Quantum machine learning device and method

Abstract

Methods and apparatus for generating quantum features for machine learning models are disclosed. The method includes providing a quantum ML device (QMLD) including one or more quantum dots, one or more source gates, one or more drain gates, and one or more control gates. The method further includes transforming input data for the machine learning model into a first voltage; applying the first voltage to the one or more control gates, and / or the one or more source gates, and / or the one or more drain gates; applying a second voltage to one or more of the one or more source gates; measuring a signal at one or more of the one or more drain gates; analyzing the measured signals to determine values of one or more parameters; and interpreting the values of the one or more parameters as a non-linear mapping of the input data to be used for the machine learning model.

Description

Technical Field

[0001] Aspects of the present disclosure relate to quantum processing devices, and more particularly, to methods and devices for implementing machine learning techniques using such quantum processing devices. Background Art

[0002] The developments described in this section are known to the inventors. However, unless otherwise indicated, it should not be assumed that any developments described in this section qualify as prior art simply by virtue of their inclusion in this section, or that the developments are known to those skilled in the art.

[0003] Machine learning (ML) has had a profound impact on our daily lives, from advanced computational methods in material design and chemical processes to pattern recognition for autonomous vehicle transportation and cell classification for cancer cell detection. ML algorithms have made rapid progress as computing power has advanced (approximately following Moore's Law and doubling every year).

[0004] To date, ML uses classical computers, where calculations are performed using binary bits - which can be in one of two different states, 0 or 1. The binary nature of classical computing bits can make them slow, and often multiple bits are required to complete the simplest equations on a classical computer. Quantum computers, on the other hand, perform calculations using quantum bits (qubits), which, unlike classical bits, can exist in multiple states. A qubit can be in 0, 1, or a superposition of these two states (called a quantum state). As a result, quantum computers can complete algorithms faster and may require fewer qubits to perform operations. Because of this superiority, it has been agreed that quantum computers will be able to solve ML problems that may be difficult to solve using classical computing.

[0005] With this in mind, recent progress has been made to use quantum computers to solve ML problems. This has given rise to the subfield of quantum machine learning, where a variety of quantum algorithms for ML tasks (partially or fully executed on quantum computers) have been shown to outperform classical algorithms (executed on classical computers). However, the performance of such quantum machine learning algorithms can be further improved. Summary of the invention

[0006] According to a first aspect of the present disclosure, a method for generating quantum features for a machine learning model is provided. The method includes: providing a quantum ML device (QMLD), the quantum ML device including one or more quantum dots, one or more source gates, one or more drain gates and one or more control gates. The method also includes: transforming input data for the machine learning model into a first voltage; applying the first voltage to the one or more control gates, and / or the one or more source gates, and / or the one or more drain gates; applying a second voltage to one or more of the one or more source gates; measuring a signal at one or more of the one or more drain gates; analyzing the measured signal to determine the value of one or more parameters; and interpreting the value of the one or more parameters as a nonlinear mapping of the input data to be used for the machine learning model.

[0007] Transforming the input data into a voltage may include: performing a random transformation of the input data; and transforming the randomly transformed input data into a voltage. In other embodiments, transforming the input data into a voltage includes: mapping the input data directly to a voltage. In this embodiment, interpreting the values ​​of the one or more parameters may include: combining the values ​​of the one or more parameters into features for the machine learning model.

[0008] In some embodiments, transforming the input data into a voltage comprises: combining data points of the input data into pairs, converting the combined data points into a combined voltage; and applying the voltage to the one or more control gates comprises: applying the combined voltage to the one or more control gates. In this case, interpreting the values ​​of the one or more parameters comprises: determining a distance metric or similarity score between the values ​​of the one or more parameters.

[0009] In some examples, the quantum ML device includes a plurality of source gates, a plurality of drain gates, and a plurality of control gates, and the quantum ML device functions as a quantum random kitchen sink device.

[0010] In other examples, the quantum ML device includes a source gate, a number of drain gates matching the desired feature dimension, a number of control gates matching the dimension of the input data, and the quantum ML device functions as a quantum extreme learning machine.

[0011] In another example, the quantum ML device includes a source gate, a drain gate, and a number of control gates that is twice the dimension of the input data, and the quantum ML device functions as a quantum kernel learning machine.

[0012] The method may further include: a step of manufacturing the quantum ML device. The manufacturing step includes: preparing a bulk layer of a semiconductor substrate; preparing a second semiconductor layer; exposing a clean crystal surface of the second semiconductor layer to dopant molecules to produce an array of dopant points on the exposed surface; annealing the arrayed surface to incorporate dopant atoms of the dopant molecules into the second semiconductor layer; and forming the one or more gates, the one or more source leads, and the one or more drain leads.

[0013] The one or more control gates may be formed in the same plane as the dopant dots.In other examples, a dielectric material may be deposited over the annealed second semiconductor layer, and the one or more control gates may be formed over the dielectric material.

[0014] In some examples, the dopant dots are phosphorus dots, the second semiconductor layer is silicon-28, and the quantum ML device includes ten quantum dots.

[0015] In another aspect of the present disclosure, a quantum ML device (QMLD) is provided. The QMLD includes: one or more quantum dots; one or more source gates; one or more drain gates; and one or more control gates. The quantum ML device is used to generate quantum features for a machine learning model by the following steps: applying a first voltage corresponding to input data for the machine learning model to the one or more control gates, and / or the one or more source gates, and / or the one or more drain gates; applying a second voltage to one or more of the one or more source gates; measuring a signal at one or more of the one or more drain gates; analyzing the measured signal to determine the value of one or more parameters; and interpreting the value of the one or more parameters as a nonlinear mapping of the input data to be used for the machine learning model.

[0016] Other aspects of the disclosure and embodiments of the aspects outlined in the immediately preceding paragraph will become apparent from the following detailed description and accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1A A schematic diagram showing a first example donor qubit device.

[0018] Figure 1B A schematic diagram showing a second example donor qubit device.

[0019] Figure 2A An example quantum ML device according to aspects of the present disclosure is shown.

[0020] Figure 2BAn example showing three current sources measured at separate drain leads.

[0021] Figure 3 is a flow chart illustrating an example method for quantum ML according to aspects of the present disclosure.

[0022] Figure 4 A schematic diagram showing an example quantum ML device used as a quantum extreme learning machine according to aspects of the present disclosure.

[0023] Figure 5 A schematic diagram showing an example quantum ML device used as a quantum kernel learning machine according to aspects of the present disclosure.

[0024] Figure 6 A schematic diagram showing an example quantum ML device used as a quantum random kitchen sink according to aspects of the present disclosure.

[0025] Figure 7 STM lithography image showing a quantum ML device used to evaluate the performance of a quantum random kitchen sink.

[0026] Figure 8 Plot showing the performance of a quantum random kitchen sink compared to a classical random kitchen sink for cosine and trigonometric functions based on a hypersphere data set.

[0027] Fig. 9 is a graphical representation of the performance of the quantum random kitchen sink compared to the classical random kitchen sink based on cosine and trigonometric functions on a binned data set.

[0028] Fig.10 is a graphical representation of the performance of a quantum random kitchen sink compared to a classical random kitchen sink based on cosine and trigonometric functions for a diatomic bond dataset.

[0029] Fig.11 STM micrograph showing another quantum ML setup used to evaluate the performance of the quantum random kitchen sink.

[0030] Fig. 12A Describe an ad hoc data set.

[0031] Fig. 12B Plotting a hypersphere dataset.

[0032] Fig. 12C Plotting the polynomial root separation data set.

[0033] Fig.12D Depicts example images from the benchmark real-world dataset.

[0034] Fig.13A is a grid of nine subplots showing the performance of the RKS, RBF, and QRKS models for the hypersphere, polynomial separation, and ad hoc data sets as a function of the hyperparameters used to perform the optimization.

[0035] Fig.14A Plot of the performance of the quantum random kitchen sink (QRKS) compared to three classical models on a polynomially separated dataset.

[0036] Fig. 14B is a graphical representation of the performance of QRKS compared with three classical models on an ad hoc dataset.

[0037] Fig. 14C is a graphical representation of the performance of QRKS compared with three classical models on the hypersphere dataset.

[0038] Fig.14D is a table showing the performance of QRKS compared with three classical models on the MNIST dataset.

[0039] Fig.14E is a graph showing the performance of QRKS compared with three classical models for a hypersphere dataset for 22-dimensional data.

[0040] Fig.14F is a graphical representation of the performance of QRKS compared with three classical models for a polynomial separation dataset for 5-dimensional data.

[0041] Figure 14G is a graph of the performance of QRKS compared with three classical models for an ad hoc dataset for 2-dimensional data.

[0042] Fig.15A Shown is an example response of a quantum ML device operating at 4K as a memory to a random binary string input.

[0043] Fig. 15B An example response of a quantum ML device operating as a reservoir at approximately 30 mK to a random binary string input is shown.

[0044] Fig.16A is a graphical representation of the storage capacity of a QMLD at 4K when operating as storage.

[0045] Fig. 16B is a graphical representation of the storage capacity of a QMLD at approximately 30 mK when operating as a memory.

[0046] Fig. 16C is a graphical representation of the processing capacity of a QMLD at 4K when operating as storage.

[0047] Fig.16D is a graphical representation of the processing capacity of a QMLD at 4K when operating as storage. DETAILED DESCRIPTION

[0048] Overview

[0049] As mentioned above, ML algorithms and models are used in almost every technology field today to help classify data, predict outcomes, or develop solutions. For example, ML algorithms can be used to automatically classify emails as spam or not spam, predict weather patterns, or develop action plans based on a given set of input conditions. To achieve these goals, a suitable ML model (such as a binary classification model or a regression model) is first selected, and then the ML model is trained on some training data. For example, to classify emails, a binary classification model can be used, and the training data can be emails. To predict weather patterns, a regression model can be selected, and the training data can be different types of weather phenomena and historical weather data, etc.

[0050] At a macro level, the ML model receives an input data vector And depending on how the model is trained to generate information For example, an ML model may be trained to take an image as input and determine whether the image includes a cat. In such an example, the ML model is first trained using a set of images. Some of the images may include a cat, while other images may not include a cat. In addition, the training data may be labeled so that the model knows which images include a cat and which do not. Once the ML model has been trained with enough data, it is able to classify unlabeled images as either a cat image or a non-cat image. The accuracy of such an ML model depends on many factors, including but not limited to: the amount of training data used, the model itself, and how well the model has been trained (i.e., the quality and quantity of the training).

[0051] One way to improve the accuracy of ML models is to use feature engineering. In machine learning, features are individual measurable properties or characteristics of a phenomenon. For example, in a spam detection algorithm, features may include the presence or absence of certain email headers, email structure, language, frequency of specific terms, grammatical correctness of text, etc. Models can use these features to help with classification, prediction, or formulation. Feature engineering refers to the process of selecting, manipulating, and transforming raw data to extract features that can be used to train ML models. Feature engineering typically utilizes data from a training dataset to generate new features. This set of new features can then be used to train the ML model with the goal of simplifying and speeding up the overall computation.

[0052] One example technique for engineering features is called the kernel method or kernel trick. This method generates features for the algorithm based solely on the inner products between pairs of input data points. This method relies on the observation that any positive semi-definite function K(x i ,x j )(in ) defines the inner product K(x) in the transformation space i ,x j )=〈φ(x i ),φ(x j )〉, where φ(x i ) and φ(x j ) are the data points x i and x j Other methods for engineering features include the random kitchen sink method, which, as the name suggests, randomly selects a subset of features from a feature set and uses these features to train a corresponding ML model.

[0053] As discussed previously, classical computers will soon reach a point where quantum mechanical effects will prevent further progress, and quantum computers will have to be used to perform calculations that classical computers cannot perform. However, it is important to note about quantum computing that the physical devices currently being constructed are still in the so-called noisy intermediate-scale quantum (NISQ) era, and it is impossible to implement fully fault-tolerant quantum algorithms. Instead, these NISQ systems can be used to solve specific problems of practical interest. Such quantum systems that are specifically constructed (or hard-coded) to perform one or more specific problems are called analog quantum computers or analog quantum processors.

[0054] Such analog quantum computers or processors have recently been constructed to simulate the Fermi-Hubbard model, magnetism, and topological phases.

[0055] The present disclosure introduces a quantum machine learning device for performing quantum machine learning with classical input and output - using semiconductor quantum dots and simulating the Fermi-Hubbard model Hamiltonian. With minimal modification to the quantum ML device, the device can be used as a quantum extreme learning machine, a quantum kernel learning machine, and a quantum random kitchen sink. It has been found that the quantum ML device and related quantum ML techniques for engineering features disclosed in the present invention perform significantly better than corresponding classical computing techniques.

[0056] Example System

[0057] Figure 1AAn example semiconductor quantum dot device 100 that can be implemented in a quantum ML device of the present disclosure is shown. As shown, the quantum dot device 100 includes a semiconductor substrate 102 and a dielectric 104. In this example, the substrate is isotopically purified silicon (silicon-28), and the dielectric is silicon dioxide. In other examples, the substrate may be silicon (Si). An interface 106 is formed where the substrate 102 and the dielectric 104 meet. In this example, the interface is a Si / SiO2 interface. To form a quantum dot, a donor atom 108 is located within the substrate 102. The quantum dot is defined by the Coulomb potential of the donor atom. The donor atom 108 can be introduced into the substrate using nanofabrication techniques, such as hydrogen lithography provided by a scanning tunneling microscope or industry standard ion implantation techniques. In some examples, the donor atom 108 can be a phosphorus atom in a silicon substrate, and the quantum dot can be referred to as a Si:P quantum dot.

[0058] exist Figure 1A In the depicted example, the quantum dot includes a single donor atom 108 embedded in a silicon-28 crystal. In other examples, the quantum dot may include multiple donor atoms embedded in close proximity to each other.

[0059] Gates 112 and 114 can be used to regulate the electron population on quantum dot 100. For example, electrons 110 can be loaded onto the quantum dot via gate electrodes such as 112. The physical state of electron 110 is described by wave function 116 - wave function 116 is defined as the probability amplitude of finding an electron at a certain location. Donor qubits in silicon rely on the use of potential wells naturally formed by donor nuclei to confine electron spins.

[0060] Figure 1B Another example semiconductor quantum dot device 150 that can be implemented in a quantum ML device of the present disclosure is shown. This device is similar to Figure 1A The quantum dot device 100 shown differs in the placement of the gate. Figure 1A 104. In some examples, the gates 112, 114 are placed on top of the dielectric 104. In this example, the gate 152 is located within the semiconductor substrate 102. In some embodiments, the gate 152 is placed in the same plane as the donor dots 108. Such an in-plane gate can be connected to the surface of the substrate via a metal via (not shown). A voltage can be applied to the gate electrode 152 to confine one or more electrons 110 in the Coulomb potential of the donor atoms 108. In some examples, the quantum dot device can include a gate located within the semiconductor substrate 102 and a gate located on top of the dielectric 104.

[0061] Figure 2AAn example quantum ML device (QMLD) 200 is shown according to aspects of the present disclosure. The QMLD 200 includes a donor quantum dot array 202, a source 204, a drain 206, and a plurality of input gate electrodes G1-G8. In one example, the quantum dot array 202 includes an array of donor quantum dots 208, wherein each quantum dot 208 is similar to Figure 1A and / or Figure 1B The quantum dots shown. Figure 2A The inset 210 in FIG. 2 shows a magnified view of a 5×5 section of the quantum dot array 202. As seen in the inset, the quantum dots 208 are arranged in a square lattice. Each of the circles in the inset represents a quantum dot, and the arrows in the quantum dot represent the spin of the electron of the donor atom coupled to the quantum dot.

[0062] It should be understood that the quantum dots 208 in the array need not be placed in a square lattice format. Instead, the quantum dots 208 can be arranged in an array of any shape without departing from the scope of the present disclosure. In some examples, the quantum dots 208 can be arranged in a random manner, where there is no symmetry available in the array. This randomness in the array design may lead to better ML predictions. In addition, the number of quantum dots 208 present in the array 202 can vary depending on the specific implementation. In general, the larger the array, the better or more accurate the results. However, it should be noted that beyond approximately 50 quantum dots, it is no longer possible to simulate the device on a classical computer.

[0063] Although a single source 204 and a single drain 206 are shown in this example, this need not always be the case. In other embodiments, QMLD 200 may include multiple drain and / or source leads. Furthermore, the number of gates utilized in QMLD 200 may vary depending on the feature generation method used.

[0064] In addition, the quantum dot array 202 can be fabricated in a 2D manner, where the input gate electrodes G1-G8 are coplanar with the array 202 (eg, Figure 1B ), and / or in a 3D manner, where gates G1-G8 can be patterned on a second layer after overgrowing a quantum dot array layer with epitaxial silicon (e.g. Figure 1A ). The ultra-low gate density of Si:P quantum dots 208 allows large quantum dot arrays to be fabricated with very few control electrodes. In embodiments of the present disclosure, low gate densities of 1 gate for hundreds of quantum dots are possible. However, more gates may be needed to manipulate the array. Thus, in some embodiments, there may be about 10 gates for controlling about 75 quantum dots. However, this is not critical and this ratio may be varied for different embodiments without departing from the scope of the present disclosure.

[0065] The quantum dot array 202 is weakly coupled to the source 204 and the drain 206 to measure the electron transfer through the quantum dot array 202. In addition, the quantum dot array 202 is capacitively coupled to a plurality of control gates G1-G8. The control gate 208 can be used to adjust the electron filling, interdot coupling and single particle energy level of the quantum dot array 202.

[0066] The Hamiltonian (i.e., the underlying mathematical description) that describes the behavior of electrons in the quantum dot array 202 is a 2D extended Hubbard model with long-range electron-electron interactions (V), on-site Coulomb interactions (U), and nearest neighbor electron transfer (t). The Hamiltonian that describes the system is:

[0067]

[0068] where the electron hopping term (t) is related to the probability of electron tunneling between nearest neighbor donor sites. The intra-site Coulomb interaction (U) is the energy required to add a second electron to a site. The inter-site Coulomb interaction (V) is the energy required to add an electron to a neighboring site—this may include interactions on all pairs of sites i and j. The parameters U, V, and t are determined by the configuration and the distance between the sites. Finally, ∈ i is the single-particle energy level at the ith site.

[0069] The Hubbard model ground state problem has been shown to be Quantum Merlin Arthur (QMA) complete (a complex type in computational complexity theory), which means that the ability to control the ground state of the Hubbard Hamiltonian offers the potential for use with large computational resources. The techniques described in the following sections exploit this computational power of the Hubbard model to perform machine learning in a way that is agnostic to the downstream task.

[0070] Generating features for ML

[0071] QMLD 200 can be used to generate features for ML models. For example, the classic input data can be transformed into a voltage applied to one or more of the gate electrodes. In some examples, a different voltage can be applied to each gate. In other examples, the same voltage can be applied to two or more of the gate electrodes. Which voltage is applied to the gate electrodes may ultimately depend on the specific ML algorithm used. The applied voltage is used to change the Hubbard parameter (∈ i). The source voltage can then be swept to measure the current profile at one or more drain leads 206 of the QMLD 200. This measured current profile can then be analyzed to find the charge excitation gap (CEG) or current at a particular source voltage. The CEG, current, or conductance is then used to output a nonlinear function map that can be used by a classical ML model.

[0072] Figure 3 is a flow chart illustrating an example method 300 for generating features for quantum ML according to aspects of the present disclosure.

[0073] Method 300 begins at step 302, where input data is applied to one or more of the control gates (e.g., one or more of the control gates G1-G8). In some examples, the raw input data is applied to the control gates as voltages. In other examples, the input data is transformed before being applied to the control gates as voltages. In some embodiments, the input data is represented as a vector. For example, if the input data is an image of a cat, the input data vector may be the color grayscale of each pixel in the image. This input data vector is then converted into a voltage and used as an input to the ML model.

[0074] Next, at step 304, a constant voltage or a voltage sweep is applied to the source lead 202. The sweep voltage may be in the range of a few millivolts. A direct current (DC) or radio frequency (RF) sweep may be used. In an RF sweep, each drain lead 206 is connected to a resonator circuit (not shown) having a different frequency. The use of RF also allows for multiplexing of measurements of several drain leads 206 for parallel operation to further reduce the processing time of the machine learning method. This multitasking can be achieved using RF sweeping when each drain lead 206 is connected to a resonator having a different frequency. In this way, a voltage sweep having a different frequency corresponding to each drain lead may be applied.

[0075] Next, at step 306, current is measured as a function of source voltage at drain lead 206. The measured current data may be plotted against source voltage to generate a current curve. Figure 2B Examples of these current curves measured at an independent drain lead 206 are shown. Specifically, Figure 2BThree graphs 220, 222, 224 are shown, each with source voltage on the x-axis and current on the y-axis. Graph 220 shows the measured current as a function of source voltage applied to gate 208 as a voltage for a first data point x1. Graph 222 shows the measured current as a function of source voltage applied to control gate 208 as a voltage for a second data point x2. Finally, graph 224 shows the measured current as a function of source voltage applied to control gate 208 as a voltage for a third data point x3.

[0076] At step 308, the current data obtained at step 306 is analyzed to determine one or more parameters. In some examples, the parameter may be a charge excitation gap (CEG) and the measured current curve may be analyzed to find the CEG. The CEG is the gap energy corresponding to the energy required to add electrons to the quantum dot array. The CEG is determined by finding the point where the current rises rapidly. Thus, the voltage that causes the fastest increase in current is considered to be the CEG. In another example, the measured current curve may be analyzed to determine the current at a specific source voltage. In another example, the parameter determined from the measured current curve is conductance.

[0077] Next, at step 310, the values ​​of the one or more parameters are interpreted as a nonlinear mapping of the input data to be used for the machine learning model. For example, if the parameter is a CEG and a quantum random kitchen sink is used, then the one or more values ​​of the CEG are interpreted as features in an augmented space to be used in the ML model. Alternatively, if a quantum kernel learning machine is used, interpreting the values ​​of the one or more parameters may include determining a distance metric or similarity score between the values ​​of the one or more parameters.

[0078] Importantly, these different features can be generated from a single voltage sweep of the source voltage at a specific set of input voltages on the gate. Alternatively, the current and conductance can be generated by making a single current measurement, greatly reducing the processing time of the QMLD 200. These quantum enhanced features are expected to be superior to classical features due to their increased computational complexity compared to classical features.

[0079] Depending on the ML technique used to generate the feature, the method 300 can be adapted. For example, although the method 300 is described as a voltage corresponding to the input data being applied to the control gate, this need not be the case in all embodiments. Rather, in some other embodiments, in addition to or in lieu of the control gate, a voltage corresponding to the input data may be applied to one or more source gates and / or one or more drain gates.

[0080] In addition, depending on the method used, the way the data is applied as voltages and the way the output is interpreted may vary. Some example methods and variations are described in the following sections. For example, when using the Quantum Random Kitchen Sink (QRKS) method, the input voltage is a random transformation of the input data, and the output parameter is an added feature dimension. In another example, using the Quantum Extreme Learning Machine (QELM), the input voltage is directly mapped to the input data, and the output parameter is interpreted as an added feature dimension. In yet another example, using the Quantum Kernel Learning Machine (QKLM) method, the input data is applied as voltages in pairs. For example, a data point x i and data point x2 are combined and applied as a voltage to gate 208. The output parameter is then interpreted as a distance metric or similarity score between them.

[0081] Furthermore, although in step 306 a current signal as a function of source voltage is measured at drain lead 206, this need not be the case in all embodiments. In some embodiments, other types of signals may be measured along with or in lieu of a current signal, such as voltage, capacitance, conductance, inductance, etc. The measured signal data may then be plotted against source voltage to generate a signal curve.

[0082] Figure 2C and Figure 2D Examples of these other signal curves measured at the independent drain lead 206 are shown. Specifically, Figure 2C The invention is used to bias the oscillation voltage (V RF ) is applied to the source 204 to measure the RF transmission of the QMLD. The drain 206 is connected to the LC resonator circuit (L) and parasitic capacitance, which converts the output current signal into a voltage signal. This voltage signal is then amplified and used with the original V RF The signal demodulates this voltage signal to obtain the amplitude and phase changes of the voltage signal traveling through the array. Figure 2DThree graphs 230, 232, 234 are shown, each with a source voltage on the x-axis and another signal (e.g., voltage output) on the y-axis. Graph 230 shows the measured voltage amplitude or phase as a function of the source voltage applied as a voltage to the gate 208 for a first data point x1. Graph 232 shows the measured voltage amplitude or phase as a function of the source voltage applied as a voltage to the control gate 208 for a second data point x2. Finally, graph 234 shows the measured voltage amplitude or phase as a function of the source voltage applied as a voltage to the control gate 208 for a third data point x3. Similar to the current signal, the amplitude and phase of the voltage signal can then be used to perform machine learning.

[0083] Although QMLD 200 has been described using donor-based quantum dots, it should be appreciated that QMLD system 200 and ML methods may also work with gate-defined quantum dots.

[0084] The following sections describe a number of different quantum ML techniques that may be performed using the QMLD 200 described herein.

[0085] Quantum extreme learning machine (QELM)

[0086] In the classical machine learning literature, extreme learning machines are a form of feed-forward neural network architecture where the parameters and structure of the network are fixed and random, thus implementing a nonlinear projection. Simple models such as linear regression are then trained on this projected feature space. Extreme learning machines have been shown to have general approximations under very loose conditions and have been shown to outperform various other techniques including support vector machines.

[0087] Figure 4 A schematic diagram 400 of a hardware-based QELM process according to aspects of the present invention is shown. The QELM process utilizes QMLD 200 and includes a quantum dot array 202, a single source lead 204, one or more drain leads 206, and one or more gates G1-G6. Each drain lead 206 may correspond to a dimensional feature. This example diagram shows a 3×3 array of quantum dots, three drain leads 206A, 206B, 206C, and six control gates G1-G6, and may generate three data dimensions. If more dimensions are desired, the number of drain leads 206 may be increased.

[0088] For each input data point x i , a nonlinear projection is achieved by mapping each input dimension to a control gate and applying voltages to the control gates G1-G6. The input data points are transformed into voltages and then used to generate additional features. The output current is then measured at the drain lead 206 and used as the enhanced feature space f(x i). The dimension of the resulting feature map is equal to the number of drain leads 206, which may limit the capabilities of this method experimentally. The enhanced feature space obtained from this technique can be used for downstream ML tasks. For example, the dataset f(x i ) can be used in ML models to classify or predict some property of the input y i In the QELM process, each training and test data point needs to be transformed. Therefore, the number of measurements is the product of the number of measurements per transformation and the number of data points.

[0089] Quantum kernel learning machine (QKLM)

[0090] Another approach for generating features is to use QMLD 200 as a quantum kernel learning machine.

[0091] Figure 5 A schematic diagram 500 of a QKLM process according to aspects of the present disclosure is shown. The QKLM process utilizes a QMLD 200 having a quantum dot array 202, a single source lead 204, a single drain lead 206, and multiple control gates G1-G6. In the QKLM method, the number of control gates limits the size of the data. This is different from the QELM method described above, which maps data onto different gate voltages. In the QKLM method for d-dimensional data, it is likely that 2d control gates will be used, so two data points can be mapped simultaneously.

[0092] The kernel trick is a technique used in ML where the dot products between vectors are replaced by kernel functions. Mercer's theorem states that if the kernel function is symmetric, continuous, and its evaluation between all pairs of data points forms a positive semidefinite matrix, then it can be expressed as an inner product in the transformation space (feature space): for some transformation φ, K(x i ,x j )=〈φ(x i ),φ(x j )〉. This means that similarity measures can be computed in high-dimensional, complex vector spaces without having to compute vector representations in those spaces, which may be more efficient or allow transformations that would otherwise be impossible. For example, a common kernel used in support vector machines (SVMs) is the radial basis function kernel: RBF(x1,x2)=exp(-γ||x1-x2|| 2 ). The feature space representation of this kernel is infinite-dimensional.

[0093] The QKLM process starts with two data points x i and x j is applied symmetrically to the control gate 208. Here, symmetry means: f(x i ,x j )=f(xj ,x i ), that is, if the order of the inputs is swapped, the result will not change. In one example, this can be achieved by the following steps: i ) is applied to the top control gate (G1-G3) and data point 2 (x j ) is applied to the bottom control gate (G4-G6), and then data point 2 (x j ) is applied to the top control gate (G1-G3) and data point 1 (x i ) is applied to the bottom control gates (G4-G6) and the outputs are summed. This ensures that if data points 1 and 2 (x i , and x j ), the results do not change. This ensures that the appropriate distance measure is maintained. For example, the two questions "What is the distance from Melbourne to Sydney" and "What is the distance from Sydney to Melbourne" will produce the same output.

[0094] A kernel function that satisfies the kernel's criteria can then be defined based on the resulting measurements of the current at the drain lead 206, and this kernel is used in the ML model. As previously described, this technique requires a single drain lead 206 and two control gates 208 per data dimension. Using the QKLM process, the kernel is calculated between each pair of training data points and between each test data point and a training data point. Therefore, for the QKLM process, the number of measurements can be given by:

[0095] Measurements per kernel calculation × (training data points 2 + (training data points × test data points))

[0096] Quantum random kitchen sink (QRKS)

[0097] Random kitchen sink is a technique that generates a feature space by randomly transforming the input data points. It should be understood that this method can approximate functions under certain conditions. For example, this method can approximate cost functions such as L-Lipschitz functions, whose weights decay faster than a given sampling distribution when the maximum size of any projected point is less than or equal to 1. It has been empirically shown that under such conditions, QRKS performance is comparable to other techniques.

[0098] Figure 6A schematic diagram 600 of a QRKS process according to aspects of the present disclosure is shown. The QRKS process may also be performed on the QMLD 200 described above. In this example, the QMLD 200 includes a quantum dot array 202, a single source lead 204, a single drain lead 206, and multiple control gates (six gates G1-G6 in this example) for each data dimension of the random linearization input data. The number of control gates may allow for better access or change to the Hamiltonian, which may result in a higher dimensional output. However, the QRKS process may be used with any number of gates.

[0099] Like QELM, Quantum Random Kitchen Sink (QRKS) implements random nonlinear projections into a new feature space, but unlike QELM, the number of dimensions of the feature space can be arbitrarily large, that is, the dimensions are not limited by the number of drain leads.

[0100] For each desired feature dimension, a random linear transformation is applied to each data point in the dataset: Where w is an n×m matrix with elements sampled from a Gaussian distribution, n is the dimension of the data, and m is the number of control gates 208. And is a vector of the same length as the number of input gates 208 with elements sampled from a uniform distribution. This transformed data set is applied directly to the input gates 208. The current is measured at the drain lead 206 and used as the enhanced feature space f(x i ). Repeat this for each desired feature dimension to arrive at the desired number of dimensions to be used in downstream ML processes.

[0101] like Figure 6 As shown, the data point x i is randomly transformed multiple times. Each random transformation corresponds to a new feature dimension, and each feature dimension has the same linear transformation for all data points. For each new feature of each data point, the transformed data is applied as gate voltage to the control gates G1-G6, and the output current is measured through the drain lead 206. Each transformation and measurement adds a dimension to the enhanced feature space representation of the data point.

[0102] Note that when sampling randomly, the corresponding transformations must be the same across different data points. The size of the augmented feature space is arbitrary in this model because more transformations can be sampled. In addition, if multiple drain leads are used, multiple dimensions can be appended to the augmented feature space with each measurement. In this model, each training and test point must be transformed, which means that the number of measurements is given by:

[0103] Measurements per transformation × data points × feature dimensions

[0104] As mentioned previously, the different ML algorithms (QELM, QKLM, and QRKS) have slightly different QMLD 200 requirements. These source, drain, and control gate requirements are summarized in Table A below.

[0105] Table A: Equipment requirements for different feature generation methods.

[0106] Among them, the parameters in Table A are defined as: n s : The number of source gates, n d : The number of drain gates, n c : The number of control gates, d f : feature dimension, d d : Input data dimension, and n x : number of data points.

[0107] Result -1

[0108] In the first set of experiments, the performance of QRKS was evaluated using a 10-quantum-dot device for three data sets (hypersphere, ad-hoc data set, and polynomial separation) and compared with the classical random kitchen sink.

[0109] Figure 7 STM lithography of a QMLD 700 for evaluating the performance of QRKS is shown. In this device, there are: 10 donor-based quantum dots 208 in a quantum dot array 202; a source 204; a drain 206; and 6 control gates G1-G6. The 10 donor quantum dots 208 are phosphorus quantum dots embedded in a silicon substrate. The device 700 is measured using two data acquisition units 702A, 702B, where a 1:50 voltage divider 704 and a current amplifier 706 are used to amplify the signal.

[0110] Ad hoc datasets

[0111] Ad hoc datasets (in Fig. 12A The dataset (schematically depicted in Figure 2) uses a quantum circuit to classify points, which is supposedly difficult to simulate classically. It is based on a low-depth quantum circuit and is designed to be fully separable via variational quantum methods. The dimensionality of this dataset corresponds to adding qubits to the quantum circuit. The coordinates of each data point in this dataset essentially parameterize the quantum circuit.

[0112] Figure 8A graph 800 showing the performance of QRKS compared to a classic random kitchen sink in 4K and mK measurements when completing an ad hoc classification task. In particular, the graph shows the performance of QRKS and a classic random kitchen sink when completing this task for different data dimensions (1D, 2D, and 3D).

[0113] The x-axis of graph 800 indicates the number of features generated and the y-axis indicates the classification error. The model was trained on approximately 1000 data points and tested on approximately 270 data points.

[0114] The performance of QRKS in 4K and mK measurements is roughly the same for all three dimensions. However, for the 2D dataset, the performance of cRKS improves compared to QRKS as the number of features generated by the model increases.

[0115] On this data set, as can be seen from graph 800, the performance of features generated using quantum functions is similar to that of classical features for both 1D and 3D data.

[0116] Hypersphere

[0117] The Hypersphere dataset is an n-dimensional version of the Circle dataset that is commonly used in simple ML models. Fig. 12B Schematic diagram showing the hypersphere dataset.

[0118] Given n-dimensional coordinates x∈[-1,1] n , if x 2 ≤r, where r is the radius of the hypersphere, then it is considered "inside" the hypersphere, otherwise it is "outside". The task of the model is to classify points as "inside" or "outside". Since linear support-vector machines (SVMs) can only separate points via hyperplanes, they are expected to achieve a maximum accuracy of only 50% on this task.

[0119] Fig. 9 A graph 900 showing the performance of QRKS in 4K and mK measurements compared to a classic random kitchen sink in completing this classification task. In particular, the graph shows the performance of QRKS and a classic random kitchen sink in completing this task for different data dimensions (1D, 3D, 10D, and 60D). On the x-axis is the number of features generated, and on the y-axis is the classification error.

[0120] On this data set, as can be seen from the diagram 900, at least for the 60D data, the features generated using the quantum function are significantly better than the classical features. In particular, as the number of features increases, the classification error decreases. For 60D, the quantum method achieves an error rate of approximately 20%, while the classical features have an error rate between 30%-40%. For lower dimensions, as the number of features increases, the performance of CRKS and QRKS is similar, but for lower numbers of features, QRKS outperforms CRKS.

[0121] Polynomial root separation dataset

[0122] Polynomial separation of data sets (such as Fig. 12C The sample space (as seen in ) consists of coefficients of univariate polynomials of order n-1. The minimum separation between the two roots of each polynomial is calculated, and any value greater than a threshold is marked. Sample spaces of larger dimensions correspond to polynomials of higher order. In 2D, the coordinates are (x, y). Use these coordinates to define a polynomial, such as (xa+y), in this case the variable a. Use the roots of this polynomial (xa+y=0) to define a data set. In 3D, the coordinates are (x, y, z), and the polynomial can be defined as (xa 2 + ya + z = 0), in 4D, the coordinates can be (x1, x2, x3, x4), and the polynomial can be (x1a 3 +x2a 2 +x3a+x4=0). The degree of the polynomial is the maximum power of a, i.e. d-1, where d is the number of dimensions.

[0123] Fig.10 A graph 900 showing the performance of quantum RKS compared to classical RKS in 4K and mK measurements. In particular, the graph shows the performance of QRKS and the classical random kitchen sink in completing this task for different data dimensions (3D, 5D, 7D, and 10D). On the x-axis is the number of features generated, and on the y-axis is the model error.

[0124] The performance of quantum signatures is again as good as that of classical signatures in both 4K and mK measurements for all data dimensions.

[0125] Results-II

[0126] In the second experiment, the performance of QRKS was evaluated using different quantum dot devices for different datasets and compared with the classic random kitchen sink.

[0127] Fig.11An STM micrograph of a QMLD 1100 used in a second experiment to evaluate the performance of QRKS is shown. This device 1100 includes: 75 donor-based quantum dots 208 in a quantum dot array 202; a source 204; a drain 206; and ten control gates G1-G10. The 75 donor quantum dots 208 are phosphorus quantum dots embedded in a silicon substrate.

[0128] As previously mentioned, the Hubbard parameters U, V, and t are fixed by the configuration and distance between dots 208 in the quantum dot array 202. The QMLD 1100 is designed to randomize these parameters (U, V, and T) to provide richer dynamics for the memory. This is achieved by constructing the quantum dot array 202 on a triangular lattice. To introduce some randomness to make the device potentially more efficient, these positions are then randomly jittered in the x and / or y coordinates so that they each move slightly by a random amount in a random direction. This results in Fig.11 The final array seen in .

[0129] The voltage applied to the control gates G1-G10 reconfigures the site energy level ε i , and the resulting charge transfer through the quantum dot array 202 is measured as a current through the source 204 and drain 206 leads. This current is a function of the quantum state of the quantum dot array 202, which is in a strong quantum state - where quantum effects dominate - due to the large coupling strength of neighboring quantum dots and the low measurement temperature (approximately 30mK). This applies to the parameter range when thermal energy is small compared to all other energy scales in the system.

[0130] In this example QMLD 1100, x e The dimension of ' is chosen to be n=10 to correspond to the number of control gates G1-G10 in the device. Each element x' e,i Directly applied as a voltage to the gate Gi and measuring the current flowing through the device returns the result of a non-linear transformation.

[0131] Each matrix w is generated by randomly sampling each matrix element from a Gaussian distribution with mean μ=0 and standard deviation σ, and each b is generated by sampling each vector element IID from a uniform distribution with interval [w,b]. Varying σ changes the volume of the grid space accessible to the algorithm, resulting in features of different complexity.

[0132] In order to prevent the silicon substrate 102 from breaking down at high voltage, thereby causing leakage current between the gates, the voltage applied to any gate must fall within the maximum range of [-0.5V, 0.5V]. The voltage generated in

[0110] is calculated, and any feature with a range greater than the allowed voltage range causes the corresponding row of the transformation matrix to be resampled until the range is small enough or reaches some trial threshold. Then, the range of uniform offset is defined by the voltage range in each feature. For all experiments, the source-drain bias is set to 4mV.

[0133] Dataset

[0134] QMLD 1100 is tested using three synthetic datasets: Hypersphere (presented in Fig. 12B ), polynomial separation (shown in Fig. 12C (in Chinese) and impromptu (shown in Fig. 12A middle). FIG. 12A to FIG. 12C Visualization showing synthetic datasets. Each dataset consists of points classified into two categories, depicted by different colors. The job of QRKS is to learn how to classify points into two categories given only the coordinates of each point.

[0135] Additionally, in each illustration, the light grey and dark grey areas represent the areas where points of each category are located. Any point in the dark area is classified as dark, and any point in the light grey area is classified as light. White areas are areas where there are no sampled points. The light grey and dark grey points in these example schematics are example points that are plotted and classified as the corresponding colors of the areas they are located in.

[0136] Ad hoc dataset (presented in Fig. 12A The dataset is based on low-depth quantum circuits and is designed to be fully separable via variational quantum methods. The dimensionality of this dataset corresponds to adding qubits to the vector quantum circuit. The coordinates of each data point essentially parameterize the quantum circuit. The results of the quantum circuit are used to classify the data points, and using higher-dimensional data points (corresponding to more values ​​in their vectors) is equivalent to running a similar circuit, but with more qubits in it.

[0137] Hypersphere datasets (such as Fig. 12B The model consists of randomly sampled points in the m-dimensional unit hypercube. The points that lie inside the hypersphere are then labeled, and the model must recognize which points are labeled. Fig. 12B The different colored points in represent different classification categories—that is, points classified as being inside the hypersphere are one color, and points classified as being outside the hypersphere are another color.

[0138] Polynomial separation of data sets (such as Fig. 12CThe sample space (as seen in ) consists of coefficients of univariate polynomials of order n-1. The minimum separation between the two roots of each polynomial is calculated, and any value greater than a threshold is marked. Sample spaces of larger dimensions correspond to polynomials of higher order. In 2D, the coordinates are (x, y). Use these coordinates to define a polynomial, such as (xa+y), in this case the variable a. Use the roots of this polynomial (xa+y=0) to define a data set. In 3D, the coordinates are (x, y, z), and the polynomial can be defined as (xa 2 + ya + z = 0), in 4D, the coordinates can be (x1, x2, x3, x4), and the polynomial can be (x1a 3 +x2a 2 +x3a+x4=0). The degree of the polynomial is the maximum power of a, i.e. d-1, where d is the number of dimensions.

[0139] For all three datasets, the output threshold was chosen such that 50% of the input data points were labeled, and points close enough to this threshold were discarded to ensure class separation.

[0140] The three synthetic datasets were chosen to present different levels of difficulty in testing the QRKS model. The hypersphere is considered a simple dataset due to the simplicity of the separation boundary, while polynomial separation and ad hoc datasets have more complex separation boundaries. In particular, it is speculated that ad hoc datasets are difficult to compute classically, meaning that ad hoc datasets based on a large number of qubits will appear completely random to a classical computer.

[0141] In addition to selecting datasets of varying difficulty, each dataset is tested in multiple dimensions. The effect of this is twofold. First, the sampling density of points decreases exponentially with the number of dimensions, which makes the datasets difficult due to the relative scarcity of data points. Second, in the case of polynomial separations and ad hoc, the computational complexity of the function defining the separation boundary increases.

[0142] Since all synthetic data points are based on randomly sampled points, the same measurements can be reused to evaluate model performance on all three datasets by simply selecting different subsets of the data and redefining the class assignment for each point. A total of 3000 points were measured, and after discarding points close to the separation boundary, approximately 2700, 2400, and 1850 points were obtained for the hypersphere, polynomial separation, and ad hoc datasets, respectively. There are some minor changes in the number of points in different dimensions. For each dataset, 70% of the points were used as a training set, and the remaining 30% were used as a test set.

[0143] QMLD 1100 was also tested using a real dataset, the Modified National Institute of Standards and Technology dataset (MNIST dataset). MNIST is a dataset of 28×28 pixel images of 70,000 handwritten digits (60,000 training examples and 10,000 test examples) and is a standard benchmark dataset in the ML field. Fig.12D Several examples of these images are shown.

[0144] In this experiment, the model was trained on the full dataset and a subset of MNIST that only included the digits 3 and 5 (these digits are the two most difficult for a linear classifier to separate). There are 11551 training examples and 1903 test examples in this subset. For the purpose of this experiment, the dimensionality of the MNIST input data was reduced from 784 to 10 dimensions using principal component analysis (PCA) decomposition.

[0145] Model

[0146] The QRKS model on QMLD 1100 is compared with the following three models: linear support vector machine (LSVM), SVM with radial basis function (RBF) kernel, and the classic version of random kitchen sinks methods with cosine linearity (CRKS).

[0147] The features produced by QMLD 1100 are classified using LSVM. Note that the random kitchen sink process does not introduce linearity (except for the linearity of the quantum mapping), which means that any performance gain of the LSVM itself is directly due to the device 1100 and not a side effect of pre- or post-processing.

[0148] Each model has a scale parameter "γ" and a regularization parameter "C", where the optimal value of each parameter depends on both the model and the data set. The scale parameter for CRKS and QRKS represents the width of the Gaussian distribution from which the transformation matrix w is sampled, and the scale parameter for RBF SVM defines the influence area of ​​each support vector. The regularization parameter defines the extent to which each model is penalized for the extremes in the weight matrix. In other words, regularization is a method of preventing overfitting when a machine learning model memorizes the data in a data set rather than learning general trends and patterns (allowing it to generalize to unseen data). Overfitted models often perform poorly when used to classify data points outside their training set. If the parameters learned by the model are very large, this may indicate that the model is overfitted. Regularization introduces the cost of having large model parameters to alleviate this phenomenon.

[0149] Fig.13 is a grid of nine subplots showing the performance of each model - RKS (left three subplots), RBF (middle three subplots), and QRKS (right three subplots) on each data set (hypersphere top three subplots, polynomial separation middle three subplots, and ad hoc bottom three subplots) as a function of the hyperparameters used to perform the optimization. The color gradient represents the accuracy of the model, with black being the highest error rate (0.5) and white being the lowest error rate (0). The axes of each subplot represent the values ​​of the hyperparameters C (x-axis) and γ (y-axis). The spots on each tile represent the best hyperparameters for each model for each data set.

[0150] Training and testing procedures

[0151] Each dataset was rescaled to the range [-1,1] before training, and the output features of the QMLD 1100 were also scaled back to this range before being fed into the LSVM. The scale and regularization hyperparameters were optimized for each dataset via grid search: each model was trained on a subset of 500 data points for each combination of hyperparameter values, and each model was tested on the validation set. The best values ​​that resulted in the best performing model were then used when training on the entire dataset.

[0152] A total of 1000 features were generated for CRKS and QRKS for each of the synthetic datasets, and 10000 features were generated for the MNIST dataset.

[0153] To establish statistics on model performance, 300 random training / test splits were generated, and randomly initialized models were trained and tested on each of those splits. In other words, error bars were created by training many models with random initial conditions and ranking their accuracy to obtain a more accurate estimate of the mean and standard deviation of the accuracy of the technique.

[0154] result

[0155] Fig.14A It is a graphical representation 1400 of the performance of the QRKS model (under 4K 1402 and under mK 1404) on a polynomial separation data set compared to three classical models, RBF SVM 1405, LSVM 1406, and CRKS 1408. On the x-axis is the dimension of the resulting feature space, and on the y-axis is the classification error.

[0156] Fig. 14B It is a graph 1410 of the performance of the QRKS model (under 4K 1412 and under mK 1404) on the ad hoc dataset compared with three classical models RBF SVM 1415, LSVM 1416, and CRKS 1418. On the x-axis is the dimension of the resulting feature space, and on the y-axis is the classification error.

[0157] Fig. 14C It is a graph 1420 of the performance of the QRKS model (under 4K 1422 and under mK 1424) on the hypersphere dataset compared to three classical models RBF SVM 1425, LSVM 1426, and CRKS 1428. On the x-axis is the dimension of the resulting feature space, and on the y-axis is the classification error.

[0158] QRKS consistently outperforms LSVM significantly across all datasets, demonstrating that the nonlinear transformation provided by QMLD 1100 is both useful and general. Beyond that, QRKS performs competitively to RBF SVM and CRKS methods, despite the fact that the technique is far less mature and implemented on noisy hardware. The inherent noise robustness of the reservoir / random kitchen sink algorithm is evident when comparing QRKS performance at 30mK to 4K. Despite the increase in measurement noise, performance only degrades slightly.

[0159] FIG. 14A to FIG. 14CThe diagrams shown also illustrate the different difficulties of each of the datasets. The hypersphere dataset is easily separable by all models (except linear) up to very large dimensions, while on the ad hoc dataset, no model performs better than random guessing for any dimension greater than three. For the polynomial separation dataset, model performance steadily decreases with dimension, making it a good dataset for judging the robustness of the model to complexity. Although RBFSVM and CRKS still outperform QRKS, QRKS does not converge to random guessing faster, which reinforces that the technique is general and can learn complex separating boundaries.

[0160] Fig.14D is a table showing the performance of the QRKS model 1440 compared with three classical models, RBF SVM 1442, LSVM 1444, and CRKS 1446, on subsets 3-5 of the MNIST dataset.

[0161] Fig.14E 1450 is a graph of the performance of each of the models for a 22D hypersphere data set as a function of the number of data points (x-axis). Specifically, graph 1456 is for the LSVM model, graph 1454 corresponds to the CRKS model, graph 1452 corresponds to the RBF model, graph 1458 corresponds to the mK QRKS model, and graph 1459 corresponds to the 4K QRKS model. Fig.14E As can be seen, no model is able to learn more effectively with fewer data points than any other model. However, as the number of data points increases, the error rate (along the y-axis) of the CRKS, RBF, and QRKS models decreases, while the error rate of the linear model remains the same.

[0162] Fig.14F is a graph showing the performance of each of the models for the 5D polynomial root separation data set as a function of the number of data points 1460. On the x-axis is the number of features generated, and on the y-axis is the classification error.

[0163] Specifically, plot 1466 is for the LSVM model, plot 1454 corresponds to the CRKS model, plot 1462 corresponds to the RBF model, plot 1468 corresponds to the mK QRKS model, and plot 1469 corresponds to the 4K QRKS model. This plot 14F emphasizes that all models predict relatively similar performance of linear models for higher dimensional polynomial root separation data sets.

[0164] Figure 14G is a graph 1470 showing the performance of each of the models as a function of the number of data points for a 2D ad hoc dataset. On the x-axis is the number of features generated, and on the y-axis is the classification error.

[0165] Specifically, graph 1476 is for the LSVM model, graph 1474 corresponds to the CRKS model, graph 1472 corresponds to the RBF model, graph 1478 corresponds to the mK QRKS model, and graph 1479 corresponds to the 4K QRKS model. This graph 14G emphasizes that for the 2D ad hoc dataset, the QRKS model performs better than the linear model, but worse than the RBF and CRKS models.

[0166] Another variant

[0167] Another way in which a quantum ML device can be operated is as a reservoir. This method of operation exploits the temporal dynamics of the device, where input signals are applied faster than the device can settle. For a random kitchen sink, this would result in the output being dependent on the order of the data points in the dataset, which is undesirable for datasets such as hyperspheres, ad hoc datasets, etc. as described previously, where each data point is independent. However, for other types of datasets, such as time series datasets, the data points are not independent and can be ordered.

[0168] Random transformations are still used in this method of operation. Specifically, multiple random transformations are generated and applied to input data (e.g., a time series), which is then provided to the QMLD as a column of input voltages. The random transformations define a path through the voltage gate space. Wherein the path in the voltage gate space is between a first voltage and a second voltage in the input voltage. Each random transformation causes a new feature to be measured. These features are then measured and used for prediction in the machine learning model.

[0169] An example response of a QMLD 1100 operating as a storage device to a random binary string input is provided in FIG15. Specifically, Fig.15A Describes the response at 4K and Fig. 15B The response at about 30 mK is plotted. The input to the quantum ML device is Fig.15A and Fig. 15B The features are depicted in with dashed lines, and the resulting features are shown with solid lines.,Five random features are highlighted in darker colors as an example of how individual,features change over time.

[0170] When input signals are provided faster than the QMLD's settling time, the history of the input signals is encoded in the instantaneous quantum state, which means that measurements at that time will encode information about both the current input and past inputs. This ability to extract information about past inputs is called storage, and the distance to the past that the QMLD can remember is called "storage capacity." In addition to this, the device is able to make the current input interact with previous inputs in a nonlinear way. The ability of the QMLD to perform complex nonlinear transformations based on points in its memory is called "nonlinear processing capacity," and the ability to perform linear transformations based on points in its storage is called "linear processing capacity."

[0171] These two properties were measured on the QMLD 1100 using binary input. The results are plotted in FIG. 16A to FIG. 16D For storage capacity, the accuracy of correctly recalling the ti-th input (where t is the current time step and i sweeps from 1 to 10) is calculated and summed to give a metric. For processing capacity, the accuracy of predicting the parity of the inputs from ti to t is calculated and summed again to give another metric. These metrics vary primarily with changes in two hyperparameters, γ and ramp length. Similar to a random kitchen sink, the γ variable controls the size of the random transformation, which defines how much of the voltage gate space the model can enter. The QMLD 1100 was measured with an input rate of 500kHz, however the rate at which data points are measured can be changed by changing the number of data points required to ramp between consecutive inputs along a path in gate space. This variable is called ramp length.

[0172] FIG. 16A to FIG. 16D The storage and processing capacity of the depicted device at 4K and approximately 30mK depends on these two hyperparameters. Specifically, Fig.16A and Fig. 16B The storage capacity at 4K and 30mK is depicted respectively. The scale represents the storage capacity or the number of data points from the past that the device can remember. As shown, the storage capacity of the device at two temperatures can vary depending on the selected gamma and / or ramp length. In addition, the maximum storage capacity for this device (i.e., QMLD 1100) is about 6 data points at 4K and 30mK. It should be understood that the storage capacity of the device can be increased by increasing the time required for the device to stabilize.

[0173] Fig. 16C and Fig.16DThe processing capacity of the device at 4K and 30mK is depicted respectively. The scale represents the processing capacity of the device based on the number of data points in its memory. In this example, the device is programmed to recognize the number of 1s of data points in its memory. As can be seen from the figure, the processing capacity of the device varies according to γ ​​and ramp length at two temperatures. In addition, the device can perform processing on up to 6 data points from its memory.

[0174] The reference to any prior art in this specification does not acknowledge or imply that such prior art forms part of the common general knowledge in any jurisdiction, or that it could reasonably be expected that such prior art would be understood, considered relevant and / or combined with other prior art by a person skilled in the art.

[0175] As used herein, the term "comprise" and variations of the term such as "comprising", "including" and "having" are not intended to exclude further additions, components, integers or steps, unless the context requires otherwise.

Claims

1. A method for generating quantum features for a machine learning model, the method comprising: Providing a quantum ML device, the quantum ML device comprising one or more quantum dots, one or more source gates, one or more drain gates, and one or more control gates; transforming input data for the machine learning model into a first voltage; applying the first voltage to the one or more control gates, and / or the one or more source gates, and / or the one or more drain gates; applying a second voltage to one or more of the one or more source gates; measuring a signal at one or more of the one or more drain gates; analyzing the measured signal to determine values ​​of one or more parameters; as well as The values ​​of the one or more parameters are interpreted as a non-linear mapping of the input data to be used for the machine learning model.

2. The method of claim 1, wherein: Converting the input data into the first voltage includes: performing a random transformation of the input data; and The randomly transformed input data is transformed into the first voltage.

3. The method of claim 1, wherein: Converting the input data to the first voltage includes directly mapping the input data to the first voltage.

4. The method according to claim 2 or 3, wherein: Interpreting the values ​​of the one or more parameters includes combining the values ​​of the one or more parameters into features for the machine learning model.

5. The method of claim 1, wherein: Converting the input data into the first voltage includes: combining data points of the input data into pairs, converting the combined data points into a combined voltage; and Applying the first voltage to the one or more control gates includes applying the combined voltage to the one or more control gates.

6. The method of claim 5, wherein: Interpreting the values ​​of the one or more parameters includes determining a distance metric or similarity score between the values ​​of the one or more parameters.

7. The method according to any one of claims 1 to 6, wherein: The quantum ML device includes a plurality of source gates, a plurality of drain gates, and a plurality of control gates, and the quantum ML device is used as a quantum random kitchen sink device.

8. The method according to any one of claims 1 to 6, wherein: The quantum ML device includes a source gate, a number of drain gates matching the desired feature dimension, a number of control gates matching the dimension of the input data, and the quantum ML device functions as a quantum extreme learning machine.

9. The method according to any one of claims 1 to 6, wherein: The quantum ML device includes a source gate, a drain gate, and control gates whose number is twice the dimension of the input data, and the quantum ML device functions as a quantum kernel learning machine.

10. The method according to any one of the preceding claims, further comprising: Manufacturing the quantum ML device, wherein manufacturing the quantum ML device comprises: preparing a bulk layer of a semiconductor substrate; preparing a second semiconductor layer; exposing the clean crystalline surface of the second semiconductor layer to dopant molecules to produce an array of dopant points on the exposed surface; annealing the arrayed surface to incorporate dopant atoms of the dopant molecules into the second semiconductor layer; and The one or more gates, the one or more source leads, and the one or more drain leads are formed.

11. The method of claim 10, wherein: The one or more control gates are formed in the same plane as the dopant dots.

12. The method of claim 10, further comprising: A dielectric material is deposited over the second semiconductor layer, and the one or more control gates are formed over the dielectric material.

13. The method according to any one of claims 10 to 12, wherein: The dopant dots are phosphorus dots.

14. The method of any one of claims 10-12, wherein the second semiconductor layer is silicon-28.

15. A quantum ML device comprising: one or more quantum dots; one or more source gates; one or more drain gates; as well as one or more control gates; The quantum ML device is used to generate quantum features for a machine learning model by the following steps: applying a first voltage corresponding to input data for the machine learning model to the one or more control gates, and / or the one or more source gates, and / or the one or more drain gates; applying a second voltage to one or more of the one or more source gates; and measuring a signal at one or more of the one or more drain gates; analyzing the measured signal to determine values ​​of one or more parameters; and The values ​​of the one or more parameters are interpreted as a non-linear mapping of the input data to be used for the machine learning model.

16. The quantum ML device of claim 15, comprising a plurality of source gates, a plurality of drain gates and a plurality of control gates, and the quantum ML device is used as a quantum random kitchen sink device.

17. The quantum ML device of claim 15, comprising one source gate, a number of drain gates matching the desired feature dimension, a number of control gates matching the dimension of the input data, and the quantum ML device functions as a quantum extreme learning machine.

18. The quantum ML device of claim 15, comprising a source gate, a drain gate, and control gates whose number is twice the dimension of the input data, and the quantum ML device is used as a quantum kernel learning machine.

19. The quantum ML device according to any one of claims 15 to 18, wherein: The one or more control gates are formed in the same plane as the quantum dots.

20. The quantum ML device according to any one of claims 15 to 19, wherein: The quantum dots are phosphorus dots.

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