We present a quantum circuit that is designed to do both purification and estimation of fidelity simultaneously, showing that the number of Bell pairs necessary to boot a quantum link can be significantly reduced. Despite the tremendous effort put into establishing a method for conducting efficient state tomography, it remains a hard problem to estimate the fidelity of a given quantum state. It is also a resource-consuming process to perform entanglement purification at the bootstrapping of a quantum network. This research contains an idea that combines fidelity estimation with purification, thereby reducing the consumption of Bell pairs at the bootstrapping of a quantum network. The research also produces numerical estimates for the number of Bell pairs actually needed to guarantee a certain threshold fidelity$F$under certain assumptions.
We present a quantum circuit that is designed to do both purification and estimation of fidelity simultaneously, showing that the number of Bell pairs necessary to boot a quantum link can be significantly reduced. Despite the tremendous effort put into establishing a method for conducting efficient state tomography, it remains a hard problem to estimate the fidelity of a given quantum state. It is also a resource-consuming process to perform entanglement purification at the bootstrapping of a quantum network. This research contains an idea that combines fidelity estimation with purification, thereby reducing the consumption of Bell pairs at the bootstrapping of a quantum network. The research also produces numerical estimates for the number of Bell pairs actually needed to guarantee a certain threshold fidelityFunder certain assumptions.
We present a method to conduct both quantum state reconstruction and entanglement purification simultaneously that is advantageous in several respects over previous work in this direction, showing that the number of Bell pairs necessary to boot a quantum network can be significantly reduced compared to an existing method. The existing method requires at least 105 Bell pairs for the state reconstruction phase to estimate that the state is of fidelity 0.99 within the error range of 10−2, whereas our approach only requires around 2,841 to be certain with 99.7% of confidence that the estimated fidelity lies within [0.99−0.01,0.99+0.01]. In addition, in our approach we can start with a lower fidelity Bell pair and purify it multiple times, estimating at the same time the resultant fidelity with guarantee of 99.7% that the fidelity estimate lies within a certain range. Moreover, the existing method cannot correct both bit-flip and phase-flip errors at the same time and can only correct one of these, whereas our approach can correct both bit-flip and phase-flip errors simultaneously. This research produces numerical estimates for the number of Bell pairs actually needed to guarantee a certain threshold fidelity F. The research can support the functioning real-world quantum networking by providing the information of the time needed for the bootstrapping of a quantum network to finish.
Quantum communication technology provides an absolute security guarantee for information transmitted between quantum applications. To establish practical quantum networks, providing entangled pairs of stable quality, suitable for varying distances, is crucial. However, due to the inherent losses and imperfections of the operations during the entanglement distribution process, the fidelity of end-to-end entangled pairs will be greatly reduced. Consequently, establishing fidelity-guaranteed entangled pairs will be challenging. In this work, we introduce an entanglement distribution method that ensures the fidelity requirements of applications across different distances, while maintaining high efficiency. The method first decomposes the end-to-end fidelity requirements to target fidelity for purification at each link, based on the worst-case consumption. Then it performs multiple-round symmetrical entanglement purification based on the backup scheme to purify each entangled pair to the target value. The experimental results indicate that the scheme has acceptable performance in resource consumption and great feasibility while ensuring high efficiency.
Entanglement routing establishes remote entanglement connection between two arbitrary nodes, which is one of the most important functions in quantum networks. The existing routing mechanisms mainly improve the robustness and throughput facing the failure of entanglement generations, which, however, rarely include the considerations on the most important metric to evaluate the quality of connection, entanglement fidelity. To solve this problem, we propose purification-enabled entanglement routing designs to provide fidelity guarantee for multiple Source-Destination (SD) pairs in quantum networks. In our proposal, we first consider the single S-D pair scenario and design an iterative routing algorithm, Q-PATH, to find the optimal purification decisions along the routing path with minimum entangled pair cost. Further, a low-complexity routing algorithm using an extended Dijkstra algorithm, Q-LEAP, is designed to reduce the computational complexity by using a simple but effective purification decision method. Then we consider the common scenario with multiple S-D pairs and design a greedy-based algorithm considering resource allocation and rerouting process for multiple routing requests. To verify the effectiveness and superiority of the proposed algorithms, extensive simulations are conducted, and the simulation results show that the proposed algorithms not only can provide fidelity-guarantee routing solutions, but also has superior performance in terms of throughput, fidelity of end-to-end entanglement connection, and resource utilization ratio, compared with the existing routing scheme.
Quantum networks, endowed with their distinct quantum properties, are poised to emerge as indispensable platforms for the implementation of quantum information technology applications in the near future. Within the realm of quantum networks, the transmission of remote quantum information presents a pivotal and intricate challenge, commonly referred to as the entanglement routing problem. While previous efforts have delved into the intricacies of entanglement routing, there has been a notable oversight concerning the crucial parameter of entanglement fidelity. Hence, this paper introduces a novel Purification-enabled Entanglement Routing Algorithm (PERA). Initially, PERA utilizes the network throughput as the routing metric and ensures fidelity guarantees on all nodes in the link through a hop-by-hop purification process. Subsequently, acknowledging the probabilistic nature of entanglement purification, a strategy involving multiple attempts at purification is employed. Finally, a comprehensive utility function is deployed to address the path selection problem for multiple source–destination pairs. Numerical simulations confirm that PERA establishes entanglement connections with outstanding fidelity guarantees. Concurrently, PERA outperforms the baseline algorithm in terms of network throughput and resource utilization.
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 k-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.
The core function of quantum networks is to establish high-fidelity quantum entanglement for long-distance communication. However, the main challenge is to efficiently allocate resources under limited conditions, maximize throughput, satisfy end-to-end (E2E) fidelity requirements, and prevent quantum decoherence caused by inefficient routing algorithms. Current research focuses on optimizing either throughput or fidelity, with a lack of approaches that optimize both simultaneously; furthermore, existing algorithms suffer from high computational complexity. To tackle these challenges, this study proposes a Satisfying Fidelity Threshold Routing and Adaptive Purification Strategy (SFTRAP). SFTRAP maximizes throughput for each request by selecting multiple paths and dynamically choosing links for entanglement purification based on the current state of link resources, thus minimizing throughput loss while satisfying fidelity threshold. The strategy also adaptively adjusts the number of purification rounds according to the fidelity threshold, thereby optimizing the time required for deep purification and enhancing algorithmic efficiency. For multi-request scenarios, SFTRAP employs a priority sorting mechanism that takes into account both path cost and path freedom, which refines request scheduling and path selection to create more efficient request combinations, thus further boosting the overall network throughput. Simulation results indicate that SFTRAP surpasses state-of-the-art methods in terms of both throughput and algorithmic efficiency, highlighting its potential for optimizing resources in quantum networks.