How Do I Create a Problem in the Right Form for the System?

The D-Wave system accepts problems formulated as binary quadratic models (BQM)

When working with the D-Wave systems and software, you need to first formulate your problem as a BQM. We can formulate many classes of problems as BQMs, such as optimization problems. We can view an optimization problem in terms of objectives and constraints. An objective is something that we want to minimize or maximize, while constraints are rules about which solutions are acceptable. 

To learn more about these concepts, and get some hands-on practice creating small BQMs, see the Learn to Formulate Problems section in the D-Wave system documentation. 

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  • How to write or convert this method in quantum programing
    Application:
    q=GCD[P,x^2+m] Classical Part of shor's #algorithm

    Prime Numbers & Draft Factorization Method

    Noted:
    factorization method (Improvement of Quadratic sieve and application of Legendre’s conjecture)

    P=w^2+m
    P=pq
    p=GCD[P,x^2+m] or q=GCD[P,x^2+m]

    Where:
    w=Floor[P^.5]
    m=P-w^2 or Mod(P,w^2)
    Range: x={0,1…w }

    Overview:

    Theorem:
    There are many infinite natural Integers in the form of P=w^2+m

    Legendre’s conjecture:
    Does there always exist at least one prime between consecutive perfect squares?

    w^2 < Prime < (w+1)^2

    Counterexample:

    16=4^2+0
    17=4^2+1(Prime)
    18=4^2+2
    19=4^2+3(Prime)
    20=4^2+4
    21=4^2+5
    22=4^2+6
    23=4^2+7(Prime)
    24=4^2+8
    25=(4+1)^2+0

    New factorization method

    Example:

    P=21 then w=4 and m=5
    x=0;GCD[21,0^2+5]=1
    x=1;GCD[21,1^2+5]=3
    x=2;GCD[21,2^2+5]=3
    x=3;GCD[21,3^2+5]=7
    x=4;GCD[21,4^2+5]=21
    x=5;GCD[21,5^2+5]=3
    x=6;GCD[21,6^2+5]=1
    x=7;GCD[21,7^2+5]=3
    x=8;GCD[21,8^2+5]=3
    *
    *
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    Open with website to view and download the softcopy
    File:
    https://www.dropbox.com/sh/shq0l3eg42rfy9h/AAC7SetZQPY68GUYriLql4Gua?dl=0

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