What are the cost function for NAND and NOR gates?

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  Sukhraan S  (Report)

  March 19, 2021 23:22

  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:

  • Illustrative examples for Boolean NOT, AND & XOR as a penalty funtion: https://docs.dwavesys.com/docs/latest/handbook_reformulating.html#elementary-boolean-operations
  • Problem Formulation Guide: https://docs.dwavesys.com/docs/latest/c_gs_workflow.html; Section 3.2 provides a step-by-step method to build a penalty function for a constraint. 

  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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