Three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit

Abstract

The present invention discloses a three-dimensional point cloud data classification method based on a rotationally invariant parameterized quantum circuit, comprising: obtaining three-dimensional point cloud data, encoding the three-dimensional point cloud data into a quantum circuit using an angle embedding method; constructing a rotationally invariant parameterized quantum circuit; obtaining an output expected value using a rotationally invariant measurement operator, calculating the difference using a loss function and updating the parameters until convergence; and classifying the three-dimensional point cloud data using a trained rotationally invariant parameterized quantum circuit, and outputting the classification result. Based on the three-dimensional point cloud data classification method using a rotationally invariant parameterized quantum circuit, the present invention designs a new rotationally invariant parameterized quantum circuit, which is a novel quantum circuit that can be scalably applied to point cloud data classification. The present invention incorporates the rotational symmetry of point cloud data into circuit design, so that the function coverage space of the designed circuit has an inductive bias, thereby achieving better generalization performance even with fewer parameters.

Description

Technical Field

[0001] The present invention relates to the field of quantum machine learning, and in particular to a three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuits. Background Art

[0002] In recent years, quantum computing has ushered in a new paradigm for machine learning, giving rise to quantum machine learning, which has been widely applied to various tasks, including image recognition, data classification, time series prediction, biomedicine, and natural language processing. However, in the specific task of 3D point cloud data classification, existing research still primarily focuses on classical machine learning methods.

[0003] In the task of classifying 3D point cloud data, obtained by laser scanning, the 3D model is represented as a discrete point cloud, with each point containing its 3D coordinates and possible other attributes. This task has been extensively studied in deep learning, leading to the development of numerous networks targeting this type of data, such as PointNet and PointNet++. Currently, research on quantum circuits for 3D point cloud data is still in its infancy, and efficient circuit designs for this type of data structure are relatively scarce.

[0004] While some existing research has attempted to apply quantum computing to point cloud data processing, these efforts typically fail to fully exploit the rotational symmetries of point cloud data, resulting in complex circuit designs and a large number of parameters, hindering the model's generalization and computational efficiency. Furthermore, these studies often fail to optimize designs for specific symmetry groups, resulting in poor circuit performance when processing point cloud data with specific symmetries. Summary of the Invention

[0005] The present invention aims to solve one of the technical problems existing in the related art at least to a certain extent.

[0006] The purpose of the present invention is to provide a three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuits. The rotational equivariant parameterized quantum circuits are designed by combining the structural characteristics of point clouds with the advantages of quantum computing, and are applied to the classification task of three-dimensional point cloud data to achieve efficient classification of three-dimensional point cloud data.

[0007] In order to achieve the above-mentioned object, the present invention provides a three-dimensional point cloud data classification method based on a rotational equivariant parameterized quantum circuit, comprising the following steps:

[0008] Acquire three-dimensional point cloud data, and encode the three-dimensional point cloud data into a quantum circuit using an angle embedding method;

[0009] Construct rotationally equivariant parameterized quantum circuits, including:

[0010] (a) Based on the basic representation of the SU(2) group, n singlet states are prepared as the initial state input circuit. The value of n is determined according to the circuit scale.

[0011] (b) Consider the tensor representation of the SU(2) group , use block diagonalization operation to transform the group representation, determine the generators that commutate with each subspace representation in the block diagonalized space, and select some generators to construct an equivariant gate set;

[0012] (c) Using data retransmission to alternately set the coding layer and parameterization layer, repeating several times to form a multi-layer structure;

[0013] Use the rotation-invariant measurement operator to obtain the expected output value, calculate the difference through the loss function and update the parameters until convergence;

[0014] The trained rotation-equivariant parameterized quantum circuit is used to classify the three-dimensional point cloud data and output the classification results.

[0015] A further preferred technical solution of the present invention is that the three-dimensional point cloud data is encoded into the quantum circuit by using an angle embedding method, specifically:

[0016] The three-dimensional coordinates of each data point are encoded onto the rotation phase of the revolving door. The encoding method is expressed as:

[0017] ;

[0018] in, represents the Cartesian coordinates of the data point, X, Y, Z represent the Pauli X, Y, Z matrices respectively, is the imaginary unit, Indicates data encoding;

[0019] This encoding method maps three-dimensional point cloud data onto the Bloch sphere of quantum bits, and the corresponding group representation is converted into the basic representation of the SU(2) group.

[0020] Preferably, the basic representation based on the SU(2) group is used to prepare n singlet states as the initial state input circuit of the circuit, and the specific method is:

[0021] Considering the rotational invariance of three-dimensional point cloud data, corresponding to the singlet state of the SU(2) group in quantum computing, the quantum bit is transformed from the initial state to the singlet state through different quantum gate combination operations.

[0022] As an advantage, the tensor representation of the SU(2) group is considered , use the block diagonalization operation to transform the group representation. In the block diagonalized space, determine the generators that commutate with each subspace representation, and select some generators to construct an equivariant gate set; specifically:

[0023] Apply the matrix transformation W to represent the tensor of the SU(2) group Convert it into block diagonal form, divide it into 3-dimensional symmetric subspace and 1-dimensional antisymmetric subspace, and realize the block diagonalization operation of group representation, which can be expressed as:

[0024] ;

[0025] in, is an irreducible representation of 3*3, is an irreducible representation of 1*1, represents the conjugate transpose of the matrix transformation W;

[0026] In the symmetric subspace, diag(1, 1, 1,-3) is selected as the generator H of the rotationally equivariant parameterized quantum circuit to construct a parameterized unitary circuit. , ,in represents the Pauli Z operator acting on the first bit, represents the Pauli Z operator acting on the second bit;

[0027] Work again , restore the block diagonal representation of the SU(2) group, and then act on the two qubits that were not originally entangled 、 as well as , establishing the entanglement relationship between all bits at the parameterized layer.

[0028] Preferably, the coding layer and the parameterization layer are alternately set in the form of data retransmission, and repeated several times to form a multi-layer structure, specifically:

[0029] Set the number of retransmissions L, the number of parameterized layer repetitions d, and alternately cycle the coding layer and parameterized layers , expressed as:

[0030] ;

[0031] in, Indicates data encoding, represents the action on each of the two quantum bits 、 as well as The combination is repeated L times to form the overall circuit.

[0032] Preferably, the method of using a rotationally invariant measurement operator to obtain an output expected value is as follows:

[0033] Use operators that satisfy the commutation relation As a local measurement operator on two quantum bits, its eigenvalues ​​are triple roots 1 and single roots -1, and the output value is in the interval [-1,1]; 、 、 、 A tensor of Pauli operators X, Y, Z, and I, acting on two bits.

[0034] As a preference, when calculating the difference and updating the parameters through the loss function, the mean square error is selected as the loss function, which is expressed as:

[0035] ;

[0036] in, is the circuit output, is the data label, x is the The data sampled in

[0037] Then, the parameters of the parameterized layer are updated through gradient descent using a classical optimizer, and the optimization is iterated continuously until the loss function value converges, completing the training of the rotationally equivariant parameterized quantum circuit.

[0038] Preferably, the application of the trained rotationally equivariant parameterized quantum circuit to classify the three-dimensional point cloud data and output the classification result is specifically:

[0039] Normalizing the 3D point cloud data to be classified, determining a normalization factor based on the characteristics of the data set so that the coordinates are in the interval [-π, π] to meet the requirements of rotational phase encoding; then encoding the 3D point cloud data into a quantum circuit to achieve data encoding from classical to quantum;

[0040] The output result is obtained through the trained rotation-equivariant parameterized quantum circuit, and a classification decision is made based on the output result to determine the category to which the data to be classified belongs. The classification result is output in the form of a label, and the label corresponds to the preset category label.

[0041] Another aspect of the present invention provides a non-transitory computer-readable storage medium having computer instructions stored thereon, which enable a computer to execute the above-mentioned three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit.

[0042] Yet another aspect of the present invention provides an electronic device comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus, and the processor calls logic instructions in the memory to execute the above-mentioned three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuits.

[0043] On the other hand, the present invention provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer executes the above-mentioned three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit.

[0044] Beneficial effects: Based on the three-dimensional point cloud data classification method of the rotation-equivariant parameterized quantum circuit, the present invention designs a new rotation-equivariant parameterized quantum circuit, which is a new quantum circuit that can be scalably applied to point cloud data classification; the present invention incorporates the rotational symmetry of point cloud data into the circuit design, so that the function coverage space of the designed circuit has an inductive bias, so that better generalization performance can be achieved with fewer parameters, while enhancing the robustness of the classification. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 The overall circuit of the rotationally equivariant parameterized quantum circuit of the present invention;

[0046] Figure 2 A quantum circuit for transforming a quantum bit from an initial state to a singlet state according to the present invention;

[0047] Figure 3 Matrix transformation for the present invention quantum circuits in action;

[0048] Figure 4 To realize the present invention Constructed quantum circuits;

[0049] Figure 5 This is a diagram showing the training results of the rotationally equivariant parameterized quantum circuit in Example 1;

[0050] Figure 6 This is a curve diagram of the classification results accuracy in Example 1;

[0051] Figure 7 The overall circuit for a general parameterized quantum circuit;

[0052] Figure 8 This is a performance comparison chart of the rotationally equivariant parameterized quantum circuit of the present invention and a general parameterized quantum circuit. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the embodiments described are part of the embodiments of the present invention, not all of the embodiments, and they should not be understood as limitations on the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0054] The following combination Figures 1-8 The present invention describes a three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit, a non-transitory computer-readable storage medium, an electronic device, and a computer program product.

[0055] Example 1: This example provides a three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuits.

[0056] First, we need to explain the process of quantum machine learning for supervised learning. The sampled data x and the corresponding label y(x) ={1, 2, n classes}, the classical data x is encoded and embedded into the data encoding layer of the parameterized quantum circuit, then passes through the parameterized layer, and finally the output expected value is measured, which is expressed as:

[0057] ;

[0058] in, represents the initial state, Indicates data encoding, represents the parameterized layer, represents the measurement operator, express The conjugate transpose of express The conjugate transpose of . The parameters of the parameterized layer are then updated based on the output expectation using a classical computer to calculate the gradient of the loss function.

[0059] The present invention focuses on constructing a rotationally equivariant parameterized quantum circuit, which adopts a data retransmission structure, that is, the data encoding layer and the parameterization layer are performed alternately.

[0060] The concept of equivariant embedding is involved in the data encoding layer. Equivariant embedding is the representation commutation of the encoding embedding function and the group operation, as shown in the following formula:

[0061] ;

[0062] in, It represents a group. is the density operator.

[0063] It also involves the concept of equivariant gates, that is, the parameterized layer and the group representation are commutative, as shown in the following formula:

[0064] ;

[0065] Finally, there are the concepts of unchanged initial state and unchanged measurement operator. The unchanged initial state means that the group does not change the initial state of the circuit, that is, , the invariant measurement operator is = .

[0066] Through the above four conditions, we can build an equivalent quantum machine learning model with inductive bias that encodes data symmetry, as shown in the following formula:

[0067] ;

[0068] This means that the output of this circuit is identical to the output of its symmetric data (e.g., rotationally symmetric, permutationally symmetric, or chirally symmetric). In this embodiment, the input features of the 3D point cloud data are limited to its 3D coordinates, making it rotationally invariant. This property is used to design a rotationally invariant circuit, which then measures the data to achieve an invariant output.

[0069] This example uses equivariant parameterized quantum circuits for the classification of spheres and toruses. The following is all done in Python using Pennylane (a quantum machine learning Python framework).

[0070] First, we need to construct a data set. For a 4-qubit circuit, each point is encoded on a qubit, so we need to randomly sample the sphere and the ring to get the 3D coordinates of the 4 points. The radius of the sphere is set to 1, the main radius of the ring is set to 1, and the minor radius is set to 0.5. To normalize it, we need to divide it by the normalization factor 1.28. Finally, all the data we get needs to be multiplied by Make it The intervals are aligned with the rotation phase, and this set of coordinates is considered a data point. The sampling frequency is set to 3000, and the input data samples and corresponding label arrays are obtained. The label for the sphere is set to -1, and the label for the ring is set to 1. At the same time, an arbitrary sample rotation matrix is ​​applied to the data to obtain a rotated copy of the data. This proves that the designed circuit is rotationally equivariant and its output is unchanged. Finally, the original dataset is split into training and test sets in a ratio of 0.8:0.2, with the copy dataset kept as a backup.

[0071] In the data encoding layer, the angle embedding method is used, that is, the data is encoded into the rotation phase of the revolving door. Each point cloud data is composed of a three-dimensional vector, so the following encoding method is used:

[0072] ;

[0073] in, represents the Cartesian coordinates of the data point, X, Y, Z represent the Pauli X, Y, Z matrices respectively, is the imaginary unit, Represents data encoding. It is known that the group corresponding to the rotation of three-dimensional data is the SO(3) group, which represents all rotations about the origin. After encoding and embedding into the rotation phase of the quantum gate, the three-dimensional data points are mapped to the Bloch sphere, and the corresponding group becomes the SU(2) group. That is, after a single data point is encoded and embedded into the quantum gate on a single bit, the corresponding group representation becomes the basic representation of SU(2). Therefore, according to the basic representation of the SU(2) group, an invariant initial state needs to be prepared. The singlet state singlet is an SU(2) invariant state. The SU(2) group representation only acts on the global phase and does not change the final measurement output expectation. n singlet states can be prepared as the initial state input circuit of the circuit. n is determined by the scale of the circuit. The quantum circuit to realize the singlet state is as follows: Figure 2 shown.

[0074] Then, we design an equivariant gate set based on the basic representation of the SU(2) group. Since only the unit matrix commutes with it, it is impossible to design an effective parameterized layer. The tensor representation of the group, that is, the tensor representation on two quantum bits To design equivariant circuits, this is because the rotation of a three-dimensional object is the same rotation matrix for each point, so the code is also the same after embedding. This embodiment considers the block diagonalization operation of the group representation and solves the equivariant gate set in the block diagonal space, thereby achieving the effect of simplifying the circuit.

[0075] The tensor representation of SU(2) is block diagonalizable, that is, the representation has a symmetric subspace and an antisymmetric subspace, then we only need to apply the matrix transformation By converting the standard basis to the basis of these two subspaces, the block diagonalization operation of the group representation can be realized. The block diagonalization operation is shown as follows:

[0076] ;

[0077] in is an irreducible representation of 3*3, is an irreducible representation of 1*1, Represents the conjugate transpose of the matrix transformation W.

[0078] Implementing matrix transformation The circuit that works like Figure 3 As shown. Then for this block diagonalized space, we can get the generator of the equivariant circuit. For the 3*3 symmetric subspace, the commutation is the scalar multiple of the 3*3 unit matrix, and for the 1*1 antisymmetric subspace, the commutation is the scalar value. Therefore, one is applied to every two quantum bits. After matrix transformation, select As the generator H of the circuit, construct a parameterized unitary circuit , to achieve the construction The quantum circuit is as follows Figure 4 As shown, because ,in represents the Pauli Z operator acting on the first bit, represents the Pauli Z operator acting on the second bit.

[0079] In order to establish entanglement between all quantum bits, it is necessary to act again Change the block diagonal representation of SU(2) back and then act on the two qubits that were not originally entangled. , ,as well as , thus establishing the entanglement relationship between all bits at the parameterized layer.

[0080] Next, the encoding layer and the parameterization layer are recycled, which can be summarized as follows:

[0081] ;

[0082] in, Indicates data encoding, represents the action on each of the two quantum bits 、 as well as The combination is repeated L times, where L is the preset number of layers, forming a Figure 1 The overall circuit shown in , Both operate on two bits, as described above. The parameterization layer can be repeated d times and the retransmission circuit can be repeated r times to improve the expressiveness of the circuit, depending on the scale of the problem.

[0083] Finally, the output is measured. The measurement operator must satisfy the commutation relationship, so ( + + + ) / 2 is a local measurement operator on two quantum bits, and its eigenvalues ​​are triple roots 1 and single roots -1, so the output value is in [-1,1], and the corresponding label setting should match it; 、 、 、 A tensor of Pauli operators X, Y, Z, and I, acting on two bits.

[0084] Based on the above circuit built based on pennylane, training is started, and the difference is calculated and the parameters are updated through the loss function. In this embodiment, the mean square error is selected as the loss function, which is expressed as:

[0085] ;

[0086] in, is the circuit output, is the data label, x is the The data sampled in

[0087] Then, the parameters of the parameterized layer are updated by gradient descent through the classic optimizer, and the optimization is iterated continuously. This embodiment uses adamOptimizer to optimize the parameters, setting , , batch_size is 32, the number of iterations is 2000, and the learning rate is 0.01. The results are as follows Figure 5 shown.

[0088] Until the loss function converges, the training of the rotation equivariant parameterized quantum circuit is completed. At this time, the trained equivariant parameterized quantum circuit becomes a quantum classifier. It only needs to input point cloud data to perform data classification. This embodiment is tested with a test set, and the test results are as follows Figure 6 As shown in Figure 3, a test accuracy of 95.2% was finally achieved.

[0089] The rotation-equivariant parameterized quantum circuit of the present invention is combined with Figure 7 The comparison of the fully entangled general parameterized quantum circuit is shown in Figure 8 As shown, it can be seen that the performance of the two is almost the same, but the quantum circuit set in this embodiment is 5 layers, with 8 parameters per layer, that is, the equivalent quantum circuit of this embodiment uses fewer parameters to achieve similar performance.

[0090] Embodiment 2: This embodiment provides a non-transitory computer-readable storage medium having computer instructions stored thereon, which enable a computer to execute a three-dimensional point cloud data classification method based on a rotational equivariant parameterized quantum circuit, the method comprising the following steps:

[0091] Acquire three-dimensional point cloud data, and encode the three-dimensional point cloud data into a quantum circuit using an angle embedding method;

[0092] Construct rotationally equivariant parameterized quantum circuits, including:

[0093] (a) Based on the basic representation of the SU(2) group, n singlet states are prepared as the initial state input circuit. The value of n is determined according to the circuit scale.

[0094] (b) Consider the tensor representation of the SU(2) group , use block diagonalization operation to transform the group representation, determine the generators that commutate with each subspace representation in the block diagonalized space, and select some generators to construct an equivariant gate set;

[0095] (c) Using data retransmission to alternately set the coding layer and parameterization layer, repeating several times to form a multi-layer structure;

[0096] Use the rotation-invariant measurement operator to obtain the expected output value, calculate the difference through the loss function and update the parameters until convergence;

[0097] The trained rotation-equivariant parameterized quantum circuit is used to classify the three-dimensional point cloud data and output the classification results.

[0098] Example 3: This embodiment provides an electronic device, which may include: a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other via the communications bus. The processor may call logic instructions in the memory to execute a three-dimensional point cloud data classification method based on a rotational equivariant parameterized quantum circuit, the method comprising the following steps:

[0099] Acquire three-dimensional point cloud data, and encode the three-dimensional point cloud data into a quantum circuit using an angle embedding method;

[0100] Construct rotationally equivariant parameterized quantum circuits, including:

[0101] (a) Based on the basic representation of the SU(2) group, n singlet states are prepared as the initial state input circuit. The value of n is determined according to the circuit scale.

[0102] (b) Consider the tensor representation of the SU(2) group , use block diagonalization operation to transform the group representation, determine the generators that commutate with each subspace representation in the block diagonalized space, and select some generators to construct an equivariant gate set;

[0103] (c) Using data retransmission to alternately set the coding layer and parameterization layer, repeating several times to form a multi-layer structure;

[0104] Use the rotation-invariant measurement operator to obtain the expected output value, calculate the difference through the loss function and update the parameters until convergence;

[0105] The trained rotation-equivariant parameterized quantum circuit is used to classify the three-dimensional point cloud data and output the classification results.

[0106] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0107] Embodiment 4: This embodiment provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can perform a three-dimensional point cloud data classification method based on a rotational equivariant parameterized quantum circuit. The method includes the following steps:

[0108] Acquire three-dimensional point cloud data, and encode the three-dimensional point cloud data into a quantum circuit using an angle embedding method;

[0109] Construct rotationally equivariant parameterized quantum circuits, including:

[0110] (a) Based on the basic representation of the SU(2) group, n singlet states are prepared as the initial state input circuit. The value of n is determined according to the circuit scale.

[0111] (b) Consider the tensor representation of the SU(2) group , use block diagonalization operation to transform the group representation, determine the generators that commutate with each subspace representation in the block diagonalized space, and select some generators to construct an equivariant gate set;

[0112] (c) Using data retransmission to alternately set the coding layer and parameterization layer, repeating several times to form a multi-layer structure;

[0113] Use the rotation-invariant measurement operator to obtain the expected output value, calculate the difference through the loss function and update the parameters until convergence;

[0114] The trained rotation-equivariant parameterized quantum circuit is used to classify the three-dimensional point cloud data and output the classification results.

[0115] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0116] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0117] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit, characterized in that: The following steps are involved: Acquire three-dimensional point cloud data, and encode the three-dimensional point cloud data into a quantum circuit using an angle embedding method; Construct rotationally equivariant parameterized quantum circuits, including: (a) Based on the basic representation of the SU(2) group, n singlet states are prepared as the initial state input circuit. The value of n is determined according to the circuit scale. (b) Consider the tensor representation of the SU(2) group , use the block diagonalization operation to transform the group representation. In the block diagonalized space, determine the generators that commutate with each subspace representation, and select some generators to construct an equivariant gate set; specifically: Applying a matrix transformation The tensor representation of the SU(2) group SU(2)⊗2 is converted into a block diagonal form, which is divided into a 3-dimensional symmetric subspace and a 1-dimensional antisymmetric subspace to implement the block diagonalization operation of the group representation, which can be expressed as: ； in, is an irreducible representation of 3*3, is an irreducible representation of 1*1, represents the conjugate transpose of the matrix transformation W; In the symmetric subspace, diag(1, 1, 1,-3) is selected as the generator H of the rotationally equivariant parameterized quantum circuit to construct a parameterized unitary circuit. , ,in represents the Pauli Z operator acting on the first bit, represents the Pauli Z operator acting on the second bit; Work again , restore the block diagonal representation of the SU(2) group, and then act on the two qubits that were not originally entangled 、 as well as , establish the entanglement relationship between all bits at the parameterized layer; (c) Using data retransmission to alternately set the coding layer and parameterization layer, repeating several times to form a multi-layer structure; Use the rotation-invariant measurement operator to obtain the expected output value, calculate the difference through the loss function and update the parameters until convergence; The trained rotation-equivariant parameterized quantum circuit is used to classify the three-dimensional point cloud data and output the classification results.

2. The three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit according to claim 1 is characterized in that: The three-dimensional point cloud data is encoded into the quantum circuit by using the angle embedding method, specifically: The three-dimensional coordinates of each data point are encoded onto the rotation phase of the revolving door. The encoding method is expressed as: ； in, represents the Cartesian coordinates of the data point, X, Y, Z represent the Pauli X, Y, Z matrices respectively, is the imaginary unit, Indicates data encoding; This encoding method maps three-dimensional point cloud data onto the Bloch sphere of quantum bits, and the corresponding group representation is converted into the basic representation of the SU(2) group.

3. The three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit according to claim 2 is characterized in that: The basic representation based on the SU(2) group is to prepare n singlet states as the initial state input circuit of the circuit. The specific method is: Considering the rotational invariance of three-dimensional point cloud data, corresponding to the singlet state of the SU(2) group in quantum computing, the quantum bit is transformed from the initial state to the singlet state through different quantum gate combination operations.

4. The three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit according to claim 1 is characterized in that: The data retransmission method is used to alternately set the coding layer and the parameterization layer, and repeat several times to form a multi-layer structure, specifically: Set the number of retransmissions L, the number of parameterized layer repetitions d, and alternately cycle the coding layer and parameterized layers , expressed as: ； in, Indicates data encoding, represents the action on each of the two quantum bits 、 as well as The combination is repeated L times to form the overall circuit.

5. The three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit according to claim 1 is characterized in that: The rotation-invariant measurement operator is used to obtain the output expected value, specifically: Use operators that satisfy the commutation relation As a local measurement operator on two quantum bits, its eigenvalues ​​are triple roots 1 and single roots -1, and the output value is in the interval [-1,1]; 、 、 、 A tensor of Pauli operators X, Y, Z, and I, acting on two bits.

6. The three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit according to claim 1 is characterized in that: When calculating the difference and updating the parameters through the loss function, the mean square error is selected as the loss function, which is expressed as: ； in, is the circuit output, is the data label, x is the The data sampled in Then, the parameters of the parameterized layer are updated through gradient descent using a classical optimizer, and the optimization is iterated continuously until the loss function value converges, completing the training of the rotationally equivariant parameterized quantum circuit.

7. The three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit according to claim 1 is characterized in that: The trained rotation-equivariant parameterized quantum circuit is used to classify the three-dimensional point cloud data and output the classification results, specifically: Normalize the 3D point cloud data to be classified and determine the normalization factor based on the characteristics of the data set so that the coordinates are in the interval [-π, π] to meet the requirements of rotational phase encoding; The three-dimensional point cloud data is then encoded into a quantum circuit to achieve data encoding from classical to quantum; The output result is obtained through the trained rotation-equivariant parameterized quantum circuit, and a classification decision is made based on the output result to determine the category to which the data to be classified belongs. The classification result is output in the form of a label, and the label corresponds to the preset category label.

8. A non-transitory computer-readable storage medium, characterized in that Computer instructions are stored thereon, which enable the computer to execute the three-dimensional point cloud data classification method based on rotational equivariant parameterized quantum circuit according to any one of claims 1 to 7.

9. An electronic device, characterized in that: include: A processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus, and the processor calls logic instructions in the memory to execute the three-dimensional point cloud data classification method based on a rotational equivariant parameterized quantum circuit according to any one of claims 1 to 7.

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