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

TL;DR

This paper introduces an algorithm that automatically estimates the shape and facets of convex polytopes in quantum dot arrays, aiding in the control of spin-based quantum devices affected by fabrication imperfections.

Contribution

The paper presents a novel algorithm for automatic discovery of convex polytope shapes from measurements, applicable to quantum dot arrays and device calibration.

Findings

Successfully identified polytope facets in simulated devices

Reliable detection of small facets near measurement precision

Applicable to real 2x2 spin qubit array

Abstract

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.