Quantum Solar Optimization
Three results about running QAOA, a method for doing optimization on quantum computers, on a problem with physical constraints. One appears to be new; two are rediscoveries of published ideas, kept for what they cost to ignore. Every study was registered before it ran, every number is pinned to its data file by a test, and the prior art is named. The problem is residential battery scheduling; nothing here claims a quantum advantage, since an ordinary program solves every instance exactly in microseconds.
Apparently new
A constrained problem goes to a quantum optimizer as a QUBO, a cost function over yes/no variables, with the constraints turned into penalty terms. The usual encoding spends extra qubits, slack variables, tracking the battery's level at every hour. The checkpoint encoding here drops them: it pins the level every k hours instead, which bounds how far the level can drift between checks. That yields a proved property: whenever the spacing satisfies a condition the code computes, every assignment with zero penalty is a schedule the battery can physically run. On the real instance this takes 117 qubits to 52 with none of the answer's value lost.
The qubit count is not the claim. Removing slack variables is a crowded field: unbalanced penalization, exponential and Heaviside penalties, Lagrangian and augmented-Lagrangian methods, and in this exact application area a Powell–Hestenes–Rockafellar formulation. Every one of those biases the search toward feasibility. A search of the published work found none that guarantees the minimum-energy assignment is feasible, and a 2026 survey of quantum methods for unit commitment describes feasibility as an open challenge. The guarantee is the part that appears to be new, and that claim rests on not finding something, which is weaker evidence than finding it.
What the guarantee is worth is measured. Below the sound penalty range, the QUBO's own minimum-energy state is not a schedule, and the standard success metric cannot tell: at one weak setting, 32 of 40 tunings “clear” the concentration bar, and every one is probability on a state that is not an answer. Three tests hold the claim up: one enumerates every zero-penalty assignment on three instances and finds all feasible, one checks the minimum-energy assignment at sizes past brute force, and one confirms the encoding refuses to build at an unsound spacing rather than silently biasing.
Not established
Known idea, measured cost
The penalty weight decides how hard the QUBO punishes breaking a constraint. The standard heuristic is roughly 10x the objective's scale; deriving it as the objective's range across feasible solutions divided by the penalty scale gives alpha* = 0.0209 on the worked instance, and makes the default a 48x overshoot. Setting penalties from the objective's range is established practice, so this is a rediscovery, and the overshoot is a critique of common practice rather than of a local mistake.
What the sources scanned do not report is what overshoot costs in reproducibility. At one circuit layer, tuning converges to a single basin at alpha* and below, and to 19 basins at the default weight; the usable window is narrow and alpha* sits at its edge. The study predicting that shape was registered in advance and its prediction was falsified: there is no lower branch, because below the sound range the tuning converges just as reliably onto a state that is not a schedule.
Known metric, measured head-to-head
Multi-start tuning yields many candidate parameter sets, and the standard rule keeps the one with the lowest energy estimate. Keeping the one with the highest in-constraint probability, the share of samples that decode to feasible schedules, picks a better circuit: the single best tuning available in 9 of 9 sound, reproducible cells on held-out instances, 12 of 12 on three fresh instances, and 4 of 4 sizes from 8 to 14 qubits. On the two hard instances, where the best tuning barely clears the concentration bar, the energy rule misses in every cell and this rule clears in every cell. The quantity is published and already used as a constraint inside optimizers; the post-hoc head-to-head among restarts is the only part a day's search did not find, and it is a small step from what is published.
The limits: only two of six instances are hard enough to separate the rules, the median margin is 5.0% and matters only at the bar, and the largest size tested is still small enough to enumerate, so the scaling result probes the regime by shot budget rather than intractability. Where shots are cheap, selecting directly on measured optimal mass is better still, until it is not: at 14 qubits and 4,096 shots the optimum appears in the sample for only 7 of 20 tunings.
Method
Every study was pre-registered: the plan is committed before the sweep runs, the sweep script refuses to run against an edited plan, and the ordering is checkable in the git history rather than asserted. Two registered predictions were falsified and are reported as falsified. Every number in every write-up, including the limiting sentences, is pinned by a test to the data file it came from.
The scope in one line: one problem family, three to seven time slots, 6 to 14 qubits, one encoding, one and two circuit layers, simulator and exact computation for everything above, and 146 seconds of IBM hardware time supporting only the separate encoding-degradation result.
FINDINGS.md is the authority for what is claimed and how strongly, with the prior-art scan's limits recorded. The write-ups: the encoding study, the penalty-weight study, and the selection rule's discovery, replication and scaling test. If you know of a slack-free encoding with a proved feasibility guarantee for a sequential running-sum constraint, the repository's issue tracker is the place to say so, and the novelty claim comes down.
Keep reading
Each of these is a self-contained page.