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arXiv:2609.00861

Low-Thrust Trajectory Optimization with Quantum Computing and Sequential Convex Programming

Carmine Giordano

Published Sep 1, 2026• 0 citations
arXivHTMLPDF

Abstract

Low-thrust trajectory optimization is a central task in interplanetary mission design, but its nonlinear dynamics and operational constraints often lead to challenging non-convex optimal-control problems. Sequential convex programming has emerged as an effective approach to address these problems, while quantum annealing offers a complementary paradigm for solving quadratic unconstrained binary optimization problems. This paper introduces quSCP, a quantum-based sequential convex programming framework that reformulates each convex subproblem as a quadratic unconstrained binary optimization problem suitable for quantum and hybrid quantum--classical solvers. Equality, inequality, and trust-region constraints are embedded through quadratic penalty terms, while an iterative refinement strategy is used to reduce the accuracy loss introduced by binary discretization. The method is assessed on a fuel-optimal Earth--Mars low-thrust transfer by comparing standard sequential convex programming, a continuous quadratic unconstrained formulation, direct quantum processing unit sampling, and D-Wave hybrid solvers. Results show that quSCP produces physically consistent trajectories with propellant consumption and nonlinear constraint violations close to classical benchmarks. Direct quantum annealing is feasible only for small instances because of embedding overhead and hardware connectivity limits, whereas hybrid solvers scale to larger discretizations. Although no computational quantum advantage is demonstrated with current hardware, the results show that quantum and hybrid quantum--classical optimization can already provide competitive solutions for demanding trajectory design problems.

DOI
10.48550/arxiv.2609.00861

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Low-thrust trajectory optimization is a central task in interplanetary mission design, but its nonlinear dynamics and operational constraints often lead to challenging non-convex optimal-control problems. Sequential convex programming has emerged as an effective approach to address these problems, while quantum annealing offers a complementary paradigm for solving quadratic unconstrained binary optimization problems. This paper introduces quSCP, a quantum-based sequential convex programming framework that reformulates each convex subproblem as a quadratic unconstrained binary optimization problem suitable for quantum and hybrid quantum--classical solvers. Equality, inequality, and trust-region constraints are embedded through quadratic penalty terms, while an iterative refinement strategy is used to reduce the accuracy loss introduced by binary discretization. The method is assessed on a fuel-optimal Earth--Mars low-thrust transfer by comparing standard sequential convex programming, a continuous quadratic unconstrained formulation, direct quantum processing unit sampling, and D-Wave hybrid solvers. Results show that quSCP produces physically consistent trajectories with propellant consumption and nonlinear constraint violations close to classical benchmarks. Direct quantum annealing is feasible only for small instances because of embedding overhead and hardware connectivity limits, whereas hybrid solvers scale to larger discretizations. Although no computational quantum advantage is demonstrated with current hardware, the results show that quantum and hybrid quantum--classical optimization can already provide competitive solutions for demanding trajectory design problems.
Abstract This study employed a quantum-annealing framework to solve spacecraft trajectory optimization problems. Quantum annealing belongs to the field of quantum computing and is a promising technique for tackling hard binary optimization problems by employing quantum annealers. To address the optimal control of a trajectory using quantum annealing, a transcription procedure was introduced to express the problem in the binary optimization form required. The proposed procedure leverages the pseudospectral method to discretize the trajectory and represents the dynamical constraints as algebraic equality constraints at specific nodes. Subsequently, both a linearization procedure and binary representation strategy for the real-valued variables of the problem were presented, leading to the quadratic binary unconstrained optimization form. The quantum-annealing-based method was tested in the context of an interplanetary low-thrust transfer from the Earth to Mars. First, we discussed which instances of the problem, especially in terms of their dimensions, are implementable on currently available quantum annealers; then, a solution was sought by employing annealers from D-Wave systems. Solutions from hybrid solvers that combine classical and quantum resources, and fully quantum solvers were explored. The results demonstrate the validity of the transcription approach, demonstrate the ability of the hybrid solver to tackle the case-study problem, and highlight the promising features and current limitations of practical trajectory optimization with quantum annealing.
Quantum annealing is a recent advancement in the field of optimization metaheuristics. Quantum annealers such as the D-Wave machines are primarily designed for solving discrete optimization problems. Solving nonlinear continuous optimization problems is also a very challenging task, in particular when nonconvex functions and multiple local optima are involved; nevertheless, convex problems can be solved efficiently using standard classical methods. It has not been explored in sufficient detail how quantum annealing could help in solving continuous optimization problems. In this work, we develop a prototype quantum-inspired solver for nonlinear continuous optimization problems. The solver is hybrid, as it has two pathways - classical and quantum-inspired. Given a continuous optimization problem via the web-based graphical interface that enables users to define and edit optimization problems, our solver computes a nonconvexity index for the problem, which determines the solution pathway. Problems with low nonconvexity indices are sent through the classical pathway and solved by standard separable programming techniques, while the others are transformed into mixed integer linear programming (MILP) problems via separable reformulations, which are restated as quadratic unconstrained binary optimization (QUBO) problems - the problem format compatible for quantum annealers, and eventually sent through the quantum pathway using D-Wave’s Neal sampler.
Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits. Quantum annealers can, in principle, accelerate the solution of problems formulated as quadratic unconstrained binary optimization instances, but their limited scale currently prevents achieving practical speedups. Quantum-classical algorithms have been proposed to take advantage of both paradigms and to allow current quantum computers to be used in larger problems. In this work, a hardware-agnostic Benders' decomposition algorithm and a series of enhancements with the goal of taking the most advantage of quantum computing are presented. The decomposition consists of a master problem with integer variables, which is reformulated as a quadratic unconstrained binary optimization problem and solved with a quantum annealer, and a linear subproblem solved by a classical computer. The enhancements consist, among others, of different embedding processes that substantially reduce the pre-processing time of the embedding computation without compromising solution quality, a conservative handling of cut constraints, and a stopping criterion that accounts for the limited size of current quantum computers and their heuristic nature. The proposed algorithm is benchmarked against classical approaches using a D-Wave quantum annealer for a scalable family of transmission network expansion planning problems.
Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that approximates solutions to unconstrained quadratic programs via a sequence of QUBO instances. Rather than encoding real variables as binary vectors, QCQO implicitly represents them using continuous QUBO weights and iteratively refines the solution by summing sampled vectors. This allows flexible control over the number of binary variables and adapts well to hardware constraints. We prove convergence properties, introduce a step size adaptation scheme, and validate the method on linear regression. Experiments with simulated and real quantum annealers show that QCQO achieves accurate results with fewer qubits, though convergence slows on noisy hardware. Our approach enables quantum annealing to address a wider class of continuous problems.
Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that approximates solutions to unconstrained quadratic programs via a sequence of QUBO instances. Rather than encoding real variables as binary vectors, QCQO implicitly represents them using continuous QUBO weights and iteratively refines the solution by summing sampled vectors. This allows flexible control over the number of binary variables and adapts well to hardware constraints. We prove convergence properties, introduce a step size adaptation scheme, and validate the method on linear regression. Experiments with simulated and real quantum annealers show that QCQO achieves accurate results with fewer qubits, though convergence slows on noisy hardware. Our approach enables quantum annealing to address a wider class of continuous problems.
Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling problems, have been applied to automate this process, solving large-scale production planning problems remains computationally demanding. Moreover, many practical scenarios involve conflicting objectives, making traditional scalarization techniques ineffective in finding diverse and useful Pareto-optimal solutions. To address these challenges, we developed a quantum-classical hybrid algorithm that decomposes the problem into two subproblems: resource allocation and task scheduling. Resource allocation is formulated as a quadratic unconstrained binary optimization problem and solved using annealing-based methods that efficiently explore complex solutions. Task scheduling is modeled as a mixed-integer linear programming problem and solved using conventional solvers to satisfy detailed scheduling constraints. We validated the proposed method using benchmark instances based on foundry production scenarios. Experimental results demonstrate that our hybrid approach achieves superior solution quality and computational efficiency compared to traditional monolithic methods. This work offers a promising direction for high-speed, multi-objective scheduling in industrial applications.