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doc/source/api-reference/qibo.rst

@@ -1213,7 +1213,7 @@ Matrix Hamiltonian
 ^^^^^^^^^^^^^^^^^^
 
 The first implementation of Hamiltonians uses the full matrix representation
-of the Hamiltonian operator in the computational basis. 
+of the Hamiltonian operator in the computational basis.
 For :math:`n` qubits, this matrix has size :math:`2^{n} \times 2^{n}`.
 Therefore, its construction is feasible only when :math:`n` is small.
 

src/qibo/derivative.py

@@ -21,8 +21,8 @@ def parameter_shift(
     parameter and an external object, such as a training variable in a Quantum
     Machine Learning problem. For example, performing a re-uploading strategy
     to embed some data into a circuit, we apply to the quantum state rotations
-    whose angles are in the form :math:`\\theta^{\\prime} = x \\, \\theta`, 
-    where :math:`\\theta` is a variational parameter, and :math:`x` an input variable. 
+    whose angles are in the form :math:`\\theta^{\\prime} = x \\, \\theta`,
+    where :math:`\\theta` is a variational parameter, and :math:`x` an input variable.
     The PSR allows to calculate the derivative with respect to :math:`\\theta^{\\prime}`.
     However, if we want to optimize a system with respect to its
     variational parameters, we need to "free" this procedure from the :math:`x` depencency.
@@ -41,7 +41,7 @@ def parameter_shift(
         parameter_index (int): the index which identifies the target parameter
             in the ``circuit.get_parameters()`` list.
         initial_state (ndarray, optional): initial state on which the circuit
-            acts. If ``None``, defaults to the zero state :math:`\\ket{\\mathbf{0}}`. 
+            acts. If ``None``, defaults to the zero state :math:`\\ket{\\mathbf{0}}`.
             Defaults to ``None``.
         scale_factor (float, optional): parameter scale factor. Defaults to :math:`1`.
         nshots (int, optional): number of shots if derivative is evaluated on
@@ -184,7 +184,7 @@ def finite_differences(
         parameter_index (int): the index which identifies the target parameter
             in the :meth:`qibo.models.Circuit.get_parameters` list.
         initial_state (ndarray, optional): initial state on which the circuit
-            acts. If ``None``, defaults to the zero state :math:`\\ket{\\mathbf{0}}`. 
+            acts. If ``None``, defaults to the zero state :math:`\\ket{\\mathbf{0}}`.
             Defaults to ``None``.
         step_size (float, optional): step size used to evaluate the finite difference.
             Defaults to :math:`10^{-7}`.

src/qibo/hamiltonians/abstract.py

@@ -70,7 +70,7 @@ def expectation(self, state, normalize=False):  # pragma: no cover
 
         Args:
             state (ndarray): state in which to calculate the expectation value.
-            normalize (bool, optional): If ``True``, the expectation value 
+            normalize (bool, optional): If ``True``, the expectation value
                 :math:`\\ell_{2}`-normalized. Defaults to ``False``.
 
         Returns:
@@ -80,15 +80,15 @@ def expectation(self, state, normalize=False):  # pragma: no cover
 
     @abstractmethod
     def expectation_from_samples(self, freq, qubit_map=None):  # pragma: no cover
-        """Computes the expectation value of a diagonal observable, 
+        """Computes the expectation value of a diagonal observable,
         given computational-basis measurement frequencies.
 
         Args:
             freq (collections.Counter): the keys are the observed values in binary form
                 and the values the corresponding frequencies, that is the number
                 of times each measured value/bitstring appears.
-            qubit_map (tuple): Mapping between frequencies and qubits. 
-                If ``None``, then defaults to 
+            qubit_map (tuple): Mapping between frequencies and qubits.
+                If ``None``, then defaults to
                 :math:`[1, \\, 2, \\, \\cdots, \\, \\mathrm{len}(\\mathrm{key})]`.
                 Defaults to ``None``.
 

src/qibo/hamiltonians/hamiltonians.py

@@ -84,7 +84,7 @@ def from_symbolic(cls, symbolic_hamiltonian, symbol_map, backend=None):
                 Defaults to ``None``.
 
         Returns:
-            :class:`qibo.hamiltonians.SymbolicHamiltonian`: object that implements the 
+            :class:`qibo.hamiltonians.SymbolicHamiltonian`: object that implements the
             Hamiltonian represented by the given symbolic expression.
         """
         log.warning(
@@ -177,7 +177,7 @@ def energy_fluctuation(self, state):
         Evaluate energy fluctuation:
 
         .. math::
-            \\Xi_{k}(\\mu) = \\sqrt{\\bra{\\mu} \\, H^{2} \\, \\ket{\\mu} 
+            \\Xi_{k}(\\mu) = \\sqrt{\\bra{\\mu} \\, H^{2} \\, \\ket{\\mu}
                 - \\bra{\\mu} \\, H \\, \\ket{\\mu}^2} \\, .
 
         for a given state :math:`\\ket{\\mu}`.