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# PauliEvolutionGate¶

class PauliEvolutionGate(operator, time=1.0, label=None, synthesis=None)[source]

Bases: Gate

Time-evolution of an operator consisting of Paulis.

For an operator $$H$$ consisting of Pauli terms and (real) evolution time $$t$$ this gate implements

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

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 $$X$$ operator is connected to the Pauli $$X$$ rotation $$R_X$$ by

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

Examples:

from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import PauliEvolutionGate
from qiskit.opflow import I, Z, X

# 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))
print(circuit.draw())


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

     ┌──────────────────────────┐
q_0: ┤0                         ├
│  exp(-it (ZZ + XI))(0.2) │
q_1: ┤1                         ├
└──────────────────────────┘


References:

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

প্যারামিটার
• operator (Pauli | PauliOp | SparsePauliOp | 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].

• time (Union[int, float, ParameterExpression]) -- The evolution time.

• 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.

• synthesis (Optional[EvolutionSynthesis]) -- A synthesis strategy. If None, the default synthesis is the Lie-Trotter product formula with a single repetition.

Methods Defined Here

 validate_parameter Gate parameters should be int, float, or ParameterExpression

Attributes

condition_bits

Get Clbits in condition.

decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

definition

Return definition in terms of other basic gates.

duration

Get the duration.

label

Return instruction label

name

Return the name.

num_clbits

Return the number of clbits.

num_qubits

Return the number of qubits.

params

return instruction params.

time

Return the evolution time as stored in the gate parameters.

রিটার্নস

The evolution time.

unit

Get the time unit of duration.