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New Journal of Physics

Weaving light-matter qubits into a one way quantum computer

Dimitris G. Angelakis, Alastair Kay

Published Feb 12, 2008• 23 citations
Publisher

Abstract

The great advantage of measurement-based quantum computation is that one would simply need the ability to prepare a particular state, known as the cluster state, and subsequently to perform single-qubit measurements on it. Nevertheless, a scalable implementation is yet to be realized. Here, we propose a hybrid light–matter system consisting of coupled cavities interacting with two level systems. Utilizing the stable, individually addressable, qubits resulting from the localized long-lived atom–photon excitations, we demonstrate how to use the natural system dynamics to 'weave' these qubits into a cluster state and propose the implementation of quantum algorithms employing just two rows of qubits. Finally, we briefly discuss the prospects for experimental implementation using atoms, quantum dots or Cooper pair boxes.

DOI
10.1088/1367-2630/10/2/023012

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The great advantage of measurement-based quantum computation is that one would simply need the ability to prepare a particular state, known as the cluster state, and subsequently to perform single-qubit measurements on it. Nevertheless, a scalable implementation is yet to be realized. Here, we propose a hybrid light–matter system consisting of coupled cavities interacting with two level systems. Utilizing the stable, individually addressable, qubits resulting from the localized long-lived atom–photon excitations, we demonstrate how to use the natural system dynamics to 'weave' these qubits into a cluster state and propose the implementation of quantum algorithms employing just two rows of qubits. Finally, we briefly discuss the prospects for experimental implementation using atoms, quantum dots or Cooper pair boxes.
Measurement-based quantum computation has revolutionized quantum information processing, and the physical systems with which it can be implemented. One simply needs the ability to prepare a particular state, known as the cluster state, and subsequently to perform single-qubit measurements on it. Nevertheless, a scalable implementation is yet to be realized. Here we propose a hybrid light-matter system comprised of coupled cavities interacting with two level systems. Utilising the stable, individually addressable, qubits resulting from the localised long-lived atom-photon excitations, we demonstrate how to use the natural system dynamics to `weave' these qubits into a cluster state and propose the implementation of quantum algorithms employing just two rows of qubits. Finally, we briefly discuss the prospects for experimental implementation using atoms, quantum dots or Cooper pair boxes.
Quantum computers promise to be more efficient and powerful than their classical counterparts. In the one-way quantum computer model [1], a sequence of measurements processes qubits, which are initially prepared in a highly entangled cluster state. We present here an optical implementation of a 4-qubit cluster state and we show how different algorithms can be experimentally realized by performing the corresponding sequence of measurements. The key advantage of this scheme over the standard network approach of quantum computing is that inherent, randomly induced measurement errors can classically be fed-forward and corrected by adapting the basis of subsequent measurement.
We propose an efficient approach for deterministically generating scalable cluster states with photons. This approach involves unitary transformations performed on atoms coupled to optical cavities. Its operation cost scales linearly with the number of qubits in the cluster state, and photon qubits are encoded such that single-qubit operations can be easily implemented by using linear optics. Robust optical one-way quantum computation can be performed since cluster states can be stored in atoms and then transferred to photons that can be easily operated and measured. Therefore, this proposal could help in performing robust large-scale optical one-way quantum computation.
Optical lattices with one atom on each site and interacting via cold controlled collisions provide an efficient way to entangle a large number of qubits with high fidelity. It has already been demonstrated experimentally that this approach is especially suited for the generation of cluster states [O. Mandel et al., Nature 425, 937 (2003)] which reduce the resource requirement for quantum computing to the ability to perform single-qubit rotations and qubit read out. In this paper, we describe how to implement these rotations in one-dimensional and two-dimensional optical lattices without having to address the atoms individually with a laser field.
We propose an array of coupled cavities interacting with two level systems and show how to construct stable, individually addressable, qubits in this system from the long‐lived atom‐photon excitations (polaritons) at each site. We derive the system dynamics and show that is described by an XY Hamiltonian. We proceed by showing how to implement non‐local quantum gates and show that combined with the inherent ability for individual addressing, universal quantum computation is possible in this system. We finally discuss the prospects for experimental implementation using various technologies involving dopants as atoms, NV centers in diamond, quantum dots or Cooper pair boxes.
Cluster state computation or the one way quantum computation (1WQC) relies on an initially highly entangled state (called a cluster state) and an appropriate sequence of single qubit measurements along different directions, together with feed-forward based on the measurement results, to realize a quantum computation process. The final result of the computation is obtained by measuring the last remaining qubits in the computational basis. In this short tutorial on cluster state quantum computation, we will also describe the basic ideas of a cluster state and proceed to describe how a single qubit operation can be done on a cluster state. Recently, we proposed a repeat-until-success (RUS) scheme that could effectively be used to realize one-way quantum computer on a hybrid system of photons and atoms. We will briefly describe this RUS scheme and show how it can be used to entangled two distant stationary qubits.