Quantum-ML Convergence and Optimization Cluster
One surviving hypothesis cluster and one shelved. The performative optimization paper confirms exact O(ε) convergence rates with a fully explicit proportionality constant and stands. The quantum battery paper does not: both of its reported results — Nash-equilibrium cavity detuning (84.9%) and Loewner matrix interpolation (54.7%) — were measured on a qubit initialised already excited, making them retention results rather than charging protocols, and its remaining hypotheses are withdrawn. The figures below cover the performative optimization work only.
2/7 confirmed
Hypotheses
1,220
GPU hours
$11k–$77k
Cost range
35 days
Critical path
Combined Impact if Confirmed
Reduced to the performative optimization work, which formally justifies warm-starting and scenario reduction in deployed ML systems with performative feedback — relevant to any production system where deployment shifts the data distribution. The quantum battery half is shelved and offers no validated framework; at its claimed optimal detuning the battery ends with zero ergotropy.
Aggregated Resource Requirements
| Paper | Timeline | GPU hrs | CPU hrs | Mem (GB) | Cost min | Cost max |
|---|---|---|---|---|---|---|
| Performative Scenario Optimization COMPLETE — both H₁ and H₂ computationally confirmed. No further experimental work required. 1/2 hypotheses confirmed | 35d | 12 | 480 | 8 | $180 | $1k |
| Ergotropy Protection in Open Quantum Batteries SHELVED 4 August 2026; H₂ withdrawn 21 August 2026. Do not run H₃–H₅ — they were scaffolding for validating a result that does not hold. If this is ever revived, the experiment worth doing is a switched protocol: charge on resonance, then detune to hold, which captures both effects rather than rediscovering that a decoupled system does not lose energy. It needs g/κ ≥ 5. Note that in the corrected simulation the battery charges to a peak at t ≈ 3.0 and is fully discharged by T = 15, so the holding phase is the part that has to be demonstrated. 0/5 hypotheses confirmed | 126d | 1,208 | — | 32 | $11k | $76k |
| Combined total | 35–35d | 1,220 | 480 | 32 | $11k | $77k |
Jun 14, 2026
35 days
Timeline
12
GPU hours
480
CPU hours
8 GB
Memory
$180
Budget (min)
$1k
Budget (full)
Required Datasets
Synthetic only — five problem families (LQ, portfolio, newsvendor, logistic regression, QP) generated programmatically. No external datasets required.
Experimental Protocol
Phase 1 (15 days): Compute x*(ε) for all 5 families × 6 ε values via stable-point iteration (convergence ‖x_{t+1}−x_t‖ < 10⁻⁶). Log-log regression of ‖x*(ε)−x*(0)‖ vs. ε to estimate slope α.
Phase 2 (10 days): Estimate empirical Lipschitz constant L̂ by measuring ‖D(x₁;ε)−D(x₂;ε)‖_W₂ / ‖x₁−x₂‖ over 500 random pairs. Test C ≤ 0.75·(L̂·‖x*(0)‖).
Phase 3 (10 days): Stress tests — non-convex objectives, non-Lipschitz distribution maps, high-dimensional LQ (d ∈ {10, 100, 1,000}).
Success Criteria
Primary (all confirmed):
- α ∈ [0.9, 1.1] for ≥4/5 problem families (R² ≥ 0.95) → 5/5 ✓
- C ≤ 0.75·(L̂·‖x*(0)‖) for all 5 families → ✓
- Convergence monotonic in ε → ✓
Secondary (confirmed):
- Rate dimension-independent: α varies < 0.1 across d = 5, 20, 50, 100 (LQ) → ✓
Failure Criteria
- Empirical ‖x*(ε)−x*(0)‖ > C·ε where C > L̂+0.01 across ≥3 families (p < 0.01)
- Super-linear divergence: α > 1.1 with R² > 0.95
- Sub-linear convergence: α < 0.9 systematically
Abort Checkpoints
- Day 3: Abort if stable-point iteration fails to converge on LQ d=10 case
- Day 7: Abort if R² < 0.70 on LQ
- Day 12: Abort if L̂ unestimable for ≥2 families
- Day 18: Abort if α outside [0.7, 1.5] for ≥3 families
- Day 25: Scope to convex objectives only if non-convex stress tests fail
Commercial ROI
Production ML systems with deployment-induced distribution shift (credit scoring, traffic routing, market-making) can now quantify the safe ε range for ignoring performative effects. Reduces over-engineering in systems where ε << 1, enabling classical SP solvers to be deployed without performative correction.
Research ROI
Formally justifies warm-starting and scenario reduction in performative algorithm design. Establishes the refined proportionality constant C = L_D·‖x*(0)‖·(1+O(ε)) as a tighter and fully explicit characterization, opening new directions in robust optimization for deployed ML.
Hypotheses
For performative scenario optimization parameterized by decision-feedback strength ε ≥ 0, the performatively stable solution x*(ε) satisfies ‖x*(ε) − x*(0)‖ ≤ L · ε, where L is the Lipschitz modulus of the distribution map D: X → P(Z). Convergence rate is O(ε · L).
Performative scenario optimization solutions θ*_PS(ε) converge to the classical stochastic optimization solution θ*_SO at rate O((1 − ε)^α) for α > 0, analogous to entropic optimal transport converging to classical OT as regularization approaches zero.
Jun 14, 2026
126 days
Timeline
1,208
GPU hours
32 GB
Memory
$11k
Budget (min)
$76k
Budget (full)
Required Datasets
H₁/H₂ (DONE): Synthetic QuTiP Lindblad simulations only — single-qubit Jaynes-Cummings (N_Fock=8, g=0.1, κ=0.10, γ₁=0.01). No external datasets required.
H₃ (VQE/QAOA): Quantum hardware access — IBM Quantum or Google Quantum AI (≥8-qubit, gate fidelity ≥99% single-qubit, ≥98.5% two-qubit).
H₄ (ergodicity): Digital quantum processor capable of N ≥ 10 qubits (Jaynes-Cummings-Hubbard model).
H₅ (dispatch): HPC+QPU hybrid scheduling testbed with ≥2 QPUs and ≥1 HPC node.
Experimental Protocol
H₁ (30 days, DONE): QuTiP Lindblad master equation; 12×5 payoff matrix; Nash equilibrium via Nashpy support enumeration; N=100 MC trajectories.
H₂ (30 days, DONE): 13-node Loewner matrix interpolation of ergotropy landscape; SVD rank-2 truncation; barycentric rational approximant.
H₃ (126 days): VQE/QAOA with ≤50 qubits, ≤O(n²) gate depth; barren plateau mitigation (layer-wise training or natural gradient); ergotropy measurement via quantum state tomography.
H₄ (98 days): Adjacent level spacing ratio r statistics on N-qubit Jaynes-Cummings-Hubbard; ergodicity onset J*/ω via r crossing from Poisson (0.386) to GOE (0.536) mean; superextensive scaling E ∝ N^α.
H₅ (90 days): Nash/correlated equilibrium LP for N_QPU × N_HPC resource allocation; ≥30 scheduling trials; paired Wilcoxon vs. FCFS baseline.
Success Criteria
H₁ (criterion met, result refuted): Ergotropy improvement ≥15% (measured: 84.9%), p < 10⁻³⁵, Cohen's d = 1.97 — met comfortably, on a simulation whose qubit began fully charged. The criterion never asked whether charging occurred.
H₂ (criterion met, result refuted): ≥15% improvement with ≤50 nodes (measured: 54.7%, 13 nodes), 0% prediction error — same initial-state defect, and the identified optimum cannot charge.
H₃: η ≥ 1.30 with ≤200-gate circuit for N=8; hardware fidelity within 15% of simulator.
H₄: Pearson r² ≥ 0.75 between J* and charging power; superextensive α > 1.05 for ≥3 values of N (p < 0.05).
H₅: Mean resource reduction ≥15% vs. FCFS across ≥30 trials (p < 0.05, Wilcoxon); overhead ≤20%.
Failure Criteria
H₃: Barren plateau unmitigated for N=4 at Day 15; VQE ergotropy variance > 50% of mean at Day 30.
H₄: Level statistics non-measurable with available qubit count; r² < 0.20 for J/ω vs. charging power in N=4.
H₅: Equilibrium dispatch improvement < 5% vs. FCFS on simplest 2-QPU scenario.
Abort Checkpoints
H₁: Day 3 (Nash convergence check), Day 7 (ergotropy improvement < 2%) — both passed, and both would pass again. Neither checkpoint inspects the initial state, which is where the error was. H₂: Day 5 (Loewner ill-conditioning check), Day 10 (non-physical ergotropy) — both passed. The ergotropy values were physical; they were physical values of the wrong quantity. H₃: Day 15 (barren plateau unmitigated for N=4). Day 30 (VQE variance > 50% of mean). H₄: Day 14 (level statistics non-measurable). Day 28 (r² < 0.20 for N=4). H₅: Day 15 (< 5% improvement on 2-QPU scenario).
Commercial ROI
Withdrawn. There is no validated detuning strategy to apply or license — at the claimed optimum the battery ends with zero ergotropy.
Research ROI
Withdrawn as stated. The equilibrium-computation and Loewner-interpolation machinery did work as machinery, and either could be applied to a correctly posed charging objective, but neither is evidenced by this study.
Hypotheses
Game-theoretic equilibrium strategies applied to optimize cavity detuning Δ = ω_cavity − ω_qubit in Jaynes-Cummings open quantum battery models will preserve ergotropy at levels ≥15% higher than unoptimized (Δ=0) parameters, with p < 0.01 across three noise models.
Hermitian matrix-valued rational interpolation of open quantum battery time-evolution superoperators will identify charging protocols achieving ≥15% efficiency improvement over constant-drive baseline using ≤50 interpolation nodes.
Variational quantum eigensolvers (VQE/QAOA) applied to ergotropy-preserving parameter search in open quantum battery systems will identify charging protocols within 5% of GRAPE-optimal using ≤200 circuit evaluations.
Ergodicity-onset parameters estimated from digital quantum processors operating at thermal equilibrium will correctly identify superextensive energy storage regimes in N ≥ 3 qubit quantum batteries.
Equilibrium-based dispatch of quantum circuits in hybrid HPC-quantum systems will reduce resource overhead during quantum battery validation experiments by ≥20% vs. sequential scheduling.
Source discoveries on solver.press
All hypotheses in this cluster were sourced from AegisMind discoveries. Each discovery carries its own EVP, adversarial debate score, and formal verification status — click any hypothesis above to view it.
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