155 lines
5.4 KiB
Plaintext
155 lines
5.4 KiB
Plaintext
---
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title: PauliEvolutionGate
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description: API reference for qiskit.circuit.library.PauliEvolutionGate
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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.PauliEvolutionGate
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---
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# PauliEvolutionGate
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<Class id="qiskit.circuit.library.PauliEvolutionGate" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.24/qiskit/circuit/library/pauli_evolution.py" signature="PauliEvolutionGate(operator, time=1.0, label=None, synthesis=None)" modifiers="class">
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Bases: [`Gate`](qiskit.circuit.Gate "qiskit.circuit.gate.Gate")
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Time-evolution of an operator consisting of Paulis.
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For an operator $H$ consisting of Pauli terms and (real) evolution time $t$ this gate implements
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$$
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U(t) = e^{-itH}.
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$$
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This gate serves as a high-level definition of the evolution and can be synthesized into a circuit using different algorithms.
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The evolution gates are related to the Pauli rotation gates by a factor of 2. For example the time evolution of the Pauli $X$ operator is connected to the Pauli $X$ rotation $R_X$ by
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$$
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U(t) = e^{-itX} = R_X(2t).
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$$
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**Examples:**
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```python
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from qiskit.circuit import QuantumCircuit
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from qiskit.circuit.library import PauliEvolutionGate
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from qiskit.opflow import I, Z, X
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# build the evolution gate
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operator = (Z ^ Z) - 0.1 * (X ^ I)
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evo = PauliEvolutionGate(operator, time=0.2)
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# plug it into a circuit
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circuit = QuantumCircuit(2)
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circuit.append(evo, range(2))
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print(circuit.draw())
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```
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The above will print (note that the `-0.1` coefficient is not printed!):
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```python
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┌──────────────────────────┐
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q_0: ┤0 ├
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│ exp(-it (ZZ + XI))(0.2) │
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q_1: ┤1 ├
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└──────────────────────────┘
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```
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**References:**
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\[1] G. Li et al. Paulihedral: A Generalized Block-Wise Compiler Optimization Framework For Quantum Simulation Kernels (2021). \[[arXiv:2109.03371](https://arxiv.org/abs/2109.03371)]
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**Parameters**
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* **operator** ([*Pauli*](qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli") *|*[*PauliOp*](qiskit.opflow.primitive_ops.PauliOp "qiskit.opflow.primitive_ops.PauliOp") *|*[*SparsePauliOp*](qiskit.quantum_info.SparsePauliOp "qiskit.quantum_info.SparsePauliOp") *|*[*PauliSumOp*](qiskit.opflow.primitive_ops.PauliSumOp "qiskit.opflow.primitive_ops.PauliSumOp") *| list*) – The operator to evolve. Can also be provided as list of non-commuting operators where the elements are sums of commuting operators. For example: `[XY + YX, ZZ + ZI + IZ, YY]`.
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* **time** (*Union\[int, float,* [*ParameterExpression*](qiskit.circuit.ParameterExpression "qiskit.circuit.ParameterExpression")*]*) – The evolution time.
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* **label** (*Optional\[str]*) – A label for the gate to display in visualizations. Per default, the label is set to `exp(-it <operators>)` where `<operators>` is the sum of the Paulis. Note that the label does not include any coefficients of the Paulis. See the class docstring for an example.
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* **synthesis** (*Optional\[*[*EvolutionSynthesis*](qiskit.synthesis.EvolutionSynthesis "qiskit.synthesis.EvolutionSynthesis")*]*) – A synthesis strategy. If None, the default synthesis is the Lie-Trotter product formula with a single repetition.
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## Methods Defined Here
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<span id="qiskit-circuit-library-paulievolutiongate-validate-parameter" />
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### validate\_parameter
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<Function id="qiskit.circuit.library.PauliEvolutionGate.validate_parameter" signature="PauliEvolutionGate.validate_parameter(parameter)">
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Gate parameters should be int, float, or ParameterExpression
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**Return type**
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float | [*ParameterExpression*](qiskit.circuit.ParameterExpression "qiskit.circuit.parameterexpression.ParameterExpression")
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</Function>
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## Attributes
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### condition\_bits
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.condition_bits">
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Get Clbits in condition.
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</Attribute>
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### decompositions
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.decompositions">
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Get the decompositions of the instruction from the SessionEquivalenceLibrary.
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</Attribute>
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### definition
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.definition">
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Return definition in terms of other basic gates.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.duration">
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Get the duration.
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</Attribute>
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### label
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.label">
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Return instruction label
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</Attribute>
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### name
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.name">
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Return the name.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.num_clbits">
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Return the number of clbits.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.num_qubits">
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Return the number of qubits.
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</Attribute>
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### params
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.params">
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return instruction params.
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</Attribute>
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### time
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.time">
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Return the evolution time as stored in the gate parameters.
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**Returns**
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The evolution time.
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.PauliEvolutionGate.unit">
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Get the time unit of duration.
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</Attribute>
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</Class>
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