2024/05/20 by Hsin, Po-Shen, Kobayashi, Ryohei, Zhu, Guanyu · 3 citations
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2405.11719
We construct a family of infinitely many new candidate non-Abelian self-correcting topological quantum memories in D≥ 5+1 spacetime dimensions without particle excitations using local commuting non-Pauli stabilizer lattice models and field theories of ℤ23 higher-form gauge fields with nontrivial topological action. We call such non-Pauli stabilizer models magic stabilizer codes. The family of topological orders have Abelian electric excitations and non-Abelian magnetic excitations that obey Ising-like fusion rules and non-Abelian braiding, including Borromean ring type braiding which is a signature of non-Abelian topological order, generalizing the dihedral group \mathbbD8 gauge theory in (2+1)D. The simplest example includes a new non-Abelian self-correcting memory in (5+1)D with Abelian loop excitations and non-Abelian membrane excitations. We prove the self-correction property and the thermal stability, and devise a probabilistic local cellular-automaton decoder. We also construct fault-tolerant non-Clifford CCZ logical gate using constant depth circuit from higher cup products in the 5D non-Abelian code. The use of higher-cup products and non-Pauli stabilizers allows us to get an O(n2/5) distance overcoming the O(n1/3) distance barrier in conventional topological stabilizer codes, including the 3D color code and the 6D self-correcting color code.