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. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both time-independent and time-dependent Hamiltonian models are constructed here. The time-independent models do not dissipate energy or degrade the system state as they evolve. They operate close to the quantum limit in that the total system energy uncertainty/computation speed is close to the limit given by the time-energy uncertainty relation. However, the model evolution is time global and the Hamiltonian is more complex. The time-dependent models do not degrade the system state. Also they are time local and the Hamiltonian is less complex.

[1]  Martin D. Davis,et al.  Computability and Unsolvability , 1959, McGraw-Hill Series in Information Processing and Computers.

[2]  D. Haar,et al.  Quantum Mechanics Vol. 1 , 1965 .

[3]  R. L. Goodstein,et al.  Theory of Recursive Functions and Effective Computability , 1969 .

[4]  Jr. Hartley Rogers.  Theory of Recursive Functions and Effective Computability , 1969 .

[5]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .

[6]  P. Benioff.  The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines , 1980 .

[7]  Paul Benioff,et al.  Quantum mechanical Hamiltonian models of discrete processes , 1981 .

[8]  J. Bekenstein.  Energy Cost of Information Transfer , 1981 .

[9]  Daniele Mundici.  Irreversibility, uncertainty, relativity and computer limitations , 1981 .

[10]  R.W. Keyes,et al.  Fundamental limits in digital information processing , 1981, Proceedings of the IEEE.

[11]  David Deutsch,et al.  Is There a Fundamental Bound on the Rate at Which Information Can Be Processed , 1982 .

[12]  R. Landauer.  Uncertainty principle and minimal energy dissipation in the computer , 1982 .

[13]  Lev B. Levitin,et al.  Physical limitations of rate, depth, and minimum energy in information processing , 1982 .

[14]  K. K. Likharev,et al.  Classical and quantum limitations on energy consumption in computation , 1982 .

[15]  P. Benioff.  Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: Application to Turing machines , 1982 .

[16]  T. Toffoli,et al.  Conservative logic , 2002, Collision-Based Computing.

[17]  Rolf Landauer,et al.  Fundamental Physical Limitations of the Computational Process , 1984 .