diff --git a/demos/qiskit_patterns/2_qiskit_patterns.ipynb b/demos/qiskit_patterns/2_qiskit_patterns.ipynb index b4a1085..09c36a1 100644 --- a/demos/qiskit_patterns/2_qiskit_patterns.ipynb +++ b/demos/qiskit_patterns/2_qiskit_patterns.ipynb @@ -7,8 +7,7 @@ "source": [ "# Scaling Quantum Optimization with Qiskit Patterns\n", "\n", - "In this how-to we will learn about Qiskit Patterns and quantum approximate optimization. Qiskit Patterns define a four-step process for running algorithms on a quantum computer:\n", - "\n", + "In this how-to we will learn about Qiskit Patterns and quantum approximate optimization. A Qiskit Pattern is an intuitive, repeatable set of steps for implementing a quantum computing workflow: \n", "\n", "\"Drawing\"\n", "\n", @@ -48,7 +47,7 @@ "id": "74b92ba5-c48a-405c-9c4b-04e985a7afbc", "metadata": {}, "source": [ - "Max-Cut is a hard to solve optimization problem with applications in clustering, network science, and statistical physics. The goal of this problem is to partition the nodes of a graph into to sets such that the number of edges traversed by this cut is maximum.\n", + "Max-Cut is a hard to solve optimization problem with applications in clustering, network science, and statistical physics. The goal of this problem is to partition the nodes of a graph into two sets such that the number of edges traversed by this cut is maximum.\n", "\n", "\"Max-Cut\"/" ] @@ -171,7 +170,6 @@ "H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n", "\\end{align}\n", "\n", - "
\n", "First, a variable change, we convert the binary variables $x_i$ to variables $z_i\\in\\{-1, 1\\}$ by doing\n", "\n", "\\begin{align}\n", @@ -195,10 +193,11 @@ "\\begin{align}\n", "H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n", "\\end{align}\n", - "
\n", "\n", - "We refer to this Hamiltonian as the **cost function Hamiltonian**. It has the property that its gound state corresponds to the solution that **minimizes the cost function $f(x)$**.\n", - "Therefore, to solve our optimization problem we now need to prepare the ground state of $H_C$ (or a state with a high overlap with it) on the quantum computer. Then, sampling from this state will, with a high probability, yield the solution to $min f(x)$." + "
\n", + "We refer to this Hamiltonian as the cost function Hamiltonian. It has the property that its gound state corresponds to the solution that minimizes the cost function $f(x)$.\n", + "Therefore, to solve our optimization problem we now need to prepare the ground state of $H_C$ (or a state with a high overlap with it) on the quantum computer. Then, sampling from this state will, with a high probability, yield the solution to $min~f(x)$.\n", + "
" ] }, { @@ -1362,7 +1361,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.10.0" } }, "nbformat": 4, diff --git a/demos/qiskit_patterns/imgs/eagle-heron-0.png b/demos/qiskit_patterns/imgs/eagle-heron-0.png new file mode 100644 index 0000000..646e729 Binary files /dev/null and b/demos/qiskit_patterns/imgs/eagle-heron-0.png differ diff --git a/demos/qiskit_patterns/imgs/eagle-heron.png b/demos/qiskit_patterns/imgs/eagle-heron.png index 646e729..7927f06 100644 Binary files a/demos/qiskit_patterns/imgs/eagle-heron.png and b/demos/qiskit_patterns/imgs/eagle-heron.png differ