81 lines
4.4 KiB
Plaintext
81 lines
4.4 KiB
Plaintext
---
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title: hamiltonian_variational_ansatz (latest version)
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description: API reference for qiskit.circuit.library.hamiltonian_variational_ansatz in the latest version of qiskit
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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.circuit.library.hamiltonian_variational_ansatz
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---
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<span id="hamiltonian-variational-ansatz" />
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# hamiltonian\_variational\_ansatz
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<Class id="qiskit.circuit.library.hamiltonian_variational_ansatz" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/n_local/evolved_operator_ansatz.py#L187-L276" signature="qiskit.circuit.library.hamiltonian_variational_ansatz(hamiltonian, reps=1, insert_barriers=False, name='HVA', parameter_prefix='t')" modifiers="class">
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Bases:
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Construct a Hamiltonian variational ansatz.
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For a Hamiltonian $H = \sum_{k=1}^K H_k$ where the terms $H_k$ consist of only commuting Paulis, but the terms do not commute among each other $[H_k, H_{k'}] \neq 0$, the Hamiltonian variational ansatz (HVA) is
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$$
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\prod_{r=1}^{R} \left( \prod_{k=K}^1 e^{-i\theta_{k, r} H_k} \right)
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$$
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where the exponentials $exp(-i\theta H_k)$ are implemented exactly \[1, 2]. Note that this differs from `evolved_operator_ansatz()`, where no assumptions on the structure of the operators are done.
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The Hamiltonian can be passed as [`SparsePauliOp`](qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp"), in which case we split the Hamiltonian into commuting terms $\{H_k\}_k$. Note, that this may not be optimal and if the minimal set of commuting terms is known it can be passed as sequence into this function.
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**Examples**
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A single operator will be split into commuting terms automatically:
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```python
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from qiskit.quantum_info import SparsePauliOp
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from qiskit.circuit.library import hamiltonian_variational_ansatz
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# this Hamiltonian will be split into the two terms [ZZI, IZZ] and [IXI]
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hamiltonian = SparsePauliOp(["ZZI", "IZZ", "IXI"])
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ansatz = hamiltonian_variational_ansatz(hamiltonian, reps=2)
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ansatz.draw("mpl")
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```
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Alternatively, we can directly provide the terms:
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```python
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from qiskit.quantum_info import SparsePauliOp
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from qiskit.circuit.library import hamiltonian_variational_ansatz
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zz = SparsePauliOp(["ZZI", "IZZ"])
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x = SparsePauliOp(["IXI"])
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ansatz = hamiltonian_variational_ansatz([zz, x], reps=2)
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ansatz.draw("mpl")
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```
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**Parameters**
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* **hamiltonian** ([*SparsePauliOp*](qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp") *| Sequence\[*[*SparsePauliOp*](qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")*]*) – The Hamiltonian to evolve. If given as single operator, it will be split into commuting terms. If a sequence of [`SparsePauliOp`](qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp"), then it is assumed that each element consists of commuting terms, but the elements do not commute among each other.
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* **reps** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")) – The number of times to repeat the evolved operators.
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* **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – Whether to insert barriers in between each evolution.
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* **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)")) – The name of the circuit.
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* **parameter\_prefix** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)")) – Set the names of the circuit parameters. If a string, the same prefix will be used for each parameters. Can also be a list to specify a prefix per operator.
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**Return type**
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[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
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**References**
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**\[1] D. Wecker et al. Progress towards practical quantum variational algorithms (2015)**
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[Phys Rev A 92, 042303](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.042303)
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**\[2] R. Wiersema et al. Exploring entanglement and optimization within the Hamiltonian**
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Variational Ansatz (2020) [arXiv:2008.02941](https://arxiv.org/abs/2008.02941)
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</Class>
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