qudit_sim.HamiltonianBuilder.noiz_frequencies

HamiltonianBuilder.noiz_frequencies(qudit_id=None, comp_dim=0)

Return the no-IZ frequencies.

No-IZ frame cancels the phase drift of a qudit on average, i.e., when the other qudits are in a fully mixed state. The frame defining matrix is

\[D_{\mathrm{noIZ}} = \sum_{j=1}^{n} \sum_{l} \frac{1}{L^{n-1}} \mathrm{tr} \left[ \left(I_{\hat{j}} \otimes | l \rangle_j \langle l |_j\right) E \right] I_{\hat{j}} \otimes | l \rangle_j \langle l |_j.\]

For comp_dim = d != 0, the trace above is replaced with the pseudo-trace

\[\mathrm{ptr}^{j}_{d} (\cdot) = \bigotimes_{k!=j} \sum_{l_k < d} \langle l_k |_k \cdot | l_k \rangle_k.\]

Parameters

qudit_id (Optional[Hashable]) – Qudit ID. If None, a dict of no-IZ frequencies for all qudits is returned.

Return type

Union[numpy.ndarray, Dict[Hashable, numpy.ndarray]]

Returns

The no-IZ frequency of the specified qudit ID, or a full mapping of qudit ID to frequency arrays.