We present a comprehensive and self-contained simplified review of the quantum computing scheme of [1,2], which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%, natural asymmetric and adjustable strength error correction and low overhead, arbitrarily long-range logical gates. These features make it by far the best and most practical quantum computing scheme devised to date. We restrict the discussion to direct manipulation of the surface code using the stabilizer formalism, both of which we also briefly review, to make the scheme accessible to a broad audience.

Quantum physics is known to allow for completely new ways to create, manipulate and store information. Quantum communication -the ability to transmit quantum information -is a primitive necessary for any quantum internet. At its core, quantum communication generally requires the formation of entangled links between remote locations. The performance of these links is limited by the classical signaling time between such locations -necessitating the need for long lived quantum memories. Here we present the design of a communications network which neither requires the establishment of entanglement between remote locations nor the use of long-lived quantum memories. The rate at which quantum data can be transmitted along the network is only limited by the time required to perform efficient local gate operations. Our scheme thus potentially provides higher communications rates than previously thought possible.

Our objective was to design a quantum repeater capable of achieving one million entangled pairs per second over a distance of 1000km. We failed, but not by much. In this letter we will describe the series of developments that permitted us to approach our goal. We will describe a mechanism that permits the creation of entanglement between two qubits, connected by fibre, with probability arbitrarily close to one and in constant time. This mechanism may be extended to ensure that the entanglement has high fidelity without compromising these properties. Finally, we describe how this may be used to construct a quantum repeater that is capable of creating a linear quantum network connecting two distant qubits with high fidelity. The creation rate is shown to be a function of the maximum distance between two adjacent quantum repeaters.

Physics and information are intimately connected, and the ultimate information processing devices will be those that harness the principles of quantum mechanics. Many physical systems have been identified as candidates for quantum information processing, but none of them are immune from errors. The challenge remains to find a path from the experiments of today to a reliable and scalable quantum computer. Here, we develop an architecture based on a simple module comprising an optical cavity containing a single negatively charged nitrogen vacancy center in diamond. Modules are connected by photons propagating in a fiber-optical network and collectively used to generate a topological cluster state, a robust substrate for quantum information processing. In principle, all processes in the architecture can be deterministic, but current limitations lead to processes that are probabilistic but heralded. We find that the architecture enables large-scale quantum information processing with existing technology.