein M<N.

2. The method of claim 1, further comprising: (2) (2)

(4) at the quantum computer, generating marginal expectation values from the packed operator; and

(5) at the classical computer, using the marginal expectation values to generate approximate marginals by approximating an expectation value of the operator.

3. The method of claim 2, wherein the input operator comprises an Ising Hamiltonian. (2) (0)

4. The method of claim 3, further comprising: (2) (1)

8. The method of claim 3, wherein forming the second operator based on the linear transformation comprises performing a packing of 2-planes. (2) (0)

5. The method of claim 2, further comprising: (0) (1)

11. The method of claim 1, wherein the input operator comprises a fermionic Hamiltonian. (0)

12. The method of claim 1, wherein the input operator comprises an ising Hamiltonian. (0)

13. The method of claim 1, wherein the linear transformation comprises a stochastic transformation. (1) (0)

15. The method of claim 1, wherein the linear transformation comprises an explicit transformation. (2) (0)

18. A system comprising: (5) (6)

a classical computer including a processor, a non-transitory computer-readable medium, and computer program instructions stored in the non-transitory computer-readable medium;

a quantum computer comprising a plurality of qubits;

wherein the computer program instructions, when executed by the processor, perform a method for reducing the number of qubits with which an operator is represented on the quantum computer, the method comprising:

(1) receiving, as input, at a classical computer, an N-qubit operator;

(2) decomposing, at the classical computer, the N-qubit operator as a linear combination of products of Majorana operators on 2N Majorana modes;

19. The system of claim 18, wherein the method further comprises: (2) (2)

(4) at the quantum computer, generating marginal expectation values from the packed operator; and

(5) at the classical computer, using the marginal expectation values to generate approximate marginals by approximating an expectation value of the operator.

20. The system of claim 19, wherein the input operator comprises an Ising Hamiltonian. (2) (0)

21. The system of claim 20, wherein the method further comprises: (2) (1)

25. The system of claim 20, wherein forming the second operator based on the linear transformation comprises performing a packing of 2-planes. (2) (0)

22. The system of claim 19, wherein the method further comprises: (0) (1)

28. The system of claim 18, wherein the input operator comprises a fermionic Hamiltonian. (0)

29. The system of claim 18, wherein the input operator comprises an ising Hamiltonian. (0)

30. The system of claim 18, wherein the linear transformation comprises a stochastic transformation. (1) (0)

32. The system of claim 18, wherein the linear transformation comprises an explicit transformation. (2) (0)

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Application US20200160204

Hybrid Quantum-Classical Computer for Packing Bits into Qubits for Quantum Optimization Algorithms

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