# Operator Evolutions (qiskit.opflow.evolutions)¶

Evolutions are converters which traverse an Operator tree, replacing any EvolvedOp e with a Schrodinger equation-style evolution CircuitOp equalling or approximating the matrix exponential of -i * the Operator contained inside (e.primitive). The Evolutions are essentially implementations of Hamiltonian Simulation algorithms, including various methods for Trotterization.

The EvolvedOp is simply a placeholder signifying that the Operator inside it should be converted to its exponential by the Evolution converter. All Operators (not state_fns) have .exp_i() methods which either return the exponential of the Operator directly, or an EvolvedOp containing the Operator.

Note

Evolutions work with parameterized Operator coefficients, so my_expectation.convert((t * H).exp_i()), where t is a scalar or Terra Parameter and H is an Operator, will produce a CircuitOp equivalent to e^iHt.

# Evolution Base Class¶

The EvolutionBase class gives an interface for algorithms to ask for Evolutions as execution settings. For example, if an algorithm contains an Operator evolution step within it, such as QAOA, the algorithm can give the opportunity for the user to pass an EvolutionBase of their choice to be used in that evolution step.

 EvolutionBase A base for Evolution converters.

# Evolutions¶

 EvolutionFactory A factory class for convenient automatic selection of an Evolution algorithm based on the Operator to be converted. EvolvedOp Class for wrapping Operator Evolutions for compilation (convert) by an EvolutionBase method later, essentially acting as a placeholder. MatrixEvolution Performs Evolution by classical matrix exponentiation, constructing a circuit with UnitaryGates or HamiltonianGates containing the exponentiation of the Operator. PauliTrotterEvolution An Evolution algorithm replacing exponentiated sums of Paulis by changing them each to the Z basis, rotating with an rZ, changing back, and Trotterizing.

# Trotterizations¶

 TrotterizationBase A base for Trotterization methods, algorithms for approximating exponentiations of operator sums by compositions of exponentiations. TrotterizationFactory A factory for conveniently creating TrotterizationBase instances. Trotter Simple Trotter expansion, composing the evolution circuits of each Operator in the sum together reps times and dividing the evolution time of each by reps. Suzuki Suzuki Trotter expansion, composing the evolution circuits of each Operator in the sum together by a recursive « bookends » strategy, repeating the whole composed circuit reps times. QDrift The QDrift Trotterization method, which selects each each term in the Trotterization randomly, with a probability proportional to its weight.