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arXiv:1904.08605 · Physical Review A

Quantum link bootstrapping using a RuleSet-based communication protocol

Takaaki Matsuo, Clément Durand, Rodney Van Meter

Published Nov 15, 2019• 53 citations
arXivHTMLPDF

Abstract

Establishing end-to-end quantum connections requires quantified link characteristics, and operations need to coordinate decision making between nodes across a network. We introduce the RuleSet-based communication protocol for supporting quantum operations over distant nodes to minimize classical packet transmissions for guaranteeing synchronicity. RuleSets are distributed to nodes along a path at connection setup time, and hold lists of operations that need to be performed in real time. We simulate the RuleSet-based quantum link bootstrapping protocol, which consists of recurrent purifications and link-level tomography, to quantify the quantum link fidelity and its throughput. Our Markov-chain Monte Carlo simulation includes various error sources, such as the memory error, gate error, and channel error, modeled on currently available hardware. We found that when two quantum nodes, each with 100 memory qubits capable of emitting photons ideally to the optical fiber, are physically connected with a 10-km MeetInTheMiddle link, the Recurrent Single selection--Single error purification (RSs-Sp) protocol is capable of bringing up the fidelity from an average input ${F}_{r}=0.675$ to around ${F}_{r}=0.865$ with a generation rate of 1106 Bell pairs per second, as determined by simulated tomography. The system gets noisier with longer channels, in which case errors may develop faster than the purification gain. In such a situation, a stronger purification method, such as the double selection-based purification, shows an advantage for improving the fidelity. The knowledge acquired from bootstrapping can later be distributed to nodes within the same network, and used for other purposes such as route selection.

DOI
10.1103/physreva.100.052320

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Establishing end-to-end quantum connections requires quantified link characteristics, and operations need to coordinate decision making between nodes across a network. We introduce the RuleSet-based communication protocol for supporting quantum operations over distant nodes to minimize classical packet transmissions for guaranteeing synchronicity. RuleSets are distributed to nodes along a path at connection setup time, and hold lists of operations that need to be performed in real time. We simulate the RuleSet-based quantum link bootstrapping protocol, which consists of recurrent purifications and link-level tomography, to quantify the quantum link fidelity and its throughput. Our Markov-chain Monte Carlo simulation includes various error sources, such as the memory error, gate error, and channel error, modeled on currently available hardware. We found that when two quantum nodes, each with 100 memory qubits capable of emitting photons ideally to the optical fiber, are physically connected with a 10-km MeetInTheMiddle link, the Recurrent Single selection--Single error purification (RSs-Sp) protocol is capable of bringing up the fidelity from an average input Fr=0.675{F}_{r}=0.675Fr​=0.675 to around Fr=0.865{F}_{r}=0.865Fr​=0.865 with a generation rate of 1106 Bell pairs per second, as determined by simulated tomography. The system gets noisier with longer channels, in which case errors may develop faster than the purification gain. In such a situation, a stronger purification method, such as the double selection-based purification, shows an advantage for improving the fidelity. The knowledge acquired from bootstrapping can later be distributed to nodes within the same network, and used for other purposes such as route selection.
Similar to the classical Internet, the quantum Internet will require knowledge regarding link qualities used for purposes such as optimal route selection. This is commonly accomplished by performing link-level tomography with or without purification -- a.k.a. quantum link bootstrapping. Meanwhile, the gate selection and the resource (Bell pair) selection for a task must be coordinated beforehand. This thesis introduces the RuleSet-based communication protocol aimed for supporting the autonomous coordination of quantum operations among distant nodes, with minimal classical packet transmission. This thesis also discusses the RuleSet-based quantum link bootstrapping protocol, which consists of recurrent purifications and link-level tomography, evaluated over a Markov-Chain Monte-Carlo simulation with noisy systems modeled on real world quality hardware. Given a 10km MeetInTheMiddle based two-node system, each with 100 memory qubits ideally connected to the optical fiber, the Recurrent Single selection - Single error purification (RSs-Sp) protocol is capable of improving the fidelity from an average input Fr=0.675F_{r}=0.675Fr​=0.675 to approximately Fr=0.865F_{r}=0.865Fr​=0.865. The system gets noisier with longer channels, in which case errors may develop faster than the purification gain. For a noisier system with a longer channel length, the double selection-based purification shows an advantage for improving the fidelity.
Quantum networking needs knowledge of the quality of a connection in order for quantum error correction to work. We are designing a classical network protocol to support quantum state analysis procedures such as tomography. This paper sketches the protocol as well as summarizes the fundamental scheme of two-node quantum communication using photons. Our protocol is a master-slave protocol. We show that we need around 2000-3000 (42000-60000) Bell pairs for tomography to achieve F > 0.99 (0.999). These stringent performance requirements result in long bootstrap times for individual network links, and suggest that tomography is inappropriate during the establishment of individual connections across a network.
Many quantum-network applications require end-to-end Bell pairs whose fidelity exceeds a request-specific threshold, but existing entanglement routing algorithms either optimize only throughput without regard for fidelity or enforce fidelity guarantees using centralized controllers with global link-state knowledge. We present Q-GUARD, an online entanglement routing algorithm that enforces per-request fidelity thresholds within a distributed protocol model in which nodes exchange link-state information only with their kkk-hop neighbors. After link outcomes are realized in each slot, Q-GUARD builds per-link purification cost tables from realized Bell pairs, allocates per-hop fidelity targets using a Werner-state equal-split rule, and selects between candidate path segments using a segment-local expected-goodput (EXG) metric that jointly accounts for swap success, purification overhead, and resource availability. We also introduce Q-GUARD-WS, an extension that exploits per-link hardware quality estimates to allocate purification effort non-uniformly across hops. On synthetic 100-node topologies with heterogeneous link fidelity and stochastic BBPSSW purification, Q-GUARD raises the qualified success rate from under 20\% to over 85\% on 4-hop paths and nearly doubles the qualified service radius in Euclidean distance relative to throughput-only and naive-purification baselines, while Q-GUARD-WS provides additional throughput gains under high hardware heterogeneity.
Entangled quantum communication is advancing rapidly, with laboratory and metropolitan testbeds under development, but to date there is no unifying Quantum Internet architecture. We propose a Quantum Internet architecture centered around the Quantum Recursive Network Architecture (QRNA), using RuleSet-based connections established using a two-pass connection setup. Scalability and internetworking (for both technological and administrative boundaries) are achieved using recursion in naming and connection control. In the near term, this architecture will support end-to-end, two-party entanglement on minimal hardware, and it will extend smoothly to multiparty entanglement and the use of quantum error correction on advanced hardware in the future. For a network internal gateway protocol, we recommend (but do not require) qDijkstra with seconds per Bell pair as link cost for routing; the external gateway protocol is designed to build recursively. The strength of our architecture is shown by assessing extensibility and demonstrating how robust protocol operation can be confirmed using the RuleSet paradigm.
Entanglement-based networks (EBNs) enable general-purpose quantum communication by combining entanglement and its swapping in a sequence that addresses the challenges of achieving long-distance communication with high fidelity associated with quantum technologies. In this context, entanglement distribution refers to the process by which two nodes in a quantum network share an entangled state, serving as a fundamental resource for communication. In this paper, we study the performance of entanglement distribution mechanisms over a physical topology comprising end nodes and quantum switches, which are crucial for constructing large-scale links. To this end, we implemented a switch-based topology in NetSquid and conducted a series of simulation experiments to gain insight into practical and realistic quantum network engineering challenges. These challenges include, on the one hand, aspects related to quantum technology, such as memory technology, gate durations, and noise; and, on the other hand, factors associated with the distribution process, such as the number of switches, distances, purification, and error correction. All these factors significantly impact the end-to-end fidelity across a path, which supports communication between two quantum nodes. We use these experiments to derive some guidelines towards the design and configuration of future EBNs.
This paper studies reliable teleportation of quantum bits (called qubits) in a quantum data network with multiple sources (S) and destinations (D) as well as repeaters. To teleport qubits for a SD pair reliably, not only an entanglement path for the SD pair, but also appropriate purification of the links along the path is required to ensure that the end-to-end (E2E) fidelity of the established entanglement connections is high enough.This is the first work on quantifying the E2E fidelity, and also using this E2E fidelity to determine critical links to achieve the most resource efficient purification. A novel approach called E2E Fidelity aware Routing and Purification (EFiRAP) is proposed to maximize network throughput, i.e., the number of entanglement connections among multiple SD pairs, with each connection having an E2E fidelity above a given required threshold. EFiRAP accomplishes this goal by first preparing multiple candidate entanglement paths and determining optimal purification schemes, and then selecting the final set of entanglement paths that can maximize network throughput under the given quantum resource constraints. Existing works only ensured the fidelity of individual links, rather than the E2E fidelity is above a given threshold. Extensive simulations show that the proposed EFiRAP can enhance network throughput by about 50% when compared with the state-of-the-art approach.