Quantum approximate optimization
In a general aspect, a computing system is configured to execute a quantum approximate optimization algorithm. In some aspects, a control system identifies a pair of qubit devices in a quantum processor. The quantum processor includes a connection that provides coupling between the pair of qubit devices. ZZ coupling between the pair of qubit devices is activated to execute a cost function defined in the quantum approximate optimization algorithm. The cost function is associated with a maximum cut problem, and the ZZ coupling is activated by allowing the pair of qubits to evolve under a natural Hamiltonian for a time period τ. One or more of the pair of qubit devices is measured to obtain an output from an execution of the quantum approximate optimization algorithm.
1. A quantum computing method comprising:
by operation of a control system in a quantum computing system, identifying a pair of qubit devices in a quantum processor, wherein the quantum processor comprises a connection that provides coupling between the pair of qubit devices;
activating a ZZ coupling between the pair of qubit devices to execute a cost function defined in a quantum approximate optimization algorithm, the cost function being associated with a maximum cut problem, wherein the ZZ coupling is activated by allowing the pair of qubit devices to evolve under a natural Hamiltonian for a time period τ; and
measuring one or more of the pair of qubit devices to obtain an output from an execution of the quantum approximate optimization algorithm.
2. The quantum computing method of claim 1 , wherein the pair of qubit devices comprises a pair of superconducting qubit devices, and the connection comprises a capacitive connection.
3. The quantum computing method of claim 2 , wherein the pair of qubit devices includes at least one transmon device.
4. The quantum computing method of claim 1 , wherein the ZZ coupling is activated for the time period τ with a coupling strength χ, to evolve the pair of qubit devices under the unitary operator
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τ
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5. The quantum computing method of claim 1 , wherein activating the ZZ coupling between the pair of qubit devices comprises applying a cost function Hamiltonian
Ĥ Cost =½( I ij −σ i z ⊗σ j z )
to the pair of qubit devices for a time period τ, wherein σ i z ⊗σ j z represents a ZZ coupling term for the pair of qubit devices.
6. The quantum computing method of claim 1 , comprising executing multiple iterations of the quantum approximate optimization algorithm, each iteration comprising:
applying a driver Hamiltonian to a set of qubit devices in the quantum processor; and
applying a cost function Hamiltonian to the set of qubit devices in the quantum processor, wherein applying the cost function Hamiltonian comprises activating ZZ couplings between respective pairs of the qubit devices in the quantum processor.
7. The quantum computing method of claim 6 , wherein a graph structure of the maximum cut problem comprises edges that are mapped to connections between the respective pairs of the qubit devices in the quantum processor.
8. A computing system comprising:
a quantum processor;
a control system configured to communicate with the quantum processor and perform operations comprising:
identifying a pair of qubit devices in the quantum processor, wherein the quantum processor comprises a connection that provides coupling between the pair of qubit devices;
activating a ZZ coupling between the pair of qubit devices to execute a cost function defined in a quantum approximate optimization algorithm, the cost function being associated with a maximum cut problem, wherein the ZZ coupling is activated by allowing the pair of qubit devices to evolve under a natural Hamiltonian for a time period τ; and
measuring one or more of the pair of qubit devices to obtain an output from an execution of the quantum approximate optimization algorithm.
9. The computing system of claim 8 , wherein the quantum processor comprises a superconducting quantum processor, the pair of qubit devices comprises a pair of superconducting qubit devices, and the connection comprises a capacitive connection.
10. The computing system of claim 9 , wherein the pair of qubit devices includes at least one transmon device.
11. The computing system of claim 8 , wherein the control system is configured to activate the ZZ coupling for the time period τ with a coupling strength χ, to evolve the pair of qubit devices under the unitary operator
U
(
τ
)
=
e
i
ℏχ
τ
(
1
0
0
0
0
e
-
2
i
ℏχ
τ
0
0
0
0
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-
2
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ℏχ
τ
0
0
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0
1
)
.
12. The computing system of claim 8 , wherein activating the ZZ coupling between the pair of qubit devices comprises applying a cost function Hamiltonian
Ĥ Cost =½( I ij −σ i z ⊗σ j z )
to the pair of qubit devices for a time period τ, wherein σ i z ⊗σ j z represents a ZZ coupling term for the pair of qubit devices.
13. The computing system of claim 8 , wherein the control system is configured to execute multiple iterations of the quantum approximate optimization algorithm, each iteration comprising:
applying a driver Hamiltonian to a set of qubit devices in the quantum processor; and
applying a cost function Hamiltonian to the set of qubit devices in the quantum processor, wherein applying the cost function Hamiltonian comprises activating ZZ couplings between respective pairs of the qubit devices in the quantum processor.
14. The computing system of claim 13 , wherein the control system is configured to map edges from a graph structure of the maximum cut problem to connections between the respective pairs of the qubit devices in the quantum processor.
15. A method comprising:
initiating an execution of a quantum approximate optimization algorithm by a computing system comprising a quantum processor, wherein the execution of the quantum approximate optimization algorithm comprises:
by operation of a control system in the computing system, identifying a pair of qubit devices in the quantum processor, wherein the quantum processor comprises a connection that provides coupling between the pair of qubit devices;
activating a ZZ coupling between the pair of qubit devices to execute a cost function defined in the quantum approximate optimization algorithm, the cost function being associated with a maximum cut problem, wherein the ZZ coupling is activated by allowing the pair of qubit devices to evolve under a natural Hamiltonian for a time period τ; and
measuring one or more of the pair of qubit devices to obtain an output from the execution of the quantum approximate optimization algorithm; and
receiving, from the computing system and in response to the initiating, data based on the output from the execution.
16. The method of claim 15 , wherein the execution is initiated by a remote device that operates remote from the computing system.
17. The method of claim 16 , wherein the remote device initiates the execution and receives the output by communicating with the computing system over a communication network.
18. The method of claim 15 , wherein the execution is initiated by a local device associated with the control system.
19. A method comprising:
identifying a graph structure associated with a maximum cut problem, the graph structure comprising vertices connected by edges;
providing a quantum processor designed to have connections based on the graph structure, the connections in the quantum processor connecting respective pairs of qubit devices in the quantum processor, each connection configured to provide coupling between the pair of qubit devices that it connects; and
configuring a control system to activate a ZZ coupling between each of the respective pairs of qubit devices to execute a cost function defined in a quantum approximate optimization algorithm, the cost function being associated with the maximum cut problem.
20. The method of claim 19 , further comprising manufacturing the quantum processor having the connections.
21. The method of claim 19 , wherein the qubit devices are superconducting qubit devices, and the connections are capacitive connections.
22. The method of claim 21 , wherein each pair of qubit devices includes at least one transmon device.
23. The method of claim 19 , wherein the connections in the quantum processor define a qubit connectivity structure that matches the graph structure of the maximum cut problem.
24. The method of claim 19 , wherein the connections in the quantum processor define a qubit connectivity structure that does not match the graph structure of the maximum cut problem.