Shor's Algorithm - September 2nd Notes
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We're getting ready to embark on the study of Shor's algorithm. This is
probably the most well-known and most important algorithm in quantum
computing, and was a major factor spurring on growth in the field during
the 1990s.

At this point I don't yet understand it myself, let alone have any good
idea exactly how to organize our study. I am pretty sure that we'll be
spending a while on Shor (including a number of supporting topics).

I would take what follows, not exactly as an outline for study, but rather
as a list of "Topics to be Investigated." And anyone who has time, please
feel free to pick one of these topics and help figure it out!

                    Topics for Investigation
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The Quantum Computing Part

  * The Quantum Fourier Transform
  * Modular Exponentiation Operator: f_{a,N}(x) = a^x mod N
  * Period Finding

Number Theory

  * Basics of Modular Arithmetic
  * GCDs - Euclid's Algorithm
  * GCDs - as Linear Combinations
  * Relationship of period finding to factoring

General Background

  * "Big O" notation and concepts
  * Sieve algorithms for factoring?
  * Public Key Cryptography, RSA, SSL, etc.