87 lines
6.6 KiB
Plaintext
87 lines
6.6 KiB
Plaintext
---
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title: ProductFormula (v1.4)
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description: API reference for qiskit.synthesis.ProductFormula in qiskit v1.4
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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.synthesis.ProductFormula
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---
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# ProductFormula
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<Class id="qiskit.synthesis.ProductFormula" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.4/qiskit/synthesis/evolution/product_formula.py#L39-L231" signature="qiskit.synthesis.ProductFormula(order, reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None, wrap=False, preserve_order=True)" modifiers="class">
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Bases: [`EvolutionSynthesis`](qiskit.synthesis.EvolutionSynthesis "qiskit.synthesis.evolution.evolution_synthesis.EvolutionSynthesis")
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Product formula base class for the decomposition of non-commuting operator exponentials.
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[`LieTrotter`](qiskit.synthesis.LieTrotter "qiskit.synthesis.LieTrotter") and [`SuzukiTrotter`](qiskit.synthesis.SuzukiTrotter "qiskit.synthesis.SuzukiTrotter") inherit from this class.
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<Admonition title="Deprecated since version 1.4" type="danger">
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The ‘Callable\[\[Pauli | SparsePauliOp, float], QuantumCircuit]’ signature of the ‘atomic\_evolution’ argument is deprecated as of qiskit 1.4. It will be removed no earlier than 3 months after the release date. Instead you should update your ‘atomic\_evolution’ function to be of the following type: ‘Callable\[\[QuantumCircuit, Pauli | SparsePauliOp, float], None]’.
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</Admonition>
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**Parameters**
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* **order** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")) – The order of the product formula.
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* **reps** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")) – The number of time steps.
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* **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – Whether to insert barriers between the atomic evolutions.
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* **cx\_structure** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)")) – How to arrange the CX gates for the Pauli evolutions, can be `"chain"`, where next neighbor connections are used, or `"fountain"`, where all qubits are connected to one. This only takes effect when `atomic_evolution is None`.
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* **atomic\_evolution** (*Callable\[\[*[*Pauli*](qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli") *|*[*SparsePauliOp*](qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")*,* [*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")*],* [*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")*] | Callable\[\[*[*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")*,* [*Pauli*](qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli") *|*[*SparsePauliOp*](qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp")*,* [*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.13)")*], None] | None*) – A function to apply the evolution of a single [`Pauli`](qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli"), or [`SparsePauliOp`](qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp") of only commuting terms, to a circuit. The function takes in three arguments: the circuit to append the evolution to, the Pauli operator to evolve, and the evolution time. By default, a single Pauli evolution is decomposed into a chain of `CX` gates and a single `RZ` gate. Alternatively, the function can also take Pauli operator and evolution time as inputs and returns the circuit that will be appended to the overall circuit being built.
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* **wrap** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – Whether to wrap the atomic evolutions into custom gate objects. Note that setting this to `True` is slower than `False`. This only takes effect when `atomic_evolution is None`.
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* **preserve\_order** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – If `False`, allows reordering the terms of the operator to potentially yield a shallower evolution circuit. Not relevant when synthesizing operator with a single term.
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## Attributes
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### settings
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<Attribute id="qiskit.synthesis.ProductFormula.settings">
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Return the settings in a dictionary, which can be used to reconstruct the object.
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**Returns**
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A dictionary containing the settings of this product formula.
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**Raises**
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[**NotImplementedError**](https://docs.python.org/3/library/exceptions.html#NotImplementedError "(in Python v3.13)") – If a custom atomic evolution is set, which cannot be serialized.
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</Attribute>
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## Methods
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### expand
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<Function id="qiskit.synthesis.ProductFormula.expand" github="https://github.com/Qiskit/qiskit/tree/stable/1.4/qiskit/synthesis/evolution/product_formula.py#L127-L143" signature="expand(evolution)">
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Apply the product formula to expand the Hamiltonian in the evolution gate.
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**Parameters**
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**evolution** ([*PauliEvolutionGate*](qiskit.circuit.library.PauliEvolutionGate "qiskit.circuit.library.PauliEvolutionGate")) – The [`PauliEvolutionGate`](qiskit.circuit.library.PauliEvolutionGate "qiskit.circuit.library.PauliEvolutionGate"), whose Hamiltonian we expand.
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**Returns**
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A list of Pauli rotations in a sparse format, where each element is `(paulistring, qubits, coefficient)`. For example, the Lie-Trotter expansion of `H = XI + ZZ` would return `[("X", [1], 1), ("ZZ", [0, 1], 1)]`.
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**Return type**
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[list](https://docs.python.org/3/library/stdtypes.html#list "(in Python v3.13)")\[[tuple](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.13)")\[[str](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)"), [tuple](https://docs.python.org/3/library/stdtypes.html#tuple "(in Python v3.13)")\[[int](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")], ParameterValueType]]
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</Function>
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### synthesize
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<Function id="qiskit.synthesis.ProductFormula.synthesize" github="https://github.com/Qiskit/qiskit/tree/stable/1.4/qiskit/synthesis/evolution/product_formula.py#L145-L167" signature="synthesize(evolution)">
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Synthesize a [`PauliEvolutionGate`](qiskit.circuit.library.PauliEvolutionGate "qiskit.circuit.library.PauliEvolutionGate").
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**Parameters**
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**evolution** ([*PauliEvolutionGate*](qiskit.circuit.library.PauliEvolutionGate "qiskit.circuit.library.PauliEvolutionGate")) – The evolution gate to synthesize.
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**Returns**
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A circuit implementing the evolution.
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**Return type**
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[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
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</Function>
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</Class>
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