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 $T$ that gives the single time step dynamics is associated with each task. ${T=T}_a{+T}_c$ is a sum of action phase and computation phase step operators. Conditions that $T_a$ and $T_c$ 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.