Quantum metric learning method based on fuzzy learning

Abstract

The present invention discloses a quantum metric learning method based on fuzzy learning, which belongs to the field of quantum machine learning technology, and includes the following steps: obtaining input features and converting them into fuzzy sets; processing uncertainty features in fuzzy sets through fuzzy components; integrating original features and fuzzy information to reduce uncertainty information in data; and using the integrated information as input of quantum feature mapping for quantum metric learning. In the present invention, through the designed fuzzy components, it is possible to process uncertainty features in real data sets, reduce data uncertainty and ambiguity caused by factors such as noise, and at the same time, it can also make up for some effective information that may be lost during data preprocessing, improve the robustness of the model, and through the fuzzy components, it is possible to effectively extract high-order potential fuzzy features, which provides a powerful supplement for the deep-level information of the data and further enhances the recognition and classification capabilities of the model.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantum machine learning, and in particular relates to a quantum metric learning method based on fuzzy learning. Background Art

[0002] Quantum machine learning combines the algorithmic principles of traditional machine learning with the powerful computing power of quantum computing, aiming to fully utilize the advantages of quantum systems to accelerate data processing and model training. This combination not only allows for more efficient processing of big data, but also provides a new way to explore data.

[0003] We are currently in a special period of quantum technology development, known as the noisy intermediate quantum era. During this period, although existing quantum devices cannot achieve large-scale, high-precision calculations, they are powerful enough to perform some specific tasks. Among them, variational quantum algorithms have emerged and become the core strategy of quantum machine learning. This algorithm relies on the close interaction between classical and quantum systems, and adjusts the parameters in the quantum circuit through classical optimization algorithms to achieve specific learning and optimization tasks.

[0004] Quantum metric learning, as a specific application of variational quantum algorithms, focuses on the problem of data classification in Hilbert space. The core idea is to maximize the Hilbert-Schmidt distance, thereby effectively quantum embedding the data samples and ensuring that different categories of data are clearly separated in the Hilbert space. This approach not only allows for easy and efficient classification, but also helps to identify complex decision boundaries in the original feature space.

[0005] Although quantum metric learning has great potential, there are also certain challenges and limitations when processing real data. For example, in low-dimensional data modeling, feature vectors are often directly input into quantum circuits. This direct processing method may not take into account the noise in the original data and may also miss some key features. For high-dimensional data sets, the current main strategy is to first reduce the dimension or use deep neural networks to extract features, and then input the processed data into the quantum circuit. This preprocessing process may cause some effective information in the original features to be lost, especially in dynamic environments. Directly encoding the feature extraction results into the quantum system may not be the best choice. These potential feature problems bring challenges, especially in practical problems, where uncertainty and noise may have a significant impact on the results, hindering the progress of data-driven machine learning. In addition, similar to classical neural networks, its training process is like a black box and lacks interpretability. This poses a huge challenge to quantum metric learning based on understanding data. Summary of the invention

[0006] The purpose of the present invention is to propose a quantum metric learning method based on fuzzy learning in order to solve the problems of noise and feature ambiguity that may be encountered in quantum metric learning when processing actual data.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A quantum metric learning method based on fuzzy learning includes the following steps: obtaining input features and converting them into fuzzy sets; processing uncertainty features in the fuzzy sets through fuzzy components; the fuzzy components include a fuzzy layer, an uncertainty measurement layer and an information fusion layer; the fuzzy layer is used to convert the input features into fuzzy sets described by Gaussian membership functions; the uncertainty measurement layer is used to quantify the inherent relationship between the fuzziness and uncertainty of the features; the information fusion layer is used to integrate the original features and fuzzy information to reduce the uncertain information in the data; and the integrated information is used as the input of quantum feature mapping to perform quantum metric learning.

[0009] As a further description of the above technical solution:

[0010] The specific steps of converting the input features into the fuzzy set described by the Gaussian membership function include:

[0011] For any input feature vector , each feature is mapped to a fuzzy set, which is converted into a fuzzy region;

[0012] The five language values ​​of "very poor", "poor", "average", "good" and "very good" are respectively mapped to {0, 0.25, 0.5, 0.75, 1.0} to establish the evaluation criteria;

[0013] The membership function is defined as:

[0014]

[0015] in represents the fuzziness of the output, and denote the center and width parameters of the Gaussian membership function, respectively. and Determined based on the clustering results of the input data and trained through a neural network;

[0016] is the corresponding fixed center value {0, 0.25, 0.5, 0.75, 1.0};

[0017] Each input variable is divided into five intervals, each interval corresponds to a Gaussian fuzzy membership function described by language, and the input space is converted into a fuzzy area that can be explained by language.

[0018] As a further description of the above technical solution:

[0019] It also includes normalizing the blur by the formula:

[0020]

[0021] The fuzzy feature representation of features in different categories is calculated through the "OR" fuzzy logic operation to retain important information while suppressing irrelevant features;

[0022] The specific calculation formula is as follows:

[0023]

[0024] in, Indicates The maximum fuzziness of a feature in all categories, Corresponds to The category that reaches the maximum value.

[0025] As a further description of the above technical solution:

[0026] The steps to quantify the inherent relationship between ambiguity and uncertainty include: When it is close to 0 or 1, the feature clearly does not belong to or completely belongs to a category, and the uncertainty is low;

[0027] When the fuzziness is close to 0.5, it indicates higher uncertainty and the feature belongs to multiple categories at the same time;

[0028] The uncertainty is quantified for each feature by the following formula :

[0029] .

[0030] As a further description of the above technical solution:

[0031] The step of integrating the original features and fuzzy information in the information fusion layer includes: converting the fuzziness of each feature and uncertainty With the corresponding input features Perform the fusion as follows:

[0032]

[0033] in In the quantum circuit The layer should be embedded in input variables.

[0034] As a further description of the above technical solution:

[0035] The integrated information is used as the input of quantum feature mapping for quantum metric learning. The specific steps include: using A quantum feature mapping circuit for a scene with 1 input;

[0036] The quantum circuit is composed of It consists of trainable layers;

[0037] In each trainable layer, first use The gate encodes the input features;

[0038] Then, trainable ZZ entanglement is imposed between each pair of adjacent qubits;

[0039] In this strategy, each qubit is entangled with its neighboring qubits, and the first and last bits also form a closed loop;

[0040] Next, a trainable parameter revolving door;

[0041] After completing all After training layers, use The gate encodes the raw input features.

[0042] As a further description of the above technical solution:

[0043] The training process for quantum metric learning specifically includes the following steps:

[0044] Input data: Contains training data set , the quantum feature mapping , the number of training cycles , batch size , learning rate and optimizer ;

[0045] Training Dataset Include Data ,in is the input data, is its corresponding label, the quantum feature map , which will input data Mapping to the quantum domain;

[0046] The specific form and parameters of the mapping are given by and Sure;

[0047] Number of training cycles Used to determine the number of traversals of the entire training set;

[0048] Batch size Used to determine the number of samples drawn from the training data set during the next iteration or update;

[0049] Learning Rate Used to control the step size of model parameter updates;

[0050] Optimizer Used to update model parameters according to the calculated cost function;

[0051] Initialization process: Initialize the parameters in the quantum feature map. Initialization includes the following two steps: Parameters Random initialization of: First, Assign random initial values ​​to ensure that the model starts learning from a diverse state;

[0052] Initialization using K-means method and : Using K-means method in training data set Clustering is performed on and Assign initial values ​​to match the distribution of training data to ensure that the model is in a suitable state when training begins;

[0053] Parameter updating process: After completing the definition of input data and initialization of parameters, the core training process of the model is carried out. The core training process of the model specifically includes updating the parameters. After the parameter update reaches the preset stopping standard, the training of quantum metric learning is completed.

[0054] As a further description of the above technical solution:

[0055] The updating of the core training process parameters of the model specifically includes the following steps:

[0056] Batch data generation: In each training cycle In the default batch size Randomly select a subset from the training dataset ;

[0057] Calculation of ambiguity and uncertainty: For subsets For each input in, the fuzziness is calculated through the fuzzy layer and the uncertainty measurement layer. and uncertainty ;

[0058] Input calculation of quantum feature map: Based on the ambiguity and uncertainty , calculating the input value of the quantum feature map for each input in the subset according to the information fusion layer;

[0059] Calculation of cost function: Based on the current batch subset And the model parameters and , calculate the value of the cost function;

[0060] Model parameter update: Use the preset optimizer and learning rate to update the model parameters according to the calculated cost function;

[0061] The cost function is calculated as follows:

[0062]

[0063] in Represents the overall category of data, Indicates categories of quantum states; the purpose of the cost function is to maximize the distance between quantum states of different categories in the Hilbert space;

[0064] in, is the penalty coefficient, which is used to enhance the separation of different categories in the Hilbert space by the quantum feature map, and is used to pass the cost function Encourage greater distance between states in different categories and ensure closer proximity of states within each category.

[0065] As a further description of the above technical solution:

[0066] It also includes optimizing the cost function by updating the parameters of the model;

[0067] Parameters can be divided into two categories: quantum circuit parameters and classical parameters;

[0068] The quantum circuit parameter gradients are obtained by finite differences or parameter displacement rules;

[0069] Classical parameters, i.e. Gaussian parameters in the fuzzy component and , the gradient is calculated by the classical back-propagation method;

[0070] After calculating the gradient, the preset optimizer and learning rate are used to update the parameters through multiple iterations until the preset stopping criteria is reached.

[0071] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0072] 1. In the present invention, the designed fuzzy components can process the uncertainty characteristics in the real data set and reduce the data uncertainty and ambiguity caused by factors such as noise. At the same time, it can also make up for some effective information that may be lost in the data preprocessing process and improve the robustness of the model. Through the fuzzy components, high-order potential fuzzy features can be effectively extracted, which provides a powerful supplement for the deep-level information of the data and further enhances the recognition and classification capabilities of the model.

[0073] 2. In the present invention, fuzzy rules are used to provide intuitive and interpretable results, so that researchers can have a deeper understanding of the feature selection mechanism in the quantum mapping process, which promotes the transparency and interpretability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 A schematic diagram of a quantum feature mapping circuit for a quantum metric learning method based on fuzzy learning proposed in the present invention. DETAILED DESCRIPTION

[0075] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0076] Firstly, the computational framework proposed in this invention is introduced. Figure 1 As shown in Figure 2, the model data is processed using the proposed fuzzy component to obtain a complete embedded representation, which is then used as the input of the quantum feature map. The fuzzy component mainly includes a fuzzy layer, an uncertainty measurement layer, and an information fusion layer.

[0077] Below, in order to facilitate those skilled in the art to understand and implement the present invention, the specific conditions of the above-mentioned fuzzy layer, uncertainty measurement layer, information fusion layer and quantum feature mapping are further described in detail:

[0078] Fuzzy layer: Converts the input features into fuzzy sets described by Gaussian membership functions. Specifically, for any input feature vector , each feature is mapped to a fuzzy set, converting it into a fuzzy region.

[0079] This implementation example uses five language values ​​of "very bad", "bad", "medium", "good" and "very good", corresponding to {0, 0.25, 0.5, 0.75, 1.0} respectively, and establishes the corresponding evaluation criteria. The membership function is defined as:

[0080]

[0081] in represents the fuzziness of the output, and They represent the center and width parameters of the Gaussian membership function respectively. These two parameters can be determined according to the clustering results of the input data and trained through a neural network. The corresponding fixed center value is {0, 0.25, 0.5, 0.75, 1.0}. In this way, each input variable is divided into five intervals, each interval corresponds to a Gaussian fuzzy membership function described by language, and the input space is converted into a fuzzy area that can be interpreted by language.

[0082] Then, this implementation example normalizes the ambiguity according to the following formula:

[0083]

[0084] Next, the “OR” fuzzy logic operation is used to calculate the fuzzy feature representation of the features under different categories. This helps to retain important information while suppressing irrelevant features. The specific calculation formula is as follows:

[0085]

[0086] in, Indicates The maximum fuzziness of a feature in all categories, Corresponds to The category that reaches the maximum value.

[0087] Uncertainty metric layer: used to quantify the inherent relationship between the ambiguity and uncertainty of a feature. When it is close to 0 or 1, it has low uncertainty because it clearly does not belong to or belongs completely to one category. In contrast, an ambiguity close to 0.5 indicates higher uncertainty because the feature may belong to multiple categories at the same time.

[0088] This implementation example quantifies the uncertainty for each feature using the following formula :

[0089]

[0090] Information fusion layer: Integrate the original features and fuzzy information to reduce the uncertainty in the data. and uncertainty With the corresponding input features Perform the fusion as follows:

[0091]

[0092] in In the quantum circuit The layer should be embedded in input variables.

[0093] Quantum feature mapping: Figure 1 The orange dashed box in the example shows the The quantum feature mapping circuit of the input scene. The quantum circuit consists of In each trainable layer, we first use The gate encodes the input features. Then, a trainable ZZ entanglement is imposed between each pair of adjacent qubits, where ZZ entanglement is a two-bit rotation gate that rotates around ZZ and makes the two qubits entangled. The ZZ interaction is achieved by utilizing a combination of two CNOT gates and a Z gate to generate entanglement between qubits.

[0094] In this strategy, each qubit is entangled with its neighboring qubits, and the first and last qubits also form a closed loop. Then, a trainable parameter is applied to each qubit. Revolving door. After training layers, use The gate encodes the raw input features.

[0095] In order to facilitate those skilled in the art to further understand the present invention, the following describes the training process of quantum metric learning according to the present invention. The training process mainly involves input data, initialization process and parameter update process.

[0096] Input data: Contains training data set , the quantum feature mapping , the number of training cycles ; Batch size ; Learning rate and optimizer . Training Dataset Include Data ,in is the input data, is its corresponding label. The quantum feature mapping , which will input data Mapped to the quantum domain. The specific form and parameters of the mapping are given by and OK. Number of training cycles Used to determine how many times the entire training set will be traversed. Used to determine the number of samples drawn from the training data set at the next iteration or update. Used to control the step size of model parameter updates. Used to update model parameters according to the calculated cost function.

[0097] Initialization process: appropriately initialize the parameters in the quantum feature map. Initialization includes the following two key steps: parameters Random initialization of: First, Assign random initial values ​​to ensure that the model starts learning from a diverse state; use the K-means method to initialize and : In order to better match the distribution of training data, this implementation example uses the K-means method to Clustering is performed on and Assign initial values. The above two steps ensure that the model is in a suitable state when training begins, which helps improve the efficiency and effectiveness of training.

[0098] Parameter update process: After completing the definition of input data and parameter initialization, the next step is the core training process of the model, in which the most critical step is parameter update. This process is described as follows:

[0099] Batch data generation: In each training cycle In the default batch size Randomly select a subset from the training dataset .

[0100] Calculation of ambiguity and uncertainty: For subsets For each input in, the fuzziness is calculated through the fuzzy layer and the uncertainty measurement layer. and uncertainty .

[0101] Input calculation of quantum feature map: Based on the ambiguity and uncertainty , the input value of the quantum feature map is calculated for each input in the subset according to the information fusion layer.

[0102] Calculation of cost function: Based on the current batch subset And the model parameters and , calculate the value of the cost function.

[0103] Model parameter update: Use the preset optimizer and learning rate to update the model parameters according to the calculated cost function. The cost function is calculated as follows:

[0104]

[0105] in Represents the overall category of data, Indicates The purpose of the cost function is to maximize the distance between quantum states of different categories in the Hilbert space. is a penalty coefficient, which is used to enhance the separation of different categories in the Hilbert space by the quantum eigenmap. In this way, the cost function Not only does it encourage greater distance between states in different categories, but it also ensures that states within each category are closer together.

[0106] In order to optimize this cost function, the parameters of the model need to be updated appropriately. These parameters can be divided into two categories: quantum circuit parameters and classical parameters. For quantum circuit parameters, their gradients are obtained by finite differences or parameter displacement rules. For classical parameters, i.e., Gaussian parameters in fuzzy components and , whose gradient is calculated by the classical back-propagation method.

[0107] Once the gradient is calculated, this implementation example uses the preset optimizer and learning rate to perform parameter updates.

[0108] This process will be repeated multiple times until a preset stopping criterion is reached, such as model convergence or reaching a set number of training rounds.

[0109] Implementations of the digital and / or quantum subject matter described in this specification may be implemented as one or more digital and / or quantum computer programs, i.e., one or more modules of digital and / or quantum computer program instructions encoded on a tangible, non-transitory storage medium for execution by a data processing apparatus or to control the operation of a data processing apparatus. The digital and / or quantum computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access storage device, one or more qubits, or a combination of one or more of them. Alternatively or additionally, the program instructions may be encoded on an artificially generated propagated signal capable of encoding digital and / or quantum information, e.g., a machine-generated electrical, optical or electromagnetic signal, which is generated to encode digital and / or quantum information, for transmission to a suitable receiver device for execution by the data processing apparatus;

[0110] For a system of one or more digital and / or quantum computers to be "configured to" perform a particular operation or action means that the system has installed thereon software, firmware, hardware, or a combination thereof that, in operation, causes the system to perform those operations or actions. One or more digital and / or quantum computer programs to be configured to perform a particular operation or action means that the one or more programs include instructions that, when executed by a digital and / or quantum data processing device, cause the device to perform the operation or action. A quantum computer may receive instructions from a digital computer that, when executed by the quantum computing device, cause the device to perform the operation or action;

[0111] The control of the various systems described in this specification or a portion thereof may be implemented in a digital and / or quantum computer program product, which includes instructions stored on one or more non-transitory machine-readable storage media and executable on one or more digital and / or quantum processing devices. The systems described in this specification or a portion thereof may each be implemented as an apparatus, method or system, which may include one or more digital and / or quantum processing devices and a memory storing executable instructions to perform the operations described in this specification.

[0112] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A quantum metric learning method based on fuzzy learning, characterized in that: The following steps are involved: Get the input features and convert them into fuzzy sets; Dealing with uncertainty characteristics in fuzzy sets through fuzzy components; The fuzzy component includes a fuzzy layer, an uncertainty measurement layer and an information fusion layer; The fuzzy layer is used to convert the input features into a fuzzy set described by a Gaussian membership function; The uncertainty measurement layer is used to quantify the inherent relationship between the ambiguity and uncertainty of the feature; The information fusion layer is used to integrate the original features and fuzzy information to reduce the uncertain information in the data; The integrated information is used as the input of quantum feature mapping for quantum metric learning; The integrated information is used as the input of quantum feature mapping for quantum metric learning. The specific steps include: using A quantum feature mapping circuit for a scene with 1 input; The quantum feature mapping circuit is composed of It consists of trainable layers; In each trainable layer, first use The gate encodes the input features; Then, trainable ZZ entanglement is imposed between each pair of adjacent qubits; In this strategy, each qubit is entangled with its neighboring qubits, and the first and last bits also form a closed loop; Next, a trainable parameter revolving door; After completing all After training layers, use The gate encodes the raw input features; The training process for quantum metric learning specifically includes the following steps: Input data: Contains training data set , the quantum feature mapping , the number of training cycles , batch size , learning rate and optimizer ; Training Dataset Include Data ,in is the input data, is its corresponding label, the quantum feature map , which will input data Mapping to the quantum domain; The specific form and parameters of the mapping are given by and Sure; Number of training cycles Used to determine the number of traversals of the entire training set; Batch size Used to determine the number of samples drawn from the training data set during the next iteration or update; Learning Rate Used to control the step size of model parameter updates; Optimizer Used to update model parameters according to the calculated cost function; Initialization process: Initialize the parameters in the quantum feature map. Initialization includes the following two steps: Parameters Random initialization of: First, Assign random initial values ​​to ensure that the model starts learning from a diverse state; Initialization using K-means method and : Using the K-means method in the training data set Clustering is performed on and Assign initial values ​​and initialize parameters to match the distribution of training data; Parameter update process: After completing the definition of input data and initialization of parameters, the core training process of the model is carried out. The core training process of the model specifically includes updating the parameters. After the parameter update reaches the preset stop standard, the training of quantum metric learning is completed; The updating of the core training process parameters of the model specifically includes the following steps: Batch data generation: In each training cycle In the default batch size Randomly select a subset from the training dataset ; Calculation of ambiguity and uncertainty: For subsets For each input in, the fuzziness is calculated through the fuzzy layer and the uncertainty measurement layer. and uncertainty ; Input calculation of quantum feature map: Based on the ambiguity and uncertainty , calculating the input value of the quantum feature map for each input in the subset according to the information fusion layer; Calculation of cost function: Based on the current batch subset And the model parameters and , calculate the value of the cost function; Model parameter update: Use the preset optimizer and learning rate to update the model parameters according to the calculated cost function; The cost function is calculated as follows: ； in Represents the overall category of data, Indicates categories of quantum states; the purpose of the cost function is to maximize the distance between quantum states of different categories in the Hilbert space; in, is the penalty coefficient, which is used to enhance the separation of different categories in the Hilbert space by the quantum feature map, and is used to pass the cost function Encourage greater distance between states in different categories and ensure closer proximity of states within each category.

2. A quantum metric learning method based on fuzzy learning according to claim 1, characterized in that: The specific steps of converting the input features into the fuzzy set described by the Gaussian membership function include: For any input feature vector , each feature is mapped to a fuzzy set, which is converted into a fuzzy region; The five language values ​​of "very poor", "poor", "average", "good" and "very good" are respectively mapped to {0, 0.25, 0.5, 0.75, 1.0} to establish the evaluation criteria; The membership function is defined as: ； in represents the fuzziness of the output, and denote the center and width parameters of the Gaussian membership function, respectively. and Determined based on the clustering results of the input data and trained through a neural network; is the corresponding fixed center value {0, 0.25, 0.5, 0.75, 1.0}; Each input variable is divided into five intervals, each interval corresponds to a Gaussian fuzzy membership function described by language, and the input space is converted into a fuzzy area that can be explained by language.

3. A quantum metric learning method based on fuzzy learning according to claim 2, characterized in that: It also includes normalizing the blur by the formula: ； The fuzzy feature representation of features in different categories is calculated through "OR" fuzzy logic operation, which is used to retain important information while suppressing irrelevant features; The specific calculation formula is as follows: ； in, Indicates The maximum fuzziness of a feature in all categories, Corresponds to The category that reaches the maximum value.

4. The quantum metric learning method based on fuzzy learning according to claim 1, characterized in that: The steps to quantify the inherent relationship between ambiguity and uncertainty include: When it is close to 0 or 1, the feature clearly does not belong to or completely belongs to a category, and the uncertainty is low; When the fuzziness is close to 0.5, it indicates higher uncertainty and the feature belongs to multiple categories at the same time; The uncertainty is quantified for each feature by the following formula : 。 5. The quantum metric learning method based on fuzzy learning according to claim 1, characterized in that: The step of integrating the original features and fuzzy information in the information fusion layer includes: converting the fuzziness of each feature and uncertainty With the corresponding input features Perform the fusion as follows: ； in In the quantum circuit The layer should be embedded in input variables.

6. The quantum metric learning method based on fuzzy learning according to claim 1, characterized in that: It also includes optimizing the cost function by updating the parameters of the model; Parameters are divided into two categories: quantum circuit parameters and classical parameters; The quantum circuit parameter gradients are obtained by finite differences or parameter displacement rules; Classical parameters, i.e. Gaussian parameters in the fuzzy component and , the gradient is calculated by the classical back-propagation method; After calculating the gradient, the preset optimizer and learning rate are used to update the parameters through multiple iterations until the preset stopping criteria is reached.

7. A device comprising: One or more classical processors; and one or more quantum computing devices in data communication with the one or more classical processors, wherein the quantum computing devices include: one or more qubit registers, each qubit register comprising one or more qubits, and a plurality of control devices configured to operate one or more qubit registers; The device is configured to execute the method according to any one of claims 1 to 6.

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