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

@article{Benioff1980TheCA,
  title={The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines},
  author={P. Benioff},
  journal={Journal of Statistical Physics},
  year={1980},
  volume={22},
  pages={563-591}
}
  • P. Benioff
  • Published 1980
  • Physics
  • Journal of Statistical Physics
In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianHNQ and a class of appropriate initial states such that if c is such an initial state, thenψQN(t)=exp(−1HNQt)ψQN(0) correctly describes at timest3,t6,⋯,t3N model states that correspond to the completion of the first, second, ⋯, Nth computation step ofQ. The model parameters can be adjusted so that for… Expand
Quantum mechanical hamiltonian models of turing machines
Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1/2 systems.Expand
Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: Application to Turing machines
Work done before on the construction of quantum mechanical Hamiltonian models of Turing machines and general discrete processes is extended here to include processes which erase their own histories.Expand
COMPARATIVE ANALYSIS ON TURING MACHINE AND QUANTUM TURING MACHINE
TLDR
This paper tried to analyze mathematically a possibility that the Universal Quantum Turing Machine (UQTM) is able to compute faster than any other classical models of computation, and tried to show that the UQTM can solve any NP-complete problem in polynomial time. Expand
Quantum mechanical Hamiltonian models of discrete processes
Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructedExpand
Review of quantum computation
Digital computers are machines that can be programmed to perform logical and arithmetical operations. Contemporary digital computers are ``universal,`` in the sense that a program that runs on oneExpand
Quantum Mechanical Hamiltonian Models of Computers a
Interest in the physical limitations of the computation process has been increasing in recent years.’.’ Landauer3“ has discussed this subject extensively, particularly from the viewpoint of energyExpand
Quantum Algorithm for Hilbert's Tenth Problem
  • T. Kieu
  • Mathematics, Physics
  • ArXiv
  • 2001
TLDR
It is argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles. Expand
A Quantum Turing Machine with a Local Hamiltonian
A universal, deterministic Turing machine can be implemented as a closed, locally interacting quantum lattice system. As a consequence, many questions about the long-term dynamics of a quantum systemExpand
Universality and programmability of quantum computers
TLDR
The extent to which universality has in fact been established by the pioneers in the field is examined and this key notion in theoretical computer science is scrutinised in quantum computing by distinguishing various connotations and concomitant results and problems. Expand
Quantum Turing Machines Computations and Measurements
TLDR
A new formulation of Quantum Turing Ma- chines is proposed, as an extension of those proposed by Bernstein and Vazirani, to define a class of quantum computable functions - any such a function is a mapping from a general quantum state to a distribution of probability of natural numbers. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 19 REFERENCES
Logical reversibility of computation
TLDR
This result makes plausible the existence of thermodynamically reversible computers which could perform useful computations at useful speed while dissipating considerably less than kT of energy per logical step. Expand
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentiethExpand
Models in nonequilibrium quantum statistical mechanics
In this paper, quantum versions of statistical models are constructed. All aspects of the systems can be explicitly solved. It is possible to give magnetic realizations of these models. The mostExpand
Fundamental Limitations in the Computational Process
Information in computers, in biological systems, or in any other form, inevitably requires the use of physical degrees of freedom. Information is not a purely mathematical or philosophical entity. ItExpand
Role of the Observer in Quantum Theory
In quantum theory as it is currently formulated the measurement of an observable quantity of a physical system is the occasion for a change of state of the system, except when the state prior to theExpand
Relativistic quantum field theory.
TLDR
The logical foundations of relativistic quantum field theory are described and it is indicated how the differential version transcends the correspondence principle and incorporates, on the same footing, two different kinds of quantum dyna-mical variable. Expand
Time, Structure, and Fluctuations
TLDR
It is shown that nonequilibrium may become a source of order and that irreversible processes may lead to a new type of dynamic states of matter called "dissipative structures" and the thermodynamic theory of such structures is outlined. Expand
The Radiation Theories of Tomonaga, Schwinger, and Feynman
A unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory. The theory is carried to aExpand
Include the Observer in the Wave Function
The classical dynamics of Einstein’s closed universe (idealized for simplicity to be empty except as excited by gravitational waves) is analyzed in no way more economically than by the standardExpand
Minimal Energy Dissipation and Maximal Error for the Computational Process
In a preceding paper, the execution of elementary logic steps was analyzed for minimal energy requirements and for bounds on the unavoidable error probabilities. This was done with the aid of aExpand
...
1
2
...