PauliEvolutionGate¶

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

Bases: qiskit.circuit.gate.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

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

References:

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

Parameters
• 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.

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

Methods Defined Here

 inverse Invert this instruction. validate_parameter Gate parameters should be int, float, or ParameterExpression

Attributes

condition_bits

Get Clbits in condition.

Return type

List[Clbit]

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

Return type

str

params

return instruction params.

time

Return the evolution time as stored in the gate parameters.

Return type

Union[float, ParameterExpression]

Returns

The evolution time.

unit

Get the time unit of duration.