**Meta-Analytics
web site quickstart for Alpha-QUBO**

**to solve problems with up to 3,000 variables**

(Click here to request access
to Advanced Alpha-QUBO to solve larger problems.)

Go to the web
address: http://**meta-analytics.com****
**

**Create an
account. **

a) Click on
Login, Upload, or QUBO Models

b) Click on
Sign up (at upper right of login dialog)

c) Sign up
using email and password, or using your Google
account. After signing up you may
receive an email email from 'meta-analytics' using the email address no-reply@auth0user.net. Click on the 'verify link' in the email to
complete the account creation.

**Upload a **QUBO** model**

a) The QUBO
model file format is a text file with information on the first line that
describes the size of the q(i,j) matrix.

Line1: p variableCount
non-zeroElementCount
(for upper triangular Q Matrix)

(The letter “p” here is invariant, and verifies that this is Line 1.)

Line2: I J q(i,j) this is also q(j,i) since the matrix is
symmetric

(Only
non-zero elements need be added. The indexes I and J satisfy I ≤ J since the

matrix is input in upper
triangular form, and I = J identifies a diagonal element.)

..

LineN: I J (qi,j)

For example, the file bqp100.txt
starts with the following lines:

p 100 475

1 35 -19

1 44 -22

1 47 27

1 49 -66

1 58 -69

1 64 63

1 72 -89

1 73 -19

1 74 -69

1 76 -12

1 84 40

1 98 33

2 2 52

Comment: The number of spaces between
numbers entered on a line is irrelevant. For instance, the last line above
could also be 2 2 52.

b)
File Compression

The
QUBO
text file can be compressed to a .7z (7-Zip) https://7-zip.org/ , (or .zip) file to
reduce the file size for upload. When
uploading compressed files check the 'Compressed File format check box'
before uploading

To
upload the file, click on 'Upload', enter a QUBO model name, click choose file and
finally click 'Upload QUBO
Model' after selecting the file. Upload progress is shown in the lower left hand corner of the webpage. Wait until the upload completes. After a successful
upload the website will display the table of QUBO models.
The web page may need to be refreshed at this point to show the new
model. Click the reload icon on your web browser, or
enter return next to the web address.

**Create
a **QUBO**
Solution.**

a)
Click on QUBO
Models

b)
Click on 'Create Solution' for the selected model

c)
Enter the 'Time Limit'.

d)
Uncheck 'Maximize' if the objective is to Minimize.

Click
Submit. The website will go to the job
queue to show the job status. The web
page will need to be refreshed to update the status of the job solution
process. The job will have a status of
'FinishedSuccess' when it has completed successfully.

**Download
the **QUBO**
solution.** The solution download is
available from the Job Queue.

EXAMPLE:

Consider
the problem:

Minimize

where
the variables, , are binary. Observations:

1. The function to be minimized is a
quadratic function in binary variables with a linear part and a quadratic part .

2. Since binary variables satisfy , the linear part can
be written as

3. Then we can re-write the model in the
following matrix form:

Minimize

4. In turn, this can be written in the
matrix notation introduced in Section 1 as

QUBO: Minimize

where x is a column vector of binary
variables and Q is the __symmetric__ matrix

__Note on
input Format:__ The
Alpha-Qubo code assumes the Q matrix is in symmetric form. Preparing this QUBO model for solution via
the Alpha-QUBO system involves presenting the non-zero diagonal and upper
triangular elements of Q in an input file as shown below. Due to symmetry, the bottom triangular
elements are automatically picked up by the code and do not have to be entered.

p 4 8

1 1 -5

1 2 2

1 3 4

2 2 -3

2 3 1

3 3 -8

3 4 5

4 4 -6

As shown above, there are 8 non-zero elements that
need to be specified. Symmetry, together
with the fact that any unspecified element is assumed to be zero, assures this
input file completely specifies the full Q matrix and the QUBO instance to be
solved.

Solving via Alpha-QUBO gives:

seed = 783458 f_best
= -11 t_best = 0.01

Best Solution :

1
0 0 1

5. As shown by f_best and the Best
Solution, the solution to the model in (3) above is:

*Note on Alternative Representations: *Some QUBO formulations assume the matrix is represented
in compact upper triangular form instead of using the symmetric form shown in the
preceding example. The compact upper triangular form doubles the size of the
off-diagonal coefficients and consequently all such coefficients not on the
main diagonal of the compact form should be halved to give the coefficients of
our symmetric form – although we only require the upper triangular half of
these coefficients to be input, as also shown in the example.

We welcome your suggestions for how we can make
the Alpha-QUBO software easier to use. Send us an email at support@meta-analytics.com