The optimization of multidrug cancer treatment schedules is a high-dimensional combinatorial optimization problem involving nonlinear tumor dynamics, pharmacokinetic interactions, and stringent toxicity constraints. When exploring large therapeutic search spaces, conventional optimization algorithms often exhibit limited scalability and become trapped in local optima. This simulation study proposes a hybrid quantum-classical optimization framework that employs QA to generate adaptive treatment schedules for precision oncology. The treatment scheduling problem is formulated as a quadratic unconstrained binary optimization (QUBO) model, which encodes drug combinations, dosing intervals, toxicity constraints, and synergistic interactions within an Ising Hamiltonian compatible with D-Wave quantum annealing hardware. Global combinatorial optimization is performed using a D-Wave Advantage quantum annealer, while sequential least squares programming refines continuous dosage parameters under pharmacokinetic and toxicity constraints. Tumor progression is represented using a modified Gompertz growth model coupled with first-order pharmacokinetic dynamics. The proposed framework was evaluated using synthetic Digital Twin datasets generated from clinically realistic pharmacokinetic and tumor growth parameters. Simulation results demonstrated a maximum tumor regression ratio of 0.98 ± 0.02, compared with 0.82 ± 0.05 for standard-of-care protocols, while maintaining a lower cumulative toxicity index (40 ± 5 versus 75 ± 8) and reducing optimization time to less than 2 s for 120-variable scheduling problems. The hybrid framework exhibited near-linear computational scalability and maintained robustness under stochastic dosage perturbations (TRR > 0.95 at σ = 0.25). However, predictive classification performance remained limited (AUC = 0.49), highlighting the need for validation using longitudinal clinical datasets and multimodal patient-specific data. These findings demonstrate the potential of hybrid quantum-classical optimization as a scalable computational framework for adaptive treatment scheduling and personalized precision oncology.
The optimization of multidrug cancer treatment schedules is a high-dimensional combinatorial optimization problem involving nonlinear tumor dynamics, pharmacokinetic interactions, and stringent toxicity constraints. When exploring large therapeutic search spaces, conventional optimization algorithms often exhibit limited scalability and become trapped in local optima. This simulation study proposes a hybrid quantum-classical optimization framework that employs QA to generate adaptive treatment schedules for precision oncology. The treatment scheduling problem is formulated as a quadratic unconstrained binary optimization (QUBO) model, which encodes drug combinations, dosing intervals, toxicity constraints, and synergistic interactions within an Ising Hamiltonian compatible with D-Wave quantum annealing hardware. Global combinatorial optimization is performed using a D-Wave Advantage quantum annealer, while sequential least squares programming refines continuous dosage parameters under pharmacokinetic and toxicity constraints. Tumor progression is represented using a modified Gompertz growth model coupled with first-order pharmacokinetic dynamics. The proposed framework was evaluated using synthetic Digital Twin datasets generated from clinically realistic pharmacokinetic and tumor growth parameters. Simulation results demonstrated a maximum tumor regression ratio of 0.98 ± 0.02, compared with 0.82 ± 0.05 for standard-of-care protocols, while maintaining a lower cumulative toxicity index (40 ± 5 versus 75 ± 8) and reducing optimization time to less than 2 s for 120-variable scheduling problems. The hybrid framework exhibited near-linear computational scalability and maintained robustness under stochastic dosage perturbations (TRR > 0.95 at σ = 0.25). However, predictive classification performance remained limited (AUC = 0.49), highlighting the need for validation using longitudinal clinical datasets and multimodal patient-specific data. These findings demonstrate the potential of hybrid quantum-classical optimization as a scalable computational framework for adaptive treatment scheduling and personalized precision oncology.
Optimizing personalized cancer treatment plans that combine chemotherapy, radiation, and immunotherapy presents a complex challenge due to the need to balance efficacy with minimizing side effects across diverse patient profiles. This study introduces a novel hybrid quantum-classical framework leveraging the Variational Quantum Eigensolver (VQE) for multi-modal optimization. Treatment planning is formulated as a parameterized Hamiltonian, where the ground state corresponds to an optimal therapy regimen tailored to individual genomic and clinical data. The quantum VQE algorithm estimates ground state energy via quantum simulators, while classical optimizers iteratively refine circuit parameters. Benchmarking on synthetic datasets demonstrates that the hybrid approach enhances treatment personalization and computational efficiency over classical methods. Although current quantum hardware constraints limit immediate deployment, our findings validate the potential for quantum-enhanced optimization in clinical oncology. This research lays foundational groundwork for integrating near-term quantum algorithms into medical decision-making, with promising implications for improving cancer treatment outcomes and patient quality of life.
Abstract : We propose a hybrid quantum–classical framework that integrates variational quantum machine learning (QML) for molecular binding affinity prediction with quantum annealing for Pareto-optimal drug formulation design. Leveraging a four-qubit variational circuit, our QML model achieves superior predictive performance compared to state-of-the-art classical baselines, effectively capturing complex molecular interactions. In parallel, we formulate drug formulation optimization as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solve it using D-Wave’s quantum annealer, enabling efficient identification of Pareto-optimal solutions that balance bioavailability, toxicity, and stability. By unifying predictive modeling and combinatorial optimization within a single pipeline, our framework demonstrates the potential of near-term quantum devices to accelerate and enhance critical stages of drug discovery. These findings underscore the transformative role of NISQ-era algorithms in bridging molecular informatics and formulation design, paving the way for scalable, data-driven pharmaceutical innovation.
Quantum computing has emerged as a promising computational paradigm with the potential to solve problems that are intractable for classical computers. This paper provides an overview of the current state of quantum computing, including its historical development, hardware advancements, applications, and challenges. Special attention is given to combinatorial optimization, which is considered one of the most promising application domains. The limitations of current quantum systems and future research directions are also discussed. This paper presents a comparative study between a conventional D-Wave-based simulated annealing approach and a proposed hybrid optimization model for solving largescale combinatorial optimization problems. The study focuses on benchmark problems, including AES, TSP gr24, and a real-world load balancing problem, all formulated as QUBO models. The D-Wave approach employs the dwave-neal simulated annealing engine with various parameter settings, while the proposed model introduces a decomposition-based framework combined with adaptive parameter control and iterative refinement. The experimental results demonstrate that the proposed model consistently outperforms the conventional approach in terms of solution quality, achieving significantly lower energy values across all problem instances. In particular, for the TSP gr24 problem, the proposed model achieves near-optimal solutions with substantially reduced computation time. For large-scale problems such as AES and load balancing, the proposed model maintains scalability and robustness, whereas the conventional approach suffers from increased computational cost and performance degradation. Although the proposed method introduces additional computational steps, its hybrid structure effectively mitigates limitations related to local minima, parameter sensitivity, and scalability. These findings indicate that integrating classical optimization techniques with quantum-inspired methods is essential for practical applications. The proposed model provides a promising framework for solving complex real-world optimization problems and highlights the importance of hybrid approaches in advancing quantum annealing technologies.
BACKGROUND: Quantum computing (QC) is emerging as a transformative tool for solving complex optimization problems across various fields, including biomedical applications. While classical optimization methods are well-established, they frequently face limitations when applied to complex and large-scale problems in radiotherapy planning. PURPOSE: This study aims to explore the implementation and evaluate the effectiveness of quantum optimization methods, specifically quantum annealing and the quantum approximate optimization algorithm (QAOA), in radiotherapy planning. In particular, we employ an Ising Hamiltonian formulation of the cost function, empirically implementing it on annealing-based quantum hardware and for the first time on circuit-based one. METHODS: We formulated a simplified radiotherapy optimization problem and solved it using quantum annealing on a D-Wave quantum annealer. Subsequently, we adapted this optimization problem for the QAOA framework and implemented it on IBM Quantum circuit-model hardware. Comparative analyses were conducted between classical and quantum methods and implementations, highlighting QC's potential advantages and limitations in specific optimization contexts. To demonstrate that the Hamiltonian formulation is valid and practically usable, we first tested it in simplified proof-of-principle examples and then extended it to a more clinically relevant bilateral prostate proton plan. In this new example, dose parameters were extracted directly from a commercial treatment planning system (RayStation) and incorporated into the Hamiltonian optimization workflow. Both one-qubit-per-voxel and two-qubits-per-voxel encodings were evaluated to illustrate scalability. Additionally, we discussed scalability considerations, practical challenges, and future research directions necessary for integrating quantum algorithms into routine clinical radiation therapy practices. RESULTS: To our knowledge, this study presents the first demonstration of using QC circuit-model hardware for radiotherapy planning optimization. The quantum annealing approach successfully determined the optimal solution. Convergence was achieved after 20 iterations on a quantum simulator (noise free) and after 100 iterations on actual quantum hardware (due to inherent hardware noise). In the bilateral prostate proton plan derived from realistic data, the Hamiltonian-based optimization assigned higher dose to the prostate relative to surrounding organs-at-risk, confirming the feasibility of applying QC optimization directly to clinically sourced parameters. CONCLUSIONS: Quantum optimization techniques demonstrate potential advantages over classical methods, particularly in complex optimization scenarios relevant to radiation therapy. The formulation of a Hamiltonian cost function, its validation on real quantum hardware, and its application to realistic data collectively represent a first concrete step toward QC-based treatment planning optimization in medical physics. Future research should focus on addressing scalability, overcoming practical implementation challenges, and advancing the development of scalable, fault-tolerant quantum systems suitable for clinical integration.
Quantum annealing has emerged as an effective meta-heuristic for solving combinatorial optimization problems by leveraging quantum tunnelling to navigate complex energy landscapes. This paper examines both the theoretical foundations and the practical implementation of quantum annealing for project scheduling and resource-allocation problems formulated as Ising or Quadratic Unconstrained Binary Optimization (QUBO) models. A comprehensive explanation of the quantum annealing process is provided through a stage-by-stage process flowchart. In addition, the study discusses hybrid quantum classical frameworks in which quantum annealing is integrated with Monte Carlo simulations or digital twin environments, supported by illustrations of the optimization energy landscape and the hybrid system architecture. The adaptability of the proposed approach is further demonstrated through analogies with unit load device (ULD) configuration and other related combinatorial optimization problems across multiple application domains. Finally, the paper outlines key implementation considerations and evaluates the current level of technological maturity of quantum annealing for applications in construction planning and logistics optimization. Keywords: quantum annealing implementation; Ising model; QUBO; combinatorial optimization; project scheduling; hybrid quantum-classical; energy landscape; digital twin; Monte Carlo; supply-chain resilience; ULD configuration
Resource constrained project scheduling and related allocation tasks can be expressed as Quadratic Unconstrained Binary Optimization (QUBO) models and submitted to quantum annealers. This paper develops the QUBO formulation in detail: choice of binary variables, linear and quadratic objective terms, conversion of precedence and resource constraints into penalty functions, and calibration of penalty weights. The resulting Hamiltonian is embedded onto quantum hardware, annealed, and post-processed. Hybrid classical–quantum workflows that wrap the QUBO solver inside Monte Carlo risk analysis or a digital twin are examined. Supporting process flowcharts and energy-landscape figures illustrate every stage. The treatment remains grounded in construction and logistics applications while remaining transferable to other combinatorial domains such as ULD configuration. Keywords: QUBO formulation; quantum annealing; Ising model; penalty methods; resource-constrained project scheduling; hybrid quantum-classical; minor embedding; Monte Carlo; digital twin.