diff --git a/community/basic_examples/entanglement/entanglement.ipynb b/community/basic_examples/entanglement/entanglement.ipynb index 027b3d6b..47eb807b 100644 --- a/community/basic_examples/entanglement/entanglement.ipynb +++ b/community/basic_examples/entanglement/entanglement.ipynb @@ -6,7 +6,7 @@ "source": [ "# Quantum Entanglement with Classiq\n", "\n", - "Entanglement is an important aspect to study the quantum algorithms. In this tutorial, we show how to create a bell pair state $|\\Phi^{+}\\rangle$ of 2 qubits, using the Hadamard and Controlled-NOT transformation." + "Entanglement is an important aspect to study the quantum algorithms. In this tutorial, we show how to create a bell pair state $|\\Phi^{+}\\rangle$ of 2 qubits, using the Hadamard and the Controlled-NOT transformation." ] }, { @@ -74,11 +74,11 @@ "$$\\begin{pmatrix} 1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 \\\\ 0 & 0 & 0 & 1 \\\\ 0 & 0 & 1 & 0 \\end{pmatrix} \\begin{pmatrix} \\frac{1}{\\sqrt{2}} \\\\ 0 \\\\ \\frac{1}{\\sqrt{2}}\\\\ 0 \\end{pmatrix} = \\begin{pmatrix} \\frac{1}{\\sqrt{2}} \\\\ 0 \\\\ 0 \\\\ \\frac{1}{\\sqrt{2}} \\end{pmatrix} = \\frac{1}{\\sqrt{2}} \\left| 00 \\right\\rangle + \\frac{1}{\\sqrt{2}} \\left| 11 \\right\\rangle$$\n", "\n", "In this situation the qubit's of Alice and Bob are correlated to each other.
\n", - "If we measure the both the qubits we will either get the state $|00\\rangle$ or the state $|11\\rangle$ with equal probability.\n", + "If we measure both the qubits we will either get the state $|00\\rangle$ or the state $|11\\rangle$ with equal probability.\n", "\n", "It is described as:\n", - "- When the Alice oberseve her state as $|0\\rangle$ then the state of Bob's qubit collapses to the state $|0\\rangle$\n", - "- When the Alice oberseve her state as $|1\\rangle$ then the state of Bob's qubit collapses to the state $|1\\rangle$ \n", + "- When Alice oberseve her state as $|0\\rangle$ then the state of Bob's qubit collapses to the state $|0\\rangle$\n", + "- When Alice oberseve her state as $|1\\rangle$ then the state of Bob's qubit collapses to the state $|1\\rangle$ \n", "\n", "The resultant entangled state is designated as a bell pair state $|\\Phi^{+}\\rangle$\n", "$$|\\Phi^{+}\\rangle = \\frac{1}{\\sqrt{2}} \\left( |00\\rangle + |11\\rangle \\right)$$\n",