Paul Benioff

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.

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. The models consist of three phases: the forward process phase in which a mapT is iterated and a history of iterations is generated, a copy phase, which is activated if and only ifT reaches a fix point, and an erase phase, which erases the iteration history, undoes the iterations ofT, and recovers the initial state except for the copy system. A ballast system is used to stop the evolution at the desired state. The general model so constructed is applied to Turing machines. The main changes are that the system undergoing the evolution corresponding toT iterations becomes three systems corresponding to the internal machine, the computation tape, and computation head. Also the copy phase becomes more complex since it is desired that this correspond also to a copying Turing machine.

Quantum robots and environments

Quantum robots and their interactions with environments of quantum systems are described, and their study justified. A quantum robot is a mobile quantum system that includes an on-board quantum computer and needed ancillary systems. Quantum robots carry out tasks whose goals include specified changes in the state of the environment, or carrying out measurements on the environment. Each task is a sequence of alternating computation and action phases. Computation phase activites include determination of the action to be carried out in the next phase, and recording of information on neighborhood environmental system states. Action phase activities include motion of the quantum robot and changes in the neighborhood environment system states. Models of quantum robots and their interactions with environments are described using discrete space and time. A unitary step operator

Quantum Mechanical Hamiltonian Models of Computers

T

Ab initio calculations of the vertical electronic spectra of NO2, NO+2, and NO−2

that gives the single time step dynamics is associated with each task.

Decision Procedures in Quantum Mechanics

{T=T}_{a}{+T}_{c}

Operator valued measures in quantum mechanics - finite and infinite processes

is a sum of action phase and computation phase step operators. Conditions that

Towards a Coherent Theory of Physics and Mathematics: The Theory¿Experiment Connection

{T}_{a}

Models of Zermelo Frankel set theory as carriers for the mathematics of physics. II

and

Towards a coherent theory of physics and mathematics.

{T}_{c}