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Nano Communication Networks

Grover enhanced quantum repeater system with 8-qubit optimization

Md. Siam Uddin, Joheb Muhammad Tanzeer Sayeed, Md Abu Talha, Shameem Ahmad, Md. Mehedi Hasan Monna

Published Dec 7, 2025• 0 citations
Publisher
DOI
10.1016/j.nancom.2025.100608

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Route determination and optimization is a persistent challenge in transportation networks due to combinatorial explosion of options, dynamically changing conditions, competing optimization criteria, and complexity of real-world systems. Classical algorithms struggle to efficiently solve route optimization at scale due to exponential growth of possibilities, NP-hardness, limitations of dynamic programming approaches, and inability to leverage quantum parallelism. This paper explores the potential application of Grover’s algorithm in optimizing road transportation. Grover’s quantum algorithm offers a potential solution by using an oracle function to recognize optimal routes based on constraints and objectives encoded in a quantum state representing all possible paths. Constructive interference and amplitude amplification drive the system toward optimal solutions. By utilizing Grover’s algorithm, road transportation networks can benefit from improved route planning, traffic management, and resource allocation, ultimately enhancing efficiency and reducing congestion. The transportation network must be efficiently encoded into a quantum representation. An optimization oracle tailored to routing objectives then recognizes optimal solutions, which are amplified via a diffusion operator utilizing interference. Repeated application concentrates amplitude in optimal routes, which can be measured. Key challenges include encoding the network effectively within qubit resource constraints, designing an oracle to evaluate routes based on real-world conditions and optimization criteria, and translating the optimized quantum state into actionable routing guidance. If these challenges can be met, Grover’s algorithm may enable route optimization at a scale intractable for classical techniques.
The quantum asymmetric key (QAE) cryptography scheme, originally proposed using the Grover quantum search algorithm and demonstrating significant advancements in theoretical generalization, is revisited. To enhance its practical implementation, the authors evaluate the protocol's performance under real-world conditions. This includes analyzing the impact of hardware limitations and the one-iteration Grover search algorithm (GSA) on QAE accuracy, with tests conducted on IBM Quantum simulators and devices. To address these challenges, the paper focuses on extending the GSA to support non-standard initial states. This is achieved by designing a tailored diffusion operator, resulting in the generalized GSA. The study marks the first practical implementation of QAE on IBM Quantum devices, introducing generalized GSA and providing empirical performance insights. Empirical results reveal scalability challenges, with success probabilities decreasing significantly as qubit count increases. For instance, the 2-qubit system achieves near-perfect accuracy, while the 4-qubit system shows notable degradation, especially on quantum hardware. These findings underscore the need for improved hardware fidelity and algorithmic optimization to advance quantum cryptography.
Quantum repeaters constitute a promising platform for enabling long-distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An efficient approach to encoding qubits within an error correcting code is provided by bosonic codes, in which even a single oscillator mode can function as a sufficiently large physical system. In this work, we initially investigate the bosonic Gottesman Kitaev Preskill (GKP) code as a promising platform for loss correcting quantum repeaters, compatible with room temperature implementation, and analyse how loss and other noise sources propagate through the circuit using Heisenberg evolution. We analyse three quantum repeater protocols in which transmission loss is suppressed at the cost of logical errors, identifying a relay-like teleamplifier as the optimal scheme. This enables long distance quantum communication via densely packed nodes without higher-level encoding, and we evaluate the resulting secure key rates exploiting analog syndrome information. Furthermore, we propose a concatenated Bell-state measurement (CBSM) scheme with a modified parity encoding based on GKP qubits, CV measurement with teleamplifier and a clipping method that corrects transmission loss without introducing logical errors. This significantly enhances the possible secure key distance. We find that GKP based repeaters can achieve performance comparable to approaches relying on photonic qubits, while requiring orders of magnitude fewer qubits. Our parity encoded GKP repeater protocol achieves a substantially higher secret key rate than existing GKP based repeater schemes while maintaining a comparable resource overhead.