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doc/source/protocols/readout_optimization.rst

@@ -1,8 +1,8 @@
 Readout optimization
 ====================
 
-Qibocal provides a protocol to improve the readout pulse amplitude by optimize 
-the assignment fidelity. 
+Qibocal provides a protocol to improve the readout pulse amplitude by optimize
+the assignment fidelity.
 
 Parameters
 ^^^^^^^^^^

doc/source/protocols/standard_rb.rst

@@ -1,20 +1,20 @@
 Standard Randomize Benchmarking
 ===============================
 
-An approach to obtain the average gate fidelity is to perform randomized 
+An approach to obtain the average gate fidelity is to perform randomized
 benchmarking :cite:p:`Emerson_2005`.
-The key idea is that if we average the error process over the uniform space of 
-unitaries the result is a depolarizing channel that maps any pure state to the 
-maximally mixed state. 
+The key idea is that if we average the error process over the uniform space of
+unitaries the result is a depolarizing channel that maps any pure state to the
+maximally mixed state.
 Such uniform space of unitaries is known as *Haar measure*.
 It can be shown :cite:p:`Emerson_2005` that the average induced error is proportional
 to the depolarization probability.
 However, this approach is inefficient because we sample randomly from the Haar measure.
-A simplification was proposed in :cite:p:`Knill2008` by restricting the unitaries 
-to the Clifford group, which consists of unitary rotations mapping the group 
+A simplification was proposed in :cite:p:`Knill2008` by restricting the unitaries
+to the Clifford group, which consists of unitary rotations mapping the group
 of Pauli operators in itself.
-Among the advantages of such group are the fact of the number of Clifford 
-gates is finite given the Hilbert space and being a group we can easily found 
+Among the advantages of such group are the fact of the number of Clifford
+gates is finite given the Hilbert space and being a group we can easily found
 the inverse within the group.
 The generic procedure to perform a randomized benchmarking is the following:
 
@@ -24,7 +24,7 @@ The generic procedure to perform a randomized benchmarking is the following:
 4. measure sequence and inverse gate
 5. repeat the process for multiple sequence of same length and varying the length
 
-The previous approach works because it has been shown :cite:p:`Nielsen_2002` that 
+The previous approach works because it has been shown :cite:p:`Nielsen_2002` that
 randomization with Clifford gates provides again a depolarized noise channel
 
 .. math::
@@ -33,7 +33,7 @@ randomization with Clifford gates provides again a depolarized noise channel
     \rho \rightarrow \frac{d}{2} I + ( 1 - d) \rho
 
 with depolarization probability :math:`d`.
-If we follow the previous procedure and we measure the survival probability, i.e. 
+If we follow the previous procedure and we measure the survival probability, i.e.
 the probability of measuring the qubit in :math:`\ket{0}`, for
 different sequence length :math:`m` we expect the following behavior
 
@@ -42,7 +42,7 @@ different sequence length :math:`m` we expect the following behavior
 
     F(m) = A p^m + B
 
-where :math:`1-p` is the rate of depolarization while :math:`A` and :math:`B` 
+where :math:`1-p` is the rate of depolarization while :math:`A` and :math:`B`
 capture state preparation and measurement errors.
 Finally, we can extract the average error per Clifford as
 
@@ -53,7 +53,7 @@ Finally, we can extract the average error per Clifford as
 
 where :math:`n` is the number of qubits. The error per gate can be derived by dividing
 the Clifford error by the physical gates per Clifford which usually is 1.875.
-One of the main feature of RB is the possibility to estimate the gate fidelity 
+One of the main feature of RB is the possibility to estimate the gate fidelity
 alone without taking into account both state preparation and measurement errors
 which can be computed using the :math:`A` and :math:`B` terms in :ref:`Eq. 2 <eq:2>`.