Fix rendering in BasicGates

Author: remilvus

BasicGates/BasicGates.ipynb

@@ -214,7 +214,7 @@
     "\n",
     "**Input:** A qubit in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$.\n",
     "\n",
-    "**Goal:** Change the qubit state to $\\alpha |0\\rangle + \\color{red}i\\beta |1\\rangle$ (add a relative phase $i$ to $|1\\rangle$ component of the superposition).\n"
+    "**Goal:** Change the qubit state to $\\alpha |0\\rangle + {\\color{red}i}\\beta |1\\rangle$ (add a relative phase $i$ to $|1\\rangle$ component of the superposition).\n"
    ]
   },
   {
@@ -251,7 +251,7 @@
     "**Goal:**  Change the state of the qubit as follows:\n",
     "- If the qubit is in state $|0\\rangle$, don't change its state.\n",
     "- If the qubit is in state $|1\\rangle$, change its state to $e^{i\\alpha} |1\\rangle$.\n",
-    "- If the qubit is in superposition, change its state according to the effect on basis vectors: $\\beta |0\\rangle + \\color{red}{e^{i\\alpha}} \\gamma |1\\rangle$.\n"
+    "- If the qubit is in superposition, change its state according to the effect on basis vectors: $\\beta |0\\rangle + {\\color{red}{e^{i\\alpha}}} \\gamma |1\\rangle$.\n"
    ]
   },
   {
@@ -479,10 +479,10 @@
    "source": [
     "### Task 2.2. Two-qubit gate - 2\n",
     "\n",
-    "**Input:** Two unentangled qubits (stored in an array of length 2) in state $|+\\rangle \\otimes |+\\rangle = \\frac{1}{2} \\big( |00\\rangle + |01\\rangle + |10\\rangle \\color{blue}+ |11\\rangle \\big)$.\n",
+    "**Input:** Two unentangled qubits (stored in an array of length 2) in state $|+\\rangle \\otimes |+\\rangle = \\frac{1}{2} \\big( |00\\rangle + |01\\rangle + |10\\rangle {\\color{blue}+} |11\\rangle \\big)$.\n",
     "\n",
     "\n",
-    "**Goal:**  Change the two-qubit state to $\\frac{1}{2} \\big( |00\\rangle + |01\\rangle + |10\\rangle \\color{red}- |11\\rangle \\big)$.\n",
+    "**Goal:**  Change the two-qubit state to $\\frac{1}{2} \\big( |00\\rangle + |01\\rangle + |10\\rangle {\\color{red}-} |11\\rangle \\big)$.\n",
     "\n",
     "> Note that while the starting state can be represented as a tensor product of single-qubit states,\n",
     "> the resulting two-qubit state can not be represented in such a way."
@@ -514,10 +514,10 @@
    "source": [
     "### Task 2.3. Two-qubit gate - 3\n",
     "\n",
-    "**Input:** Two unentangled qubits (stored in an array of length 2) in an arbitrary two-qubit state $\\alpha |00\\rangle + \\color{blue}\\beta |01\\rangle + \\color{blue}\\gamma |10\\rangle + \\delta |11\\rangle$.\n",
+    "**Input:** Two unentangled qubits (stored in an array of length 2) in an arbitrary two-qubit state $\\alpha |00\\rangle + {\\color{blue}\\beta} |01\\rangle + {\\color{blue}\\gamma} |10\\rangle + \\delta |11\\rangle$.\n",
     "\n",
     "\n",
-    "**Goal:**  Change the two-qubit state to $\\alpha |00\\rangle + \\color{red}\\gamma |01\\rangle + \\color{red}\\beta |10\\rangle + \\delta |11\\rangle$.\n",
+    "**Goal:**  Change the two-qubit state to $\\alpha |00\\rangle + {\\color{red}\\gamma} |01\\rangle + {\\color{red}\\beta} |10\\rangle + \\delta |11\\rangle$.\n",
     "\n",
     "> This task can be solved using one intrinsic gate; as an exercise, try to express the solution using several (possibly controlled) Pauli gates."
    ]
@@ -549,9 +549,9 @@
     "### Task 2.4. Toffoli gate\n",
     "\n",
     "**Input:** Three qubits (stored in an array of length 3) in an arbitrary three-qubit state \n",
-    "$\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\zeta|101\\rangle + \\color{blue}\\eta|110\\rangle + \\color{blue}\\theta|111\\rangle$.\n",
+    "$\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\zeta|101\\rangle + {\\color{blue}\\eta}|110\\rangle + {\\color{blue}\\theta}|111\\rangle$.\n",
     "\n",
-    "**Goal:** Flip the state of the third qubit if the state of the first two is $|11\\rangle$, i.e., change the three-qubit state to $\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\zeta|101\\rangle + \\color{red}\\theta|110\\rangle + \\color{red}\\eta|111\\rangle$."
+    "**Goal:** Flip the state of the third qubit if the state of the first two is $|11\\rangle$, i.e., change the three-qubit state to $\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\zeta|101\\rangle + {\\color{red}\\theta}|110\\rangle + {\\color{red}\\eta}|111\\rangle$."
    ]
   },
   {
@@ -581,9 +581,9 @@
     "### Task 2.5. Fredkin gate\n",
     "\n",
     "**Input:** Three qubits (stored in an array of length 3) in an arbitrary three-qubit state \n",
-    "$\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\color{blue}\\zeta|101\\rangle + \\color{blue}\\eta|110\\rangle + \\theta|111\\rangle$.\n",
+    "$\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + {\\color{blue}\\zeta}|101\\rangle + {\\color{blue}\\eta}|110\\rangle + \\theta|111\\rangle$.\n",
     "\n",
-    "**Goal:** Swap the states of second and third qubit if and only if the state of the first qubit is $|1\\rangle$, i.e., change the three-qubit state to $\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\color{red}\\eta|101\\rangle + \\color{red}\\zeta|110\\rangle + \\theta|111\\rangle$."
+    "**Goal:** Swap the states of second and third qubit if and only if the state of the first qubit is $|1\\rangle$, i.e., change the three-qubit state to $\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + {\\color{red}\\eta}|101\\rangle + {\\color{red}\\zeta}|110\\rangle + \\theta|111\\rangle$."
    ]
   },
   {