This exercise contains three small programs which illustrate two qubit interactions in QUBO models. Understanding these small problems is vital for writing QUBOs for much larger problems.
Open two_same.py. Read through the code and take a look at the
structure of the program. Notice the basic parts:
- Obtain a sampler/solver
- Define the Q matrix
- Run the problem, using the sampler/solver
- Print the results
In this exercise, we want to penalize the two qubit solutions in which the qubits have different values; we want to favor the two qubit solutions in which the qubits have the same values.
In the results, you should notice that the solutions (0 0) and (1 1) have lower energy than the solutions (0 1) and (1 0).
Open two_different.py. In this exercise, we want to penalize the two qubit solutions in which the
qubits have the same values; we want to favor the two qubit solutions in
which the qubits have different values.
In the results, you should notice that the solutions (0 1) and (1 0) have lower energy than the solutions (0 0) and (1 1).
Open two_implies.py. Here is a definition of the implies function, from
Wikiversity:
The concept of logical implication is associated with an operation on two
logical values, typically the values of two propositions, that produces a
value of false just in case the first operand is true and the second operand
is false.
Hence, the implies function in logic has the following truth table:
| X | Y | X -> Y |
|---|---|---|
| F | F | T |
| F | T | T |
| T | F | F |
| T | T | T |
In QUBO variables (0 = False, 1 = True), we can write the problem as
| x_1 | x_2 | result (energy) |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
and and thus we want to penalize the (1 0) solution, relative to the others. This explains why the energy of (1 0) is 1, whereas the energy of the other states is zero. Your results should agree with this.
Released under the Apache License 2.0. See LICENSE file.