A targeted computer-modeling workflow generated charge-stability diagrams for quantum-dot devices with far fewer calculations than a full voltage-grid sweep, according to a preprint. For the Intel device, the approach used 32 simulations and took about 1,251 minutes, compared with 441 simulations and about 26,593 minutes for a 21 by 21 sweep. That represents a reduction of roughly 14 times in simulation count and 21 times in computing time.
Instead of calculating every point in the grid, the workflow selected operating points for specific charge states. It combined MDMM and MaSQE to autotune gate-voltage configurations, then used FCI energy calculations to extract effective Hubbard parameters. Those parameters provide the interaction and energy-offset information used to generate the charge-state maps.
A faster route, with an unresolved mismatch
The study evaluated two device cases: an Intel triple quantum dot operated as a double dot, and an overlapping-gate double dot. It compared the generated diagrams with experimental charge-stability data and with extracted Hubbard parameters. In the Intel case, the 32 calculations consisted of 27 self-consistent simulations and five FCI calculations.
The Intel fit produced on-site interaction values of 3.69 and 2.98 millielectronvolts, an interdot interaction of 0.72 millielectronvolts, and energy offsets of 142.3 and 140.7 millielectronvolts. The on-site values were below the reported experimental ranges, while the interdot term and offsets fell within them. The on-site terms describe interaction within each dot, the interdot term describes interaction between the dots, and the offsets set the energy reference for each site.
The quantitative match depended on the assumed insulating oxide layer. With a 5 nanometre HfO2 layer, the Hubbard cell underestimated charging energy relative to experiment, while the self-consistent Schrodinger-Poisson result overestimated it. A version with no HfO2 layer was closest to the measured cell.
Tests of 5, 2 and 0 nanometre HfO2 stacks showed how strongly the fitted parameters changed with that assumption. The two on-site values moved from 3.69 and 2.98 millielectronvolts at 5 nanometres to 5.18 and 5.15 millielectronvolts at zero thickness. The interdot value moved from 0.72 to minus 0.16 millielectronvolts. The zero-thickness cell was closest to experiment, but its negative interdot value was unphysical, and no tested oxide thickness put all three interaction parameters within their experimental ranges.
The method also worked on another gate design
For the overlapping-gate device, the operating points, lever arms and Hubbard parameters were obtained solely from the gate geometry and assumed material heterostructure. The targeted calculation used 38 simulations, including 33 self-consistent simulations and five FCI calculations, and took about 2,884 minutes. The comparable 13 by 13 bias sweep used 169 self-consistent simulations and about 40,439 minutes, a reported reduction of about four times in simulations and 14 times in computing time.
The overlapping-gate fit returned on-site interaction values of 6.11 and 6.10 millielectronvolts, an interdot term of minus 0.484 millielectronvolts, and energy offsets of 2.20 and 2.19 millielectronvolts. The authors described the negative interdot value as indicating minimal interaction between the two dots.
The simulations also examined lever arms, which describe how strongly gate voltages shift the energies of the dots. Reducing the nominal Al2O3 thickness from 5 to 3 nanometres was associated with a 6.7% increase in the diagonal lever arms and moved them toward measured values. The thinner-oxide result accounted for roughly half of the diagonal discrepancy, while off-diagonal elements remained largely unchanged.
What the calculations leave open
Within the tested low-charge configurations, the extracted lever arms varied little enough for the researchers to reuse one linear model. At the Intel (1, 1) configuration, the FCI and Schrodinger-Poisson estimates agreed within 1%. An appendix also compared constant tunnel-coupling values of 0, 100 and 300 microelectronvolts and reported rounding of the triple points as the main effect.
The paper reports that no single tested HfO2 thickness placed the Intel values for U1, U2 and U12 simultaneously within their experimental ranges. That leaves the oxide thickness as a useful sensitivity test, but not a unique explanation for the mismatch between calculation and experiment.
The reported efficiency figures are tied to the tested 21 by 21 Intel grid and 13 by 13 overlapping-gate grid. They show the cost of the targeted workflow in those comparisons, while the parameter results underline how much the output can depend on the assumed device materials.
The document is arXiv:2608.28263v1, dated 28 August 2026. The work used Hoffman2 Cluster computing and storage services and acknowledged Army Research Office support under grant numbers W911NF-25-1-0141 and W911NF-23-1-0104.
Paper data and sources
Original title: Rapid Charge Stability Diagram Generation from Device-level Modeling of Semiconductor Quantum Dots
Authors: Ron Nodel, David W. Kanaar, Connor Nasseraddin et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text