# 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} }

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

#### 729 Citations

Quantum mechanical hamiltonian models of turing machines

- Mathematics
- 1982

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

- Mathematics
- 1982

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

- Computer Science
- 2012

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

- Mathematics
- 1981

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 constructed… Expand

Review of quantum computation

- Physics
- 1993

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 one… Expand

Quantum Mechanical Hamiltonian Models of Computers a

- Physics
- 1986

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 energy… Expand

Quantum Algorithm for Hilbert's Tenth Problem

- Mathematics, Physics
- ArXiv
- 2001

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 system… Expand

Universality and programmability of quantum computers

- Computer Science, Physics
- Theor. Comput. Sci.
- 2008

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

- Computer Science
- ArXiv
- 2017

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

#### References

SHOWING 1-10 OF 19 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. Expand

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… Expand

Models in nonequilibrium quantum statistical mechanics

- Mathematics
- 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… Expand

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… Expand

Role of the Observer in Quantum Theory

- Physics
- 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… Expand

Relativistic quantum field theory.

- Physics, Medicine
- Science
- 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. Expand

Time, Structure, and Fluctuations

- Physics, Medicine
- Science
- 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. Expand

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… Expand

Include the Observer in the Wave Function

- Mathematics
- 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… Expand

Minimal Energy Dissipation and Maximal Error for the Computational Process

- Physics
- 1971

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 a… Expand