ihu[source]

ihu(ham_func, u0, evolution_time, no_time_step_for_eval, **kwargs)

evolves the unitary

Parameters

ham_func : function Function which produces the Hamiltonian as it appears at time t form ham_func(t) u0 : ndarray Unitary at time 0 evolution_time : float Evolution time no_time_step_for_eval : int no of time steps for evaluation in the final output **kwargs Arbitrary optional keyword arguments. w : float Defaults to 6.28

Returns

Bunch object with the following fields defined: t : [ndarray, shape (n_points,)] Time points. y : [ndarray, shape (n, n_points)] Values of the solution at t. sol: [OdeSolution or None] Found solution as OdeSolution instance; None if dense_output was set to False. t_events: [list of ndarray or None] Contains for each event type a list of arrays at which an event of that type event was detected. None if events was None. nfev: [int] Number of evaluations of the right-hand side. njev: [int] Number of evaluations of the Jacobian. nlu :[int] Number of LU decompositions. status [int] Reason for algorithm termination: • -1: Integration step failed. • 0: The solver successfully reached the end of tspan. • 1: A termination event occurred. message: [string] Human-readable description of the termination reason. success: [bool] True if the solver reached the interval end or a termination event occurred (status

= 0).

u_series :[ndarray, shape (sqrt(n), sqrt(n), n_points)] Values of the solution at t.

Steps:

• Determines Shape of U0.
• Determines Shape of H (at any random time t).
• If anyone of U, H are non square exit.
• If shapes match proceed else exit.
• make sure Output of H is Hermitian (by trying it out at 3 different times)
• Initialize inputs T, Nt
• Flatten u0 to get y0
• calculate dt = T/ Nt
• make y_der
• evolve y
• collect results
• y_series to u_series
• print messages
• return stuff + u_series

Call syntax

u_series, result = ihu(ham_func, u0, T, no_time_step_for_eval, **kwargs)

linspace(1, 10, 10)

array([ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])

linspace(1, 10, 100)

array([ 1.        ,  1.09090909,  1.18181818,  1.27272727,  1.36363636,
        1.45454545,  1.54545455,  1.63636364,  1.72727273,  1.81818182,
        1.90909091,  2.        ,  2.09090909,  2.18181818,  2.27272727,
        2.36363636,  2.45454545,  2.54545455,  2.63636364,  2.72727273,
        2.81818182,  2.90909091,  3.        ,  3.09090909,  3.18181818,
        3.27272727,  3.36363636,  3.45454545,  3.54545455,  3.63636364,
        3.72727273,  3.81818182,  3.90909091,  4.        ,  4.09090909,
        4.18181818,  4.27272727,  4.36363636,  4.45454545,  4.54545455,
        4.63636364,  4.72727273,  4.81818182,  4.90909091,  5.        ,
        5.09090909,  5.18181818,  5.27272727,  5.36363636,  5.45454545,
        5.54545455,  5.63636364,  5.72727273,  5.81818182,  5.90909091,
        6.        ,  6.09090909,  6.18181818,  6.27272727,  6.36363636,
        6.45454545,  6.54545455,  6.63636364,  6.72727273,  6.81818182,
        6.90909091,  7.        ,  7.09090909,  7.18181818,  7.27272727,
        7.36363636,  7.45454545,  7.54545455,  7.63636364,  7.72727273,
        7.81818182,  7.90909091,  8.        ,  8.09090909,  8.18181818,
        8.27272727,  8.36363636,  8.45454545,  8.54545455,  8.63636364,
        8.72727273,  8.81818182,  8.90909091,  9.        ,  9.09090909,
        9.18181818,  9.27272727,  9.36363636,  9.45454545,  9.54545455,
        9.63636364,  9.72727273,  9.81818182,  9.90909091, 10.        ])

y_der[source]

y_der(t, y, u_shape, ham_func)

Basically dy/dt

Does some stuff.

Parameters

t : float Current time value during the integration y : ndarray flattened unitary at the current time

Returns

dydt : ndarray flattened derivative of the unitary

check_for_stupidity[source]

check_for_stupidity(ham_func, u0)

Perform checks for invalid inputs and the lot

sqrt(9)

3.0