# 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={Paul Benioff}, journal={Journal of Statistical Physics}, year={1980}, volume={22}, pages={563-591} }

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…

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## References

SHOWING 1-10 OF 20 REFERENCES

Logical reversibility of computation

- Computer Science
- 1973

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.

Mathematical Foundations of Quantum Mechanics

- Physics
- 1955

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 twentieth…

Models in nonequilibrium quantum statistical mechanics

- Physics
- 1972

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 most…

Fundamental Limitations in the Computational Process

- Engineering
- 1976

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. It…

Role of the Observer in Quantum Theory

- Philosophy
- 1963

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 the…

Time, Structure, and Fluctuations

- PhysicsScience
- 1978

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.

Irreversibility and heat generation in the computing process

- PhysicsIBM J. Res. Dev.
- 1961

Two simple, but representative, models of bistable devices are subjected to a more detailed analysis of switching kinetics to yield the relationship between speed and energy dissipation, and to estimate the effects of errors induced by thermal fluctuations.

The Radiation Theories of Tomonaga, Schwinger, and Feynman

- Physics
- 1949

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 a…

Include the Observer in the Wave Function

- Physics
- 1977

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 standard…

Relativistic quantum field theory.

- PhysicsScience
- 1966

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.