Implementing D-Wave QBSolve in Python

*To implement D-Wave QBSolve in Python, we need to perform the following steps:*

- Install D-Wave’s Ocean SDK: D-Wave’s Ocean SDK is a collection of software tools for developing and running quantum applications on D-Wave’s quantum annealing processors. To install the SDK, follow the instructions on the D-Wave website.
- Define the QUBO problem: Define the QUBO problem as a Python dictionary, where the keys are the (i,j) pairs of the Q matrix and the values are the corresponding Q_ij elements. Define the c vector as a Python list.
- Create a QUBO object: Use the QBSolv class from the dimod library to create a QUBO object from the QUBO dictionary and c vector.
- Solve the QUBO problem: Use the solve_qubo function of the dwave.system.samplers.DWaveSampler class to solve the QUBO problem on D-Wave’s quantum annealing processor. The function returns a response object that contains the solution to the problem.
- Extract the solution: Extract the solution from the response object and print it to the console. A solution is a dictionary that maps the binary variables to their values, with keys being the indices of the variables.

Let’s now walk through these steps in more detail with a code example.

**Step 1: Install D-Wave’s Ocean SDK**

To install D-Wave’s Ocean SDK, follow the instructions on the D-Wave website. Once you have installed the SDK, you can import the necessary modules in Python as follows:

**Step 2: Define the QUBO problem**

For this example, let’s consider the following QUBO problem:

minimize Q(x) = 2 x_1 x_2 + 3 x_1 x_3 + x_2 x_3 – 2 x_1 – x_2 – 3 x_3

subject to x_i ∈ {0, 1}, for i = 1, 2, 3

We can define the QUBO problem as a Python dictionary as follows:

Note that we use the 0-based indexing for the variables.

**Step 3: Create a QUBO object**

To create a QUBO object from the QUBO dictionary and c vector, we use the QBSolv class from the dimod library as follows:

The `asqubo`

the function converts the QUBO problem to a binary quadratic model (BQM) object, which is a data structure used by the D-Wave Ocean tools. The `as_bqm`

the function converts the BQM to a QUBO object, which is a data structure used by the QBSolv class.