Automatic tuning of a donor in a silicon quantum device using machine learning

TL;DR

This work presents the first machine learning algorithm with the ability to automatically locate the charge transitions of an ion-implanted donor in a silicon device, tune single-shot charge readout, and identify the gate voltage parameters where tunnelling rates in and out the donor site are the same.

Abstract

Donor spin qubits in silicon offer one- and two-qubit gates with fidelities beyond 99%, coherence times exceeding 30 seconds, and compatibility with industrial manufacturing methods. This motivates the development of large-scale quantum processors using this platform, and the ability to automatically tune and operate such complex devices. In this work, we present the first machine learning algorithm with the ability to automatically locate the charge transitions of an ion-implanted donor in a silicon device, tune single-shot charge readout, and identify the gate voltage parameters where tunnelling rates in and out the donor site are the same. The entire tuning pipeline is completed on the order of minutes. Our results enable both automatic characterisation and tuning of a donor in silicon devices faster than human experts.

Figures (7)

• Figure 1: (a) Ion-implanted donor in a silicon device. Charge sensing readout is carried out by measuring the current across an SET defined by gate voltages $V_{\mathrm{TG}}$, $V_{\mathrm{LB}}$, $V_{\mathrm{RB}}$, and $V_{\mathrm{PL}}$, with $V_{\mathrm{bias}}$ the source-drain bias. Four gate voltages, $V_{\mathrm{DFL}}$, $V_{\mathrm{DFR}}$, $V_{\mathrm{DBL}}$, and $V_{\mathrm{DBR}}$, control the electrostatic potential around the ion-implantation site window center, indicated with a dark grey square. (b) Charge stability diagram acquired by measuring the SET current $I_\mathrm{SET}$ while sweeping $V_{\mathrm{PL}}$ and $V_{\mathrm{DFL}}$. White dashed lines mark charge transitions between the SET and several donor sites, as suggested by the different line slopes. Within a charge stability diagram, each donor-SET transition is visited by the algorithm. Here, the SET current is measured at different locations (e.g. at the triangular and diamond markers), to build a telegraph signal classifier that would later be used during the fine tuning stage. (c) During the fine tuning stage, gate voltages are adjusted to achieve an approximately equal proportion of tunnelling-in and tunnelling-out events. This corresponds to the regime where the electron spin-down electrochemical potential ($\mu_{\downarrow}$) aligns with that of the SET ($\mu_{\mathrm{SET}}$), allowing for efficient loading and unloading of spin-down electrons in the presence of a magnetic field B$_\mathrm{0}$, of 1.1 T.
• Figure 1: Overview of the charge transition locator module, a computer vision and image analysis-based algorithm that identifies the charge transition locations in a charge stability diagram. (a) $I_{\mathrm{SET}}$ current heat maps are first threshold to a binarised image, and lines are detected using the Hough transform. (b) After applying a Gaussian filter to the binarised image, the algorithm outlines the contours of the Coulomb peaks (blue solid lines). (c) The medial axis and the end-points (turquoise) of these outlined contours are identified and provide a first estimation for the location of the donor-SET charge transitions. (d) The original input charge stability diagram is used as a mask to filter out false Coulomb peak end-points at the edges of the image and false end-points generated in the previous step (c). The filtered end-point locations (red) and extracted Coulomb peak gradients are returned and passed to the telegraphic signal classifier module.
• Figure 2: Outline of donorsearch's workflow. The coarse tuning stage characterises, checks the functioning of, and tunes the SET, as well as acquiring a charge stability diagram of the donor-SET gate voltage space. The Handshake stage consists of signal processing routines to locate donor-SET charge transitions within the acquired stability diagram. Multiple current traces are acquired in the vicinity of the donor-SET charge transitions to build a classifier based on two thresholds $X^{th}_{\mathrm{1}}$ and $X^{th}_{\mathrm{2}}$, utilised in the fine tuning stage. In the fine tuning stage, the algorithm takes control of 7 out of the 8 gate voltages and attempts to tune each donor-SET charge transition ($n_{\mathrm{i}}$) to the point of observing a telegraphic signal in $I_\mathrm{{SET}}$. $V_{\mathrm{bias}}$ is fixed before commencing the algorithm.
• Figure 2: K-means cluster map of the trace features, $X_1$ and $X_2$. The clusters do not satisfy the K-means assumption of circular groupings, but their rough identification can be used to separate regions of the feature space with relatively high accuracy. Current traces containing telegraphic signals are identified by the pink coloured point cluster, whereas traces containing mainly noise (identified by black points) are clustered in the bottom left of the map. The feature values used as classification thresholds by the classifier in the fine tuning stage ($X_{1}^{'}$, $X_{2}^{'}$), are found by locating the first pink point along the $X_1$ axis. Although this boundary may cause false negatives (middle current trace cutout), this method is fast and reduces the chances of false positives. Current traces acquired during the fine tuning stage that fall in the non-shaded region of the cluster map are then scored with the dynamic threshold method. Whereas traces which fall in the shaded region are considered as noise and assigned a score of 1.
• Figure 3: Current traces acquired during the search for telegraphic signals, showing the first 2 ms of four current traces acquired at various iterations of the fine tuning stage (It: 0, 4, 28, 32) at one particular donor-SET charge transition. Each current trace is scored (Sc). Current traces that do not exhibit any clear tunnelling events or have low current ($\sim 100$ pA) are classified as noise (for example, iteration 0) and receive a score of Sc = 1. Those that are classified as telegraphic signals are scored using a dynamic current threshold (dashed line). The condition for optimal charge readout is achieved once a score Sc $<$ 0.1 is reached.