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.
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.
Path planning in complex and obstacle-constrained environments remains a challenging combinatorial optimization problem due to the exponential growth of the solution space and the limitations of classical algorithms in dynamic decision-making scenarios. Traditional approaches such as Dijkstra or A* may experience high computational costs and susceptibility to local optima when dealing with large-scale directed graphs containing obstacles. This study proposes a hybrid quantum computing approach that integrates the Grover Search Algorithm and the Quantum Approximate Optimization Algorithm (QAOA) to address optimal path planning on obstacle-oriented directed graphs. The Grover algorithm is first employed as an oracle-based filtering mechanism to detect and eliminate obstacle-containing edges, thereby generating a valid subgraph of feasible paths. Following this preprocessing step, QAOA is applied to the filtered graph within a nonlinear optimization framework to determine the minimum-cost path between source and destination nodes. The optimization model represents the graph as G=(V,E), where binary decision variables indicate whether an edge is included in the selected route while satisfying flow conservation constraints. By narrowing the solution space through Grover-based obstacle detection and performing optimization only on valid edges, the proposed method significantly reduces computational complexity compared to conventional approaches. Experimental analysis demonstrates that the hybrid quantum model effectively identifies optimal routes and adapts to different obstacle configurations while maintaining efficient convergence behavior. The results highlight the potential of integrating quantum search and quantum optimization techniques for solving combinatorial graph problems. This work contributes to the growing body of research on quantum-assisted optimization and demonstrates the feasibility of applying hybrid quantum algorithms to directed path planning problems relevant to autonomous navigation systems.
Quantum computing introduces new computational methods that address complex optimization and machine learning challenges in transportation engineering. This literature survey reviews fundamental quantum principles, including qubits, superposition, entanglement, and quantum gates, and examines their applications in transportation. Fundamental quantum algorithms, including Shor's algorithm, the Quantum Approximate Optimization Algorithm (QAOA), and Grover's search, are described for their applications in transportation, such as network analysis, traffic management, and vehicle routing. Quantum optimization techniques, including hybrid quantum-classical approaches and quantum annealing, have been explored for combinatorial challenges such as the Vehicle Routing Problem (VRP) and dynamic traffic signal control. Additionally, quantum machine learning models, such as Quantum Convolutional Neural Networks (QCNNs) and quantum clustering, present applications in traffic prediction and anomaly detection. Despite its potential, quantum computing in transportation faces challenges related to hardware limitations, error rates, and a lack of established quantum programming frameworks. Addressing these challenges necessitates progress in hardware scalability, error mitigation techniques, and algorithm refinement. As quantum computing continues to evolve, its integration into transportation engineering could improve computational efficiency and enable new capabilities in optimization, traffic management, and intelligent transportation systems. This survey outlines key developments, challenges, and future research directions in this emerging field.
Intelligent Transportation Systems (ITS) occupy a pivotal position in the contemporary societal landscape, with one of their widespread applications being the vehicle routing problem, renowned for its classification as an NP-hard challenge. Traditional algorithms often require considerable time to address such problems or can only provide approximate solutions. Recent progress in quantum computation, however, offer a promising alternative by utilizing the parallelism inherent in quantum mechanics. In this study, we propose to solve the vehicle routing problem using the Grover adaptive algorithm. Compared to classical algorithms and existing quantum methods, our innovative algorithm achieves a quadratic speedup, with a time complexity ofO(KMN). Additionally, it is applicable to a broader range of real-world scenarios, as it can directly handle linear inequality constraints without introducing slack variables. Notably, the algorithm operates independently of classical optimizers and gradient-based methods, thereby circumventing potential challenges such as the “barren plateaus” phenomenon. Experimental results from four instances demonstrate the feasibility and correctness of the proposed approach, highlighting its capability to handle inequality constraints easily.
Optimization is central to urban mobility, where ride-sharing platforms must continuously match passengers with vehicles under complex constraints such as destination compatibility, cost, route efficiency, and acceptable waiting time. Classical exact methods like integer programming scale poorly as the problem size grows and struggle with highly dynamic inputs such as fluctuating demand, travel times, and vehicle capacities. Quantum computing offers an alternative paradigm: by exploiting superposition and interference, quantum search algorithms can explore large combinatorial spaces more efficiently than classical brute-force search. This study presents a proof-of-concept quantum formulation of a foundational ride-sharing assignment problem and investigates the use of Grover’s search algorithm. The model considers five unique passengers (Mehmet, Aytuğ, Filiz, Alara, and Ayliz) and two vehicles. Each passenger must be assigned to one of the two vehicles, subject to a balanced distribution objective (either a 3–2 or 2–3 split) and individual feasibility constraints. The problem is encoded on a 5-qubit quantum register, where the state of each qubit (|0⟩ or |1⟩) denotes assignment to Vehicle A or Vehicle B, mapping the full 2⁵ = 32-state Hilbert space to all possible allocations. A Grover oracle is designed to “mark” all assignments that satisfy the balanced-split and feasibility conditions by applying a phase flip to those computational basis states. The algorithm is implemented and simulated using IBM’s Qiskit framework. The results show that, after two Grover iterations, the total probability of measuring one of the ten valid “balanced” states increases from 31.25% to over 95%, in line with the expected quadratic speed-up of Grover’s algorithm over classical exhaustive search, which requires O(N) evaluations for N = 32 states. Although intentionally simplified—excluding realistic factors such as travel times, traffic, capacities, and time windows—this work demonstrates that a vehicle-sharing assignment problem can be cast as a quantum search task. Future work will focus on scaling to larger instances, incorporating richer operational constraints, and exploring quantum-classical hybrid approaches for real-world logistics optimization.
Current flight search platforms primarily consider four essential factors when planning a trip: departure/arrival dates, as well as the origin and destination locations. However, when additional parameters are added to this search, the problem shifts from a simple to a complex search, as the engine must sift through a massive dataset of flights, including information on airlines, flight routes, fees, and more. To address this challenge and improve flight search efficiency amidst data-intensive and resource-demanding environments, this paper proposes the use of Grover's search algorithm. This algorithm is demonstrated as the optimal solution for searches with increased constraints. The paper highlights the practical application of Grover's search algorithm across three datasets of assorted sizes, as well as various quantum hardware and simulators available in the NISQ era. Furthermore, this paper provides an in-depth understanding of the complexity of quantum circuit design, including the key phases of state encoding and amplitude amplification. The effectiveness of these approaches is evaluated through analysis of execution times and quantum measurement results. The aim is to showcase the potential of quantum computing in revolutionizing real-world search tasks, particularly in the realm of flight selection.
In large-scale heterogeneous communication networks, routing optimization involves complex demands such as high-dimensional state spaces, multiple constraints, and real-time dynamics. A quantum-classical hybrid computing paradigm, leveraging quantum superposition and entanglement, offers a promising pathway to efficiently address NP-hard routing problems. By analyzing representative routing scenarios, a modeling framework for quantum algorithms was outlined, and key technical obstacles in applying quantum approaches to network routing were systematically summarized. These include conflicts between structural constraints and model expressiveness, biases in multi-objective formulations and delayed responses, the trade-off between diversity and convergence in high-dimensional solution spaces, and limited generalization capability under dynamic conditions. To overcome these issues, several directions were proposed: algorithmic expressiveness was enhanced through improved structural modeling, evolutionary design, and integrated scheduling strategies; computational accuracy and responsiveness were improved via multi-objective optimization, modular decoupling, and tight quantum-classical interaction; convergence and diversity were balanced through hybrid architectural design, evolutionary policy adaptation, and structural constraint management; and adaptability and generalization in dynamic environments were boosted by incorporating meta-learning, task decomposition, and structural transfer techniques. Furthermore, the co-development of quantum algorithms and hardware architectures were advocated, paving the way for practical deployment of quantum computing in communication networks within the NISQ era.