Accelerating hybrid quantum/classical algorithms
In a general aspect, hybrid quantum/classical algorithms are executed in a computing system. A first set of values representing a measurement of a reduced density matrix (RDM) is obtained. The first set of values is based on sampling quantum states generated by a quantum processor. A classical processor generates a second, different set of values to represent the measurement of the RDM. The second set of values is constructed based on the first set of values by a process that imposes one or more n-representability conditions on the second set of values to represent the measurement of the RDM.
1. A computing method comprising:
obtaining a first set of values representing a measurement of a reduced density matrix (RDM), wherein the first set of values is based on sampling quantum states generated by one or more quantum processors;
computing expectation values by performing a partial tomography of the first set of values; and
by operation of one or more classical processors, constructing a second, different set of values to represent the measurement of the RDM, wherein the second set of values is constructed based on the first set of values by a process that imposes one or more n-representability conditions on the second set of values to represent the measurement of the RDM,
wherein the process that imposes the one or more n-representability conditions receives the expectation values as input and produces the second set of values as output.
2. The computing method of claim 1 , wherein constructing the second set of values removes errors associated with the first set of values.
3. The computing method of claim 1 , wherein the one or more quantum processors include at least one gate-based quantum processor or at least one annealing quantum processor.
4. The computing method of claim 1 , wherein the computing method is performed by a hybrid classical-quantum computing system comprising the one or more classical processors and the one or more quantum processors, and the computing method further comprises providing the second set of values for use in an iteration of a hybrid quantum-classical algorithm executed by the hybrid classical-quantum computing system.
5. The computing method of claim 1 , wherein the one or more n-representability conditions comprise one or more fermionic n-representability conditions.
6. The computing method of claim 1 , wherein the RDM comprises a two-particle RDM.
7. The computing method of claim 1 , wherein the process that imposes the one or more n-representability conditions executes a semidefinite program.
8. The computing method of claim 1 , wherein the process that imposes the one or more n-representability conditions performs a positive-semidefinite projection.
9. The computing method of claim 1 , wherein the process that imposes the one or more n-representability conditions performs a positive-semidefinite projection with fixed trace.
10. The computing method of claim 1 , wherein the process that imposes the one or more n-representability conditions comprises an iterative process.
11. The computing method of claim 1 , wherein the one or more quantum processors comprise at least two quantum processors.
12. A system comprising:
one or more classical processors; and
one or more quantum processors;
wherein the one or more classical processors are configured to:
obtain a first set of values representing a measurement of a reduced density matrix (RDM), wherein the first set of values is based on sampling quantum states generated by the one or more quantum processors;
compute expectation values by performing a partial tomography of the first set of values; and
construct a second, different set of values to represent the measurement of the RDM, wherein the second set of values is constructed based on the first set of values by a process that imposes one or more n-representability conditions on the second set of values to represent the measurement of the RDM,
wherein the process that imposes the one or more n-representability conditions receives the expectation values as input and produces the second set of values as output.
13. The system of claim 12 , wherein constructing the second set of values removes errors associated with the first set of values.
14. The system of claim 12 , wherein the one or more quantum processors include at least one gate-based quantum processor or at least one annealing quantum processor.
15. The system of claim 12 , wherein the system comprises a hybrid classical-quantum computing system comprising the one or more classical processors and the one or more quantum processors, and the one or more classical processors are further configured to provide the second set of values for use in an iteration of a hybrid quantum-classical algorithm executed by the hybrid classical-quantum computing system.
16. The system of claim 12 , wherein the one or more n-representability conditions comprise one or more fermionic n-representability conditions.
17. The system of claim 12 , wherein the RDM comprises a two-particle RDM.
18. The system of claim 12 , wherein the process that imposes the one or more n-representability conditions executes a semidefinite program.
19. The system of claim 12 , wherein the process that imposes the one or more n-representability conditions performs a positive-semidefinite projection.
20. The system of claim 12 , wherein the process that imposes the one or more n-representability conditions performs a positive-semidefinite projection with fixed trace.
21. The system of claim 12 , wherein the process that imposes the one or more n-representability conditions comprises an iterative process.
22. The system of claim 12 , wherein the one or more quantum processors comprise at least two quantum processors.