diff --git "a/AtFAT4oBgHgl3EQfrx4U/content/tmp_files/load_file.txt" "b/AtFAT4oBgHgl3EQfrx4U/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/AtFAT4oBgHgl3EQfrx4U/content/tmp_files/load_file.txt" @@ -0,0 +1,981 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf,len=980 +page_content='Automated extraction of capacitive coupling for quantum dot systems Joshua Ziegler,1, ∗ Florian Luthi,2 Mick Ramsey,2 Felix Borjans,2 Guoji Zheng,2 and Justyna P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Zwolak1, † 1National Institute of Standards and Technology, Gaithersburg, MD 20899, USA 2Intel Components Research, Intel Corporation, 2501 NW 229th Avenue, Hillsboro, Oregon 97124, USA (Dated: January 23, 2023) Gate-defined quantum dots (QDs) have appealing attributes as a quantum computing platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' However, near-term devices possess a range of possible imperfections that need to be accounted for during the tuning and operation of QD devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' One such problem is the capacitive cross-talk between the metallic gates that define and control QD qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' A way to compensate for the capacitive cross-talk and enable targeted control of specific QDs independent of coupling is by the use of virtual gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Here, we demonstrate a reliable automated capacitive coupling identification method that combines machine learning with traditional fitting to take advantage of the desirable properties of each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' We also show how the cross-capacitance measurement may be used for the identification of spurious QDs sometimes formed during tuning experimental devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Our systems can autonomously flag devices with spurious dots near the operating regime which is crucial information for reliable tuning to a regime suitable for qubit operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' INTRODUCTION Quantum dot (QD) arrays, in which charge carriers are trapped in localized potential wells and qubits can be made by use of the spin and permutation symmetries of the carriers, are a promising quantum computing plat- form [1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In fact, last year has shown the first demon- stration of QD two-qubit gates with fidelities exceeding the thresholds for fault-tolerant computing [4–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' How- ever, because the individual charge carriers that make up qubits have electrochemical sensitivity to minor im- purities and imperfections, calibration and tuning of QD devices is a nontrivial and time-consuming process, with each QD requiring a careful adjustment of a gate voltage to define charge number, and multiple gate voltages to specify tunnel coupling between QDs for two-qubit gates or to reservoirs for reset and measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' While manual calibration is achievable for small, few-QD devices, with increasing size and complexity of QD arrays, the relevant control parameter space grows quickly, necessitating the development of autonomous tuning methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' There have been numerous demonstrations of automa- tion of the various phases of the tuning process for sin- gle and double-QD devices [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Some approaches seek to tackle tuning starting from device turn-on to coarse tun- ing [8–11] while others assume that bootstrapping (cal- ibration of measurement devices and identification of a nominal regime for further investigation) and basic tun- ing (confirmation of controllability and device character- istics) have been completed and focus on a more tar- geted automation of the coarse and charge tuning [12–16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' While the initial auto-tuning approaches relied mainly on the appealingly intuitive and relatively easy to imple- ment conventional algorithms that typically involved a ∗ Current address: Intel Components Research, Intel Corporation, 2501 NW 229th Avenue, Hillsboro, Oregon 97124, USA † jpzwolak@nist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='gov combination of techniques from regression analysis, pat- tern matching, and quantum control theory, the more re- cent algorithms take advantage of the modern computer vision and machine learning [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' A typical accumulation-mode QD device consists of two sets of gates—plungers and barriers—that collec- tively control the overall potential profile, QD-specific single-particle energy detuning of individual QDs, the tunnel couplings between QDs, and tunnel rates between the most outer QDs and reservoirs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Ideally, each plunger gate would affect only the electrochemical potential of a single targeted QD and each barrier gate only one in- tended tunnel barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Due to the tight proximity, how- ever, each gate capacitively couples to nearby potential and tunnel barriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' This makes careful control of these key parameters challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' One way to compensate for the capacitive cross-talk between gates is to enable orthogonal control of the QDs potential by implementing so-called virtual gates [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Specifically, linear combinations of gate voltage changes can be mapped onto onsite energy differences [17–20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' These approaches have been key for the initialization and control of larger QD arrays [21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To autonomously identify capacitive couplings in a device, various approaches have been demonstrated us- ing both conventional fitting and machine learning (ML) techniques [23–26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' However, these approaches, typically relying on the Hough transform or conventional least- squares fitting procedures, may be unreliable in the pres- ence of data imperfections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Hough transforms can ex- tract slopes directly but may be sensitive to noise or be excessively complex to analyze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The conventional fitting can be more flexible but is susceptible to local minima and can be time-consuming at inference time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Convolutional neural networks (CNN) are well suited for extracting high-level features from images and can remain effective in the presence of noise or other imper- fections [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' However, ML methods can have difficulties identifying data outside of the training distribution even if it contains similar features [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Fortunately, given a arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='08654v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='mes-hall] 20 Jan 2023 2 simplified, high-level representation of the data, conven- tional fitting approaches can be more targeted to extract key information more effectively and quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Here we develop a reliable automated capacitive cou- pling identification method that combines ML with tra- ditional fitting to take advantage of the desirable proper- ties of each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' We use an ML module for pixel classification followed by linear regression for extracting targeted in- formation and demonstrate effective performance across noise levels and data variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Testing each of these methods on a set of eight simulated QD devices with large variability and realistic noise variation mimicking experimental conditions shows that the approach com- bining ML and traditional fitting works well, with a root mean square error (RMSE) of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='034(14), corresponding to a roughly 7 % error, for predicting virtual gate ma- trix off-diagonal values (normalizing such that diagonal values are one).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' We also demonstrate how the cross-capacitance mea- surement may be used for the identification of spurious QDs formed during tuning experimental devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Many of the auto-tuning approaches proposed to date rely on a series of small 2D scans capturing a relatively narrow range of the voltage space [13, 14, 27, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' While such ap- proaches improve the efficiency of tuning, they may result in unexpected and difficult to assess failure modes when the tuning algorithm terminates at an anti-crossing with a spurious QD that may form in small potential wells due to interface defects, surface roughness, or strain within the device [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' They are highly undesirable since they may interfere with the QDs intended for use as qubits and cannot themselves be used as qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To avoid de- vice tuning failure, spurious QDs must be identified when present and avoided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' We test the utility of our approach for capacitive coupling estimation by identifying spurious QD in experimental measurements of QD devices [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The manuscript is organized as follows: In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' II we introduce the framework of combining traditional fitting techniques with a pixel classifier to process the high-level information extracted from experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' III we show the utility of the proposed framework to auto- matically extract virtual gates as well as identify charge transitions resulting from a formation of spurious QD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Finally, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' IV we summarize the results and discuss the outlook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' METHODS: MACHINE LEARNING AND FIT Capacitive couplings in a QD device can be measured and, in a constant capacitance approximation, described by a matrix that maps the physical gate voltages onto the effect they each have on the QD’s chemical poten- tials or barriers [17, 23, 24, 31–33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Measurement of the elements of this matrix must be performed distinctly for electrochemical potentials and tunnel barriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Cou- plings of the chemical potentials to each QD—which is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='27 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='29 VP2(V) (a) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='4 Current (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' units) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='32 VP1(V) (b) NT LT CT RT PL (c) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' An example 2D scan and corresponding pixel classifi- cation, class clusters, and linear fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' (a) A simulated voltage scan showing left and right transitions as well as a polariza- tion line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' (b) Pixel classification for the scan shown in (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' (c) Regions of pixels and linear fits from the pixel classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The large dark points indicate the centers of pixel regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' the focus of this work—can be extracted from shifts in charge transition lines when each voltage is varied [17] while the effect of each gate on tunnel barriers can be assessed by measuring changes in the width of inter-dot transitions, assuming the electron temperature is suffi- ciently low [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Measured this way, the couplings are relative, usually scaled with respect to the coupling of the QD to the nearest gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' An absolute energy scale can be obtained by measuring the gate lever arms with photon-assisted tunneling, Coulomb diamonds, or bias triangles [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' However, for establishing the orthogonal control the relative scale is sufficient [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' For a double QD, the virtualization matrix Gvirt re- lating the physical plunger gates to virtual gates can be represented by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Each row is normalized such that the diagonal entries are 1 to reflect the relative nature of our virtual gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Gvirt ≡ �VP ′ 1 VP ′ 2 � = � 1 α12 α21 1 � � VP1 VP2 � (1) The relative cross-capacitances for chemical potentials manifest themselves via the slopes of charge transition lines, with the dominant terms of the cross-capacitance matrix determined from a measurement in the space of neighboring pairs of gates [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' We address the iden- tification of the cross-capacitances as captured in two- dimensional (2D) plunger-plunger gate scans, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To translate the low-level QD data into high- level information useful for automation we use a pixel classifier, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=', a CNN model with a structure similar to a feature pyramid network [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The pixel classifier takes as 3 an input a small 2D plunger voltage scan obtained using a charge sensor, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' It then identi- fies each pixel within the scan as belonging to one of the charge transition classes—left, right, central, or inter-dot (polarization line) transition, denoted as LT, RT, CT, or PL, respectively—or to the no transition (NT) class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In other words, the CNN provides a high-level classification of the raw experimental data while keeping spatial infor- mation about the relative location and orientation of the detected features, which is useful for algorithmic process- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Figure 1(b) shows the pixel classification of a scan from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To translate pixel classifications to capacitive cou- plings, we identify contiguous regions within each class of pixels in an image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' A labeling algorithm from the mul- tidimensional image processing package in SciPy is then used to determine the relevant clusters of connected pix- els [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' This separates fragments of charge transitions into distinct clusters so that each can be processed indi- vidually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Each region of pixels classified as LT, CT, or RT is then independently fitted using linear regression, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' When multiple segments for a given class are present in an image, the capacitive coupling re- turned is the average for all fitted lines weighted by the standard deviations of each fit, yielding the solid lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1(b) (offset arbitrarily for comparison with the pixel regions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Standard deviations σ are computed from the standard error of the fit, S, by σ = S/√n, where n is the size of the pixel region, as in Student’s t-distribution [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In addition, each region is tagged with its center in volt- age space, shown by the large black points in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1(c), which allows tracking the changes in charge transitions and their slopes within the larger space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Data The data used for training the ML tools and testing the methods was generated using a simulation of QD de- vices [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The simulation is composed of a calculation of the electron density in the Thomas-Fermi approximation and a capacitance matrix to determine the stable electron configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To improve the robustness of the models, the data is augmented with synthetic white, pink (1/f), and telegraph noise [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The effect of a QD charge sen- sor strongly coupled to the plunger gates is varied during the scan to improve performance on this type of experi- mental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The training dataset consists of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='6 × 105 devices with parameters varied over a uniform distribution with a standard deviation equal to 1 % of each parameter’s value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To train the ML models we randomly sample 10 small scans per device and use charge state ground truth to label each scan on a pixel level with the presence and type of transition, yielding NT, LT, CT, RT, and PL la- bels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Additionally, we extract the slopes of the transition lines directly using the gradients of the device charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The test data is composed of eight simulated devices with large variations in screening length and device pitch 1× 5× 10× 15× 20× 25× 30× 35× 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='6 RMSE (a) 1× 15× 30× 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='6 (b) 1× 15× 30× Noise Level (c) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' (a) Root mean square error (RMSE) for all transition classes (left, central, and right [LT, CT, RT]) as a function of the synthetic noise level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' (b) RMSE as a function of noise level for the LT class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' (c) RMSE as a function of noise level for the RT class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' and with large shifts in the position of one of the plunger gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' These changes lead to large variations in the slopes of the charge transition lines, the capacitive coupling between QDs, spacing between lines, and the relative amount of left and right QD, making them largely dis- tinct from the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To facilitate a controlled study and track the performance of the pixel classifier as data quality degrades, each large scan is randomly sampled 50 times and the resulting small scans are aug- mented with increasing levels of synthetic noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' This results in a set of 400 simulated test scans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Finally, sev- eral large experimental measurements acquired using a double-QD configuration on a three-QD Six/SiGe1−x de- vice, fabricated on an industrial 300 mm process line [1], are used to test the performance of the virtualization algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Experimental scans capturing spurious QDs are used to demonstrate the algorithm for spurious QD detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' RESULTS We test the effectiveness of our automated approach to extracting the cross-capacitance by first evaluating the performance of each component, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=', the pixel classifier and the slope extractions, on each scan in the simulated test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The error of the pixel classifier in our frame- work is defined as a fraction of pixels belonging to true transitions that are not contained in line segments in the CNN output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' This captures type-I errors without the 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='20 VP1(V) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='20 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='40 VP2(V) (a) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='40 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='55 VP ′ 1(V) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='60 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='70 VP ′ 2(V) (b) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='35 VP ′′ 1 (V) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='30 VP ′′ 2 (V) (c) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='8 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='6 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='2 Virt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' gate off diag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' (a) Large experimentally measured charge stability diagram with a scatter plot of centers of pixel class regions overlaid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The colors of the points indicate the virtual gate off-diagonal values identified by fits to the region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The sizes of the points indicate the weights used when averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Only points with relative error less than 20 % are plotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' (a,b) Charge stability diagram after applying virtual gates acquired near the (0, 0) − (1, 1) charge transition in (a) and near the (1, 3) − (2, 4) charge transition in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In both (b) and (c) the virtualization is performed off-line, via an affine transform to the original scan shown in (a) and the points are plotted using the same parameters as in (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' effect of false type-II errors due to imperfect labels [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Figure 2(a) shows the change in RMSE as a function of the noise level in the simulated data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' At the noise level of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=', the noise level estimated from experimental data in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' [29], we observe an RMSE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='17(5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The RMSE increases significantly to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='50(11) at the noise level of 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' For reference, a pixel classifier that always predicts the NT class would have an RMSE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='62 ( √ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' For the LT and RT classes relevant to cross-capacitances, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 2(b) and (c), the pixel classifier for noise level 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0 has an RMSE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='20(8) and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='11(8), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To verify that the slope extraction tool works as in- tended, we test it across the eight large simulated test devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' For these tests, we evaluate the pixel classifier in windows of size roughly 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='5× the charging energy, as estimated by the spacing of the first two charge transi- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Outputs from the pixel classifier are cropped by one pixel from the edge of the image before processing due to missing context reducing CNN performance [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The resulting classes of pixels are then grouped into dis- tinct clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' For each cluster consisting of more than five pixels an independent linear fit is performed, return- ing both the slope and the standard error of the fitted line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' This information can be used to find the orthog- onal “virtual” control space or to flag transitions that potentially belong to spurious dots, as described in the following sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Deriving virtual gates As stated in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' II, in our approach the off-diagonal elements, defining the virtual gates transformation, are determined based on the slopes of the LT and RT cap- tured in a given image, and the diagonal elements of the capacitance matrix are set to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' When multiple lines belonging to the same class are detected, as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1(a), the capacitive coupling is calculated through a weighted average, with the weight accounting for both the size of the clusters and the standard deviations of respective fits [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The off-diagonal elements of the virtualization matrix computed this way have an RMSE of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='034(14) at the noise level of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0 defined in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' [29], corresponding to a roughly 8 % error compared to the ground truth values derived from simulated data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' We further test them on a range of levels of synthetic noise and find the RMSE rises by a factor of two at a level of noise of roughly 15× the level of noise defined in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' [29], consistent with the pixel classifier error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To better understand the trends of the virtualization matrix in the plunger-plunger space, we carry out a per- formance analysis using the test set of eight large sim- ulated charge stability diagrams and several experimen- tally measured scans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' For each scan, we calculate the fits to the pixel classification clusters based on a series of small scans sampled at each point within the large scan with the exclusion of a margin implemented to ensure that all sampled scans fall within the full scan bound- aries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The small scans and the margins are set to have a size 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='5× the charging energy of a given simulated device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Figure 3(a) shows the centers of the pixel region identi- fied in each small scan [as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 1(c)] as the sampling window is swept across a large experimentally measured charge stability diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The regions identified by the pixel classification are consistently placed correctly on the charge transition lines regardless of the position of the 5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='09 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='18 VP1(V) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='50 Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' virt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' gate off-diag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' (a) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='26 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='34 VP2(V) (b) 0 1 2 3 4 Density ×10−2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Histograms of the off-diagonal elements of the virtu- alization matrix for an experimentally measured scan shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 3(a) as a function of plunger gates, (a) VP1 and (b) VP2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Off-diagonal values are normalized to the mean of the virtual gates in the (1, 1) charge state for ease of comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Virtual gate values are extracted from a strip of small scans shifted by 6 mV (four pixels) to better visualize variation at each plunger gate value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' line within a small scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Region centers shift along the charge transition lines as different portions of the line are captured within the small scan and remain fixed when- ever the same fragment of the charge transition is cap- tured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The color of the points indicates the off-diagonal values of the virtual gate matrix, α12 and α21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' As ex- pected, these coupling constants get larger in magnitude as charges are added to each QD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Finally, the size of the points in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 3(a) indicates the 1/σ2 weight of the slopes used when averaging multiple slopes from the same type of transition within a small scan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' As desired, the posi- tions of the points with smaller sizes indicate that lines that are smaller or less captured within a small scan have fits with larger errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Overall, this plot confirms that the pixel classification and the fits are working as intended at capturing charge transition lines and their slopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To demonstrate the spatial relevance of the virtual gates derived from a set of fits across a device’s charge landscape, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 3(b) and (c) we plot affine-transformed charge stability diagrams, with points indicating fits overlaid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The points plotted are the centers of pixel re- gions with colors indicating the α12 and α21 values and size indicating the inverse of the fit error squared (the weight of the fit in the average).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The affine transfor- mation applied in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 3(b) corresponds to virtual gates derived from an image near the (0, 0) − (1, 1) charge transition with off-diagonal values α12 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='282(4), α21 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='331(4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' For Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 3(c), the affine transformation applied has virtual gates from the (1, 3) − (2, 4) charge transition, with off-diagonal values α12 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='363(4), α21 = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='480(4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' As can be seen in the insets in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 3(b) and (c), these virtual gates are very effective at trans- forming the target region to an orthogonal space, but the difference between the extracted virtual gate off-diagonal values are about 50 % higher for the latter case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' This highlights the importance of an efficient local method for determining virtual gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To further understand how capacitive coupling varies across a charge stability diagram, we can calculate varia- tion as each plunger gate is adjusted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Figure 4(a) and (b) show how virtual gates extracted from small scans change as VP1 and VP2 are varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' To better show the trend, vir- tual gates from small scans shifted by 3 mV (two pixels) in the opposing direction are included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' This shows that the virtual gates extracted from small scans effectively capture variation across charge stability diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Detection of spurious dots Visually, spurious QDs are recognized in large 2D scans as charge transitions with slopes diverging from a mono- tonic trend, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In this framework, they may be identified as transition lines with anomalous capaci- tive couplings relative to the transitions around them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' As a demonstration, we use the pixel classification and fit tools to analyze five experimental charge stability di- agrams: two capturing properly formed QD, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5(a) and (b), and three capturing spurious QDs, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5(a), (b), and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' While for extraction of the virtualization matrix small scans are sufficient, de- tection of spurious QD requires somewhat bigger scans to ensure that the neighboring charge transitions are ad- equately captured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In our analysis, we rely on 2D scans of a size roughly three times the charging energy (four times the area of scans typically used in auto-tuning al- gorithms [13, 14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' We also consider only clusters con- sisting of at least 20 pixels to ensure better reliability of the linear fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' After pixel classification, contiguous clusters of pixels belonging to a given class of transitions are analyzed in- dividually, resulting in a cluster-based fit and standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Cases where more than one cluster belongs to a given charge transition result in separate fits, as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5(b) and (e) where the LT lines are split into groups to either side of the RT lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' This separation serves two purposes: to ensure that variation along a given transi- tion isn’t included and to treat each additional line inde- pendent of the charge on another QD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Within a class and group of transitions, the magni- tude of the capacitive coupling is expected to increase monotonically as the charge is added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Such behavior is clearly visible in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5(k) and (l), with the latter having to separate groups of fits (shown with different shades of green) for the groups of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' On the contrary, a spu- rious QD manifests itself by a non-monotonic behavior of the capacitive coupling between transitions, as depicted graphically by the center point (or group of points) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5(m), (n), and (o).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The severity of this divergence can be quantified using a Z-test [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In practical applications, the automated detection of spurious QD ���ts nicely within the auto-tuning paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' As mentioned earlier, many of the proposed approaches utilize a series of small 2D scans [13, 14, 27, 29] or 1D rays [41, 42] as means to improve the tuning effi- 6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='26 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='32 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='33 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='39 VP2(V) (a) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='26 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='32 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='33 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='39 (f) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='33 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='39 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='26 α12 (k) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='38 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='44 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='31 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='37 VR1 (b) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='2 Current (arb.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='3 (n) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='48 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='52 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='49 VR2 (e) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='8 0.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='49 VP2(V) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='2 (o) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Spurious dot detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The top row shows two charge stability diagrams capturing properly formed QD [panels (a) and (b)] and three charge stability capturing spurious QD [panels (c), (d), and (e)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The black boxes in (b) and (e) in highlight small 2D scans, denoted as VR1 and VR2, typical of the auto-tuning approaches proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Panels (f)–(j) in the middle row show pixel classification results for charge stability diagrams shown in the top row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Plots of fitting results used to determine whether a spurious QD is present are shown in the bottom row [panels (k)–(o)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The different groups of transition are shown with different shades of green.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The monotonicity within each group of transitions is clearly visible in panels (k) and (l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' On the contrary, in the three plots shown in panels (m), (n), and (o), there is a clear divergence from the expected trend for the spurious QD (middle) transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Error bars indicate one standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' ciency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' While these approaches deliver measurement- cost-effective solutions, they are prone to unexpected and difficult-to-detect failure even when the data quality is high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5(b) and (e) show examples of such potentially problematic cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The small 2D regions in the plunger- plunger space, highlighted in these scans with the black boxes, are typical for topology setting algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In both cases, they are classified by a state classifier model as double QD state, with state prediction vectors being p(VR1) = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='04, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=', 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='04, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='92] for VR1 region high- lighted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5(b) and p(VR2) = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=', 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=', 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='18, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='76] for region VR2 highlighted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' 5(b), where p(VR) = [pND, pSDL, pSDC, pSDR, pDD] with ND denoting no QDs formed, SDL, SDC, and SDR denoting the left, central, and right single QD, respectively, and DD denoting the double-QD state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Moreover, the data quality for these images is high in both cases, with q(VR1) = [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0] for region VR1 and q(VR1) = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='99, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='0] for VR2, where q(VR) = [phigh, pmod, plow] with phigh, pmod, and plow denoting the probability of region VR being assessed by the data quality control module as “high,”, “moder- ate,” and “low” quality, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Thus, from the ML perspective, both these predictions are confidently cor- rect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' However, when looked at within a slightly larger voltage range, it is clear that in the latter case the small scan captures an anti-crossing with a spurious QD, which for practical tuning purposes is a failure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' If not recognized and corrected for, termination at this point will result in an incorrect charge setting and virtualiza- tion [13, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The spurious QD detection algorithm can be easily implemented in the auto-tuning algorithm proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' [27] as a safety check before the unloading step is ini- tiated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' An automated identification and characterization of spurious QDs may also be useful to inform fabrication procedures and prevent them in future devices [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' CONCLUSIONS As quantum dot devices grow in size and complexity, the need for reliable and automated tune-up procedures becomes more pressing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Establishing orthogonal con- trol of the chemical potentials of quantum dots is one of the first steps in the tune-up of any larger quantum dot array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Here, we demonstrated a method that com- bines machine-learning-based pixel-classification and tra- ditional curve fitting to reliably determine voltage cross- talk coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The advantage of this method over pre- vious approaches is highlighted by increased reliability 7 and resilience to experimental noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Further on, un- wanted spurious dots that would reduce or inhibit de- vice performance can be detected and flagged when this module is used as part of a larger tune-up algorithm [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The capability to automatically and reliably detect spuri- ous dots is especially important on wafer-scale fabrication characterization tools that produce more data than can efficiently be processed by human analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' In extensions, our tools could allow for automated navigation of volt- age space for more targeted measurement of all chemical potential and tunnel barrier cross-capacitances [17, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' ACKNOWLEDGMENTS This research was performed while J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' held a NRC Research Associateship award at the National Institute of Standards and Technology (NIST).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The views and con- clusions contained in this paper are those of the authors and should not be interpreted as representing the of- ficial policies, either expressed or implied, of the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Government.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' The U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Government is authorized to reproduce and distribute reprints for Government pur- poses notwithstanding any copyright noted herein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' Any mention of commercial products is for information only;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFAT4oBgHgl3EQfrx4U/content/2301.08654v1.pdf'} +page_content=' it does not imply recommendation or endorsement by NIST.' metadata={'source': 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