# PauliEvolutionGate

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

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.quantum_info import SparsePauliOp
X = SparsePauliOp("X")
Z = SparsePauliOp("Z")
I = SparsePauliOp("I")
# 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]

**Parameters**

**operator**(*Pauli**|**SparsePauliOp**|**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.

## Attributes

### base_class

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 behavioral 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 parametrized gate with a particular set of parameters for the purposes of distinguishing it in a `Target`

from the full parametrized 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)
True
>>> type(XGate()) is XGate
False
>>> XGate().base_class is XGate
True
```

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that `Instruction.name`

should be a more suitable discriminator in most situations.

### condition

The classical condition on the instruction.

### 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

### mutable

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.

### name

Return the name.

### num_clbits

Return the number of clbits.

### num_qubits

Return the number of qubits.

### params

The parameters of this `Instruction`

. Ideally these will be gate angles.

### time

Return the evolution time as stored in the gate parameters.

**Returns**

The evolution time.

### unit

Get the time unit of duration.

## Methods

### validate_parameter

`validate_parameter(parameter)`

Gate parameters should be int, float, or ParameterExpression

**Return type**