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IEEE Journal on Selected Areas in Communications

A Probability-Based Optimization Approach for Entanglement Distribution and Source Position in Quantum Networks

Giovanni Iacovelli, Francesco Vista, Nicola Cordeschi, Luigi Alfredo Grieco

Published Mar 21, 2024• 8 citations
Publisher

Abstract

Quantum Internet (QI) is a system of interconnected quantum computers able to exchange information encoded in the so called quantum bits (qubits). Differently from the classical counterpart, qubits benefit from a manifold properties guaranteed by quantum mechanics, such as superposition and entanglement. Despite the fact that quantum networks bring significant advantages, several phenomena can negatively impact the overall system, potentially hindering communication. In order to evaluate the network performance, a comprehensive probability expression is derived in this work to ultimately determine how many qubits are expected to be successfully received by nodes. On this basis, a Mixed-Integer Non-Linear Programming (MINLP) problem is formulated to fairly maximize the qubits exchanged between node pairs and jointly optimize (i) the position of the quantum source, and (ii) the entanglement distribution plan. To cope with the non-convexity of the problem, an iterative optimization algorithm, leveraging Block Coordinate Descendent (BCD) and Successive Convex Approximation (SCA) techniques, is proposed. A thorough simulation campaign is conducted to corroborate the theoretical findings. Numerical results demonstrates, under different parameter setups, that the proposed algorithm provides superior performance with respect to a baseline approach.

DOI
10.1109/jsac.2024.3380084

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Quantum Internet (QI) is a system of interconnected quantum computers able to exchange information encoded in the so called quantum bits (qubits). Differently from the classical counterpart, qubits benefit from a manifold properties guaranteed by quantum mechanics, such as superposition and entanglement. Despite the fact that quantum networks bring significant advantages, several phenomena can negatively impact the overall system, potentially hindering communication. In order to evaluate the network performance, a comprehensive probability expression is derived in this work to ultimately determine how many qubits are expected to be successfully received by nodes. On this basis, a Mixed-Integer Non-Linear Programming (MINLP) problem is formulated to fairly maximize the qubits exchanged between node pairs and jointly optimize (i) the position of the quantum source, and (ii) the entanglement distribution plan. To cope with the non-convexity of the problem, an iterative optimization algorithm, leveraging Block Coordinate Descendent (BCD) and Successive Convex Approximation (SCA) techniques, is proposed. A thorough simulation campaign is conducted to corroborate the theoretical findings. Numerical results demonstrates, under different parameter setups, that the proposed algorithm provides superior performance with respect to a baseline approach.
Quantum communication networks are emerging as a promising technology that could constitute a key building block in future communication networks in the 6G era and beyond. These networks have an inherent feature of parallelism that allows them to boost the capacity and enhance the security of communication systems. Recent advances led to the deployment of small- and large-scale quantum communication networks with real quantum hardware. In quantum networks, entanglement is a key resource that allows for data transmission between different nodes. However, to reap the benefits of entanglement and enable efficient quantum communication, the number of generated entangled pairs must be optimized. Indeed, if the entanglement generation rates are not optimized, then some of these valuable resources will be discarded and lost. In this paper, the problem of optimizing the entanglement generation rates and their distribution over a quantum memory is studied. In particular, a quantum network in which users have heterogeneous distances and applications is considered. This problem is posed as a mixed integer nonlinear programming optimization problem whose goal is to efficiently utilize the available quantum memory by distributing the quantum entangled pairs in a way that maximizes the user satisfaction. An interior point optimization method is used to solve the optimization problem and extensive simulations are conducted to evaluate the effectiveness of the proposed system. Simulation results show the key design considerations for efficient quantum networks, and the effect of different network parameters on the network performance.
Quantum networks are envisioned to enable reliable distribution and manipulation of quantum information across distances, forming the foundation of a future quantum internet. The fair and efficient allocation of communication resources in such networks has been addressed through the quantum network utility maximization (QNUM) framework, which optimizes network utility under the assumption of predetermined routes for competing user demands. In this work, we relax this assumption and aim to identify optimal routes that correspond to the maximum achievable network utility. Specifically, we formulate the single-path utility-based entanglement routing problem as a Mixed-Integer Convex Program (MICP). The formulation is exact when negativity is chosen as the entanglement measure for utility quantification or the network supports sufficiently high entanglement generation rates across demands. For other entanglement measures considered, the formulation approximates the problem with over 99.99% accuracy on evaluated real-world examples. To improve computational tractability, we propose a randomized rounding-based heuristic and an upper bound via the relaxation of the MICP. Furthermore, based on min-congestion routing, we introduce an alternative randomized heuristic and upper bound. This heuristic is computationally faster, while both the heuristic and the upper bound often outperform their counterparts on considered real-world networks. Our work provides the framework for extending classical flow-based and quality of service-aware routing concepts to quantum networks.
Quantum networks are envisioned to enable reliable distribution and manipulation of quantum information across distances, forming the foundation of a future quantum internet. The fair and efficient allocation of communication resources in such networks has been addressed through the quantum network utility maximization (QNUM) framework, which optimizes network utility under the assumption of predetermined routes for competing user demands. In this work, we relax this assumption and aim to identify optimal routes that correspond to the maximum achievable network utility. Specifically, we formulate the single-path utility-based entanglement routing problem as a Mixed-Integer Convex Program (MICP). The formulation is exact when negativity is chosen as the entanglement measure for utility quantification or the network supports sufficiently high entanglement generation rates across demands. For other entanglement measures considered, the formulation approximates the problem with over 99.99 % accuracy on evaluated real-world examples. To improve computational tractability, we propose a randomized rounding-based heuristic and an upper bound via the relaxation of the MICP. Furthermore, based on min-congestion routing, we introduce an alternative randomized heuristic and upper bound. This heuristic is computationally faster, while both the heuristic and the upper bound often outperform their counterparts on considered real-world networks. Our work provides the framework for extending classical flow-based and quality of service-aware routing concepts to quantum networks.
Quantum nodes exchange qubits to achieve largescale quantum computing applications in a quantum network (QN). However, due to environmental influences, entangled links used for data transmission would decohere over time. Besides, the scarcity of quantum memory in each quantum node necessitates frequent communication between nodes, leading to significant variations in the traffic matrix. Thus, providing real-time services in QNs becomes particularly important. To this end, this paper presents a new optimization problem and proposes a novel online algorithm, which combines the game-theoretic analysis results with the linear programming (LP) by the primal-dual technique. Finally, the simulation results demonstrate that the proposed algorithm outperforms the other baselines by up to 90 %.
Quantum network communication is challenging, as the No-Cloning theorem in quantum regime makes many classical techniques inapplicable. For long-distance communication, the only viable approach is teleportation of quantum states, which requires a prior distribution of entangled pairs (EPs) of qubits. Establishment of EPs across remote nodes can incur significant latency due to the low probability of success of the underlying physical processes. To reduce EP generation latency, prior works have looked at selection of efficient entanglement-routing paths and simultaneous use of multiple such paths for EP generation.In this paper, we propose and investigate a complementary technique to reduce EP generation latency—to pre-distribute EPs over certain (pre-determined) pairs of network nodes; these pre-distributed EPs can then be used to generate EPs for the requested pairs, when needed, with lower generation latency. For such a pre-distribution approach to be most effective, we need to address an optimization problem of selection of node-pairs where the EPs should be pre-distributed to minimize the generation latency of expected EP requests, under a given cost constraint. In this paper, we appropriately formulate the above optimization problem and design two efficient algorithms, one of which is a greedy approach based on an approximation algorithm for a special case. Via extensive evaluations over the NetSquid simulator [1], we demonstrate the effectiveness of our approach and developed techniques; we show that our developed algorithms outperform a naive approach by up to an order of magnitude.
Quantum networks are designed to transmit quantum bits (qubits) among quantum devices to enable new network resources for the applications. Entanglement distribution and entanglement swapping are fundamental procedures that are required in several network operations. However, they are probabilistic operations, which can lead to severe network performance degradation. This article investigates the engineering problem of resource allocation in quantum networks, considering factors like entanglement distribution probability, quantum memory characteristics, and fidelity. We model this as an optimization model to obtain an optimal solution. In particular, we formulate an integer linear programming (ILP) and develop a heuristic algorithm, aiming to minimize the number of required entangled qubit pairs (Bell pairs or EPR pairs) in any adjacent pair in the quantum network. Extensive simulations are performed to compare the performance of proposed ILP and heuristic. In all the cases, the heuristic produces a comparable solution to the optimal one. Simulation results ensure that the value of maximum utilized Bell pairs in a quantum network highly depends on the value of the probability of entangled pairs established, considering the time in the quantum memory besides the number of incoming requests.