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

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. We present an algorithm that automatically discovers count, shape and size of the facets of a convex polytope from measurements by alternating a phase of model-fitting with a phase of querying new measurements, based on the fitted model. We evaluate the algorithm on simulated polytopes and devices, as well as a real 2 × 2 spin qubit array. Results show that we can reliably find the facets of the convex polytopes, including small facets with sizes on the order of the measurement precision.

Learning Coulomb Diamonds in Large Quantum Dot Arrays

“…The assumption of linear transitions is strong, as it is unlikely that the device has perfectly linear boundaries between ground-states. However, prior work [9] has already shown in practical application that at least some small devices have coulomb diamonds that are sufficiently linear to fit a convex polytope to them, showing that the strategy has the potential to become practical on some devices.…”

“…Compared to our approach, the approach in [9] used much weaker assumptions on the shape of the polytope, which affects computation time. In their results, computing a polytope for a 2x2 array took 4 hours, while our approach takes less than 1h on a 4x4 array (scenario S 5 ).…”

“…Moreover, since the number of control voltages grows linearly with the number of quantum dots, hand-tuning their values becomes more and more challenging due to cross-talk between the dots. Only recently did we see the emergence of automatic tuning algorithms, often implemented using machinelearning [6][7][8][9][10][11][12]. These approaches were used only for small arrays, and still lag behind the results achievable via manual tuning.…”

“…With this, we only rely on the use of line scans to detect the nearest transition in a chosen direction, and use a machine-learning model to estimate transitions from measurements. Compared to previous works on the same tuning step [8,9], we will also make use of explicit knowledge of the underlying physics to constrain the problem to make the algorithm more efficient. We restrict ourselves to quantum dot devices described by the constant interaction model [13], appropriate for instance for arrays of gate-controlled spin qubits.…”

“…Our goal is to answer the question whether the tuning problem of identifying desired single-and multi-electron transitions is reliably possible for large-devices that follow the constant-interaction model exactly. This is a different starting point than the work in [9] that aimed to develop a practical algorithm that works on small devices that do not require exact adherence to the constant interaction model, but ultimately does not scale to the devices considered in this work.…”