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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Cluster state generation with ageing qubits

Pieter Kok

Published Jun 1, 2013• 0 citations
Publisher

Abstract

Cluster states for measurement-based quantum computing can be created with entangling operations of arbitrary low success probability. This will place a lower bound on the minimum lifetime of the qubits used in the implementation. Here, we present a simple scaling argument for the T2time of the qubits for various cluster state geometries. The results suggest that the required T2times are not unrealistic for the practical implementation of universal quantum computing with cluster states.

DOI
10.1109/cleopr.2013.6600223

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Cluster states for measurement-based quantum computing can be created with entangling operations of arbitrary low success probability. This will place a lower bound on the minimum lifetime of the qubits used in the implementation. Here, we present a simple scaling argument for the T2time of the qubits for various cluster state geometries. The results suggest that the required T2times are not unrealistic for the practical implementation of universal quantum computing with cluster states.
Cluster states for measurement-based quantum computing can be created with entangling operations of arbitrary low success probability. This will place a lower bound on the minimum lifetime of the qubits used in the implementation. Here, we present a simple scaling argument for the T2{T}_{2}T2​ time of the qubits for various cluster-state geometries, and we estimate the size of the qubit reservoir that is needed for the creation of miniclusters.
Cluster states can be used to perform measurement-based quantum computation. The cluster state is a useful resource, because once it has been generated only local operations and measurements are needed to perform universal quantum computation. In this paper, we explore techniques for quickly and deterministically building a cluster state. In particular, we consider generating cluster states on a qubus quantum computer, a computational architecture which uses a continuous variable ancilla to generate interactions between qubits. We explore several techniques for building the cluster, with the number of operations required depending on whether we allow the ability to destroy previously created controlled-phase links between qubits. In the case where we cannot destroy these links, we show how to create an $n\ifmmode\times\else\texttimes\fi{}m$ cluster using just $3nm\ensuremath{-}2n\ensuremath{-}\ensuremath{\lceil}3m/2\ensuremath{\rceil}+3$ operations. This gives more than a factor of 2 savings over a naive method. Further savings can be obtained if we include the ability to destroy links, in which case we only need $\ensuremath{\lceil}\frac{1}{3}(8nm\ensuremath{-}4n\ensuremath{-}4m\ensuremath{-}8)\ensuremath{\rceil}$ operations. Unfortunately, the latter scheme is more complicated so choosing the correct order to interact the qubits is considerably more difficult. A halfway scheme, that keeps a modular generation but saves additional operations over never destroying links requires only $3nm\ensuremath{-}2n\ensuremath{-}2m+4$ operations. The first scheme and the last scheme are the most practical for building a cluster state because they split up the generation into the repetition of simple sections.
Measurement based quantum computation requires the generation of a cluster state (quantum resource) prior to starting a computation. Generation of this entangled state can be difficult with many schemes already proposed. We present an abstract scheme which can create 2D cluster states as a universal resource for quantum computing. We find a linear scaling of grid size with cluster depth. The scheme is also capable of creating more exotic topologies including 3D structures and the unit cell for topological error correction. We note its relevance to the cavity QED scheme in [30] although it could be applied to various architectures.
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The Measurement Based Quantum Computation (MBQC) model achieves universal quantum computation by employing projective single qubit measurements with classical feedforward on a highly entangled multipartite cluster state. Rapid advances in improving scalability of quantum computing systems have enabled the generation of large cluster states for implementing MBQC on various platforms. This review focuses on three such efforts, each utilizing a different quantum computing technology viz., superconducting qubits, trapped ion qubits and squeezed photon states. MBQC is being increasingly employed on optical platforms which can generate large entangled resource states but lack the ability to perform deterministic entangling gates.