What are the cost function for NAND and NOR gates?


In this chart cost function for NOT, AND, OR and XOR gate are given. So i have tried to formulate cost function for NOR and NAND gate. But some how it didn't work out. Please help. 



1 comment
  • Hi Aniruddha,

    The QUBO penalty function for a Boolean NOR constraint is -x1-x2-z+x1x2+2x2z+2x1z  and for a Boolean NAND constraint is -2x1-2x2-3z+x1x2+2x2z+2x1z.

    The Ising model notation for these Boolean operations were fetched from  'A quantum annealing approach for Boolean Satisfiability problem' by J. Su, T. Tu and L. He (2016), and then converted to the equivalent QUBO by following the method described in Section 2.4 of the 'Problem Formulation Guide' linked below. 

    Here are some relevant resources that may be helpful:

    There are a few different ways to formulate penalty models, as you can see in the resources above. Please let me know if you have any questions about either approach or about the approach you tried.

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