Abstract

The topological protection of the toric code ground states make it a promising candidate for the creation of logical (stable) qubits in the quest of a universal quantum computer. However, creating such a state is very challenging due to its highly entangled nature. In April 2021, Google released on arXiv, a paper entitled "Realizing topological ordered states on a quantum processor" where they claimed to produce such a state. In this talk I will review the main steps of the Google experiment. Two types of boundary conditions are used: The first one, called the "matching boundary condition" creates a non-degenerated ground states. After giving a "recipe" to produce such a state, Google researchers checked their success by measuring all the qubits and deducing the X/Z parity of every plaquettes/vertex terms. They also measure the topological entanglement entropy of the state to demonstrate its topological nature. They investigate the first topological excitation of the system. They extract the anyonic statistics by braiding these quasi-particles. The second boundary condition, called "mixed boundary condition" aims to create a 2-fold degenerated ground state (useful for the creation of a logical qubit). They inject arbitrary logical states and study their behavior against decoherence.