More On Operations

I added some more functionality to the code this week.

I gave the code the ability to build single qbit gates that work in multi-Qbit settings.

In order to do this, I had to take the matrix-representation of the gate operating on a single Qbit and take the tensor product of it with Unities; these Unities belong in the place of the qbits that are unaffected by the gate. Thus, a Hadamard Gate on the 1st bit in a 4-qbit setting is the tensor product (I x I x H x I), where I is a 2x2 unity matrix and H is the Hadamard Matrix.

For this to work, I would have to implement a Kronecker (Tensor) Product for matrices. The Kronecker Product function that I created does the Kronecker Product for an arbitrary number of input matrices of arbitrary size. I also produced test files that tested the Product against the Kronecker product that already exists in a Python library called Numpy. With this product working, I was able to make the single qbit gates act on any number of qbits.

Dr. Granger told me to implement an apply method which would be able to apply the gates to any number of qbits without doing a full matrix representation using Tensor Products. To do this, I used Qbit objects to represent a single state inside a ket with a probability amplitude multiplying. This works like this:

In [7]: circuit = HadamardGate(0)*XGate(1)*Qbit(0,0,0,0,0)

In [8]: print circuit

Out [8]: H(0)*X(1)*|00000>

In [9]: apply_gates(circuit)

Out[9]: 2**(1/2)/2*|00010> + 2**(1/2)/2*|00011>

This output is clearly much cleaner than the output given by the represent() function, which prints a long matrix. Having an output with states inside kets multiplied by their respective probability amplitude makes quite a bit more sense than a long column matrix. As such, I taught the code to take the matrix representation and turn it into this format using the matrix_to_qbits function.

The ability to switch the matrix representation into an expression in Dirac Notation allowed me to test to see if the apply and represent functions produced the same results. The testing stage of my code is far from complete so I need to continue debugging and creating tests in my test file. Also, I plan on creating a simpgate() function that will rearrange gates so gates that operate on the same qbit are grouped together (gates that operate on different Qbits commute; if they operate on the same qbit, they do not) and then make any obvious simplifications.