System and method for automated discovery of quantum dot configurations

Abstract

This disclosure relates to a computer implementation method for determining the boundary locations of phase states in a charge stability diagram of a capacitively coupled quantum dot, the method comprising: applying a first voltage vector to the charge stability diagram generated by the coupled quantum dot in order to define a first phase state of the coupled quantum dot; determining the phase transition location of the coupled quantum dot from the first phase state to a neighboring second phase state in the charge stability diagram by varying the voltage vector to change the energy level of the quantum dot state until a phase transition occurs; repeating the above step with respect to at least the second voltage vector; and fitting the phase transition location to a plurality of sets of fitting parameters in order to determine the boundary location of the phase state.

Description

Technical Field

[0001] (Field of Disclosure) The present disclosure relates to methods and systems for the automatic and robust estimation of phase boundaries in coupled quantum dots.

Background Art

[0002] (Background) The quantum dot electron charge stability diagram, also known as the Coulomb blockade diagram, is a graph showing the behavior of electrons confined within a quantum dot, which is a nanoscale structure capable of capturing and controlling the motion of individual electrons.

[0003] The diagram plots the energy levels of the electrons within the quantum dot as a function of the number of electrons present. Each energy level corresponds to a specific electronic configuration within the dot, and the number of electrons can be controlled by applying a voltage to the electrodes surrounding the dot.

[0004] Coulomb blockade diagrams are used to study the electrical properties of quantum dots, including their electron transport and charge storage capabilities. These diagrams are particularly useful in the field of quantum computing, where quantum dots are being investigated as potential fundamental elements related to qubits, which are the basic units of quantum information.

[0005] Charge stability diagrams are tools used to analyze the behavior of quantum dots, which are small regions of matter capable of capturing and controlling the motion of individual electrons. In a charge stability diagram, the number of electrons within the quantum dot is plotted as a function of two control parameters, typically the voltages applied to neighboring electrodes.

[0006] On the other hand, a spin qubit is a qubit that encodes information in the spin state of an individual electron. In some types of spin qubits, the qubit is generated by confining a single electron within a quantum dot and using the electron's spin as the qubit. To manipulate the electron's spin, a magnetic field is applied to the quantum dot, which can cause the spin to precess or rotate.

[0007] Charge stability diagrams can be used to study the behavior of spin qubits by providing a method for mapping regions of the diagram where the number of electrons in a quantum dot is stable. By understanding how the number of electrons in a quantum dot changes in response to changes in control parameters, researchers can better design and control the behavior of spin qubits.

[0008] For example, researchers can use charge stability diagrams to determine the optimal range of voltages to apply to nearby electrodes to confine a single electron within a quantum dot. They can also use the diagrams to identify regions where electron spin is particularly stable, which may be useful for encoding and manipulating qubit information.

[0009] The dimensions of a charge stability diagram depend on the number of quantum dots, the number of electrodes near the quantum dots acting as qubit gates, and the couplings between the quantum dots. Typically, in state-of-the-art quantum dot circuits used to conduct quantum transport experiments, the number of dimensions is greater than in the common 2D charge stability diagrams used to visualize data. Precise navigation between different quantum dot configurations in these multidimensional diagrams is not straightforward and requires enormous computational power due to the numerous intercorrelated variables and the paths that can be considered as different possibilities available in higher-dimensional space. The complexity in characterizing these multidimensional diagrams is hindering the development and improvement of real-world quantum dot devices, and this is considered a barrier in the field.

[0010] In summary, charge stability diagrams provide a useful tool for studying the behavior of quantum dots, which can be used as a platform for implementing spin qubits. By understanding the behavior of quantum dots, researchers can better design and control the behavior of spin qubits for applications in quantum computing and other areas of quantum technology.

[0011] Considering the prior art described above, the purpose of this disclosure is to provide a solution for analyzing and manipulating multiple quantum dots. As systems aiming to realize quantum computing evolve, the number of quantum dots used also increases. As a result, conventional methods for manually analyzing and interpreting charge stability diagrams of N quantum dots can be difficult for researchers, especially when N is large, such as N>4 or N>5. [Overview of the project] [Means for solving the problem]

[0012] (summary) The objective can be achieved by a computer implementation method for determining the boundary locations of phase states in the charge stability diagram of a capacitively coupled quantum dot. The method includes an initial step of applying a first voltage vector to the charge stability diagram generated by the coupled quantum dot in order to define a first phase state of the coupled quantum dot. Subsequently, the method includes an additional step of determining the phase transition location of the coupled quantum dot from the first phase state to a neighboring second phase state in the charge stability diagram by varying the voltage vector to change the energy level of the quantum dot state until a phase transition occurs. A final step is performed in which the phase transition location is fitted to a set of fitting parameters in order to determine the boundary location of the phase state by repeating at least two steps with respect to the second voltage vector. From the set of fitting parameters, at least one set of the set of fitting parameters may be a set of nonlinear fitting parameters, which are preferably extracted using a machine learning model such as a deep neural network. Utilizing a set of nonlinear fitting parameters may enable fitting of realistic coupled quantum dot charge stability diagrams, where tunneling effects are evident and lead to curvilinear phase transition locations.

[0013] A method by which phase transitions can be identified is by recording the device conductance as a function of the applied voltage. Specifically, this method is 2e 2 A differential conductance of less than 20% of / h is measured inside the first or second phase state in the charge stability diagram, while 2e 2The method may be configured to determine that at least 70% of the differential conductance of / h can be measured from the first phase state or during the phase transition from the second phase state in the charge stability diagram. Using these approximate ranges of conductance, the method can distinguish between phase states and phase transitions. Specifically, in various experiments, it may be useful to investigate the ratio between the differential conductance inside the first or second phase state and the differential conductance from the first phase state or during the phase transition from the second phase state. This ratio may be about 0.1.

[0014] Therefore, it is conceivable that this method can be used to automatically determine the phase boundary of any given state of a coupled quantum dot system. In one embodiment, it is conceivable that this method can be carried out by starting from a (0,0) state, where each of the two coupled quantum dots represents a charged state with zero electrons. Voltage fluctuations to change the energy level of the quantum dot state may be applied by varying the voltage of one of the voltage vectors in the charge stability diagram, or the voltage fluctuations may comprise the voltages of multiple electrodes that control and define the capacitively coupled quantum dot. This process may be repeated at least 10 times, more preferably at least 50 times, and even more preferably at least 200 times, until the phase boundary of the state under study is determined.

[0015] Furthermore, the above process can be carried out in different initial states such as (0,1) and (1,0), which result in a wider area mapping of the charge stability diagram.

[0016] In summary, this disclosure provides researchers with a useful tool for determining the phase boundaries of coupled quantum dots by applying voltage vectors to identify phase transitions, and the disclosure enables the automatic fitting of these transitions to map charge stability diagrams. In conclusion, it is possible to estimate the multidimensional phase boundaries of complex coupled quantum dot systems with various tunneling and capacitive couplings by using robust and accurate machine learning models.

[0017] This disclosure also relates to a computer program that, when executed by a computing device or system, comprises instructions causing the computing device or system to perform the steps of the Method.

[0018] The disclosure also relates to a computer-readable medium comprising stored instructions which, when executed by a computing device or system, cause the computing device or system to perform the steps of the Method, wherein the computing device or system may be connected to a cryostat which comprises a plurality of coupled quantum dots for defining and controlling a plurality of coupled quantum dots, and a cryostat which comprises a plurality of coupled quantum dots for controlling the voltage of electrodes of a cryostat.

[0019] (definition) Charge Stability Diagram: The charge stability diagram of a coupled quantum dot can be understood by those skilled in the art as an area of ​​suppressed conductance, divided by an area of ​​higher conductance, also known as boundary locations, transition lines, or parity lines. At the boundary locations, current can flow through the quantum dot, leading to increased conductance at the boundary locations. In the remainder of the charge stability diagram, the suppressed conductance is an indication of Coulomb blockade in the coupled quantum dot. [Brief explanation of the drawing]

[0020] [Figure 1]Figure 1 shows an example of a charge stability diagram of a coupled quantum dot.

[0021] [Figure 2] Figure 2 is the same charge stability diagram as in Figure 1, illustrating various voltage vectors for adding electrons to a quantum dot or exchanging electrons between quantum dots.

[0022] [Figure 3] Figure 3 is a flowchart example of a functional algorithm method for determining the polytope facets in the charge stability diagram of coupled quantum dots.

[0023] [Figure 4] Figure 4 is the same charge stability diagram as in Figure 1, highlighting the learned polytopes of a simulated device without tunneling.

[0024] [Figure 5] Figure 5 is an example of a charge stability diagram of coupled double quantum dots, showing a learned polytope for a device with finite tunneling between quantum dots. [Modes for carrying out the invention]

[0025] (Detailed explanation) This disclosure relates to a computer implementation method for determining the boundary locations of phase states in a charge stability diagram of a capacitively coupled quantum dot. An embodiment of a charge stability diagram (100) comprising a first phase state (n,m)(101), a second phase state (102), and a third phase state (106) is shown in Figure 1. The method includes an initial step a) of applying a first voltage vector to the charge stability diagram generated by the coupled quantum dot in order to define the first phase state of the coupled quantum dot.

[0026] This is understood as a voltage vector to a series of voltage values, each value representing the voltage applied to each electrode used to define and manipulate the quantum dots. For example, in a system consisting of two quantum dots, the voltage vector V0:(v1,v2)=(0.25,0.25) may be applied within the first phase state (101), as shown in Figure 1, to define the first phase state (n,m), where n is the number of electrons on one quantum dot and m is the number of electrons on the other quantum dot. The voltage vector is V Origin It is possible that the origin can be at (0,0), or that V0 can be considered as the initial voltage point, from which a first phase state is defined and the following steps can be performed.

[0027] Next, the second step b) would be to determine the phase transition location of the coupled quantum dot from the first phase state (n,m) to the neighboring second phase state in the charge stability diagram by varying the voltage vector to change the energy level of the quantum dot state until a phase transition occurs. For example, it is possible to record the phase transition (103) by starting from V0, applying the voltage vector (102) V1:(v1',v2)=(0.35,0.25), and continuously measuring the differential conductance as the voltage changes from V0 to V1. It is possible to determine the boundary location of the phase state (103) by repeating the above steps for at least the second voltage vector and fitting the phase transition location to multiple sets of fitting parameters. For example, as seen in Figure 1, it is possible to map the entire polygon (black dashed line) by selecting additional voltage vectors in different directions and recording different phase boundaries for each facet. Specifically, from a set of fitting parameters, at least one of the sets of fitting parameters may be a set of nonlinear fitting parameters extracted using a machine learning model such as a deep neural network. The term “extracted” can also be understood as optimizing a set of fitting parameters to fit phase transition locations, or producing a set of fitting parameters to fit phase transition locations. The machine learning model may comprise a set of fitting parameters that can be optimized and then extracted to fit phase transition locations and determine the boundary locations of phase states. For example, the machine learning model may be used to produce linear and / or nonlinear fitting parameters, which may then be used to fit phase transition locations in a charge stability diagram. The nonlinear fitting parameters may be used to describe deviations from a constant interaction model.For example, if a coupled quantum dot system has significant tunneling between two quantum dots, the phase transition locations will evolve rounding features, which require the use of nonlinear fitting parameters for fitting. Further details on nonlinear fitting parameters and machine learning models are provided in later sections of this disclosure.

[0028] In one embodiment, the method may include a step in which the initial random voltage point is sampled inside a phase state such as the phase state (0,0). This phase state would be one in which zero electrons occupy both sides of the coupled quantum dot. This option may be beneficial to researchers as a starting state because it is easier to understand and interpret. This arises because, in some cases, the electron-electron interactions within the quantum dot can cause anomalies in the charge stability diagram, and the more electrons added to the quantum dot, the more complex the system can become. It is also possible to consider having the initial voltage point inside another state, which would be a few-electron form. In that form, the electron-electron interactions may be limited, so fitting the phase boundary of the model may be easier than for the multiple-electron form.

[0029] Furthermore, in one embodiment, the method may include a step in which a second voltage vector is applied to define a second initial random voltage point sampled within the first phase state. For example, it may be useful to select a voltage vector that is located within the same state (107), since the recorded conductance should remain in the same order of magnitude and can therefore be used as a calibration tool. This may be a process that is automatically performed by the model in an initial series of measurements to calibrate the recorded conductance value.

[0030] With regard to voltage manipulation, this method may include a step in which the voltage vector is varied by varying one voltage component of the voltage vector in the charge stability diagram. For example, starting with a voltage vector V0:(v1,v2)=(0.25,0.25) (Figure 1), it is possible to change the voltage across electrode v1 to form a voltage vector V1:(v1',v2)=(0.35,0.25) (Figure 1(102)), thus only the v1 voltage is changed.

[0031] On the other hand, this method may include a step in which the components of the vector voltage are the voltages of multiple electrodes that control and define the capacitively coupled quantum dot. For example, it is conceivable that starting with a voltage vector V0:(v1,v2)=(0.25,0.25)(Figure 1(101)), the voltage vector V2:(v1',v2')=(0.35,0.35)(Figure 1(104)) can be formed by changing the voltages of electrodes v1 and v2, and thus the voltages of v1 and v2 have changed.

[0032] The above voltage vector can be performed multiple times. Specifically, the method includes steps a) and b) being performed at least 10 times, preferably at least 50 times, and more preferably at least 200 times. For example, in Figure 1(105), the black dots relate to six locations of phase transitions in a given state, one for each side of the polygon. This may be the minimum number used to determine the phase transitions of a given state, but ideally, more phase transition locations are preferable to extract a higher-resolution schematic of the state. With respect to a given device, if the coupled quantum dot has at least one small facet (on a hypersurface), then steps a) and b) may need to be performed a sufficient number of times to accurately reproduce the polygon.

[0033] In addition, the method may include steps a) and b) being performed at an initial random voltage point located in a second phase state in the charge stability diagram. For example, instead of starting with the voltage vector V0:(v1,v2)=(0.25,0.25) (Figure 1(101)) and then performing the vector to identify the phase transition for state (n,m) in Figure 1, it is also possible to start with V1:(v1',v2)=(0.35,0.25) (Figure 1(102)) and then identify the phase transition (108).

[0034] With respect to differential conductance, this method determines that the differential conductance is 2e inside the first or second phase state in the charge stability diagram. 2 This may include steps that are less than 20% of / h. This would refer to the fact that differential conductance is usually suppressed within the quantum dot unless the voltage location of the recorded differential conductance is on a phase transition. Thus, 2e 2 By measuring a value of less than 20% or less than 30% of / h, this method can safely determine that the measurement location is within the phase state. In addition, this method can determine that the differential conductance is 2e between the phase transition from the first phase state or from the second phase state in the charge stability diagram. 2 This may include steps that are at least 70% or at least 80% of / h. For example, if the voltage vector is connected to the dashed line in Figure 1(103), these points reflect a phase transition, and the differential conductance is higher, and possibly 2e 2 It is found to be approximately 70% of / h. Using this knowledge, this method can determine that the location associated with the conductance of that value is related to the location of the phase transition.

[0035] In another embodiment, the method can include the step that the ratio between the differential conductance inside the first or second phase state and the differential conductance during the phase transition from the first phase state or from the second phase state is less than 0.8, preferably less than 0.6, more preferably less than 0.4, even more preferably less than 0.1, and most preferably about 0.05. Since each device is unique due to process variations that can lead to device changes, it can be useful to identify the ratio between the two conductances. As a result, this can lead to different coupling rates between the electrode and the quantum dot or different sizes of the quantum dot due to changes in lithography techniques. However, despite the possible occurrence of device-to-device variations, the difference in the order of the differential conductance inside the phase state and during the phase transition for a given device should be significant. Therefore, it can be beneficial that the present disclosure can record such a ratio. Further, since the differential conductance can be measured while there is no application of any finite DC voltage bias across the device, the differential conductance is an experimentally easier task, and since the differential conductance does not distort the charge stability diagram measurements and the fitted results, the differential conductance may be recorded instead of the conductance.

[0036] (Fitting Model for Determining Phase Transition) To automatically perform all of the above, a fitting algorithm described below has been developed. The machine learning model of the Coulomb diamond with an electronic configuration n can have the following general form. [Number] Here, f k is M linear functions intended to learn the transitions of interest, and m(υ) calculates the probability for each voltage υ as to whether each voltage υ is part of the Coulomb diamond. To generate f k , the user enumerates a list of transitions they desire to learn, the transition vector tk Select the transition vector. This transition vector describes the change in the occupied state of individual quantum dots as they traverse the facet. The set of transitions is likely to be large and include all transitions that need to be learned. These are typically transitions that add or remove a single electron, as well as transitions that move electrons between neighboring dots. For example, moving along the orbit shown in Figure 2(200) adds an electron to one quantum dot, moving along the (201) orbit adds an electron to a second quantum dot, and moving along the (202) orbit moves an electron from one quantum dot to the other. In addition, the user can add even smaller transitions of particular interest. However, the list does not need to be exhaustive, as the algorithm can handle smaller transitions that are not part of the model. Equation f k This can be described as follows:

number

number

[0037] In one embodiment, the method may include the step of having at least one set of fitting parameters being a set of linear fitting parameters. For example, in equation (2) described above, the voltage υ is a parameter

number

number

[0038] To further improve the performance of this method, it may include a step in which a machine learning model is trained using training data. Such an embodiment can be seen in Figure 3, where the process flow relating to the algorithm is illustrated (300). First, the user may provide an initial voltage point μ0 which will be located inside the Coulomb diamond (301). The initial dataset is created by taking the user-supplied point μ0. The dataset consists of random point pairs u + ,u - (302) may contain, and the algorithm is data point u + While the data point u is inside the polytope, - Assume that is outside. The method may then proceed to create a line search in random directions around that point to calculate a better estimate of the center of the polytope (303). The model can then be fitted by solving an optimization problem (304). Further data can be obtained and a stopping criterion can be calculated (305). The stopping criterion of the algorithm is based on the check that for all facets discovered by the algorithm, it is established that either the facet is correct or it is too small to be reliably estimated with the available line search accuracy. Finally, after training has been performed, the algorithm can identify a point on the transition that allows the method to be performed for each transition line (306). As an example, it is possible to choose the mean (or median) of a pair of points that the algorithm has identified as separated by a given boundary as the initial voltage point. The transition is μ(vs u + ,u - (consisting of) can be queryed by performing a voltage ramp to a target neighbor state through a given boundary point.

[0039] In addition, the method may include a step in which the training data comprises the locations and / or orientations of phase transitions in known charge stability diagrams. For example, in process (300) described above, user-provided points may also comprise more detailed data points that may be located adjacent to or on phase transitions. These points may help extract the slope of each phase transition, which may provide information regarding the capacitive coupling of the gate electrode to the quantum dot. This information may therefore be useful with respect to the functionality of the model.

[0040] The machine learning model may also be configured to calculate the difference between the measured location and orientation of phase transitions in a capacitively coupled quantum dot system and those from an ideal constant interaction model. As shown in Figure 1, the boundary transitions of the quantum dots are not perfectly perpendicular or horizontal with respect to the v1, v2 axes. This indicates that finite cross-capacitive coupling exists between each electrode and each quantum dot, and that real-world data cannot be fully interpreted by an ideal constant interaction model. Therefore, it is useful for the model to account for this capacitive coupling and non-ideal parameters, which the model can achieve by utilizing terms in model (2) to account for them. For example, one term may be used to be identical to that in the constant interaction model, while the other term may capture some of the error where the capacitance changes. These parameters may allow modeling errors with respect to facets that add or remove a single electron from the quantum dot. The above parameters may also be used to further configure the machine learning model to calculate the deviation between the measured phase transition boundary and the phase transition boundary calculated by the ideal constant interaction approximation. The model can account for changes in the slope of phase transition boundaries, which can also reduce errors when calculating their positions in real devices.

[0041] Furthermore, the method may include a step in which at least one set of linear fitting parameters describes the boundary locations of phase states with respect to electron additions in the initial phase state to neighboring phase states.

[0042] In addition, the method may include a step in which at least one set of linear fitting parameters describes the boundary location of the phase state with respect to electron removal from the initial phase state. For example, model (2) described above has a transition vector t that can take values ​​of -1, 0, and 1. k It may have a value t. k Regarding =1, it would reflect the addition of electrons to the quantum dot. On the other hand, t k Regarding =-1, it would mean that an electron is removed from the quantum dot. Such transitions can also be seen in Figure 2 (200, 203), where electrons are added to or removed from a quantum dot. Furthermore, the method may include a step in which at least one set of linear fitting parameters describes the boundary locations of the phase states for transporting an electron from one of the coupled quantum dots to the other. An example of such a process (202) can be seen in Figure 2, where a voltage vector is used to effectively transport an electron from one quantum dot to the other, adding an electron to one quantum dot (n+1) and removing an electron from the other quantum dot (m-1). Since these transitions are part of a coupled quantum dot polytope, it may be beneficial for the method to have such fitting parameters that can describe their boundary locations, and it may be useful to have dedicated fitting parameters for them, as they may have different slopes with respect to other boundary locations.

[0043] The method may include a step in which at least one of several sets of fitting parameters is a set of nonlinear fitting parameters. For example, the equation described above.

number

number

[0044] Otherwise, a voltage point υ located on a line μ+t·p for a given t>0 is scaled to position υ'=μ+ts(p)·p by a coefficient s(p). The effect is that the convex polytope is distorted. The function s can be any machine learning model. In some embodiments, the function s can be a machine learning model that allows for vectors of length 1. This could be, for example, a neural network or a kernel extension model. Thus, the above use of the nonlinear parameter s in the function Φ(υ) enables the method described herein to successfully model coupled quantum dots having a visible tunneling effect (i.e., distortion of the charge stability diagram) in their corresponding charge stability diagrams, resulting in nonlinear boundary locations of the phase states. Thus, using such a nonlinear fitting parameter can enable fitting of charge stability diagrams with curvilinear boundary locations.

[0045] For example, the nonlinear fitting parameter s(p) can be described as follows:

number

[0046] The method may further include a step in which a set of nonlinear fitting parameters is extracted using a machine learning model and / or a nonlinear model, such as a deep neural network. For example, the s() function shown above can be provided by a neural network, and the s() function, along with other fitting parameters, can be used to fit the phase transition locations of a charge stability diagram. Further information regarding nonlinear parameters is provided in the Examples section. As described above, the advantage of nonlinear parameters is that the method can determine the boundaries of phase states having curved boundaries.

[0047] Furthermore, the method may be configured such that at least one set of nonlinear fitting parameters is used to determine the boundary locations of phase states. This feature may be beneficial in some cases because the boundary locations of phase states are not perfectly linear, but rather have some curvature. This can occur when the wave functions of quantum dots overlap, resulting in a mixture of the states of two quantum dots. In such cases, the hybridization of quantum dots can cause some bending of the shape of the phase transition line. In addition, the method may include a step in which the nonlinear fitting parameters are adapted to tunneling effects between coupled quantum dots. One way to adapt to tunneling effects is to consider that, since the Coulomb diamond of interest has a center μ and the polytopes are substantially convex, all of its transitions can be reached by the intersection of lines starting from μ in the direction of the transition. In coupled quantum dots, the tunneling effect between two quantum dots, also known as inter-dot tunneling, can produce a roundness effect at the boundary locations. Next, it is conceivable to model the roundness by a scaling coefficient that scales the intersection to match the learned polytope in that direction. An example of such a model using the above features can be seen in the Examples section of this application, and a Φ(υ) function, as described in the preceding section, consisting of a nonlinear term, may be used to fit such a polytope with a curved boundary location. Such a model can effectively scale the fitted boundary location of the phase state by some coefficient, leading to the distortion of the convex polytope. The function may be any machine learning model that can accept a vector of length 1. It may be, for example, a neural network or a kernel extension model. An example showing a simulation of a device with a distorted angle can be seen in Figure 5, where a charge stability diagram of a coupled double quantum dot is shown. Significant tunneling exists between the coupled quantum dots and is evident by the curved boundary location 501.To highlight the potential effects of tunneling between coupled quantum dots, simulations of coupled quantum dots without any tunneling between them are superimposed on the curvilinear boundary locations (502). Therefore, it is important to incorporate nonlinear fitting parameters into the model in order to properly fit the coupled quantum dots.

[0048] In another embodiment, the method may further include the step of reconstructing the fitted polytopes and state labels of a capacitively coupled quantum dot device according to a fitted set of fitting parameters at the boundary locations. An embodiment of this can be seen in Figure 4, in which the steps of the model described in the preceding paragraph are implemented, and the fitted polytopes are identified as the black dashed line (400). In this embodiment, the black dot (401) is a transition point discovered from the final step of the algorithm introduced above, which can be used to perform a transition that can be queried by performing a voltage ramp from the central portion of the Coulomb diamond through the identified point to a target neighbor state. The benefit of this additional step is that the trained model can be fully automatic, preferably without the assistance of any human operator.

[0049] This method may include a step in which voltage line scanning is performed after measuring the boundary locations of phase states to neighboring phase states until a new boundary location of a phase state is measured. As described above, this process can be carried out by selecting a voltage vector that starts from the center of the Coulomb diamond and passes through the transition boundary toward neighboring states. This can be a useful tool not only for verifying the location of the phase boundary of a given state, but also for investigating additional Coulomb diamonds and potentially exploring potential changes in neighboring states, such as coupling changes between two quantum dots.

[0050] The method may include an additional step in which the phase state fitting and reconstruction are performed starting from the midpoint of a line scan of random voltage points sampled inside the phase.

[0051] This method may include steps in which the fitted polytopes have more than 3 dimensions. For example, if the system is extended to accommodate multiple quantum dots, the charge stability diagram will not only have two axes, but this will require more electrode voltages to describe each polytope. Thus, the dimensions of the fitted polytopes may depend on the number of coupled quantum dots and the corresponding number of electrodes controlling them.

[0052] Therefore, the dimensions of the polytope to be determined are set by the experimental setup and are known before performing the method disclosed herein. On the other hand, the precise number of transition boundaries is not known a priori. The transition boundaries with respect to location, arrangement, length, and neighboring electronic states, which this method should determine, are influenced by the experimental properties of the quantum dot. For example, nanofabrication heterogeneity of the quantum dot, noise in the experimental setup, or uncertainty in measurement and applied voltage may affect the number, location, and / or length of facets of the polytope. Thus, machine learning and deep neural network models need to be trained with data from known transition boundaries to estimate the location of the boundaries describing the polytope under study. Known transition boundaries can be determined, for example, by conventional methods that manually determine changes in charge states, and these known transition boundaries may be used as results for machine learning models or deep neural network models, and the discovered phase transition locations of coupled quantum dots based on this method may be used as input for machine learning models or deep neural network models. The dimensions of the polytope may also be input for machine learning models or deep neural networks.

[0053] The disclosure may further include a computer program that, when executed by a computing device or system, provides instructions to cause the computing device or system to perform any of the steps of the Method described above. The computer program may be stored on any suitable type of storage medium, such as a non-transient storage medium.

[0054] This disclosure may include a computer-readable medium having stored instructions that, when executed by a computing device or system, cause the computing device or system to perform the steps of the Method described in any of the above paragraphs.

[0055] The disclosure further relates to a system for determining the boundary locations of phase states in a charge stability diagram of capacitively coupled quantum dots, the system comprising a processor and memory, and configured to perform any one of the steps of the method in any one of the preceding paragraphs.

[0056] The disclosure further relates to a system for determining the boundary locations of phase states in a charge stability diagram of a capacitively coupled quantum dot, the system comprising a plurality of sources, such as voltage sources, for controlling a plurality of electrodes connected to the capacitively coupled quantum dot, the system being configured to determine the phase transition locations of the coupled quantum dot from the first phase state to a neighboring second phase state in the charge stability diagram by applying a first voltage vector to the charge stability diagram generated by the coupled quantum dot in order to define a first phase state of the coupled quantum dot, and by varying the voltage vector to change the energy level of the quantum dot state until a phase transition occurs, and to fit the phase transition locations to a plurality of sets of fitting parameters in order to determine the boundary locations of the phase states, by repeating steps a) and b) with respect to at least the second voltage vector.

[0057] In one embodiment, the system may include an input interface for acquiring data from a charge stability diagram and / or an output interface for outputting fitted phase transition locations of the charge stability diagram.

[0058] Furthermore, the system can be configured to be connected to a cryostat for housing coupled quantum dots and multiple electrodes. For example, the system can be connected to a cryostat on which a device is disposed. The device may have any number of quantum devices, such as coupled quantum dots. The device can be connected via transmission lines to an external voltage, current, and / or high-frequency signal source for controlling the voltages of various electrodes and gates on the device.

[0059] In one embodiment, the system may be configured to automatically control signals to multiple electrodes of a cryostat in order to define and control multiple coupled quantum dots, thereby enabling the automatic determination of the boundary locations of phase states in the charge stability diagram. For example, the system may be connected to external voltage, current, and / or radio frequency signal sources to control sources and explore the device according to the user's plan. It is conceivable that the system can characterize the coupled quantum dot device by automatically controlling all sources, such as voltage sources, and determining the boundary locations of phase states in the charge stability diagram. The system may also tune the device to different coupling configurations and identify the boundary locations of phase states in different configurations. The user may also control sources as needed to select a specific coupling configuration or to tune the device in different configurations.

[0060] Furthermore, the system can be configured so that multiple sources are selected from a group of voltage sources, current sources, or radio frequency sources. Different types of sources or probes can be used depending on the type of experiment, as different types of measurements are suitable for different experiments or specific tasks. For example, the voltage source can be any type of DC or AC voltage source, such as a digital / analog (DAC) voltage source. The applied voltage may vary from -50mV to 50mV in steps as small as nV. In some situations, voltages up to 50V may be applied to a certain electrode type. In various cases, a voltage divider may also be used to adjust the voltage reaching the device. Different voltage ranges or steps may be used depending on the type of coupled quantum dot. Various current sources may be used in four-terminal measurements or current bias measurements, etc., and a current signal can be transmitted to the coupled quantum dot, and conductance or voltage measurements can be performed.

[0061] For example, the step of determining the location of the phase transition of a coupled quantum dot from a first phase state to a neighboring second phase state in a charge stability diagram can be performed by detecting a change in current or differential conductance, by varying the voltage vector to change the energy level of the quantum dot state until a phase transition occurs.

[0062] In some embodiments, high-frequency measurements may be set up, and radio signals can be used as probes for various electrodes of the device. Such high-frequency measurements have the advantage of being time-efficient and can lead to measurements that can be performed quickly in contrast to DC measurements. For example, when the system operates on multiple coupled quantum dots, radio frequency signals may be preferred for exploring the device because they can significantly reduce the measurement time required to estimate the boundary locations of their phase states.

[0063] The system may further include peripheral components such as one or more memories that can be used to store instructions that may be executed by any of the processors. The system may further include internal and external network interfaces, input and / or output ports, a keyboard, or a mouse, etc. As will be understood by those skilled in the art, the processing unit may also be a single processor in a multicore / multiprocessor system. Both the computing hardware accelerator and the central processing unit may be connected to a data communication infrastructure.

[0064] The system may include memory such as random access memory (RAM) and / or read-only memory (ROM), or any preferred type of memory. The system may further include a communication interface that enables software and / or data to be transferred between the system and external devices. The software and / or data transferred via the communication interface may be any preferred form of electrical, optical, or RF signal. The communication interface may include, for example, a cable or a wireless interface.

[0065] In one embodiment, the system can be configured such that the cryostat comprises a temperature control channel and a magnet, the magnet being configured to generate a magnetic field, and the system controls the temperature control channel and the magnet. Further information regarding various experiments related to coupled quantum dots can be extracted by modifying the temperature of the coupled quantum dots or by applying a magnetic field. It is known in the latest art that modifying the temperature and / or magnetic field leads to changes in the charge stability diagram of the coupled quantum dots. Therefore, it is conceivable to modify the temperature and magnetic field to fit the phase transition locations of the coupled quantum dots and correlate the changes in the charge stability diagram with the changes in temperature and / or magnetic field.

[0066] In one embodiment, the system may include an interface and / or display for obtaining the boundary locations of phase states. Such an interface or display may be available to the user for visualizing the fitting results.

[0067] In addition, the system can be configured to perform any one of the steps of the method described in any one of the paragraphs mentioned above.

[0068] (Examples) Embodiments of this disclosure relate to models used to estimate the phase boundaries of coupled quantum dot systems. Specifically, machine learning models intended to be able to learn the rounded polytopes of real devices can be used. A machine learning model of Coulomb diamond with an electronic configuration n can have the following general form:

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[0069] Item 1

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[0070] Further model examples provide guidelines on how to modify the model to account for the rounding effect of the polytope. When Φ(υ)=υ is set, the trained model still closely resembles a convex polytope, and changes in the linear term only alter the symmetry of the polytope, not allowing the inventors to learn significantly rounded angles. Appropriately small c kWhile it is possible to obtain some effect from m(υ) by selecting a specific parameter, rounding is not induced and affects the entire transition length, not just the vertices. Therefore, a model is needed to fit a significant rounding effect.

[0071] While various methods for handling this may exist, this book discloses the following embodiment. Since the Coulomb diamond of interest has a center μ and its polytope is approximately convex, it can be considered that all of its transitions can be reached by the intersection of lines starting from μ in the direction of the transition. It is then possible to model the roundness by a scaling factor that scales this intersection to match the learned polytope in that direction. This can be modeled by selecting the following.

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[0072] If the function s(·) = 1, this method yields Φ(υ) = υ. Otherwise, a point υ located on the line μ + t·p for some t > 0 is scaled to position υ' = μ + ts(p)·p by some coefficient s(p). The effect is that the convex polytope is distorted. The function s can be any machine learning model that can accept a vector of length 1. This could be, for example, a neural network or a kernel extension model.

[0073] (Example of fitting a model to data) The fitting example may include a model that uses normalized maximum likelihood fitting. In prior art documentation, the role of normalization is primarily to ensure that the optimizer does not fall into poor local optima, but here normalization is an important aspect of model fitting. The parameterization introduced in the above example is not unique. Here, there are three matrices, namely A, A, and A, which have roughly the same role. + , and A -However, such a thing exists. For example, since A = ΛΓ, the denormalization optimizer sets Λ = 0 and A + =A - =Γ can be set. More importantly, this means the algorithm is able to set the transition label t k This would allow learning parameter selections that ignore the initial hardcoded connection between the normals of the learned transitions and the normals of the transitions. Similarly, a model s that remains unnormalized might attempt to bend a single transition to cover multiple transitions in space. Both failure conditions need to be prevented.

[0074] Therefore, an example of the algorithm is that the data is for υ + ,υ - It is supplied in υ + Samples belonging to are considered to be inside the polytope, while sample υ - However, let's assume it's on the outside.

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[0075] c ii >0, Λ ii Under the constraints that >0 and Ω1 and Ω2 are normalization terms, the function L is defined as follows: + and L - This is a loss term that penalizes incorrectly estimating the correct class. In this example, a logistic loss function is used.

[0076] The normalization term Ω1 may be the same as that used in the prior art, as follows:

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[0077] With these terms in place, the model is fitted to the data by solving an optimization problem. In this embodiment, the method uses LBFGS and exponential encoding, for example, c ii =exp(γ i Encode the positive constraint by setting and removing the constraint.

[0078] (Automatic identification of transitions) The overall algorithm proceeds again, as in the cited research mentioned above. Primitively, the algorithm lies between two points ν along the half-line μ+tp, t>0, as discussed in the Model Fitting section. + ,ν - This relies on the existence of a line search algorithm that can produce the device. The user controls the linear search accuracy to control the hyperparameters of the device.

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[0079] 1. This method uses random voltage point pairs ν + ,ν - The method begins with an initial dataset containing the following. The method may create this dataset by taking a user-supplied point μ0 located within a Coulomb diamond. The method may then proceed to create a line search in random directions around that point. The data is then,

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[0080] As a proof of concept, this method simulates a series of devices without tunneling, executes the algorithm in the simulation, hardcodes Φ(ν)=ν, that is, a i =0 was fixed. With the presented data, the algorithm was executed successfully, and a visualization of its execution on a dual-dot device is shown in Figure 2.

[0081] (Data acquisition) Large variations exist in the size and surface area of ​​facets in Coulomb diamonds.

[0082] Therefore, this method is unlikely to obtain enough samples for each facet using only random sampling. Instead, general P n Regarding this, this method uses the inventors' learned estimates

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[0083] This would likely generate additional facets for sampling new candidate points. If facets do not exist, these points would eventually result in further facets being pushed out until these could only be placed at the corners of the model, thus excluding them.

[0084] This can be expressed as follows:

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[0085] Subsequently, this method, by dealing with two cases,

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[0086] For each of these candidate points, the method performs a line search starting from the estimated midpoint of the polytope through sampled points on the boundary. Each line search is another pair (ν) that the method adds to the dataset. - ,ν +This method returns ). To prevent multiple copies of similar points from being added to the dataset, this method will only add a new point if no points already exist in the dataset within a distance of δ / 4.

[0087] (stopping criteria) The algorithm's stopping criteria are based on a check that, for all facets discovered by the algorithm, the method establishes either that the facet is correct or that it is too small to be reliably estimated with the available line search accuracy.

[0088] This method checks the correctness of facets based on the fact that a plane in G dimensions can be uniquely defined through G linearly independent points that it passes through. However, the line search procedure is not a single point, but pairs of points that boundary the transitions of the polytope.

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[0089] If a facet is small in a certain direction, the limited accuracy of line search may make it impossible to reliably estimate its parameters, or even disprove their existence. Therefore, for each facet, this method calculates the radius r of the largest inscribed hypersphere (see the section "Calculation of the Largest Inscribed Hypersphere" below). This method assumes radius r > r min The algorithm considers only the correctness of equations belonging to facets that are associated with a certain condition, and treats smaller facets as undecided. The algorithm returns these facets but does not assert that they are correct. In this study and evaluation, the method considers these facets to be non-existent / undiscovered.

[0090] In this implementation, this method is used min We selected =2δ. Next, r>rmin For facets with parameters w and b, this method calculates the number of point pairs in the dataset that are separated by them.

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[0091] In summary, the stopping criterion of the inventors' algorithm is, for each facet of the polytobe P, r <r min Either this is the case, or this separates more than G+3 pairs of points.

[0092] (Calculation of the largest inscribed hypersphere) linear inequality

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[0093] This is equivalent

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[0094] In our patent application, the present invention requires the calculation of the largest inscribed hypersphere on the i-th facet of P, which is a G-1 dimensional object. To do this, the present invention first calculates the facet

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[0095] Therefore, this method substitutes the coordinate x = Qz and sets the equality constraint of the i-th facet as

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[0096] (item) 1. A computer implementation method for determining the boundary locations of phase states in a charge stability diagram of a capacitively coupled quantum dot, The first step of defining the first phase state of the coupled quantum dot is to apply a first voltage vector to the charge stability diagram generated by the coupled quantum dot, The steps include: determining the location of the phase transition of a coupled quantum dot from a first phase state to a neighboring second phase state in the charge stability diagram by varying the voltage vector to change the energy level of the quantum dot state until a phase transition occurs; - Repeat steps a) and b) with respect to at least the second voltage vector, • To determine the boundary locations of phase states, the step involves fitting the phase transition locations to multiple sets of fitting parameters. Methods that include...

[0097] 2. The method according to item 1, wherein a first voltage vector is applied to define a first initial random voltage point that is sampled within a first phase state such as (0,0).

[0098] 3. The second voltage vector is applied to define a second initial random voltage point sampled within the first phase state, as described in any one of the preceding items.

[0099] 4. The step of varying the voltage vector is applied by varying one of the voltage components of the voltage vector in the charge stability diagram, as described in any one of the preceding items.

[0100] 5. The components of the voltage vector are the voltages of multiple electrodes that control and define the capacitively coupled quantum dot, as described in any one of the preceding items.

[0101] 6. The method according to any one of the preceding items, wherein steps a) and b) are performed at least 10 times, preferably at least 50 times, and more preferably at least 200 times.

[0102] 7. Steps a) and b) are performed at the initial random voltage point located in the second phase state in the charge stability diagram, as described in any one of the preceding items.

[0103] 8. Differential conductance is 2e inside the first or second phase state in the charge stability diagram. 2 The method described in any one of the above items, which is less than 20% of / h.

[0104] 9. Differential conductance is 2e between the phase transition from the first phase state or from the second phase state in the charge stability diagram. 2 The method described in any one of the above items, which is at least 70% of / h.

[0105] 10. The method according to any one of the preceding items, wherein the ratio of the differential conductance inside the first or second phase state to the differential conductance between the phase transition from the first phase state or from the second phase state is less than 0.8, preferably less than 0.6, more preferably less than 0.4, even more preferably less than 0.1, and most preferably about 0.05.

[0106] 11. The method described in any one of the preceding items, wherein at least one of the sets of fitting parameters is a set of linear fitting parameters.

[0107] 12. The step of fitting at least one set of linear fitting parameters is provided using a machine learning model, as described in item 11.

[0108] 13. A machine learning model is trained using training data, as described in item 12.

[0109] 14. The training data is provided as described in item 13, with the location and / or orientation of phase transitions in a known charge stability diagram.

[0110] 15. The machine learning model according to any one of items 11–14, configured to calculate the difference between the measured location and orientation of phase transitions in a capacitively coupled quantum dot system and the location and orientation of phase transitions in an ideal constant-interaction model.

[0111] 16. The method according to any one of items 11–15, wherein the machine learning model is configured to calculate the deviation between the measured phase transition boundary of a capacitively coupled quantum dot system and the phase transition boundary calculated by an ideal constant interaction model.

[0112] 17. A method described in any one of the preceding items, wherein at least one set of linear fitting parameters describes the boundary location of a phase state with respect to electron addition in a first phase state to a neighboring phase state.

[0113] 18. At least one set of linear fitting parameters describes the boundary location of the phase state with respect to electron removal from the first phase state, as described in any one of the preceding items.

[0114] 19. The method described in any one of the preceding items, wherein at least one set of linear fitting parameters describes the boundary location of the phase state for transporting electrons from one coupled quantum dot to the other coupled quantum dot.

[0115] 20. The method described in any one of the preceding items, wherein at least one of the sets of fitting parameters is a set of nonlinear fitting parameters.

[0116] 21. The method described in item 20, wherein at least one set of nonlinear fitting parameters is extracted using a machine learning model and / or a nonlinear model such as a deep neural network.

[0117] 22. The method described in any one of items 20-21, wherein at least one set of nonlinear fitting parameters determines the boundary location of the phase state.

[0118] 23. The nonlinear fitting parameters are adapted to the tunneling effect between coupled quantum dots, as described in any one of items 20-22.

[0119] 24. The method described in any one of the preceding items for reconstructing the fitted polytopes and state labels of a capacitively coupled quantum dot device according to a fitted set of fitting parameters.

[0120] 25. Voltage line scanning is performed after determining the location of the phase transition of the phase state to a neighboring phase state, as described in any one of the preceding items.

[0121] 26. The method of item 25, wherein voltage line scanning is performed until a new boundary location of the phase state is measured.

[0122] 27. Phase state fitting and reconstruction are performed starting from the midpoint of the line scan, as described in any one of the preceding items.

[0123] 28. A fitted polytope having more than 3 dimensions, as described in any one of the preceding items.

[0124] 29. A computer program comprising instructions, the instructions causing the computing device or system to perform one of the steps of the method described in any one of the preceding items when the program is executed by the computing device or system.

[0125] 30. A computer-readable medium having stored instructions, the instructions, when executed by a computing device or system, cause the computing device or system to perform one of the steps described in any one of items 1-28 above.

[0126] 31. A system for determining the boundary locations of phase states in a charge stability diagram of capacitively coupled quantum dots, comprising a processor and a memory, and configured to perform any one of the steps of the method described in any one of items 1-28 above.

[0127] 32. A system for determining the boundary locations of phase states in a charge stability diagram of a capacitively coupled quantum dot, the system comprising multiple sources, such as voltage sources for controlling multiple electrodes connected to the capacitively coupled quantum dot, • To define the first phase state of the coupled quantum dot, a first voltage vector is applied to the charge stability diagram generated by the coupled quantum dot, • Determining the location of the phase transition of a coupled quantum dot from a first phase state to a neighboring second phase state in the charge stability diagram by varying the voltage vector to change the energy level of the quantum dot state until a phase transition occurs, Repeat steps a) and b) with respect to at least the second voltage vector, • To determine the boundary locations of phase states, the phase transition locations are fitted to multiple sets of fitting parameters. A system configured to perform the following actions.

[0128] 33. The system described in item 32, which is connected to a cryostat for housing coupled quantum dots and multiple electrodes.

[0129] 34. A system as described in any one of items 32-33, in which multiple sources are selected from the group consisting of voltage sources, current sources, or radio frequency sources.

[0130] 35. A cryostat comprising a temperature control channel and a magnet, the magnet configured to generate a magnetic field, and the system configured to control the temperature control channel and the magnet, as described in any one of sections 33-34.

[0131] 36. The system described in any one of items 32–35, configured to automatically control signals to multiple electrodes of a cryostat in order to define and control multiple coupled quantum dots, thereby enabling the automatic determination of the boundary locations of phase states in a charge stability diagram.

[0132] 37. The system described in any one of items 32-36, configured to perform any one of the steps of the method described in any one of items 1-28 above.

Claims

1. A computer implementation method for determining the boundary locations of phase states in the charge stability diagram of capacitively coupled quantum dots, a. A step of applying a first voltage vector to the charge stability diagram generated by the coupled quantum dot in order to define the first phase state of the coupled quantum dot, b. A step of determining the location of the phase transition of the coupled quantum dot from the first phase state to a neighboring second phase state in the charge stability diagram by varying the voltage vector until a phase transition occurs, wherein the determining step is for changing the energy level of the state of the quantum dot. c. Repeating steps a) and b) with respect to at least the second voltage vector, d. A step of fitting the phase transition location to a plurality of sets of fitting parameters in order to determine the boundary location of the phase state, wherein at least one of the plurality of sets of fitting parameters is a set of nonlinear fitting parameters extracted using a machine learning model such as a deep neural network. Methods that include...

2. The method according to claim 1, wherein at least one set of the nonlinear fitting parameters determines the boundary location of the phase state and adapts to the tunneling effect between coupled quantum dots.

3. The method according to any one of the preceding claims, wherein at least one set of the plurality of sets of fitting parameters is a set of linear fitting parameters.

4. The method according to claim 3, wherein the machine learning model is trained using training data.

5. The method according to claim 4, wherein the training data comprises the locations and / or orientations of phase transitions in known charge stability diagrams.

6. The method according to any one of claims 3 to 5, wherein the machine learning model is configured to calculate the difference between the measured location and orientation of phase transitions in a capacitively coupled quantum dot system and the location and orientation of phase transitions in an ideal constant interaction model.

7. The method according to any one of claims 3 to 6, wherein the machine learning model is configured to calculate the deviation between a measured phase transition boundary of a capacitively coupled quantum dot system and a phase transition boundary calculated by the ideal constant interaction model.

8. The method according to any of the preceding claims, wherein the components of the voltage vector are the voltages of a plurality of electrodes that control and define the capacitively coupled quantum dot.

9. The method according to any of the preceding claims, wherein the at least one set of linear fitting parameters describes the boundary location of the phase state with respect to the addition of electrons in the first phase state to the neighboring phase states.

10. The method according to any of the preceding claims, wherein the boundary locations reconstruct the fitted polytopes and state labels of the capacitively coupled quantum dot device according to the fitted set of fitting parameters.

11. The method according to any of the preceding claims, wherein the voltage line scanning is performed after determining the location of the phase transition of the phase state to a neighboring phase state.

12. The method according to any of the preceding claims, wherein the ratio of the differential conductance inside the first or second phase state to the differential conductance between the phase transition from the first or second phase state is less than 0.8, preferably less than 0.6, more preferably less than 0.4, even more preferably less than 0.1, and most preferably about 0.

05.

13. The method according to any one of the preceding claims, wherein the fitted polytope has more than 3 dimensions.

14. A computer program comprising instructions, wherein, when the program is executed by a computing device or system, the instructions cause the computing device or system to perform one of the steps of the method described in any one of the preceding claims.

15. A computer-readable medium having stored instructions, wherein, when executed by a computing device or system, the instructions cause the computing device or system to perform one of the steps of the method according to any one of claims 1 to 13.

16. A system for determining the boundary locations of phase states in a charge stability diagram of a capacitively coupled quantum dot, the system comprising a processor and a memory, and configured to perform any one of the steps of the method according to any one of the above claims 1 to 13.

17. A system for determining the boundary locations of phase states in a charge stability diagram of a capacitively coupled quantum dot, wherein the system comprises a plurality of sources, such as voltage sources, for controlling a plurality of electrodes connected to the capacitively coupled quantum dot, and the system a. In order to define the first phase state of the coupled quantum dot, a first voltage vector is applied to the charge stability diagram generated by the coupled quantum dot, b. Determining the location of the phase transition of the coupled quantum dot from the first phase state to a neighboring second phase state in the charge stability diagram by varying the voltage vector until a phase transition occurs, wherein the determination is for the purpose of changing the energy level of the state of the quantum dot. c. Repeating steps a) and b) with respect to at least the second voltage vector, d. To determine the boundary location of the phase state, the phase transition location is fitted to a set of fitting parameters. A system configured to perform the following actions.

18. The system according to claim 17, wherein the system is connected to a cryostat for housing the coupled quantum dot and the plurality of electrodes.

19. The system according to any one of claims 17 to 18, wherein the plurality of sources are selected from the group consisting of voltage sources, current sources, or radio frequency sources.

20. The system according to any one of claims 18 to 19, wherein the cryostat comprises a temperature control channel and a magnet, the magnet being configured to generate a magnetic field, and the system is configured to control the temperature control channel and the magnet.

21. The system according to any one of claims 17 to 20, wherein the system is configured to automatically control the signals to the plurality of electrodes of the cryostat in order to define and control the plurality of coupled quantum dots, thereby enabling the automatic determination of the boundary locations of phase states in a charge stability diagram.

22. The system according to any one of claims 17 to 21, wherein the system is configured to perform any one of the steps of the method described in any one of the preceding claims 1 to 13.

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