Purpose: We report on the first application of quantum annealing (QA) to the process of beamlet intensity optimization for IMRT. QA is a new technology, which employs novel hardware and software techniques to address various discrete optimization problems in many fields. Methods: We apply the D‐Wave Inc. proprietary hardware, which natively exploits quantum mechanical effects for improved optimization. The new QA algorithm, running on this hardware, is most similar to simulated annealing, but relies on natural processes to directly minimize the free energy of a system. A simple quantum system is slowly evolved into a classical system, representing the objective function. To apply QA to IMRT‐type optimization, two prostate cases were considered. A reduced number of beamlets were employed, due to the current QA hardware limitation of ∼500 binary variables. The beamlet dose matrices were computed using CERR, and an objective function was defined based on typical clinical constraints, including dose‐volume objectives. The objective function was discretized, and the QA method was compared to two standard optimization Methods: simulated annealing and Tabu search, run on a conventional computing cluster. Results: Based on several runs, the average final objective function value achieved by the QA was 16.9 for the first patient, compared with 10.0 for Tabu and 6.7 for the SA. For the second patient, the values were 70.7 for the QA, 120.0 for Tabu, and 22.9 for the SA. The QA algorithm required 27–38% of the time required by the other two methods. Conclusion: In terms of objective function value, the QA performance was similar to Tabu but less effective than the SA. However, its speed was 3–4 times faster than the other two methods. This initial experiment suggests that QA‐based heuristics may offer significant speedup over conventional clinical optimization methods, as quantum annealing hardware scales to larger sizes.
Purpose: We report on the first application of quantum annealing (QA) to the process of beamlet intensity optimization for IMRT. QA is a new technology, which employs novel hardware and software techniques to address various discrete optimization problems in many fields. Methods: We apply the D‐Wave Inc. proprietary hardware, which natively exploits quantum mechanical effects for improved optimization. The new QA algorithm, running on this hardware, is most similar to simulated annealing, but relies on natural processes to directly minimize the free energy of a system. A simple quantum system is slowly evolved into a classical system, representing the objective function. To apply QA to IMRT‐type optimization, two prostate cases were considered. A reduced number of beamlets were employed, due to the current QA hardware limitation of ∼500 binary variables. The beamlet dose matrices were computed using CERR, and an objective function was defined based on typical clinical constraints, including dose‐volume objectives. The objective function was discretized, and the QA method was compared to two standard optimization Methods: simulated annealing and Tabu search, run on a conventional computing cluster. Results: Based on several runs, the average final objective function value achieved by the QA was 16.9 for the first patient, compared with 10.0 for Tabu and 6.7 for the SA. For the second patient, the values were 70.7 for the QA, 120.0 for Tabu, and 22.9 for the SA. The QA algorithm required 27–38% of the time required by the other two methods. Conclusion: In terms of objective function value, the QA performance was similar to Tabu but less effective than the SA. However, its speed was 3–4 times faster than the other two methods. This initial experiment suggests that QA‐based heuristics may offer significant speedup over conventional clinical optimization methods, as quantum annealing hardware scales to larger sizes.
Optimization methods are critical to radiation therapy. A new technology, quantum annealing (QA), employs novel hardware and software techniques to address various discrete optimization problems in many fields. We report on the first application of quantum annealing to the process of beamlet intensity optimization for IMRT. We apply recently-developed hardware which natively exploits quantum mechanical effects for improved optimization. The new algorithm, called QA, is most similar to simulated annealing, but relies on natural processes to directly minimize a system's free energy. A simple quantum system is slowly evolved into a classical system representing the objective function. If the evolution is sufficiently slow, there are probabilistic guarantees that a global minimum will be located. To apply QA to IMRT-type optimization, two prostate cases were considered. A reduced number of beamlets were employed, due to the current QA hardware limitations. The beamlet dose matrices were computed using CERR and an objective function was defined based on typical clinical constraints, including dose-volume objectives, which result in a complex non-convex search space. The objective function was discretized and the QA method was compared to two standard optimization methods, simulated annealing and Tabu search, run on a conventional computing cluster. Based on several runs, the average final objective function value achieved by the QA was 16.9 for the first patient, compared with 10.0 for Tabu and 6.7 for the simulated annealing (SA) method. For the second patient, the values were 70.7 for the QA, 120.0 for Tabu and 22.9 for the SA. The QA algorithm required 27-38% of the time required by the other two methods. In this first application of hardware-enabled QA to IMRT optimization, its performance is comparable to Tabu search, but less effective than the SA in terms of final objective function values. However, its speed was 3-4 times faster than the other two methods. This initial experiment suggests that more research into QA-based heuristics may offer significant speedup over conventional clinical optimization methods, as quantum annealing hardware scales to larger sizes.
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.
We apply a new hardware and software platform called the Hamiltonian Engine for Radiotherapy Optimization (HERO) to the problem of Intensity-Modulated Radiation Therapy (IMRT) treatment planning. HERO solves large general-form binary optimization problems by decomposing them into sub-problems and approximating them using a quadratic pseudo-boolean function. Optimizing the resulting function becomes a quadratic unconstrained binary optimization (QUBO) problem, which has been widely studied and has numerous applications in various fields. A Quantum Annealer (QA) approach has been previously investigated to solve QUBO problems, including IMRT optimization. However, the QA can only accommodate a small number of variables and requires several hours to obtain optimized plans. HERO acts as an optimizer for QUBO problems, which not only addresses these shortcomings but also relies solely on conventional hardware design while operating at room temperature. We evaluate HERO on seven prostate IMRT cases with clinical objectives, each using approximately 6000 beamlets. Our method was compared to the commercial treatment planning software, Eclipse, for both time-to-solution and plan quality. HERO solves most cases in about 30 seconds, with significantly lower objective function scores than Eclipse. The results indicate that HERO is promising for radiation therapy optimization problems. Additionally, HERO has the potential to be applied to Volumetric-Modulated Arc Therapy (VMAT) and other complex types of treatment planning.
Quantum annealing (QA) is a promising quantum computing paradigm for solving optimization problems. However, the performance of QA is often limited by issues such as slow convergence rates and sensitivity to parameter settings. This paper presents a novel optimization method designed to address these limitations. The approach introduces refined parameters and an adaptive strategy to enhance the algorithm's convergence speed and solution accuracy. We explore the application of this optimized QA method to complex problems, demonstrating its potential for improved performance. The core of the optimization lies in modifying the annealing schedule and incorporating a dynamic adjustment of the magnetic field strength, denoted as H(t), where t represents time. The objective function to be minimized is typically represented as E[s], where s is the state vector of the quantum annealer. We introduce a variance reduction technique, denoted as σ(t), which is dynamically adjusted based on the error estimates of the current state. The overall optimization process can be summarized as: minsE[s]subject todtdS=−β(t)E[s]−γ(t)H(t)s where β(t) is the annealing rate and γ(t) is the magnetic field strength. The adaptive strategy involves updating β(t) and γ(t) based on the error in the current solution, aiming to reduce the variance σ(t) and improve the convergence. The theoretical analysis suggests that this approach can significantly reduce the computational cost and improve the solution quality compared to traditional QA methods. Furthermore, we investigate the impact of different parameter settings on the algorithm's performance, highlighting the importance of careful tuning for optimal results. The results demonstrate a notable improvement in solution quality and convergence speed across various benchmark problems.
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 very first successful application of tensor network methods (TNMs) to the solution of the dose optimization in Intensity Modulated Radiation Therapy (IMRT) is considered. This technique provides a method to modulate the local beam intensities, dividing the beam into smaller beamlets. This allows to reduce the radiation toxicity for healthy organs and deal with irregular and inhomogeneous tumors. Plan's goals are encoded as mathematical constraints into a cost function expressing the distance between the prescribed and delivered dose. Aim of the optimization is to minimize the function associating to each beamlet the optimal weight xj. In this thesis a classical quadratic cost function is mapped into an Insing-like Hamiltonian, where the beamlets weights are described by a system of long-range interacting qubits. The aim of the work is to solve the dose optimization problem using a binary tree tensor network (bTTN) to find the Hamiltonian's groundstate and to show the applicability of TNM to the IMRT dose optimization problem.