QFT + NP = P Quantum Field Theory (QFT): A Possible Way of Solving NP-Complete Problems in Polynomial Time

  • Vladik Kreinovich
  • Luc Longpré
  • Adriana Beltran
Part of the Studies in Big Data book series (SBD, volume 33)


It has been recently theoretically shown that the dependency of some (potential observable) quantities in quantum field theory (QFT) on the parameters of this theory is discontinuous. This discovery leads to the theoretical possibility of checking whether the value of a given physical quantity is equal to 0 or different from 0 (here, theoretical means that this checking requires very precise measurements and because of that, this conclusion has not yet been verified by a direct experiment). This result from QFT enables us to do what we previously could not: check whether two computable real numbers are equal or not. In this paper, we show that we can use this ability to solve NP-complete (“computationally intractable”) problems in polynomial (“reasonable”) time. Specifically, we will introduce a new model of computation. This new model is based on solid mainstream physics (namely, on quantum field theory). It is capable of solving NP-complete problems in polynomial time.



This work was supported in part:

\(\bullet \) by the National Science Foundation grants

\(\quad \bullet \) HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and

\(\quad \bullet \) DUE-0926721, and

\(\bullet \) by an award “UTEP and Prudential Actuarial Science Academy and Pipeline Initiative” from

   Prudential Foundation.

We are thankful:

\(\bullet \) to Andrei A. Grib and Vladimir M. Mostepanenko who patiently explained their physical results

   to us,

\(\bullet \) to Michael G. Gelfond and Yuri Gurevich for valuable discussions of constructive real numbers,


\(\bullet \) to James M. Salvador for valuable discussions of the corresponding chemical algorithms.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Vladik Kreinovich
    • 1
  • Luc Longpré
    • 1
  • Adriana Beltran
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA

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