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Related Experiment Videos

P/NP, and the quantum field computer

M H Freedman1

  • 1Microsoft Research 9N, 1 Microsoft Way, Redmond, WA 98052, USA.

Proceedings of the National Academy of Sciences of the United States of America
|January 14, 1998
PubMed
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This study proposes that physical theories can support computational models. Non-Abelian topological quantum field theories may solve intractable #P-hard problems, potentially offering a new avenue for analog computing.

Area of Science:

  • Theoretical Computer Science
  • Quantum Field Theory
  • Computational Complexity

Background:

  • The P versus NP problem is a central question in computer science.
  • Physical theories may impose limits on computational power.
  • Classical physics supports Turing machine implementations.

Purpose of the Study:

  • To explore the potential of physical theories to support computational models beyond current limitations.
  • To investigate the use of non-Abelian topological quantum field theories for solving computationally intractable problems.
  • To propose a framework for analog computers capable of solving NP and #P-hard problems.

Main Methods:

  • Analysis of non-Abelian topological quantum field theories, specifically SU(2)-field theory.

Related Experiment Videos

  • Connecting expectation values in these theories to the Jones polynomial.
  • Identifying #P-hard properties of the Jones polynomial.

    • Main Results:

    • Non-Abelian topological quantum field theories possess mathematical features suitable for solving #P problems in polynomial time.
    • Expectation values in SU(2)-field theory relate to #P-hard Jones polynomial values.
    • Physical systems with non-Abelian topological terms could function as analog computers for NP and #P-hard problems.

    Conclusions:

    • Physical systems may offer a pathway to solve problems currently considered computationally intractable.
    • Further research is needed to define such physical systems and address practical challenges like accuracy.
    • This work suggests a novel approach to computational complexity by leveraging principles from quantum field theory.