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arXiv:0707.3821 · Physical Review A

One-way quantum computing in optical lattices with many-atom addressing

Tim Friesen, David L. Feder

Published Sep 10, 2008• 6 citations
arXivHTMLPDF

Abstract

One of the fundamental conditions for one-way quantum computation (1WQC) is the ability to make sequential measurements on isolated qubits that comprise the highly entangled resource for 1WQC, the cluster state. This has been a significant impediment in the implementation of 1WQC with ultracold atoms confined in optical lattices, because the width of the measuring lasers is generally much greater than the atomic (qubit) spacing. We demonstrate that deterministic 1WQC is nevertheless possible, with a polynomial increase in the number of operations, as long as the center of the beams can be positioned with high accuracy and the beam width is reproducible. Extending the number of cluster atoms, the scheme is also able to compensate for accidental measurements of an arbitrary number of nearby qubits.

DOI
10.1103/physreva.78.032312

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One of the fundamental conditions for one-way quantum computation (1WQC) is the ability to make sequential measurements on isolated qubits that comprise the highly entangled resource for 1WQC, the cluster state. This has been a significant impediment in the implementation of 1WQC with ultracold atoms confined in optical lattices, because the width of the measuring lasers is generally much greater than the atomic (qubit) spacing. We demonstrate that deterministic 1WQC is nevertheless possible, with a polynomial increase in the number of operations, as long as the center of the beams can be positioned with high accuracy and the beam width is reproducible. Extending the number of cluster atoms, the scheme is also able to compensate for accidental measurements of an arbitrary number of nearby qubits.
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 present an approach to one-way quantum computation (1WQC) that can compensate for single-qubit errors by encoding the logical information residing on physical qubits into five-qubit error-correcting code states. A logical two-qubit cluster state that is the fundamental resource for encoded quantum teleportation is then described by a graph state containing ten vertices with constant degree seven. Universal 1WQC that incorporates error correction requires only multiple copies of this logical two-qubit state and a logical four-qubit linear cluster state, which are prepared only just in advance of their use in order to minimize the accumulation of errors. We suggest how to implement this approach in systems characterized by qubits in regular two-dimensional lattices for which entangling gates are generically global operations, such as atoms in optical lattices, quantum dots, or superconducting qubits.
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.
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.
In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation is determined from the classical data of all the measurement outcomes. This is in contrast to the more familiar gate array model in which computational steps are unitary operations, developing a large entangled state prior to some final measurements for the output. Two principal schemes of measurement based computation are teleportation quantum computation (TQC) and the so-called cluster model or one-way quantum computer (1WQC). We will describe these schemes and show how they are able to perform universal quantum computation. We will outline various possible relationships between the models which serve to clarify their workings. We will also discuss possible novel computational benefits of the measurement based models compared to the gate array model, especially issues of parallelisability of algorithms.
We introduce a novel scheme for one-way quantum computing (QC) based on the use of information encoded qubits in an effective cluster state resource. With the correct encoding structure, we show that it is possible to protect the entangled resource from phase damping decoherence, where the effective cluster state can be described as residing in a decoherence-free subspace (DFS) of its supporting quantum system. One-way QC then requires either single or two-qubit adaptive measurements. As an example where this proposal can be realized, we describe an optical lattice set-up where the scheme provides robust quantum information processing. We also outline how one can adapt the model to provide protection from other types of decoherence.