We study a proof-of-concept workflow that reformulates planar inverse kinematics (IK) for robotic manipulators as a Quadratic Unconstrained Binary Optimization (QUBO) using a linear binary discretization of joint angles and one-hot (big-M) constraints, and then solves the QUBO with quantum annealing on D-Wave hardware. We (i) define and report time-to-solution (TTS) rigorously, (ii) evaluate solution accuracy back in the original IK space via end-effector error and feasibility of one-hot constraints, and (iii) analyze embedding choices on Pegasus/Zephyr. On the tested two-link planar IK instances, Global Embedding on Zephyr uses fewer physical qubits and yields shorter access times than alternatives (see Tables 1,2), and a hybrid quantum-classical solver achieves lower TTS than classical QUBO baselines at larger Q sizes (see Figure 6). These results do not claim superiority over state-of-the-art continuous IK solvers; rather, they demonstrate that an IK-to-QUBO mapping can be executed on current quantum annealing systems with quantified accuracy and runtime, clarifying where such an approach may be useful as hardware improves.
We study a proof-of-concept workflow that reformulates planar inverse kinematics (IK) for robotic manipulators as a Quadratic Unconstrained Binary Optimization (QUBO) using a linear binary discretization of joint angles and one-hot (big-M) constraints, and then solves the QUBO with quantum annealing on D-Wave hardware. We (i) define and report time-to-solution (TTS) rigorously, (ii) evaluate solution accuracy back in the original IK space via end-effector error and feasibility of one-hot constraints, and (iii) analyze embedding choices on Pegasus/Zephyr. On the tested two-link planar IK instances, Global Embedding on Zephyr uses fewer physical qubits and yields shorter access times than alternatives (see Tables 1,2), and a hybrid quantum-classical solver achieves lower TTS than classical QUBO baselines at larger Q sizes (see Figure 6). These results do not claim superiority over state-of-the-art continuous IK solvers; rather, they demonstrate that an IK-to-QUBO mapping can be executed on current quantum annealing systems with quantified accuracy and runtime, clarifying where such an approach may be useful as hardware improves.
We benchmark current annealing-based optimization workflows on a greenhouse-inspired quadratic unconstrained binary optimization problem for binary heater scheduling, where the horizon H denotes the number of hourly control decisions. For the main one-day instance (H=24), all solver outputs are decoded back into heater schedules and evaluated in the original greenhouse simulator using the same physical objective and feasibility criterion. Classical simulated annealing and path-integral simulated quantum annealing produce feasible near-optimal solutions in all repetitions, with best objectives close to the exact optimum. In contrast, the tested D-Wave Leap Hybrid BQM workflow is less reliable and does not outperform the classical baselines under 15--60~s requested time limits. Direct D-Wave QPU execution on reduced instances remains feasible in all runs and recovers the exact optimum for H=10 and H=12, but the exact-hit rate drops from 5/10 to 2/10 and then to 0/10 at H=14, with substantially higher variance than the classical baselines. The results do not indicate quantum advantage, but provide a reproducible, physically decoded benchmark that exposes the current strengths and limitations of classical, hybrid, and direct quantum annealing workflows on structured control QUBOs.
Quantum computing has gained attention for its potential to surpass classical computing in large-scale computations. In this study, we propose a method for solving the inverse kinematics of a robot using quantum computing. The approach leverages the ability of qubits to represent points on a sphere in three-dimensional space. Forward kinematics calculations are performed using qubits that encode the posture of each robot link, while inverse kinematics solutions are obtained through iterative optimization on a classical computer. Furthermore, we demonstrate that the robot's end-effector position can be effectively represented using a 2-qubit rotation gate, where the root joint angle influences the tip joint angle, resulting in accelerated convergence during inverse kinematics optimization. The proposed method was validated on an actual quantum computer, confirming its feasibility and efficiency. These findings suggest that hybrid quantum-classical approaches can enhance robotic motion planning and optimization in future quantum computing applications.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.
Abstract We benchmark classical, simulated-quantum, hybrid, and direct quantum-annealing workflows on a structured binary control problem formulated as a quadratic unconstrained binary optimization (QUBO) model. The benchmark is motivated by greenhouse heater scheduling, where the horizon (H) denotes the number of hourly binary control decisions, but the focus is on solver behavior for a physically decoded control-QUBO formulation. For the main one-day instance ((H=24)), all solver outputs are decoded back into heater schedules and evaluated using the same simulator-side objective and feasibility criterion. Classical simulated annealing and path-integral simulated quantum annealing produce feasible near-optimal solutions in all repetitions, with best objectives close to the exact optimum. In contrast, the tested D-Wave Leap Hybrid binary quadratic model workflow is less reliable and does not outperform the classical baselines under 15--60 s requested time limits. Direct D-Wave quantum processing unit execution on reduced instances remains feasible in all runs and recovers the exact optimum for (H=10) and (H=12), but the exact-hit rate decreases with increasing horizon. The results do not indicate quantum advantage, but provide a reproducible benchmark for evaluating annealing-based natural and quantum computing workflows on structured control QUBOs. MSC Classification: 90C27 , 90C59 , 81P68 , 93C55
Abstract It has been demonstrated that Binary Integer Programming (BIP) formulations can be reformulated to a corresponding quadratic unconstrained binary optimization (QUBO) problem. The reformulation allows for BIPs to run as QUBOs on adiabatic quantum annealing hardware. Current BIP to QUBO reformulation techniques propagate dense QUBO structures that are not ideal for current hardware where quantum bits, and the connections between them, are scarce. We propose a methodology for BIP to QUBO reformulation that results in a sparse QUBO that, when used to embed set-partitioning problems onto a D-Wave Pegasus topology, requires 80% fewer qubits and is embedded is 41 times faster. The same methodology for set-covering problems requires 77% fewer qubits and is embedded 26 times faster. We discuss the limitations of the technique and avenues for future extensions.