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Journal of Statistical Physics

The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

Paul A. Benioff

Published May 1, 1980• 1,260 citations
Publisher
DOI
10.1007/bf01011339

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Now-a-days every computing device is based on the Turing Machine. It is known that classical physics is sufficient to explain macroscopic phenomena, but is not to explain microscopic phenomena like the interference of electrons. In these days, speed-up and down-sizing of computing devices have been carried out using quantum physical effects; however, principles of computation on these devices are also based on classical physics. This paper tries to analyze mathematically a possibility that the Universal Quantum Turing Machine (UQTM) is able to compute faster than any other classical models of computation. Basically we focused on comparative study on computation power of Universal Turing Machine (UTM) and UQTM. Namely, in the equal, we tried to show that the UQTM can solve any NP-complete problem in polynomial time. The result analysis showed that UQTM is faster for any computation.

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Physical Review Letters•Jun 7, 1982•296 citations
The physics and the mathematics of computation are examined to provide a foundation and perspective for the investigation of the quantum mechanics of computation. Our purpose is to explore the fundamental limits and constraints imposed on computation by Nature through the laws of physics and the mathematics of computational complexity. Inasmuch as information storage and transmission are an integral part of computation, their physical bounds are considered. The computer is viewed both physically and mathematically as a dynamical system, and is depicted in terms of the basic Turing machine paradigm. Three fundamental classes of the Turing machine are defined; the deterministic, stochastic and quantum Turing machines. Hamiltonian models and physical realizations of quantum computing are described. Quantum computers can perform some tasks which have no classical analogue, but they cannot compute functions that are non-computable by classical means. Some classically intractable problems can be solved with quantum computers.
Now-a-days every computing device is based on the Turing Machine. It is known that classical physics is sufficient to explain macroscopic phenomena, but is not to explain microscopic phenomena like the interference of electrons. In these days, speed-up and down-sizing of computing devices have been carried out using quantum physical effects; however, principles of computation on these devices are also based on classical physics. This paper tries to analyze mathematically a possibility that the Universal Quantum Turing Machine (UQTM) is able to compute faster than any other classical models of computation. Basically we focused on comparative study on computation power of Universal Turing Machine (UTM) and UQTM. Namely, in the equal, we tried to show that the UQTM can solve any NP-complete problem in polynomial time. The result analysis showed that UQTM is faster for any computation.