Web Guitar

I finally got around to porting some of my old code to use HTML5's Web Audio API. It's a guitar tab editor that uses web audio to playback your tabs. The sound is synthesized using the code in the textarea below the editor. By default, the code is a basic string pluck synthesis, but you can change it to produce whatever waveforms you'd like.

It's primitive. It hasn't been tested on anything other than chrome. The UI has no documentation. It's got some growing up to do, but it's still fun to play around with.

Here it is: Web Guitar Demo

Load the example "Moonlight sonata" and press play.


Hint: clicking above the strings in the editor will toggle between 4, 8, 16, 1, 2 which is the reciprocal of the duration of the note. Also, after clicking on a string, you can navigate the editor using the arrow keys.

Quantum Algorithms

I've added a few examples to my quantum circuit editor / simulator. The most interesting of which being Grover's Algorithm for unsorted search.

Go ahead and try it out.

Hit "Enter" to evaluate the circuit and get a table of probable outcomes.

The gate F7 makes the fifth qubit in the "|1>" state if the first four qubits are in the state "|0111>" (seven). The circuit is able to determine that "|0111>" is the magic number with over 96% accuracy and only three calls to F7.

I also included an F5 gate. Go ahead and right click those F7 gates away, select the F5 gate, and then drag it into the three places the F7 was. Now it will find "|0101>".

You can save the entire circuit by pressing Ctrl+S. Double click on the GROV, F7, and F5 gates to see what their circuits look like (or to edit them to create your own versions).

Some of the other examples include:

• Toffoli gate (you can make one simply by dragging to controls onto an X gate, but this is an implementation using only CNots and single-qubit gates)
• Bell State (the "Hello World" of quantum computing)
• 2 Qubit QFT and 4 Qubit QFT (again, the editor has it's own quantum fourier transform gate, but these are implementations using only Hadamard gates, controlled rotations, and swaps)

More general info can be found in the help menu on the very top right of the application.

Quantum Circuit Simulator

All I wanted for Christmas was a quantum circuit simulator. So I wrote one in Javascript using NumericJS.

Check it out: http://www.davyw.com/quantum

For a good "Hello world" circuit, here's the diagram for a Bell State...

Try evaluating it yourself and see that |00> or |11> are the only possible outcomes.

You can even compile your own circuits into gates to use in other circuits.

Construct a circuit that transforms a single qubit into |0> with 75% probability and |1> with 25% probability, such as:

Then compile that into gate "F" and use it to create a superposition of |00> with 75% prob and |11> with 25% prob, like this:

Let me know if you find any use out of this. And definitely let me know if you find any bugs.

NumericJS Logistic Regression Classifier

The other day I posted about numericjs and provided a simple PCA implementation using it. Today I rewrote my logistic regression classifer using numericjs. Below is the commented sourcecode and demo in jsFiddle.

For the demo, you click on the large square (in the "Result" panel) to add a point. The dropdown box labeled "group" allows you to select the color of point to add. You can change the learning rate (alpha) and the regularization parameter (lambda) to see how it changes the classification.

In case you're using a feed reader and can't see the box below, click here.

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Numeric Javascript

I just recently found this javascript library. So far it's looking pretty good. I've always wanted some sort of Javascript equivalent to NumPy and while this isn't anywhere near that extreme, it does offer some pretty handy features.

Here's a jsFiddle I put together to show it performing a simple implementation of PCA (Principle Component Analysis) on a fictional dataset. The first component should have a slope of approximately 0.357

Here's a quick snippet, the actual PCA function using numericjs...

function pca(X) {
    /*
        Return matrix of all principle components as column vectors
    */        
    var m = X.length;
    var sigma = numeric.div(numeric.dot(numeric.transpose(X), X), m);
    return numeric.svd(sigma).U;
}

Pi Day Part 2

Pi-zza:

Apple-Pi:

Pi Day Part 1

We've decided to celebrate a two part Pi day this year (to honor 3 . 14 and 15). It began with egg*pi (quiche)...



And ended with pot*pi...



Tomorrow should conclude with apple*pi and pizza*pi.