Ray-Based Framework for State Identification in Quantum Dot Devices

Open Access

Ray-Based Framework for State Identification in Quantum Dot Devices

Justyna P. Zwolak, Thomas McJunkin, Sandesh S. Kalantre, Samuel F. Neyens, E.R. MacQuarrie, Mark A. Eriksson, and Jacob M. Taylor

PRX Quantum 2, 020335 – Published 7 June 2021

Abstract

Quantum dots (QDs) defined with electrostatic gates are a leading platform for a scalable quantum computing implementation. However, with increasing numbers of qubits, the complexity of the control parameter space also grows. Traditional measurement techniques, relying on complete or near-complete exploration via two-parameter scans (images) of the device response, quickly become impractical with increasing numbers of gates. Here we propose to circumvent this challenge by introducing a measurement technique relying on one-dimensional projections of the device response in the multidimensional parameter space. Dubbed the “ray-based classification (RBC) framework,” we use this machine learning approach to implement a classifier for QD states, enabling automated recognition of qubit-relevant parameter regimes. We show that RBC surpasses the $82 %$ accuracy benchmark from the experimental implementation of image-based classification techniques from prior work, while reducing the number of measurement points needed by up to $70 %$ . The reduction in measurement cost is a significant gain for time-intensive QD measurements and is a step forward toward the scalability of these devices. We also discuss how the RBC-based optimizer, which tunes the device to a multiqubit regime, performs when tuning in the two-dimensional and three-dimensional parameter spaces defined by plunger and barrier gates that control the QDs. This work provides experimental validation of both efficient state identification and optimization with machine learning techniques for nontraditional measurements in quantum systems with high-dimensional parameter spaces and time-intensive measurements.

Received 23 February 2021
Accepted 12 May 2021
Corrected 24 March 2022

DOI:https://doi.org/10.1103/PRXQuantum.2.020335

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Machine learning Quantum control Quantum information architectures & platforms Quantum information with solid state qubits

Double quantum dots Semiconductor compounds

Quantum Information, Science & Technology

Corrections

24 March 2022

Correction: Reference [33] contained incorrect source information for the dataset accompanying this work and has been fixed.

Authors & Affiliations

Justyna P. Zwolak ^1,*, Thomas McJunkin ^2,†, Sandesh S. Kalantre ^3,4, Samuel F. Neyens², E.R. MacQuarrie², Mark A. Eriksson ², and Jacob M. Taylor^1,3,4

¹National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
²Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
³Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
⁴Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA

^*jpzwolak@nist.gov
^†tmcjunkin@wisc.edu

Popular Summary

Qubits, the building blocks of quantum computers, can be constructed using a variety of platforms, such as atoms, photons, superconducting circuits, or individual electrons in solid-state systems. Quantum dots (QDs) are fabricated semiconductor nanostructures that confine individual electrons. The integration of semiconductor technologies, including control of individual QDs using electric gates, suggests a pathway to scaling to large numbers of qubits. However, the same gates provide an obstacle: the problem of autonomous control of many analog parameters remains unresolved. Here we develop and implement in situ a machine learning–enhanced framework to rapidly differentiate between QD states within experimental devices, enabling automated tune-up of a QD-based quantum computer.

While previous efforts in this direction leveraged existing machine learning techniques for images and movies, we strike out in a different direction with a ray-based classification (RBC) framework that relies on a small collection of one-dimensional measurements—the rays. These rays allow us to fingerprint a QD charge state without the need for time-intensive scans. Furthermore, we demonstrate a RBC-based autotuner to dynamically tune between QD states, a crucial step toward fully automatic QD calibration for quantum computing.

The development of an autotuning system such as the one we propose mitigates the time and budget limitations associated with the manual tuning of these systems and thus paves the way for experiments with a larger number of QDs. Moreover, the simplicity and efficiency of the RBC enable easier on-chip implementation and will facilitate autonomous control protocols.

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Vol. 2, Iss. 2 — June - August 2021

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Figure 1
Visualization of the ray-based fingerprinting framework. (a) A preview of five points in the space of plunger gates $(P_{1}, P_{2})$ with six evenly distributed rays overlaying a sample measurement. Different colors represent different QD states. The inset shows the potential landscape of the double-quantum-dot system. Gate voltages $V_{P_{1}}$ and $V_{P_{2}}$ control the occupation of each QD. Gate voltage $V_{B_{2}}$ controls the inter-QD tunneling. (b) The preprocessed charge sensor (CS) signal for six evenly distributed rays measured from a point $(V_{P_{1}}, V_{P_{2}}) = (0.193, 0.193) V$ [the most central point in (a)] as a function of ray length. The length resolution is 0.5 mV per pixel. In each ray, the position of the transition line nearest to the point $(V_{P_{1}}, V_{P_{2}}) \equiv x_{o}$ —that is, the critical feature along a given ray—is marked with a dot. (c) The flow of the RBC framework adapted from Ref. [29]. A vector of critical features $x$ is processed using a weight function $Γ (x)$ . The resulting fingerprint $F_{x_{o}}$ is processed by a DNN classifier, returning a probability vector $p (x_{o})$ quantifying the current state of the device at point $x_{o}$ .
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Figure 2
(a) Classifier performance for various weight functions $γ (x)$ and for different numbers of rays and ray lengths using off-line experimental data (averaged over $N = 20$ models). The inset at the top shows the performance on simulated data. (b) Classifier performance for different numbers of rays as a function of the total number of pixels measured for off-line experimental data (averaged over $N = 20$ models). The dotted black horizontal line represents the benchmark from Ref. [21], while the dashed vertical line represents the minimum data requirement for a CNN classifier as used in Ref. [21]. In both panels, the connecting lines are a guide for the eye only. The error bars (a) and bands (b) correspond to one standard deviation.
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Figure 3
Scatter plot showing the performance of the ray-based classifier on live data (a) and off-line (b) using six rays of length 22 mV (44 pixels) overlaying a sample measured raw scan. Colors on both plots correspond to the state predicted by the RBC. The gray points indicate $M$ -projections that are determined as poorly charge sensed and thus are inappropriate for classification.
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Figure 4
(a) Scatter plot of the final state obtained in off-line tuning using the RBC framework. The tuner is set to tune to the double-quantum-dot state. We obtain a tuning success rate of $78.7 %$ , calculated as the fraction of points that end up inside the green region, with an additional $10.2 %$ of the points landing in an area that moderately resembles double-quantum-dot features, highlighted in white. (b) The three-dimensional space formed by 2D scans of the charge sensor response in the two plunger-gates space and the middle barrier gate. The arrow schematically shows the flow of the autotuner in the optimization loop from barrier voltages with no double quantum dot to lower voltages with a double-quantum-dot region. In both plots, the cyan square highlights the area where the initial points are uniformly sampled, while the green polygons mark the target double-quantum-dot region.
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