On the Hamiltonian Operators for Adiabatic Quantum Reduction of SAT

We study the Hamiltonians resulting from the Adiabatic Quantum Computing treatment of the Satisfiability Problem SAT. We provide respective procedures for explicit calculation of the involved Hamiltonians. The statement of the ending Hamiltonians allows us to pose a variant of SAT which is also NP-complete.

[1]  M. Sipser,et al.  Quantum Computation by Adiabatic Evolution , 2000, quant-ph/0001106.

[2]  T. Hogg.  Adiabatic Quantum Computing for Random Satisfiability Problems , 2002, quant-ph/0206059.

[3]  E. Farhi,et al.  A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem , 2001, Science.

[4]  Umesh V. Vazirani,et al.  How powerful is adiabatic quantum computation? , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[5]  Seth Lloyd,et al.  Adiabatic quantum computation is equivalent to standard quantum computation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[6]  Alberto Leporati,et al.  Three "quantum" algorithms to solve 3-SAT , 2007, Theor. Comput. Sci..

[7]  Tad Hogg,et al.  Solving Random Satisfiability Problems with Quantum Computers , 2001 .