Latex fix

Author: haggaila

docs/API_DOCS.md

@@ -24,11 +24,11 @@ The default value for each parameter is indicated with an equality sign (only th
     * output_files_prefix = "lindblad" (str): The path and file name prefix to be used for the input file generated for the solver, as well as output files generated by the solver. The default value indicates saving files in the working directory with the file name prefix "lindblad". If only a directory path is given, the "lindblad" file name prefix will be added.
     * b_unique_id = False (bool): If True, a unique id will be generated for the simulation and appended to all generated file name prefixes.
 * Hamiltonian coefficients:
-    * h_x = 0 (float): The $h_{x,i}$ coefficient in the Hamiltonian. If a vector is given, it specifies <img src="https://render.githubusercontent.com/render/math?math=h_{x,i}" style="vertical-align:middle"> for each qubit. If a scalar is given, it is uniform for all qubits.
-    * h_y = 0 (float): The $h_{y,i}$ coefficient in the Hamiltonian. If a vector is given, it specifies <img src="https://render.githubusercontent.com/render/math?math=h_{y,i}" style="vertical-align:bottom"> for each qubit. If a scalar is given, it is uniform for all qubits.
-    * h_z = 0 (float): The $h_{z,i}$ coefficient in the Hamiltonian. If a vector is given, it specifies <img src="https://render.githubusercontent.com/render/math?math=h_{z,i}" style="vertical-align:bottom"> for each qubit. If a scalar is given, it is uniform for all qubits.
-    * J_z = 0 (float): The $J^z_{ij}$ coefficient in the interaction part of the Hamiltonian. If a matrix is given, it specifies $J^z_{ij}$ for each coupled pair of qubits. If a scalar is given, it is uniform for all qubits of a lattice. If either one of $J$ or $J_z$ is a matrix, then the other one must be either a matrix as well, or 0.
-    * J = 0 (float): The $J_{ij}$ coefficient in the interaction part of the Hamiltonian. If a matrix is given, it specifies $J_{ij}$ for each coupled pair of qubits. If a scalar is given, it is uniform for all qubits of a lattice. If either one of $J$ or $J_z$ is a matrix, then the other one must be either a matrix as well, or 0.
+    * h_x = 0 (float): The $h_{x,i}$ coefficient in the Hamiltonian. If a vector is given, it specifies $h_{x,i}$ for each qubit. If a scalar is given, it is uniform for all qubits.
+    * h_y = 0 (float): The $h_{y,i}$ coefficient in the Hamiltonian. If a vector is given, it specifies $h_{y,i}$ for each qubit. If a scalar is given, it is uniform for all qubits.
+    * h_z = 0 (float): The $h_{z,i}$ coefficient in the Hamiltonian. If a vector is given, it specifies $h_{z,i}$ for each qubit. If a scalar is given, it is uniform for all qubits.
+    * J_z = 0 (float): The $J^z_{ij}$ coefficient in the interaction part of the Hamiltonian. If a matrix is given, it specifies $J^z_{ij}$ for each pair of qubits. If a scalar is given, it is uniform for all qubits of a lattice. If either one of $J$ or $J_z$ is a matrix, then the other one must be either a matrix as well, or 0.
+    * J = 0 (float): The $J_{ij}$ coefficient in the interaction part of the Hamiltonian. If a matrix is given, it specifies $J_{ij}$ for each pair of qubits. If a scalar is given, it is uniform for all qubits of a lattice. If either one of $J$ or $J_z$ is a matrix, then the other one must be either a matrix as well, or 0.
 * Dissipation coefficients:
     * g_0 = 0 (float): $g_{0,i}$ coefficient in the Lindbladian. If a vector is given, it specifies $g_{0,i}$ for each qubit. If a scalar is given, it is uniform for all qubits.
     * g_1 = 0 (float): The $g_{1,i}$ coefficient in the Lindbladian. If a vector is given, it specifies $g_{1,i}$ for each qubit. If a scalar is given, it is uniform for all qubits.
@@ -37,7 +37,7 @@ The default value for each parameter is indicated with an equality sign (only th
     The initial state of the simulator either takes a predefined default value, is defined explicitly by the parameters, or is loaded from files saved by a previous solver execution. Using the initialization parameters the state can be initialized to a product state as detailed below, and then optional controlled-Z (CZ) gates can be applied to (some) pairs of qubits, which allows creating an initial (possibly nonideal) graph state.
 
     * init_product_state = "+z": A float (or a one-element float tuple), a tuple of two or three floats, a two-character string, or a length-N vector of such entries. A single entry applies to all qubits.
-         * The supported strings take either the form "$\pm a$", or "id". The latter indicates the fully mixed-state (identity) density matrix, and the former indicate an eigenstate of one of the Pauli matrices, $\sigma_i^a\left|\pm a_i\rangle = \pm \right|\pm a_i\rangle.$
+         * The supported strings take either the form "+a", "-a", or "id". The latter indicates the fully mixed-state (identity) density matrix, and the former indicate an eigenstate of one of the Pauli matrices, $\sigma_i^a\left|\pm a_i\rangle = \pm \right|\pm a_i\rangle.$
          * If an entry is a float, it should be between 0 and 1, and indicates the population of the "|0>" ("|up>" state, aligned with +z) in a diagonal mixed-state density matrix for the qubit.
          * If an entry is a tuple of two floats (theta, phi), it indicates an arbitrary pure-state superposition in Bloch-sphere polar coordinates with the formula "cos(theta/2)|0> + sin(theta/2) exp{i phi}|1>".
          * If an entry is a tuple of three floats (a, b, c), it indicates the density matrix "a|0><0| + (1-a)|1><1| + [(b + ic) |0><1| + H.c.]"