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CRC Press eBooks

Quantum Robots

Paul A. Benioff

Published Nov 15, 2018• 3 citations
Publisher

Abstract

Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and sytems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A very small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with environments of quantum systems. The dynamics of these systems are described in terms of tasks that consist of sequences of computation and action phases. For each task a step operator is defined which can then be used to define finite time interval step dynamics or a task Hamiltonian. A specific task carried out on a very simple environment is used to illustrate the models.

DOI
10.1201/9780429500459-12

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Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and sytems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A very small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with environments of quantum systems. The dynamics of these systems are described in terms of tasks that consist of sequences of computation and action phases. For each task a step operator is defined which can then be used to define finite time interval step dynamics or a task Hamiltonian. A specific task carried out on a very simple environment is used to illustrate the models.
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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 TTT that gives the single time step dynamics is associated with each task. T=Ta+Tc{T=T}_{a}{+T}_{c}T=Ta​+Tc​ is a sum of action phase and computation phase step operators. Conditions that Ta{T}_{a}Ta​ and Tc{T}_{c}Tc​ should satisfy are given along with a description of the evolution as a sum over paths of completed phase input and output states. A simple example of a task---carrying out a measurement on a very simple environment---is analyzed in detail. A decision tree for the task is presented and discussed in terms of the sums over phase paths. It is seen that no definite times or durations are associated with the phase steps in the tree, and that the tree describes the successive phase steps in each path in the sum over phase paths.
A quantum robot is a mobile quantum system, including an on board quantum computer and needed ancillary systems, that interacts with an arbitrary environment of quantum systems. Quantum robots carry out tasks whose goals include carrying out measurements or physical experiments on the environment. A dynamical model of quantum robots and their interactions is discussed in which each task, as a sequence of alternating computation and action phases, is described by a unitary single time step operator T=T a +T c (discrete space and time are assumed). The overall system dynamics is described as a sum over paths of completed computation (T c ) and action (T a ) phases. A simple example of a task, measuring the distance between the quantum robot and a particle on a 1D lattice with quantum phase path dispersion present, is analyzed.
Quantum robots are described as mobile quantum computers and ancillary systems that move in and interact with arbitrary environments. Their dynamics is given as tasks which consist of sequences of alternating computation and action phases. A task example is considered in which a quantum robot searches a space region to find the location of a system. The possibility that the search can be more efficient than a classical search is examined by considering use of Grover's Algorithm to process the search results. For reversible searches this is problematic for two reasons. One is the removal of entanglements generated by the search process. The other is that even if the entanglement can be avoided, the search process in 2-D space regions is no more efficient than a classical search. However, quantum searches of space regions with 3 or more dimensions are more efficient than classical searches. Reasons why quantum robots are interesting independent of these results are briefly summarized.
The physics and the mathematics of computation are examined to provide a foundation and perspective for the investigation of the quantum mechanics of computation. Our purpose is to explore the fundamental limits and constraints imposed on computation by Nature through the laws of physics and the mathematics of computational complexity. Inasmuch as information storage and transmission are an integral part of computation, their physical bounds are considered. The computer is viewed both physically and mathematically as a dynamical system, and is depicted in terms of the basic Turing machine paradigm. Three fundamental classes of the Turing machine are defined; the deterministic, stochastic and quantum Turing machines. Hamiltonian models and physical realizations of quantum computing are described. Quantum computers can perform some tasks which have no classical analogue, but they cannot compute functions that are non-computable by classical means. Some classically intractable problems can be solved with quantum computers.