Change detection in high-dimensional data stream using quantum device

Abstract

To provide a method for change detection in a data stream.SOLUTION: The method may include obtaining first and second quantum states that represent different subsets of a multivariate dataset and configuring a quantum circuit that includes an ancillary qubit initialized to a zero state, a first qubit including the first quantum state, and a second qubit including the second quantum state. The method may include applying a first Hadamard transformation to the ancillary qubit, and in response to the first Hadamard transformation returning a particular value, swapping the first and second qubits such that the second qubit represents the first quantum state and the first qubit represents the second quantum state. The method may include applying a second Hadamard transformation to the ancillary qubit, and in response to observation of a measurement outcome of zero, it may be determined that a change point does not occur between the data samples corresponding to the first and second data subsets.SELECTED DRAWING: Figure 5

Description

[Technical field]

[0001] The present disclosure relates generally to change detection in high-dimensional data streams using quantum devices. [Background technology]

[0002] Quantum computers can use quantum bits ("qubits") that can represent information as 1's, 0's, or 1's and 0's simultaneously. Quantum computers can perform some types of calculations, such as optimization problems, integer factorization, simulation modeling, and / or data analysis, more efficiently and / or accurately than classical computing systems. Quantum logic gates, or quantum gates, can represent unitary matrices that can be applied to one or more qubits to reversibly transform the qubits and perform logical operations.

[0003] The subject matter claimed in this disclosure is not limited to embodiments that solve any problem or operate only in the above-described environments. Rather, this background discussion is only provided to illustrate one example technology area where embodiments described in this disclosure may be practiced. Summary of the Invention

[0004] According to one aspect of an embodiment, a method may include obtaining first and second quantum states representing distinct subsets of a multivariate data set. The method may include configuring a quantum circuit including an ancillary qubit initialized to a 0 state, a first qubit including a first quantum state, and a second qubit including a second quantum state. The method may include applying a first Hadamard transform to the ancillary qubit, and in response to the first Hadamard transform returning a particular value, swapping the first and second qubits such that the second qubit represents the first quantum state and the first qubit represents the second quantum state. The method may include applying a second Hadamard transform to the ancillary qubit, and in response to observing a measurement result of 0, determining that no change point has occurred between data samples corresponding to the first and second data subsets.

[0005] The object and advantages of the embodiments will be realized and achieved at least by the elements, features and combinations particularly pointed out in the claims. It is to be understood that both the foregoing general description and the following detailed description are given by way of example and explanation and are not restrictive of the invention as claimed. [Brief description of the drawings]

[0006] Example embodiments will be described and explained with additional specificity and detail through the accompanying drawings, including the following figures: [Figure 1] FIG. 1 illustrates an example operating environment for determining whether a change point has occurred in a high-dimensional dataset, in accordance with one or more embodiments of the present disclosure. [Diagram 2] 1 shows an example dataset including change points. [Diagram 3] 1 illustrates an example data streaming process in accordance with one or more embodiments of the present disclosure. [Figure 4] 1 illustrates a second swap test example in accordance with one or more embodiments of the present disclosure. [Diagram 5]1 is a flowchart of an example method for determining whether a change-point has occurred in a high-dimensional dataset, in accordance with one or more embodiments of the present disclosure. [Figure 6] 1 is an example computer system in accordance with one or more embodiments of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0007] Statistically analyzed data sets on highly complex subjects may contain a large number of variables that characterize the data contained in those complex data sets. For example, a data set on biosciences, such as hospital patient information, may be described in terms of several different variables, including age, height, weight, medical history, certain genetic characteristics, health behavior, drug predisposition, and other health-related information about the patient. As a further or alternative example, data sets on subjects such as computer vision, stock market performance, or text analysis may also contain different variables that may describe the data samples contained in those data sets. In some circumstances, such data sets may contain a number of variables by which the data is represented that is greater than the sample size of the data set and may be referred to as high-dimensional data.

[0008] High-dimensional data can be difficult to analyze by existing methods of statistical analysis. Existing statistical measures, such as linear regression parameters and standard deviation values, may not be able to accurately describe the data samples contained in the high-dimensional data due to the relatively small number of data samples and the relatively large number of variables by which the data samples may be analyzed. Additionally or alternatively, high-dimensional data can be difficult to process due to the larger digital file sizes of the data entries contained in the high-dimensional data set. Thus, not only does storing high-dimensional data pose a potential hurdle, but the allocation of computing resources to process and analyze high-dimensional data can also be a challenge.

[0009] In analyzing high-dimensional data, change points can be an important statistical metric that facilitates the analysis of a data set. Change points can indicate the time points in a time-ordered data set where a statistically significant change occurs in the collected data. Detecting change points is important to analyzing a particular data set because change points can be an identifiable quantitative representation of a shift in the behavior of the data samples contained in that particular data set. For example, detecting change points can facilitate identifying the points where an upward or downward trend in a data set begins or ends. Additionally or alternatively, understanding the implications and characteristics of the data at or near the change point can improve the analysis and prediction of the future behavior of the data set.

[0010] In traditional data sets that include relatively large sample sizes and fewer descriptive data variables, change points may be detected based on shifts in statistical parameters such as the mean, variance, or correlation of the data. However, such detection methods may not be applicable to high-dimensional data sets because change points in multivariate high-dimensional data sets may or may not be represented in terms of linear functions with respect to the data points contained in the data set. Change point detection in high-dimensional data sets may rely on careful modeling of the data set and specifically defining what constitutes a change point with respect to the data set.

[0011] Quantum computing systems may be well suited to solving computational tasks that may be challenging for classical computing systems. For example, classical computing systems may require significant computational resources to determine a solution to a complex computational task, such as identifying a solution set for an optimization problem. Furthermore, a solution determined by a classical computing system may or may not represent the best solution, or even a satisfactory solution, to a specified computational task. Quantum computing systems are configured to represent data as quantum bits, or qubits, which may include quantum states having values ​​of 0, 1, or superpositions of 1 and 0. The ability of quantum computing systems to represent data differently than bits associated with classical computing systems enhances the ability of quantum computing systems to solve certain types of computational tasks, such as complex optimization problems, and to compute on highly multivariate data samples. Thus, it may be desirable to model computational tasks designed for classical computing systems such that a quantum computing system may perform processing related to the computational task.

[0012] However, modeling a particular computational task for input to a quantum computing system may require that the particular computational task and the input information related to the particular computational task be presented in a particular format such that the quantum computing system may obtain and process the information. The manner in which a classical computing system obtains and processes information is different from the manner in which a quantum computing system obtains and processes information. Thus, the manner in which a particular computational task and the inputs related to the particular computational task are represented as qubits that can be input to a quantum computing system can greatly affect how effectively the quantum computing system processes the obtained information to solve the computational task.

[0013] The present disclosure may relate, in part, to modeling a particular high-dimensional data set as one or more qubits. Qubit-associated processing may facilitate faster detection of change points in the data with less allocation of computing resources than using traditional statistical and classical computing approaches. Thus, by creating methods and systems that perform processing of high-dimensional data more efficiently in accordance with the present disclosure, the computing process and performance of the computer itself may be improved.

[0014] Furthermore, due to file size limitations associated with high-dimensional data, a streaming computational model may be implemented to process the high-dimensional data. The streaming computational model may involve obtaining a portion of a dataset to be analyzed and performing a data analysis process on the obtained dataset portion. After outputting the analysis results corresponding to the obtained dataset portion, the computing system may obtain a new portion of the dataset for analysis. The data streaming process may involve a faster frequency of data acquisition, which in turn results in faster data analysis being required to process a particular portion of the dataset before receiving a subsequent portion of the dataset, which may be unattainable with classical computing approaches. Thus, processing a streamed dataset using a quantum computing approach may enable processing of a particular dataset using a streaming computational model.

[0015] Additionally or alternatively, data being analyzed in a streaming computational model may or may not be stored, which may conserve or reduce computational resource usage. Because the streamed data does not have to be stored, anonymous analysis of the data may be performed, which may be beneficial for maintaining data privacy. In one or more embodiments of the present disclosure, the underlying dataset being analyzed may be encoded into one or more quantum states that may be obtained piecewise as part of the data stream. Because the encoded quantum states based on the underlying dataset do not directly reveal information about the underlying dataset, determining the change points corresponding to the underlying dataset may or may not involve processing any of the underlying dataset by the quantum computing system. Also, because the encoded quantum states may be obtained piecewise as part of the data stream, the quantum computing system may or may not receive a complete representation of the underlying dataset. Thus, information about the underlying dataset may be obscured, and data privacy may be improved.

[0016] Embodiments of the present disclosure will now be described with reference to the accompanying drawings.

[0017] 1 is a diagram of an example operating environment 100 for determining whether a change point has occurred in a high-dimensional dataset, in accordance with one or more embodiments of the present disclosure. The environment 100 may include a quantum transformation module 110 configured to output a quantum state 115 corresponding to the high-dimensional dataset 105. A quantum circuit generator 120 may generate a quantum circuit 125 based on the quantum state 115, which may be retrieved by a quantum computing module 130. Processing performed by the quantum computing module 130 on the quantum circuit 125 in accordance with one or more embodiments of the present disclosure may result in the output of a change point determination 135.

[0018] In some embodiments, one or more of the quantum transformation module 110, the quantum circuit generator 120, and / or the quantum computing module 130 (collectively referred to herein as “computing modules”) may include code and routines configured to enable a computing system to perform one or more operations. Additionally or alternatively, one or more of the computing modules may be implemented using hardware, including a processor, a microprocessor (e.g., for performing or controlling the execution of one or more operations), a field programmable gate array (FPGA), or an application specific integrated circuit (ASIC). In some other examples, the computing modules may be implemented using a combination of hardware and software. In this disclosure, a process described as being performed by a computing module may include a process that the computing module may instruct one or more corresponding systems to perform. The computing modules may be configured to perform a series of operations on the high-dimensional dataset 105, the quantum state 115, the quantum circuit 125, and / or the change point determination 135, as described in more detail below in connection with an example method 500 described with respect to FIG. 5.

[0019] The high-dimensional dataset 105 may include multivariate data samples, where each data sample is described by multiple different measurable characteristics. In some circumstances, the high-dimensional dataset 105 may include fewer data samples than the characteristics or variables used to describe each of the data samples. For example, a hospital patient dataset may describe hospital patients according to a number of classifications, including the genetic characteristics of the hospital patients. In some cases, the number of hospital patients included in the dataset may not be greater than the number of possible genetic characteristics used to describe a particular person, which may represent thousands or tens of thousands of possible data variables. The high-dimensional dataset 105 may be difficult to analyze using traditional statistical analysis approaches, since a particular variable may contain little, if any, data with which the particular variable can be analyzed. Returning to the previous example of a hospital patient dataset, a statistical analysis of the dataset for a particular genetic characteristic may produce inaccurate results because the number of hospital patients exhibiting the particular genetic characteristic may be insufficient to analyze the hospital patient dataset for the particular genetic characteristic.

[0020] In some embodiments, the high-dimensional dataset 105 may be represented as a matrix, where each row or each column of the matrix represents a particular data entry included in the high-dimensional dataset 105. Additionally or alternatively, the high-dimensional dataset 105 may be represented as a collection of multi-dimensional vectors, where each of the data entries included in the high-dimensional dataset 105 is represented as a particular multi-dimensional vector. The quantum transform module 110 may be configured to take the high-dimensional dataset 105 and output quantum states 115 that encode the classically represented data of the high-dimensional dataset 105 as one or more qubits. In some embodiments, the quantum transform module 110 may be configured to output two quantum states 115, where each quantum state 115 represents a binary classification of a data entry included in the high-dimensional dataset 105. For example, the quantum transform module 110 may be configured to encode a data sample included in the high-dimensional dataset 105 as either a first quantum state including normal data or a second quantum state including anomalous data. In this and other examples, the initial classification of the data sample as either normal data or anomalous data may be specified by a data provider (e.g., a human user). Additionally or alternatively, the initial classification of the data samples may be represented by particular variables included in the high dimensional dataset 105 for which each of the data samples includes a value. In these and other embodiments, the quantum transform module 110 may thus be configured to encode the data samples as either a first quantum state or a second quantum state based on any other variables.

[0021] Additionally or alternatively, quantum transform module 110 may be configured to encode a data sample included in high-dimensional dataset 105 as three or more quantum states. For example, quantum transform module 110 may be configured to encode a particular data entry as one of five possible quantum states, each of which represents a different degree of anomaly of the data sample. In these and other embodiments, quantum transform module 110 may be configured to encode a data sample into any number of quantum states based on particular variables that describe the data sample in high-dimensional dataset 105.

[0022] In some embodiments, encoding the quantum state 115 may be performed outside of the environment 100. In other words, the processing of the quantum transformation module 110 may be performed outside of the environment 100, such that the quantum state 115 is presented by a data provider. Performing the processing of the quantum transformation module 110 outside of the environment 100 may facilitate data anonymity and improve data privacy, since the quantum state 115 may or may not provide information about the specific data entries included in the high-dimensional dataset 105. Thus, the environment 100 may be used to identify change points in the high-dimensional dataset 105 without some information about the individual data entries included in the high-dimensional dataset 105.

[0023] FIG. 2 illustrates an example dataset 200 that includes a change point 210. The dataset 200 may represent the monetary value of, for example, a particular stock, a number of different stocks (e.g., as an index fund), a product, or a service, over a period of time. The change point 210 in the dataset 200 may represent a statistically abrupt shift in a data sample across one or more variables. As illustrated in FIG. 2, the change point 210 represents a sudden drop in the monetary value of a particular stock between two time points, or across several time points. Although illustrated with respect to monetary value, it may be contemplated that the change point 210 may be detected in other variable relationships for the same dataset 200, either as a positive or negative change point depending on the variable involved. For example, an analysis of the dataset 200 with respect to a variable related to the number of shares of a stock being sold may indicate that the stock experiences a positive change point that corresponds to the approximate time of the change point 210.

[0024] A classic change point detection approach may involve observing a statistical metric associated with a dataset 200 and identifying a change in the observed statistical metric that is greater than a threshold amount at a particular time. As shown in the dataset 200, for example, a significant drop in the monetary value associated with two or more data points within a short period of time may represent a change point 210. A change point 210 observed with respect to the dataset 200 in terms of the monetary value of the data points may or may not be detectable in response to representing the dataset 200 in terms of different variables. Thus, detection of change points in multivariate data, such as the high dimensional dataset 105 described in connection with the environment 100, may or may not be as visually noticeable as shown in the dataset 200 of FIG. 2.

[0025] Returning to the description of FIG. 1 , quantum state 115 may be obtained by quantum circuit generator 120 to generate quantum circuit 125. In some embodiments, quantum circuit 125 may include two or more qubits that variously include quantum state 115. For example, quantum state 115 may include a first quantum state encoded with normal data of high-dimensional dataset 105 and a second quantum state encoded with anomalous data of high-dimensional dataset 105. A corresponding quantum circuit 125 may consist of a first qubit that includes the first quantum state and a second qubit that includes the second quantum state. In these and other embodiments, quantum circuit 125 may include an ancillary qubit initialized to a zero quantum state. As a further or alternative example, quantum circuit 125 may include an ancillary qubit with an initialized zero quantum state, a first qubit corresponding to the first quantum state, a second qubit corresponding to the second quantum state, and any other number of qubits corresponding to additional quantum states defined in quantum state 115.

[0026] In some embodiments, the quantum state 115 may be acquired as a data stream rather than as an entire representation of the high-dimensional dataset 105. In other words, a portion of the high-dimensional dataset 105 rather than the entire high-dimensional dataset 105 may be acquired in the environment 100 (e.g., by the quantum transformation module 110 and / or the quantum circuit generator 120), and the processing of the quantum transformation module 110, the quantum circuit generator 120, and / or the quantum computing module 130 may be performed on the acquired portion of the high-dimensional dataset 105 rather than the entire high-dimensional dataset 105. Performing the operation of the environment 100 according to a data streaming approach may result in piecewise processing and analysis of the high-dimensional dataset 105, such that the change point determination 135 is output taking into account the acquired portion of the high-dimensional dataset 105 and / or one or more portions of the high-dimensional dataset 105 previously acquired in the environment 100.

[0027] FIG. 3 illustrates an example data streaming process 300 in accordance with one or more embodiments of the present disclosure. The data streaming process 300 may involve obtaining input data 310 in the form of several portions or packets. In some embodiments, the input data 310 may represent the high-dimensional dataset 105 and / or quantum state 115 split into several packets. For example, the high-dimensional dataset 105 may include packets relating to a number of different securities and the performance of the securities over time. The packets may break down the data relating to the performance of the securities into data over a first period, a second period, a third period, or any other number of periods. Additionally or alternatively, the input data 310 may include new packets relating to the performance of the securities over the past minute, five minutes, one hour, two hours, three hours, one day, two days, or any other period that may be obtained as the data becomes available.

[0028] The stream processing engine 320 can obtain input data 310 and return output 330, which may include an output stream 332 and analysis results 334 on the obtained input data 310. In some embodiments, the stream processing engine 320 may be configured to perform the same or similar processing as that performed by the computing modules of the environment 100 of FIG. 1, including the quantum transform module 110, the quantum circuit generator 120, and the quantum computing module 130. In these and other embodiments, the stream processing engine 320 may be configured to obtain one, two, three, or any other number of packets of the input data 310 for analysis. The stream processing engine 320 may be configured to generate the output 330 based only on the currently obtained packet of the input data 310. Additionally or alternatively, the stream processing engine 320 may be configured to generate the output 330 based on the currently obtained packet of the input data 310 and one or more previously obtained packets of the input data 310.

[0029] The output 330 may include an output stream 332 detailing the input data 310 that was analyzed to generate analysis results 334. Additionally or alternatively, the stream processing engine 320 may be configured to apply one or more processes to the input data 310 such that the output stream 332 is changed in some amount relative to the corresponding input data 310. In the context of the environment 100, for example, the output 330 may include an output stream 332 that specifies which portions of the high dimensional dataset 105 were obtained for analysis by the stream processing engine 320, and the analysis results 334 may specify whether a change point was determined and, if so, between which data entries the change point occurred.

[0030] Returning to the description of FIG. 1 , the data streaming process 300 may be applied to processing in the environment 100. In some embodiments, a first portion of the high-dimensional dataset 105 is acquired, rather than the entire high-dimensional dataset 105, and the quantum transformation module 110 may generate a quantum state 115 based on the acquired portion of the high-dimensional dataset 105. The quantum circuit 125 may thus consist of ancillary qubits and a quantum state 115 that represents the acquired portion of the high-dimensional dataset 105. As additional data, such as other portions of the high-dimensional dataset 105, are acquired by the quantum transformation module 110, additional quantum states 115 may be generated that may be added to the existing quantum circuit 125 or used to generate new quantum circuits 125, and may be analyzed by the quantum computing module 130.

[0031] Quantum computing module 130 may be configured to obtain quantum circuit 125, perform processing on quantum circuit 125 related to detecting change points in data represented by quantum circuit 125, and output one or more change point decisions 135. Quantum computing module 130 may be configured to perform a controlled swap test on quantum circuit 125 to make change point decisions 135. In some embodiments, the controlled swap test may involve applying a first Hadamard transform to an ancillary qubit having a 0 quantum state to cause the ancillary qubit to output a quantum state having a value of 0 or 1. Application of the first Hadamard transform to the ancillary qubit may return an output value of 0 or 1 with a predetermined probability. In response to the first Hadamard transform returning an output value of 0, the first qubit and the second qubit (and / or any other qubits included in quantum circuit 125) may be left unchanged. In response to the first Hadamard transform returning an output value of 1, the first qubit and the second qubit may be swapped such that the first qubit has the second quantum state originally assigned to the second qubit and the second qubit has the first quantum state originally assigned to the first qubit. In some embodiments, quantum circuit 125 may include a third qubit, a fourth qubit, or any other number of qubits, and the first Hadamard transform returning an output value of 1 may result in two or more of the qubits being swapped.

[0032] The controlled swap test may involve applying a second Hadamard transform to the ancillary qubit and observing whether the measurement includes a value of 0 or a value of 1. The measurement of the second Hadamard transform may indicate whether the first qubit and the second qubit include the same quantum state. In response to observing a measurement of 1, it may be concluded that the first qubit and the second qubit do not include the same quantum state and a change point has occurred between the data sample associated with the first qubit and the data sample associated with the second qubit. In response to observing a measurement of 0, it may be concluded that the first qubit and the second qubit may include the same quantum state with a first predetermined probability.

[0033] However, in response to observing a measurement result of the second Hadamard transform being zero, it may be possible with a second predetermined probability that the first qubit and the second qubit do not contain the same quantum state. In other words, the second Hadamard transform returning an output value of zero is not conclusive with respect to determining whether a change point has occurred between the data samples associated with the first qubit and the data samples associated with the second qubit. To ascertain whether a change point has occurred, input information in the form of a new portion of the high-dimensional data set 105 and / or a new quantum state 115 may be obtained, and the processing of the quantum computing module 130 may be applied to the newly obtained input information. Since observing a measurement result having a value of one reliably indicates that a change point has occurred, as the processing of the quantum computing module 130 is iteratively repeated with the newly obtained input information, the probability that an output value of zero of the second Hadamard transform indicates no change point has occurred increases. Thus, the processing of the new input information by the data streaming process may facilitate a more accurate determination of whether a change point has occurred between two or more sets of data samples.

[0034] Modifications, additions, or omissions may be made to environment 100 without departing from the scope of the present disclosure. For example, the designation of different elements in the manner described is intended to aid in explaining the concepts described herein and is not intended to be limiting. For example, in some embodiments, high-dimensional dataset 105, quantum state 115, quantum circuit 125, and / or change point determination 135 are depicted in the particular manner described to aid in explaining the concepts described herein, but such depictions are not intended to be limiting. Additionally, environment 100 may include any number of other elements and may be implemented in systems or contexts other than those described.

[0035] 4 illustrates an example environment 400 in which a controlled swap test involving n consecutive data streams may be performed in accordance with one or more embodiments of the present disclosure. Each of the data streams may include a quantum circuit 430 consisting of an ancillary qubit 410 and two or more qubits 420. For each of the quantum circuits 430, a controlled swap test may be performed by applying a first Hadamard transform 440 and a second Hadamard transform 450 to the ancillary qubit 410.

[0036] Applying a controlled swap test to a quantum circuit 430 may involve performing a random permutation of swaps between qubits 420 based on the results of applying a first Hadamard transform 440 to ancillary qubits 410. As the number of qubits 420 included in a quantum circuit 430 increases, the number of swap permutations increases at a corresponding factorial rate. Applying random permutations to a particular quantum circuit 430 may become costly in terms of use of computational resources as the number of qubits 420 increases due to the factorial rate of increase in the number of possible swap permutations.

[0037] Environment 400 may represent quantum circuits 430 having different numbers of qubits 420. For example, first quantum circuit 432 represents a quantum circuit including an ancillary qubit 412, a first qubit 422, and a second qubit 424, while second quantum circuit 434 and third quantum circuit 436 represent quantum circuits including a larger number of qubits. Although environment 400 shows first Hadamard transform 440 and second Hadamard transform 450 performed before and after a qubit swap, respectively, in some embodiments, a series of quantum circuits the same or similar to first quantum circuit 432 may be implemented. In other words, first quantum circuit 432 may be implemented repeatedly or iteratively at each time step in the data streaming process to identify change points in some embodiments.

[0038] In some embodiments, a series of two-qubit swaps may be performed to generate a particular permutation configuration of the quantum circuit 430. For example, the first quantum circuit 432 may include only the ancillary qubit 412, the first qubit 422, and the second qubit 424. Applying the controlled swap test to the first quantum circuit 432 may include swapping a quantum state associated with the first qubit 422 with a quantum state associated with the second qubit 424. In comparison, the second quantum circuit 434 may include the ancillary qubit 414, the first qubit 422, the second qubit 424, and the third qubit 426. To configure the second quantum circuit 434, the second Hadamard transform 450 may include performing a first swap operation such that the quantum state associated with the first qubit 422 and the quantum state associated with the third qubit 426 are swapped. The second Hadamard transform 450 may include performing a second swap operation to exchange the quantum state associated with the second qubit 424 with the quantum state associated with the third qubit 426, which was the quantum state originally associated with the first qubit 422, resulting in the second quantum circuit 434 having a configuration in which the first qubit 422 has the quantum state originally associated with the third qubit 426, the second qubit 424 has the quantum state originally associated with the first qubit 422, and the third qubit 426 has the quantum state originally associated with the second qubit 424.

[0039] In some embodiments, application of a controlled swap test by a series of swap operations between two qubits included in a particular quantum circuit may be used instead of a random permutation of the qubits. For example, the third quantum circuit 436 may include n qubits, including the first qubit 422, the second qubit 424, the third qubit 426, and qubits 428 up to n. Performing a series of swap operations rather than computationally generating a particular permutation of qubits for a particular quantum circuit may accelerate execution of the process in environment 400 because performing a series of swap operations may scale linearly rather than at an exponential-factorial rate with respect to the number of qubits included in the particular quantum circuit.

[0040] Modifications, additions, or omissions may be made to environment 400 without departing from the scope of the present disclosure. For example, the designation of different elements in the manner described is intended to aid in explaining the concepts described herein and is not intended to be limiting. For example, in some embodiments, ancillary qubits 410, qubits 420, quantum circuit 430, first Hadamard transform 440, and / or second Hadamard transform 450 are depicted in the particular manner described to aid in explaining the concepts described herein, but such depictions are not intended to be limiting. Additionally, controlled swap testing of environment 400 may include any number of other elements and may be implemented in systems or contexts other than those described.

[0041] 5 is a flowchart of an example method 500 for determining whether a change point has occurred in a high-dimensional dataset, in accordance with one or more embodiments of the present disclosure. Method 500 may be performed by any suitable system, apparatus, or device. For example, quantum transformation module 110, quantum circuit generator 120, and / or quantum computing module 130 of FIG. 1 may perform one or more operations associated with method 500. Although shown with discrete blocks, steps and operations associated with one or more of the blocks of method 500 may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the particular implementation.

[0042] Method 500 may begin at block 502, where a first quantum state and a second quantum state are obtained. The first quantum state may represent a first data subset of a multivariate data set describing a data sample with respect to several variables, and the second quantum state represents a second data subset of the multivariate data set. In some embodiments, a data sample may be included in the first data subset or the second data subset based on a predefined classification of the data sample as normal data or anomalous data. For example, a data sample may be classified as normal data included in a first group, and a data sample may be classified as anomalous data included in a second group. In some embodiments, the first quantum state and the second quantum state may be obtained as portions of a data stream where the first quantum state and the second quantum state are encrypted when obtained and discarded after observing a measurement result of a second Hadamard transform.

[0043] A quantum circuit including an ancillary qubit may be configured to include the obtained first quantum state and the obtained second quantum state at block 504. In some embodiments, a third quantum state representing a third data subset of the multivariate data set may be obtained, and the quantum circuit may be configured to include a third qubit having the third quantum state.

[0044] At block 506, a first Hadamard transform may be applied to the ancillary qubit, with the first Hadamard transform returning a particular output value (e.g., an output value of 1) indicating that the first qubit and the second qubit of the quantum circuit should be swapped. In some embodiments that include a third qubit or other additional qubits in the quantum circuit, the first Hadamard transform returning a particular output value may result in swapping two or more quantum states associated with the qubits included in the quantum circuit.

[0045] At block 508, in response to the first Hadamard transform returning a particular output value, the first qubit and the second qubit may be swapped such that the second qubit represents the first quantum state and the first qubit represents the second quantum state. In response to the first Hadamard transform not returning a particular output value (e.g., returning an output value of 0), the first qubit and the second qubit may not be swapped.

[0046] At block 510, a second Hadamard transform may be applied to the ancillary qubit and a measurement result of the second Hadamard transform may be observed.

[0047] At block 512, it may be determined whether a change point has occurred between a data sample corresponding to a first data subset associated with a first quantum state and a data sample corresponding to a second data subset associated with a second quantum state based on the observed measurement. In response to observing the measurement result having a value of 1, it may be determined that a change point has occurred. In response to observing the measurement result having a value of 0, it may be concluded that a change point has not occurred between the data sample corresponding to the first data subset and the data sample corresponding to the second data subset. Additionally or alternatively, in response to observing the measurement result having a value of 0, a change point may have occurred between the data sample corresponding to the first data subset and the data sample corresponding to the second data subset.

[0048] Modifications, additions, or omissions may be made to method 500 without departing from the scope of the disclosure. For example, the designation of different elements in the described manner is intended to help explain the concepts described herein, and is not intended to be limiting. Additionally, method 500 may include any number of other elements and may be implemented in systems or contexts other than those described.

[0049] 6 is an example of a computer system 600 in accordance with one or more embodiments of the present disclosure. Computing system 600 may include a processor 610, a memory 620, data storage 630, and / or a communication unit 640, all of which may be communicatively coupled. Any or all of environment 100 of FIG. 1 may be implemented as a computing system consistent with computing system 600.

[0050] In general, the processor 610 may include any suitable special purpose or general purpose computer, computing entity, or processing device, including various computer hardware or software modules, and may be configured to execute instructions stored on any applicable computer-readable medium. For example, the processor 610 may include a microprocessor, a microcontroller, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other digital or analog circuitry configured to interpret and / or execute program instructions and / or process data.

[0051] 6 as a single processor, it is understood that processor 610 may include any number of processors distributed across any number of networks or physical locations configured to individually or collectively perform any number of operations described in this disclosure. In some embodiments, processor 610 may interpret and / or execute program instructions and / or process data stored in memory 620, data storage 630, or memory 620 and data storage 630. In some embodiments, processor 610 may fetch program instructions from data storage 630 and load the program instructions into memory 620.

[0052] After program instructions are loaded into memory 620, processor 610 may execute the program instructions, such as, for example, instructions that cause computer system 600 to perform the operations of method 500 of Figure 5. For example, computing system 600 may execute the program instructions to obtain a first quantum state and a second quantum state, configure a quantum circuit, apply a first Hadamard transform to an ancillary qubit, swap the first qubit and the second qubit, apply a second Hadamard transform, and / or determine if a change point has occurred.

[0053] Memory 620 and data storage 630 may include a computer-readable storage medium or one or more computer-readable storage media for storing computer-executable instructions or data structures. Such computer-readable storage media may be any available media that may be accessed by a general-purpose or special-purpose computer, such as, for example, processor 610. For example, memory 620 and / or data storage 630 may include high-dimensional dataset 105, quantum state 115, quantum circuit 125, and / or change point determination 135 of FIG. 1. In some embodiments, computing system 600 may or may not include any of memory 620 and data storage 630.

[0054] By way of example, and not limitation, such computer-readable storage media may include tangible or non-transitory computer-readable storage media, including random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), compact disk read-only memory (CD-ROM) or other optical disk storage, magnetic disk storage or other magnetic storage devices, flash memory devices (e.g., solid-state memory devices), or other storage media that can be used to store desired program code or data structures in the form of computer-executable instructions and that can be accessed by a general-purpose or special-purpose computer. Combinations of the above may also be included within the scope of computer-readable storage media. Computer-executable instructions may include, for example, instructions and data configured to cause the processor 610 to perform a particular process or group of processes.

[0055] The communication unit 640 may include any component, device, system, or combination thereof configured to transmit or receive information over a network. In some embodiments, the communication unit 640 may communicate with other devices at other locations or the same location, or with other components in the same system. For example, the communication unit 640 may include a modem, a network card (wireless or wired), an optical communication device, an infrared communication device, a wireless communication device (e.g., an antenna, etc.), and / or a chipset (e.g., a Bluetooth® device, an 802.6 device (e.g., a metropolitan area network (MAN)), a WiFi® device, a WiMax® device, a cellular communication facility, or the like), and / or the like. The communication unit 640 may enable data exchange with a network and / or any other device or system described in this disclosure. For example, the communication unit 640 may enable the system 600 to communicate with other systems, such as computing devices and / or other networks.

[0056] Those skilled in the art may recognize after reviewing this disclosure that modifications, additions, or omissions may be made to system 600 without departing from the scope of the disclosure. For example, system 600 may include more or fewer components than explicitly shown and described.

[0057] The above disclosure is not intended to limit the disclosure to the precise form or particular field of use disclosed. It is therefore contemplated that various alternative embodiments and / or modifications to the disclosure, whether expressly described or implied herein, may be made in light of the disclosure. Although embodiments of the disclosure have thus been described, it will be appreciated that changes may be made in form and detail without departing from the scope of the disclosure. The disclosure is therefore limited only by the claims.

[0058] In some embodiments, the various components, modules, engines, and services described herein may be implemented as multiple objects or processes executing (e.g., as separate threads) on a computer system. Although some of the systems and processes described herein are generally described as being implemented in software (stored on and / or executed by general-purpose hardware), specific hardware implementations, or combinations of software and specific hardware implementations, are also possible and contemplated.

[0059] The terms used in this disclosure, and particularly in the appended claims (e.g., the body of the appended claims), are generally intended to be "open language" (e.g., the term "including..." should be interpreted as "including, but not limited to...").

[0060] Also, if a specific number of claim recitations to be introduced is intended, such intent will be expressly recited in the claim, and in the absence of such recitation, such intent does not exist. For example, as an aid to understanding, the claims attached below may include the use of the preamble phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed as meaning that the introduction of a claim recitation with the indefinite article "a" or "an" limits any particular claim that includes a claim recitation so introduced to an embodiment that includes only such recitations, even when the same claim includes the preamble phrases "at least one" and "one or more" and an indefinite article such as "a" or "an" (e.g., "a" and / or "an" should be construed to mean "at least one" or "one or more"). The same applies to the use of definite articles used to introduce claim recitations.

[0061] Moreover, even when a specific number of claim recitations is explicitly recited, those skilled in the art will recognize that such recitation should be interpreted to mean at least the recited number (e.g., the bare recitation of "two things" without other modifiers means at least two things, or more than two things). Also, where traditional language similar to "at least one of A, B, and C, etc." or "one or more of A, B, and C, etc." is used, such construction is generally intended to include A only, B only, C only, A and B together, A and C together, B and C together, or A, B, and C together, etc.

[0062] Also, a disjunctive term or phrase preceding two or more other terms, whether in the description of the embodiments, the claims, or the drawings, should be understood to contemplate the possibility of including one of those terms, either of those terms, or both of those terms. For example, the phrase "A or B" should be understood to include the possibilities of "A" or "B" or "A and B."

[0063] All examples and conditional language described in this disclosure are intended for educational purposes to assist the reader in understanding the disclosure and the concepts provided by the inventors of this application to advance the art, and should not be construed as limitations to the examples and conditions specifically described as such. Although the embodiments of the present disclosure have been described in detail, various modifications, substitutions, and alterations may be made to these embodiments without departing from the spirit and scope of the present disclosure.

[0064] In addition to the above description, the following notes are also disclosed. (Supplementary Note 1) Obtaining a first quantum state representing a first data subset of a multivariate data set describing a plurality of data samples with respect to a plurality of variables; obtaining a second quantum state representing a second data subset of the multivariate data set; constructing a quantum circuit including an ancillary qubit initialized to a 0 state, a first qubit including the first quantum state, and a second qubit including the second quantum state; applying a first Hadamard transform to the ancillary qubit, the first Hadamard transform returning a particular value resulting in swapping the first qubit and the second qubit; in response to the first Hadamard transform returning the particular value, permuting the first qubit and the second qubit such that the second qubit represents the first quantum state and the first qubit represents the second quantum state; applying a second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; in response to the measurement being observed to have a value of zero, determining that no change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset. How to have that. (Supplementary Note 2) applying the second Hadamard transform to the ancillary qubit and observing a second measurement result; determining that a change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset in response to the second measurement being observed as having a value of one. 2. The method of claim 1, further comprising: (Supplementary Note 3) applying the second Hadamard transform to the ancillary qubit and observing a third measurement result; determining that a change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset in response to the third measurement being observed as having a value of zero. 2. The method of claim 1, further comprising: (Supplementary Note 4) Obtaining a third quantum state representing a third data subset of the multivariate data set; configuring the quantum circuit to include a third qubit that includes the third quantum state; applying the first Hadamard transform to the ancillary qubit, and failure of the first Hadamard transform to return the particular value results in the first qubit, the second qubit, and the third qubit being unpermuted. 2. The method of claim 1, further comprising: (Supplementary Note 5) obtaining a third quantum state representing a third data subset of the multivariate data set; configuring the quantum circuit to include a third qubit that includes the third quantum state; applying the first Hadamard transform to the ancillary qubit, the first Hadamard transform returning the particular value resulting in swapping one or more quantum states associated with the first qubit, the second qubit, and the third qubit; in response to the first Hadamard transform returning the particular value, permuting the one or more quantum states associated with the first qubit, the second qubit, and the third qubit; applying the second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; in response to observing the measurement have a value of one, determining that a change-point has occurred between data samples corresponding to the swapped one or more quantum states associated with the first qubit, the second qubit, and the third qubit. 2. The method of claim 1, further comprising: (Supplementary Note 6) The method of Supplementary Note 1, wherein the first quantum state and the second quantum state are obtained as portions of a data stream in which the first quantum state and the second quantum state are encrypted when obtained and are discarded after observing the measurement result. (Supplementary Note 7) The method of Supplementary Note 1, wherein the first data subset includes data samples classified as normal data, and the second data subset includes data samples classified as abnormal data. (Supplementary Note 8) One or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause a system to perform a process, the process comprising: obtaining a first quantum state representing a first data subset of a multivariate data set describing a plurality of data samples with respect to a plurality of variables; obtaining a second quantum state representing a second data subset of the multivariate data set; constructing a quantum circuit including an ancillary qubit initialized to a 0 state, a first qubit including the first quantum state, and a second qubit including the second quantum state; applying a first Hadamard transform to the ancillary qubit, the first Hadamard transform returning a particular value resulting in swapping the first qubit and the second qubit; in response to the first Hadamard transform returning the particular value, permuting the first qubit and the second qubit such that the second qubit represents the first quantum state and the first qubit represents the second quantum state; applying a second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; in response to the measurement being observed to have a value of zero, determining that no change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset. One or more non-transitory computer-readable storage media. (Supplementary Note 9) The process further comprises: applying the second Hadamard transform to the ancillary qubit and observing a second measurement; determining that a change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset in response to the second measurement being observed as having a value of one. 9. One or more non-transitory computer-readable storage media as recited in claim 8, (Supplementary Note 10) The process further comprises: applying the second Hadamard transform to the ancillary qubit and observing a third measurement; determining that a change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset in response to the third measurement being observed as having a value of zero. 9. One or more non-transitory computer-readable storage media as recited in claim 8, (Supplementary Note 11) The process further comprises: obtaining a third quantum state representing a third data subset of the multivariate data set; configuring the quantum circuit to include a third qubit that includes the third quantum state; applying the first Hadamard transform to the ancillary qubit, and failure of the first Hadamard transform to return the particular value results in the first qubit, the second qubit, and the third qubit being unpermuted. 9. One or more non-transitory computer-readable storage media as recited in claim 8, (Supplementary Note 12) The process further comprises: obtaining a third quantum state representing a third data subset of the multivariate data set; configuring the quantum circuit to include a third qubit that includes the third quantum state; applying the first Hadamard transform to the ancillary qubit, the first Hadamard transform returning the particular value resulting in swapping one or more quantum states associated with the first qubit, the second qubit, and the third qubit; in response to the first Hadamard transform returning the particular value, permuting the one or more quantum states associated with the first qubit, the second qubit, and the third qubit; applying the second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; in response to observing the measurement have a value of one, determining that a change-point has occurred between data samples corresponding to the swapped one or more quantum states associated with the first qubit, the second qubit, and the third qubit. 9. One or more non-transitory computer-readable storage media as recited in claim 8, (Supplementary Note 13) One or more non-transitory computer-readable storage media described in Supplementary Note 8, wherein the first quantum state and the second quantum state are obtained as portions of a data stream in which the first quantum state and the second quantum state are encrypted when obtained and are discarded after observing the measurement result. (Supplementary Note 14) The one or more non-transitory computer-readable storage media of Supplementary Note 8, wherein the data samples are included in the first data subset or the second data subset based on a predetermined classification of the data samples as normal data or abnormal data, and data samples classified as normal data are included in the first data subset and data samples classified as abnormal data are included in the second data subset. (Supplementary Note 15) A system comprising: one or more processors; one or more non-transitory computer-readable storage media configured to store instructions; having The instructions, in response to being executed, cause the system to perform a process, the process comprising: obtaining a first quantum state representing a first data subset of a multivariate data set describing a plurality of data samples with respect to a plurality of variables; obtaining a second quantum state representing a second data subset of the multivariate data set; constructing a quantum circuit including an ancillary qubit initialized to a 0 state, a first qubit including the first quantum state, and a second qubit including the second quantum state; applying a first Hadamard transform to the ancillary qubit, the first Hadamard transform returning a particular value resulting in swapping the first qubit and the second qubit; in response to the first Hadamard transform returning the particular value, permuting the first qubit and the second qubit such that the second qubit represents the first quantum state and the first qubit represents the second quantum state; applying a second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; in response to the measurement being observed to have a value of zero, determining that no change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset. Having that, system. (Supplementary Note 16) The process further comprises: applying the second Hadamard transform to the ancillary qubit and observing a second measurement; determining that a change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset in response to the second measurement being observed as having a value of one. 16. The system of claim 15, comprising: (Supplementary Note 17) The process further comprises: applying the second Hadamard transform to the ancillary qubit and observing a third measurement; determining that a change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset in response to the third measurement being observed as having a value of zero. 16. The system of claim 15, comprising: (Appendix 18) The process further comprises: obtaining a third quantum state representing a third data subset of the multivariate data set; configuring the quantum circuit to include a third qubit that includes the third quantum state; applying the first Hadamard transform to the ancillary qubit, and failure of the first Hadamard transform to return the particular value results in the first qubit, the second qubit, and the third qubit being unpermuted. 16. The system of claim 15, comprising: (Supplementary Note 19) The process further comprises: obtaining a third quantum state representing a third data subset of the multivariate data set; configuring the quantum circuit to include a third qubit that includes the third quantum state; applying the first Hadamard transform to the ancillary qubit, the first Hadamard transform returning the particular value resulting in swapping one or more quantum states associated with the first qubit, the second qubit, and the third qubit; in response to the first Hadamard transform returning the particular value, permuting the one or more quantum states associated with the first qubit, the second qubit, and the third qubit; applying the second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; in response to observing the measurement have a value of one, determining that a change-point has occurred between data samples corresponding to the swapped one or more quantum states associated with the first qubit, the second qubit, and the third qubit. 16. The system of claim 15, comprising: (Supplementary Note 20) The system of Supplementary Note 15, wherein the first quantum state and the second quantum state are acquired as portions of a data stream in which the first quantum state and the second quantum state are encrypted when acquired and are discarded after observing the measurement result.

Claims

1. obtaining a first quantum state representing a first data subset of a multivariate data set describing a plurality of data samples with respect to a plurality of variables; obtaining a second quantum state representing a second data subset of the multivariate data set; constructing a quantum circuit including an ancillary qubit initialized to a 0 state, a first qubit including the first quantum state, and a second qubit including the second quantum state; applying a first Hadamard transform to the ancillary qubit, the first Hadamard transform returning a particular value resulting in swapping the first qubit and the second qubit; in response to the first Hadamard transform returning the particular value, swapping the first qubit and the second qubit such that the second qubit represents the first quantum state and the first qubit represents the second quantum state; applying a second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; determining that no change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset in response to the measurement being observed to have a value of zero. How to have that.

2. applying the second Hadamard transform to the ancillary qubit and observing a second measurement; determining that a change-point has occurred between data samples corresponding to the first data subset and data samples corresponding to the second data subset in response to the second measurement being observed as having a value of one. The method of claim 1 further comprising:

3. applying the second Hadamard transform to the ancillary qubit and observing a third measurement; determining that a change-point has occurred between data samples corresponding to the first data subset and data samples corresponding to the second data subset in response to the third measurement being observed to have a value of zero. The method of claim 1 further comprising:

4. obtaining a third quantum state representing a third data subset of the multivariate data set; configuring the quantum circuit to include a third qubit that includes the third quantum state; applying the first Hadamard transform to the ancillary qubit, and failure of the first Hadamard transform to return the particular value results in the first qubit, the second qubit, and the third qubit being unpermuted. The method of claim 1 further comprising:

5. obtaining a third quantum state representing a third data subset of the multivariate data set; configuring the quantum circuit to include a third qubit that includes the third quantum state; applying the first Hadamard transform to the ancillary qubit, the first Hadamard transform returning the particular value, resulting in swapping one or more quantum states associated with the first qubit, the second qubit, and the third qubit; in response to the first Hadamard transform returning the particular value, swapping the one or more quantum states associated with the first qubit, the second qubit, and the third qubit; applying the second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; in response to observing the measurement have a value of one, determining that a change point has occurred between data samples corresponding to the swapped one or more quantum states associated with the first qubit, the second qubit, and the third qubit. The method of claim 1 further comprising:

6. 2. The method of claim 1 , wherein the first quantum state and the second quantum state are obtained as portions of a data stream in which the first quantum state and the second quantum state are encrypted when obtained and are discarded after observing the measurement.

7. The method of claim 1 , wherein the first data subset includes data samples classified as normal data and the second data subset includes data samples classified as abnormal data.

8. One or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause the system to perform an operation, the operation including: obtaining a first quantum state representing a first data subset of a multivariate data set describing a plurality of data samples with respect to a plurality of variables; obtaining a second quantum state representing a second data subset of the multivariate data set; constructing a quantum circuit including an ancillary qubit initialized to a 0 state, a first qubit including the first quantum state, and a second qubit including the second quantum state; applying a first Hadamard transform to the ancillary qubit, the first Hadamard transform returning a particular value resulting in swapping the first qubit and the second qubit; in response to the first Hadamard transform returning the particular value, swapping the first qubit and the second qubit such that the second qubit represents the first quantum state and the first qubit represents the second quantum state; applying a second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; determining that no change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset in response to the measurement being observed to have a value of zero. One or more non-transitory computer readable storage media.

9. 1. A system comprising: one or more processors; one or more non-transitory computer-readable storage media configured to store instructions; having The instructions, in response to being executed, cause the system to perform a process, the process comprising: obtaining a first quantum state representing a first data subset of a multivariate data set describing a plurality of data samples with respect to a plurality of variables; obtaining a second quantum state representing a second data subset of the multivariate data set; constructing a quantum circuit including an ancillary qubit initialized to a 0 state, a first qubit including the first quantum state, and a second qubit including the second quantum state; applying a first Hadamard transform to the ancillary qubit, the first Hadamard transform returning a particular value resulting in swapping the first qubit and the second qubit; in response to the first Hadamard transform returning the particular value, swapping the first qubit and the second qubit such that the second qubit represents the first quantum state and the first qubit represents the second quantum state; applying a second Hadamard transform to the ancillary qubit and observing a measurement result of the second Hadamard transform; determining that no change-point has occurred between the data samples corresponding to the first data subset and the data samples corresponding to the second data subset in response to the measurement being observed to have a value of zero. Having that, system.

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