ms_infidelity
- Graph.ms_infidelity(phases, displacements, target_phases, mean_phonon_numbers=None, *, name=None)
Calculate the final operational infidelity of the Mølmer–Sørensen gate.
This function calculates the operational infidelity with respect to the target phases that you specify in the target_phases array. It can use the tensors returned from
ms_phases()
andms_displacements()
to calculate the infidelity tensor.- Parameters
phases (np.ndarray(real) or Tensor(real)) – Acquired phases \(\{\Phi_{kl}\}\) for all ion pairs with shape
(N, N)
without time samples or(T, N, N)
, whereT
is the number of samples andN
is the number of ions. For each sample the phases array must be a strictly lower triangular matrix.displacements (np.ndarray(complex) or Tensor(complex)) – Motional displacements \(\{\eta_{jkl} \alpha_{jkl}\}\) in phase-space with shape
(3, N, N)
without time samples or(T, 3, N, N)
, whereT
is the number of samples,3
is the number of spatial axes, andN
is the number of ions that is equal to the number of modes along an axis. The first dimension \(j\) indicates the axis, the second dimension \(k\) indicates the mode number along the axis, and the third dimension \(l\) indicates the ion.target_phases (np.ndarray) – 2D array containing target relative phases \(\{\psi_{kl}\}\) between ion pairs. For ions \(k\) and \(l\), with \(k > l\), the total relative phase target is the \((k, l)\)-th element. The target_phases must be a strictly lower triangular matrix.
mean_phonon_numbers (np.ndarray, optional) – 2D array with shape
(3, N)
of positive real numbers for each motional mode which corresponds to the mean phonon occupation \(\{\bar{n}_{jk}\}\) of the given mode, where3
is the number of spatial axes andN
is the number of ions. If not provided, \(\bar{n}_{jk} = 0\), meaning no occupation of each mode.name (str, optional) – The name of the node.
- Returns
A scalar or 1D tensor of infidelities with shape
(T,)
whereT
is the number of samples and one infidelity value per sample.- Return type
Tensor(real)
See also
ms_dephasing_robust_cost
Cost for robust optimization of a Mølmer–Sørensen gate.
ms_displacements
Displacements for each mode/ion combination.
ms_phases
Relative phases for all pairs of ions.
Notes
The infidelity function is defined as 1:
\[\begin{split}1 - \mathcal{F}_\mathrm{av} = 1 - \left| \left( \prod_{\substack{k=1 \\ l<k}}^N \cos ( \Phi_{kl} - \psi_{kl}) \right) \left( 1 - \sum_{j=1}^3 \sum_{k,l=1}^N \left[ |\eta_{jkl}|^2 |\alpha_{jkl}|^2 \left(\bar{n}_{jk}+\frac{1}{2} \right) \right] \right) \right|^2 .\end{split}\]References
Examples
Refer to the How to optimize error-robust Mølmer–Sørensen gates for trapped ions user guide to find how to use this and related nodes.