QUANTUM-ENHANCED FEATURES FOR CLASSICAL MACHINE LEARNING

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

BACKGROUND

The subject disclosure relates to machine learning, and more specifically to quantum-enhanced features for classical machine learning.

Quantum computing has shown promise in addressing classically-intractable computation problems. Currently, state-of-the-art quantum computing devices are considered as Noisy Intermediate-Scale Quantum (NISQ) devices. Such a quantum computing device implements a small number of error-prone qubits, less than the hundreds or thousands thought to be needed to implement error correction of a single logical qubit given current error rates of physical qubits. Unfortunately, full realization of fault tolerant, error corrected quantum computers will require devices that implement thousands or even millions of physical qubits. Thus, state-of-the-art quantum computing devices cannot yet support enough qubits to solve many classically-intractable computation problems of interest. Indeed, because quantum computing is in its nascency, well-established classical computing techniques are still widely-used in various technical fields. Thus far, quantum computing research focuses heavily on physically building quantum computing devices that can implement larger numbers of qubits. In contrast, limited quantum computing research focuses on how existing quantum computing devices can be leveraged to improve the performance of classical computing techniques. Thus, the present inventors have observed that systems and/or techniques that can address this technical problem can be desirable.

SUMMARY

According to one or more embodiments, a system is provided. The system can comprise a memory that can store computer-executable components. The system can further comprise a processor that can be operably coupled to the memory and that can execute the computer-executable components stored in the memory. In various embodiments, the computer-executable components can comprise a receiver component that can access a classical dataset. In various aspects, the computer-executable components can further comprise a feature component that can generate one or more machine learning input features based on a quantum transformation of the classical data set. In various embodiments, the computer-executable components can further comprise a conversion component that can convert the classical dataset into a set of quantum probability amplitudes. In various instances, the computer-executable components can further comprise a quantum component that can execute a quantum circuit on the set of quantum probability amplitudes, thereby yielding the quantum transformation of the classical dataset. In various cases, the computer-executable components can further comprise an execution component that can execute a classical machine learning model on the one or more machine learning input features.

According to one or more embodiments, the above-described system can be implemented as a computer-implemented method and/or computer program product.

According to one or more embodiments, a system is provided. The system can comprise a memory that can store computer-executable components. The system can further comprise a processor that can be operably coupled to the memory and that can execute the computer-executable components stored in the memory. In various embodiments, the computer-executable components can comprise a receiver component that can receive a classical timeseries dataset from an operator device. In various aspects, the computer-executable components can further comprise a feature component that can generate one or more quantum-enhanced machine learning input features based on a quantum transformation of the classical timeseries dataset. In various embodiments, the computer-executable components can further comprise a conversion component that can generate quantum probability amplitudes based on the classical timeseries dataset. In various instances, the computer-executable components can further comprise a quantum component that can execute a quantum algorithm on the quantum probability amplitudes, thereby yielding the quantum transformation of the classical timeseries dataset. In various cases, the computer-executable components can further comprise an execution component that can transmit to the operator device the one or more quantum-enhanced machine learning input features.

According to one or more embodiments, the above-described system can be implemented as a computer-implemented method and/or computer program product.

DETAILED DESCRIPTION

As mentioned above, quantum computing has shown promise in addressing classically-intractable computation problems in various technical fields, such as computational chemistry, optimization, and machine learning. Currently, state-of-the-art quantum computing devices are called Noisy Intermediate-Scale Quantum (NISQ) devices. A NISQ device can physically implement less than the number of qubits required for error correction given the error rate of physical qubits. Unfortunately, full realization of error corrected quantum computers will require devices that implement thousands of, millions of, or even more qubits, which is many orders of magnitude above the numbers of qubits which can be supported by near-term systems. Thus, state-of-the-art quantum computing devices cannot yet physically support enough qubits to solve many classically-intractable computation problems of interest. Because quantum computing is still in its nascency (e.g., because the number of qubits that can be supported by NISQ devices is rather limited), well-established classical computing techniques remain widely-used in various technical fields.

One technical field in particular in which classical computational techniques are still heavily relied upon is machine learning (e.g., artificial intelligence). Various industries involve the logging of data, and such 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 case, a set of classical data can be recorded and/or generated in any suitable fashion, the set of classical data can be fed as input to a machine learning (“ML”) model, and the ML model can generate as output a label, classification, and/or prediction based on the set of classical data. For example, the set of classical data can be timeseries data (e.g., product/service sales recorded over time, resource consumption recorded over time, any other measured quantity of interest recorded over time), and it can be desired to forecast future data points based on the timeseries data. In such case, the timeseries data can be fed as input to a suitably-configured ML model, and the ML model can produce as output one or more forecasted data points based on the timeseries data (e.g., can predict how the timeseries data will continue and/or change at future time steps).

Thus far, much research has been conducted on constructing quantum computing devices that can physically support larger numbers of qubits. In contrast, limited research has been conducted on how the performance and/or capabilities of classical computing techniques in general, and classical ML techniques in particular, can be improved by existing quantum computing devices. Thus, systems and/or techniques that can address this technical problem can be desirable.

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

As mentioned above, a classical ML model can be configured to receive as input a set of classical data, and to produce as output a determination 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 determination 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 determination is a label that classifies and/or segments the audio recording. As yet another example, if the set of classical data is a timeseries, the classical ML model can be configured such that the determination is one or more forecasted data points that likely follow in the timeseries. Accordingly, at a high level, the classical ML model can be considered as detecting patterns, trends, and/or distributions that are exhibited by the set of classical data, where the determination generated by the classical ML model depends upon the detected patterns, trends, and/or distributions.

The inventors of various embodiments of the invention recognized that, in various cases, importing the set of classical data into a quantum Hilbert space (e.g., a complex-valued mathematical space that is native to quantum computing) and/or performing various quantum transformations on the set of classical data in the quantum Hilbert space can reveal additional patterns, trends, and/or distributions in the set of classical data, which additional patterns, trends, and/or distributions were previously hidden from and/or otherwise undetectable by the classical ML model. In other words, the inventors of various embodiments of the invention recognized that the set of classical data can be enriched/enhanced by converting the set of classical data into quantum state information and/or by transforming such quantum state information with quantum circuits/algorithms. So, if the classical ML model is configured to receive only the set of classical data, the classical ML model can have no access to the additional patterns, trends, and/or distributions that are hidden within the set of classical data. On the other hand, if the classical ML model is configured to receive both the set of classical data and a quantum transformation of the set of classical data, the classical ML model can have access to the additional patterns, trends, and/or distributions hidden within the set of classical data, which can help to improve the accuracy/precision of the determination generated by the classical ML model.

Accordingly, a computerized tool as described herein can, in various aspects, generate quantum-enhanced input features for classical ML models based on classical data. Specifically, in various embodiments, such a computerized tool can comprise a receiver component, a conversion component, a quantum component, a feature component, and an execution component.

In various embodiments, the receiver component can electronically receive and/or otherwise electronically access a classical dataset, which is desired to be analyzed by a 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., graph data structure, relational data structure, hybrid data structure), whether remote from and/or local to the receiver component. As those having ordinary skill in the art will appreciate, the classical dataset can be formatted in any suitable fashion (e.g., formatted as classical bits, formatted as classical integers, formatted as classical floating-point numbers).

In various embodiments, the conversion component can electronically import the classical dataset into a quantum Hilbert space. More specifically, the conversion component can electronically convert, via any suitable amplitude embedding and/or amplitude encoding technique, the classical dataset to a set of quantum probability amplitudes, where the set of quantum probability amplitudes collectively represent a quantum state vector, and where such quantum state vector can be operated on and/or otherwise manipulated by quantum circuits.

For example, suppose that the classical dataset contains x data points, for any suitable positive integer x. In such case, amplitude embedding/encoding can be applied, such that each of the x data points is converted to a corresponding quantum probability amplitude, thereby yielding x quantum probability amplitudes.

As those having ordinary skill in the art will appreciate, a quantum probability amplitude can be a complex number (e.g., having a real part and/or an imaginary part) associated with a quantum state, where the square of the quantum probability amplitude represents a probability of occurrence of the associated quantum state. Accordingly, quantum probability amplitudes can be normalized, such that the sum of the squares of the quantum probability amplitudes equals 1 (e.g., each quantum probability amplitude corresponds to a quantum state, each squared quantum probability amplitude represents the probability of its corresponding quantum state occurring, and so summing such probabilities over all possible states of a system equates to unity).

In particular, the conversion component can convert the classical dataset to quantum probability amplitudes by considering the classical dataset as an x-element vector, by computing the norm (e.g., magnitude, length) of that x-element vector (e.g., square root of the sum of the squares of each of the x data points), and by dividing each of the x data points by the computed norm. In various aspects, the result can be that the x data points are normalized such that the sum of their squares now equates to unity, and so each of the normalized x data points can be considered as a quantum probability amplitude. In various aspects, the set of quantum probability amplitudes can be considered as a quantum-version and/or a quantum-format of the classical dataset.

In various instances, the quantum component can electronically apply and/or otherwise electronically facilitate the application of a quantum circuit to the 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) that are combined in series (e.g., via matrix multiplication) and/or in parallel (e.g., via tensor products and/or Kronecker products). A quantum circuit can be executed on a quantum computing device that comprises physical qubits. In various aspects, the quantum component can be electronically integrated with a quantum computing device and can thus execute any suitable quantum gates and/or quantum circuits that are compatible with the quantum computing device.

In various cases, the quantum component can initialize the quantum computing device with the quantum probability amplitudes generated by the conversion component. That is, the set of quantum probability amplitudes can collectively represent a quantum state vector, and the quantum component can execute any suitable initialization circuit on the quantum computing device so as to put the states of the qubits of the quantum computing device in accordance with the quantum state vector. Those having ordinary skill in the art will appreciate that the composition of such an initialization circuit can depend upon the particular values of the set of quantum probability amplitudes.

In various instances, once the qubits of the quantum computing device are initialized with the set of quantum probability amplitudes, the quantum component can execute a quantum circuit on the quantum computing device, thereby transforming the set of quantum probability amplitudes into a set of resultant quantum probability amplitudes. In various cases, the set of resultant quantum probability amplitudes can represent a resultant quantum state vector of the qubits of the quantum computing device. In various aspects, the set of resultant quantum probability amplitudes (e.g., the resultant quantum state vector) can be considered as a quantum-transformed version and/or a quantum-transformed format of the classical dataset.

Consider again the above example where the classical dataset contains x data points, and where the conversion component generates x quantum probability amplitudes based on the x data points. As those having ordinary skill in the art will appreciate, the set of x quantum probability amplitudes can be considered as an x-element quantum state vector that describes a superposition of quantum states of log2x qubits. Thus, the quantum computing device employed by the quantum component can comprise log2x qubits. If log2x is not an integer, it can be rounded up to the next larger integer.

In various cases, the log2x qubits can begin by having a known quantum state vector. For instance, the log2x qubits can begin by all being in the 10) state. Given the known beginning quantum state vector, the quantum component can execute an initialization circuit on the quantum computing device such that the states of the log2x qubits are transformed from the known beginning quantum state vector to the quantum state vector represented by the x quantum probability amplitudes. As those having ordinary skill in the art will appreciate, the composition 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 beginning quantum state vector and based on the quantum state vector represented by the set of x quantum probability amplitudes. In other words, when given a starting quantum state vector and a desired quantum state vector, those having ordinary skill in the art will understand how to combine which quantum gates so as to transform the starting quantum state vector to the desired quantum state vector.

Once the log2x qubits of the quantum computing device are initialized with the quantum state vector represented by the x quantum probability amplitudes generated by the conversion component, the quantum component can execute any suitable quantum circuit on the quantum computing device. In some cases, the quantum circuit can be the Quantum Fourier Transform. In any case, the quantum circuit can transform and/or rotate the quantum state vector represented by the x quantum probability amplitudes to some resultant quantum state vector represented by x resultant quantum probability amplitudes.

In various embodiments, the feature component can electronically generate quantum-enhanced ML input features based on the set of resultant quantum probability amplitudes generated by the quantum component. Specifically, the set of resultant quantum probability amplitudes can be considered as a set of complex numbers, and the feature component can electronically apply any suitable mathematical functions to the set of complex numbers. In various cases, the result of application of such mathematical functions can be considered as the quantum-enhanced ML input features. For instance, the feature component can, in some cases, multiplicatively scale (e.g., scale up and/or down) the set of resultant quantum probability amplitudes, such that the scaled amplitudes can be considered as the quantum-enhanced ML input features. In other cases, the feature component can additively offset (e.g., bias up and/or down) the set of resultant quantum probability amplitudes, such that the offset amplitudes can be considered as the quantum-enhanced ML input features. In still other cases, since the resultant quantum probability amplitudes can be complex numbers, the feature component can compute magnitudes of the resultant quantum probability amplitudes, such that the magnitudes can be considered as the quantum-enhanced ML input features. In various embodiments, the feature component can refrain from mathematically changing the resultant quantum probability amplitudes at all, such that the set of resultant quantum probability amplitudes can themselves be considered as the quantum-enhanced ML input features.

To continue the above example, the feature component can extract (e.g., with and/or without mathematical manipulation) the x resultant quantum probability amplitudes generated by the quantum component, thereby yielding x quantum-enhanced ML input features. For instance, in some cases, the x quantum-enhanced ML input features can be equal to the x resultant quantum probability amplitudes. In other cases, the x quantum-enhanced ML input features can be any suitable function of the x resultant quantum probability amplitudes.

In various embodiments, the execution component can electronically execute and/or can otherwise electronically facilitate the execution of the classical ML model on the classical dataset and/or on 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 feed the classical dataset and/or the quantum-enhanced ML input features to the classical ML model. As explained above, the quantum-enhanced ML input features can be created by importing the classical dataset into a quantum Hilbert space (e.g., specifically, by converting the classical dataset into quantum probability amplitudes) and/or by transforming the classical dataset in the quantum Hilbert space (e.g., specifically, by initializing a quantum computer with the quantum probability amplitudes and by then executing a quantum circuit on the quantum computer). Thus, the quantum-enhanced ML input features can exhibit patterns, trends, and/or distributions that characterize the classical dataset but that were previously hidden in the classical dataset. Accordingly, because the classical ML model can be configured to receive as input the quantum-enhanced ML input features, the classical ML model can base its outputted determination on such previously-hidden patterns, trends, and/or distributions. Therefore, the classical ML model can generate a more accurate determination than it could in the absence of the quantum-enhanced ML input features.

The computerized tool described herein can, in various aspects, electronically receive as input a classical dataset, and can electronically produce as output quantum-enhanced ML input features based on the classical dataset, where the quantum-enhanced ML input features can be considered as an enriched version of the classical dataset. As explained herein, the computerized tool can facilitate this functionality by electronically converting the classical dataset to quantum probability amplitudes (e.g., via amplitude embedding/encoding), by initializing a quantum computer with such quantum probability amplitudes, and/or by executing a quantum circuit (e.g., Quantum Fourier Transform) on the quantum computer so as to rotate and/or transform such quantum probability amplitudes. In some cases, the rotated/transformed quantum probability amplitudes can be considered as the 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 computation) so as to yield the quantum-enhanced ML input features. In various cases, the computerized tool can electronically execute a classical ML model on the quantum-enhanced ML input features, and/or can otherwise electronically store and/or transmit the quantum-enhanced ML input features.

Various embodiments of the invention can be employed to use hardware and/or software to solve problems that are highly technical in nature (e.g., to facilitate quantum-enhanced features for classical machine learning), that are not abstract and that cannot be performed as a set of mental acts by a human. Further, some of the processes performed can be performed by a specialized computer (e.g., amplitude embedder, quantum computer, classical machine learning model). In various aspects, some defined tasks associated with various embodiments of the invention can include: accessing, by a device operatively 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 executing, 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 invention can include: converting, by the device, the classical dataset into a set of quantum probability amplitudes; and executing, by the device, a quantum circuit on the set of quantum probability amplitudes, thereby yielding the quantum transformation of the classical dataset. Such defined tasks are not typically performed manually by humans. Moreover, neither the human mind nor a human with pen and paper can electronically access a classical dataset, electronically convert the classical dataset to quantum probability amplitudes, electronically execute a quantum circuit on the quantum probability amplitudes to generate quantum-enhanced input features, and/or electronically execute a classical ML model on the quantum-enhanced input features. Instead, various embodiments of the invention are inherently and inextricably tied to computer technology and cannot be implemented outside of a computing environment (e.g., quantum circuits and classical ML models are inherently computerized objects that cannot exist outside of computing systems; likewise, a computerized tool that leverages quantum circuits to create enriched input features for classical ML models is also an inherently computerized device that cannot be practicably implemented in any sensible way without computers).

In various instances, embodiments of the invention can integrate into a practical application the disclosed teachings regarding quantum-enhanced features for classical machine learning. Indeed, as described herein, various embodiments of the invention, which can take the form of systems and/or computer-implemented methods, can be considered as a computerized tool that facilitates the enrichment of a classical dataset by generating a quantum state representation of the classical dataset and/or by transforming the quantum state representation via quantum circuits. As explained above, much quantum research has been dedicated to the design and/or construction of quantum computing devices that can support more physical qubits than NISQ devices, but 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 invention recognized that applying quantum transformations to a classical dataset can yield an enhanced/enriched version of the classical dataset. Furthermore, the inventors of various embodiments of the invention experimentally verified that a classical ML model which is configured to receive as input both the classical dataset and the enhanced/enriched version of the classical dataset can achieve higher performance metrics (e.g., increased prediction accuracy), as compared to a classical ML model which is configured to receive as input only the classical dataset. As explained herein, this improvement in performance metrics can be due to the fact that the enhanced/enriched version of the classical dataset can exhibit data patterns, data trends, and/or data distributions which are hidden and/or undetectable in the classical dataset. Thus, a classical ML model that is configured to receive as input the enhanced/enriched version of the classical dataset can base its outputted determination on such previously-hidden data patterns, data trends, and/or data distributions. Systems and/or techniques that can improve the very performance of computing devices such as classical ML models clearly constitute a concrete and tangible technical improvement in the field of machine learning.

Furthermore, various embodiments of the invention can control tangible, hardware-based, and/or software-based devices based on the disclosed teachings. For example, embodiments of the invention can actually execute, on tangible quantum hardware, quantum circuits so as to enhance/enrich classical data, and/or can actually facilitate the execution of tangible ML hardware on the enhanced/enriched classical data.

It should be appreciated that the figures and the herein disclosure describe non-limiting examples of various embodiments of the invention.

FIG. 1illustrates a block diagram of an example, non-limiting system100that can facilitate quantum-enhanced features for classical machine learning in accordance with one or more embodiments described herein. As shown, a quantum-enhanced feature system102can be electronically integrated, via any suitable wired and/or wireless electronic connections, with classical data104, with a classical machine learning model106(“classical ML model106”), and/or with a quantum computer122.

In various aspects, the classical data104can include any suitable classical data values (e.g., classical bits, classical integers, classical floating point numbers). In some cases, the classical data104can be timeseries data. That is, the data values of the classical data104can be collated by time (e.g., the classical data104can include one or more first data values that are associated with a first time step, the classical data104can include one or more second data values that are associated with a second time step). In various instances, the classical data104can 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 data104can represent measured values of any suitable quantity of interest, either recorded over time or recorded at any given instant in time (e.g., number of transactions recorded over time, data characterizing transactions that occurred during a snapshot in time, amount of resources consumed over time, data characterizing resources that were consumed during a snapshot in time). Although some herein examples describe various embodiments of the invention with respect to timeseries data, those having ordinary skill in the art will appreciate that this is a mere non-limiting example. In various aspects, any suitable set of classical data can be implemented in various embodiments of the invention, whether or not the set of classical data is organized as a timeseries (e.g., even if the set of classical data is collated by position, location, and/or some other index/identifier that is not time).

In various instances, the classical ML model106can implement any suitable type of classical machine learning algorithm, technique, and/or architecture. For instance, the classical ML model106can be and/or can comprise 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 cases, the classical ML model106can be configured to receive any suitable type and/or dimensionality of input data and to generate any suitable type and/or dimensionality of output data based on the input data. In various aspects, the output data can be a determination, inference, classification, segmentation, and/or prediction that is based on the input data.

In various cases, the quantum computer122can be any suitable type of quantum computing device and/or quantum simulator. That is, the quantum computer122can exhibit any suitable quantum computing architecture.

In various instances, it can be desired to generate an enriched/enhanced version of the classical data104, and it can be desired to execute the classical ML model106on the classical data104and/or on the enriched/enhanced version of the classical data104. In various embodiments, this can be facilitated by the quantum-enhanced feature system102, as described below. More specifically, the quantum-enhanced feature system102can leverage the quantum computer122so as to create the enriched/enhanced version of the classical data104.

In various embodiments, the quantum-enhanced feature system102can comprise a processor108(e.g., computer processing unit, microprocessor) and a computer-readable memory110that is operably connected to the processor108. The memory110can store computer-executable instructions which, upon execution by the processor108, can cause the processor108and/or other components of the quantum-enhanced feature system102(e.g., receiver component112, conversion component114, quantum component116, feature component118, execution component120) to perform one or more acts. In various embodiments, the memory110can store computer-executable components (e.g., receiver component112, conversion component114, quantum component116, feature component118, execution component120), and the processor108can execute the computer-executable components.

In various embodiments, the quantum-enhanced feature system102can comprise a receiver component112. In various aspects, the receiver component112can electronically retrieve and/or otherwise electronically access the classical data104from any suitable centralized and/or decentralized data structure (not shown), whether remote from and/or local to the receiver component112. Accordingly, in various aspects, other components of the quantum-enhanced feature system102can manipulate and/or otherwise interact with (e.g., read, write, copy, edit) the classical data104.

In various embodiments, the quantum-enhanced feature system102can comprise a conversion component114. In various aspects, the conversion component114can electronically convert the classical data104(e.g., can convert an electronic copy of the classical data104) into a quantum format. In other words, the classical data104can be in a classical format as is, meaning that the classical data104can be unamenable to processing by a quantum computing device. Thus, the conversion component114can electronically generate a version of the classical data104that can be processed by a quantum computing device.

Specifically, in various aspects, the conversion component114can generate, via any suitable amplitude embedding and/or amplitude encoding technique, a set of probability amplitudes based on the classical data104. In various cases, the set of probability amplitudes can collectively be considered as a quantum state vector that represents the classical data104. In other words, the set of probability amplitudes can be considered as a format and/or version of the classical data104that can be processed by a quantum computing device. In various instances, the set of probability amplitudes can respectively correspond to the classical data104. That is, the conversion component114can generate one probability amplitude for each of the data elements in the classical data104(e.g., if the classical data104is a timeseries, the conversion component114can, in some cases, generate one probability amplitude for each of the time steps represented in the classical data104). In particular, the conversion component114can, in various aspects, treat the classical data104as a vector of data elements, can compute the magnitude of such vector, and can divide each data element by that computed magnitude, thereby resulting in a normalized vector of data elements. In various cases, the normalized vector of data elements can be considered as the set of probability amplitudes.

Although the herein figures and disclosure describe various embodiments of the invention in which the conversion component114implements amplitude embedding in order to encode the classical data104into a quantum-processible format, this is a mere non-limiting example. In various aspects, any other suitable quantum embedding technique can be implemented to convert the classical data104into a form that is amenable to quantum computation (e.g., the conversion component114can implement basis embedding).

In various embodiments, the quantum-enhanced feature system102can comprise a quantum component116. In various aspects, the quantum component116can electronically apply a quantum circuit to the set of probability amplitudes, thereby generating a set of resultant probability amplitudes. More specifically, in various embodiments, the quantum component116can be electronically integrated (e.g., via any suitable wired and/or wireless electronic connection) with the quantum computer122, which can be any suitable quantum computing device and/or simulator. In various cases, as shown, the quantum computer122can be remote from the quantum component116. However, in other cases, the quantum computer122can be local to the quantum component116. In various instances, the quantum computer122can comprise physical qubits and/or can otherwise simulate the behavior of qubits, such that the quantum computer122can perform quantum computations. In various cases, the quantum component116can initialize the quantum computer122with the set of probability amplitudes, and can then execute any suitable quantum circuit (e.g., Quantum Fourier Transform) on the quantum computer122, thereby transforming and/or rotating the set of probability amplitudes into the set of resultant probability amplitudes.

In other words, the set of probability amplitudes can be considered as a quantum state vector representing the classical data104. In various aspects, the quantum component116can initialize the quantum computer122with such quantum state vector. That is, the quantum component116can manipulate (e.g., via any suitable quantum gates) the qubits of the quantum computer122, such that the initial states of the qubits are in accordance with the probability amplitudes. In various instances, the quantum component116can then transform/rotate that quantum state vector (e.g., the probability amplitudes) by executing the quantum circuit on the quantum computer122. The result can be a resultant quantum state vector (e.g., resultant probability amplitudes).

In various cases, the conversion component114can be considered as importing the classical data104into a quantum Hilbert space (e.g., can convert the classical data104into a quantum-processible format), and the quantum component116can be considered as manipulating the classical data104in the quantum Hilbert space (e.g., can transform and/or rotate the quantum-processible format of the classical data104via execution of quantum gates).

In various embodiments, the quantum-enhanced feature system102can comprise a feature component118. In various aspects, the feature component118can electronically generate a set of enhanced ML input features based on the resultant probability amplitudes generated by the quantum component116. In various instances, the feature component118can apply any suitable mathematical functions to the resultant probability amplitudes, thereby yielding the enhanced ML input features. For example, in some cases, the feature component118can multiplicatively scale the resultant probability amplitudes upward (e.g., by a multiplicative factor greater than1) and/or downward (e.g., by a multiplicative factor less than1), and such scaled probability amplitudes can be considered as the enhanced ML input features. As another example, in some cases, the feature component118can additively offset the resultant probability amplitudes upward (e.g., by adding a bias value) and/or downward (e.g., by subtracting a bias value), and such offset probability amplitudes can be considered as the enhanced ML input features. As yet another example, the resultant probability amplitudes can be complex numbers, and so the feature component118can compute the norm of each resultant probability amplitude, such that the computed magnitudes can be considered as the enhanced ML input features. As still a further example, the feature component118can refrain from changing the resultant probability amplitudes, such that the resultant probability amplitudes can themselves be considered as the enhanced ML input features.

In various embodiments, the quantum-enhanced feature system102can comprise an execution component120. In various aspects, the execution component120can electronically execute and/or can otherwise electronically facilitate the execution of the classical ML model106on the enhanced ML input features generated by the feature component118. That is, the execution component120can electronically feed the enhanced ML input features to the classical ML model106, and/or can otherwise electronically instruct the classical ML model106to analyze the enhanced ML input features. In some cases, the execution component120can electronically train (e.g., via supervised training, unsupervised training, reinforcement learning) and/or can otherwise electronically facilitate the training of the classical ML model106on the enhanced ML input features.

FIGS. 2-3illustrate block diagrams of example, non-limiting systems200and300including quantum probability amplitudes that can facilitate quantum-enhanced features for classical machine learning in accordance with one or more embodiments described herein. As shown, the system200can, in various embodiments, comprise the same components as the system100, and can further comprise probability amplitudes202.

In various aspects, the conversion component114can electronically generate the probability amplitudes202based on the classical data104. Specifically, in various instances, the conversion component114can electronically apply any suitable amplitude embedding technique and/or amplitude encoding technique to the classical data104, thereby yielding the probability amplitudes202. Amplitude embedding and/or amplitude encoding can be mathematical techniques by which classical data is embedded and/or encoded into the probability amplitudes of a quantum state vector. In other words, the probability amplitudes202can be a set of complex numbers whose values collectively represent the classical data104, and whose squares represent the probabilities and/or likelihoods of occurrence of various quantum states. In other words, the probability amplitudes202can collectively be considered as a quantum-processible version and/or a quantum-processible format of the classical data104(e.g., the classical data104can be formatted in a way that cannot be processed by a quantum computer, but the probability amplitudes202can be formatted in a way that can be processed by a quantum computer).

More specifically, the conversion component114can, in various aspects, electronically generate the probability amplitudes202by normalizing the classical data104. That is, the conversion component114can, in various instances, treat the classical data104as a vector of elements. In such case, the conversion component114can normalize that vector. In other words, the conversion component114can compute the norm (e.g., magnitude, length) of that vector, and can divide each of the elements in the vector by the computed norm. In various instances, the result can be a normalized vector. In various cases, the elements of the normalized vector can be considered as the probability amplitudes202.

FIG. 3illustrates, in a non-limiting and example way, how the conversion component114can generate the probability amplitudes202based on the classical data104. As shown inFIG. 3, the classical data104can, in some cases, comprise n data points, for any suitable positive integer n (e.g., can comprise a data point1to a data point n). In various aspects, if the classical data104is a timeseries, this can indicate that the classical data104includes n time steps (e.g., the classical data104can comprise a data point for time1, the classical data104can comprise a data point for time n). However, this is a mere non-limiting example. In some cases, if the classical data104is a timeseries, the classical data104can comprise more than one data point per time step. For example, if the classical data104comprises n data points in total, and if the classical data104is a timeseries that has two data points per time step, then the classical data104can include n/2time steps. In any case, the classical data104can comprise n data points in total.

In various instances, as shown, the classical data104can respectively correspond to the probability amplitudes202. That is, since the classical data104comprises n data points, the probability amplitudes202can likewise comprise n amplitudes (e.g., can comprise amplitude 1 to amplitude n). In various cases, each amplitude in the probability amplitudes202can be based on and/or otherwise generated from a corresponding data point in the classical data104. For instance, the amplitude 1 can be based on and/or otherwise generated from the data point1, and the amplitude n can be based on and/or otherwise generated from the data point n.

As mentioned above, the conversion component114can apply any suitable amplitude embedding/encoding technique to create the probability amplitudes202. In some cases, one such technique can be normalization. For example, consider the classical data104as a vector (and/or a set) represented by the variable y. In such case, the data point1can be represented by yi, and the data point n can be represented by yn. In various instances, the conversion component114can calculate the norm of y as √{square root over (Σi=1n(yi2))}. Accordingly, the conversion component114can normalize y by dividing each element of y by the calculated norm. That is,

where ynormcan be a vector (and/or a set) representing the probability amplitudes202. In other words, the amplitude 1 can be equal to the quotient of the data point1and the norm of the classical data104

and the amplitude n can be equal to the quotient of the data point n and the norm of the

In various aspects, the probability amplitudes202can be considered as collectively representing an n-element quantum state vector. As those having ordinary skill in the art will appreciate, an n-element quantum state vector can be implemented by log2n qubits. In various cases, if log2n is not an integer, it can be rounded up to the next larger integer (e.g., since fractions of a qubit cannot be implemented). If log2n is rounded up to the next larger integer, those having ordinary skill in the art will appreciate that one or more dummy values can be concatenated to the end (and/or to the beginning, and/or anywhere else) of the probability amplitudes202. For example, suppose that n=5. In such case, the classical data104can have five data points, and five probability amplitudes can be computed as described above. However, log25 is not an integer, and log25 rounded up to the next larger integer is equal to 3. This can mean that the probability amplitudes202can be processed by a quantum computer having three qubits. However, the quantum state vector for a three-qubit system is defined by eight probability amplitudes (e.g., 23=8), not by five probability amplitudes. Accordingly, the probability amplitudes202can have eight amplitudes in total, the first five of which can be generated as described above, and the last three of which can be dummy values which are not of interest.

FIGS. 4-5illustrate block diagrams of example, non-limiting systems400and500including a quantum circuit and resultant quantum probability amplitudes that can facilitate quantum-enhanced features for classical machine learning in accordance with one or more embodiments described herein. As shown, the system400can, in some cases, comprise the same components as the system200, and can further comprise a quantum circuit402and resultant probability amplitudes404.

In various aspects, the quantum component116can electronically apply the quantum circuit402to the probability amplitudes202, thereby yielding the resultant probability amplitudes404. More specifically, the quantum component116can be electronically integrated with and/or can otherwise have electronic access to and/or electronic control of the quantum computer122. In various aspects, the quantum computer122can implement log2n physical qubits and/or can otherwise simulate the behavior of log2n qubits (e.g., again, if log2n is not an integer, it can be rounded up). Accordingly, the quantum computer122can facilitate quantum computations of n-element quantum state vectors. In various cases, the quantum component116can electronically initialize the quantum computer122with the probability amplitudes202. That is, the quantum component116can cause the qubits of the quantum computer122to enter a superposition of quantum states that is given by and/or in accordance with the probability amplitudes202. After initialization, the quantum component116can electronically cause the quantum circuit402to be executed on the quantum computer122. Because the quantum computer122can be initialized with the probability amplitudes202, execution of the quantum circuit402can cause the probability amplitudes202to be rotated and/or transformed, thereby yielding the resultant probability amplitudes404.

In various aspects, the quantum circuit402can include any suitable combination and/or arrangement of quantum gates. In some cases, the quantum circuit402can be a Quantum Fourier Transform.

FIG. 5illustrates, in a non-limiting and example way, how the quantum component116can generate the resultant probability amplitudes404based on the probability amplitudes202. As shown inFIG. 5, because the probability amplitudes202can have n amplitude values (e.g., amplitude 1 to amplitude n), the resultant probability amplitudes404can likewise have n amplitude values (e.g., resultant amplitude 1 to resultant amplitude n). Just as the probability amplitudes202can collectively represent an n-element quantum state vector for log2n qubits, the resultant probability amplitudes404can likewise collectively represent a resulting n-element quantum state vector for log2n qubits. In various aspects, when the quantum circuit402is applied to the probability amplitudes202(e.g., when the quantum circuit402is executed on the quantum computer122after the quantum computer122has been initialized with the probability amplitudes202), the quantum circuit402can alter (e.g., rotate, transform) the probability amplitudes202, and the result of such alteration can be considered as the resultant probability amplitudes404. In other words, the quantum computer122can be initialized with an initial quantum state (e.g., the probability amplitudes202), and execution of the quantum circuit402on the quantum computer122can convert the initial quantum state (e.g., the probability amplitudes202) to a resulting quantum state (e.g., the resultant probability amplitudes404).

This is further explained inFIG. 6.FIG. 6illustrates an example, non-limiting quantum circuit diagram600in accordance with one or more embodiments described herein. The quantum circuit diagram600can illustrate how the quantum computer122employed by the quantum component116operates.

As shown, the quantum computer122can comprise log2n qubits (e.g., qubit 1, qubit 2, . . . , qubit log2n). Again, if log2n is not an integer, it can be rounded up. In various instances, the log2n qubits can begin with any suitable starting quantum states. In the non-limiting example shown, all of the log2n qubits can begin by being in the10) state, as indicated by numeral604. However, this is a mere non-limiting example. In various other cases, the log2n qubits can begin by being in any suitable known quantum states (e.g., all of the log2n qubits can be in the |1> state, some of the log2n qubits can be in the |0> state while others of the log2n qubits can be in the |1> state). In any case, the log2n qubits of the quantum computer122can begin at numeral604by being in some known quantum state (e.g., can have some known quantum state vector).

In various instances, the quantum component116can execute an initialization circuit606on the quantum computer122. In various aspects, execution of the initialization circuit606can rotate and/or transform the quantum states of the log2n qubits from the known beginning quantum state at numeral604to a quantum state defined by the probability amplitudes202at numeral608. In other words, the initialization circuit606can comprise 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), so as to cause the log2n qubits to enter a quantum state defined by the probability amplitudes202. As those having ordinary skill in the art will appreciate, the particular composition of the initialization circuit606can depend upon the known beginning quantum states at numeral604and upon the desired initial quantum states at numeral608(e.g., the probability amplitudes202). In other words, when given a known quantum state and a desired quantum state, those having ordinary skill in the art understand which quantum gates to combine in which arrangement and/or order so as to convert the given known quantum state into the desired quantum state. Thus, when given the known beginning quantum states at numeral604and the desired initial quantum states at numeral608(e.g., the probability amplitudes202), the quantum component116can determine how to structure the initialization circuit606so as to rotate/transform the known beginning quantum states at numeral604into the desired initial quantum states at numeral608(e.g., the probability amplitudes202). Once the log2n qubits exhibit quantum states that are in accordance with the probability amplitudes202(e.g., at numeral608, after execution of the initialization circuit606), the quantum computer122can be considered as having been initialized with the probability amplitudes202.

In various aspects, once the quantum computer122is initialized with the probability amplitudes202, the quantum component116can execute the quantum circuit402on the quantum computer122. In various instances, execution of the quantum circuit402can rotate and/or transform the quantum states of the log2n qubits from the quantum state defined by the probability amplitudes202, at numeral608, to some resultant quantum state, indicated at numeral610. In various aspects, the resultant quantum state, at numeral610, can correspond to the resultant probability amplitudes404. In other words, the quantum circuit402can rotate/transform the probability amplitudes202(e.g., which define the quantum states of the log2n qubits at numeral608) into the resultant probability amplitudes404(e.g., which define the quantum states of the log2n qubits at numeral610). In various cases, the resultant probability amplitudes404can thus be considered as a function of the probability amplitudes202and of the quantum circuit402.

Those having ordinary skill in the art will appreciate that the quantum computer122can implement any suitable quantum state measurement techniques.

FIGS. 7-8illustrate block diagrams of example, non-limiting systems700and800including enhanced machine learning input features that can facilitate quantum-enhanced features for classical machine learning in accordance with one or more embodiments described herein. As shown, the system700can, in some cases, comprise the same components as the system400, and can further comprise enhanced ML input features702.

In various aspects, the feature component118can electronically generate the enhanced ML input features702based on the resultant probability amplitudes404. In other words, the feature component118can apply any suitable mathematical functions to the resultant probability amplitudes404, thereby yielding the enhanced ML input features702.

This is shown in a non-limiting and example way inFIG. 8. As shown inFIG. 8, because the resultant probability amplitudes404can comprise n amplitudes (e.g., resultant amplitude 1 to resultant amplitude n), the enhanced ML input features702can likewise comprise n quantum-enhanced input features (e.g., quantum-enhanced input feature1to quantum-enhanced input feature n). In various cases, the enhanced ML input features702can respectively correspond to the resultant probability amplitudes404. That is, the quantum-enhanced feature1can correspond to and/or otherwise be generated based on the resultant amplitude1, and the quantum-enhanced feature n can correspond to and/or otherwise be generated based on the resultant amplitude n.

In various cases, the enhanced ML input features702can be any suitable function of the resultant probability amplitudes404. For example, in some instances, the feature component118can multiplicatively scale the resultant probability amplitudes404to generate the enhanced ML input features702. In such case, the quantum-enhanced feature1can be equal to the product of the resultant amplitude 1 and any suitable multiplicative factor, and the quantum-enhanced feature n can likewise be equal to the product of the resultant amplitude n and any suitable multiplicative factor. As another example, in some aspects, the feature component118can additively offset the resultant probability amplitudes404to generate the enhanced ML input features702. In such case, the quantum-enhanced feature1can be equal to the sum of the resultant amplitude 1 and any suitable bias value, and the quantum-enhanced feature n can likewise be equal to the sum of the resultant amplitude n and any suitable bias value. As still another example, sine the resultant probability amplitudes404can be complex numbers, the feature component118can compute magnitudes of the resultant probability amplitudes404to generate the enhanced ML input features702. In such case, the quantum-enhanced feature1can be equal to the magnitude of the resultant amplitude 1, and the quantum-enhanced feature n can likewise be equal to the magnitude of the resultant amplitude n. In yet another example, the feature component118can refrain from altering the resultant probability amplitudes. In such case, the quantum-enhanced feature1can be equal to the resultant amplitude1, and the quantum-enhanced feature n can likewise be equal to the resultant amplitude n.

In various instances, the enhanced ML input features702can be considered as a quantum-transformed and/or quantum-enriched version of the classical data104. In various cases, the term “enhanced” and/or “enriched” can be used to describe the enhanced ML input features702, because the enhanced ML input features702can exhibit data patterns, data trends, and/or data distributions that were previously hidden and/or undetectable in the classical data104. As explained above, the inventors of various embodiments of the invention recognized that importing a classical dataset into a quantum Hilbert space and then transforming the classical dataset in the quantum Hilbert space can reveal otherwise hidden patterns, trends, and/or distributions that characterize the classical dataset. As described herein, the actions of the conversion component114can be considered as importing the classical data104into a quantum Hilbert space (e.g., the conversion component114can convert the classical data104into a quantum-processible format, namely the probability amplitudes202), and the actions of the quantum component116can be considered as transforming the classical data104in the quantum Hilbert space (e.g., the quantum component116can apply a quantum circuit to the probability amplitudes202). Accordingly, enhanced ML input features702can contain patterns, trends, and/or distributions that are not identifiable in the classical data104.

In various embodiments, as mentioned above, the execution component120can electronically execute and/or can otherwise electronically facilitate the execution of the classical ML model106on the enhanced ML input features702. This is illustrated in a non-limiting and example way inFIG. 9.FIG. 9illustrates an example, non-limiting block diagram that shows how quantum-enhanced features for classical machine learning can be practicably utilized in accordance with one or more embodiments described herein.

As shown,FIG. 9depicts two scenarios: a scenario902, and a scenario904. In the scenario902, the classical ML model106can be configured to receive as input only the classical data104, and to produce as output the prediction906. On the other hand, in the scenario904, the classical ML model106can be configured to receive as input both the classical data104and the enhanced ML input features702, and to produce as output the prediction908. As mentioned above, the classical ML model106can generate predictions/determinations by recognizing patterns, trends, and/or distributions in its input data. In the scenario902, the classical ML model106is not configured to receive as input the enhanced ML input features702, and thus the classical ML model106does not have access to the patterns, trends, and/or distributions that are exhibited by the enhanced ML input features702but that are hidden within the classical data104. In contrast, in the scenario904, the classical ML model106is configured to receive as input the enhanced ML input features702, and thus the classical ML model106does have access to the patterns, trends, and/or distributions that are exhibited by the enhanced ML input features702but that are hidden within the classical data104. Because the classical ML model106can have access to additional patterns, trends, and/or distributions in its input data in the scenario904, the prediction908can be more accurate than the prediction906. In other words, the performance of the classical ML model106can be improved when the classical ML model106is configured to receive as input the enhanced ML input features702. Such an increase in performance (e.g., an increase in prediction/detection accuracy) is a concrete and tangible technical benefit.

Indeed, the inventors of various embodiments of the invention experimentally verified such benefits. 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 considered as timeseries data) for various stocks, and fed such data to various classical ML models (e.g., such as an autoregressive integrated moving average model) that forecasted future volatility index values. The inventors computed the accuracy of such forecasts by comparing the forecasts to the known volatility index values that actually occurred at the forecasted time steps. Additionally, the inventors enhanced/enriched the compiled volatility index data as described herein with a Quantum Fourier Transform (e.g., in such experiments, the quantum circuit402was a Quantum Fourier Transform), and fed both the volatility index data and the QFT version of the volatility index data to the classical ML models, which again forecasted future volatility index values. As above, the inventors computed the accuracy of such forecasts by comparing the forecasts to the known volatility index values that actually occurred at the forecasted time steps. Finally, the inventors compared the accuracies of the forecasts that were based on only the compiled volatility index data to the accuracies of the forecasts that were based on both the compiled volatility index data and on the QFT version of the volatility index data.

In one experiment, forecasts that were based on both the compiled volatility index data for some first stock and on the QFT version of the volatility index data for that first stock achieved an accuracy that was 17.90% higher than the forecasts that were based on only the compiled volatility index data for that first stock. In a second experiment, forecasts that were based on both the compiled volatility index data for some second stock and on the QFT version of the volatility index data for that second stock achieved an accuracy that was 19.61% higher than the forecasts that were based on only the compiled volatility index data for that second stock. This is a significant improvement in the performance of such classical ML models.

In some other experiments, the inventors further computed the Fast Fourier Transform (FFT) of the compiled volatility index data for various stocks. In such cases, the inventors fed the classical ML models the compiled volatility index data, the QFT version of the volatility index data, and the FFT version of the volatility index data. In one of such cases, the classical ML models achieved a forecast accuracy that was 20.01% higher as compared to forecasts that were based only on the compiled volatility index data. In another such case, the classical ML models achieved a forecast accuracy that was 66.91% higher as compared to forecasts that were based only on the compiled volatility index data. Again, this is a significant improvement in the performance of such classical ML models.

In various aspects, the inventors of various embodiments of the invention noted that enhancing/enriching classical data as described herein can have a smoothing and/or noise-reduction effect on the classical data (e.g., at least when the classical data is transformed with a Quantum Fourier Transform).

FIG. 10illustrates a flow diagram of an example, non-limiting computer-implemented method1000that can facilitate quantum-enhanced features for classical machine learning in accordance with one or more embodiments described herein. In some cases, the computer-implemented method1000can be implemented by the quantum-enhanced feature system102.

In various embodiments, act1002can include receiving, by a device (e.g.,112) operatively coupled to a processor, a classical dataset (e.g.,104).

In various aspects, act1004can include converting, by the device (e.g.,114), the classical dataset to probability amplitudes (e.g.,202).

In various instances, act1006can include initializing, by the device (e.g.,116), a quantum computing device and/or simulator (e.g.,122) with the probability amplitudes.

In various cases, act1008can include applying, by the device (e.g.,116) and via the quantum computing device and/or simulator, a quantum circuit (e.g.,402) to the probability amplitudes, thereby yielding resultant probability amplitudes (e.g.,404).

In various aspects, act1010can include adjusting, by the device (e.g.,118), values of the resultant probability amplitudes in any suitable fashion, thereby yielding quantum-enhanced features (e.g.,702). As mentioned above, it can sometimes be the case that no adjustment to the resultant probability amplitudes is made, in which case the quantum-enhanced features would be equal to the resultant probability amplitudes.

In various instances, act1012can include executing, by the device (e.g.,120), a classical machine learning model (e.g.,106) on both the classical dataset and the quantum-enhanced features.

FIG. 11illustrates a block diagram of an example, non-limiting system1100including a visualization component that can facilitate quantum-enhanced features for classical machine learning in accordance with one or more embodiments described herein. As shown, the system1100can, in some cases, comprise the same components as the system700, and can further comprise a visualization component1102.

In various aspects, the visualization component1102can electronically render, display, graph, and/or plot the enhanced ML input features702. For instance, in various cases, the visualization component1102can be electronically integrated (e.g., via any suitable wired and/or wireless electronic connection) with a computer monitor/screen (not shown). In such cases, the visualization component1102can electronically display graphs/plots of the enhanced ML input features702on the computer monitor/screen. In some cases, the visualization component1102can electronically display graphs/plots of the classical data104on the computer monitor/screen as well, so that the classical data104can be visually compared with the enhanced ML input features702. Those having ordinary skill in the art will appreciate that any suitable graphs and/or plots can be implemented by the visualization component1102(e.g., histograms, bar graphs, Bloch spheres,2D and/or3D plots).

FIG. 12illustrates a block diagram of an example, non-limiting system1200including an operator device that can facilitate quantum-enhanced features for classical machine learning in accordance with one or more embodiments described herein. As shown, the system1200can, in some cases, comprise the same components as the system1100, and can further comprise an operator device1202.

In various aspects, the quantum-enhanced feature system102can be electronically integrated, via any suitable wired and/or wireless electronic connection, with the operator device1202. In various instances, the operator device1202can be associated with an entity (e.g., a client) that desires to utilize the functionality offered by the quantum-enhanced feature system102. For instance, such entity can own and/or maintain the classical data104, and such entity can desire to have the classical data104quantum-enriched. In such case, the operator device1202can provide the classical data104to the quantum-enhanced feature system102(e.g., can electronically transmit a copy of the classical data104to the receiver component112). In various aspects, the operator device1202can further identify the quantum circuit402. In other words, the entity associated with the operator device1202can desire to have the classical data104transformed and/or enhanced by a particular quantum circuit, and the operator device1202can electronically transmit to the receiver component112an identifier of that particular quantum circuit. Accordingly, after the conversion component114converts the classical data104into the probability amplitudes202, and after the quantum component116initializes the quantum computer122with the probability amplitudes202, the quantum component116can execute on the quantum computer122the quantum circuit indicated by the operator device1202. In some instances, the quantum component116can provide a list of available quantum circuits (not shown) to the operator device1202, and the operator device1202can select from such list the quantum circuit that the entity associated with the operator device1202desires to be executed. In various instances, once the enhanced ML input features702are generated, the execution component120can electronically transmit the enhanced ML input features702(and/or any graphs/plots generated by the visualization component1102) to the operator device1202.

FIGS. 13-14illustrate flow diagrams of example, non-limiting computer-implemented methods1300and1400that can facilitate quantum-enhanced features for classical machine learning in accordance with one or more embodiments described herein.

First consider the computer-implemented method1300. In various embodiments, act1302can include accessing, by a device (e.g.,112) operatively coupled to a processor, a classical dataset (e.g.,104).

In various aspects, act1304can include generating, by the device (e.g.,118), one or more machine learning input features (e.g.,702) based on a quantum transformation (e.g., collectively involving202,402, and/or404) of the classical dataset.

In various instances, act1306can include executing, by the device (e.g.,120), a classical machine learning model (e.g.,106) on the one or more machine learning input features.

Although not explicitly shown inFIG. 13, the computer-implemented method1300can further comprise: converting, by the device (e.g.,114), the classical dataset into a set of quantum probability amplitudes (e.g.,202); and executing, by the device (e.g.,116), a quantum circuit (e.g.,402) on the set of quantum probability amplitudes, thereby yielding the quantum transformation of the classical dataset.

Although not explicitly shown inFIG. 13, the computer-implemented method1300can further comprise: visually rendering, by the device (e.g.,1102), both the classical dataset and the one or more machine learning input features.

Now, consider the computer-implemented method1400. In various embodiments, act1402can include receiving, by a device (e.g.,112) operatively coupled to a processor, a classical timeseries dataset (e.g.,104) from an operator device (e.g.,1202).

In various aspects, act1404can include generating, by the device (e.g.,118), one or more quantum-enhanced machine learning input features (e.g.,702) based on a quantum transformation (e.g., collectively involving202,402, and/or404) of the classical timeseries dataset.

In various instances, act1406can include transmitting, by the device (e.g.,120), to the operator device the one or more quantum-enhanced machine learning input features.

Although not explicitly shown inFIG. 14, the computer-implemented method1400can further comprise: generating, by the device (e.g.,114), quantum probability amplitudes (e.g.,202) based on the classical timeseries dataset; and executing, by the device (e.g.,116), on the quantum probability amplitudes a quantum algorithm (e.g.,402) selected by the operator device, thereby yielding the quantum transformation of the classical timeseries dataset.

Although not explicitly shown inFIG. 14, the computer-implemented method1400can further comprise: graphing, by the device (e.g.,1102), the classical timeseries dataset or the one or more quantum-enhanced machine learning input features.

Various embodiments of the invention can enhance, enrich, and/or otherwise augment classical datasets by leveraging quantum computing. Specifically, various embodiments of the invention can be considered as a computerized tool that can receive as input a classical dataset, that can convert the classical dataset into quantum probability amplitudes (e.g., thereby importing the classical dataset into a quantum Hilbert space), that can initialize a quantum computer with the quantum probability amplitudes, and that can execute a quantum circuit on the quantum computer (e.g., thereby transforming the classical dataset in the quantum Hilbert space). In various instances, the resulting quantum probability amplitudes can be used to generate enhanced ML input features. Indeed, in various cases, the resulting quantum probability amplitudes can be themselves considered as the enhanced ML input features. As explained herein, the enhanced ML input features can exhibit more nuanced data patterns, trends, and/or distributions that were previously hidden within the classical dataset. Accordingly, the enhanced ML input features can be fed as input to a classical ML model, which can improve the performance (e.g., accuracy) of the classical ML model.

In various aspects, such a computerized tool can be implemented to enhance any suitable type of classical data (e.g., timeseries data, non-timeseries data, financial data, geospatial data, image data, audio data, video data, pressure data, voltage/current data, sales data, resource data). For example, in some cases, such a computerized tool can be implemented in the field of supply chain analysis (e.g., the computerized tool can enhance a timeseries that indicates resource consumption over time, and such enhanced data can be fed to a classical ML model to more accurately forecast future resource consumption). As another example, in some cases, such a computerized tool can be implemented in the field of market science (e.g., the computerized tool can enhance a timeseries that indicates number of visitors to an online website over time, and such enhanced data can be fed to a classical ML model to more accurately forecast future numbers of online visitors). In various instances, any other suitable type of classical data can be enhanced by various embodiments of the invention.

Although various examples described herein discuss enhancing classical data by applying the Quantum Fourier Transform to such classical data, this is a non-limiting example. In various cases, those having ordinary skill in the art will appreciate that any suitable quantum circuit and/or quantum algorithm can be used to enhance and/or enrich classical data.

With reference again toFIG. 15, the example environment1500for implementing various embodiments of the aspects described herein includes a computer1502, the computer1502including a processing unit1504, a system memory1506and a system bus1508. The system bus1508couples system components including, but not limited to, the system memory1506to the processing unit1504. The processing unit1504can be any of various commercially available processors. Dual microprocessors and other multi processor architectures can also be employed as the processing unit1504.

The system bus1508can be any of several types of bus structure that can further interconnect 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 memory1506includes ROM1510and RAM1512. A basic input/output system (BIOS) can be stored in a non-volatile memory such as ROM, erasable programmable read only memory (EPROM), EEPROM, which BIOS contains the basic routines that help to transfer information between elements within the computer1502, such as during startup. The RAM1512can also include a high-speed RAM such as static RAM for caching data.

The computer1502further includes an internal hard disk drive (HDD)1514(e.g., EIDE, SATA), one or more external storage devices1516(e.g., a magnetic floppy disk drive (FDD)1516, a memory stick or flash drive reader, a memory card reader, etc.) and a drive1520, e.g., such as a solid state drive, an optical disk drive, which can read or write from a disk1522, such as a CD-ROM disc, a DVD, a BD, etc. Alternatively, where a solid state drive is involved, disk1522would not be included, unless separate. While the internal HDD1514is illustrated as located within the computer1502, the internal HDD1514can also be configured for external use in a suitable chassis (not shown). Additionally, while not shown in environment1500, a solid state drive (SSD) could be used in addition to, or in place of, an HDD1514. The HDD1514, external storage device(s)1516and drive1520can be connected to the system bus1508by an HDD interface1524, an external storage interface1526and a drive interface1528, respectively. The interface1524for external drive implementations can include at least one or both of Universal Serial Bus (USB) and Institute of Electrical and Electronics Engineers (IEEE)1394interface technologies. Other external drive connection technologies are within contemplation of the embodiments described herein.

A number of program modules can be stored in the drives and RAM1512, including an operating system1530, one or more application programs1532, other program modules1534and program data1536. All or portions of the operating system, applications, modules, and/or data can also be cached in the RAM1512. The systems and methods described herein can be implemented utilizing various commercially available operating systems or combinations of operating systems.

Computer1502can optionally comprise emulation technologies. For example, a hypervisor (not shown) or other intermediary can emulate a hardware environment for operating system1530, and the emulated hardware can optionally be different from the hardware illustrated inFIG. 15. In such an embodiment, operating system1530can comprise one virtual machine (VM) of multiple VMs hosted at computer1502. Furthermore, operating system1530can provide runtime environments, such as the Java runtime environment or the .NET framework, for applications1532. Runtime environments are consistent execution environments that allow applications1532to run on any operating system that includes the runtime environment. Similarly, operating system1530can support containers, and applications1532can be in the form of containers, which are lightweight, standalone, executable packages of software that include, e.g., code, runtime, system tools, system libraries and settings for an application.

A monitor1546or other type of display device can be also connected to the system bus1508via an interface, such as a video adapter1548. In addition to the monitor1546, a computer typically includes other peripheral output devices (not shown), such as speakers, printers, etc.

The computer1502can 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(s)1550. The remote computer(s)1550can be a workstation, a server computer, a router, a personal computer, portable computer, microprocessor-based entertainment appliance, a peer device or other common network node, and typically includes many or all of the elements described relative to the computer1502, although, for purposes of brevity, only a memory/storage device1552is illustrated. The logical connections depicted include wired/wireless connectivity to a local area network (LAN)1554and/or larger networks, e.g., a wide area network (WAN)1556. Such LAN and WAN networking environments are commonplace in offices and companies, and facilitate enterprise-wide computer networks, such as intranets, all of which can connect to a global communications network, e.g., the Internet.

When used in a LAN networking environment, the computer1502can be connected to the local network1554through a wired and/or wireless communication network interface or adapter1558. The adapter1558can facilitate wired or wireless communication to the LAN1554, which can also include a wireless access point (AP) disposed thereon for communicating with the adapter1558in a wireless mode.

When used in a WAN networking environment, the computer1502can include a modem1560or can be connected to a communications server on the WAN1556via other means for establishing communications over the WAN1556, such as by way of the Internet. The modem1560, which can be internal or external and a wired or wireless device, can be connected to the system bus1508via the input device interface1544. In a networked environment, program modules depicted relative to the computer1502or portions thereof, can be stored in the remote memory/storage device1552. It will be appreciated that the network connections shown are example and other means of establishing a communications link between the computers can be used.

When used in either a LAN or WAN networking environment, the computer1502can access cloud storage systems or other network-based storage systems in addition to, or in place of, external storage devices1516as described above, such as but not limited to a network virtual machine providing one or more aspects of storage or processing of information. Generally, a connection between the computer1502and a cloud storage system can be established over a LAN1554or WAN1556e.g., by the adapter1558or modem1560, respectively. Upon connecting the computer1502to an associated cloud storage system, the external storage interface1526can, with the aid of the adapter1558and/or modem1560, manage storage provided by the cloud storage system as it would other types of external storage. For instance, the external storage interface1526can be configured to provide access to cloud storage sources as if those sources were physically connected to the computer1502.

Referring now toFIG. 16, illustrative cloud computing environment1600is depicted. As shown, cloud computing environment1600includes one or more cloud computing nodes1602with which local computing devices used by cloud consumers, such as, for example, personal digital assistant (PDA) or cellular telephone1604, desktop computer1606, laptop computer1608, and/or automobile computer system1610may communicate. Nodes1602may communicate with one another. They may be grouped (not shown) physically or virtually, in one or more networks, such as Private, Community, Public, or Hybrid clouds as described hereinabove, or a combination thereof. This allows cloud computing environment1600to offer infrastructure, platforms and/or software as services for which a cloud consumer does not need to maintain resources on a local computing device. It is understood that the types of computing devices1604-1610shown inFIG. 16are intended to be illustrative only and that computing nodes1602and cloud computing environment1600can communicate with any type of computerized device over any type of network and/or network addressable connection (e.g., using a web browser).

Referring now toFIG. 17, a set of functional abstraction layers provided by cloud computing environment1600(FIG. 16) is shown. Repetitive description of like elements employed in other embodiments described herein is omitted for sake of brevity. It should be understood in advance that the components, layers, and functions shown inFIG. 17are intended to be illustrative only and embodiments of the invention are not limited thereto. As depicted, the following layers and corresponding functions are provided.

Hardware and software layer1702includes hardware and software components. Examples of hardware components include: mainframes1704; RISC (Reduced Instruction Set Computer) architecture based servers1706; servers1708; blade servers1710; storage devices1712; and networks and networking components1714. In some embodiments, software components include network application server software1716and database software1718.

Virtualization layer1720provides an abstraction layer from which the following examples of virtual entities may be provided: virtual servers1722; virtual storage1724; virtual networks1726, including virtual private networks; virtual applications and operating systems1728; and virtual clients1730.

In one example, management layer1732may provide the functions described below. Resource provisioning1734provides dynamic procurement of computing resources and other resources that are utilized to perform tasks within the cloud computing environment. Metering and Pricing1736provide cost tracking as resources are utilized within the cloud computing environment, and billing or invoicing for 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 portal1738provides access to the cloud computing environment for consumers and system administrators. Service level management1740provides cloud computing resource allocation and management such that required service levels are met. Service Level Agreement (SLA) planning and fulfillment1742provide pre-arrangement for, and procurement of, cloud computing resources for which a future requirement is anticipated in accordance with an SLA.

Workloads layer1744provides examples of functionality for which the cloud computing environment may be utilized. Examples of workloads and functions which may be provided from this layer include: mapping and navigation1746; software development and lifecycle management1748; virtual classroom education delivery1750; data analytics processing1752; transaction processing1754; and differentially private federated learning processing1756. Various embodiments of the present invention can utilize the cloud computing environment described with reference toFIGS. 16 and 17to execute one or more differentially private federated learning process in accordance with various embodiments described herein.