Search Results (46)

In this work, we benchmark two prominent quantum algorithms: Quantum Imaginary-Time Evolution (QITE) and the Quantum Approximate Optimization Algorithm (QAOA) for obtaining the ground state of Ising-type Hamiltonians. Specifically, we apply them to the Markowitz portfolio optimization problem in quantitative finance, on both digital quantum computers and local quantum simulators with controllable two-qubit errors (noise). In noiseless settings, we find that QAOA achieves excellent convergence to the optimal results. Under noisy conditions, the QITE method exhibits greater robustness and stability, though it incurs substantially more classical numerical cost. In contrast, we demonstrate that QAOA offers better scalability and can still yield robust results if the noise can be effectively mitigated. Our findings provide valuable insights into the trade-offs between scalability and noise tolerance and demonstrate the practical potential of quantum algorithms for solving real-world optimization problems on near-term quantum devices. Full article

Single-path transmission optimization is a core task for resource scheduling and operation of complex networks, which requires coordinated optimization of transmission cost and flow. Classical algorithms bear heavy computational loads in high-dimensional decision spaces as networks grow. This paper constructs a hybrid quantum model integrating quantum approximate optimization algorithm (QAOA) and cubic spline interpolation. Paths, discrete flows, and trade-off coefficients are unified within a quadratic unconstrained binary optimization (QUBO) model. Least-squares fitting converts native parameters into QUBO coefficients, whose fitting errors are measured to verify robustness and penalty sensitivity, and auxiliary variables eliminate high-order terms to exponentially cut qubit consumption. QAOA narrows the feasible range via global coarse search, and cubic spline interpolation further yields precise continuous flow values. Powered by quantum superposition for parallel full-space exploration, the framework avoids repeated modeling for separate bias coefficients. Mixed integer programming (MIP) and genetic algorithm (GA) are adopted as comparative benchmarks. For the small-scale network instance, the relative error between the proposed method and the global optimum solved by MIP is less than 1%. For the large-scale case, the overall error of our approach remains within an acceptable range even when discrepancies exist between results yielded by classical algorithms. Full article

Alzheimer’s disease remains one of the hardest disorders to drug, and most computational pipelines still tackle one target at a time and ignore brain penetration until late. We bring all of that into a single optimization problem. Our framework, called CAGE-QMol(Constraint-Aware Quantum-inspired Molecular optimization), turns the search for a brain-penetrant, dual BACE1/AChE inhibitor into a constrained quadratic unconstrained binary optimization (QUBO) and solves it with an ensemble of classical, quantum-inspired, and Quantum Approximate Optimization Algorithm (QAOA) backends. The pipeline begins with three real public datasets—MoleculeNet BACE, ChEMBL CHEMBL4822 (BACE1) and CHEMBL220 (AChE), and the TDC BBB_Martins blood–brain-barrier set—which together yield 12,465 unique molecules with at least one measured endpoint. Multi-task ExtraTrees predictors trained on Morgan ECFP4 fingerprints and physicochemical descriptors deliver scaffold-split test-set metrics of $R^2=0.624$ ($\mathrm{MAE}=0.587$) for BACE1 and $R^2=0.383$ ($\mathrm{MAE}=0.793$) for AChE. The optimizer combines these predictions with a Lipinski-based feasibility cone, a TDC-derived BBB classifier, and similarity-driven diversity into a constrained QUBO. We adapt the classical exact-penalty rule, $\lambda >{\Delta }_S/{\delta }_g$, which guarantees every global minimizer of the penalized energy is feasible, and specialize it so that the multiplier is computed from the data rather than hand-tuned. A 10-qubit PennyLane QAOA circuit is benchmarked against exact enumeration, simulated annealing, genetic search, Bayesian TPE, and random search across ten seeds; the QUBO formulation lets a genetic solver match the exact ground state on every seed, while ablations show that removing the QUBO selection collapses the mean therapeutic score from 6.242 to 5.976 ($p<{10}^{-3}$, paired t-test). Top-50 candidates exhibit a mean BBB probability of 0.716, a mean QED of 0.768, and 100% Lipinski feasibility, with leading scaffolds (tetrahydroisoquinolinone, methoxy-tetrahydronaphthalene-urea, indanone-piperidine) reproducing motifs found in published dual BACE1/AChE inhibitor families. This paper contributes (i) a mathematically grounded penalty selection rule for constrained drug-discovery QUBOs, (ii) a single end-to-end pipeline from raw public data to ranked, 3D-embedded leads, and (iii) reproducible head-to-head benchmarks between classical, quantum-inspired, and QAOA-simulated optimizers on a real Alzheimer’s task. Full article

Martian dust storms cut off communication and break standard robot navigation. We built a hybrid system that keeps robot swarms alive during these blackouts and recovers their data quickly. Our rovers use Spiking Neural Networks (SNNs) on their own edge processors to navigate without a signal. Once the storm passes, we use the Quantum Approximate Optimization Algorithm (QAOA) on a cloud platform to merge the fragmented maps the rovers collected while they were offline. We tested this system in a Robot Operating System 2 (ROS 2) and Gazebo environment using a simulated 10-rover Martian deployment. During the simulated blackout, our SNN edge navigation achieved a 92.0% survival rate, outperforming traditional planners like Dynamic Window Approach (DWA) (29.0%) and Timed Elastic Band (TEB) (24.3%). The neuromorphic approach also reduced overall system power consumption by 80.0% compared to a traditional unoptimized Graphics Processing Unit (GPU)-based Simultaneous Localization and Mapping (SLAM) baseline. For the map recovery phase, our simulated QAOA proof-of-concept evaluated the map constraints in just 1.2 ms, compared to 50.0 ms for a classical Generalized Iterative Closest Point (G-ICP) and g2o pose-graph approach. Despite the noisy sensor data collected during the blackout, the final quantum-stitched map achieved an 8.54 cm Root Mean Square Error (RMSE). These results show that combining edge-based neuromorphic processing with quantum cloud computing secures swarm survival and accelerates post-disaster data recovery for deep-space missions. Full article

Selecting a compact subgraph of a document graph while maximising a learned coherence function, subject to flow conservation and temporal ordering, is important in storyline detection, event threading, and Narrative Map extraction. Existing Narrative Map methods either recover a single optimal path (a Narrative Trail) or solve a linear program with an output size which grows with graph density (Narrative Maps). We propose a hybrid classical–quantum pipeline that casts the problem as a Quadratic Unconstrained Binary Optimisation (QUBO) problem and solves it both with the Quantum Approximate Optimisation Algorithm (QAOA) and with off-the-shelf classical QUBO solvers (simulated annealing, Tabu search) on the same Hamiltonian; this approach uses a classical mean field active space reduction and Matrix Product State tensor network simulation to scale beyond 16 qubits. We evaluate node- and edge-level qubit encodings under a range of QAOA circuit variants (transverse field and XY mixers; classical warm-start deeper circuits) on a 418-document news corpus across four graph densities and ten endpoint pairs, and audit their reproducibility across optimiser seeds. The QUBO formulations—whether solved by QAOA or by classical QUBO solvers on the same Hamiltonian—produce maps averaging $4.7$–$9.0$ nodes versus $26.6$ for Narrative Maps ($p<{10}^{-7}$) and they are far more focused on their main storyline (main path fraction $0.61$–$0.99$ versus $0.20$). The Hamming-weight-preserving XY mixer goes the furthest: the node-level XY mixer variant produces the most compact ($4.7$ nodes) and most spine-focused ($0.99$ main path fraction) maps of any method tested, and a multi-seed audit identifies it as the most reproducible of the eight QAOA variants we compared. Main path coherence is on par with Narrative Maps’ and $0.031$–$0.072$ below the bottleneck-optimising baselines—Narrative Trails ($0.770$) and Iterative Maximin ($0.758$). These results position QAOA not as a uniformly stronger alternative but as a distinct trade-off region favouring compactness and spine focus over raw bottleneck coherence and corpus topic breadth. Full article

The rapid advancement of beyond-5G and 6G services is creating computational challenges that classical optimisation methods for Elastic Optical Networks (EONs) cannot effectively handle. Specifically, the multi-objective Routing and Spectrum Assignment (RSA) problem—aimed at minimising blocking probability, maximising spectral efficiency, and reducing fragmentation—poses significant challenges and is NP-hard, particularly in dynamic traffic. This paper introduces a hybrid framework that combines quantum and classical computing, dividing the optimisation tasks into classical pre-processing, a quantum optimisation core, and classical post-processing with Pareto frontier management. The RSA problem is modelled using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation that accounts for blocking, efficiency, and a quadratic fragmentation metric. Simulations conducted on NSFNET and UBN topologies under Poisson traffic conditions revealed that even in realistic, noisy quantum environments, this hybrid method reduces the blocking probability by 14% and improves fragmentation by 7.3% compared to the top classical heuristics. A scaling analysis indicates a key point of around 220 variables where this hybrid strategy surpasses traditional meta-heuristics in both solution quality and execution time, emphasising its significant potential in the current NISQ era. Full article

Quantum finance represents a pivotal and cutting-edge application domain within the burgeoning field of quantum computing. In this work, we propose a two-step quantum approximate optimization algorithm (two-step QAOA) for portfolio optimization and risk assessment. The algorithm initiates by formulating the stock selection problem as a quadratic unconstrained binary optimization (QUBO) problem and employs a classical-quantum hybrid method to find the ground state of the Hamiltonian. We then introduce an energy-based characteristic indicator $U\in [0,1)$, which quantitatively evaluates portfolio performance under customizable investment preferences, effectively capturing the trade-off between expected return and risk. The number of qubits required scales with the number of stocks N in the pool, and the number of Hamiltonian terms is $\mathcal{O}\left(N^2\right)$. Numerical simulations show that the algorithm provides consistent and reasonable assessment results on both training and test datasets under different investment preferences (aggressive or conservative), validating the capability of the characteristic indicator to extract intrinsic information from the portfolios. Additionally, by incorporating warm-starting and digitized counterdiabatic techniques, the algorithm achieves improved scalability and faster convergence. Our work presents a flexible and practical algorithmic framework for applying quantum computing in the financial domain. Full article

The selection of the right topology (ansatz) for a Variational Quantum Algorithm (VQA) is a complex task that usually involves deep knowledge of a particular problem. The importance of the selection is greater when we consider the current state of quantum hardware, particularly the noise associated with the complexity of Variational Quantum Circuits (VQCs) that implement VQAs. Here, a comparison is presented between two confronted approaches for solving the MaxCut problem: QAOA, which has a theoretical proof of convergence, and the automatic design proposal (QNAS), which relies on evolutionary algorithms (NSGA-II) to discover efficient circuits. The comparison was made across 490 graph instances from different graph topologies and sizes ($n=4$ to $n=16$), accounting for noise models such as depolarizing noise, gate errors, and readout noise. The results show that QAOA achieves an approximation ratio ($r_A$) $\approx 1$ on complete graphs at the cost of being almost 12 times more complex than QNAS in ideal conditions while approaching the random noise floor ($r_A\approx 0.5)$. QNAS was capable of finding circuits less complex while maintaining $69\%$ of the fidelity at a cost of having an $r_A$ on the interval $0.7\le r_A\le 0.8$. However, when the comparison is made across sparse graphs, performance is comparable, while QNAS is less complex. Full article

This article presents a systematic survey of six prominent quantum computing applications in finance, unified under the paradigm of optimization as the foundational use case from which derivative applications are constructed. We formalize the transition from the classical Markowitz portfolio optimization framework to a quantum implementation via the Quantum Approximate Optimization Algorithm (QAOA), including explicit mathematical derivations, theoretical performance bounds, and convergence guarantees. Beyond algorithmic formalism, we critically assess prevailing hardware limitations, focusing on noise thresholds and coherence constraints that currently preclude a demonstrable quantum advantage over classical counterparts. Furthermore, we address the underexplored institutional prerequisites for financial deployment, including regulatory compliance, model validation protocols, and structural barriers to adoption. We conclude that despite ongoing hardware maturation, proactive engagement with quantum algorithm development is imperative for financial institutions to preempt technological obsolescence upon the achievement of hardware parity. Full article

The quantum approximate optimization algorithm (QAOA) is an efficient method for solving combinatorial optimization problems in quantum computing. These problems involve finding the best solution from a finite set of possibilities. At its core, the QAOA uses an Ansatz circuit composed of alternating unitary operators, the mixing and problem Hamiltonians, that are controlled by a set of parameters. Its goal is to find the optimal parameters so that the final quantum state of the circuit encodes the problem’s solution. While this parameter optimization is often handled by classical optimizers, including constrained optimization by linear approximations (COBYLA) and Nelder–Mead, these methods frequently present local extrema. Therefore, we developed a layerwise grid search (LGS) method as an alternative. Since a full grid search is too time-consuming, the LGS method significantly reduces the search time while still finding a good solution. To demonstrate its effectiveness, we present experimental results for the max-cut problem, comparing the performance of our LGS method against conventional classical optimizers. Full article

Quantum optimization has recently drawn considerable attention as one of the possible applications of noisy intermediate-scale quantum computation, yet the problem of qubit requirement remains a major bottleneck when combinatorial optimization problems are converted into quantum circuits. This issue becomes especially critical in solving the capacitated vehicle routing problem (CVRP) with the quantum approximate optimization algorithm (QAOA), since the number of required qubits increases polynomially with respect to the number of nodes. This study investigates whether a heuristic divide-and-conquer strategy can be adapted to the quantum setting so as to improve qubit efficiency while preserving the optimization capability to a reasonable extent. The proposed method decomposes a single CVRP into multiple traveling salesman problems (TSPs) by the sweeping-based clustering method, searches for the sector configuration with the smallest angle sum by Grover’s search algorithm, and then solves each sector-wise TSP with the QAOA aided by the gravitational search algorithm. Experiments on five benchmark datasets show that the proposed approach attains feasible solutions within 3.4 to 12.7% of the reinforcement-learning baseline on the main test set. These results suggest that the proposed approach serves as a plausible quantum heuristic framework for constrained routing optimization, with the advantage of reducing the qubit burden by decomposing the original problem into smaller subproblems. Full article

Background: This paper investigates hybrid quantum–classical optimization approaches for addressing core supply chain management (SCM) problems. A unified hybrid framework is implemented and evaluated across five representative domains: vehicle routing, scheduling, facility location, inventory optimization, and demand forecasting. Methods: The framework integrates quantum algorithms—namely the Quantum Approximate Optimization Algorithm (QAOA), Quantum Annealing (QA), and the Variational Quantum Eigensolver (VQE)—with classical constraint-handling and local refinement procedures in an iterative workflow. Quantum solvers are employed for global solution exploration, while classical optimization ensures feasibility and convergence stability. Results: Experiments conducted on standardized synthetic benchmarks demonstrate that the proposed hybrid framework consistently outperforms classical-only and quantum-only baselines, achieving 12–18% reductions in operational costs and 20–35% faster convergence. In routing and fulfilment tasks, quantum-generated candidate solutions provide effective warm starts for classical refinement. Robustness analysis based on stochastic SCM simulations further indicates lower performance variance under uncertainty. Conclusions: These results demonstrate that hybrid quantum–classical optimization constitutes a practical and scalable strategy for near-term SCM decision-making under current Noisy Intermediate-Scale Quantum (NISQ) hardware constraints. Full article

This paper proposes a hybrid quantum–classical framework for distribution network reconfiguration (DNR) under high distributed generation (DG) penetration, integrating nonlinear AC power-flow validation with the Quantum Approximate Optimization Algorithm (QAOA). Unlike prior quantum-assisted studies that rely on simplified DC or surrogate models, the proposed approach embeds AC-feasible loss evaluation directly within the combinatorial optimization loop. The methodology first evaluates all admissible switching configurations of the IEEE 33-bus system under DG integration using full AC power flow. The resulting loss landscape is compressed into a Quadratic Unconstrained Binary Optimization (QUBO) representation and mapped to an Ising Hamiltonian, enabling variational optimization via QAOA. The dominant configuration suggested by the quantum layer is subsequently validated through AC feasibility analysis. Simulation results show that the coordinated DG + QAOA strategy reduces active power losses from 282.938 kW (baseline) to 95.773 kW, corresponding to a 66.15% reduction relative to the original topology and an additional 20.62% improvement beyond DG-only operation. The minimum bus voltage increases from 0.8828 p.u. to 0.9531 p.u., satisfying IEEE 1547 limits, while requiring only two switching operations. These results demonstrate that embedding AC-consistent validation within a hybrid QAOA framework enhances physical realism, scalability, and solution quality for combinatorial optimization in active distribution networks. Full article

The superposition principle in quantum mechanics enables the encoding of an entire solution space within a single quantum state. By employing quantum routines such as amplitude amplification or the Quantum Approximate Optimization Algorithm (QAOA), this solution space can be explored in a computationally efficient manner to identify optimal or near-optimal solutions. In this article, we propose quantum circuits that operate on binary data representations to address a central task in prototype-based classification and representation learning, namely the so-called winner determination, which realizes the nearest prototype principle. We investigate quantum search algorithms to identify the closest prototype during prediction, as well as quantum optimization schemes for prototype selection in the training phase. For these algorithms, we design oracles based on arithmetic circuits that leverage quantum parallelism to apply mathematical operations simultaneously to multiple inputs. Furthermore, we introduce an oracle for prototype selection, integrated into a learning routine, which obviates the need for formulating the task as a binary optimization problem and thereby reduces the number of required auxiliary variables. All proposed oracles are implemented using the Python 3-based quantum machine learning framework PennyLane and empirically validated on synthetic benchmark datasets. Full article

This paper addresses the Pickup and Delivery Problem with Time Windows (PDPTW), an NP-hard combinatorial optimization problem with major practical relevance in logistics and transportation. The study focuses on a quadratic unconstrained binary optimization (QUBO) formulation for quantum annealing and benchmarks it against two classical optimization paradigms. A modular Python framework is developed that encodes PDPTW in three ways: a mixed-integer linear programming (MILP) model that serves as an exact reference, a genetic algorithm (GA) metaheuristic, and a QUBO model that is compatible with quantum annealers. The framework supports test scenarios with increasing structural complexity, with both feasible and intentionally infeasible instances. An additional contribution is the conceptual design and preliminary analysis of an automatic-penalty weight-tuning scheme for the QUBO model. Experimental results show that the proposed QUBO formulation can produce high-quality solutions for simpler PDPTW instances, but its performance strongly depends on the careful calibration of penalty weights. MILP provides optimal baselines on small instances but becomes intractable as problem size grows. The GA scales to the largest scenario and finds feasible solutions of reasonable quality, but they are not necessarily optimal. The evaluation also includes a large number of problem instances and runs on IBM Quantum hardware using the Quantum Approximate Optimization Algorithm (QAOA). Full article