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

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Bases: RealTimeEvolver

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


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


  • 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.



Returns an estimator.


Returns the number of timesteps.


Returns a product formula.




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.


evolution_problem (TimeEvolutionProblem) – Instance defining evolution problem. For the included Hamiltonian, Pauli or PauliSumOp are supported by TrotterQRTE.


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


Return type



classmethod supports_aux_operators()

Whether computing the expectation value of auxiliary operators is supported.


True if aux_operators expectations in the TimeEvolutionProblem can be evaluated, False otherwise.

Return type

bool(opens in a new tab)

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