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arXiv:quant-ph/0702209 · New Journal of Physics

Efficient growth of complex graph states via imperfect path erasure

Earl T. Campbell, Joseph Fitzsimons, Simon C Benjamin, Pieter Kok

Published Jun 29, 2007• 10 citations
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Abstract

Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect entanglement into an extended graph state formalism. The subsequent growth of the improper graph state can be guided, through a series of strategic decisions, in such a way as to bound the growth of the error and eventually yield a high-fidelity graph state. As an implementation of these techniques, we develop an analytic model for atom (or atom-like) qubits in mismatched cavities, under the double-heralding entanglement procedure of Barrett and Kok (2005 Phys. Rev. A 71 060310). Compared to straightforward post-selection techniques our protocol offers a dramatic improvement in growing complex high-fidelity graph states.

DOI
10.1088/1367-2630/9/6/196

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Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect entanglement into an extended graph state formalism. The subsequent growth of the improper graph state can be guided, through a series of strategic decisions, in such a way as to bound the growth of the error and eventually yield a high-fidelity graph state. As an implementation of these techniques, we develop an analytic model for atom (or atom-like) qubits in mismatched cavities, under the double-heralding entanglement procedure of Barrett and Kok (2005 Phys. Rev. A 71 060310). Compared to straightforward post-selection techniques our protocol offers a dramatic improvement in growing complex high-fidelity graph states.
Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: Path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect entanglement into an extended graph state formalism. The subsequent growth of the improper graph state can be guided, through a series of strategic decisions, in such a way as to bound the growth of the error and eventually yield a high-fidelity graph state. As an implementation of these techniques, we develop an analytic model for atom (or atom-like) qubits in mismatched cavities, under the double-heralding entanglement procedure of Barrett and Kok [Phys. Rev. A 71, 060310 (2005)]. Compared to straightforward postselection techniques our protocol offers a dramatic improvement in growing complex high-fidelity graph states.
Graph states (or cluster states) are the entanglement resource that enables one-way quantum computing. They can be grown by projective measurements on the component qubits. Such measurements typically carry a significant failure probability. Moreover, they may generate imperfect entanglement. Here we describe strategies to adapt growth operations in order to cancel incurred errors. Nascent states that initially deviate from the ideal graph states evolve toward the desired high fidelity resource without impractical overheads. Our analysis extends the diagrammatic language of graph states to include characteristics such as tilted vertices, weighted edges, and partial fusion, which arise from experimental imperfections. The strategies we present are relevant to parity projection schemes such as optical path erasure with distributed matter qubits.
The cluster state, the highly entangled state that is the central resource for one-way quantum computing, can be efficiently generated in a variety of physical implementations via global nearest-neighbor interactions. In practice, a systematic phase error is expected in the entangling process, resulting in imperfect cluster states. We present a stochastic measurement technique to generate large perfect cluster states and other graph states with high probability from imperfect cluster states even when their initial entanglement is weak.
We propose a scheme to distribute graph states over quantum networks in the presence of noise in the channels and in the operations. The protocol can be implemented efficiently for large graph sates of arbitrary (complex) topology. We benchmark our scheme with two protocols where each connected component is prepared in a node belonging to the component and subsequently distributed via quantum repeaters to the remaining connected nodes. We show that the fidelity of the generated graphs can be written as the partition function of a classical Ising-type Hamiltonian. We give exact expressions of the fidelity of the linear cluster and results for its decay rate in random graphs with arbitrary (uncorrelated) degree distributions.
We present a scheme for rapidly entangling matter qubits in order to create graph states for one-way quantum computing. The qubits can be simple 3-level systems in separate cavities. Coupling involves only local fields and a static (unswitched) linear optics network with detectors that need not be photon number resolving. Fusion of graph state sections occurs with, in principle, zero probability of damaging the nascent graph state. We avoid the finite thresholds of other schemes by operating on two entangled pairs, so that each generates exactly one photon. We do not require the relatively slow single qubit local flips to be applied during the growth phase: growth of the graph state can then become a purely optical process. The scheme naturally generates graph states with vertices of high degree and so is easily able to construct minimal graph states, with consequent resource savings. The most efficient approach will be to create new graph state edges even as qubits elsewhere are measured, in a 'just in time' approach. An error analysis indicates that the scheme is robust against imperfections in the apparatus.
We present a scheme for rapidly entangling matter qubits in order to create graph states for one-way quantum computing. The qubits can be simple three-level systems in separate cavities. Coupling involves only local fields and a static (unswitched) linear optics network. Fusion of graph-state sections occurs with, in principle, zero probability of damaging the nascent graph state. We avoid the finite thresholds of other schemes by operating on two entangled pairs, so that each generates exactly one photon. We do not require the relatively slow single qubit local flips to be applied during the growth phase: growth of the graph state can then become a purely optical process. The scheme naturally generates graph states with vertices of high degree and so is easily able to construct minimal graph states, with consequent resource savings. The most efficient approach will be to create new graph-state edges even as qubits elsewhere are measured, in a 'just in time' approach. An error analysis indicates that the scheme is relatively robust against imperfections in the apparatus.