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Changed documentation of channels. #808

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Mar 1, 2023
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Changed documentation of channels. #808

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8 changes: 4 additions & 4 deletions src/qibo/gates/channels.py
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Original file line number Diff line number Diff line change
Expand Up @@ -310,15 +310,15 @@ class DepolarizingChannel(Channel):
""":math:`n`-qubit Depolarizing quantum error channel,

.. math::
\\mathcal{E}(\\rho ) = (1 - \\lambda) \\rho +\\lambda \\text{Tr}[\\rho] \\frac{I}{2^n}
\\mathcal{E}(\\rho ) = (1 - \\lambda) \\rho +\\lambda \\text{Tr}_q[\\rho]\\otimes \\frac{I}{2^n}

where :math:`\\lambda` is the depolarizing error parameter and :math:`0 \\le \\lambda \\le 4^n / (4^n - 1)`.

* If :math:`\\lambda = 1` this is a completely depolarizing channel
:math:`E(\\rho) = I / 2^n`
* If :math:`\\lambda = 4^n / (4^n - 1)` this is a uniform Pauli
error channel: :math:`E(\\rho) = \\sum_j P_j \\rho P_j / (4^n - 1)` for
all :math:`P_j != I`.
all :math:`P_j \\neq I`.

Args:
q (tuple): Qubit ids that the noise acts on.
Expand Down Expand Up @@ -371,7 +371,7 @@ class ResetChannel(Channel):

.. math::
\\mathcal{E}(\\rho ) = (1 - p_0 - p_1) \\rho
+ \\mathrm{Tr}\\rho \\otimes (p_0|0\\rangle \\langle 0| + p_1|1\\rangle \\langle 1|)
+ \\mathrm{Tr}_q[\\rho] \\otimes (p_0|0\\rangle \\langle 0| + p_1|1\\rangle \\langle 1|),

Args:
q (int): Qubit id that the channel acts on.
Expand Down Expand Up @@ -400,7 +400,7 @@ class ThermalRelaxationChannel(Channel):

.. math::
\\mathcal{E} (\\rho ) = (1 - p_z - p_0 - p_1)\\rho + p_zZ\\rho Z
+ \\mathrm{Tr}\\rho \\otimes (p_0|0\\rangle \\langle 0| + p_1|1\\rangle \\langle 1|)
+ \\mathrm{Tr}_q[\\rho] \\otimes (p_0|0\\rangle \\langle 0| + p_1|1\\rangle \\langle 1|)


while if :math:`T_1 < T_2`:
Expand Down