L. Lo: "S3 topological order for universal computation" (Harvard)

  • Starts: 3:30 pm on Wednesday, May 15, 2024
Topological quantum computation is a promising route in realizing fault-tolerant computation in noisy quantum computers. S3 (the smallest nonabelian group) topological order is a minimal example which intrinsically enables universal quantum computation using braiding and measurements alone. We provide a protocol for implementing computation on the S3 quantum double model in a square lattice embedded on a torus: the internal degrees of freedom of nonabelian anyons are used to store logical information, which can be manipulated by braiding and fusion of these nonabelian anyons. We provide explicit implementations of the universal gate set for qubits (Hadamard gate, S gate, CZ gate, and the non-Clifford CCZ gate) by braiding and fusing anyons. Another interesting feature of nonabelian topological orders is the possibility of single-particle excitation by overlapping two distinct noncontractible Wilson loops of anyons around the torus; we showed that S3 topological order allows for nonabelian single particle excitations. This protocol can be readily realized in current trapped ion platforms with all-to-all connectivity between qubits.
SCI 352
Leo Lo