ContinuousTime.optimal_runtime(state=None, step=1)#

Find the optimal running time of a quantum-walk-based search.

This method simulates the use of the set_evolution operator, taking the state as an input for the simulation. It then calculates the success probability for each intermediate state and fits these probabilities to a sine-squared function. The optimal running time corresponds to the point in the domain where the sine-squared function reaches its first peak.

statenumpy.ndarray, default=None

The state initial state for the simulation. If None, uses the uniform state.


Step of the simulation range. See range argument in simulate() for details.

int or float

The optimal runtime that was found after fitting the sine-squared function. The returned type depends on the quantum walk model.