# Quantagonia QUBO File Format#

Here we describe the syntax of the QUBO file format used to model problems of the form \(x^TQx\) , where \(x\in\{0, 1\}^n\) is the sought solution vector, and \(Q \in \mathbb{R}^{n \times n}\) is a symmetric matrix.

For stored QUBOs, the file ending .qubo is used.

## Description#

The file should have no header.

All in-line separators should be spaces.

The first line is a string that sets the optimization sense, which can be

`MINIMIZE`

or`MAXIMIZE`

.The second line needs to be a single integer:

`num_problems`

. This number specifies the number of the QUBO matrices in the file. Each of these can, in principle, be viewed as a separate optimization problem. When there is more than 1 matrix present in a file, the solver will accumulate all problems by summing them up and reporting the solution for the accumulated problem.The following structure then recurses

`num_problems`

times. Each on a new line, we have:one float:

`penalty`

.one float:

`offset`

: constant offset of the energytwo integers:

`n`

`nnz`

:`n`

is the dimension of the problem (number of rows and columns of the QUBO matrix);`nnz`

is the number of non-zero entries in the upper triangle matrixfor each non-zero entry in the matrix, the following is written in a new line of the file:

two integers and a float:

`i`

`j`

`q_{ij}`

:`i`

is the row of the entry;`j`

is the column of the entry;`q_{ij}`

is the value at the position`i`

. Because the matrix \(Q\) is symmetric, only the diagonal and upper-triangular entries of the matrix should be specified. The solver will automatically make the matrix symmetric. Formally, this means that \(i \le j\).

a number of variable fixings, i.e., variables whose assignment is set ahead of time. The format is

`f ix val`

where`ix`

is the variable’s index and`val`

sets the value of the variable to either`0`

or`1`

## File syntax#

```
MAXIMIZE <--- optimization sense
1 <--- please set to 1 (a deprecated feature which will be removed soon)
# the QUBO matrix
1.0 <--- penalty
2.0 <--- constant energy offset
6 7 <--- first number: dimension, second number: number of entries
0 0 1.0 <-- entries
1 1 1.0
2 2 1.0
3 3 1.0
3 4 1.0
4 4 1.0
5 5 1.0
f 2 1 <--- fix variable #2 to value of 1
```

Here is the same problem from above, but without the comments, in a formally correct syntax:

```
MAXIMIZE
1
1.0
2.0
6 7
0 0 1.0
1 1 1.0
2 2 1.0
3 3 1.0
3 4 1.0
4 4 1.0
5 5 1.0
f 2 1
```

## Example#

If we take the example from above, the solver would be solving the following problem: