Robert Raussendorf

Persistent Entanglement in Arrays of Interacting Particles

We study the entanglement properties of a class of N-qubit quantum states that are generated in arrays of qubits with an Ising-type interaction. These states contain a large amount of entanglement as given by their Schmidt measure. They also have a high persistency of entanglement which means that approximately N/2 qubits have to be measured to disentangle the state. These states can be regarded as an entanglement resource since one can generate a family of other multiparticle entangled states such as the generalized Greenberger-Horne-Zeilinger states of <N/2 qubits by simple measurements and classical communication.

Measurement-based quantum computation on cluster states

We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe why its underlying computational model is different from the network model of quantum computation, and relate quantum algorithms to mathematical graphs. Further we investigate the scaling of required resources and give a number of examples for circuits of practical interest such as the circuit for quantum Fourier transformation and for the quantum adder. Finally, we describe computation with clusters of finite size.

Fault-tolerant quantum computation with high threshold in two dimensions.

We present a scheme of fault-tolerant quantum computation for a local architecture in two spatial dimensions. The error threshold is 0.75% for each source in an error model with preparation, gate, storage, and measurement errors.

Measurement-based quantum computation

Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics are harnessed and exploited. A number of models of quantum computation exist. These models have been shown to be formally equivalent, but their underlying elementary concepts and the requirements for their practical realization can differ significantly. A particularly exciting paradigm is that of measurement-based quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in a highly entangled state. We review recent developments in measurement-based quantum computation with a view to both fundamental and practical issues, in particular the power of quantum computation, the protection against noise (fault tolerance) and steps towards experimental realization. Finally, we highlight a number of connections between this field and other branches of physics and mathematics. So-called one-way schemes have emerged as a powerful model to describe and implement quantum computation. This article reviews recent progress, highlights connections to other areas of physics and discusses future directions.

Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects

The practical construction of scalable quantum-computer hardware capable of executing nontrivial quantum algorithms will require the juxtaposition of different types of quantum systems. We analyze a modular ion trap quantum-computer architecture with a hierarchy of interactions that can scale to very large numbers of qubits. Local entangling quantum gates between qubit memories within a single register are accomplished using natural interactions between the qubits, and entanglement between separate registers is completed via a probabilistic photonic interface between qubits in different registers, even over large distances. We show that this architecture can be made fault tolerant, and demonstrate its viability for fault-tolerant execution of modest size quantum circuits.

Quantum walks in optical lattices

We propose an experimental realization of discrete quantum walks using neutral atoms trapped in optical lattices. The quantum walk is taking place in position space and experimental implementation with present-day technology\char22{}even using existing setups\char22{}seems feasible. We analyze the influence of possible imperfections in the experiment and investigate the transition from a quantum walk to the classical random walk for increasing errors and decoherence.

A fault-tolerant one-way quantum computer

We describe a fault-tolerant one-way quantum computer on cluster states in three dimensions. The presented scheme uses methods of topological error correction resulting from a link between cluster states and surface codes. The error threshold is 1.4% for local depolarizing error and 0.11% for each source in an error model with preparation-, gate-, storage-, and measurement errors.

Efficient Quantum Computation with Probabilistic Quantum Gates

With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability p. The required computational overhead scales efficiently both with 1/p and n, where n is the number of qubits in the computation. This approach provides an efficient way to combat noise in a class of quantum computation implementation schemes, where the dominant noise leads to probabilistic signaled errors with an error probability 1-p far beyond any threshold requirement.

Experimental demonstration of topological error correction

Scalable quantum computing can be achieved only if quantum bits are manipulated in a fault-tolerant fashion. Topological error correction—a method that combines topological quantum computation with quantum error correction—has the highest known tolerable error rate for a local architecture. The technique makes use of cluster states with topological properties and requires only nearest-neighbour interactions. Here we report the experimental demonstration of topological error correction with an eight-photon cluster state. We show that a correlation can be protected against a single error on any quantum bit. Also, when all quantum bits are simultaneously subjected to errors with equal probability, the effective error rate can be significantly reduced. Our work demonstrates the viability of topological error correction for fault-tolerant quantum information processing.

Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal quantum computational resource.

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki states has recently been intensively explored and shown to provide restricted computation. Here, we show that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal resource for measurement-based quantum computation.