# TrotterQRTE

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

Bases: `RealEvolver`

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The TrotterQRTE class has been superseded by the `qiskit.algorithms.time_evolvers.trotterization.TrotterQRTE`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

The class `qiskit.algorithms.evolvers.trotterization.trotter_qrte.TrotterQRTE`

is deprecated as of qiskit-terra 0.24.0. It will be removed no earlier than 3 months after the release date. Instead, use the class `qiskit.algorithms.time_evolvers.trotterization.TrotterQRTE`

. See https://qisk.it/algo_migration(opens in a new tab) for a migration guide.

**Parameters**

**product_formula**(*ProductFormula**| None*) – A Lie-Trotter-Suzuki product formula. The default is the Lie-Trotter first order product formula with a single repetition.**expectation**(*ExpectationBase**| None*) – An instance of ExpectationBase which defines a method for calculating expectation values of EvolutionProblem.aux_operators.**quantum_instance**(*QuantumInstance**|**Backend**| None*) – A quantum instance used for calculating expectation values of EvolutionProblem.aux_operators.

## Attributes

### expectation

Returns an expectation used in the algorithm.

### product_formula

Returns a product formula used in the algorithm.

### quantum_instance

Returns a quantum instance used in the algorithm.

## 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 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.

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

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

is not provided in the EvolutionProblem.

**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 EvolutionProblem can be evaluated, False**

otherwise.

**Return type**