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arXiv:1908.10758

Simulation of a Dynamic, RuleSet-based Quantum Network

Takaaki Matsuo

Published Aug 26, 2019• 15 citations
arXivHTMLPDF

Abstract

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 $F_{r}=0.675$ to approximately $F_{r}=0.865$. 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.

DOI
10.48550/arxiv.1908.10758

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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.
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.
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.
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.
Efficient entanglement distribution is a cornerstone of the Quantum Internet. However, physical link parameters such as photon loss, memory coherence time, and gate error rates fluctuate dynamically, rendering static purification strategies suboptimal. In this paper, we propose an Adaptive Purification Controller (APC) that automatically optimizes the entanglement distillation sequence to maximize the goodput, i.e., the rate of delivered pairs meeting a strict fidelity threshold. By treating protocol selection as a resource allocation problem, the APC dynamically switches between purification depths and protocols (BBPSSW vs. DEJMPS) to navigate the trade-off between generation rate and state quality. Using a dynamic programming planner with Pareto pruning, simulation results show that our approach mitigates the "fidelity cliffs" inherent in static protocols and reduces resource wastage in high-noise regimes. Furthermore, we extend the controller to heterogeneous scenarios, and evaluate it for both multipartite GHZ state generation and continuous-variable systems using effective noiseless linear amplification models. We benchmark its computational overhead, showing decision latencies in the millisecond range per link in our implementation.
Entanglement purification protocols, designed to improve the fidelity of Bell states over quantum networks for inter-node communications, have attracted significant attention over the last few decades. These protocols have great potential to resolve a core challenge in quantum networking of generating high-fidelity Bell states. However, previous studies focused on the theoretical discussion with limited consideration of realistic errors. Studies of dynamically selecting the right purification protocol under various realistic errors that occur in practice have yet to be performed. In this work, we study the performance of various purification protocols under realistic errors by conducting density matrix simulations over a large suite of error models. Based on our findings of how specific error channels affect the performance of purification protocols, we propose a module that can be embedded in the quantum network. This module determines and selects the appropriate purification protocol, considering not only expected specifications from the network layer but also the capabilities of the physical layer. Finally, the performance of our proposed module is verified using two benchmark categories. Compared with the default approach and exhaustive search approach, we show a success rate approaching 90% in identifying the optimal purification protocol for our target applications.
A scalable and robust infrastructure for arbitrary quantum communication and distributed quantum computation will realize enhanced as well as new applications that are beyond the reach of classical communication networks. Quantum internetworking, which achieves large-scale quantum networks by building recursively on smaller quantum networks, is a promising approach. However, there are two big difficulties: decomposing end-to-end quantum communication, which is actually a complex distributed computing spanning classical and quantum computing, into processing for each subnetwork; and supporting future network functionality sustainably. In this work, we propose design principles for a quantum internetworking protocol based on the quantum recursive network architecture (QRNA) utilizing the RuleSet-based approach. We design two distinct approaches for recursion in quantum networks, namely link- and node-recursion. We demonstrate how end-to-end Bell pairs are generated over our internetworking systems, and evaluate the scaling of inputs to the distributed processing, via implementation on the Quantum Internet Simulation Package (QuISP). Our subnetwork recursion demonstrates the long-term future scalability as the size of and demands made on the Quantum Internet.