Quantum-enhanced features for classical machine learning

Abstract

Systems and techniques are provided that facilitate quantum enhanced features for classical machine learning. In various embodiments, the system can include a receiver component that can access a classical dataset. In various aspects, the system can further include a feature component that can generate one or more machine learning input features based on a quantum transformation of the classical dataset. In various cases, the system can further include an execution component that can execute a classical machine learning model against the one or more machine learning input features.

Description

[Technical Field]

[0001] The subject disclosure relates to machine learning, and more particularly to quantum-enhanced features for classical machine learning. [Background technology]

[0002] Quantum computing has shown promise in addressing classically intractable computational challenges. Currently, prior art quantum computing devices are considered noisy intermediate-scale quantum (NISQ) devices. Such quantum computing devices implement a small number of error-prone qubits—fewer than the hundreds or thousands that would be needed to implement error correction for a single logical qubit, given the current error rate of physical qubits. Unfortunately, the full realization of a fault-tolerant, error-correcting quantum computer would require devices implementing thousands or even millions of physical qubits. As such, prior art quantum computing devices cannot yet support enough qubits to solve many classically intractable computational challenges. In fact, quantum computing is still in its infancy, and well-established classical computing techniques are still widely used in various technological fields. To date, quantum computing research has focused significantly on physically constructing quantum computing devices capable of implementing a large number of qubits. In contrast, quantum computing research has been limited, focusing on how existing quantum computing devices can be leveraged to improve the performance of classical computing techniques. Therefore, the inventors recognized that systems and / or techniques that can address this technical challenge may be desirable. Summary of the Invention

[0003] The following summary is presented in order to provide a basic understanding of one or more embodiments of the present invention. This summary is not intended to identify key or critical elements or to delineate the scope of particular embodiments or the scope of the claims. The summary's sole purpose is to present concepts in a simplified form as a prelude to the more detailed description that is presented later. In one or more embodiments described herein, a device, system, computer-implemented method, apparatus, or computer program product, or combination thereof, is described that can facilitate quantum-enhanced features for classical machine learning.

[0004] According to one or more embodiments, a system is provided. The system may include a memory capable of storing computer-executable components. The system may further include a processor operably coupled to the memory and capable of executing the computer-executable components stored in the memory. In various embodiments, the computer-executable component may include a receiver component capable of accessing a classical dataset. In various aspects, the computer-executable component may further include a feature component capable of generating one or more machine learning input features based on a quantum transformation of the classical dataset. In various embodiments, the computer-executable component may further include a transformation component capable of converting the classical dataset into a set of quantum probability amplitudes. In various cases, the computer-executable component may further include a quantum component capable of executing a quantum circuit on the set of quantum probability amplitudes, thereby providing a quantum transformation of the classical dataset. In various cases, the computer-executable component may further include an execution component capable of executing a classical machine learning model on the one or more machine learning input features.

[0005] According to one or more embodiments, the above-described systems may be implemented as computer-implemented methods and / or computer program products.

[0006] According to one or more embodiments, a system is provided. The system may include a memory capable of storing computer-executable components. The system may further include a processor operably coupled to the memory and capable of executing the computer-executable components stored in the memory. In various embodiments, the computer-executable component may include a receiver component capable of receiving a classical time series dataset from an operator device. In various aspects, the computer-executable component may further include a feature component capable of generating one or more quantum-enhanced machine learning input features based on a quantum transformation of the classical time series dataset. In various embodiments, the computer-executable component may further include a transformation component capable of generating quantum probability amplitudes based on the classical time series dataset. In various cases, the computer-executable component may further include a quantum component capable of executing a quantum algorithm on the quantum probability amplitudes, thereby providing a quantum transformation of the classical time series dataset. In various cases, the computer-executable component may further include an execution component capable of transmitting the one or more quantum-enhanced machine learning input features to the operator device.

[0007] According to one or more embodiments, the above-described systems may be implemented as computer-implemented methods and / or computer program products. [Brief explanation of the drawings]

[0008] [Figure 1]FIG. 1 is a block diagram of an example, non-limiting system that facilitates quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 2] FIG. 1 is a block diagram of an example, non-limiting system including quantum probability amplitudes that facilitate quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 3] FIG. 1 is a block diagram of an example, non-limiting system including quantum probability amplitudes that facilitate quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 4] FIG. 1 is a block diagram of an example, non-limiting system including a quantum circuit and a composite quantum probability amplitude that facilitates quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 5] FIG. 1 is a block diagram of an example, non-limiting system including a quantum circuit and a composite quantum probability amplitude that facilitates quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 6] FIG. 1 is an exemplary, non-limiting quantum circuit diagram according to one or more embodiments described herein. [Figure 7] FIG. 1 is a block diagram of an example, non-limiting system including enhanced machine learning input features that facilitate quantum enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 8] FIG. 1 is a block diagram of an example, non-limiting system including enhanced machine learning input features that facilitate quantum enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 9] FIG. 1 is an exemplary, non-limiting block diagram illustrating how quantum-enhanced features for classical machine learning can be practically utilized, according to one or more embodiments described herein. [Figure 10]FIG. 1 is a flow diagram of an example, non-limiting, computer-implemented method for facilitating quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 11] FIG. 1 is a block diagram of an example, non-limiting system including a visualization component that facilitates quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 12] FIG. 1 is a block diagram of an example, non-limiting system including an operator device that facilitates quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 13] FIG. 1 is a flow diagram of an example, non-limiting, computer-implemented method for facilitating quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 14] FIG. 1 is a flow diagram of an example, non-limiting, computer-implemented method for facilitating quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. [Figure 15] FIG. 1 is a block diagram of an example, non-limiting operating environment capable of facilitating one or more embodiments described herein. [Figure 16] FIG. 1 is a diagram of an exemplary, non-limiting cloud computing environment according to one or more embodiments described herein. [Figure 17] FIG. 1 is a diagram of an example, non-limiting abstract model layer, according to one or more embodiments described herein. DETAILED DESCRIPTION OF THE INVENTION

[0009] The following detailed description is illustrative only and is not intended to limit the embodiments or the application and / or uses of the embodiments, nor is it intended to be bound by any stated or implied information presented in the preceding "Background" or "Summary" sections or in the "Detailed Description" section.

[0010] One or more embodiments will now be described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. It will be apparent, however, that in various instances, one or more embodiments may be practiced without these specific details.

[0011] As mentioned above, quantum computing has shown promise in addressing classically intractable computational challenges in various technical fields, such as computational chemistry, optimization, and machine learning. Currently, prior art quantum computing devices are called Noisy Intermediate-Scale Quantum (NISQ) devices. NISQ devices can physically implement fewer qubits than are required for error correction, given the error rate of the physical qubits. Unfortunately, fully realizing a quantum computer with error correction requires devices implementing thousands, millions, or even more qubits, which exceeds the number of qubits that can be supported by systems in the near future by several orders of magnitude. Therefore, prior art quantum computing devices cannot yet physically support enough qubits to solve many classically intractable computational challenges. Because quantum computing is still in its infancy (e.g., the number of qubits that can be supported by NISQ devices is still limited), well-established classical computing techniques remain widely used in various technical fields.

[0012] In particular, one technology field that still relies heavily on classical computational techniques is machine learning (e.g., artificial intelligence). Various industries involve data logging, and these industries often utilize classical machine learning techniques (e.g., artificial neural networks, support vector machines, regression models, naive Bayes) to analyze such logged data. In such cases, a set of classical data can be recorded and / or generated in any suitable manner, and the set of classical data can be provided as input to a machine learning (“ML”) model. The ML model can generate a label, classification, or prediction, or a combination thereof, as output based on the set of classical data. For example, the set of classical data can be time series data (e.g., product / service sales recorded over time, resource consumption recorded over time, or any other desired measured quantity recorded over time), and it may be desired to forecast future data points based on the time series data. In such cases, the time series data can be provided as input to a suitably configured ML model, which can produce one or more predicted data points as output based on the time series data (e.g., predicting how the time series data will continue and / or change in future time steps).

[0013] To date, much research has been devoted to building quantum computing devices that can physically support large numbers of qubits. In contrast, limited research has been devoted to how existing quantum computing devices can improve the performance and / or capabilities of classical computing techniques in general, and classical ML techniques in particular. Therefore, systems and / or techniques that can address this technical challenge may be desirable.

[0014] Various embodiments of the present invention can address one or more of these technical challenges. Specifically, various embodiments of the present invention can provide systems and / or techniques that can facilitate quantum-enhanced features for classical machine learning. In various aspects, embodiments of the present invention can be thought of as a computerized tool (e.g., a combination of computer hardware and / or computer software) that can electronically receive a set of classical data as input and electronically generate a set of ML input features as output based on a quantum transformation of the set of classical data. These ML input features may be referred to as quantum-enhanced input features, quantum-enhanced independent variables, or both. In other words, a computerized tool such as those described herein can transform a set of classical data via a quantum circuit and / or a quantum algorithm, and the results of such quantum transformation (as well as the original set of classical data) can be provided as input to a classical ML model. As described herein, a classical ML model configured to receive both a set of classical data and a quantum transformation of the set of classical data as input can exhibit increased prediction / labeling accuracy compared to a classical ML model configured to receive only a set of classical data.

[0015] As mentioned above, a classical ML model can be configured to receive a set of classical data as input and to produce a judgment as output based on the set of classical data. For example, if the set of classical data is an image, the classical ML model can be configured such that the judgment is a label that classifies and / or segments the image. As another example, if the set of classical data is an audio recording, the classical ML model can be configured such that the judgment is a label that classifies and / or segments the audio recording. As yet another example, if the set of classical data is a time series, the classical ML model can be configured such that the judgment is one or more expected data points that may follow in the time series. Thus, at a high level, a classical ML model can be thought of as detecting patterns, trends, and / or distributions revealed by the set of classical data, where the judgment generated by the classical ML model depends on the detected patterns, trends, and / or distributions.

[0016] The inventors of various embodiments of the present invention have recognized that, in various cases, importing a collection of classical data into a quantum Hilbert space (e.g., a complex-valued mathematical space native to quantum computing) and / or performing various quantum transformations on the collection of classical data within the quantum Hilbert space can reveal additional patterns, trends, and / or distributions in the collection of classical data. These additional patterns, trends, and / or distributions were previously hidden and / or undetectable to classical ML models. In other words, the inventors of various embodiments of the present invention have recognized that a collection of classical data can be enriched / enhanced by converting the collection of classical data into quantum state information and / or by transforming such quantum state information with quantum circuits / algorithms. Thus, if a classical ML model is configured to receive only a collection of classical data, the classical ML model will not be able to access the additional patterns, trends, and / or distributions hidden in the collection of classical data. On the other hand, if a classical ML model is configured to receive both a set of classical data and a quantum variant of the set of classical data, the classical ML model can access additional patterns, trends, and / or distributions hidden in the set of classical data, which can help increase the accuracy / precision of the decisions generated by the classical ML model.

[0017] Thus, a computerized tool as described herein can, in various aspects, generate quantum-enhanced input features for a classical ML model based on classical data. Specifically, in various embodiments, such a computerized tool can include a receiver component, a transform component, a quantum component, a feature component, and an execution component.

[0018] In various embodiments, the receiver component can electronically receive and / or access the classical dataset desired to be analyzed by the classical ML model. In various cases, the receiver component can electronically retrieve the classical dataset from any suitable centralized and / or decentralized data structure (e.g., a graph data structure, a relational data structure, a hybrid data structure), whether remote and / or local to the receiver component. As one skilled in the art will appreciate, the classical dataset can be formatted in any suitable manner (e.g., formatted as classical bits, formatted as classical integers, formatted as classical floating-point numbers).

[0019] In various embodiments, the transformation component can electronically import a classical data set into quantum Hilbert space. More specifically, the transformation component can electronically transform the classical data set into a set of quantum probability amplitudes via any suitable amplitude embedding and / or amplitude encoding techniques, where the set of quantum probability amplitudes collectively represent a quantum state vector, and such quantum state vector can be operated on and / or manipulated by a quantum circuit.

[0020] For example, suppose a classical data set contains x data points, for any suitable positive integer x. In such a case, amplitude embedding / encoding can be applied such that each of the x data points is converted into a corresponding quantum probability amplitude to give an x ​​quantum probability amplitude.

[0021] As one skilled in the art will appreciate, quantum probability amplitudes can be complex numbers (e.g., having real or imaginary parts or both) associated with quantum states, where the square of the quantum probability amplitude represents the probability of the associated quantum state occurring. Thus, quantum probability amplitudes can be normalized so that the sum of the squares of the quantum probability amplitudes equals unity (e.g., each quantum probability amplitude corresponds to a quantum state, and each squared quantum probability amplitude represents the probability of that corresponding quantum state occurring; thus, adding up such probabilities over all possible states of a system equals identity).

[0022] In particular, the conversion component can convert a classical dataset into quantum probability amplitudes by considering the classical dataset as an x-element vector, calculating the norm (e.g., magnitude, length) of this x-element vector (e.g., the square root of the sum of the squares of each of the x data points), and then dividing each of the x data points by the calculated norm. In various embodiments, the result can be that the x data points are normalized so that the sum of their squares equals identity, so that each of the normalized x data points can be thought of as a quantum probability amplitude. In various embodiments, the collection of quantum probability amplitudes can be thought of as a quantum version and / or format of the classical dataset.

[0023] In various instances, the quantum component can electronically apply a quantum circuit to a set of quantum probability amplitudes and / or can electronically facilitate the application of a quantum circuit to a set of quantum probability amplitudes. Specifically, a quantum circuit can be a sequence of quantum gates (e.g., unitary matrix operators that transform / rotate the states of qubits) coupled in series (e.g., by matrix multiplication) or in parallel (e.g., by tensor products and / or Kronecker products). The quantum circuit can be implemented on a quantum computing device that includes physical qubits. In various embodiments, the quantum component can be electronically integrated with the quantum computing device and thus can implement any suitable quantum gates and / or quantum circuits compatible with the quantum computing device.

[0024] In various cases, the quantum component can initialize the quantum computing device with the quantum probability amplitudes generated by the transformation component. That is, the set of quantum probability amplitudes can collectively represent a quantum state vector, and the quantum component can implement any suitable initialization circuitry on the quantum computing device to cause the states of the qubits of the quantum computing device to conform to the quantum state vector. As one skilled in the art will appreciate, the configuration of such initialization circuitry can depend on the particular values ​​of the set of quantum probability amplitudes.

[0025] In various instances, once the qubits of a quantum computing device have been initialized with a set of quantum probability amplitudes, a quantum component can execute a quantum circuit on the quantum computing device, thereby transforming the set of quantum probability amplitudes into a set of composite quantum probability amplitudes. In various instances, the set of composite quantum probability amplitudes can represent a composite quantum state vector of the qubits of the quantum computing device. In various aspects, the set of composite quantum probability amplitudes (e.g., a composite quantum state vector) can be thought of as a quantum-transformed version and / or format of a classical data set.

[0026] Consider again the example above, where the classical data set contains x data points and the transformation component generates x quantum probability amplitudes based on the x data points. As one skilled in the art will appreciate, the set of x quantum probability amplitudes can be thought of as an x-element quantum state vector that describes a superposition of quantum states for log2x qubits. Thus, a quantum computing device utilized by the quantum component can contain log2x qubits. If log2x is not an integer, it can be rounded up to the next higher integer.

[0027] In various cases, the log2x qubit can start by having a known quantum state vector. For example, the log2x qubit can start with all of the |0> state. Given the known starting quantum state vector, a quantum component can execute an initialization circuit on the quantum computing device such that the state of the log2x qubit is transformed from the known starting quantum state vector to a quantum state vector represented by x quantum probability amplitudes. As one skilled in the art will appreciate, the configuration of the initialization circuit (e.g., the particular combination and / or arrangement of quantum gates in the initialization circuit) can be chosen and / or selected by the quantum component based on the known starting quantum state vector and based on the quantum state vector represented by a set of x quantum probability amplitudes. In other words, given a starting quantum state vector and a desired quantum state vector, one skilled in the art will understand which quantum gates to combine and how to transform the starting quantum state vector into the desired quantum state vector.

[0028] Once the log2x qubits of a quantum computing device have been initialized with a quantum state vector represented by the x quantum probability amplitudes generated by the transformation component, the quantum component can execute any suitable quantum circuit on the quantum computing device. In some cases, the quantum circuit may be a quantum Fourier transform. In all cases, the quantum circuit can transform and / or rotate the quantum state vector represented by the x quantum probability amplitudes into some composite quantum state vector represented by the x composite quantum probability amplitudes.

[0029] In various embodiments, the feature component can electronically generate quantum-enhanced ML input features based on the set of composite quantum probability amplitudes generated by the quantum component. Specifically, the set of composite quantum probability amplitudes can be considered a set of complex numbers, and the feature component can electronically apply any suitable mathematical function to the set of complex numbers. In various cases, the result of applying such a mathematical function can be considered a quantum-enhanced ML input feature. For example, in some cases, the feature component can multiplicatively scale (e.g., scale up or scale down, or both) the set of composite quantum probability amplitudes such that the scaled amplitudes can be considered quantum-enhanced ML input features. In other cases, the feature component can additively offset (e.g., bias up or bias down, or both) the set of composite quantum probability amplitudes such that the offset amplitudes can be considered quantum-enhanced ML input features. In still other cases, because the composite quantum probability amplitudes can be complex numbers, the feature component can calculate the magnitude of the composite quantum probability amplitude, thereby considering that magnitude as a quantum-enhanced ML input feature. In various embodiments, the feature component can avoid mathematically modifying the composite quantum probability amplitudes in any way, such that the set of composite quantum probability amplitudes can itself be thought of as the quantum-enhanced ML input feature.

[0030] Continuing with the above example, the feature component can extract the x composite quantum probability amplitude generated by the quantum component (e.g., with or without mathematical manipulation, or both), thereby providing an x ​​quantum-enhanced ML input feature. For example, in some cases, the x quantum-enhanced ML input feature may be equal to the x composite quantum probability amplitude. In other cases, the x quantum-enhanced ML input feature can be any suitable function of the x composite quantum probability amplitude.

[0031] In various embodiments, the execution component can electronically execute and / or facilitate the execution of a classical ML model against the classical dataset and / or against the quantum enhanced ML input features generated by the feature component. In other words, after the feature component generates the quantum enhanced ML input features, the execution component can electronically provide the classical dataset and / or the quantum enhanced ML input features to the classical ML model. As described above, the quantum enhanced ML input features can be created by importing the classical dataset into quantum Hilbert space (e.g., specifically, by converting the classical dataset to quantum probability amplitudes), or by transforming the classical dataset within quantum Hilbert space (e.g., specifically, by initializing a quantum computer with quantum probability amplitudes and running a quantum circuit on the quantum computer), or both. Thus, the quantum enhanced ML input features can reveal patterns, trends, or distributions, or a combination thereof, that characterize the classical dataset but were previously hidden in the classical dataset. Thus, because a classical ML model can be configured to receive quantum-enhanced ML input features as inputs, the classical ML model can base its output decisions on such previously hidden patterns, trends, and / or distributions, and thus generate more accurate decisions than would be possible without the quantum-enhanced ML input features.

[0032] The computerized tools described herein, in various embodiments, can electronically receive a classical dataset as input and electronically produce quantum-enhanced ML input features as output based on the classical dataset, in which case the quantum-enhanced ML input features can be considered enriched versions of the classical dataset. As described herein, the computerized tools can facilitate this functionality by electronically converting the classical dataset into quantum probability amplitudes (e.g., via amplitude embedding / encoding), by initializing a quantum computer with such quantum probability amplitudes, by executing quantum circuits (e.g., quantum Fourier transforms) on the quantum computer to rotate and / or transform such quantum probability amplitudes, or by combinations thereof. In some cases, the rotated / transformed quantum probability amplitudes can be considered quantum-enhanced ML input features. In other cases, the rotated / transformed quantum probability amplitudes can be further manipulated via any suitable mathematical function (e.g., scaling, offset, norm calculation) to provide quantum-enhanced ML input features. In various cases, the computerized tool may electronically execute a classical ML model on quantum-enhanced ML input features, or may be capable of electronically storing and / or transmitting quantum-enhanced ML input features.

[0033] Various embodiments of the present invention can be employed to use hardware and / or software to solve problems that are highly technical in nature (e.g., facilitating quantum-enhanced features for classical machine learning), are not abstract, and cannot be performed as a set of mental acts by a human. Furthermore, some of the processes performed can be performed by specialized computers (e.g., amplitude embedders, quantum computers, classical machine learning models). In various aspects, some defined tasks associated with various embodiments of the present invention can include: accessing, by a device operably coupled to a processor, a classical dataset; generating, by the device, one or more machine learning input features based on a quantum transformation of the classical dataset; and running, by the device, a classical machine learning model on the one or more machine learning input features. Further defined tasks associated with various embodiments of the present invention can include converting, by the device, a classical dataset into a set of quantum probability amplitudes; and running, by the device, a quantum circuit on the set of quantum probability amplitudes, thereby providing a quantum transformation of the classical dataset. Such defined tasks are typically not performed manually by a human. Moreover, neither the human mind nor a person with pen and paper can electronically access a classical data set, electronically convert a classical data set to quantum probability amplitudes, electronically execute a quantum circuit on the quantum probability amplitudes to generate quantum-enhanced input features, or electronically execute a classical ML model on the quantum-enhanced input features, or any combination thereof. Instead, various embodiments of the present invention are intrinsically and intimately tied to computer technology and cannot be implemented outside of a computing environment (e.g., quantum circuits and classical ML models are inherently computerized entities and cannot exist outside of a computing system).Similarly, computerized tools that leverage quantum circuits to create enriched input features for classical ML models are also inherently computerized devices and cannot be practically implemented in any sensible way without a computer.

[0034] In various instances, various embodiments of the present invention can integrate the disclosed teachings regarding quantum-enhanced features for classical machine learning into practical applications. Indeed, as described herein, various embodiments of the present invention, which may take the form of systems and / or computer-implemented methods, can be thought of as computerized tools that facilitate the enrichment of classical datasets by generating quantum state representations of the classical datasets and / or by transforming the quantum state representations via quantum circuits. As explained above, while much quantum research has contributed to the design and / or construction of quantum computing devices capable of supporting more physical qubits than NISQ devices, no research has been dedicated to investigating how NISQ devices can be leveraged to improve the performance of classical machine learning techniques. In stark contrast, the inventors of various embodiments of the present invention recognized that applying quantum transformations to classical datasets can provide enhanced / enriched versions of the classical datasets. Furthermore, the inventors of various embodiments of the present invention have experimentally verified that a classical ML model configured to receive both a classical dataset and an enriched / enriched version of the classical dataset as input can achieve higher performance metrics (e.g., improved prediction accuracy) when compared to a classical ML model configured to receive only the classical dataset as input. As described herein, this improvement in performance metrics can be due to the fact that the enriched / enriched version of the classical dataset can reveal data patterns, data trends, and / or data distributions that are hidden and / or undetectable in the classical dataset. Thus, a classical ML model configured to receive an enriched / enriched version of the classical dataset as input can base its output decisions on such previously hidden data patterns, data trends, and / or data distributions.Systems and / or techniques that can improve the performance of computing devices, including classical ML models, clearly establish concrete, tangible technological improvements in the field of machine learning.

[0035] Moreover, various embodiments of the present invention may control tangible, hardware-based, or software-based devices, or a combination thereof, based on the disclosed teachings. For example, embodiments of the present invention may actually execute quantum circuits in tangible quantum hardware to augment / enrich classical data, or may actually facilitate the execution of tangible ML hardware on augmented / enriched classical data, or both.

[0036] It should be appreciated that the drawings and disclosure herein illustrate non-limiting examples of various embodiments of the present invention.

[0037] 1 is a block diagram of an example, non-limiting system 100 that can facilitate quantum-enhanced features for classical machine learning according to one or more embodiments described herein. As shown, the quantum-enhanced feature system 102 can be electronically integrated with classical data 104, a classical machine learning model 106 (“classical ML model 106”), and / or a quantum computer 122 via any suitable wired and / or wireless electronic connections.

[0038] In various embodiments, the classical data 104 can include any suitable classical data values ​​(e.g., classical bits, classical integers, classical floating-point numbers). In some cases, the classical data 104 can be time-series data. That is, the data values ​​of the classical data 104 can be collated by time (e.g., the classical data 104 can include one or more first data values ​​associated with a first time step, the classical data 104 can include one or more second data values ​​associated with a second time step). In various cases, the classical data 104 can have any suitable size (e.g., can have any suitable number of data elements / values; if collated by time, can have any suitable number of time steps). In various cases, the classical data 104 can represent a desired measured value of any suitable quantity, either recorded over time or recorded at a given moment in time (e.g., the number of transactions recorded over time, data characterizing transactions that occurred during a time snapshot, the amount of resources consumed over time, data characterizing the resources consumed during a time snapshot). While some examples herein describe various embodiments of the present invention with respect to time series data, those skilled in the art will appreciate that this is merely a non-limiting example. In various aspects, any suitable collection of classical data can be implemented in various embodiments of the present invention, regardless of whether the collection of classical data is organized as a time series (e.g., even if the collection of classical data is collated by position, location, and / or some other index / identifier that is not time).

[0039] In various instances, the classical ML model 106 may implement any suitable type of classical machine learning algorithm, technique, or architecture, or a combination thereof. For example, the classical ML model 106 may be and / or include one or more support vector machines, one or more artificial neural networks, one or more expert systems, one or more Bayesian belief networks, one or more fuzzy logic models, one or more data fusion engines, one or more linear regression models, one or more polynomial regression models, one or more logistic regression models, one or more autoregressive integrated moving average models, and / or one or more decision trees. In various instances, the classical ML model 106 may be configured to receive input data of any suitable type and / or dimension and to generate output of any suitable type and / or dimension based on the input data. In various embodiments, the output data may be a judgment, inference, classification, segmentation, or prediction, or a combination thereof, based on the input data.

[0040] In various cases, quantum computer 122 can be any suitable type of quantum computing device and / or quantum simulator, i.e., quantum computer 122 can represent any suitable quantum computing architecture.

[0041] In various instances, it may be desirable to generate an enriched / enriched version of the classical data 104, and it may be desirable to run the classical ML model 106 on the classical data 104, on the enriched / enriched version of the classical data 104, or both. In various embodiments, this may be facilitated by the quantum enhanced feature system 102, as described below. More specifically, the quantum enhanced feature system 102 may leverage a quantum computer 122 to create the enriched / enriched version of the classical data 104.

[0042] In various embodiments, quantum enhanced characterization system 102 may include a processor 108 (e.g., a computer processing unit, microprocessor) and a computer-readable memory 110 operably coupled to processor 108. Memory 110 may store computer-executable instructions that, when executed by processor 108, cause processor 108 and / or other components of quantum enhanced characterization system 102 (e.g., receiver component 112, transformation component 114, quantum component 116, characterization component 118, execution component 120) to perform one or more operations. In various embodiments, memory 110 may store, and processor 108 may execute, the computer-executable components (e.g., receiver component 112, transformation component 114, quantum component 116, characterization component 118, execution component 120).

[0043] In various embodiments, quantum enhanced characterization system 102 can include a receiver component 112. In various aspects, receiver component 112 can electronically retrieve and / or access classical data 104 from any suitable centralized and / or decentralized data structure (not shown), whether remote and / or local to receiver component 112. Thus, in various aspects, other components of quantum enhanced characterization system 102 can manipulate and / or interact with (e.g., read, write, copy, edit) classical data 104.

[0044] In various embodiments, quantum-enhanced feature system 102 can include a conversion component 114. In various aspects, conversion component 114 can electronically convert classical data 104 into a quantum format (e.g., convert an electronic copy of classical data 104). In other words, classical data 104 may remain in a classical format, meaning that classical data 104 may not withstand processing by a quantum computing device. As such, conversion component 114 can electronically generate a version of classical data 104 that is processable by a quantum computing device.

[0045] Specifically, in various embodiments, the transformation component 114 can generate a set of probability amplitudes based on the classical data 104 via any suitable amplitude embedding and / or amplitude encoding techniques. In various cases, the set of probability amplitudes can be thought of as a quantum state vector that collectively represents the classical data 104. In other words, the set of probability amplitudes can be thought of as a format and / or version of the classical data 104 that can be processed by a quantum computing device. In various cases, the set of probability amplitudes can each correspond to the classical data 104. That is, the transformation component 114 can generate one probability amplitude for each data element in the classical data 104 (e.g., if the classical data 104 is a time series, in some cases the transformation component 114 can generate one probability amplitude for each time step represented in the classical data 104). In particular, the transformation component 114, in various embodiments, can treat the classical data 104 as a vector of data elements, calculate the magnitude of such vectors, and divide each data element by its calculated magnitude, thereby obtaining a normalized vector of data elements. In various cases, the normalized vector of data elements can be thought of as a collection of probability amplitudes.

[0046] Although the figures and disclosure herein describe various embodiments of the present invention in which transformation component 114 implements amplitude embedding to encode classical data 104 into a quantum-processable format, this is by way of non-limiting example only. In various aspects, any other suitable quantum embedding technique can be implemented to convert classical data 104 into a form amenable to quantum computation (e.g., transformation component 114 can implement basis embedding).

[0047] In various embodiments, quantum-enhanced feature system 102 can include quantum component 116. In various aspects, quantum component 116 can electronically apply a quantum circuit to the set of probability amplitudes to generate a set of composite probability amplitudes. More specifically, in various embodiments, quantum component 116 can be electronically integrated (e.g., via any suitable wired and / or wireless electronic connection) with quantum computer 122, which can be any suitable quantum computing device and / or simulator. In various cases, as shown, quantum computer 122 can be remote from quantum component 116. However, in other cases, quantum computer 122 can be local to quantum component 116. In various cases, quantum computer 122 can include physical qubits and / or simulate the behavior of qubits, such that quantum computer 122 can perform quantum computations. In various cases, quantum component 116 can initialize quantum computer 122 with a set of probability amplitudes and then run any suitable quantum circuit (e.g., a quantum Fourier transform) on quantum computer 122, thereby transforming and / or rotating the set of probability amplitudes into a set of composite probability amplitudes.

[0048] In other words, a set of probability amplitudes can be thought of as a quantum state vector that represents classical data 104. In various embodiments, quantum component 116 can initialize quantum computer 122 with such a quantum state vector. That is, quantum component 116 can manipulate the qubits of quantum computer 122 (e.g., via any suitable quantum gate) so that the initial states of the qubits conform to the probability amplitudes. In various instances, quantum component 116 can then transform / rotate that quantum state vector (e.g., probability amplitudes) by executing quantum circuits on quantum computer 122. The result can be a composite quantum state vector (e.g., composite probability amplitudes).

[0049] In various cases, the transformation component 114 can be thought of as importing classical data 104 into quantum Hilbert space (e.g., the classical data 104 can be converted into a quantum-processable format), and the quantum component 116 can be thought of as manipulating classical data 104 within quantum Hilbert space (e.g., the quantum-processable format of classical data 104 can be transformed and / or rotated via the execution of quantum gates).

[0050] In various embodiments, the quantum enhanced feature system 102 can include a feature component 118. In various aspects, the feature component 118 can electronically generate a set of enhanced ML input features based on the composite probability amplitudes generated by the quantum component 116. In various cases, the feature component 118 can apply any suitable mathematical function to the composite probability amplitudes to provide the enhanced ML input features. For example, in some cases, the feature component 118 can multiplicatively scale the composite probability amplitudes upward (e.g., by a multiplication factor greater than 1) or downward (e.g., by a multiplication factor less than 1), or both, and the so-scaled probability amplitudes can be considered enhanced ML input features. As another example, in some cases, the feature component 118 can additively offset the composite probability amplitudes upward (e.g., by adding a bias value) or downward (e.g., by subtracting a bias value), or both, and the so-offset probability amplitudes can be considered enhanced ML input features. As yet another example, the composite probability amplitudes can be complex numbers, so that feature component 118 can calculate the norm of each composite probability amplitude, thereby allowing the calculated magnitude to be considered as an enhanced ML input feature. As yet a further example, feature component 118 can avoid modifying the composite probability amplitudes, so that the composite probability amplitudes themselves can be considered as enhanced ML input features.

[0051] In various embodiments, the quantum enhanced feature system 102 can include an execution component 120. In various aspects, the execution component 120 can electronically execute the classical ML model 106 against the enhanced ML input features generated by the feature component 118, and / or electronically facilitate the execution of the classical ML model 106. That is, the execution component 120 can electronically provide the enhanced ML input features to the classical ML model 106, and / or electronically instruct the classical ML model 106 to analyze the enhanced ML input features. In some cases, the execution component 120 can electronically train the classical ML model 106 against the enhanced ML input features (e.g., via supervised training, unsupervised training, reinforcement learning), and / or electronically facilitate the training of the classical ML model 106 against the enhanced ML input features.

[0052] 2-3 are block diagrams of example, non-limiting systems 200 and 300 including quantum probability amplitudes that facilitate quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. As shown, system 200 can, in various embodiments, include the same components as system 100 and can further include probability amplitude 202.

[0053] In various embodiments, the transformation component 114 can electronically generate the probability amplitudes 202 based on the classical data 104. Specifically, in various instances, the transformation component 114 can electronically apply any suitable amplitude embedding and / or amplitude encoding technique to the classical data 104 to provide the probability amplitudes 202. Amplitude embedding and / or amplitude encoding can be mathematical techniques that embed and / or encode classical data into the probability amplitudes of a quantum state vector. In other words, the probability amplitudes 202 can be a set of complex numbers whose values ​​collectively represent the classical data 104, the squares of which represent the probabilities and / or likelihoods of the occurrence of various quantum states. In other words, probability amplitudes 202 can be thought of collectively as classical data 104 that is a quantum-processable version and / or format (e.g., classical data 104 may be formatted in a way that cannot be processed by a quantum computer, while probability amplitudes 202 can be formatted in a way that can be processed by a quantum computer).

[0054] More specifically, in various embodiments, the transformation component 114 can electronically generate the probability amplitudes 202 by normalizing the classical data 104. That is, in various instances, the transformation component 114 can treat the classical data 104 as a vector of elements. In such instances, the transformation component 114 can normalize the vector. In other words, the transformation component 114 can calculate a norm (e.g., magnitude, length) of the vector and divide each of the elements in the vector by the calculated norm. In various instances, the result can be a normalized vector. In various instances, the elements of the normalized vector can be considered probability amplitudes 202.

[0055] 3 illustrates, in a non-limiting, exemplary manner, how the transformation component 114 can generate the probability amplitude 202 based on the classical data 104. As shown in FIG. 3, the classical data 104 may, in some instances, include n data points (e.g., data point 1 through data point n), for any suitable positive integer n. In various embodiments, if the classical data 104 is a time series, this may indicate that the classical data 104 includes n time steps (e.g., the classical data 104 may include one data point at time 1, and the classical data 104 may include one data point at time n). However, this is merely a non-limiting example. In some instances, if the classical data 104 is a time series, the classical data 104 may include more than one data point per time step. For example, if the classical data 104 can include a total of n data points, and if the classical data 104 is a time series with 2 data points per time step, then the classical data 104 can include n / 2 time steps. In either case, the classical data 104 can include a total of n data points.

[0056] In various instances, as shown, the classical data 104 can each correspond to a probability amplitude 202. That is, because the classical data 104 includes n data points, the probability amplitudes 202 can similarly include n amplitudes (e.g., amplitude 1 through amplitude n). In various instances, each amplitude in the probability amplitudes 202 can be based on and / or generated from a corresponding data point in the classical data 104. For example, amplitude 1 can be based on and / or generated from data point 1, and amplitude n can be based on and / or generated from data point n.

[0057] As mentioned above, the transformation component 114 can apply any suitable amplitude embedding / encoding technique to create the probability amplitudes 202. In some cases, such a technique can be normalization. For example, consider the classical data 104 as a vector (and / or set) represented by a variable y. In such a case, data point 1 can be represented by y1, data point n by y n In various cases, the transformation component 114 may be configured to transform the norm of y into

number

number

number

number

[0058] In various embodiments, probability amplitudes 202 can be thought of as collectively representing an n-element quantum state vector. As one skilled in the art will appreciate, an n-element quantum state vector can be implemented with log2n qubits. In various cases, if log2n is not an integer, it can be rounded up to the next highest integer (e.g., because fractional qubits cannot be implemented). When rounding up log2n to the next highest integer, one skilled in the art will appreciate that one or more dummy values ​​may be concatenated to the end (and / or the beginning, and / or anywhere) of probability amplitude 202. For example, assume n=5. In such a case, classical data 104 may have five data points, and five probability amplitudes can be calculated as described above. However, log25 is not an integer, and log25 rounded up to the next highest integer is 3. This means that probability amplitudes 202 can be processed by a quantum computer with three qubits. However, a quantum state vector for a three-qubit system may have eight probability amplitudes (e.g., 2 3 = 8). Thus, the probability amplitude 202 can have a total of eight amplitudes, the first five of which can be generated as described above, and the last three of which can be dummy values ​​of no interest.

[0059] 4-5 are block diagrams of example, non-limiting systems 400 and 500 including quantum circuits and composite quantum probability amplitudes that can facilitate quantum-enhanced features for classical machine learning according to one or more embodiments described herein. As shown, system 400 can, in some cases, include the same components as system 200 and can further include a quantum circuit 402 and a composite probability amplitude 404.

[0060] In various embodiments, quantum component 116 can electronically apply quantum circuit 402 to probability amplitude 202 to provide composite probability amplitude 404. More specifically, quantum component 116 can be electronically integrated with quantum computer 122, or can have electronic access to and / or control of quantum computer 122. In various embodiments, quantum computer 122 can implement log2n physical qubits, or simulate the behavior of log2n qubits, or both (e.g., again, log2n can be rounded up if it is not an integer). Thus, quantum computer 122 can facilitate quantum computation of an n-element quantum state vector. In various cases, quantum component 116 can electronically initialize quantum computer 122 with probability amplitude 202. That is, quantum component 116 can place the qubits of quantum computer 122 into a superposition of quantum states given by and / or according to probability amplitude 202. After initialization, quantum component 116 can electronically execute quantum circuit 402 on quantum computer 122. Quantum computer 122 can be initialized with probability amplitude 202, such that execution of quantum circuit 402 can result in a rotation and / or transformation of probability amplitude 202 to provide a composite probability amplitude 404.

[0061] In various embodiments, quantum circuit 402 may include any suitable combination and / or arrangement of quantum gates. In some cases, quantum circuit 402 may be a quantum Fourier transform.

[0062] 5 illustrates, in a non-limiting, exemplary manner, how quantum component 116 can generate composite probability amplitudes 404 based on probability amplitudes 202. As shown in FIG. 5, because probability amplitudes 202 can have n amplitude values ​​(e.g., amplitude 1 through amplitude n), composite probability amplitudes 404 can similarly have n amplitude values ​​(e.g., composite amplitude 1 through composite amplitude n). Just as probability amplitudes 202 can collectively represent an n-element quantum state vector for log2n qubits, composite probability amplitudes 404 can similarly collectively represent an n-element quantum state vector resulting from log2n qubits. In various aspects, when quantum circuit 402 is applied to probability amplitudes 202 (e.g., when quantum computer 122 is initialized with probability amplitudes 202 and quantum circuit 402 is implemented on quantum computer 122), quantum circuit 402 can alter (e.g., rotate, translate) probability amplitudes 202, and the result of such alteration can be considered composite probability amplitude 404. In other words, the quantum computer 122 can be initialized with an initial quantum state (e.g., probability amplitude 202), and execution of the quantum circuit 402 on the quantum computer 122 can transform the initial quantum state (e.g., probability amplitude 202) into a resulting quantum state (e.g., composite probability amplitude 404).

[0063] This is further explained in Figure 6. Figure 6 is an example, non-limiting quantum circuit diagram 600 according to one or more embodiments described herein. The quantum circuit diagram 600 can illustrate how the quantum computer 122 utilized by the quantum component 116 operates.

[0064] As shown, quantum computer 122 can include log2n qubits (e.g., qubit 1, qubit 2, ..., qubit log2n). Again, if log2n is not an integer, it can be rounded up. In various cases, the log2n qubits can begin in any suitable starting quantum state. In the non-limiting example shown, all of the log2n qubits can begin by assuming the |0> state, as shown by numeral 604. However, this is merely a non-limiting example. In various other cases, the log2n qubits can begin by assuming any suitable known quantum state (e.g., all of the log2n qubits can assume the |1> state, some of the log2n qubits can assume the |0> state while others of the log2n qubits can assume the |1> state). In either case, the log2n qubits of quantum computer 122 can begin at numeral 604 by assuming some known quantum state (e.g., can have some known quantum state vector).

[0065] In various instances, quantum component 116 may execute initialization circuit 606 on quantum computer 122. In various embodiments, execution of initialization circuit 606 may rotate and / or transform the quantum state of the log2n qubit from a known starting quantum state at numeral 604 to a quantum state defined by probability amplitude 202 at numeral 608. In other words, initialization circuit 606 may include any suitable combination and / or arrangement of quantum gates (e.g., Hadamard gates, Phase gates, Pauli X gates, Pauli Y gates, Pauli Z gates, CNOT gates, SWAP gates, Toffoli gates) to place the log2n qubit into the quantum state defined by probability amplitude 202. As one skilled in the art will appreciate, the specific configuration of initialization circuit 606 may depend on the known starting quantum state at numeral 604 and the desired initial quantum state (e.g., probability amplitude 202) at numeral 608. In other words, given a known quantum state and a desired quantum state, one skilled in the art would understand which quantum gates to combine in which arrangement and / or order to transform the given known quantum state into the desired quantum state. Thus, given a known starting quantum state at numeral 604 and a desired initial quantum state (e.g., probability amplitude 202) at numeral 608, quantum component 116 can determine how to structure initialization circuit 606 to rotate / transform the known starting quantum state at numeral 604 into the desired initial quantum state (e.g., probability amplitude 202) at numeral 608. Once the log2n qubits have exhibited quantum states according to probability amplitude 202 (e.g., after execution of initialization circuit 606 at numeral 608), quantum computer 122 can be considered to have been initialized with probability amplitude 202.

[0066] In various embodiments, once quantum computer 122 has been initialized with probability amplitudes 202, quantum component 116 can execute quantum circuit 402 on quantum computer 122. In various instances, execution of quantum circuit 402 can rotate and / or transform the quantum state of the log 2n qubits from the quantum state defined by probability amplitudes 202 at numeral 608 to some composite quantum state, shown at numeral 610. In various embodiments, the composite quantum state at numeral 610 can correspond to composite probability amplitude 404. In other words, quantum circuit 402 can rotate / transform probability amplitudes 202 (e.g., defining the quantum state of the log 2n qubits at numeral 608) into composite probability amplitude 404 (e.g., defining the quantum state of the log 2n qubits at numeral 610). As such, in various instances, composite probability amplitude 404 can be thought of as a function of probability amplitudes 202 and of quantum circuit 402.

[0067] Those skilled in the art will appreciate that quantum computer 122 may implement any suitable quantum state measurement technique.

[0068] 7-8 are block diagrams of example, non-limiting systems 700 and 800 including enhanced machine learning input features that can facilitate quantum enhanced features for classical machine learning, according to one or more embodiments described herein. As shown, system 700 can, in some cases, include the same components as system 400 and can further include enhanced ML input features 702.

[0069] In various embodiments, the feature component 118 can electronically generate the enhanced ML input features 702 based on the composite probability amplitudes 404. In other words, the feature component 118 can apply any suitable mathematical function to the composite probability amplitudes 404 to provide the enhanced ML input features 702.

[0070] This is illustrated in a non-limiting, exemplary manner in Figure 8. As shown in Figure 8, since composite probability amplitude 404 can include n amplitudes (e.g., composite amplitude 1 through composite amplitude n), enhanced ML input features 702 can similarly include n quantum enhanced input features (e.g., quantum enhanced input feature 1 through quantum enhanced input feature n). In various cases, enhanced ML input features 702 can each correspond to composite probability amplitude 404. That is, quantum enhanced feature 1 can correspond to and / or be generated based on composite amplitude 1, and quantum enhanced feature n can correspond to and / or be generated based on composite amplitude n.

[0071] In various cases, the enhanced ML input feature 702 can be any suitable function of the composite probability amplitude 404. For example, in some instances, the feature component 118 can multiplicatively scale the composite probability amplitude 404 to generate the enhanced ML input feature 702. In such a case, quantum enhanced feature 1 can be equal to the product of composite amplitude 1 and any suitable multiplication factor, and quantum enhanced feature n can similarly be equal to the product of composite amplitude n and any suitable multiplication factor. As another example, in some embodiments, the feature component 118 can additively offset the composite probability amplitude 404 to generate the enhanced ML input feature 702. In such a case, quantum enhanced feature 1 can be equal to the sum of composite amplitude 1 and any suitable bias value, and quantum enhanced feature n can similarly be equal to the sum of composite amplitude n and any suitable bias value. As yet another example, the composite probability amplitude 404, which is a sine, can be a complex number, and the feature component 118 can calculate the magnitude of the composite probability amplitude 404 to generate the enhanced ML input feature 702. In such a case, quantum enhanced feature 1 may be equal to the magnitude of composite amplitude 1, and quantum enhanced feature n may similarly be equal to the magnitude of composite amplitude n. In yet another example, feature component 118 may avoid modifying the composite probability amplitude. In such a case, quantum enhanced feature 1 may be equal to composite amplitude 1, and quantum enhanced feature n may similarly be equal to composite amplitude n.

[0072] In various instances, the enhanced ML input features 702 can be thought of as quantum transformations and / or quantum enriched versions of the classical data 104. In various cases, the enhanced ML input features 702 can reveal data patterns, data trends, and / or data distributions that were previously hidden and / or undetectable in the classical data 104, and therefore the terms “enhanced” and / or “enriched” can be used to describe the enhanced ML input features 702. As explained above, the inventors of various embodiments of the present invention recognized that importing a classical dataset into quantum Hilbert space and then transforming the classical dataset within quantum Hilbert space can reveal otherwise hidden patterns, trends, and / or distributions that characterize the classical dataset. As described herein, the actions of the transformation component 114 can be thought of as importing the classical data 104 into quantum Hilbert space (e.g., the transformation component 114 can convert the classical data 104 into a quantum-processable format, i.e., probability amplitudes 202), and the actions of the quantum component 116 can be thought of as transforming the classical data 104 within quantum Hilbert space (e.g., the quantum component 116 can apply a quantum circuit to the probability amplitudes 202). Thus, the enhanced ML input features 702 can include patterns, trends, and / or distributions that cannot be discerned within the classical data 104.

[0073] In various embodiments, as mentioned above, the execution component 120 can electronically execute the classical ML model 106 against the enhanced ML input features 702 and / or electronically facilitate the execution of the classical ML model 106. This is illustrated in a non-limiting, exemplary manner in Figure 9. Figure 9 is an exemplary, non-limiting block diagram showing how quantum enhanced features for classical machine learning can be practically utilized, according to one or more embodiments described herein.

[0074] As shown, FIG. 9 depicts two scenarios: scenario 902 and scenario 904. In scenario 902, the classical ML model 106 can be configured to receive only classical data 104 as input and produce a prediction 906 as output. Meanwhile, in scenario 904, the classical ML model 106 can be configured to receive both classical data 104 and enhanced ML input features 702 as input and produce a prediction 908 as output. As mentioned above, the classical ML model 106 can generate predictions / judgments by recognizing patterns, trends, and / or distributions in its input data. In scenario 902, the classical ML model 106 is not configured to receive enhanced ML input features 702 as input, and therefore the classical ML model 106 does not have access to the patterns, trends, and / or distributions revealed by the enhanced ML input features 702 but hidden in the classical data 104. In contrast, in scenario 904, because the classical ML model 106 is configured to receive the enhanced ML input features 702 as input, the classical ML model 106 has access to patterns, trends, and / or distributions revealed by the enhanced ML input features 702 but hidden in the classical data 104. Because the classical ML model 106 can have access to additional patterns, trends, and / or distributions in its input data in scenario 904, prediction 908 can be more accurate than prediction 906. In other words, the performance of the classical ML model 106 can be improved when the classical ML model 106 is configured to receive the enhanced ML input features 702 as input. Such improved performance (e.g., improved prediction / detection accuracy) is a concrete, tangible technological advantage.

[0075] Indeed, the inventors of various embodiments of the present invention have experimentally verified such advantages. Specifically, the inventors conducted various experiments using various volatility index data. In such experiments, the inventors compiled volatility index data (e.g., which can be thought of as time series data) for various stocks and fed such data to various classical ML models (e.g., autoregressive integrated moving average models) that predicted future volatility index values. The inventors calculated the accuracy of such predictions by comparing the predictions with known volatility index values ​​that actually occurred at the predicted time steps. In addition, the inventors enhanced / enriched the compiled volatility index data using a quantum Fourier transform (e.g., in such experiments, the quantum circuit 402 was a quantum Fourier transform) as described herein, and fed both the volatility index data and a QFT version of the volatility index data to a classical ML model that also predicted future volatility index values. As above, the inventors calculated the accuracy of such forecasts by comparing them to known volatility index values ​​that actually occurred at the forecasted time step. Finally, the inventors compared the accuracy of forecasts based solely on the compiled volatility index data to the accuracy of forecasts based on both the compiled volatility index data and a QFT version of the volatility index data.

[0076] In one experiment, predictions based on both volatility index data compiled for a first portion of a stock and a QFT version of the volatility index data for that first stock achieved 17.90% higher accuracy than predictions based solely on the volatility index data compiled for that first stock. In a second experiment, predictions based on both volatility index data compiled for a second portion of a stock and a QFT version of the volatility index data for that second stock achieved 19.61% higher accuracy than predictions based solely on the volatility index data compiled for that second stock. This is a significant improvement in the performance of such classical ML models.

[0077] In some other experiments, the inventors further calculated the Fast Fourier Transform (FFT) of the compiled volatility index data for various stocks. In such cases, the inventors fed the compiled volatility index data, a QFT version of the volatility index data, and an FFT version of the volatility index data to a classical ML model. In one such case, the classical ML model achieved a 20.01% higher accuracy rate compared to predictions based solely on the compiled volatility index data. In another such case, the classical ML model achieved a 66.91% higher accuracy rate compared to predictions based solely on the compiled volatility index data. Again, this is a significant improvement in the performance of such classical ML models.

[0078] In various aspects, the inventors of various embodiments of the present invention have realized that enhancing / enriching classical data as described herein can have a smoothing and / or noise-reducing effect on the classical data (e.g., at least when the classical data is transformed with a quantum Fourier transform).

[0079] 10 is a flow diagram of an example, non-limiting, computer-implemented method 1000 that can facilitate quantum-enhanced features for classical machine learning, according to one or more embodiments described herein. In some cases, the computer-implemented method 1000 can be performed by a quantum-enhanced feature system 102.

[0080] In various embodiments, operation 1002 may include receiving, by a device (e.g., 112) operably coupled to the processor, the classical data set (e.g., 104).

[0081] In various embodiments, operation 1004 can include converting, by a device (e.g., 114), the classical data set into probability amplitudes (e.g., 202).

[0082] In various cases, operation 1006 may include initializing, by a device (e.g., 116), a quantum computing device and / or simulator (e.g., 122) with the probability amplitude.

[0083] In various cases, operation 1008 may include applying a quantum circuit (e.g., 402) to the probability amplitudes by a device (e.g., 116) and via a quantum computing device and / or simulator to provide a composite probability amplitude (e.g., 404).

[0084] In various aspects, operation 1010 may include adjusting, by a device (e.g., 118), the value of the combined probability amplitude in any suitable manner to provide the quantum enhanced feature (e.g., 702). As noted above, sometimes no adjustment is made to the combined probability amplitude, and in such cases, the quantum enhanced feature is equal to the combined probability amplitude.

[0085] In various cases, operation 1012 may include running, by a device (e.g., 120), a classical machine learning model (e.g., 106) on both the classical dataset and the quantum-enhanced features.

[0086] 11 is a block diagram of an example, non-limiting system 1100 including a visualization component that can facilitate quantum-enhanced features for classical machine learning according to one or more embodiments described herein. As shown, system 1100 can, in some cases, include the same components as system 700 and can further include a visualization component 1102.

[0087] In various embodiments, the visualization component 1102 can electronically render, display, graph, or plot the enhanced ML input features 702, or a combination thereof. For example, in various cases, the visualization component 1102 can be electronically integrated with a computer monitor / screen (not shown) (e.g., via any suitable wired and / or wireless electronic connection). In such cases, the visualization component 1102 can electronically display a graph / plot of the enhanced ML input features 702 on the computer monitor / screen. In some cases, the visualization component 1102 can also electronically display a graph / plot of the classical data 104 on the computer monitor / screen, thereby allowing the classical data 104 to be visually compared to the enhanced ML input features 702. Those skilled in the art will appreciate that any suitable graph and / or plot can be implemented by the visualization component 1102 (e.g., histograms, bar graphs, Bloch spheres, 2D and / or 3D plots).

[0088] 12 is a block diagram of an example, non-limiting system 1200 including an operator device that can facilitate quantum-enhanced features for classical machine learning according to one or more embodiments described herein. As shown, system 1200 can, in some cases, include the same components as system 1100 and can further include an operator device 1202.

[0089] In various embodiments, the quantum enhanced character system 102 can be electronically integrated with the operator device 1202 via any suitable wired and / or wireless electronic connection. In various instances, the operator device 1202 can be associated with an entity (e.g., a client) that desires to utilize the functionality provided by the quantum enhanced character system 102. For example, such an entity may own and / or maintain classical data 104, and such an entity may desire to quantum enrich the classical data 104. In such instances, the operator device 1202 can provide the classical data 104 to the quantum enhanced character system 102 (e.g., can electronically transmit a copy of the classical data 104 to the receiver component 112). In various embodiments, the operator device 1202 can further identify the quantum circuit 402. In other words, an entity associated with operator device 1202 may desire that classical data 104 be transformed and / or enhanced by a particular quantum circuit, and operator device 1202 may electronically transmit an identifier of that particular quantum circuit to receiver component 112. Thus, after transformation component 114 converts classical data 104 into probability amplitudes 202, and after quantum component 116 initializes quantum computer 122 with the probability amplitudes 202, quantum component 116 may execute the quantum circuit directed by operator device 1202 on quantum computer 122. In some instances, quantum component 116 may provide operator device 1202 with a list of available quantum circuits (not shown), and operator device 1202 may select from such list the quantum circuit that the entity with which operator device 1202 is associated wishes to execute.In various instances, once the enhanced ML input features 702 have been generated, the execution component 120 can electronically transmit the enhanced ML input features 702 (and / or any graphs / plots generated by the visualization component 1102) to the operator device 1202.

[0090] 13-14 are flow diagrams of example, non-limiting, computer-implemented methods 1300 and 1400 that can facilitate quantum-enhanced features for classical machine learning, according to one or more embodiments described herein.

[0091] Consider first the computer-implemented method 1300. In various embodiments, operation 1302 may include accessing a classical dataset (e.g., 104) by a device (e.g., 112) operably coupled to the processor.

[0092] In various embodiments, operation 1304 may include generating, by a device (e.g., 118), one or more machine learning input features (e.g., 702) based on a quantum transformation of a classical dataset (e.g., involving 202, 402, or 404 collectively, or a combination thereof).

[0093] In various cases, operation 1306 may include running, by a device (e.g., 120), a classical machine learning model (e.g., 106) on one or more machine learning input features.

[0094] Although not explicitly shown in FIG. 13 , the computer-implemented method 1300 may further include: converting, by a device (e.g., 114), the classical dataset into a set of quantum probability amplitudes (e.g., 202); and running, by a device (e.g., 116), a quantum circuit (e.g., 402) on the set of quantum probability amplitudes, thereby providing a quantum transformation of the classical dataset.

[0095] Although not explicitly shown in FIG. 13 , the computer-implemented method 1300 may further include: visually rendering, by a device (e.g., 1102), both the classical dataset and the one or more machine learning input features.

[0096] Consider now the computer-implemented method 1400. In various embodiments, operation 1402 can include receiving, by a device (e.g., 112) operably coupled to the processor, a classical time series dataset (e.g., 104) from an operator device (e.g., 1202).

[0097] In various embodiments, operation 1404 may include generating, by a device (e.g., 118), one or more quantum-enhanced machine learning input features (e.g., 702) based on a quantum transformation of a classical time series dataset (e.g., involving 202, 402, or 404 collectively, or a combination thereof).

[0098] In various cases, operation 1406 may include transmitting, by a device (e.g., 120), one or more quantum-enhanced machine learning input features to an operator device.

[0099] Although not explicitly shown in FIG. 14, the computer-implemented method 1400 may further include: generating, by a device (e.g., 114), quantum probability amplitudes (e.g., 202) based on the classical time series dataset; and running, by a device (e.g., 116), a quantum algorithm (e.g., 402) selected by the operator device on the quantum probability amplitudes, thereby providing a quantum transformation of the classical time series dataset.

[0100] Although not explicitly shown in FIG. 14 , the computer-implemented method 1400 may further include: graphing, by a device (e.g., 1102), the classical time series dataset or one or more quantum-enhanced machine learning input features.

[0101] Various embodiments of the present invention may leverage quantum computing to enhance, enrich, or augment classical datasets, or a combination thereof. Specifically, various embodiments of the present invention may be considered computerized tools that can receive a classical dataset as input, convert the classical dataset into quantum probability amplitudes (e.g., thereby importing the classical dataset into quantum Hilbert space), initialize a quantum computer with the quantum probability amplitudes, and execute quantum circuits on the quantum computer (e.g., thereby transforming the classical dataset within quantum Hilbert space). In various instances, the resulting quantum probability amplitudes can be used to generate enhanced ML input features. Indeed, in various instances, the resulting quantum probability amplitudes themselves can be considered enhanced ML input features. As described herein, the enhanced ML input features can reveal more subtle data patterns, trends, or distributions, or combinations thereof, that were previously hidden in the classical dataset. Thus, the enhanced ML input features can be provided as inputs to classical ML models, thereby improving the performance (e.g., accuracy) of the classical ML models.

[0102] In various aspects, such computerized tools can be implemented to enhance any suitable type of classical data (e.g., time-series data, non-time-series data, financial data, geospatial data, image data, audio data, video data, pressure data, voltage / current data, sales data, resource data). For example, in some instances, such computerized tools can be implemented in the field of supply chain analysis (e.g., a computerized tool can enhance a time series showing resource consumption over time and feed such enhanced data into a classical ML model to more accurately predict future resource consumption). As another example, in some instances, such computerized tools can be implemented in the field of marketing science (e.g., a computerized tool can enhance a time series showing the number of visitors to an online website over time and feed such enhanced data into a classical ML model to more accurately predict future online visitor numbers). In various instances, any other suitable type of classical data can be enhanced by various embodiments of the present invention.

[0103] While various examples described herein have discussed enhancing classical data by applying a quantum Fourier transform to such classical data, this is a non-limiting example, and in various cases, those skilled in the art will appreciate that any suitable quantum circuitry and / or quantum algorithms may be used to enhance and / or enrich the classical data.

[0104] To provide further context for the various embodiments described herein, Figure 15 and the following discussion are intended to provide a brief, general description of a suitable computing environment 1500 in which various embodiments described herein may be implemented. While the embodiments are described in the general context of computer-executable instructions that may be executed on one or more computers, those skilled in the art will appreciate that the embodiments may also be implemented in combination with other program modules, or as a combination of hardware and software, or both.

[0105] Generally, program modules include routines, programs, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the methods of the present invention can be practiced with other computer system configurations, including single-processor or multi-processor computer systems, minicomputers, mainframe computers, Internet of Things (IoT) devices, distributed computing systems, as well as personal computers, handheld computing devices, microprocessor-based or programmable consumer electronics, and the like, each of which can be operatively coupled to one or more associated devices.

[0106] The illustrated embodiments of the present disclosure may also be practiced in distributed computing environments where certain tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0107] A computing device typically includes a variety of media, which may include computer-readable storage media, machine-readable storage media, and / or communication media, and these two terms are used interchangeably herein as follows: A computer-readable storage medium or machine-readable storage medium can be any available storage medium that can be accessed by a computer and includes both volatile and nonvolatile media, removable and non-removable media. By way of example, and not limitation, a computer-readable storage medium or machine-readable storage medium can be implemented in conjunction with any method or technology for storage of information, such as computer-readable or machine-readable instructions, program modules, structured or unstructured data, etc.

[0108] A computer-readable storage medium may include, but is not limited to, random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD), Blu-ray disc (BD) or other optical disc storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage device, solid state drive or other solid state storage device, or other tangible and / or non-transitory medium that can be used to store the desired information. In this regard, the terms "tangible" or "non-transitory," when applied herein to storage, memory, or computer-readable medium, should be understood as qualifiers to exclude only propagating transitory signals per se, and not to disclaim all standard storage, memory, or computer-readable media that are not propagating transitory signals per se.

[0109] The computer-readable storage medium can be accessed by one or more local or remote computing devices for various operations on the information stored by the medium, e.g., via access requests, queries, or other data retrieval protocols.

[0110] Communication media typically embodies computer-readable instructions, data structures, program modules, or other structured or unstructured data in a data signal, such as a modulated data signal, e.g., carrier wave or other transport mechanism, and includes any information transmission or transport media. The term "modulated data signal" or signal refers to a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal or signals. By way of example, and not limitation, communication media include wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media.

[0111] 15 , an exemplary environment 1500 for implementing various embodiments of the aspects described herein includes a computer 1502, which includes a processing unit 1504, a system memory 1506, and a system bus 1508. The system bus 1508 couples system components, including but not limited to the system memory 1506, to the processing unit 1504. The processing unit 1504 can be any of a variety of commercially available processors. Dual microprocessors and other multiprocessor architectures can also be employed as the processing unit 1504.

[0112] The system bus 1508 may be any of several types of bus structures, which may be further interconnected to a memory bus (with or without a memory controller), a peripheral bus, and a local bus using any of a variety of commercially available bus architectures. The system memory 1506 includes ROM 1510 and RAM 1512. The basic input / output system (BIOS) may be stored in non-volatile memory, such as ROM, erasable programmable read-only memory (EPROM), or EEPROM, and includes basic routines that help transfer information between elements within the computer 1502, such as during startup. The RAM 1512 may also include high-speed RAM, such as static RAM for caching data.

[0113] The computer 1502 further includes an internal hard disk drive (HDD) 1514 (e.g., EIDE, SATA), one or more external storage devices 1516 (e.g., a magnetic floppy disk drive (FDD) 1516, a memory stick or flash drive reader, a memory card reader, etc.), and a drive 1520, such as a solid-state drive, optical disk drive, or the like, capable of reading from and writing to a disk 1522, such as a CD-ROM disk, DVD, or BD. Alternatively, if a solid-state drive is included, the disk 1522 is not included unless it is separate. While the internal HDD 1514 is illustrated as being located within the computer 1502, the internal HDD 1514 could also be configured for external use within a suitable chassis (not shown). Additionally, although not shown in the environment 1500, a solid-state drive (SSD) could be used in addition to or instead of the HDD 1514. HDD 1514, external storage device 1516, and drive 1520 can be connected to system bus 1508 by HDD interface 1524, external storage interface 1526, and drive interface 1528, respectively. Interface 1524 for external drive implementations can include at least one or both of Universal Serial Bus (USB) and Institute of Electrical and Electronics Engineers (IEEE) 1394 interface technologies. Other external drive connection technologies are within the contemplation of the embodiments described herein.

[0114] The drives and their associated computer-readable storage media provide non-volatile storage of data, data structures, computer-executable instructions, etc. For the computer 1502, the drives and storage media accept the storage of any data in a suitable digital format. While the above description of computer-readable storage media refers to particular types of storage devices, those skilled in the art will appreciate that other types of computer-readable storage media, whether now existing or later developed, can also be used in the exemplary operating environment, and further, any such storage media can contain computer-executable instructions for performing the methods described herein.

[0115] A number of program modules can be stored in the drives and RAM 1512, including an operating system 1530, one or more application programs 1532, other program modules 1534, and program data 1536. All or portions of the operating system, applications, modules, and / or data can also be cached in RAM 1512. The systems and methods described herein can be implemented using a variety of commercially available operating systems or combinations of operating systems.

[0116] The computer 1502 may optionally include emulation technology. For example, a hypervisor (not shown) or other intermediary may emulate a hardware environment for the operating system 1530, although the emulated hardware may optionally be different from the hardware illustrated in FIG. 15 . In such an embodiment, the operating system 1530 may comprise one of multiple virtual machines (VMs) hosted on the computer 1502. Furthermore, the operating system 1530 may provide a runtime environment, such as the Java® Runtime Environment or the .NET Framework, for the application 1532. The runtime environment is a consistent execution environment that allows the application 1532 to run on any operating system that includes the runtime environment. Similarly, the operating system 1530 may support containers, and the application 1532 may be in the form of a container, which is a lightweight, standalone, executable package of software that includes, for example, code, runtime, system tools, system libraries, and settings for the application.

[0117] Additionally, computer 1502 can be enabled with a security module such as a Trusted Processing Module (TPM). For example, with a TPM, a boot component temporally hashes the next boot component and waits for the result to match a secure value before loading the next boot component. This process can occur at any layer in the code execution stack of computer 1502, for example, at the application execution level or the operating system (OS) kernel level, thereby enabling security at all levels of code execution.

[0118] A user can enter commands and information into the computer 1502 through one or more wired or wireless input devices, such as a keyboard 1538, a touch screen 1540, and a pointing device such as a mouse 1542. Other input devices (not shown) can include a microphone, an infrared (IR) remote control, a radio frequency (RF) remote control, or other remote controls, a joystick, a virtual reality controller and / or headset, a game pad, a stylus pen, an image input device such as a camera, a gesture sensor input device, a visual motion sensor input device, an emotion or face detection device, and a biometric input device such as a fingerprint or iris scanner. These and other input devices are often connected to the processing unit 1504 through an input device interface 1544, which can be coupled to the system bus 1508 but not by other interfaces, such as a parallel port, an IEEE 1394 serial port, a game port, a USB port, an IR interface, or a BLUETOOTH® interface.

[0119] A monitor 1546 or other type of display device can also be connected to the system bus 1508 via an interface, such as a video adapter 1548. In addition to the monitor 1546, computers typically include other peripheral output devices (not shown), such as speakers, printers, etc.

[0120] The computer 1502 can operate in a networked environment using logical connections via wired and / or wireless communications to one or more remote computers, such as a remote computer 1550. The remote computer 1550 may be a workstation, a server computer, a router, a personal computer, a portable computer, a microprocessor-based entertainment device, a peer device or other common network node, and typically includes many or all of the elements described relative to the computer 1502, although for simplicity, only a memory / storage device 1552 is illustrated. The logical connections depicted include wired and / or wireless connections to a local area network (LAN) 1554 or a wide area network (WAN) 1556. Such LAN and WAN networking environments are commonplace in offices and companies, facilitating enterprise-wide computer networks, such as intranets, all of which may connect to global communications networks, such as the Internet.

[0121] When used in a LAN networking environment, the computer 1502 can be connected to the local network 1554 through a wired and / or wireless communication network interface or adapter 1558. The adapter 1558 facilitates wired or wireless communication to the LAN 1554, which can also include a wireless access point (AP) disposed thereon for communicating with the adapter 1558 in a wireless mode.

[0122] When used in a WAN networking environment, the computer 1502 may include a modem 1560 or may be connected to a communications server on the WAN 1556 via other means for establishing communications over the WAN 1556, such as using the Internet. The modem 1560, which may be an internal or external device and may be a wired or wireless device, may be connected to the system bus 1508 via the input device interface 1544. In a networked environment, program modules depicted relative to the computer 1502, or portions thereof, may be stored in the remote memory / storage device 1552. It will be appreciated that the network connections shown are exemplary and other means of establishing a communications link between the computers may be used.

[0123] When used in either a LAN or WAN networking environment, the computer 1502 can access a cloud storage system or other network-based storage system, such as, but not limited to, a network virtual machine, that implements one or more aspects of information storage or processing, in addition to or instead of the external storage device 1516 described above. Typically, the connection between the computer 1502 and the cloud storage system can be established over the LAN 1554 or WAN 1556, for example, by an adapter 1558 or a modem 1560, respectively. Once the computer 1502 is connected to an associated cloud storage system, the external storage interface 1526, aided by the adapter 1558 or the modem 1560, or both, can manage the storage provided by the cloud storage system like any other type of external storage. For example, the external storage interface 1526 can be configured to provide access to cloud storage sources as if those sources were physically connected to the computer 1502.

[0124] The computer 1502 is operable to communicate with any wireless device or entity operatively disposed within a wireless network, such as, for example, a printer, a scanner, a desktop or portable computer, or both, a portable data assistant, a communications satellite, fixtures or locations associated with radio-detectable tags (e.g., kiosks, newsstands, store shelves, etc.), and telephones. This includes Wireless Fidelity (Wi-Fi) and BLUETOOTH® wireless technologies. As such, communication can be of a predetermined structure, similar to a traditional network, or can simply be ad-hoc communication between at least two devices.

[0125] Referring now to FIG. 16, an exemplary cloud computing environment 1600 is depicted. As shown, the cloud computing environment 1600 includes one or more cloud computing nodes 1602 that can communicate with local computing devices used by cloud consumers, such as, for example, a personal digital assistant (PDA) or mobile phone 1604, a desktop computer 1606, a laptop computer 1608, and / or an automotive computer system 1610. The nodes 1602 can communicate with each other. They can be physically or virtually grouped in one or more networks (not shown), such as a private, community, public, or hybrid cloud, or combinations thereof, as described herein above. This enables the cloud computing environment 1600 to provide infrastructure, platform, and / or software as a service, eliminating the need for cloud consumers to maintain resources on their local computing devices. It will be understood that the types of computing devices 1604-1610 shown in FIG. 16 are intended to be exemplary only, and that computing node 1602 and cloud computing environment 1600 can communicate with any type of computerized device over any type of network and / or network-addressable connection (e.g., using a web browser).

[0126] Referring now to Figure 17, a set of functional abstraction layers provided by cloud computing environment 1600 (Figure 16) is shown. Repeated descriptions of similar elements employed in other embodiments described herein are omitted for brevity. It should be understood in advance that the components, layers, and functions shown in Figure 17 are intended to be merely exemplary, and embodiments of the present invention are not limited thereto. As depicted, the following layers and corresponding functions are provided:

[0127] Hardware and software layer 1702 includes hardware and software components. Examples of hardware components include mainframe 1704, RISC (reduced instruction set computer) architecture-based server 1706, server 1708, blade server 1710, storage device 1712, and network and networking components 1714. In some embodiments, software components include network application server software 1716 and database software 1718.

[0128] The virtualization layer 1720 provides an abstraction layer over which the following examples of virtual entities may be provided: virtual servers 1722, virtual storage 1724, virtual networks including virtual private networks 1726, virtual applications and operating systems 1728, and virtual clients 1730.

[0129] In one example, management layer 1732 can provide the functions described below. Resource provisioning 1734 provides dynamic procurement of computing resources and other resources utilized to perform tasks within the cloud computing environment. Metering and billing 1736 provides cost tracking as resources are utilized within the cloud computing environment and billing or invoicing for the consumption of these resources. In one example, these resources may include application software licenses. Security provides identity verification for cloud consumers and tasks, as well as protection for data and other resources. User portal 1738 provides consumers and system administrators with access to the cloud computing environment. Service level management 1740 provides allocation and management of cloud computing resources to ensure required service levels are met. Service level agreement (SLA) planning and fulfillment 1742 provides advance agreement on and procurement of cloud computing resources in anticipation of future demand according to SLAs.

[0130] Workload layer 1744 provides examples of functionality for which a cloud computing environment may be utilized. Examples of workloads and functions that may be provided from this layer include mapping and navigation 1746, software development and lifecycle management 1748, virtual classroom instruction delivery 1750, data analytics processing 1752, transaction processing 1754, and differentially private federated learning processing 1756. Various embodiments of the present invention may utilize the cloud computing environment described with reference to Figures 16 and 17 to perform one or more differentially private federated learning processing in accordance with various embodiments described herein.

[0131] The present invention may be a system, method, apparatus, or computer program product, or combinations thereof, at any possible level of technical detail of integration. The computer program product may include a computer-readable storage medium having computer-readable program instructions for causing a processor to perform aspects of the present invention. The computer-readable storage medium may be a tangible device capable of holding and storing instructions for use by an instruction-execution device. The computer-readable storage medium may be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of computer-readable storage media further includes: portable computer diskettes, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disk read-only memory (CD-ROM), digital versatile disks (DVD), memory sticks, floppy disks, mechanically encoded devices such as punch cards or grooved structures having instructions recorded thereon, and any suitable combination of the foregoing. As used herein, computer-readable storage media should not be construed as being ephemeral signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission medium (e.g., light pulses passing through fiber optic cable), or electrical signals transmitted over electrical wires.

[0132] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to an individual computing / processing device or to an external computer or external storage device over a network, such as the Internet, a local area network, a wide area network, or a wireless network, or a combination thereof. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, or edge servers, or a combination thereof. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in a computer-readable storage medium within the individual computing / processing device. The computer readable program instructions for carrying out the operations of the present invention may be either source code or object code written in any combination of one or more programming languages, including assembler instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state configuration data, configuration data for integrated circuits, or object-oriented programming languages ​​such as Smalltalk®, C++, and procedural or similar programming languages. The computer readable program instructions may be executed entirely on the user's computer, partially on the user's computer as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server.In the latter scenario, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be to an external computer (e.g., via the Internet using an Internet Service Provider). In some embodiments, electronic circuitry, including, for example, programmable logic circuits, field programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), can execute computer-readable program instructions to individualize the electronic circuitry by utilizing state information of the computer-readable program instructions to perform aspects of the present invention.

[0133] Aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions. These computer-readable program instructions may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, executed by a processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in one or more blocks of the flowchart illustrations and / or block diagrams. These computer-readable program instructions may also be stored on a computer-readable storage medium having the instructions stored thereon, directing a computer, programmable data processing apparatus, or other device, or combination thereof, to function in a particular manner, such that the computer-readable storage medium comprises an article of manufacture including instructions for implementing aspects of the functions / acts specified in one or more blocks of the flowchart illustrations and / or block diagrams. The computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to create a computer-implemented process, causing the computer, other programmable apparatus, or other device to perform a series of operable functions, such that the instructions, which execute on the computer, other programmable apparatus, or other device, implement the functions / acts specified in one or more blocks of the flowcharts and / or block diagrams.

[0134] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of instructions, including one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions shown in the blocks may occur out of the order shown in the figures. For example, two blocks shown in succession may in fact be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending on the functionality involved. It should also be noted that each block in the block diagrams and / or flowchart diagrams, and combinations of blocks in the block diagrams and / or flowchart diagrams, may be implemented by special-purpose hardware-based systems that perform the specified functions or actions or execute a combination of special-purpose hardware and computer instructions.

[0135] While the subject matter has been described above in the general context of computer-executable instructions for a computer program product executing on one or more computers, those skilled in the art will appreciate that the present disclosure can also be implemented in combination with other program modules. Generally, program modules include routines, programs, components, data structures, etc. that perform particular tasks and / or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the computer-implemented methods of the present invention can be practiced with other computer system configurations, including single-processor or multiprocessor computer systems, minicomputing devices, mainframe computers, as well as computers, handheld computing devices (e.g., PDAs, telephones), microprocessor-based or programmable home or business electronic devices, etc. The illustrated aspects can also be practiced in distributed computing environments where tasks are performed by remote processing devices linked through a communications network. However, some, if not all, aspects of the present disclosure can be practiced on stand-alone computers. In a distributed computing environment, program modules can be located in both local and remote memory storage devices.

[0136] As used in this application, the terms “component,” “system,” “platform,” “interface,” etc. may refer to and / or include computer-related entities or entities related to machines operable with one or more specialized functionalities. The entities disclosed herein can be hardware, a combination of hardware and software, software, or software in execution. For example, a component can be, but is not limited to, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, or a computer, or any combination thereof. By way of illustration, both an application running on a server and the server can be a component. One or more components can reside within a process and / or thread of execution, and a component can be localized on one computer or distributed between two or more computers or both. In another example, individual components can execute from various computer-readable media having various data structures stored thereon. Components may communicate through local and / or remote processes, such as through signals carrying one or more data packets (e.g., data from one component may interact with another component within a local system, within a distributed system, or across networks, or a combination thereof, such as the Internet, which interacts with other systems via signals). As another example, a component may be a device having specialized functionality imparted by mechanical parts operated by electrical or electronic circuits, operated by a software or firmware application executed by a processor. In such cases, the processor may be internal or external to the device and may execute at least a portion of the software or firmware application.As yet another example, a component can be a device that provides specialized functionality through electronic components without mechanical parts, in which case the electronic components can include a processor or other means for executing software or firmware that provides at least some of the functionality of the electronic components. In one aspect, a component can emulate an electronic component via a virtual machine, for example, within a cloud computing system.

[0137] Additionally, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or." That is, unless otherwise specified or clear from the context, "X utilizes A or B" is intended to mean any of the natural inclusive permutations. That is, if X utilizes A, X utilizes B, or X utilizes both A and B, then "X utilizes A or B" is satisfied under any of the foregoing cases. Moreover, as used within the specification of the present subject matter and the accompanying drawings, the articles "a" and "an" should be construed generally to mean "one or more" unless otherwise specified to cover the singular or clear from the context. As used herein, the terms "example," "illustrative," and / or "exemplary" are used to mean serving as an example, instance, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited by such examples. Additionally, any aspect or design described herein as "example" and / or "exemplary" is not necessarily to be construed as preferred or advantageous over other aspects or designs, and is not intended to exclude equivalent exemplary structures and techniques known to those skilled in the art.

[0138] As employed in the subject specification, the term "processor" can refer to substantially any computing processing unit or device, including, but not limited to, a single-core processor, a single processor with software multithreaded execution capabilities, a multi-core processor, a multi-core processor with software multithreaded execution capabilities, a multi-core processor with hardware multithreading technology, a parallel platform, and a parallel platform with distributed shared memory. Additionally, a processor can refer to an integrated circuit, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field-programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. Furthermore, a processor can utilize nanoscale architectures, such as, but not limited to, molecular and quantum dot-based transistors, switches, and gates, to optimize space usage or improve the performance of user equipment. A processor can also be implemented as a combination of computing processing units. In this disclosure, terms such as "store," "storage," "data store," "database," and substantially any other information storage component associated with the operation and functionality of a component are utilized to refer to a "memory component" entity embodied in a "memory" or a component that includes a memory. It should be appreciated that the memory and / or memory components described herein can be either volatile memory or non-volatile memory, or can include both volatile and non-volatile memory.By way of example, and not limitation, non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory may include, for example, RAM that can act as external cache memory. By way of example, and not limitation, RAM is available in many forms, such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), SyncLink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). Additionally, the disclosed memory components of the systems or computer-implemented methods herein are intended to include these and any other suitable types of memory, but are not intended to be limited to including such.

[0139] What has been described above includes merely exemplary systems and computer-implemented methods. Of course, for purposes of describing this disclosure, it is not possible to describe every conceivable combination of components or computer-implemented methods, but one of ordinary skill in the art will recognize that many further combinations and permutations of the present disclosure are possible. Furthermore, to the extent that the terms "includes," "has," "possesses," and the like are used in the detailed description, claims, appendices, and drawings, such terms are intended to be inclusive in a manner similar to how the term "comprising" is interpreted when employed as a transitional phrase in a claim.

[0140] While the description of various embodiments has been presented for purposes of illustration, it is not intended to be exhaustive or to be limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein has been chosen to best explain the principles of the embodiments, practical applications, or technical improvements over technologies found in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. 1. A system comprising: A processor executing computer-executable components stored in a computer-readable memory, the computer-executable components comprising: a receiver component that accesses the classical dataset; a transformation component that transforms the classical data set into quantum state information; a quantum component that performs a quantum circuit including a quantum Fourier transform on the quantum state information, thereby providing a quantum transformation of the classical data set; a feature component that generates one or more machine learning input features based on the quantum transformation of the classical dataset; and an execution component that integrates the one or more machine learning input features into a classical machine learning model to generate a predicted output; A system comprising the processor.

2. The system described in claim 1, wherein the execution component inputs both the classical dataset and the one or more machine learning input features to the classical machine learning model.

3. A system as described in claim 1 or 2, wherein the number of elements of the classical dataset is n, and the number of elements of the one or more machine learning input features is n.

4. The system of claim 1 , wherein the quantum state information is a set of quantum probability amplitudes.

5. the computer-executable components: a visualization component that visually renders both the classical dataset and the one or more machine learning input features. The system of claim 1 , further comprising:

6. The system of claim 1 , wherein the classical data set comprises time series data.

7. 7. The system of claim 1, wherein the quantum circuit is implemented on a quantum computing device that includes physical qubits.

8. The system of claim 7 , wherein the quantum component is electronically integrated with the quantum computing device.

9. A system with the features of claim 4, as claimed in any one of claims 1 to 8, wherein the set of quantum probability amplitudes collectively represents a quantum state vector.

10. 10. The system of claim 7, wherein the quantum component is configured to execute any suitable initialization circuit on the quantum computing device to cause the states of the qubits of the quantum computing device to conform to the quantum state vector.

11. 1. A computer-implemented method comprising: accessing the classical data set by a device operatively coupled to the processor; converting the classical data set into quantum state information by the device; performing, by said device, a quantum circuit including a quantum Fourier transform on said quantum state information, thereby providing a quantum transformation of said classical data set; generating, by the device, one or more machine learning input features based on the quantum transformation of the classical dataset; Integrating, by the device, the one or more machine learning input features into a classical machine learning model to generate a predicted output.

11. A computer-implemented method comprising:

12. The step of generating the predicted output comprises: inputting, by the device, both the classical dataset and the one or more machine learning input features to the classical machine learning model. The computer-implemented method of claim 11 , comprising:

13. A computer-implemented method as described in claim 11 or 12, wherein the number of elements of the classical dataset is n, and the number of elements of the one or more machine learning input features is n.

14. 14. The computer-implemented method of claim 11, wherein the quantum state information is a set of quantum probability amplitudes.

15. visually rendering, by the device, both the classical dataset and the one or more machine learning input features.

15. The computer-implemented method of claim 11, further comprising:

16. 16. The computer-implemented method of claim 11, wherein the classical data set comprises time series data.

17. 17. The computer-implemented method of claim 11, wherein the quantum circuit is executed on a quantum computing device that includes physical qubits.

18. 1. A computer program for facilitating quantum enhanced features for classical machine learning, the computer program comprising: Accessing classical datasets; converting the classical data set into quantum state information; performing a quantum circuit including a quantum Fourier transform on the quantum state information, thereby providing a quantum transformation of the classical data set; generating one or more machine learning input features based on the quantum transformation of the classical dataset; Integrating the one or more machine learning input features into a classical machine learning model to generate a predicted output; A computer program that causes the

19. generating the predicted output comprises:

20. The computer program product of claim 18, further comprising inputting, by the processor, both the classical dataset and the one or more machine learning input features to the classical machine learning model.

20. A computer program as described in claim 18 or 19, wherein the number of elements of the classical dataset is n, and the number of elements of the one or more machine learning input features is n.

21. 21. The computer program product of claim 18, wherein the quantum state information is a set of quantum probability amplitudes.

22. causing the processor to visually render both the classical dataset and the one or more machine learning input features.

22. A computer program product according to any one of claims 18 to 21, which causes the computer program product to perform the following:

23. 1. A system comprising: A processor executing computer-executable components stored in a computer-readable memory, the computer-executable components comprising: a receiver component that receives a classical time series dataset from an operator device; a transformation component that generates quantum state information based on the classical time series dataset; a quantum component that performs a quantum algorithm, including a quantum Fourier transform, on the quantum state information, thereby providing a quantum transformation of the classical time series data set; a feature component that generates one or more quantum-enhanced machine learning input features based on the quantum transformation of the classical time series dataset; and an execution component that integrates the one or more machine learning input features into a classical machine learning model to predict or detect a temporal phenomenon; A system comprising the processor.

24. The system described in claim 23, wherein the execution component inputs both the classical dataset and the one or more machine learning input features to the classical machine learning model.

25. The system described in claim 23 or 24, wherein the number of time steps of the classical time series dataset is n, and the number of elements of the one or more machine learning input features is n.

26. 26. The system of any of claims 23 to 25, wherein the quantum state information is a quantum probability amplitude.

27. the computer-executable components: a visualization component that graphs the classical time series dataset or the one or more quantum enhanced machine learning input features.

27. The system of any of claims 23 to 26, further comprising:

28. 1. A computer-implemented method comprising: receiving, by a device operatively coupled to the processor, a classical time series data set from an operator device; generating, by the device, quantum state information based on the classical time series data set; performing, by the device, a quantum algorithm including a quantum Fourier transform on the quantum state information, thereby providing a quantum transformation of the classical time series data set; generating, by the device, one or more quantum-enhanced machine learning input features based on the quantum transformation of the classical time series dataset; Integrating the one or more machine learning input features into a classical machine learning model by the device to predict or detect a temporal phenomenon.

11. A computer-implemented method comprising:

29. Integrating into the classical machine learning model comprises: inputting, by the device, both the classical dataset and the one or more machine learning input features to the classical machine learning model.

30. The computer-implemented method of claim 28, comprising:

30. A computer-implemented method as described in claim 28 or 29, wherein the number of time steps of the classical time series dataset is n, and the number of elements of the one or more machine learning input features is n.

31. 31. The computer-implemented method of any of claims 28 to 30, wherein the quantum state information is a quantum probability amplitude.

32. graphing, by the device, the classical time series dataset or the one or more quantum enhanced machine learning input features.

32. The computer-implemented method of any of claims 28 to 31, further comprising:

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