Step5

 To finish the cirq max-cut tutorial. We have reached Step 5.

We first produce a graph of the structure of the max-cut. This is possible because

we are working from the original Sycamore structure shown earlier.

Yes, in the QAOA Max-Cut tutorial, we start with the initial Sycamore structure. The Sycamore processor is a quantum processor developed by Google, and it's used to demonstrate quantum supremacy and perform various quantum algorithms, including QAOA.

In the context of the Max-Cut problem, the Sycamore structure refers to the specific layout and connectivity of qubits on the Sycamore processor. This structure is used to define the graph on which the Max-Cut problem is solved. By visualizing the nodes and edges of this graph, we can better understand the problem setup and how the QAOA algorithm operates on it.

Next, we are given the best control parameters:

The code in Step 5 is used to find the best control parameters from a set of experimental values. Specifically, it identifies the index of the maximum value in the exp_values array, retrieves the corresponding parameters from the par_values array, and prints them.

Follows the actual simulation:

                                                                        

We are looking for the best cut size. 

cirq max-cut tutorial; how does minimizing the cost function maximize the cut?

The Max-Cut problem involves partitioning the vertices of a graph into two distinct sets such that the number of edges between the sets is maximized. In the context of the Quantum Approximate Optimization Algorithm (QAOA) implemented in Cirq, the cost function represents the number of edges that are cut by a given partition.

Here's how minimizing the cost function maximizes the cut:

1. Cost Function Definition: The cost function is defined as the negative of the number of edges between the two sets. Therefore, minimizing the cost function is equivalent to maximizing the number of edges cut.

2. QAOA Circuit: The QAOA circuit is designed to find the optimal partition by evolving a quantum state through a series of unitary operations. These operations are parameterized to minimize the cost function.

3. Optimization Loop: An outer optimization loop adjusts the parameters of the QAOA circuit to minimize the cost function. As the cost function decreases, the number of edges between the sets increases, thus maximizing the cut.

4. Expected Value Calculation: The expected value of the cost function is calculated for different parameter settings. The parameters that yield the lowest expected value correspond to the partition with the maximum cut.

On 12 qubits, the max-cut size is 28.02....... What are the units here?

In the context of the Max-Cut problem, the value 28.02 represents the expected value of the cut size, which is a dimensionless quantity. This value is derived from the optimization process and indicates the average number of edges that are cut by the partition of the graph. Since it's an expected value, it doesn't have specific units but rather reflects the performance of the algorithm in finding a good partition.

Code for the random cut:

                                                                      

The print functions:

                                                                        

The max-cut:

                                                                      

The random:

Just examining the two images, the max-cut red notes have 14 links, whereas the random 

reds show 11...

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