Optimal universal generator sets#

Here we demonstrate the feature get_optimal_su_2_n_generators with which we obtain generating sets of \(\mathfrak{su}(2^n)\) that have optimal generation rate. To this end, we start with some universal generator set and find the graph with an anticommutation fraction nearest to \(0.706\).

from paulie import get_optimal_su_2_n_generators, G_LIE, get_pauli_string as p

n = 4  # dimension of the system
initial_generators = p(G_LIE["a12"], n=n)
optimal_generators = get_optimal_su_2_n_generators(initial_generators)
print(f" {optimal_generators} fraction={optimal_generators.get_anticommutation_fraction()}")

which outputs:

XZYX,ZZXZ,IYYY,XZYY,IXZX,YYXY,YYYY,ZZIX,XXZY fraction=0.6944444444444444

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