Realization of Topological Quantum Computation with surface codes

TL;DR

This paper demonstrates how to realize topological quantum computation using surface codes derived from Z2 topological order, employing a designer Hamiltonian to analyze tunneling effects and implement quantum operations.

Contribution

It introduces a method to perform topological quantum computation with surface codes by tuning quantum tunneling effects in a specific Hamiltonian model.

Findings

Effective theory of tunneling in surface codes derived

Procedures for initialization, transformation, and measurement established

Surface codes can be used as a protected quantum subspace

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.