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arXiv:quant-ph/0412156 · International Journal of Quantum Information

AN ECONOMICAL ROUTE TO ONE-WAY QUANTUM COMPUTATION

Mark Tame, Mauro Paternostro, M. S. Kim, Vlatko Vedral

Published Aug 1, 2006• 11 citations
arXivHTMLPDF

Abstract

We assess the effects of a realistic intrinsic model for imperfections in cluster states by introducing noisy cluster states and characterizing their role in the one-way computational model. A suitable strategy to counter-affect these non-idealities is represented by the use of small clusters, stripped of any redundancy, which leads to the search for compact schemes for one-way quantum computation. In light of this, we quantitatively address the behavior of a simple four-qubit cluster which simulates a controlled-NOT under the influences of our model for decoherence. Our scheme can be particularly useful in an all-optical setup and the strategy we address can be directly applied in those experimental situations where small cluster states can be constucted.

DOI
10.1142/s0219749906002092

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We assess the effects of a realistic intrinsic model for imperfections in cluster states by introducing noisy cluster states and characterizing their role in the one-way computational model. A suitable strategy to counter-affect these non-idealities is represented by the use of small clusters, stripped of any redundancy, which leads to the search for compact schemes for one-way quantum computation. In light of this, we quantitatively address the behavior of a simple four-qubit cluster which simulates a controlled-NOT under the influences of our model for decoherence. Our scheme can be particularly useful in an all-optical setup and the strategy we address can be directly applied in those experimental situations where small cluster states can be constucted.
We provide an analysis of basic quantum-information processing protocols under the effect of intrinsic nonidealities in cluster states. These nonidealities are based on the introduction of randomness in the entangling steps that create the cluster state and are motivated by the unavoidable imperfections faced in creating entanglement using condensed-matter systems. Aided by the use of an alternative and very efficient method to construct cluster-state configurations, which relies on the concatenation of fundamental cluster structures, we address quantum-state transfer and various fundamental gate simulations through noisy cluster states. We find that a winning strategy to limit the effects of noise is the management of small clusters processed via just a few measurements. Our study also reinforces recent ideas related to the optical implementation of a one-way quantum computer.
We report an experimental realization of one-way quantum computing on a two-photon four-qubit cluster state. This is accomplished by developing a two-photon cluster state source entangled both in polarization and spatial modes. With this special source, we implemented a highly efficient Grover's search algorithm and high-fidelity two-qubit quantum gates. Our experiment demonstrates that such cluster states could serve as an ideal source and a building block for rapid and precise optical quantum computation.
One-way quantum computing [1, 2] is an important approach for quantum computation based on a series of one-qubit measurements starting from a cluster state of a qubit array. Cluster states are highly-entangled states involving all qubits and are typically generated from an Ising-like Hamiltonian, starting from an initial product state |Ψ0〉 ≡ |Ψ(t = 0)〉 = Πi=1|+〉i , where |±〉i = (|0〉i±|1〉i)/ √ 2. Here, |0〉i and |1〉i are the two states of the i-th qubit in an N -qubit system. In ref. [3], we showed that cluster states in charge qubits[4–17] can be created by applying a single gate bias pulse, right after preparing the initial product state (one-step generation method), and are more robust against nonuniformities among qubits than decoherence-free (DF) states [18, 19] under a noise environment generated by a quantum point contact (QPC) detector, which is a sensitive detector of electric charge distribution[20, 21]. However, trap sites are often unavoidable in solid-state qubits owing to their small fabrication size and several experiments show that trap states significantly affect electric transport properties of nanoscale devices[22–25]. Here, we model the trap site as the island (discrete energy state) between double QPCs (DQPC) and investigate robustness of cluster states in charge qubits measured by the DQPC detector (Fig. 1). The charge qubits are based on quantum dots (QD), in which the position of the excess charge in a qubit affects the QPC current electrically, resulting in detection of charged state. Owing to this additional external degrees of freedom, this setup is considered to be a harsher and more realistic condition for qubits than that of ref .[3]. Here, we calculate a time-dependent fidelity of four charge qubits with DQPC by solving density matrix (DM) equations.
One-way quantum computation is a promising approach to achieving universal, scalable, and fault-tolerant quantum computation. However, a main challenge lies in the creation of universal, scalable three-dimensional cluster states. Here, an experimental scheme is proposed for building large-scale canonical three-dimensional cubic cluster states, which are compatible with the majority of qubit error-correcting codes, using the spatiospectral modes of an optical parametric oscillator. Combining with Gottesman-Kitaev-Preskill states, one-way fault-tolerant optical quantum computation can be achieved with a lower fault-tolerant squeezing threshold. Our scheme drastically simplify experimental configurations, paving the way for compact realizations of one-way fault-tolerant optical quantum computation.
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.