Grant Sanderson on PI, Galperin's Puzzle and QC Grover's Search

In summary, the connection between the digits of pi, colliding blocks, and quantum search algorithms is explored in two papers, one from 2003 and one from December 2019. These papers bridge the areas of dynamics, geometry, and quantum computation, demonstrating the surprising physical relevance of seemingly abstract mathematical concepts. One of the papers, "Play Pool with PI" by Galperin, discusses the connections between pi and billiards, while the other, "Playing Pool with |ψ⟩: from Bouncing Billiards to Quantum Search" by Adam Brown, delves into the relationship between colliding blocks and quantum search algorithms. Together, these papers shed light on the unexpected connections between different fields of study and the potential for abstract
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what do the digits of pi, colliding blocks and quantum search algorithms have in common? More than you might expect. Two playful papers, one from 2003 and one from last month, provide the links between them. Together, they connect the worlds of dynamics, geometry and quantum computation, highlighting how even the most abstract math puzzles can have surprising physical relevance.
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jedishrfu said:
Summary:: what do the digits of pi, colliding blocks and quantum search algorithms have in common? More than you might expect. Two playful papers, one from 2003 and one from last month, provide the links between them. Together, they connect the worlds of dynamics, geometry and quantum computation, highlighting how even the most abstract math puzzles can have surprising physical relevance.

https://www.quantamagazine.org/how-...locks-to-a-quantum-search-algorithm-20200121/

and related papers:

Play Pool with PI (2003 paper by Galperin)

https://www.maths.tcd.ie/~lebed/Galperin. Playing pool with pi.pdf

and

Playing Pool with |ψ⟩: from Bouncing Billiards to Quantum Search (Dec 2019 paper by Adam Brown)

https://arxiv.org/abs/1912.02207

Here the related puzzle video by Grant from one year ago:

 
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1. What is the significance of Grant Sanderson's work on PI?

Grant Sanderson's work on PI is significant because it provides a visual representation of the infinite and irrational number. His videos on PI have helped many people understand the concept of PI and its importance in mathematics and science.

2. Can you explain Galperin's Puzzle and its connection to quantum computing?

Galperin's Puzzle is a mathematical problem that involves finding the shortest path between two points on a grid. It is relevant to quantum computing because it can be solved using the Grover's Search algorithm, which is a quantum algorithm that can efficiently search through a large number of possibilities.

3. How does QC Grover's Search work and what are its applications?

QC Grover's Search is a quantum algorithm that uses quantum superposition and interference to efficiently search through a large number of possibilities. It works by amplifying the correct answer while suppressing the incorrect ones. Its applications include database searching, optimization problems, and cryptography.

4. What are the limitations of QC Grover's Search?

One of the limitations of QC Grover's Search is that it can only find one correct answer out of a set of possibilities. It also requires a large number of qubits and a highly precise quantum computer to achieve a speedup over classical algorithms.

5. How does Grant Sanderson use visualizations to explain complex mathematical concepts?

Grant Sanderson uses animations and visualizations to break down complex mathematical concepts into simpler and more intuitive explanations. This approach helps viewers to better understand and visualize these concepts, making them more accessible and engaging.

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