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arXiv:quant-ph/0504111 · Physical Review A

Comment on “Efficient high-fidelity quantum computation using matter qubits and linear optics”

Simon C. Benjamin

Published Nov 30, 2005• 36 citations
arXivHTMLPDF

Abstract

Recently Barrett and Kok proposed an elegant method for entangling separated matter qubits. They outlined a strategy for using their entangling operation (EO) to build graph states, the resource for one-way quantum computing. Here I argue that their strategy considerably underrates the power and utility of their EO. By viewing their EO as a graph fusion event, one perceives that each successful event introduces an ideal redundant graph edge, which growth strategies should exploit. For example, if each EO succeeds with probability $p\ensuremath{\gtrsim}0.4$ then a highly connected graph can be formed with an overhead of only about ten EO attempts per graph edge. The Barrett and Kok (BK) scheme then becomes competitive with the more elaborate entanglement procedures designed to permit $p$ to approach unity [Phys. Rev. Lett. 95, 030505 (2005)].

DOI
10.1103/physreva.72.056302

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Recently Barrett and Kok proposed an elegant method for entangling separated matter qubits. They outlined a strategy for using their entangling operation (EO) to build graph states, the resource for one-way quantum computing. Here I argue that their strategy considerably underrates the power and utility of their EO. By viewing their EO as a graph fusion event, one perceives that each successful event introduces an ideal redundant graph edge, which growth strategies should exploit. For example, if each EO succeeds with probability p\ensuremath≳0.4p\ensuremath{\gtrsim}0.4p\ensuremath≳0.4 then a highly connected graph can be formed with an overhead of only about ten EO attempts per graph edge. The Barrett and Kok (BK) scheme then becomes competitive with the more elaborate entanglement procedures designed to permit ppp to approach unity [Phys. Rev. Lett. 95, 030505 (2005)].
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.
Measurement-based quantum computing relies on the generation of large entangled cluster states that act as a universal resource on which logical circuits can be imprinted and executed through local measurements. A number of strategies for constructing sufficiently large photonic cluster states propose fusing many smaller resource states generated by a series of quantum emitters. However, the fusion process is inherently probabilistic with a 50% success probability in standard guise. A recent proposal has shown that, in the limit of low loss, the probability of achieving successful fusion may be boosted to near unity by redundantly encoding the vertices of linear graph states using Greenberger-Horne-Zeilinger states [Quantum 7, 992 (2023)]. Here we present a protocol for deterministically generating redundantly encoded photonic resource states using single quantum emitters, and study the impact of protocol errors and photonic losses on the generated resource states and type-II photonic fusion. Our work provides a route for efficiently constructing complex entangled photonic qubit states for photonic quantum computing and quantum repeaters.
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.
We propose a practical, scalable, and efficient scheme for quantum computation using spatially separated matter qubits and single-photon interference effects. The qubit systems can be nitrogen-vacancy centers in diamond, Pauli-blockade quantum dots with an excess electron, or trapped ions with optical transitions, which are each placed in a cavity and subsequently entangled using a double-heralded single-photon detection scheme. The fidelity of the resulting entanglement is extremely robust against the most important errors such as detector loss, spontaneous emission, and mismatch of cavity parameters. We demonstrate how this entangling operation can be used to efficiently generate cluster states of many qubits, which, together with single-qubit operations and readout, can be used to implement universal quantum computation. Existing experimental parameters indicate that high-fidelity clusters can be generated with a moderate constant overhead.