Hector Bombin

Abstract We introduce fusion based quantum computing (FBQC) - a model of universal quantum computation in which entangling measurements, called fusions, are performed on the qubits of small constant sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems, such as linear optics. FBQC can offer significant architectural simplifications, enabling hardware made up of many identical modules, and reducing classical processing requirements. We present two pedagogical examples of fault-tolerant schemes constructed in this framework and numerically evaluate their threshold under a general error model with measurement erasure and error, and a linear-optical error model with fusion failure and photon loss. In these schemes, fusion failures, as well as errors, are directly dealt with by the quantum error correction protocol. We find that tailoring the fault-tolerance framework to the physical system allows the scheme to have a higher threshold than schemes reported in literature. We present a ballistic scheme which can tolerate a 10.3% probability of suffering photon loss in each fusion.

By characterizing codes in terms of "lattice groups" on infinite lattices, we show that they can all be understood in terms of topological charges and string operators. This is true either for subspace or subsystem codes, and it has direct applications for error correction, for example. Subspace codes are directly connected to topologically ordered condensed matter systems. We show that all 2D topological stabilizer codes are equivalent up to local transformations to several copies of one universal phase: Kitaev's topological code.