Rotational irrigation scheduling in water-scarce Central Asia is a densely coupled combinatorial problem: soil-moisture memory links each irrigation decision to all later days within a zone, field adjacency couples zones on overlapping window days, and rigid canal rotations quantize water delivery in time. We formulate it as a Quadratic Unconstrained Binary Optimization (QUBO) by linearizing the root-zone water balance, so the quadratic crop-stress objective generates the physical couplings as 2-local Ising interactions with no higher-order terms; only the water-budget constraint requires an artificial all-to-all penalty, which we certify with an instance-adaptive weight bound an order of magnitude tighter than generic prescriptions. Every instance is built from observed data for a cotton district in Khorezm, Uzbekistan: NASA POWER meteorology, FAO-56 Penman--Monteith evapotranspiration, SoilGrids~2.0 hydraulics, measured capillary fluxes, and documented canal-rotation windows that enter as qubit-count reductions. We benchmark four tiers -- exact solvers, matched-budget heuristics, ideal-statevector quantum approximate optimization algorithm (QAOA), and noise-model plus IBM Heron execution -- and add a scaling study on soil instances up to 584 variables. Exact branch-and-bound proves optimality in seconds through 150 variables, and heuristic degradation at fixed evaluation budget is repaired by scaling the budget, so no classical scalability wall appears at deployment-relevant sizes, and none is claimed. On hardware, the informative signal is optimum-sampling enrichment over uniform sampling. We claim no quantum advantage; we deliver a physically grounded, data-complete, reproducible encoding of a societally critical scheduling problem for the quantum-utility era.
Rotational irrigation scheduling in water-scarce Central Asia is a densely coupled combinatorial problem: soil-moisture memory links each irrigation decision to all later days within a zone, field adjacency couples zones on overlapping window days, and rigid canal rotations quantize water delivery in time. We formulate it as a Quadratic Unconstrained Binary Optimization (QUBO) by linearizing the root-zone water balance, so the quadratic crop-stress objective generates the physical couplings as 2-local Ising interactions with no higher-order terms; only the water-budget constraint requires an artificial all-to-all penalty, which we certify with an instance-adaptive weight bound an order of magnitude tighter than generic prescriptions. Every instance is built from observed data for a cotton district in Khorezm, Uzbekistan: NASA POWER meteorology, FAO-56 Penman--Monteith evapotranspiration, SoilGrids~2.0 hydraulics, measured capillary fluxes, and documented canal-rotation windows that enter as qubit-count reductions. We benchmark four tiers -- exact solvers, matched-budget heuristics, ideal-statevector quantum approximate optimization algorithm (QAOA), and noise-model plus IBM Heron execution -- and add a scaling study on soil instances up to 584 variables. Exact branch-and-bound proves optimality in seconds through 150 variables, and heuristic degradation at fixed evaluation budget is repaired by scaling the budget, so no classical scalability wall appears at deployment-relevant sizes, and none is claimed. On hardware, the informative signal is optimum-sampling enrichment over uniform sampling. We claim no quantum advantage; we deliver a physically grounded, data-complete, reproducible encoding of a societally critical scheduling problem for the quantum-utility era.
Efficient irrigation scheduling is a major challenge in precision agriculture due to increasing water scarcity, climate variability, and growing agricultural demand. Conventional irrigation strategies based on fixed thresholds, heuristic rules, or classical optimization techniques often suffer from scalability limitations, inefficient resource allocation, and poor adaptability under dynamic environmental conditions. This paper presents a hybrid quantum-classical optimization framework for intelligent irrigation scheduling using the Quantum Approximate Optimization Algorithm (QAOA). The irrigation decision problem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model integrating soil moisture conditions, irrigation constraints, and water allocation objectives. The proposed framework employs variational quantum optimization to determine optimal irrigation decisions while minimizing unnecessary water consumption. Experimental evaluations conducted using Qiskit-based simulations demonstrate that the proposed QAOA framework successfully generates irrigation decisions fully consistent with classical threshold-based optimization for the evaluated dataset. Comprehensive visualization analyses including soil moisture distribution, irrigation decision mapping, threshold boundary analysis, and water utilization comparison validate the correctness and interpretability of the proposed optimization mechanism. Although the current experimental setup primarily serves as a proof-of-concept validation, the results indicate strong scalability potential for future large-scale agricultural systems involving complex multi-objective optimization constraints. The proposed framework establishes a foundational architecture for future quantum-enabled precision agriculture systems integrating IoT sensing, real-time environmental monitoring, and intelligent resource optimization for sustainable smart farming applications.
This paper presents a Quantum-Optimized Decision Support System (QoDSS) for IoT-driven precision irrigation, addressing critical challenges in water conservation and real-time agricultural monitoring. We propose a hybrid quantum-classical architecture combining soil moisture sensors with the Quantum Approximate Optimization Algorithm (QAOA) to optimize irrigation control. The system dynamically adjusts valve and pump operations based on real-time field data, achieving 61% higher decision accuracy (reducing error from 158% to 62%) compared to classical methods, 58% water savings (310L/day), and complete prevention of waterlogging scenarios (tested up to 95% moisture levels). Field experiments demonstrate reliable operation with 2.1s average decision latency, validated across extreme moisture conditions (10% drought to 95% saturation). Key innovations include: (1) A novel QUBO formulation for moisture optimization (α = 2.3, β = 1.7, γ = 3.0), (2) Edge-quantum integration (RPi4 + IBMQ 5-qubit backend), and (3) Automated anomaly correction. This work provides a practical framework for quantum-IoT solutions in agriculture, demonstrating 38% energy reduction and 95% system reliability in real-world conditions.
Combinatorial optimization problems are typically formulated using Quadratic Unconstrained Binary Optimization (QUBO), where constraints are enforced through penalty terms that introduce auxiliary variables and rapidly increase Hamiltonian complexity, limiting scalability on near term quantum devices. In this work, we systematically study Quadratic Unconstrained D-ary Optimization (QUDO) as an alternative formulation in which decision variables are encoded directly in higher dimensional Hilbert spaces. We demonstrate that QUDO naturally captures structural constraints across a range of problem classes, including the Traveling Salesman Problem, two variants of the Vehicle Routing Problem, graph coloring, job scheduling, and Max-K-Cut, without the need for extensive penalty constructions. Using a qudit-level implementation of the Quantum Approximate Optimization Algorithm (qudit QAOA), we benchmark these formulations against their binary QUBO counterparts and exact classical solutions. Our study show consistently improved approximation ratios and substantially reduced computational overhead at comparable circuit depths, highlighting QUDO as a scalable and expressive representation for quantum combinatorial optimization.
Real-time control of a compact spherical-tokamak breeder poses, at several points, a combinatorial-optimization problem inside a control cycle: which actuators to schedule, how to lay out a discrete blanket, and — the control-relevant case — how to sequence poloidal- and toroidal-field coil currents under hard constraints while tracking a shape and vertical-position target. Because these problems are naturally binary and quadratic, they are the canonical near-term target for quantum optimization, and it is a fair, testable question whether a quantum processor solves them faster or better than a classical one. This paper answers that question with a formal treatment and a pre-registered result. We derive compact quadratic-unconstrained-binary-optimization (QUBO) encodings for all three problems from first principles — pulse cadence as a number-partitioning Ising model, blanket layout as a penalty-embedded assignment, and coil-current/actuator scheduling as a fixed-point-encoded quadratic tracking objective built on the free-boundary equilibrium shape-response Jacobian — and map each to two fault-tolerant primitives, a depth-three quantum approximate optimization ansatz (QAOA, p=3) and a D\"urr–Hyer Grover minimum-finder. At the frozen breeder design point (I_p=9.66 MA, Q=3.076, P_fus=85.04 MW, negative triangularity δ=-0.30, B_0=8 T, κ=2.0, =1.20 m, aspect ratio A=2.5, centrepost peak field 16.84 T) the design-scale instances need 23–61 logical qubits and 5×10^3–5.5×10^7 T-gates, verified against the Fowler surface-code and D\"urr–Hyer formulas across 50 resource rows with zero discrepancies. On the question of whether quantum hardware helps, we report an explicit negative: classical simulated annealing matches or beats QAOA on all three breeder QUBOs out to n=120 variables; the exact-to-heuristic crossover sits at n=12–16 (exact optima in 0.03–292 s of wall time); the QAOA approximation ratio plateaus at 0.90–0.95 and the circuits become classically unverifiable past n≈24; and a fleet-scale (n=120) Grover formulation would need 1.8×10^18 oracle calls and 1.2×10^23 T-gates — a resource boundary, not a route. We therefore place variational quantum reinforcement learning for shape and vertical-position control on a dated, benchmark-gated schedule: a quantum policy is admitted only if it meets or beats the classical controller at equal wall-clock with a control-barrier-certified safety filter held inviolate. All quantum and classical runs were carried out on the NVIDIA GPU HPC campaign. The deliverable is the honest, resource-grounded map of where quantum computing does — and does not — pay for real-time fusion control. Key results (frozen anchors): N_T = 1.2 ×10^23. Methods & codes: FreeGSNKE, FreeGS, Sauter, QAOA, VQE, ADAPT-VQE. Live verification: 4 gate validator(s) with live-recompute cards (2 reproduced, 1 revised, 1 estimated). See the Verification section and data/verification.csv. Related: Paper page · De-risking register · 3D model · Learn more about Kronos Part of the 2026 Kronos publication series; independently re-run and stamped in the Kronos de-risking register (DOI 10.5281/zenodo.22645689). All numerical values are frozen design-point anchors; see the register. Public research artifact. No proprietary, financial, or supply-chain information is included.
Heterogeneous HPC workflow scheduling under multiple hard constraints poses a challenging combinatorial optimization problem. Classical exact solvers provide optimal solutions but often face scalability limitations, motivating interest in quantum-inspired Quadratic Unconstrained Binary Optimization (QUBO) formulations as alternative optimization paradigms. This work presents a systematic and reproducible empirical evaluation of QUBO-based scheduling methods against established classical baselines, including MILP, CP-SAT, GA, and HEFT. We evaluate three QUBO variants, single-run simulated annealing, multi-attempt annealing, and a layered QAOA-inspired schedule, together with hybrid enhancement strategies on both ground-truth validation workflows (3–4 tasks) and synthetic scaling instances (5–20 tasks). All solvers are assessed through a unified evaluation pipeline that explicitly tracks feasibility, makespan, and resource utilization under progressive constraint activation and controlled penalty sweeps. Results show that all approaches recover the expected optimal makespan on validation instances, confirming formulation correctness. However, feasibility degradation emerges for specific QUBO variants as constraint interactions intensify, particularly when communication costs are introduced. Penalty sensitivity analysis reveals a sharp feasibility threshold for QUBO-SA, where insufficient penalties consistently fail and moderate-to-strong penalties restore feasibility. Scaling experiments delineate the regimes in which classical solvers and heuristics remain robust across all tested sizes, while QUBO-SA loses feasibility beyond 15 tasks and the QAOA-inspired variant beyond 10 tasks. Overall, the study provides a clear empirical characterization of the reliability boundaries of quantum-inspired QUBO formulations for heterogeneous HPC scheduling and identifies the regimes where classical approaches remain preferable under current formulations and solver capabilities.
Large-scale combinatorial scheduling problems -- job-shop scheduling, flow-shop scheduling, and vehicle routing among them -- remain NP-hard at practically relevant scale, and quantum computing has entered this space along two related tracks: genuinely quantum solvers, principally quantum annealers and gate-based devices running the quantum approximate optimization algorithm (QAOA), and quantum-inspired classical solvers, such as coherent Ising machines and digital annealers, that borrow the same Ising/QUBO problem structure without requiring quantum hardware. This article synthesizes both tracks as applied specifically to scheduling. We trace the theoretical foundations from quantum and simulated annealing through the QUBO formulation techniques that make scheduling problems solver-ready, then review direct applications to job-shop, flow-shop, and vehicle-routing problems, reporting the concrete, verified numbers the underlying studies provide. The consistent finding is that quantum hardware remains constrained by qubit connectivity, embedding overhead, and shallow achievable circuit depth to small benchmark instances, while quantum-inspired classical solvers, unconstrained by qubit count, already reach scheduling-relevant problem sizes with reported performance competitive with or exceeding classical heuristics. We close by identifying benchmarking rigor, hardware connectivity, and the near-total absence of work on dynamic, online scheduling as the field's clearest open problems.