Source-linked AI summary
A Backend-Agnostic MWIS Kernel for Stochastic Unit Commitment with Neutral-Atom Hardware Validation
Jiying Chen, Min Lin, Jingwei Wen, Zhihong Zhang, Chuixiong Wu
TL;DR
Stochastic unit commitment requires solving a large combinatorial commitment problem while recovering feasible continuous dispatch, but existing quantum workflows do not provide this full operational bridge. This paper compiles valid commitment moves into MWIS, uses classical LP repair, and deploys the representation on QuEra Aquila. Across 15 days at 50 nodes, refined hardware solutions match or exceed exact-MWIS dispatch margins, while scaling to 144 nodes exposes full-array validity as the main bottleneck.
Problem
Stochastic unit commitment has a combinatorial on/off layer over a large search space, while practical quantum workflows still require hardware-compatible encoding and feasible dispatch recovery.
Method
The paper compiles locally valid commitment moves into a weighted conflict-graph MWIS problem, solves it on Aquila, and applies classical LP repair with optional simulated-annealing refinement.
Results
Mean dispatch margin was £12,458 for AHS+SA versus £12,358 for exact MWIS+LP across 15 days at N = 50, with hardware matching or exceeding the exact baseline every day.
Takeaways & Limitations
The backend-agnostic MWIS interface connects industrial UC decisions to neutral-atom hardware while preserving classical feasibility recovery and supporting other graph-based backends.
Takeaways & Limitations
At larger scale, valid-shot rate falls from 0.720 at N = 50 to 0.095 at N = 100, making full-array validity rather than field-of-view occupancy the binding AHS scale limit.
Abstract
from arXiv · showhide
Quantum hardware is beginning to address structured combinatorial optimisation, but two steps still block practical use: mapping real operational models onto hardware-compatible instances, and converting noisy hardware output back into feasible decisions. Here we introduce a backend-agnostic computational interface that compiles the discrete decision layer of stochastic unit commitment into a move-based maximum-weight independent set (MWIS) problem, while retaining continuous dispatch and feasibility recovery in the classical computational layer. We validate the approach in a green hydrogen scheduling setting and deploy it on the QuEra Aquila neutral-atom quantum processor. This is the first end-to-end industrial scheduling workflow that connects real operational decisions to programmable neutral-atom hardware through a solver-agnostic MWIS representation. Across a 15-day hardware campaign on 50-node instances, hardware-generated solutions after classical refinement match or exceed the dispatch margins obtained from exact MWIS on every day. When scaling to 144 nodes, encoding quality remains stable, while the probability that the full atom array survives, rather than graph embedding, emerges as the dominant bottleneck to further scaling. Together, these results establish a hardware-compatible computational pathway toward larger problem scales, and lay the groundwork for exploring regimes in which exact classical optimisation may no longer scale efficiently.
1 Introduction
Stochastic unit commitment combines a combinatorial on/off layer with continuous dispatch under uncertainty, creating a large infeasible search space. The paper addresses this by compiling valid schedule moves into a weighted conflict graph that can be solved across hardware backends and repaired classically.
- Motivation: For N = 6 and T = 24, the naive binary search space is approximately 2.2 × 10^43 configurations, most infeasible under production and inventory constraints.The commitment layer is combinatorial, while dispatch remains a continuous program.
- Industrial setting: The industrial case is a six-module green-hydrogen electrolyser park under stochastic wind and solar supply, with coupled production, storage, delivery, and impurity constraints.The park provides reference schedules, duals, and dispatch data for the stochastic UC kernel.
- Hardware embedding: Two-row folding embeds the 24-hour instance within Aquila’s field of view without gadget overhead, while greedy post-processing repairs broken inter-row edges.The layout places each eligible move at a distinct module-hour cell with King-grid conflicts.
- Computational interface: The kernel builds locally valid schedule moves from one feasible commitment, assigns them LP-derived weights, selects compatible moves through MWIS, and validates the result with classical LP repair.This move-based representation resembles local branching but compiles the neighborhood into a weighted conflict graph.
- Backend portability: The same weighted conflict-graph representation supports Aquila analog Hamiltonian simulation, quantum annealing, and coherent Ising machines.MWIS is native to unit-disk Rydberg arrays, while QUBO-style backends can use the shared graph representation.
- End-to-end validation: The paper reports a closed UC→MWIS→Aquila→100-scenario LP-repair workflow, with hybrid hardware and simulated-annealing refinement evaluated against exact MWIS.The contribution targets an end-to-end industrial scheduling workflow rather than an isolated graph benchmark.
2 Methods — Architecture
The kernel compiles a feasible stochastic-UC reference schedule into a weighted conflict graph of local moves, then uses exact or hardware graph solving followed by classical refinement and LP repair. Its architecture separates solver-independent compilation and validation from the backend-specific graph-solving step.
- Reference schedule and move generation: A feasible reference commitment is perturbed using six local move types spanning de-commitment, swaps, exchanges, delete/insert operations, and clustered-integer adjustments.Each move specifies slots to switch off and slots to switch on.
- LP-dual scoring: One classical stochastic LP solve supplies dual values that score every move as a first-order estimate of its effect on the LP objective.The score uses coupling information from electricity cost, tank inventory, grid load, delivery contracts, and terminal conditions, and outperformed a naive electricity-price proxy that achieved 35% sign agreement.
- Pruning and graph construction: Diversity top-k pruning retains the 50 highest-absolute-score moves while limiting concentration on any module-hour slot.This produces a spread of candidate perturbations for graph optimisation rather than redundant variants.
- Pruning and graph construction: The retained moves form a conflict graph whose nodes carry LP-dual weights and whose edges connect moves touching a shared module-hour slot.HiGHS solves the resulting MWIS exactly, while AHS uses the same move nodes on a King-graph unit-disk layout to approximate the objective.
- Refinement and validation: The selected moves are refined with simulated annealing, applied to the reference schedule, and checked by a 100-scenario stochastic LP repair for feasibility and realised margin.The repair LP is read-only and is not used during move generation or MWIS selection.
- Backend adaptation: The backend-agnostic interface makes only graph solving backend-dependent, while move generation, LP-dual scoring, pruning, and simulated-annealing refinement remain common across solvers.The embedding compresses a fully populated 24-hour, six-module instance from 120 µm to 55 µm in x and fits within Aquila’s 75 µm field of view; post-processing removes lower-weight endpoints of broken edges and retains a mean 94.0% of the ex...
3 Results
The Aquila workflow was evaluated through inner-kernel, total-kernel, hardware-validity, parameter-sweep, and scaling experiments. Classical refinement recovered strong dispatch performance, while full-array shot validity—not embedding geometry—limited larger instances.
- Encoding quality: Rank 3, not rank 1, was the best encoding rank in the N = 12 exact-diagonalisation study, with the target state appearing within the bottom-10 eigenstates.The best-achieved rank occurred in a narrow encoding window near the freeze point.
- Experimental setup: 15 hardware days used identical AHS parameters and pipeline configuration for 50-node, 200-shot tasks, with all scheduled days completing successfully.Dispatch validation used a 100-scenario stochastic LP repair.
- Inner-kernel performance: 0.940 was the mean AHS-post ratio across 15 days, with a 0.748 minimum and 1.000 maximum; every day exceeded the 0.60 viability threshold.The weakest ratio occurred on Day 2, while Day 7 had the lowest valid-shot rate but recovered to 0.808 after post-processing.
- Inner-kernel performance: AHS post-processing outperformed the greedy baseline on 13 of 15 days, while greedy produced negative objectives on days dominated by negative node weights.The comparison isolates the value of the AHS-selected seed set because both methods use the same greedy augmentation rule in phase 4.
- Total-kernel performance: £12,458 was the mean SA-refined LP dispatch margin versus £12,358 for exact MWIS, with the SA-refined margin matching or exceeding exact MWIS on all 15 days.Eleven days achieved parity and four showed modest improvement; the difference reflects the mismatch between the LP-dual proxy and realised 100-scenario dispatch margin.
- N-scaling and hardware limits: 0.720 at N = 50 fell to 0.095 at N = 100 and recovered to 0.245 at N = 144, while AHS-post ratios remained 0.881–0.950 with mean 0.918.FOV geometry remained within hardware limits, making per-shot validity the binding scaling constraint.
4 Discussion
The discussion positions the kernel as a closed, backend-agnostic UC workflow whose feasibility is recovered classically, while identifying valid-shot survival—not embedding—as the main scaling constraint. The 15-day campaign demonstrates dispatch performance against exact MWIS, but the tested instances remain classically easy and the hydrogen model is not multiphysics.
- End-to-end workflow: The closed loop connects stochastic UC to move-MWIS, Aquila AHS, and 100-scenario LP repair, with the same conflict graph solved by classical and analog backends.LP-dual scoring, two-row folding without gadget ancillae, and simulated-annealing refinement form the transferable kernel.
- End-to-end workflow: The King graph is a conservative compatibility proxy, while downstream LP repair—not the geometry—enforces scheduling feasibility.Every reported day returns a 100-scenario LP margin, so the geometric approximation is not asserted as a physical scheduling rule.
- Campaign results: Over 15 days, hybrid AHS+SA matches or exceeds exact MWIS+LP on dispatch margin, averaging £12,458 versus £12,358, with four days improving by 2.9–11.6%.The campaign used one 50-node, 200-shot task per day with identical schedule parameters.
- Campaign results: The hybrid advantage reflects mismatch between the LP-dual MWIS proxy and realised stochastic LP objective, not quantum speedup.HiGHS solves the same 50-node MWIS in under a second; the operational test is whether noisy sampling harms repaired dispatch margin, which it did not over 15 days.
- Scaling: FOV folding remains stable through N = 144, but valid-shot rate falls from 0.720 at N = 50 to 0.095 at N = 100, making full-array survival the binding scale limit.Even at p = 0.995, only ≈49% of shots survive at N = 144 and ≈28% at the 256-atom maximum.
- Scaling: The N = 50–144 King-graph instances are classically easy, so the campaign measures repaired pipeline fidelity rather than computational speedup.A larger reference instance is needed before a quantum role can be assessed, while shot validity is expected to become limiting before FOV occupancy.
- Scope and outlook: The hydrogen model uses an electrical conversion factor rather than a multiphysics plant, although additional constraints can compile to the same weighted MWIS graph.Multi-cell moves remain classical and would require gadget or parity encodings for hardware deployment.
5 Conclusion
The paper presents a move-MWIS kernel that compiles stochastic unit commitment into a weighted conflict graph, solves it classically or on analog hardware, and repairs decisions with a dispatch LP. In the green-hydrogen case, hybrid hardware solutions match or exceed exact-MWIS dispatch margins, while valid-shot rate limits scaling.
- Contribution: The kernel compiles stochastic unit commitment into a weighted conflict graph scored from one LP, solved classically or on analog hardware, and repaired by a 100-scenario dispatch LP.The industrial case is a six-module green-hydrogen electrolyser park.
- Results: Over 15 cloud days at N = 50, AHS+SA matches or exceeds exact MWIS+LP dispatch margins, averaging £12,458 versus £12,358, with four days improving by 2.9–11.6%.The difference reflects mismatch between realised LP objective and the dual-proxy MWIS objective.
- Interpretation: The campaign measures pipeline fidelity on a repaired industrial dispatch loop, not computational speedup, because the tested instances are classically easy.The result therefore validates the workflow rather than demonstrating a quantum runtime advantage.
- Outlook: The released kernel and hardware-result files use the same weighted conflict graph as input for quantum annealing and coherent Ising machines.Those backends are identified as subsequent hardware tests at scales where full-array post-selection remains affordable.