# Day 3 Week 2 REU

Published on: Thu Jun 16 2011

Yesterday was a most exciting day. The morning was spent on Shor's Algorithm again.  The final part I am working on is the classical algorithm for continuous fraction expansion. In Shor's Algorithm the quantum circuit outputs a phase shift of the form s/r where r is an unknown variable. To determine r, continuous fraction expansion is used. How exactly this works I am not yet certain.

Next there was a talk (part 1 of 4) on machine learning as applied to neural networks. The talk covered how to determine the probabilities of various patterns of nerve signals firing. Of particular interest was the importance placed on the discrete vs continuous choice. For example, each firing of a signal could be viewed as a discrete event occurring at some point t in a continuous time. Or time could be partitioned into discrete quantities, with a probability of some number of events occurring per time.

In the afternoon there was a talk by the owner of an optical consulting firm. He talked about some of the practical projects the company has worked on, like a vein imager, barcode scanners and barcode auto-focusing. One project involved using a mask with a UPN pattern on it. I feel like I have seen these patterns around but I have not known there origin before. The practical applications reminded me of the reactivision table (computer vision system) and the ARToolkit (for augmented reality).

Finally on the way home I was toying with the idea of an optical Turing machine, both to increase my understanding of Turing machines and understand how light could be used to (Classically) compute. At home I was investigating this and did not find much information on how an optical Turing machine might work. This is in a way good because it gives me plenty of freedom in thinking of how I would like one to work. At the same time I am wondering if this might be impractical? Along the way I began investigating optical logic gates. I thought I would try and build a simple AND gate from optical components, and this proved much more difficult than I initially thought. I was hoping to use as my two states Horizontal |0> and Vertical |1>. This did not go well. The best I could come up with was

0 0 0
0 1 0
1 0 0
11 Empty

The big problem is that 1 1 is giving me 'Empty'. Empty wasen't even one of my states! That's like if instead of my gate saying yes/no it just stares at me in silence. So after this disappointment I began investigating various ideas for quantum logic gates. I found some information on them, and that's where I left off for the night. The plan for today is to continue reading about experimental quantum gates.