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class qiskit.circuit.library.PauliEvolutionGate(operator, time=1.0, label=None, synthesis=None)

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Bases: Gate

Time-evolution of an operator consisting of Paulis.

For an operator HH consisting of Pauli terms and (real) evolution time tt this gate implements

U(t)=eitH.U(t) = e^{-itH}.

This gate serves as a high-level definition of the evolution and can be synthesized into a circuit using different algorithms.

The evolution gates are related to the Pauli rotation gates by a factor of 2. For example the time evolution of the Pauli XX operator is connected to the Pauli XX rotation RXR_X by

U(t)=eitX=RX(2t).U(t) = e^{-itX} = R_X(2t).


from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import PauliEvolutionGate
from qiskit.quantum_info import SparsePauliOp
X = SparsePauliOp("X")
Z = SparsePauliOp("Z")
# build the evolution gate
operator = (Z ^ Z) - 0.1 * (X ^ I)
evo = PauliEvolutionGate(operator, time=0.2)
# plug it into a circuit
circuit = QuantumCircuit(2)
circuit.append(evo, range(2))

The above will print (note that the -0.1 coefficient is not printed!):

exp(-it (ZZ + XI))(0.2)


[1] G. Li et al. Paulihedral: A Generalized Block-Wise Compiler Optimization Framework For Quantum Simulation Kernels (2021). [arXiv:2109.03371(opens in a new tab)]


  • operator (Pauli |SparsePauliOp |list(opens in a new tab)) – 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].
  • time (Union[int(opens in a new tab), float(opens in a new tab), ParameterExpression]) – The evolution time.
  • label (Optional[str(opens in a new tab)]) – 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.
  • synthesis (Optional[EvolutionSynthesis]) – A synthesis strategy. If None, the default synthesis is the Lie-Trotter product formula with a single repetition.



Get the base class of this instruction. This is guaranteed to be in the inheritance tree of self.

The “base class” of an instruction is the lowest class in its inheritance tree that the object should be considered entirely compatible with for _all_ circuit applications. This typically means that the subclass is defined purely to offer some sort of programmer convenience over the base class, and the base class is the “true” class for a behavioural perspective. In particular, you should not override base_class if you are defining a custom version of an instruction that will be implemented differently by hardware, such as an alternative measurement strategy, or a version of a parametrised gate with a particular set of parameters for the purposes of distinguishing it in a Target from the full parametrised gate.

This is often exactly equivalent to type(obj), except in the case of singleton instances of standard-library instructions. These singleton instances are special subclasses of their base class, and this property will return that base. For example:

>>> isinstance(XGate(), XGate)
>>> type(XGate()) is XGate
>>> XGate().base_class is XGate

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that should be a more suitable discriminator in most situations.


The classical condition on the instruction.


Get Clbits in condition.


Get the decompositions of the instruction from the SessionEquivalenceLibrary.


Return definition in terms of other basic gates.


Get the duration.


Return instruction label


Is this instance is a mutable unique instance or not.

If this attribute is False the gate instance is a shared singleton and is not mutable.


Return the name.


Return the number of clbits.


Return the number of qubits.


The parameters of this Instruction. Ideally these will be gate angles.


Return the evolution time as stored in the gate parameters.


The evolution time.


Get the time unit of duration.




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Gate parameters should be int, float, or ParameterExpression

Return type

float(opens in a new tab) | ParameterExpression

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