# Estimation of Convex Polytopes for Automatic Discovery of Charge State Transitions in Quantum Dot Arrays

arXiv: https://arxiv.org/abs/2108.09133 · HTML: https://mlsanity.com/paper/2108.09133/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 20 Aug 2021.

## Builds on (most cited first, 5 of 5)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Ray-based framework for state identification in quantum dot devices](https://mlsanity.com/paper/2102.11784/) (2021)
- [Ray-based classification framework for high-dimensional data](https://mlsanity.com/paper/2010.00500/) (2020)
- [Theoretical bounds on data requirements for the ray-based classification](https://mlsanity.com/paper/2103.09577/) (2021)

## Built on by (most cited first, 3 of 3)

- [Colloquium: Advances in automation of quantum dot devices control](https://mlsanity.com/paper/2112.09362/) (2021)
- [Learning Coulomb Diamonds in Large Quantum Dot Arrays](https://mlsanity.com/paper/2205.01443/) (2022)
- [Robust quantum dots charge autotuning using neural network uncertainty](https://mlsanity.com/paper/2406.05175/) (2024)

## Abstract (arXiv)

In spin based quantum dot arrays, material or fabrication imprecisions affect the behaviour of the device, which must be taken into account when controlling it. This requires measuring the shape of specific convex polytopes. In this work, we present an algorithm that automatically discovers count, shape and size of the facets of a convex polytope from measurements. Results on simulated devices as well as a real 2x2 spin qubit array show that we can reliably find the facets of the convex polytopes, including small facets with sizes on the order of the measurement precision.