hiperwalk.ContinuousTime.set_evolution

ContinuousTime.set_evolution(**kwargs)

Set the evolution operator.

This method defines the evolution operator for a specified time.

Parameters:

**kwargs

Additional arguments for setting Hamiltonian and time. If omitted, the default arguments are used. See hiperwalk.ContinuousTime.set_hamiltonian(), hiperwalk.ContinuousTime.set_time(), and

See also

set_hamiltonian

set_time

Notes

The evolution operator is given by

\[U(t) = \text{exp}(-\text{i}tH),\]

where \(H\) is the Hamiltonian, and \(t\) is the time.

To calculate \(U(t)\), the eigenvalues of \(H\) are calculated first,

\[H = \sum_\lambda \lambda \ket{\lambda} \bra{\lambda}.\]

Then, the evolution operator is computed by

\[U(t) = \sum_\lambda \text{exp}(-\text{i}t\lambda) \ket{\lambda} \bra{\lambda}.\]