83 lines
4.4 KiB
Plaintext
83 lines
4.4 KiB
Plaintext
---
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title: SuzukiTrotter
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description: API reference for qiskit.synthesis.SuzukiTrotter
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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.SuzukiTrotter
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---
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# SuzukiTrotter
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<Class id="qiskit.synthesis.SuzukiTrotter" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.25/qiskit/synthesis/evolution/suzuki_trotter.py" signature="qiskit.synthesis.SuzukiTrotter(order=2, reps=1, insert_barriers=False, cx_structure='chain', atomic_evolution=None)" modifiers="class">
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Bases: [`ProductFormula`](qiskit.synthesis.ProductFormula "qiskit.synthesis.evolution.product_formula.ProductFormula")
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The (higher order) Suzuki-Trotter product formula.
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The Suzuki-Trotter formulas improve the error of the Lie-Trotter approximation. For example, the second order decomposition is
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$$
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e^{A + B} \approx e^{B/2} e^{A} e^{B/2}.
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$$
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Higher order decompositions are based on recursions, see Ref. \[1] for more details.
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In this implementation, the operators are provided as sum terms of a Pauli operator. For example, in the second order Suzuki-Trotter decomposition we approximate
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$$
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e^{-it(XX + ZZ)} = e^{-it/2 ZZ}e^{-it XX}e^{-it/2 ZZ} + \mathcal{O}(t^3).
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$$
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**References**
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\[1]: D. Berry, G. Ahokas, R. Cleve and B. Sanders, “Efficient quantum algorithms for simulating sparse Hamiltonians” (2006). [arXiv:quant-ph/0508139](https://arxiv.org/abs/quant-ph/0508139) \[2]: N. Hatano and M. Suzuki, “Finding Exponential Product Formulas of Higher Orders” (2005). [arXiv:math-ph/0506007](https://arxiv.org/pdf/math-ph/0506007.pdf)
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<Admonition title="Deprecated since version 0.20.0" type="danger">
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Setting order to an odd number in the constructor of SuzukiTrotter is deprecated as of qiskit-terra 0.20.0. It will be removed no earlier than 3 months after the release date. Suzuki product formulae are symmetric and therefore only defined for even orders.
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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 v3.12)")) – The order of the product formula.
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* **reps** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")) – The number of time steps.
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* **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")) – 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 v3.12)")) – 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.
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* **atomic\_evolution** ([*Callable*](https://docs.python.org/3/library/typing.html#typing.Callable "(in Python v3.12)")*\[\[*[*Pauli*](qiskit.quantum_info.Pauli "qiskit.quantum_info.operators.symplectic.pauli.Pauli") *|*[*SparsePauliOp*](qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.operators.symplectic.sparse_pauli_op.SparsePauliOp")*,* [*float*](https://docs.python.org/3/library/functions.html#float "(in Python v3.12)")*],* [*QuantumCircuit*](qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")*] | None*) – A function to construct the circuit for the evolution of single Pauli string. Per default, a single Pauli evolution is decomposed in a CX chain and a single qubit Z rotation.
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## Attributes
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### settings
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<Attribute id="qiskit.synthesis.SuzukiTrotter.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 v3.12)") – 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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### synthesize
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<Function id="qiskit.synthesis.SuzukiTrotter.synthesize" signature="synthesize(evolution)">
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Synthesize an `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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