Realization of Topological Quantum Computation with surface codes

Abstract

In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling effect. Using a designer Hamiltonian - the Kitaev toric-code model as an example, we study quantum tunneling effects of the surface codes and obtain its effective theory. Finally, we show how to do topological quantum computation including the initialization, the unitary transformation and the measurement.

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• Fault-tolerant quantum computation with high threshold in two dimensions
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Topological fault-tolerance in cluster state quantum computation
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Arbitrarily accurate composite pulses
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Thresholds for topological codes in the presence of loss
• Anyonic interferometry and protected memories in atomic spin lattices
• Emergent Fermions and Anyons in the Kitaev Model
• Mutual Chern-Simons theory for Z_2 topological order
• Creation and Manipulation of Anyons in the Kitaev Model
• On measurement-based quantum computation with the toric code states
• Manipulation of Single Neutral Atoms in Optical Lattices
• Anyonic Braiding in Optical Lattices
• The Wavefunction of an Anyon
• Implementing topological quantum manipulation with superconducting circuits
• Macroscopic Quantum Tunneling Effect of Z2 Topological Order
• Probing $n$-Spin Correlations in Optical Lattices

Cited by in corpus (8)

• Compass-Heisenberg Model on the Square Lattice : Spin Order and Excitations
• Non-Hermitian Dynamic Strings and Anomalous Topological Degeneracy on non-Hermitian Toric-code Model with Parity-time Symmetry
• Magnetic properties of nanoscale compass-Heisenberg planar clusters
• Non-Hermitian Avalanche Effect: Non-Perturbative Effect Induced by Local Non-Hermitian Perturbation on a Z2 Topological Order
• Majorana Edge States for Z2 Topological Orders of the Wen-plaquette Model and the Toric-code Model
• Effective non-Hermitian physics for degenerate ground states of a nonHermitian Ising model with $\mathcal{R}\mathcal{T}$ symmetry
• Quench dynamics of topological quantum phase transition in Wen-plaquette model
• Exact description of the boundary theory of the Kitaev Toric Code with open boundary conditions