I really wanted to delve deeper into why the mean photon number of embedding a graph requires a very high mean photon number. So I calculated the squeezing parameter of embedding a graph in a GBS and found something quite strange. The squeezing parameters are good except for the first mode having a very high squeezing parameter. Here is the code.
A = nx.adjacency_matrix(gnp_random_graph(8,0.5)).todense() #generate adjacency matrix of a graph _, s, _ = np.linalg.svd(A, full_matrices=True) c = 1 / ( np.max(s) + 1e-8 ) #the singular value p,_=sf.decompositions.takagi(A, rounding=2) #decompose that matrix to get the diagonal values to estimate squeezing qw= [i * c for i in p] qwe=np.arctanh(qw) #inverse of tanh for c*the diagonal values zx= np.sinh(qwe) #getting squeezing parameter zx= np.square(zx) zx=np.around(zx,3) print(qwe). #print squeezing parameters print(zx). #print mean photon number per mode
Is there any explanation for this because it is just one mode giving such a high value
Again apologies for my continuous queries. As an undergrad, I am trying to work on things myself but I just want to trust you experts when it comes to these queries❤️