In quantum satellite networks, routing is an important task for providing key relay services to ground stations (GSs). For the demand of quantum keys for multiple concurrent requests between GS pairs, we formulate a multi-objective optimization routing (MOOR) problem to allocate the quantum key and time-slot resources to find routes for simultaneous services. The proposed optimization scheme maximizes the number of successful requests while minimizing the routing cost. Specifically, we consider that the fewer available quantum keys on the link, the greater the cost of occupying the link. Then we use the reciprocal of the number of available keys on links to represent link costs, and find the route with the minimum link costs. Simulation results show that the success probability of MOOR scheme is higher than that of the comparison routing strategy based on Dijkstra algorithm, especially when the number of keys forwarded by a request is not too large, the improvement is significant.
In quantum satellite networks, routing is an important task for providing key relay services to ground stations (GSs). For the demand of quantum keys for multiple concurrent requests between GS pairs, we formulate a multi-objective optimization routing (MOOR) problem to allocate the quantum key and time-slot resources to find routes for simultaneous services. The proposed optimization scheme maximizes the number of successful requests while minimizing the routing cost. Specifically, we consider that the fewer available quantum keys on the link, the greater the cost of occupying the link. Then we use the reciprocal of the number of available keys on links to represent link costs, and find the route with the minimum link costs. Simulation results show that the success probability of MOOR scheme is higher than that of the comparison routing strategy based on Dijkstra algorithm, especially when the number of keys forwarded by a request is not too large, the improvement is significant.
Quantum key resources in quantum satellite networks are fundamental to confidential data forwarding, which highly depends on the network topology. In this paper, we propose a network topology construction scheme via formulating the dynamic link establishment among network nodes as an integer linear programming to maximize the number of available quantum keys in the topology. Then we solve this topology optimization problem through subgradient method based on the Lagrange duality theory. Under the optimized topology, we further propose a key-based routing and resource allocation (KRRA) algorithm to forward secret keys for ground stations. The simulation results show that our scheme performs better than the benchmark method with the minimum route distance in terms of the number of quantum keys and the success probability of real-time secret key forwarding service.
Multicast is an important service type in both terrestrial and space communication networks but has security issues because more than one destination node can receive information. Point-to-point quantum key distribution can be achieved end-to-end over long distances by using a quantum satellite (e.g., Micius) as a relay node. Hence, how to provide secret keys for remote multicast services and efficiently distribute secret keys between the source node and multiple destination nodes for long-distance secure multicast services (SMSs) has become a critical problem. In this paper, a quantum satellite network with a special node structure is designed to complete point-to-multipoint key distribution, and a point-to-multipoint satellite relay scheme is proposed. The weight information of the link is dynamically described by the method of auxiliary topology, and a satellite relay tree is constructed. Finally, this paper proposes a satellite relay algorithm for multicast services to route and allocate key resources to solve the problem of long-distance point-to-multipoint key relay and improve the success probability of multicast service requests. Simulation results show that the proposed algorithm can improve the success probability of SMS requests by about 51.32% in a static scenario and 17.33% in a dynamic scenario.
Quantum key distribution (QKD) has attracted much attention on secure communications across global networks. QKD over satellite networks can overcome the limitations of terrestrial optical networks, such as large attenuation over long distance fiber channel and difficulty of intercontinental domain communications. Different QKD networks (around the world) can intercommunicate through quantum satellites, leading to a global quantum network in near future. This raises a new resource allocation and management problem of QKD involving multiple satellite layers and distributed ground stations. Using existing schemes, a single satellite cannot perform QKD for ground stations for the whole day. Moreover, the research problem is more challenging due to limitations of satellite coverage: limited cover time of low earth orbit (LEO) satellite, high channel losses of geostationary earth orbit (GEO) satellite, etc. To overcome these limitations, our study proposes a double-layer quantum satellite network (QSN) implemented quantum key pool (QKP) to relay keys for ground stations. We propose a new architecture of trusted-repeater-based double-layer quantum satellite networks, comprising GEO and LEO satellites. We also address the routing and key allocation (RKA) problem for key-relay services over QSNs. We propose a novel joint GEO-LEO routing and key allocation (JGL-RKA) algorithm to solve the RKA problem. Simulative results show that the proposed scheme can increase success probability of key-relay services significantly. We also present the impact of different route selections mechanisms, number of satellite links, satellite node capability, and service granularity on network performance.
Quantum Key Distribution (QKD) is a foundational technology for future secure communications, and several QKD networks have been already deployed and tested around the world using optical fibers. However, these networks cannot scale in size due to the inefficiency of fiber QKD networks with increasing distances, making satellite networks a major candidate for long-distance QKD networks. In satellite QKD networks, satellites and ground stations can act as trusted relays, distributing keys between satellite-ground station pairs to serve requests among ground stations. Satellite QKD networks face fundamental challenges due the time-varying nature of the connection between ground stations and satellites, caused by both the satellite’s orbital movement and fluctuating atmospheric attenuation. Thus, it is necessary to design novel schemes to dynamically allocate resources for satellite QKD networks that adapt to evolving network conditions in different time intervals. In this work, we investigate the problem of resource allocation in satellite QKD networks taking into account the changing key generation rates, calculated according to evolving weather conditions and satellite visibility. We first model the achievable key rate of connections between satellite and ground stations under different weather conditions, which is used as an input for optimization. We formulate a Mixed-Integer Linear Programming (MILP) model to allocate resources in satellite QKD networks, which decides both link assignments (i.e., deciding which ground to connect to for satellites) and the appropriate routing path for the trusted relay. In addition, the MILP models multiple timeslots and considers keys stored in the quantum key pool (QKP), allowing keys generated during low-load periods to be used later during high-load periods. Moreover, we propose to decide the link configuration with heuristic algorithms and then utilize ILP to decide the appropriate routing path for the trusted relay, which significantly reduces the execution time. The numerical results show that incorporating link configuration within the ILP achieves up to 20% more total served keys compared to heuristicbased baseline approaches, but with an execution time up to 700x longer.
A multi-objective optimization problem involves optimizing two or more conflicting objectives simultaneously. This type of problem arises in many scientific and industrial areas and it is classified as NP-Hard. Network routing optimization with multiple objectives falls into this category. In the context of 6G networks, solving this problem will become even more challenging due to the exponential growth of Internet of Things devices and the high quality of service requirements. Finding good quality solutions for large-scale networks will be increasingly difficult. In this paper, we introduce a quantum-inspired routing optimization scheme in which noisy-intermediate scale quantum computers (NISQ) can be used to solve the Multi-Objective Routing Problem (MORP). We evaluate the application of the proposed scheme in detail by first developing the mathematical formulas for both single-objective and multi-objective routing and mapping the problem onto gate-based models by using the quadratic unconstrained binary optimization (QUBO) approach. To validate the proposed scheme, we use the quantum approximate optimization algorithm (QAOA), the go-to approach for solving combinatorial optimization problems that are classically intractable. For the simulation, we use the IBM-Qasm simulator and Qiskit framework. Additionally, we use the Chernoff Bound as a standard technique to estimate the sample complexity of QAOA. Finally, we provide a detailed numerical and theoretical analysis of the proposed scheme, including its time complexity, resource requirements, and the challenges associated with it. Our results demonstrate that the proposed approach operates with a time complexity of O ( E 2 ) per iteration in both single and multi-objective scenarios, with an overall runtime of ( n iteration + n CB ) ⋅ O ( E 2 ) influenced by the sampling overhead, significantly outperforming Dijkstra’s algorithm in the multi-objective case, where the complexity increases to O ( 2 k ( N ( k + log N ) + 2 k E ) ) .
Free-space long-distance quantum key distribution (QKD) has the characteristics of low attenuation and wide coverage, which can overcome the limitation of transmission distance based on ground optical fiber QKD networks. Long-distance QKD requests can be relayed by quantum satellites to achieve intercontinental QKD. At present, there is only one quantum satellite in space, quantum satellite network with multiple quantum satellites is necessary to be deployed to cover the global. Thus, how to construct the quantum satellite network becomes a new challenge. In this paper, we propose a centralized and distributed collaborative scheme of quantum satellite network. Low-Earth-orbit (LEO) quantum satellites, as important relay satellites, will affect the performance of the global QKD network. Based on the above architecture, we analyze the influence of the structure of LEO quantum satellite constellation on the QKD performance. Simulation results show that the key relay performance of the constellation is related to the form of inter-satellite link. and the more the number of satellites is, the greater the successful probability of the key relay services will be.