The P versus NP Problem in Quantum Physics

Motivated by the fact that information is encoded and processed by physical systems, the P versus NP problem is examined in terms of physical processes. In particular, we consider P as a class of deterministic, and NP as nondeterministic, polynomial-time physical processes. Based on these identifications, we review a self-reference physical process in quantum theory, which belongs to NP but cannot be contained in P.

[1]  A. Church An Unsolvable Problem of Elementary Number Theory , 1936 .

[2]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[3]  STEPHEN COOK,et al.  The P versus NP Problem , 2010, ArXiv.

[4]  D. Deutsch Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  David Deutsch,et al.  Machines, logic and quantum physics , 2000, Bull. Symb. Log..

[6]  R. D. Wolf Quantum Computation and Shor's Factoring Algorithm , 1999 .

[7]  J. Bell On the Einstein-Podolsky-Rosen paradox , 1964 .

[8]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[9]  Tereza Tusarova Quantum Complexity Classes , 2004, ArXiv.

[10]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[11]  Lance Fortnow,et al.  The status of the P versus NP problem , 2009, CACM.

[12]  Oded Goldreich,et al.  Computational complexity: a conceptual perspective , 2008, SIGA.

[13]  David Deutsch,et al.  Information flow in entangled quantum systems , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  A. Turing On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[15]  R. Landauer Information is physical , 1991 .

[16]  H. S. Allen The Quantum Theory , 1928, Nature.

[17]  Gerd Folkers,et al.  On computable numbers , 2016 .

[18]  Scott Aaronson,et al.  NP-complete Problems and Physical Reality , 2005, Electron. Colloquium Comput. Complex..

[19]  Gilles Brassard,et al.  Strengths and Weaknesses of Quantum Computing , 1997, SIAM J. Comput..

[20]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[21]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[22]  Lov K. Grover Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[23]  Andrew Chi-Chih Yao,et al.  Quantum Circuit Complexity , 1993, FOCS.

[24]  Daegene Song,et al.  Non-Computability of Consciousness , 2007, ArXiv.

[25]  Developing the Deutsch?Hayden approach to quantum mechanics , 2006, quant-ph/0609085.

[26]  D. Gottesman The Heisenberg Representation of Quantum Computers , 1998, quant-ph/9807006.

[27]  R. Landauer The physical nature of information , 1996 .