Equilibrium Computation, Matrix Interpolation, and Ergodicity-Onset Optimization for Ergotropy Protection in Open Quantum Batteries
Abstract
SHELVED 4 August 2026; H₂ additionally withdrawn 21 August 2026. The programme proposed five computational hypotheses for protecting ergotropy in open quantum batteries. Two were reported as validated and neither holds, for the same reason. Both simulations initialised the qubit already excited with the cavity in vacuum — the script says so in a comment: "Initial state: qubit excited, cavity vacuum" — so no energy ever had to be transferred, and what was measured was how well a pre-loaded excitation is retained rather than how well a battery charges. H₁ claimed 84.9% improvement from Nash-equilibrium cavity detuning at Δ = −10g; re-run with a real charging phase (cavity charger, qubit starting in the ground state) the optimum inverts to exact resonance and Δ = −10g yields exactly zero ergotropy. H₂ claimed 54.7% improvement at an interpolated optimum of g* = 0.01; with κ = 0.10 that is g/κ = 0.1, and charging requires g/κ ≥ 3, so the identified optimum lies in the regime where the battery cannot charge at all. Both optima also sat at the edge of their sampled grids. The original parameters (g/κ = 1.0) could not charge at any detuning in any case, since transfer time π/2g = 15.7 exceeds cavity lifetime 1/κ = 10. The simulation and the statistics were sound; the initial state was not, and a p-value of 10⁻³⁵ on a correct simulation of the wrong setup is still worthless. H₃–H₅ were never tested and are withdrawn with the programme. This work was never deposited and has no DOI.
0/5 confirmed · 3 withdrawn
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.
Key Findings
- 1REFUTED: both validated hypotheses measured a battery that started full. The qubit was initialised excited with the cavity in vacuum, so nothing was ever charged and both results describe retention
- 2H₁'s optimum inverts under a real charging phase — peak ergotropy 0.684 at exact resonance and 0.0000 at the claimed optimum of Δ = −10g
- 3H₂'s optimum g* = 0.01 gives g/κ = 0.1, an order of magnitude below the g/κ ≥ 3 needed to charge at all; both optima also sat at the edge of their sampled grids
- 4The methods were sound and the statistics were real — p < 10⁻³⁵, 0% interpolation error. Neither is evidence of anything, because both were applied to the wrong quantity
- 5Transferable result: an optimum lying at the boundary of the sampled grid is a signal to widen the grid, and a physical simulation needs its initial state checked against the claim being made before its statistics mean anything
Source Discoveries
Hypotheses in this paper were sourced from the following AegisMind discoveries on solver.press.
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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.
Aggregated EVP Package
This paper is part of the Quantum-ML Convergence EVP cluster. The aggregated EVP combines evidence from multiple papers targeting related mechanisms, enabling shared experimental infrastructure and compounded validation.
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