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arXiv:1811.10214

Optimized protocol to create repeater graph states for all-photonic quantum repeater

Ming Lai Chan

Published Nov 26, 2018• 2 citations
arXivHTMLPDF

Abstract

All-photonic quantum repeater is not yet commercially applicable due to difficulty in the generation of repeater graph states (RGS) and the probabilistic nature of Bell-state measurement. In recent years, several deterministic protocols have been proposed to generate RGS. However, they can only create bare RGS and a rate-distance analysis for the deterministic approach is currently missing. We present a deterministic generation scheme of encoded RGS and show that after optimization, the repeater using our scheme performs at least 4.9 times better than the traditional probabilistic generation scheme in terms of secret key rate, with a significant reduction in the total number photons by 2 orders of magnitude. The duration of our generation protocol is only half of the existing deterministic schemes. We also describe in detail an experimental method using cavity QED-enhanced resonance fluorescence and time-bin encoding to implement our protocol.

DOI
10.48550/arxiv.1811.10214

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All-photonic quantum repeater is not yet commercially applicable due to difficulty in the generation of repeater graph states (RGS) and the probabilistic nature of Bell-state measurement. In recent years, several deterministic protocols have been proposed to generate RGS. However, they can only create bare RGS and a rate-distance analysis for the deterministic approach is currently missing. We present a deterministic generation scheme of encoded RGS and show that after optimization, the repeater using our scheme performs at least 4.9 times better than the traditional probabilistic generation scheme in terms of secret key rate, with a significant reduction in the total number photons by 2 orders of magnitude. The duration of our generation protocol is only half of the existing deterministic schemes. We also describe in detail an experimental method using cavity QED-enhanced resonance fluorescence and time-bin encoding to implement our protocol.
All-photonic repeater scheme based on a repeater graph state (RGS) promises tolerance to photon losses as well as operational errors. An attractive promise of this scheme is that it offers a fast Bell pair generation rate, limited only by the RGS creation time. This is in stark contrast to the traditional quantum repeater with quantum memories, where the Bell pair generation time is limited by the round-trip wait time leading to poor Bell pair generation performance and quality due to the decoherence of quantum memories. Prior research has focused on lowering the cost of RGS generation and improving upon the probabilistic generation to a deterministic generation with required photon counts to be the same as the number of qubits in the RGS. The operations of creating and manipulating the RGS into an end-to-end Bell pair are complex and have not been fully figured out in detail. Here, we focus on improving the practicality of the RGS scheme in real-world implementation and address three open questions of the RGS scheme, namely; how do end nodes participate in the connection, what classical information needs to be exchanged and processed between nodes, and how to make RGS scheme work hand in hand with the traditional quantum repeaters with memories.
The all-photonic quantum repeater scheme, utilizing a type of graph state called the repeater graph state (RGS), promises resilience to photon losses and operational errors, offering a fast Bell pair generation rate limited only by the RGS creation time (rather than enforced round-trip waits). While existing research has predominantly focused on RGS generation and secret key sharing rate analysis, there is a need to extend investigations to encompass broader applications, such as distributed computation and teleportation, the main tasks envisioned for the Quantum Internet. Here we propose a new emitter-photonic qubit building block and an RGS protocol that addresses several key considerations: end node involvement in connection establishment, decoding of logical qubits within the RGS, and computing the Pauli frame corrections at each participating node to ensure the desired correct end-to-end Bell pair state. Our proposed building block significantly reduces the total number of emissive quantum memories required for end nodes and seamlessly integrates all-photonic and memory-based repeaters under the same communication protocol. We also present an algorithm for decoding logical measurement results, employing graphical reasoning based on graph state manipulation rules.
All-photonic quantum repeaters use multi-qubit photonic graph states, called repeater graph states (RGS), instead of matter-based quantum memories, for protection against predominantly loss errors. The RGS comprises tree-graph-encoded logical qubits for error correction at the repeaters and physical {\em link} qubits to create entanglement between neighboring repeaters. The two methods to generate the RGS are probabilistic stitching -- using linear optical Bell state measurements (fusion) -- of small entangled states prepared via multiplexed-probabilistic linear optical circuits fed with single photons, and a direct deterministic preparation using a small number of quantum-logic-capable solid-state emitters. The resource overhead due to fusions and the circuit depth of the quantum emitter system both increase with the size of the RGS. Therefore engineering a resource-efficient RGS is crucial. We propose a new RGS design, which achieves a higher entanglement rate for all-photonic quantum repeaters using fewer qubits than the previously known RGS would. We accomplish this by boosting the probability of entangling neighboring repeaters with tree-encoded link qubits. We also propose a new adaptive scheme to perform logical BSM on the link qubits for loss-only errors. The adaptive BSM outperforms the previous schemes for logical BSM on tree codes when the qubit loss probability is uniform. It reduces the number of optical modes required to perform logical BSM on link qubits to improve the entanglement rate further.
The all-photonic quantum repeater scheme based on repeater graph states (RGS) offers a promising approach for constructing quantum networks without relying on long-coherence-time quantum memories, which remain a significant technological challenge. Despite substantial progress in defining new schemes for generating RGSs, and in analyzing their performance for the task of secret key generation, the integration of all-photonic schemes with memory-equipped quantum repeaters remains underexplored. We propose an architecture that enables seamless interoperability between all-photonic and memory-based quantum repeaters through an emitter-photon qubit building block, significantly reducing the number of quantum memories required at end nodes from a multiplicative dependence on the trial rate and number of RGS arms to an additive scaling. The core idea of our architecture is to abstract the all-photonic sections of the network as link-level connections between memory-equipped nodes, enabling integration into existing network-level protocols. Additionally, we outline the content and semantics of the messages necessary for a communication protocol based on graph state manipulation rules for computing Pauli frame corrections for obtaining the correct Bell pair. Our approach also provides a simplified method for calculating state fidelity directly from graph state properties.
By encoding logical qubits into specific types of photonic graph states, one can realize quantum repeaters that enable fast entanglement distribution rates approaching classical communication. However, the generation of these photonic graph states requires a formidable resource overhead using traditional approaches based on linear optics. Overcoming this challenge, a number of new schemes have been proposed that employ quantum emitters to deterministically generate photonic graph states. Although these schemes have the potential to significantly reduce the resource cost, a systematic comparison of the repeater performance among different encodings and different generation schemes is lacking. Here, we quantitatively analyze the performance of quantum repeaters based on two different graph states, i.e. the tree graph states and the repeater graph states. For both states, we compare the performance between two generation schemes, one based on a single quantum emitter coupled to ancillary matter qubits, and one based on a single quantum emitter coupled to a delayed feedback. We identify the numerically optimal scheme at different system parameters. Our analysis provides a clear guideline on the selection of the generation scheme for graph-state-based quantum repeaters, and lays out the parameter requirements for future experimental realizations of different schemes.
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.