minor docs tweaks

docs/source/cost/index.rst

@@ -19,4 +19,5 @@ Custom cost functions can be implemented using PennyLane.
    linear_inequalities
    entropic_quantities
    magic_squares_game
+   negativity
    nonlocality_witnesses/index

docs/source/cost/negativity.rst

@@ -0,0 +1,6 @@
+Partial Transpose Negativity
+============================
+
+.. currentmodule:: qnetvo
+
+.. autofunction:: negativity_cost_fn

docs/source/cost/qnodes.rst

@@ -14,6 +14,11 @@ Probability QNodes
 
 .. autofunction:: joint_probs_qnode
 
+Density Matrix QNodes
+---------------------
+
+.. autofunction:: density_matrix_qnode
+
 Parity Observable QNodes
 ------------------------
 

docs/source/utilities.rst

@@ -3,6 +3,12 @@ Utilities
 
 .. currentmodule:: qnetvo
 
+
+Mathematical Operations
+-----------------------
+
+.. autofunction:: partial_transpose
+
 Circuit Tomography
 ------------------
 

src/qnetvo/cost/negativity.py

@@ -21,7 +21,7 @@ def negativity_cost_fn(network_ansatz, m, n, wires, qnode_kwargs={}):
     the :math:`B` party, and :math:`\\lambda_i` are all of the eigenvalues of :math:`\\rho^{\\Gamma_B}`.
 
     For more information on negativity and its applications in quantum information theory,
-    see [Vidal and Werner (2001)](https://arxiv.org/pdf/quant-ph/0102117).
+    (see `Vidal and Werner, 2001 <https://arxiv.org/pdf/quant-ph/0102117>`_).
 
     :param ansatz: The ansatz circuit on which the negativity is evaluated.
     :type ansatz: NetworkAnsatz

src/qnetvo/utilities.py

@@ -196,16 +196,16 @@ def partial_transpose(dm, d1, d2):
     :param dm: The density matrix to be partially transposed.
     :type dm: np.array
 
-    :param d1: The dimension of the first subsystem (e.g., 2^m where m is the number of qubits in the first subsystem).
+    :param d1: The dimension of the first subsystem (e.g., :math:`2^m` where :math:`m` is the number of qubits in the first subsystem).
     :type d1: int
 
-    :param d2: The dimension of the second subsystem (e.g., 2^n where n is the number of qubits in the second subsystem).
+    :param d2: The dimension of the second subsystem (e.g., :math:`2^n` where :math:`n` is the number of qubits in the second subsystem).
     :type d2: int
 
     :returns: The partially transposed density matrix.
     :rtype: np.array
 
-    :raises ValueError: If the product of `d1` and `d2` does not match the size of the density matrix.
+    :raises ValueError: If the product of ``d1`` and ``d2`` does not match the size of the density matrix.
     """
 
     if d1 * d2 != dm.shape[0]: