Code
Eventually, I hope to provide some useful snippets of code that I have used in my research.
How to quantify MULTI-qubit Magic
via Convex Optimization of a Linear Program
Matlab code for calculating Robustness
The files Amat2.mat ,..., Amat5.mat correspond to the A matrices for the linear system Ax=b. Each column corresponds to a stabilizer state written in the Pauli operator basis. The same ordering should be used for decomposing a state rho as vector b. We use the ordering
IIIII
IIIIX
IIIIY
IIIIZ
IIIXI
IIIXX
.....
ZZZZZ
The syntax for calculating robustness (assuming a working CVX [http://cvxr.com/cvx/] installation) is :
%n is one of {60,1080,36720,2423520}
cvx_begin
variable x(n)
minimize( norm( x, 1 ) )
subject to
A * x == b
cvx_end
robustness=cvx_optval;
Another option is to ask for a certificate, y, of optimality
cvx_begin
variable x(n)
dual variable y;
minimize( norm( x, 1 ) )
subject to
y: A * x == b
cvx_end
robustness=cvx_optval;
