First application of quantum annealing to IMRT beamlet intensity optimization

This paper explores the potential of quantum computing on a WCET(Worst-Case Execution Time (of a program).)-related combinatorial optimization problem applied to a set of several polynomial special cases. We consider the maximization problem of determining the most expensive path in a control flow graph. In these graphs, vertices represent blocks of code whose execution times are fixed and known in advance. We port the considered optimization problem to the quantum framework by expressing it as a QUBO. We then experimentally compare the performances in solving the problem of classic Simulated Annealing (SA), Quantum Annealing (QA), and Quantum Approximate Optimization Algorithm (QAOA). Our experiments suggest that QA represents a fast equivalent of simulated annealing. Indeed, we measured the approximation ratio on the results of QA and SA, showing that their performances are comparable, at least on our set of simplified problems.KeywordsWCETsQuantum computingQUBOCombinatorial optimizationQuantum annealingQAOA

Carefully injected noise can speed the average convergence of Markov chain Monte Carlo (MCMC) estimates and simulated annealing optimization. This includes quantum annealing and the MCMC special case of the Metropolis-Hastings algorithm. MCMC seeks the solution to a computational problem as the equilibrium probability density of a reversible Markov chain. The algorithm must cycle through a long burn-in phase until it reaches equilibrium because the Markov samples are statistically correlated. The special injected noise reduces this burn-in period in MCMC. A related theorem shows that it reduces the cooling time in simulated annealing. Simulations showed that optimal noise gave a 76% speed-up in finding the global minimum in the Schwefel optimization benchmark. The noise-boosted simulations found the global minimum in 99.8% of trials compared with only 95.4% of trials in noiseless simulated annealing. Simulations also showed that the noise boost is robust to accelerated cooling schedules and that noise decreased convergence times by more than 32% under aggressive geometric cooling. Molecular dynamics simulations showed that optimal noise gave a 42% speed-up in finding the minimum potential energy configuration of an eight-argon-atom gas system with a Lennard-Jones 12-6 potential. The annealing speed-up also extends to quantum Monte Carlo implementations of quantum annealing. Noise improved ground-state energy estimates in a 1024-spin simulated quantum annealing simulation by 25.6%. The quantum noise flips spins along a Trotter ring. The noisy MCMC algorithm brings each Markov step closer on average to equilibrium if an inequality holds between two expectations. Gaussian or Cauchy jump probabilities reduce the noise-benefit inequality to a simple quadratic inequality. Simulations show that noise-boosted simulated annealing is more likely than noiseless annealing to sample high probability regions of the search space and to accept solutions that increase the search breadth.

Quantum annealing has gained considerable attention because it can be applied to combinatorial optimization problems, which have numerous applications in logistics, scheduling, and finance. In recent years, with the technical development of quantum annealers, research on solving practical combinatorial optimization problems using them has accelerated. However, researchers struggle to find practical combinatorial optimization problems, for which quantum annealers outperform mathematical optimization solvers. Moreover, there are only a few studies that compare the performance of quantum annealers with the state-of-the-art solvers, such as Gurobi and CPLEX. This study determines that quantum annealing demonstrates better performance than the solvers in that the solvers take longer to reach the objective function value of the solution obtained by the quantum annealers for the break minimization problem in a mirrored double round-robin tournament. We also explain the desirable performance of quantum annealing for the sparse interaction between variables and a problem without constraints. In this process, we demonstrate that this problem can be expressed as a 4-regular graph. Through computational experiments, we solve this problem using our quantum annealing approach and two-integer programming approaches, which were performed using the latest quantum annealer D-Wave Advantage, and Gurobi, respectively. Further, we compare the quality of the solutions and the computational time. Quantum annealing was able to determine the exact solution in 0.05 seconds for problems with 20 teams, which is a practical size. In the case of 36 teams, it took 84.8 s for the integer programming method to reach the objective function value, which was obtained by the quantum annealer in 0.05 s. These results not only present the break minimization problem in a mirrored double round-robin tournament as an example of applying quantum annealing to practical optimization problems, but also contribute to find problems that can be effectively solved by quantum annealing.

Quantum annealing (QA) is a new method to solve nonlinear inverse problems based on quantum tunneling effect of state transitions. Compared with simulated annealing, quantum annealing has a potential advantage in some aspects such as annealing convergent rate and avoiding being trapped in a local minimum. So the study of quantum annealing inversion is of important academic significance and practical value. In this paper, the inversion tests of some models and actual data show that QA has higher efficiency and accuracy. It is the first time to apply QA method to the geophysical inverse problem.

Multi-objective Quantum Annealing approach for solving flexible job shop scheduling in manufacturing

We study the frustrated Ising model on the two-dimensional $L \times L$ square lattice with ferromagnetic (FM) nearest-neighbor and antiferromagnetic diagonal-neighbor interactions using the D-wave quantum annealing machine (D-QAM) with 5000+ qubits composed on structure of the Pegasus graph. As the former Monte Carlo and mean field results, we find the FM to stripe order phase transition, through observations of the magnetization $M$, energy, magnetic susceptibility and structure factor. We also analyze probability which occurs any $M$ at a given interaction for many quantum annealing shots to estimate the shape of objective function $f$. The only one value of $M$ with specific phase is observed in the regions far from phase transition for many quantum annealing shots, while several values of $M$ with different possibilities are appeared in the regimes of phase transition. We guess that $f$ in the regimes of phase transition retains the multi-modal structure with several local minimums, due to the strong degeneracies caused by frustrations. Finally, we discuss fail of the quantum annealing simulations, through analysis of the number of the chains, defined as the same variable with $N$-qubits, as a function of $L$.

Quantum annealing has been applied to combinatorial optimization problems in recent years. In this paper we study the possibility to use quantum annealing for solving the combinatorial FIFO Stack-Up problem, where bins have to be stacked-up from a conveyor belt onto pallets. The problem is NP-hard and can be solved using linear programming approaches. We developed two QUBO (quadratic unconstrained binary optimization) objective functions based on a bin stack-up solution and a pallet stack-up solution for this problem suitable for a quantum annealer. The number of variables was minimized to increase the performance and their dependence on the number of bins and pallets was discussed. The performances of both methods were studied for various small problem sizes on a D-Wave quantum annealer. We found that only tiny instances could be solved and looked at the terms of the QUBO-formulations, which cause the quantum annealer to fail for larger problem sizes. Furthermore we compare the results to the performance of a classic computer using the same QUBO-formulations.

The idea of quantum annealing (QA) is a late offspring of the celebrated simulated thermal annealing by Kirkpatrick et al. [1]. In simulated annealing, the problem of minimizing a certain cost (or energy) function in a large configuration space is tackled by the introduction of a fictitious temperature, which is slowly lowered in the course of a Monte Carlo or Molecular Dynamics simulation [1]. This device allows an exploration of the configuration space of the problem at hand, effectively avoiding trapping at unfavorable local minima through thermal hopping above energy barriers. It makes for a very robust and effective minimization tool, often much more effective than standard, gradient-based, minimization methods.

With quantum computers still under heavy development, already numerous quantum machine learning algorithms have been proposed for both gate-based quantum computers and quantum annealers. Recently, a quantum annealing version of a reinforcement learning algorithm for grid-traversal using one agent was published. We extend this work based on quantum Boltzmann machines, by allowing for any number of agents. We show that the use of quantum annealing can improve the learning compared to classical methods. We do this both by means of actual quantum hardware and by simulated quantum annealing.

Earthquake rupture forecasting is a critical component of seismic hazard analysis and requires identifying physically plausible rupture paths across complex fault networks. At its core, this task could be formulated as a large-scale combinatorial optimization problem, which involves selecting an optimal subset of fault segments from a set of candidates. Such problems pose significant challenges for traditional algorithms, as the number of admissible multi-fault ruptures grows combinatorially. Current operational workflows rely on locally applied plausibility filters. While computationally efficient, such greedy local heuristics risk excluding globally competitive rupture scenarios, particularly in regions with dense fault connectivity and competing rupture pathways. This work investigates whether quantum annealing hardware can serve as a sampling accelerator for exploring the ensemble of physically plausible ruptures beyond what is currently accessible to classical approaches. Designing a problem formulation that remains scientifically meaningful while respecting the constraints of current quantum hardware (size, noise, etc.) is nontrivial, and naïve encodings often collapse under these limitations. We encode rupture plausibility modeling as low energy solutions to a quadratic unconstrained binary optimization (QUBO) problem defined on a fault-network middle graph. Binary variables represent activated fault segments, while local interaction terms encode Coulomb stress transfer (as a proxy for pairwise rupture compatibility), continuity preferences, and branching behavior. Here, we adopt a classical-quantum hybrid workflow: the quantum annealer is used to sample globally competitive rupture candidates, while classical post-processing implements physical constraints to filter out non-physical ruptures. The workflow is demonstrated on a subset of the fault network used in the 2023 USGS National Seismic Hazard Model including over 200 fault segments, using both simulated thermal and quantum annealing on D-Wave hardware. Results show that our hardware-aware formulation and conditioning enable robust sampling on comparatively large fault-network instances. Views on quantum computing are polarized: some overstate its power, while others dismiss it as impractical. Our results help bridge this by establishing a concrete, testable pathway for integrating quantum annealing into rupture-modeling workflows on existing purpose-built quantum devices.—---This work is supported by the ICSC National Research Centre for High Performance Computing, Big Data and Quantum Computing (CN00000013, CUP D53C22001300005) within the European Union-NextGenerationEU program (National Recovery and Resilience Plan (PNRR) - Mission 4 Component 2 Investment 1.4.)

The optimal design of gas generator was conducted. Turbo pump system with fuel rich combustion in gas generator was the system considered in this study. The objective function is the specific impulse of main thrust chamber operating with RP-11LOX propellants. Sensitivity analyses to the objective function were used to measure the relative dependence of design variables the objective function. Also optimization method was adopted with two different algorithms; GBM (Gradient based method) and non-GBM. GBM includes SLP, MMFD, and SQP algorithms and the result of GBM were compared with non-GBM result; SA (Simulated Annealing) method. As a result, it was confirmed that SA could yield a global optimization regardless of initial variations. Whereas GBM showed the results were dependent on the initial conditions. And the global optimization could provide a better configuration of gas generator in the design stage. The present study aims at the optimization of gas generator design. Thus optimization methodology was tested with variety of optimization technique applied to the gas generator design with various constraints. Also, the present study compares the results from GBM algorithms with that of SA in order to check the validity of global solution

This paper investigates the basic behavior and performance of simulated\nquantum annealing (QA) in comparison with classical annealing (CA). Three\nsimple one dimensional case study systems are considered, namely a parabolic\nwell, a double well, and a curved washboard. The time dependent Schr\\"odinger\nevolution in either real or imaginary time describing QA is contrasted with the\nFokker Planck evolution of CA. The asymptotic decrease of excess energy with\nannealing time is studied in each case, and the reasons for differences are\nexamined and discussed. The Huse-Fisher classical power law of double well CA\nis replaced with a different power law in QA. The multi-well washboard problem\nstudied in CA by Shinomoto and Kabashima and leading classically to a\nlogarithmic annealing even in the absence of disorder, turns to a power law\nbehavior when annealed with QA. The crucial role of disorder and localization\nis briefly discussed.\n

Although there are several well -known methods such as RCWA, FMM, for analyzing the diffraction properties of gratings, design of these optical elements with specified spectral properties is commonly a challenging problem. It is relatively not easy for the researchers to design narrow line-with diffraction filters based on guided mode resonance phenomenon with common diffraction algorithm. Simulated Annealing (SA) method is evolutionary, robust technique that has been widely utilized to design optical diffraction components. This method is inspired by the physical process of heating and controlled cooling of metal material to increase the size of its crystals and reduce their defects. The most distinctive features of this method lie in its powerful ability of convergence towards the global minimum in a reasonable computation time and the independence of the initial parameter values. In this paper, first, the physical basis of SA and its mathematical realization are introduced. Then, a Guided-Mode Resonant Grating (GMRG) filters with single layer is designed by using SA algorithm. The central wavelength of GMRG filter is locked at 532nm and its line-width is fixed at 1nm. The plane wave light radiates the grating from air cover with normal incidence. The optimized parameters are refractive indices and thicknesses of high and low material of grating, other parameters are grating period and fill factor of the grating. It is shown from our calculation that an excellent reflection spectrum with narrow line-width, high peak and low sideband can be obtained after optimizing the grating parameters. Next, a double layered GMRG filter with line-width of 4nm, which is relatively easy fabrication in experiment, is designed at central wavelength of 1064nm. The optimized parameters are grating period, groove depth, refractive index of waveguide layer and fill factor respectively. The grating substrate and waveguide layer are Sio2 and Hfo2 respectively, the grating structure is directly etched on the waveguide layer. The above grating values should be included in reasonable ranges in consideration of grating fabrication in our experiment condition. It is demonstrated from the calculations with the parameters obtained from SA optimization algorithm that the peak diffraction efficiency is more than 99% at central wavelength 1064nm and the sideband reflection is depressed at the level bellow 5% in a large wavelength range. Moreover, the parameters of a triple layer GMRG filter structure are also provided with this powerful method. Meanwhile, the results found by SA method are compared with RCWA theory.

This paper presents the application of simulated annealing (SA), Tabu search (TS) and hybrid TS---SA to solve a real-world mining optimisation problem called open pit block sequencing (OPBS). The OPBS seeks the optimum extraction sequences under a variety of geological and technical constraints over short-term horizons. As industry-scale OPBS instances are intractable for standard mixed integer programming (MIP) solvers, SA, TS and hybrid TS---SA are developed to solve the OPBS problem. MIP exact solution is also combined with the proposed metaheuristics to polish solutions in feasible neighbourhood moves. Extensive sensitivity analysis is conducted to analyse the characteristics and determine the optimum sets of values of the proposed metaheuristics algorithms' parameters. Computational experiments show that the proposed algorithms are satisfactory for solving the OPBS problem. Additionally, this comparative study shows that the hybrid TS---SA is superior to SA or TS in solving the OPBS problem in several aspects.

In striving to remain competitive in the global market, the concept of optimization of manufacturing processes has been extensively employed to meet the diverse production requirements. Optimization analysis of machining processes is usually based on either minimizing or maximizing certain objective functions. Recently, various non-traditional optimization techniques have evolved to optimize the process parameters of machining processes. The objective of this work is to study the effectiveness of the most commonly used non-traditional optimization methods as applied to a particular machining optimization problem. In this work, surface grinding processes are optimized using i) Particle Swarm Optimization (PSO) ii) Adaptive Genetic Algorithm (AGA) iii) Simulated Annealing (SA) and iv) Memetic algorithm (MA). Memetic algorithm used here has two variations as MA-1 and MA-2, each having the combination of PSO and SA and AGA and SA respectively. The mathematical model of surface grinding operations was adopted from a literature. A computer program was written in Visual C++ for the optimization computations. The computation results of various optimization methods are compared and it is observed that the results of PSO method have outperformed the results of other methods in terms of the combined objective function (COF).