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New Journal of Physics

A cavity-QED scheme for cluster-state quantum computing using crossed atomic beams

Peter Blythe, Benjamin T. H. Varcoe

Published Oct 9, 2006• 43 citations
Publisher

Abstract

A quantum computer is a hypothetical device in which elements of quantum mechanics are used to introduce a degree of parallelism into computations, which could significantly improve on the computational speed of a classical computer at certain tasks. The ideas of cluster state quantum computing (introduced by Raussendorf and Briegel) extend quantum computing to systems that are capable of performing quantum gates, but are intrinsically one-way in their operation. Using the techniques of cluster state quantum computing, we show how a scalable quantum computer could potentially be constructed using microwave cavity quantum electrodynamics (QED). In a departure from the traditional understanding of a computer as a fixed array of computational elements, we show that cluster state quantum computing is actually well suited to atomic beam experiments and that an atomic beam quantum computer could be constructed using elements of microwave cavity QED. While existing experimental parameters do not meet current thresholds for fault-tolerant computing, improvements in both the experiments and in the understanding of fault-tolerance are expected to change this situation.

DOI
10.1088/1367-2630/8/10/231

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A quantum computer is a hypothetical device in which elements of quantum mechanics are used to introduce a degree of parallelism into computations, which could significantly improve on the computational speed of a classical computer at certain tasks. The ideas of cluster state quantum computing (introduced by Raussendorf and Briegel) extend quantum computing to systems that are capable of performing quantum gates, but are intrinsically one-way in their operation. Using the techniques of cluster state quantum computing, we show how a scalable quantum computer could potentially be constructed using microwave cavity quantum electrodynamics (QED). In a departure from the traditional understanding of a computer as a fixed array of computational elements, we show that cluster state quantum computing is actually well suited to atomic beam experiments and that an atomic beam quantum computer could be constructed using elements of microwave cavity QED. While existing experimental parameters do not meet current thresholds for fault-tolerant computing, improvements in both the experiments and in the understanding of fault-tolerance are expected to change this situation.
A quantum computer is a hypothetical device in which the laws of quantum mechanics are used to introduce a degree of parallelism into computations and which could therefore significantly improve on the computational speed of a classical computer at certain tasks. Cluster state quantum computing (recently proposed by Raussendorf and Briegel) is a new paradigm in quantum information processing and is a departure from the conventional model of quantum computation. The cluster state quantum computer begins by creating a highly entangled multi-particle state (the cluster state) which it uses as a quantum resource during the computation. Information is processed in the computer via selected measurements on individual qubits that form the cluster state. We describe in detail how a scalable quantum computer can be constructed using microwave cavity QED and, in a departure from the traditional understanding of a computer as a fixed array of computational elements, we show that cluster state quantum computing is well suited to atomic beam experiments. We show that all of the necessary elements have been individually realised, and that the construction of a truly scalable atomic beam quantum computer may be an experimental reality in the near future.
We propose two experimental schemes to generate the cluster states in the context of microwave cavity quantum electrodynamics (QED). In the first scheme to prepare many cavities into the cluster states, we encode the vacuum state and one-photon state of the microwave cavity as the logic zero and one of the qubits. The second scheme is to prepare many atoms into the cluster states, where qubits are represented by the states of Rydberg atoms. Both schemes require the resonant atom-cavity interaction so that the quantum dynamics operates at a high speed, which is important in view of decoherence.
The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.
We propose two schemes for the generation of cluster states. One is based on cavity quantum electrodynamics (QED) techniques. The scheme only requires resonant interactions between two atoms and a single-mode cavity. The interaction time is very short, which is important in view of decoherence. Furthermore, we also discuss the cavity decay and atomic spontaneous emission case. The other is based on atomic ensembles. The scheme has an inherent fault tolerance function and is robust to realistic noise and imperfections. All the facilities used in our schemes are well within the current technology.
Quantum Computing The development of a practical quantum computer requires universality, scalability, and fault tolerance. Although much progress is being made in circuit platforms in which arrays of qubits are addressed and manipulated individually, scale-up of such systems is experimentally challenging. Asavanant et al. and Larsen et al. explore an alternative route: measurement-based quantum computation, which is a platform based on the generation of large-scale cluster states. As these are optically prepared and easier to handle (one simply performs local measurements on each individual component of the cluster state), such a platform is readily scalable and fault tolerant. The topology of the cluster state ensures that the approach meets the requirements for quantum computation. Science , this issue p. [373][1], p. [369][2] [1]: /lookup/doi/10.1126/science.aay2645 [2]: /lookup/doi/10.1126/science.aay4354