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A Gentle Introduction to Quantum Computing Algorithms with Applications to Universal Prediction
In this technical report we give an elementary introduction to Quantum
Computing for non-physicists. In this introduction we describe in detail some
of the foundational Quantum Algorithms including: the Deutsch-Jozsa Algorithm,
Shor's Algorithm, Grocer Search, and Quantum Counting Algorithm and briefly the
Harrow-Lloyd Algorithm. Additionally we give an introduction to Solomonoff
Induction, a theoretically optimal method for prediction. We then attempt to
use Quantum computing to find better algorithms for the approximation of
Solomonoff Induction. This is done by using techniques from other Quantum
computing algorithms to achieve a speedup in computing the speed prior, which
is an approximation of Solomonoff's prior, a key part of Solomonoff Induction.
The major limiting factors are that the probabilities being computed are often
so small that without a sufficient (often large) amount of trials, the error
may be larger than the result. If a substantial speedup in the computation of
an approximation of Solomonoff Induction can be achieved through quantum
computing, then this can be applied to the field of intelligent agents as a key
part of an approximation of the agent AIXI