rydiqule.sensor_utils.convert_dm_to_complex

rydiqule.sensor_utils.convert_dm_to_complex(dm: ndarray) → ndarray

Converts density matrices from rydiqule’s computational basis (real, with state 0 removed) to a standard complex basis with all states present.

Solutions computed using one of rydiqule’s built in solvers will always output solutions in the real, 1-dimensional computational basis which is intended as the input for this function. Note that while a full complex density matrix can be useful to view solutions, performing calculations with the full complex density matrix can often add considerable unwanted rounding errors.

Parameters:

dm (numpy.ndarray) – Density matrices in rydiqule’s computational basis (real, with state 0 removed). Has shape (..., b**2-1) where b is the number of states in the basis.

Returns:

Density matrices in the complex basis with state 0 present. Will have shape (..., b, b).

Return type:

numpy.ndarray

Raises:

RydiquleError – If final dimension is of invalid size (i.e. does not correspond to b**2-1, where b is an integer)

Examples

>>> [g, e] = rq.D2_states('Rb85')
>>> c = rq.Cell('Rb85', [g, e], cell_length =  0.00001)
>>> c.add_coupling(states=(g, e), rabi_frequency=1, detuning=1)
>>> sols = rq.solve_steady_state(c)
>>> print(sols.rho)
[0.001313 0.02558  0.000664]
>>> print(rq.sensor_utils.convert_dm_to_complex(sols.rho))
[[9.993359e-01+0.j      1.31399e-03+0.025581j]
 [1.313990e-03-0.025581j 6.64016e-04+0.j     ]]