# TrotterQRTE

`qiskit.algorithms.time_evolvers.trotterization.TrotterQRTE(product_formula=None, estimator=None, num_timesteps=1)`

Bases: `RealTimeEvolver`

Quantum Real Time Evolution using Trotterization. Type of Trotterization is defined by a `ProductFormula`

provided.

## Examples

```
from qiskit.opflow import PauliSumOp
from qiskit.quantum_info import Pauli, SparsePauliOp
from qiskit import QuantumCircuit
from qiskit.algorithms import TimeEvolutionProblem
from qiskit.algorithms.time_evolvers import TrotterQRTE
from qiskit.primitives import Estimator
operator = PauliSumOp(SparsePauliOp([Pauli("X"), Pauli("Z")]))
initial_state = QuantumCircuit(1)
time = 1
evolution_problem = TimeEvolutionProblem(operator, time, initial_state)
# LieTrotter with 1 rep
estimator = Estimator()
trotter_qrte = TrotterQRTE(estimator=estimator)
evolved_state = trotter_qrte.evolve(evolution_problem).evolved_state
```

**Parameters**

**product_formula**(*ProductFormula**| None*) – A Lie-Trotter-Suzuki product formula. If`None`

provided, the Lie-Trotter first order product formula with a single repetition is used.`reps`

should be 1 to obtain a number of time-steps equal to`num_timesteps`

and an evaluation of`TimeEvolutionProblem.aux_operators`

at every time-step. If`reps`

is larger than 1, the true number of time-steps will be`num_timesteps * reps`

.**num_timesteps**(*int*(opens in a new tab)) – The number of time-steps the full evolution time is devided into (repetitions of`product_formula`

)**estimator**(*BaseEstimator**| None*) – An estimator primitive used for calculating expectation values of`TimeEvolutionProblem.aux_operators`

.

## Attributes

### estimator

Returns an estimator.

### num_timesteps

Returns the number of timesteps.

### product_formula

Returns a product formula.

## Methods

### evolve

`evolve(evolution_problem)`

Evolves a quantum state for a given time using the Trotterization method based on a product formula provided. The result is provided in the form of a quantum circuit. If auxiliary operators are included in the `evolution_problem`

, they are evaluated on the `init_state`

and on the evolved state at every step (`num_timesteps`

times) using an estimator primitive provided.

**Parameters**

**evolution_problem** (*TimeEvolutionProblem*) – Instance defining evolution problem. For the included Hamiltonian, `Pauli`

or `PauliSumOp`

are supported by TrotterQRTE.

**Returns**

Evolution result that includes an evolved state as a quantum circuit and, optionally, auxiliary operators evaluated for a resulting state on an estimator primitive.

**Raises**

**ValueError**(opens in a new tab) – If`t_param`

is not set to`None`

in the`TimeEvolutionProblem`

(feature not currently supported).**ValueError**(opens in a new tab) – If`aux_operators`

provided in the time evolution problem but no estimator provided to the algorithm.**ValueError**(opens in a new tab) – If the`initial_state`

is not provided in the`TimeEvolutionProblem`

.**ValueError**(opens in a new tab) – If an unsupported Hamiltonian type is provided.

**Return type**

### supports_aux_operators

`classmethod supports_aux_operators()`

Whether computing the expectation value of auxiliary operators is supported.

**Returns**

`True`

if `aux_operators`

expectations in the `TimeEvolutionProblem`

can be evaluated, `False`

otherwise.

**Return type**