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arXiv:1012.1778 · Physical Review A

Generation of graph-state streams

Daniel Ballester, Jaeyoon Cho, M. S. Kim

Published Jan 10, 2011• 6 citations
arXivHTMLPDF

Abstract

We propose a protocol to generate a stream of mobile qubits in a graph state through a single stationary parent qubit and discuss two types of its physical implementation, namely, the generation of photonic graph states through an atomlike qubit and the generation of flying atoms through a cavity-mode photonic qubit. The generated graph states fall into an important class that can hugely reduce the resource requirement of fault-tolerant linear optics quantum computation, which was previously known to be far from realistic. In regard to the flying atoms, we also propose a heralded generation scheme, which allows for high-fidelity graph states even under the photon loss.

DOI
10.1103/physreva.83.010302

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We propose a protocol to generate a stream of mobile qubits in a graph state through a single stationary parent qubit and discuss two types of its physical implementation, namely, the generation of photonic graph states through an atomlike qubit and the generation of flying atoms through a cavity-mode photonic qubit. The generated graph states fall into an important class that can hugely reduce the resource requirement of fault-tolerant linear optics quantum computation, which was previously known to be far from realistic. In regard to the flying atoms, we also propose a heralded generation scheme, which allows for high-fidelity graph states even under the photon loss.
Abstract Quantum emitter-based schemes for the generation of photonic graph states offer a promising, resource-efficient methodology for realizing distributed quantum computation and communication protocols on near-term hardware. We present a heralded scheme for making photonic graph states that is compatible with the typically poor photon collection from state-of-the-art coherent quantum emitters. We demonstrate that the construction time for large graph states can be polynomial in the photon collection efficiency, as compared to the exponential scaling of current emitter-based schemes, which assume deterministic photon collection. The additional overhead here consists of an extra spin qubit plus one additional spin-spin entangling gate per photon added to the graph. While the proposed scheme requires both non-demolition measurement and efficient storage of photons in order to generate graph states for arbitrary applications, we show that many useful tasks, including measurement-based quantum computation, can be implemented without these requirements. As a use case of our scheme, we construct a protocol for secure two-party computation that can be implemented efficiently on current hardware. Estimates of the fidelity to produce graph states used in the computation are given assuming current and near-term fidelities for highly coherent quantum emitters.
Highly entangled multiphoton graph states are a crucial resource in photonic quantum computation and communication. Yet, the lack of photon-photon interactions makes the construction of such graph states especially challenging. Typically, these states are produced through probabilistic single-photon sources and linear-optics entangling operations that require indistinguishable photons. The resulting inefficiency of these methods necessitates a large overhead in the number of sources and operations, creating a major bottleneck in the photonic approach. Here, we show how harnessing single-atom-based photonic operations can enable deterministic generation of photonic graph states, while also lifting the requirement for photon indistinguishability. To this end, we introduce a multigate quantum node comprising a single atom in a W -type level scheme coupled to an optical resonator. This configuration provides a versatile toolbox for generating graph states, allowing the operation of both the controlled- Z and photon-atom gates, as well as the deterministic generation of single photons. Furthermore, the ability to deterministically entangle photonic qubits enables the expansion of the generated state by stitching together graph states produced by different nodes. We investigate the implementation of this gate-based approach using 87 Rb atoms and evaluate its performance through numerical simulations.
Multiqubit entangled photonic graph states are an important ingredient for all-photonic quantum computing, repeaters, and networking. Preparing them using probabilistic stitching of single photons using linear optics presents a formidable resource challenge due to multiplexing needs. Quantum emitters provide a viable solution to prepare photonic graph states, as they enable deterministic production of photons entangled with emitter qubits and deterministic two-qubit interactions among emitters. A handful of emitters often suffice to generate useful-size graph states that would otherwise require millions of emitters used as single photon sources, using the linear-optics method. Photon loss, however, impedes the emitter method due to a large circuit depth and hence loss accrual on the photons of the graph state produced, given the typically large number of slow two-qubit controlled-not (cnot) gates between emitters. We propose an algorithm that can trade the number of emitters with the graph-state depth, while minimizing the number of emitter cnot gates. We apply our algorithm to generate a repeater graph state (RGS) for an alternative all-photonic repeater protocol, which achieves a far superior rate-distance trade-off compared to using the least number of emitters needed to generate the RGS. Yet it needs five orders of magnitude fewer emitters than the multiplexed linear-optics method---with each emitter used as a photon source---to achieve a desired rate-distance performance.
Abstract Scalable graph states are essential for measurement-based quantum computation and many entanglement-assisted applications in quantum technologies. Generation of these multipartite entangled states requires a controllable and efficient quantum device with delicate design of generation protocol. Here we propose to prepare high-fidelity and scalable graph states in one and two dimensions, which can be tailored in an atom-nanophotonic cavity via state carving technique. We propose a systematic protocol to carve out unwanted state components, which facilitates scalable graph states generations via adiabatic transport of a definite number of atoms in optical tweezers. An analysis of state fidelity is also presented, and the state preparation probability can be optimized via multiqubit state carvings and sequential single-photon probes. Our results showcase the capability of an atom-nanophotonic interface for creating graph states and pave the way toward novel problem-specific applications using scalable high-dimensional graph states with stationary qubits.
Graph states constitute the main building block for quantum computing with photons. Quantum emitters with a hosted spin can deterministically generate photonic graph states, strongly lowering the overhead of multiplexing highly probabilistic linear-optics graph state generation. However, they generally suffer from various noise sources, resulting in reduced fidelities of the produced states. To mitigate this issue, we develop purification schemes for entangled photonic states. We first develop purification schemes to purify arbitrary photonic GHZ and other CSS states, which we generalize to all photonic graph states and stabilizer states. The proposed purification schemes have a high success probability of up to 1/21/21/2 and require only linear optics and photon detectors. We optimize cascaded purification schemes for various graph states, taking into account phenomenological Pauli errors or physical noise in time-bin-encoded graph state generation with quantum emitters.
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.