# TrotterQRTE

*class *`TrotterQRTE(product_formula=None, expectation=None, quantum_instance=None)`

Bases: `qiskit.algorithms.evolvers.real_evolver.RealEvolver`

Pending deprecation: Quantum Real Time Evolution using Trotterization.

The TrotterQRTE class has been superseded by the `qiskit.algorithms.time_evolvers.trotterization.TrotterQRTE`

class. This class will be deprecated in a future release and subsequently removed after that.

Type of Trotterization is defined by a ProductFormula provided.

Examples:

```
from qiskit.opflow import X, Z, Zero
from qiskit.algorithms import EvolutionProblem, TrotterQRTE
from qiskit import BasicAer
from qiskit.utils import QuantumInstance
operator = X + Z
initial_state = Zero
time = 1
evolution_problem = EvolutionProblem(operator, 1, initial_state)
# LieTrotter with 1 rep
backend = BasicAer.get_backend("statevector_simulator")
quantum_instance = QuantumInstance(backend=backend)
trotter_qrte = TrotterQRTE(quantum_instance=quantum_instance)
evolved_state = trotter_qrte.evolve(evolution_problem).evolved_state
```

**Parameters**

**product_formula**(`Optional`

[`ProductFormula`

]) – A Lie-Trotter-Suzuki product formula. The default is the Lie-Trotter first order product formula with a single repetition.**expectation**(`Optional`

[`ExpectationBase`

]) – An instance of ExpectationBase which defines a method for calculating expectation values of EvolutionProblem.aux_operators.**quantum_instance**(`Union`

[`Backend`

,`QuantumInstance`

,`None`

]) – A quantum instance used for calculating expectation values of EvolutionProblem.aux_operators.

## Methods

### evolve

`TrotterQRTE.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 an evolved state using a backend provided.

Time-dependent Hamiltonians are not yet supported.

**Parameters**

**evolution_problem** (`EvolutionProblem`

) – Instance defining evolution problem. For the included Hamiltonian, `PauliOp`

, `SummedOp`

or `PauliSumOp`

are supported by TrotterQRTE.

**Return type**

**Returns**

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

**Raises**

**ValueError**– If`t_param`

is not set to None in the EvolutionProblem (feature not currently supported).**ValueError**– If the`initial_state`

is not provided in the EvolutionProblem.

### supports_aux_operators

*classmethod *`TrotterQRTE.supports_aux_operators()`

Whether computing the expectation value of auxiliary operators is supported.

**Return type**

`bool`

**Returns**

**True if aux_operators expectations in the EvolutionProblem can be evaluated, False**

otherwise.