Computational complexity for physicists

@article{Mertens2002ComputationalCF,
  title={Computational complexity for physicists},
  author={Stephan Mertens},
  journal={Comput. Sci. Eng.},
  year={2002},
  volume={4},
  pages={31-47}
}
  • S. Mertens
  • Published 11 December 2000
  • Physics
  • Comput. Sci. Eng.
The theory of computational complexity has some interesting links to physics, in particular to quantum computing and statistical mechanics. The article contains an informal introduction to this theory and its links to physics. 

Figures from this paper

Building an adiabatic quantum computer simulation in the classroom
We present a didactic introduction to adiabatic quantum computation (AQC) via the explicit construction of a classical simulator of quantum computers. This constitutes a suitable route to introduce
Using Quantum Computing to Learn Physics
  • N. Wiebe
  • Physics, Education
    Bull. EATCS
  • 2014
TLDR
It is shown that quantum computers can sometimes be used to address problems of quantum mechanics and that quantum computer science can assign formal complexities to learning facts about nature.
Using Quantum Computers to Learn Physics
TLDR
It is shown that quantum computers can sometimes be used to address problems of quantum mechanics and that quantum computer science can assign formal complexities to learning facts about nature.
Phase transitions and complexity in computer science : an overview of the statistical physics approach to the random satis % ability problem
Phase transitions, ubiquitous in condensed matter physics, are encountered in computer science too. The existence of critical phenomena has deep consequences on computational complexity, that is the
Quantum Walks for Computer Scientists
TLDR
The purpose of this lecture is to provide a concise yet comprehensive introduction to quantum walks, an emerging field of quantum computation, is a generalization of random walks into the quantum mechanical world.
A cross-disciplinary introduction to quantum annealing-based algorithms
TLDR
The structure of quantum annealing-based algorithms as well as two examples of this kind of algorithms for solving instances of the max-SAT and Minimum Multicut problems are introduced.
Recurring Models and Sensitivity to Computational Constraints
Why are some models repeatedly used within and across scientific domains? Examples of such striking phenomena are the harmonic oscilla- tor, the Ising model, a few Hamiltonians in quantum mechanics,
Computer Systems - Simple, Complicated or Complex
TLDR
The main goal of this paper is to present a few examples (reasons) that will justify, why the computer systems are the complex systems and why the complex system approach should be taken.
Accidental Algorithms
TLDR
It is shown that for the NP-complete general 3CNF problem no such elementary matchgrid algorithm can exist, however, that it remains open for many natural #Pcomplete problems whether such Elementary matchgrid algorithms exist, and for the general CNF problem whether non-elementary match grid algorithms exist.
...
...

References

SHOWING 1-10 OF 91 REFERENCES
The Complexity of Computing the Permanent
  • L. Valiant
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1979
Application of statistical mechanics to NP-complete problems in combinatorial optimisation
Recently developed techniques of the statistical mechanics of random systems are applied to the graph partitioning problem. The averaged cost function is calculated and agrees well with numerical
Polynomial-Time Approximation Algorithms for the Ising Model
TLDR
A randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy is presented.
Polynomial-Time Approximation Algorithms for Ising Model (Extended Abstract)
TLDR
Computational solutions to some classical combinatorial problems in statistical physics stem from the Ising model, which has been the focus of much attention in the physics and mathematics communities since it was first introduced by Lenz and Ising in the early 1920s.
A Conjecture on random bipartite matching
In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have
Spin Glass Theory and Beyond
This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular
Quantum computation
  • Lov K. Grover
  • Physics
    Proceedings Twelfth International Conference on VLSI Design. (Cat. No.PR00013)
  • 1999
TLDR
This paper introduces quantum mechanics and shows how this can be used for computation in devices designed to carry out classical functions.
Quantum Computation
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if
Solving Models in Statistical Mechanics
...
...