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arXiv:2510.04946 · Physical Review A

Leveraging analog neutral-atom quantum computers for diversified pricing in hybrid column-generation frameworks

Cédrick Perron, Yves Bérubé-Lauzière, Victor Drouin-Touchette

Published Jan 27, 2026• 1 citation
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Abstract

In this work, we develop new pulse designs and embedding strategies to improve the analog quantum subroutines of hybrid column generation (CG) algorithms based on neutral-atoms quantum computers (NAQCs). These strategies are designed to improve the quality and diversity of the samples generated. We apply these to an important combinatorial optimization (CO) problem in logistics, namely the fleet assignment. Depending on the instance tested, our quantum protocol has a performance that is either comparable or worse than the best classical method tested, both in terms of the number of iterations and final objective value. We identify the cause of these suboptimal solutions as a result of our quantum protocol often generating high-quality but degenerate samples. We address this limitation by introducing a greedy post-processing technique, Make\_Diff, which applies bit-wise modifications to degenerate samples in order to return a non-degenerate set. With this modification, our quantum protocol becomes competitive with an exact solver for the subproblem, all the while being resilient to state preparation and measurements (SPAM) errors. We also compare our CG scheme with a Gurobi solver and find that it performs better on over 50\% of our synthetic instances and that, despite Gurobi having a more extensive runtime. These improvements and benchmarks herald the potential of deploying hybrid CG schemes on NISQ devices for industrially relevant CO problems.

DOI
10.1103/9bsf-gb5v

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•Oct 20, 2026•0 citations
In this work, we develop new pulse designs and embedding strategies to improve the analog quantum subroutines of hybrid column generation (CG) algorithms based on neutral-atoms quantum computers (NAQCs). These strategies are designed to improve the quality and diversity of the samples generated. We apply these to an important combinatorial optimization (CO) problem in logistics, namely the fleet assignment. Depending on the instance tested, our quantum protocol has a performance that is either comparable or worse than the best classical method tested, both in terms of the number of iterations and final objective value. We identify the cause of these suboptimal solutions as a result of our quantum protocol often generating high-quality but degenerate samples. We address this limitation by introducing a greedy post-processing technique, Make_Diff, which applies bit-wise modifications to degenerate samples in order to return a non-degenerate set. With this modification, our quantum protocol becomes competitive with an exact solver for the subproblem, all the while being resilient to state preparation and measurements (SPAM) errors. We also compare our CG scheme with a Gurobi solver and find that it performs better on over 50% of our synthetic instances and that, despite Gurobi having a more extensive runtime. These improvements and benchmarks herald the potential of deploying hybrid CG schemes on NISQ devices for industrially relevant CO problems.
In this work we present a complete hybrid classical-quantum algorithm involving a quantum sampler based on neutral-atom platforms. This approach is inspired by classical column-generation frameworks developed in the field of operations research and shows how quantum procedures can assist classical solvers in addressing hard combinatorial problems. We benchmark our method on the minimum vertex coloring problem and show that the proposed hybrid quantum-classical column-generation algorithm can yield good solutions in relatively few iterations. We compare our results with state-of-the-art classical and quantum approaches.
Neutral atom quantum computers (NAQCs) have emerged as a promising platform for solving the maximum weighted independent set (MWIS) problem. However, analog quantum approaches face two key limitations: constraints of the atomic layout on realizable graph geometries and the absence of performance guarantees. We introduce Lp-Quts, a hybrid quantum-classical framework that integrates an NAQC sampler into a classical cutting-plane algorithm. At each iteration, a relaxed linear program (RLP) bounds the MWIS and induces a reduced graph from which independent sets are sampled using an analog quantum sampler. A novel sample-informed separation problem guides odd-cycle cut selection and accelerates convergence. For t-perfect graphs, Lp-Quts inherits polynomial-time convergence guarantees from the classical theory of cutting planes. We evaluate our approach on instances with up to 300 vertices -- a scale that exceeds the capabilities of current NAQC hardware. In this regime, Lp-Quts reaches solutions within 5--10\% of optimality, outperforming direct analog quantum protocols and greedy baselines under equal sampling budgets. As expected, simulated annealing remains the strongest sample-based solver at this scale. These results demonstrate how quantum samplers can be effectively embedded within classical optimization frameworks to deliver near-optimal solutions with reduced quantum resources while preserving formal guarantees.
Efficient end-to-end entanglement distribution in quantum information networks requires routing under limited resources and fidelity constraints. We study entanglement routing as a fidelity-constrained unsplittable multicommodity flow problem that maximizes the number of admitted requests. As a proof of concept, we integrate neutral-atom quantum optimization into a hybrid classical--quantum column-generation framework. A classical restricted master problem selects routes, while a pricing problem generates fidelity-feasible paths. We formulate this NP-hard constrained shortest-path pricing problem as a quadratic unconstrained binary optimization (QUBO) problem and address it with hardware-aware register embedding and instance-driven pulse shaping. To our knowledge, this is the first study of neutral-atom quantum optimization as a pricing oracle for fidelity-constrained entanglement routing. On small benchmark instances evaluated with neutral-atom processor emulators, the method, combined with warm-start and post-processing, achieves an optimality gap below 1% across all tested sizes; the selected simulated-annealing route-generation baseline exhibits gaps of up to 6%. These results indicate that the generated bitstrings can provide useful candidate routes for classical refinement within column generation. This proof of concept does not establish quantum utility or scalability; further evaluation on larger instances, against stronger classical baselines, and on quantum hardware is needed.
Over the past decades, the operations research community has developed numerous effective optimization algorithms, yet quantum computing is emerging as a new computational paradigm with the potential to approach optimization problems more efficiently. Grover's algorithm offers a provable speedup for combinatorial optimization, but its circuit depth places it beyond current noisy intermediate-scale quantum (NISQ) devices. A more accessible alternative is to reformulate the optimization problem as a quadratic unconstrained binary optimization (QUBO) problem and apply quantum annealing; however, practical problem instances remain out of reach for existing hardware. We introduce AtomTreeSearch, a hybrid classical-quantum algorithm that integrates a quantum subroutine natively implementable on neutral-atom quantum computers within a Monte Carlo Tree Search framework. At each expansion step, a maximal weighted independent set of candidate actions provided by the quantum processor is selected, and these collective actions are performed to obtain a child node. We benchmark our method on the Traveling Salesman Problem, with instances of up to 60 cities on random Euclidean instances and up to 100 cities on TSPLIB instances. Our hybrid algorithm generally matches or outperforms both OR-Tools and simulated annealing on these instances, and we find that the quantum subroutine produces more diverse and higher-quality branches compared to classical alternate subroutines. These results suggest that carefully scoped quantum subroutines embedded in classical search frameworks represent a promising path toward near-term quantum utility in combinatorial optimization.
Combinatorial optimization is a challenging problem applicable in a wide range of fields from logistics to finance. Recently, quantum computing has been used to attempt to solve these problems using a range of algorithms, including parameterized quantum circuits, adiabatic protocols, and quantum annealing. These solutions typically have several challenges: 1) there is little to no performance gain over classical methods; 2) not all constraints and objectives may be efficiently encoded in the quantum ansatz; and 3) the solution domain of the objective function may not be the same as the bit strings of measurement outcomes. This work presents “nonnative hybrid algorithms”: a framework to overcome these challenges by integrating quantum and classical resources with a hybrid approach. By designing nonnative quantum variational anosatzes that inherit some but not all problem structure, measurement outcomes from the quantum computer can act as a resource to be used by classical routines to indirectly compute optimal solutions, partially overcoming the challenges of contemporary quantum optimization approaches. These methods are demonstrated using a publicly available neutral-atom quantum computer on two simple problems of Maxkkk-Cut and maximum independent set. We find improvements in solution quality when comparing the hybrid algorithm to its “no quantum” version, a demonstration of a “comparative advantage.”
Abstract: Global logistics networks, intercontinental air-freight consolidators, and maritime energy fleets continuously solve large-scale Mixed-Integer Linear Programs (MILPs) such as the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and multi-vessel Maritime Inventory Routing Problems (MIRP). When weather disruptions, port congestion, or geopolitical airspace closures invalidate baseline schedules, classical branch-and-cut solvers (Gurobi, CPLEX) experience exponential worst-case tree growth on subproblems exceeding 2,000 binary decision variables, often failing to converge within strict 5-to-15-minute operational re-dispatch windows. Conversely, current Noisy Intermediate-Scale Quantum (NISQ) processors remain limited to 100-to-1,000 physical qubits with finite two-qubit gate fidelity (99.2%−99.8%99.2\%-99.8\%99.2%−99.8%), preventing direct encoding of full enterprise logistics instances. This paper presents a production-grade Quantum-Classical Hybrid Cloud Architecture that bridges enterprise Kubernetes clusters with co-located quantum processing units (QPUs) via AWS Braket Hybrid Jobs and IBM Quantum Qiskit Runtime primitives. Our framework applies Benders and Dantzig-Wolfe column generation on classical cloud HPC nodes to decompose a 25,000-variable global fleet MILP into a continuous master problem and hard combinatorial pricing/routing subproblems of 60 to 140 binary variables. These subproblems are transformed into Quadratic Unconstrained Binary Optimization (QUBO) and Ising Hamiltonians, warm-started from classical linear programming (LP) relaxations (WS-QAOA), compiled with dynamical decoupling and Zero-Noise Extrapolation (ZNE), and executed inside co-located QPU-CPU sessions while a GPU-accelerated Simulated Bifurcation (SB) digital annealer runs in parallel as a deterministic SLA fallback. Evaluated on disruption recovery workloads modeled on ExxonMobil maritime LNG routing and DHL Global Forwarding air-cargo container loading, our hybrid WS-QAOA + Column Generation workflow improves optimality gap closure at a 10-minute SLA cutoff from 6.84% (classical branch-and-bound alone) to 1.42%, reduces emergency re-routing compute wall-clock time by 61.5%, and cuts fleet fuel and charter penalty costs by 4.7%. Research Domain & Specialization Track Master of Science in Information Technology (MSIT) — Quantum Cloud Computing, Hybrid Orchestration, and Operations Research. Core Technical Highlights Empirical Production Case Studies: Rigorous architectural blueprints and telemetry evaluation across enterprise cloud deployments. Four-Tier Reference Architecture: Formal specification from edge ingress to distributed hardware execution pools. Mathematical Formulation: Formally derived algorithmic and optimization models with closed-loop verification. Multi-Modal Benchmarking: Comparative empirical baselines under fault-injection and synthetic workload scaling. Author Information Author: Sonu Kumar SinghRole: Senior Consultant Affiliation: Independent Researcher Publication Status: Preprint / Working Paper (MSIT AI & Cloud Systems Research Series) Reproducibility & Open Science All included architecture diagrams, telemetry schemas, and benchmark curves are open-access under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.