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Playing Pool with $|psi rangle$: from Bouncing Billiards to Quantum Search

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 Added by Adam R. Brown
 Publication date 2019
  fields Physics
and research's language is English
 Authors Adam R. Brown




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In Playing Pool with $pi$, Galperin invented an extraordinary method to learn the digits of $pi$ by counting the collisions of billiard balls. Here I demonstrate an exact isomorphism between Galperins bouncing billiards and Grovers algorithm for quantum search. This provides an illuminating way to visualize Grovers algorithm.



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73 - Owen Lockwood , Mei Si 2021
Despite the successes of recent works in quantum reinforcement learning, there are still severe limitations on its applications due to the challenge of encoding large observation spaces into quantum systems. To address this challenge, we propose using a neural network as a data encoder, with the Atari games as our testbed. Specifically, the neural network converts the pixel input from the games to quantum data for a Quantum Variational Circuit (QVC); this hybrid model is then used as a function approximator in the Double Deep Q Networks algorithm. We explore a number of variations of this algorithm and find that our proposed hybrid models do not achieve meaningful results on two Atari games - Breakout and Pong. We suspect this is due to the significantly reduced sizes of the hybrid quantum-classical systems.
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We investigate a particular type of classical nonsingular bouncing cosmology, which results from general relativity if we allow for degenerate metrics. The simplest model has a matter content with a constant equation-of-state parameter and we get the modified Hubble diagrams for both the luminosity distance and the angular diameter distance. Based on these results, we present a Gedankenexperiment to determine the length scale of the spacetime defect which has replaced the big bang singularity. A possibly more realistic model has an equation-of-state parameter which is different before and after the bounce. This last model also provides an upper bound on the defect length scale.
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256 - Lov K. Grover 2001
The quantum search algorithm is a technique for searching N possibilities in only sqrt(N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schrodingers equation. This paper also provides a self-contained introduction to the quantum search algorithm from a new perspective.
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