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Update src/qibo/quantum_info/metrics.py
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Co-authored-by: Matteo Robbiati <[email protected]>
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renatomello and MatteoRobbiati authored Dec 9, 2023
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Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions src/qibo/quantum_info/metrics.py
Original file line number Diff line number Diff line change
Expand Up @@ -1157,16 +1157,16 @@ def frame_potential(
For :math:`n` qubits and moment :math:`t`, the frame potential
:math:`\\mathcal{F}_{\\mathcal{U}}^{(t)}` if given by [1]
..math::
.. math::
\\mathcal{F}_{\\mathcal{U}}^{(t)} = \\int_{U,V \\in \\mathcal{U}} \\,
dU \\, dV \\, \\abs{\\tr(U^{\\dagger} \\, V)}^{2t} \\, ,
\\text{d}U \\, \\text{d}V \\, \\text{abs}\\bigl[\\text{tr}(U^{\\dagger} \\, V)\\bigr]^{2t} \\, ,
where :math:`\\mathcal{U}` is the group of unitaries defined by the parametrized circuit.
The frame potential is approximated by the average
..math::
.. math::
\\mathcal{F}_{\\mathcal{U}}^{(t)} \\approx \\frac{1}{N} \\,
\\sum_{k=1}^{N} \\, \\abs{\\tr(U_{k}^{\\dagger} \\, V_{k})}^{2t} \\, ,
\\sum_{k=1}^{N} \\, \\text{abs}\\bigl[ \\text{tr}(U_{k}^{\\dagger} \\, V_{k})\\bigr]^{2t} \\, ,
where :math:`N` is the number of ``samples``.
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