167 lines
11 KiB
Plaintext
167 lines
11 KiB
Plaintext
---
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title: QAOA
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description: API reference for qiskit.algorithms.minimum_eigensolvers.QAOA
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.algorithms.minimum_eigensolvers.QAOA
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---
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# QAOA
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<Class id="qiskit.algorithms.minimum_eigensolvers.QAOA" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.25/qiskit/algorithms/minimum_eigensolvers/qaoa.py" signature="qiskit.algorithms.minimum_eigensolvers.QAOA(sampler, optimizer, *, reps=1, initial_state=None, mixer=None, initial_point=None, aggregation=None, callback=None)" modifiers="class">
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Bases: [`SamplingVQE`](qiskit.algorithms.minimum_eigensolvers.SamplingVQE "qiskit.algorithms.minimum_eigensolvers.sampling_vqe.SamplingVQE")
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The Quantum Approximate Optimization Algorithm (QAOA).
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QAOA is a well-known algorithm for finding approximate solutions to combinatorial-optimization problems \[1].
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The QAOA implementation directly extends [`SamplingVQE`](qiskit.algorithms.minimum_eigensolvers.SamplingVQE "qiskit.algorithms.minimum_eigensolvers.SamplingVQE") and inherits its optimization structure. However, unlike VQE, which can be configured with arbitrary ansatzes, QAOA uses its own fine-tuned ansatz, which comprises $p$ parameterized global $x$ rotations and $p$ different parameterizations of the problem hamiltonian. QAOA is thus principally configured by the single integer parameter, `reps`, which dictates the depth of the ansatz, and thus affects the approximation quality.
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An optional array of $2p$ parameter values, as the [`initial_point`](#qiskit.algorithms.minimum_eigensolvers.QAOA.initial_point "qiskit.algorithms.minimum_eigensolvers.QAOA.initial_point"), may be provided as the starting $\beta$ and $\gamma$ parameters for the QAOA ansatz \[1].
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An operator or a parameterized quantum circuit may optionally also be provided as a custom [`mixer`](#qiskit.algorithms.minimum_eigensolvers.QAOA.mixer "qiskit.algorithms.minimum_eigensolvers.QAOA.mixer") Hamiltonian. This allows in the case of quantum annealing \[2] and QAOA \[3], to run constrained optimization problems where the mixer constrains the evolution to a feasible subspace of the full Hilbert space.
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The following attributes can be set via the initializer but can also be read and updated once the QAOA object has been constructed.
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### sampler
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<Attribute id="qiskit.algorithms.minimum_eigensolvers.QAOA.sampler">
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The sampler primitive to sample the circuits.
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**Type**
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[BaseSampler](qiskit.primitives.BaseSampler "qiskit.primitives.BaseSampler")
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</Attribute>
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### optimizer
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<Attribute id="qiskit.algorithms.minimum_eigensolvers.QAOA.optimizer">
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A classical optimizer to find the minimum energy. This can either be a Qiskit [`Optimizer`](qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer") or a callable implementing the [`Minimizer`](qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer") protocol.
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**Type**
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[Optimizer](qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer") | [Minimizer](qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer")
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</Attribute>
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### reps
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<Attribute id="qiskit.algorithms.minimum_eigensolvers.QAOA.reps">
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The integer parameter $p$. Has a minimum valid value of 1.
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**Type**
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[int](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")
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</Attribute>
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### initial\_state
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<Attribute id="qiskit.algorithms.minimum_eigensolvers.QAOA.initial_state">
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An optional initial state to prepend the QAOA circuit with.
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</Attribute>
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### mixer
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<Attribute id="qiskit.algorithms.minimum_eigensolvers.QAOA.mixer">
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The mixer Hamiltonian to evolve with or a custom quantum circuit. Allows support of optimizations in constrained subspaces \[2, 3] as well as warm-starting the optimization \[4].
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**Type**
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[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") | BaseOperator | [PauliSumOp](qiskit.opflow.primitive_ops.PauliSumOp "qiskit.opflow.primitive_ops.PauliSumOp")
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</Attribute>
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### aggregation
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<Attribute id="qiskit.algorithms.minimum_eigensolvers.QAOA.aggregation">
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A float or callable to specify how the objective function evaluated on the basis states should be aggregated. If a float, this specifies the $\alpha \in [0,1]$ parameter for a CVaR expectation value.
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**Type**
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[float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)") | Callable\[\[[list](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.12)")\[[float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")]], [float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")] | None
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</Attribute>
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### callback
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<Attribute id="qiskit.algorithms.minimum_eigensolvers.QAOA.callback">
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A callback that can access the intermediate data at each optimization step. These data are: the evaluation count, the optimizer parameters for the ansatz, the evaluated value, the the metadata dictionary, and the best measurement.
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**Type**
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Callable\[\[[int](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)"), np.ndarray, [float](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)"), [dict](https://docs.python.org/3/library/stdtypes.html#dict "(in Python v3.12)")\[[str](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.12)"), Any]], None] | None
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</Attribute>
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**References**
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**\[1]: Farhi, E., Goldstone, J., Gutmann, S., “A Quantum Approximate Optimization Algorithm”**
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[arXiv:1411.4028](https://arxiv.org/abs/1411.4028)
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**\[2]: Hen, I., Spedalieri, F. M., “Quantum Annealing for Constrained Optimization”**
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[PhysRevApplied.5.034007](https://doi.org/10.1103/PhysRevApplied.5.034007)
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**\[3]: Hadfield, S. et al, “From the Quantum Approximate Optimization Algorithm to a Quantum**
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Alternating Operator Ansatz” [arXiv:1709.03489](https://arxiv.org/abs/1709.03489)
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**\[4]: Egger, D. J., Marecek, J., Woerner, S., “Warm-starting quantum optimization”**
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[arXiv: 2009.10095](https://arxiv.org/abs/2009.10095)
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**Parameters**
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* **sampler** ([*BaseSampler*](qiskit.primitives.BaseSampler "qiskit.primitives.BaseSampler")) – The sampler primitive to sample the circuits.
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* **optimizer** ([*Optimizer*](qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer") *|*[*Minimizer*](qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer")) – A classical optimizer to find the minimum energy. This can either be a Qiskit [`Optimizer`](qiskit.algorithms.optimizers.Optimizer "qiskit.algorithms.optimizers.Optimizer") or a callable implementing the [`Minimizer`](qiskit.algorithms.optimizers.Minimizer "qiskit.algorithms.optimizers.Minimizer") protocol.
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* **reps** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")) – The integer parameter $p$. Has a minimum valid value of 1.
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* **initial\_state** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") *| None*) – An optional initial state to prepend the QAOA circuit with.
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* **mixer** ([*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") *| BaseOperator |*[*PauliSumOp*](qiskit.opflow.primitive_ops.PauliSumOp "qiskit.opflow.primitive_ops.PauliSumOp")) – The mixer Hamiltonian to evolve with or a custom quantum circuit. Allows support of optimizations in constrained subspaces \[2, 3] as well as warm-starting the optimization \[4].
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* **initial\_point** (*np.ndarray | None*) – An optional initial point (i.e. initial parameter values) for the optimizer. The length of the initial point must match the number of `ansatz` parameters. If `None`, a random point will be generated within certain parameter bounds. `QAOA` will look to the ansatz for these bounds. If the ansatz does not specify bounds, bounds of $-2\pi$, $2\pi$ will be used.
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* **aggregation** ([*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)") *| Callable\[\[*[*list*](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.12)")*\[*[*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")*]],* [*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")*] | None*) – A float or callable to specify how the objective function evaluated on the basis states should be aggregated. If a float, this specifies the $\alpha \in [0,1]$ parameter for a CVaR expectation value.
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* **callback** (*Callable\[\[*[*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")*, np.ndarray,* [*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")*,* [*dict*](https://docs.python.org/3/library/stdtypes.html#dict "(in Python v3.12)")*\[*[*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.12)")*, Any]], None] | None*) – A callback that can access the intermediate data at each optimization step. These data are: the evaluation count, the optimizer parameters for the ansatz, the evaluated value, the metadata dictionary.
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## Attributes
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### initial\_point
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<Attribute id="qiskit.algorithms.minimum_eigensolvers.QAOA.initial_point">
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Return the initial point.
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</Attribute>
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## Methods
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### compute\_minimum\_eigenvalue
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<Function id="qiskit.algorithms.minimum_eigensolvers.QAOA.compute_minimum_eigenvalue" signature="compute_minimum_eigenvalue(operator, aux_operators=None)">
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Compute the minimum eigenvalue of a diagonal operator.
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**Parameters**
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* **operator** (*BaseOperator |* [*PauliSumOp*](qiskit.opflow.primitive_ops.PauliSumOp "qiskit.opflow.primitive_ops.PauliSumOp")) – Diagonal qubit operator.
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* **aux\_operators** (*ListOrDict\[BaseOperator |* [*PauliSumOp*](qiskit.opflow.primitive_ops.PauliSumOp "qiskit.opflow.primitive_ops.PauliSumOp")*] | None*) – Optional list of auxiliary operators to be evaluated with the final state.
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**Returns**
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A [`SamplingMinimumEigensolverResult`](qiskit.algorithms.minimum_eigensolvers.SamplingMinimumEigensolverResult "qiskit.algorithms.minimum_eigensolvers.SamplingMinimumEigensolverResult") containing the optimization result.
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**Return type**
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[SamplingMinimumEigensolverResult](qiskit.algorithms.minimum_eigensolvers.SamplingMinimumEigensolverResult "qiskit.algorithms.minimum_eigensolvers.SamplingMinimumEigensolverResult")
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</Function>
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### supports\_aux\_operators
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<Function id="qiskit.algorithms.minimum_eigensolvers.QAOA.supports_aux_operators" signature="supports_aux_operators()" modifiers="classmethod">
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Whether computing the expectation value of auxiliary operators is supported.
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If the minimum eigensolver computes an eigenstate of the main operator then it can compute the expectation value of the aux\_operators for that state. Otherwise they will be ignored.
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**Returns**
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True if aux\_operator expectations can be evaluated, False otherwise
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**Return type**
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[bool](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")
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</Function>
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</Class>
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