We present a family of three-dimensional local quantum codes with pairs of fractal logical operators. It has two polynomials over finite fields as input parameters which generate fractal shapes of anti-commuting logical operators, and possesses exotic topological order with quantum glassiness which is beyond descriptions of conventional topological field theory. A necessary and sufficient condition for being free from string-like logical operators is obtained under which the model works as marginally self-correcting quantum memory. We also provide theoretical tools to analyze physical and coding properties of translation symmetric stabilizer Hamiltonians.


Talk Number PIRSA:13010101
Speaker Profile Beni Yoshida