MachineLearningtechniquesforstaterecognitionandauto-tuninginquantumdots
Current semiconductor-based quantum computing approaches use adjacent, isolatedelectron spins as quantum bits. Establishing a stable configuration of electrons in space isachieved via electrostatic confinement, band-gap engineering, and dynamically adjustedvoltagesonnearbyelectricalgates.Akeytaskistodetermineagoodsetofcontrolparameters(gatevoltages)toachieveadesiredchargeconfiguration–inbothnumberandlocation–forasuccessfulexperiment.SeeFig.1foragenericmodelofananowire.
Inrecentyears,machinelearning(ML)hasemergedasa“goto”techniqueforautomatedcharacterization,givingreliableoutputwhentrainedonarepresentative,comprehensivedataset. Specifically, we focus on the classification of data into categories (also referred to as aclassification problem). The categories can be either predefined and stored as labels(supervisedlearning)orextractedfromthedata(unsupervisedlearning).Thealgorithmlearnsabout the categories from the training set and produces amodel that can assignpreviouslyunseen inputstothosecategories.Artificialneuralnetworks(ANNs)–aMLapproachinspiredbyanalogousbiologicalunits–turnedouttobeparticularlysuitableforthistask.ANNswereoriginally intendedtomimictheworkingsofhumans’brain.Theyarecomposedof(so-called)artificialneuronsorganized in fully-connected layers (thus the term“deepneuralnetworks”),witheachlayerperformingaspecifictransformationofthedata.Deepneuralnetworks(DNNs),with multiple hidden layers, can be used to classify complex data into categories with highaccuracy. One architecture that has performed particularly well in these settings are theconvolutionalneuralnetworks(CNNs),comprisingofasetofconvolutionalandpoolinglayerspreceding the series of hidden layers. Each convolutional layer consists of a number sets ofweightsconvolutedwiththeinputthataredeterminedbythetrainingonthedataset.Inorderto learn larger scale features in the inputmore efficiently, a convolutional layer is generallyfollowedbyapoolinglayerthattakesinasub-regionintheinputandreplacesitbyaneffectiveelement(e.g.,themaximumelement)inthatregion.
Figure1. Agenericmodelofananowirewith5gates.ThebarriervoltagesaresettoVB1=VB2=VB3=-200mV.Forplungers,voltagesvariedbetween0mVand400mV.
Inourproject,weusetoolsfrommachinelearningtodevelopgoodheuristicsforthegate
voltages from a training set and design an effective and efficient neural network for thecharacterization of experimental data in semiconductor quantum dot experiments. In a firststage,weestablishedareliabletrainingandevaluationdatasets,basedonsimulateddata.Weuse a modified Thomas-Fermiapproximation to model a reference semiconductor systemcomprisingaquasi-1Dnanowirewithaseriesofdepletiongateswhosevoltagesdeterminethenumberofislandsandthechargesoneachofthoseislands,aswellastheconductancethroughthewire.Wegenerated1000gateconfigurationsaveragingoverdifferentpossiblefabricationsof the same type of quasi-1D device,with plunger voltages ranging from 0 to 400mV.Eachsampledatawasstoredasa100x100pixelmapfromplungervoltagestocurrent,netcharge,state and sensormaps (each stored separately)which can then be used as observables andlabelsfortrainingandtesting.Thetrainingandevaluationsetwasthengeneratedbytaking25random30x30pixelssub-imagesofeachmaptogofrom1000realizationsto25000effectiverealizations.A secondstage involved trainingof theCNNs to “recognize” theelectronic statewithinquantumdotarrays,basedonthecurrentdata.Wefound>95%agreementbetweentheCNN characterization and the Thomas-Fermi model predictions for nanowires. Having thenetworktrained, we tested it on theexperimental data and found that it correctlyidentifiessingleanddoubledotstateconfigurations,aswellas the intermediatecases.Finally, instagethree,wewereabletoauto-tunethemultidimensionalgatevoltagespacetoobtainarequiredconfigurationby recasting the tuningproblemasanoptimizationproblemover thenanowirestateinthespaceofgatevoltages.
Figure 2. An example of full 2Dmap (100x100 points) from the space of plunger gate voltages(VP1,VP2)tocurrent(a)andasub-regionwithdoubledotconfiguration(b).A statemap(c)andchargemap(d)correspondingtothecurrentmappresentedin(a).N1andN2denotethenumberofchargesoneachdot.
