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arXiv:quant-ph/0003006

Space Searches with a Quantum Robot

Paul A. Benioff

Published Mar 1, 2000• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.quant-ph/0003006

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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.
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Localization is a critical aspect of mobile robotics, enabling robots to navigate their environment efficiently and avoid obstacles. Current probabilistic localization methods, such as the Adaptive-Monte Carlo localization (AMCL) algorithm, are computationally intensive and may struggle with large maps or high-resolution sensor data. This paper explores the application of quantum computing in robotics, focusing on the use of Grover's search algorithm to improve the efficiency of localization in mobile robots. We propose a novel approach to utilize Grover's algorithm in a 2D map, enabling faster and more efficient localization. Despite the limitations of current physical quantum computers, our experimental results demonstrate a significant speedup over classical methods, highlighting the potential of quantum computing to improve robotic localization. This work bridges the gap between quantum computing and robotics, providing a practical solution for robotic localization and paving the way for future research in quantum robotics.
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