QALU and Measurement Gates

As I said in the last blog post, measurement has been implemented as a one-shot irreversible function in my code; I made it a function because measurement should not distribute to each orthogonal state inside the quantum state of the system. This could not easily be implemented in Sympy as every object (including my gates) is assumed to be distributive. This leads to some generality problems as one cannot construct a general circuit object with a mix of measurement gates and Unitary Gates. I did a one-shot measurement rather than an ensemble measurement as the one-shot measurement was needed immediately for my implementation of Shor's algorithm.

This week, I fixed these problems. In order to ensure measurement did not distribute, I had to subclass Gate into a NonDistributiveGate class which would be given special logic inside my apply method. This required me to carefully review apply and make sure that the .expand() method was used judiciously so that integer factors combined correctly while ensuring that gates did not distribute to the individual orthogonal states. This took much longer than I thought it would. I have also begun to implement a notion of ensemble measurement which will return a tuple of measurement outcomes.

Another thing I have been putting off is the creation of a set of quantum logic which implements common arithmetic quantum mechanically; this logic would be key in doing a legitimate and realistic simulation of all processes needed to do Shor's or Grover's algorithms. Making this logic required a look through the literature on reversible logic and a review of my old notes from my assembly language class. Reversible logic requires some junk bits which store extra information; since I am simulating a quantum computer and not a purely classical reversible machine, I can cheat a little and use measurement to irreversibly destroy information which bring down the number of necessary junk bits and the logic needed to manage them. Thus, I was able to implement a quantum mechanical Add, Bitshift and Multiply. I still need to create logic which can take powers and preform the mod function. Also, I might want to consider optimizing the number of gates and junk bits needed for these operations as they require quite a few.

The addition of tests to my code has been going smoothly as well. If I want to merge this code by the end of GSoC, I will need to begin to base my code off Matt Curry's code and document-test my code like crazy. These will likely be my primary concern for the next few weeks.