Exotic topological order from quantum fractal code



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PIRSA Number: 
13010101

Abstract

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.