usami / qc-approx-eq

Compute two quantum circuits are approximately equivalent or not.

approxeq

approxeq is a Matlab function that computes whether two quantum circuits are approximately equivalent or not.

Usage

This function has the following syntax:

approxeq(epsilon, u11, u12, u21, u22)

To use this function in the Matlab prompt, simply run Matlab in the same directory, and then call the function like this.

>> approxeq(0.0001, 1, 0, 0, 1)

ans =

YES

Example

Here are some test runs for U = X, Y, Z, H, S or T. In each test, epsilon is set to 0.0001.

X = [0 1; 1 0]

>> approxeq(0.0001, 0, 1, 1, 0)

ans =

YES

Y = [0 -i; i 0]

>> approxeq(0.0001, 0, -i, i, 0)

ans =

YES

Z = [1 0; 0 -1]

>> approxeq(0.0001, 1, 0, 0, -1)

ans =

YES

H = [0.7071 0.7071; 0.7071 -0.7071]

>> approxeq(0.0001, 0.7071, 0.7071, 0.7071, -0.7071)

ans =

YES

S = [1 0; 0 i]

>> approxeq(0.0001, 1, 0, 0, i)

ans =

NO

T = [1 0; 0 0.7071+0.7071i]

>> approxeq(0.0001, 1., 0., 0., 0.7071+0.7071i)

ans =

NO

Results for another epsilon

epsilon	X	Y	Z	H	S	T
0.0001	YES	YES	YES	YES	NO	NO
0.00001	YES	YES	YES	NO	NO	NO