Webpage sorting method based on quantum walking

Abstract

The invention discloses a webpage sorting method based on quantum walking, which comprises the following steps of: obtaining a directed unweighted graph according to a jump relationship among a plurality of webpages, processing the directed unweighted graph to obtain a quantum webpage sorting operator, and calculating quantum initial states of a plurality of webpage nodes; the method comprises the steps that an evolution operator is used for conducting iteration on a quantum initial state to obtain the iteration probability of each webpage, the variance, the power law, the correlation and the entanglement of the iteration probability of the last period are solved, the rotation phase of the quantum initial state is changed, the k-means algorithm is used for conducting clustering on the variances of different rotation phases to obtain a clustering result, and positive correlation and negative correlation are obtained through analysis. An adjustable phase parameter is introduced based on a quantum walk operator, so that a result of a corresponding quantum webpage sorting algorithm presents a clustering effect in a parameter space, phase parameters in different clustering ranges in the parameter space are set to carry out quantum webpage sorting, and importance sorting of important nodes in a complex network is mined; and a tool is provided for complex network node analysis.

Description

Technical Field

[0001] The present application relates to the technical field of web page sorting, and in particular to a web page sorting method based on quantum walk. Background Art

[0002] Traditional computing uses a binary system with 0 and 1 as basic units for calculations. Quantum computers use quantum bits, which can be in multiple states at the same time. Therefore, quantum bits can carry more information than traditional bits, thereby reducing the amount of calculation exponentially, allowing quantum computers to perform more efficiently when processing web page sorting algorithms.

[0003] With the rapid development of information technology, traditional algorithms such as web page sorting have shown limitations in dealing with large-scale and highly complex problems. In this context, quantum computing, as a new computing paradigm based on the principles of quantum mechanics, has shown great potential. Under the peculiar properties of quantum mechanics, the superposition and entanglement of quantum bits give quantum computers unique advantages over classical computers. In addition, the characteristics of quantum entanglement enable quantum computers to perform efficient parallel computing and solve many complex problems that traditional computers cannot handle. As an important concept in quantum artificial intelligence algorithms, quantum walks have many unique properties and are widely used in search algorithms. Compared with classical random walks, they have faster search speeds and higher search accuracy. They use quantum superposition and interference effects to improve the efficiency and accuracy of the search process. At the same time, quantum walks have the advantage of parallelism and can explore multiple possible paths at the same time, thereby accelerating the search process. Traditional graph-based web page sorting algorithms require long and large amounts of calculations, and as the number of web pages increases, the structural complexity of the graph also increases exponentially, which ultimately leads to the inability to explore and calculate the sorting characteristics of web pages, but this is indeed the advantage of quantum computing.

[0004] In summary, quantum walks, with their characteristics of quantum superposition and interference effects, can perform more efficiently in graph theory problems such as web page sorting, especially in complex network structures, where they can mine effective information more quickly. Moreover, due to the parallel computing advantages of quantum itself, the bits in quantum walks can be in a superposition of multiple states at the same time, which makes the search process have a certain degree of parallelism and can explore multiple possible paths at the same time, thus improving the efficiency of the search. The web page sorting algorithm was first designed to evaluate the importance and ranking of web pages on the Internet, and is the most classic and important method in search engine ranking algorithms.

[0005] However, as the essential ideas of graph theory continue to expand, its application scenarios are becoming more and more extensive. However, as the number of web page nodes increases, the applicability of the algorithm itself has also ushered in challenges. The time complexity of the algorithm will increase exponentially with the increase in the number of web page nodes. Therefore, how to improve the efficiency of the algorithm operation has become one of the many problems that technicians in this field need to solve. Summary of the invention

[0006] The purpose of this application is to provide a web page sorting method based on quantum walk in order to overcome the existing technical defects, introduce an adjustable phase parameter in the quantum walk operator, so that the results of the corresponding quantum web page sorting algorithm show a clustering effect in the parameter space.

[0007] The purpose of this application is achieved through the following technical solutions:

[0008] In a first aspect, the present application proposes a web page sorting method based on quantum walk, the method comprising:

[0009] Step S1, obtaining a directed unweighted graph of web page jump relations according to the jump relations between multiple web pages;

[0010] Step S2, processing the directed unweighted graph to obtain a quantum web page sorting operator;

[0011] Step S3, using the quantum webpage sorting operator to calculate the quantum initial states of multiple webpage nodes, and using the evolution operator to iterate the quantum initial states to obtain the iteration probability of each webpage;

[0012] Step S4, calculating the variance, power law, correlation and entanglement of the iterative probability of the last cycle;

[0013] Step S5, changing the rotation phase of the variable sub-initial state, repeating steps S2 to S4 to obtain the variance, power law, correlation and entanglement of different rotation phases;

[0014] Step S6, clustering the variances of different rotation phases using a k-means algorithm to obtain a clustering result;

[0015] Step S7: Based on the clustering results, the probability variance, power law, correlation and entanglement of web pages in different phases are analyzed to obtain positive correlation and negative correlation.

[0016] In a possible implementation, step S2, the step of processing the directed unweighted graph to obtain a quantum web page sorting operator, includes:

[0017] Normalizing the directed unweighted graph to obtain a coherent connectivity matrix;

[0018] Matrix operations on the coherent connectivity matrix give the quantum web page sorting operator.

[0019] In a possible implementation, the step of performing matrix operations on the coherent connectivity matrix to obtain a quantum webpage sorting operator includes:

[0020] Assign values ​​to the elements in the coherent connectivity matrix to obtain the Google matrix;

[0021] Perform matrix operations on the Google matrix to obtain the quantum web page sorting operator;

[0022] The assignment process is: H is the Google matrix, P j is a web page node, outdeg(P j ) is the out-degree of the web page node, B i are all nodes linked to the web page node, and N is the number of nodes.

[0023] In one possible implementation, the quantum web page sorting operator G is: Where α is the damping parameter, N is the number of nodes, and H is the Google matrix.

[0024] In a possible implementation, step S3, using a quantum webpage sorting operator to calculate the quantum initial states of multiple webpage nodes, and using an evolution operator to iterate the quantum initial states to obtain the iteration probability of each webpage, includes:

[0025] The quantum web page sorting operator uses the tensor calculation formula to calculate the intermediate tensor |ψ i >, the tensor calculation formula is: Where i is the symbol of the graph node in the original graph in the Szegedy quantum walk algorithm, k is the symbol of the graph node in the replica graph in the Szegedy quantum walk algorithm, |>1 is the quantum state of the original graph in the quantum walk algorithm, |>2 is the quantum state of the replica graph in the quantum walk algorithm, is a tensor operator;

[0026] The quantum initial state |ψ0> of multiple web page nodes is calculated by using the intermediate tensor in a normalized manner. The calculation formula of the quantum initial state |ψ0> is: Where N is the number of nodes;

[0027] The iterative formula is used to iterate the quantum initial state |ψ0> to obtain the iterative result. The iterative formula is: |ψ f (t,θ1,θ2)>=W t |ψ0>, t is the number of iterations, θ1 and θ2 are both rotation phases, and W is the evolution operator of the quantum web page sorting operator;

[0028] Perform quantum observation on the iteration results to obtain the iteration probability I of each web page q (P i,t,θ1,θ2), where the iteration probability I q (P i ,t,θ1,θ2)=||2 <i||ψ f (t,θ1,θ2)>|| 2 , P i Represents the probability of the i-th web page node.

[0029] In a possible implementation, the step of calculating the variance of the iterative probability of the last cycle is:

[0030] Calculate the probability mean of the last period Where T is the period, t is the number of iterations, I q (P i ,t,θ1,θ2) is the iteration probability;

[0031] Calculate the variance σ(θ1,θ2) based on the probability mean:

[0032] In a possible implementation, the steps of finding the power law of the iterative probability of the last cycle are:

[0033] By using the least squares method, I q (P i ,θ1,θ2)=i -β The slope of is fitted, where β is the slope obtained by fitting, i represents the corresponding i-th ordinal number in the probability vector obtained by web page ranking, and N represents the total number of web page nodes in the web page ranking.

[0034] In a possible implementation, the calculation formula of the correlation C(θ1, θ2) is: where λ j for |ψ f (t,θ1,θ2)><ψ f (t,θ1,θ2)||ψ f (t)><ψ f (t)|eigenvalue, diag means taking the diagonal elements of the corresponding matrix.

[0035] In one possible implementation, the steps for calculating entanglement are:

[0036] For the quantum state |ψ f (t,θ1,θ2)> is processed to obtain the intermediate matrix EM=|ψ f (t,θ1,θ2)><ψ f (t,θ1,θ2)|;

[0037] The eigenvalues ​​of the intermediate matrix EM are obtained to obtain multiple eigenvalues ​​{λ1,λ2,λ3,...,λE};

[0038] Processing the eigenvalues ​​yields a measure of quantum entanglement for a period

[0039] The above-mentioned main scheme of the present application and its further options can be freely combined to form multiple schemes, all of which are schemes that can be adopted and claimed for protection in the present application; and in the present application, (non-conflicting options) options and other options can also be freely combined. After understanding the scheme of the present application, those skilled in the art can understand that there are multiple combinations based on the prior art and common knowledge, all of which are technical schemes to be protected by the present application, and they are not exhaustively listed here.

[0040] The present application discloses a webpage sorting method based on quantum walk. First, a directed unweighted graph of webpage jump relations is obtained according to the jump relations between multiple webpages. The directed unweighted graph is processed to obtain a quantum webpage sorting operator. The quantum initial states of multiple webpage nodes are calculated. The evolution operator is used to iterate the quantum initial state to obtain the iteration probability of each webpage. The variance, power law, correlation and entanglement of the iteration probability of the last cycle are calculated. The rotation phase of the variable quantum initial state is changed. The variance of different rotation phases is clustered using the k-means algorithm to obtain clustering results. The positive correlation and negative correlation are obtained by analysis. An adjustable phase parameter is introduced in the quantum walk operator so that the result of the corresponding quantum webpage sorting algorithm shows a clustering effect in the parameter space. The phase parameters within different clustering ranges in the parameter space are set to sort quantum webpages, and the importance of important nodes in complex networks is sorted, providing a tool for complex network node analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A web page sorting method based on quantum walk proposed in an embodiment of the present application is shown.

[0042] Figure 2 A web page jump relationship diagram of 32 nodes is abstracted for the embodiment of this application

[0043] Figure 3 The clustering results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown.

[0044] Figure 4 The variance results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown.

[0045] Figure 5 The power law results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown.

[0046] Figure 6 The coherence results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown.

[0047] Figure 7 The entanglement results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown.

[0048] Figure 8 The clustering results of the unitary matrix W2 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown.

[0049] Fig. 9 The clustering results of the unitary matrix W3 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown.

[0050] Fig.10 The clustering results of the unitary matrix W4 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown.

[0051] Fig.11 The reverse tracing diagram of the unitary matrix W4(θ1, θ2) proposed in the embodiment of the present application is the clustering result after quantum web page sorting at different phases. DETAILED DESCRIPTION

[0052] The following describes the embodiments of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. The present application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0053] Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making any creative work shall fall within the scope of protection of this application.

[0054] In the prior art, as the essential ideas of graph theory continue to expand, its application scenarios are becoming more and more extensive. However, as the number of web page nodes increases, the applicability of the algorithm itself has also ushered in challenges. The time complexity of the algorithm will increase exponentially with the increase in the number of web page nodes. Therefore, how to improve the efficiency of the algorithm operation has become one of the many problems that technicians in this field need to solve.

[0055] In order to solve the problems existing in the current traditional computing paradigm, the embodiment of the present application proposes a web page sorting method based on quantum walk. First, according to the jump relationship between each web page, a jump relationship diagram between web pages is abstracted; secondly, the quantum initial state of web page sorting is prepared according to the jump relationship diagram, and the unitary matrix of state transfer is constructed; then a loop iteration is performed, and the quantum state of each iteration process is observed and saved; finally, the quantum state in the last cycle is averaged, and its variance, coherence, correlation and other characteristics are calculated, and repeated calculations are taken with different phases to finally obtain the characteristics of web page sorting, which are described in detail below.

[0056] Please refer to Figure 1 , Figure 1 A webpage sorting method based on quantum walking proposed in an embodiment of the present application is shown, and the method includes the following steps:

[0057] Step S1: obtaining a directed unweighted graph of web page jump relations according to the jump relations between multiple web pages.

[0058] First, count the jump relationships between N web pages to obtain a directed unweighted graph of the web page jump relationship Graph, where N is the number of vertices in the graph. In the embodiment of the present application, the number of vertices is set to N=32. Figure 2 , Figure 2 A web page jump relationship diagram with 32 nodes is abstracted for the embodiment of the present application. Each node represents a web page or page, and the line segment represents the jump relationship from one web page to another. There are four nodes with numbers specially marked in the center of the image: No. 2, No. 14, No. 1 and No. 3, which can jump to the page corresponding to the number connected to them as the center.

[0059] Step S2: Process the directed unweighted graph to obtain a quantum web page sorting operator.

[0060] Step S2 includes:

[0061] The directed unweighted graph is normalized to obtain the coherent connectivity matrix;

[0062] Matrix operations on the coherent connectivity matrix give the quantum web page sorting operator.

[0063] Initialize a 32*32 coherent connectivity matrix, count the out-degree of each web page node, assign values ​​to the elements in the coherent connectivity matrix, and then process them to obtain the quantum web page sorting operator G: Where α is the damping parameter, which can be set to 0.85, N is the number of nodes, and H is the Google matrix.

[0064] The step of performing matrix operations on the coherent connectivity matrix to obtain a quantum web page sorting operator comprises:

[0065] Assign values ​​to the elements in the coherent connectivity matrix to obtain the Google matrix;

[0066] Perform matrix operations on the Google matrix to obtain the quantum web page sorting operator;

[0067] The assignment process is: H is the Google matrix, P j is a web page node, outdeg(P j ) is the out-degree of the web page node, B i are all nodes linked to the web page node, and N is the number of nodes.

[0068] First, calculate the out-degree of each web page node, that is, the number of links from the node to other nodes. Then create a 32x32 zero matrix as the initial coherent connectivity matrix, assuming there are 32 web page nodes. For each non-diagonal element (i, j) in the matrix, if web page i has a link pointing to web page j, the value in the matrix is ​​equal to 1 / out-degree (i), which uses the out-degree of web page i to perform probability distribution, ensuring that the sum of the probabilities of traversing the network from any web page is 1.

[0069] For each element in the matrix, check whether the corresponding webpage node belongs to a certain set and whether the out-degree of the node (i.e. the number of links pointing to other pages) is non-zero. 1 / outdeg(P j ) j ∈B i ,outdeg(P j )≠0 is to reflect the link influence of the node. The larger the out-degree, the smaller the contribution of a single link.

[0070] If p j ∈B i ,outdeg(P j )≠0, the matrix element values ​​at the corresponding positions are set to 0, which means that these links do not contribute to the current calculation. j )=0), in order to avoid division by zero, the corresponding value of the node in the matrix will be uniformly set to 1 / N, where N is the number of all nodes. This processing ensures that each node in the network has at least a certain contribution.

[0071] A Google matrix is ​​obtained, which reflects the adjusted link weights between nodes in the network. In order to obtain the quantum web ranking operator, further linear algebra operations need to be performed on this assigned matrix. First, normalization is performed to ensure that the sum of each column of the matrix is ​​1, ensuring the characteristics of the probability distribution, so that the matrix can be directly applied to probability transfer models such as web page ranking. The core of the conversion from the coherent connectivity matrix to the quantum web ranking operator is to adjust the weights to reflect the characteristics of the network structure, and use linear algebra tools to construct a stable probability distribution model that reflects the relative importance of pages.

[0072] Step S3, using the quantum webpage sorting operator to calculate the quantum initial states of multiple webpage nodes, and using the evolution operator to iterate the quantum initial states to obtain the iteration probability of each webpage;

[0073] The quantum initial state |ψ0> of N web page nodes is calculated by the quantum web page sorting operator and the four types of quantum state transfer unitary matrices W1(θ1,θ2), W2(θ1,θ2), W3(θ1,θ2), W4(θ1,θ2) are determined. The evolution operator is used to continuously iterate the quantum initial state to obtain the iteration probability result of each web page node I q (P i ,t,θ1,θ2).

[0074] Each column of the quantum web ranking operator represents the probability distribution of traversing the network starting from the corresponding web page. In the framework of quantum computing, the PageRank vector (i.e., the initial ranking probability of each web page) is regarded as a quantum state. Let the total number of web pages be N, and define a normalized N-dimensional vector as the quantum initial state, in which each component corresponds to the initial probability of a web page, and these probabilities are usually uniformly distributed.

[0075] In quantum PageRank, the evolution operator is generalized to a unitary matrix, which keeps the length of the vector unchanged. The four types of transfer unitary matrices refer to a set of matrices defined according to different quantum walk strategies or search strategies, and each matrix represents a specific probability transfer rule. For example: local transfer that only transfers probability between connected web pages, global transfer that is similar to the random wanderer effect to achieve jumps between global web pages, custom transfers customized according to specific rules (such as topic relevance), and hybrid transfers of matrices that combine the above strategies. Using one or more of the above transfer unitary matrices, the quantum initial state is continuously iterated through quantum gate operations. Each iteration can be regarded as an evolution of the probability distribution of web page nodes, that is, the unitary matrix is ​​applied to the current quantum state to obtain a new quantum state.

[0076] Step S3, using a quantum webpage sorting operator to calculate the quantum initial states of multiple webpage nodes, and using an evolution operator to iterate the quantum initial states to obtain the iteration probability of each webpage, comprises:

[0077] The quantum web page sorting operator uses the tensor calculation formula to calculate the intermediate tensor |ψ i >, the tensor calculation formula is: Where i is the symbol of the graph node in the original graph in the Szegedy quantum walk algorithm, k is the symbol of the graph node in the replica graph in the Szegedy quantum walk algorithm, |>1 is the quantum state of the original graph in the quantum walk algorithm, |>2 is the quantum state of the replica graph in the quantum walk algorithm, is a tensor operator;

[0078] The quantum initial state |ψ0> of multiple web page nodes is calculated by using the intermediate tensor in a normalized manner. The calculation formula of the quantum initial state |ψ0> is: Where N is the number of nodes;

[0079] The iterative formula is used to iterate the quantum initial state |ψ0> to obtain the iterative result. The iterative formula is: |ψ f (t,θ1,θ2)>=W t |ψ0>, t is the number of iterations, θ1 and θ2 are both rotation phases, and W is the evolution operator of the quantum web page sorting operator;

[0080] Perform quantum observation on the iteration results to obtain the iteration probability I of each web page q (P i ,t,θ1,θ2), where the iteration probability I q (P i ,t,θ1,θ2)=||2 <i||ψ f (t,θ1,θ2)>|| 2 , P i Represents the probability of the i-th web page node.

[0081] In order to convert the quantum state representation from the classical web page graph, the quantum state information of the original image and its copy image is integrated through the tensor calculation formula, that is, the intermediate tensor is calculated using the quantum web page sorting operator G Then the quantum initial state of the web page node is obtained by normalization. The quantum state transfer unitary matrix W1(θ1,θ2), W2(θ1,θ2), W3(θ1,θ2), and W4(θ1,θ2) can also be calculated, where θ1 and θ2 are set to 0. The calculation formula of the quantum state transfer unitary matrix is: W1(θ1,θ2)=U(θ2)U(θ1), W2(θ1,θ2)=U(θ1)U(θ1)U(θ2)U(θ2), W3(θ1,θ2)=U(θ1)U(-θ1)U(θ2)U(-θ2), W4(θ1,θ2)=U(θ1)U(π)U(θ2)U(π), where

[0082] Through the formula |ψ f (t,θ1,θ2)>=W t |ψ0>Iterate the quantum initial state (use the evolution operator to continuously iterate the quantum initial state), the number of iterations can be set to 4000-5000 times, the probability value of the network node is obtained through quantum observation, and the probability value of 4000-5000 times is saved, and then the iterative probability result of each web page node is obtained as I q (P i ,t,θ1,θ2)=||2 <i|ψ f (t,θ1,θ2)>|| 2 .

[0083] Step S4: Calculate the variance, power law, correlation and entanglement of the iterative probability of the last cycle.

[0084] The variance and power law of the web page probability in the last period are calculated respectively, and the correlation and entanglement of the web page quantum state in the last period are calculated respectively. This is an advanced statistical and quantum informatics analysis of the output results of the quantum PageRank algorithm, which can not only evaluate the performance of the algorithm, but also reveal the potential laws and special quantum properties in the web page network.

[0085] The steps for calculating the variance of the iterative probability in the last cycle are:

[0086] Calculate the probability mean of the last period Where T is the period, t is the number of iterations, and I q (P i ,t,θ1,θ2) is the iteration probability;

[0087] Calculate the variance σ(θ1,θ2) based on the probability mean:

[0088] The steps to find the power law of the iterative probability of the last cycle are:

[0089] By using the least squares method, I q (P i ,θ1,θ2)=i-β The slope of is fitted, where β is the slope obtained by fitting, i represents the corresponding i-th ordinal number in the probability vector obtained by web page ranking, and N represents the total number of web page nodes in the web page ranking.

[0090] In order to find the variance and power law of the web page probability in the last cycle, first calculate the average probability of the last cycle Calculate the variance of all nodes based on the probability average in Then, the least square method is used to calculate the formula I q (P i ,θ1,θ2)=i -β Fit the β in the equation and transform it into logI q =-βlogi, we can get

[0091] In calculating the variance, first determine the iteration probability of all web pages in the last cycle, then calculate the average probability, find the average of all web page iteration probabilities, and finally calculate the variance.

[0092] In power law analysis, data preprocessing can be performed first to ensure that the probability data is arranged in order of size, and then logarithmic transformation is performed on the ranking of the web pages (usually the serial number after being arranged in descending order of probability) and the corresponding probability. Next, the least squares method is used for fitting, and the power law exponent and intercept are solved by the least squares method. Finally, the fitting effect is evaluated, and the residual sum of squares and R are tested. 2 The applicability of the power law model can be judged by the value.

[0093] The calculation formula of correlation C(θ1,θ2) is:

[0094] where λ j for |ψ f (t,θ1,θ2)><ψ f (t,θ1,θ2)||ψ f (t)><ψ f (t)|eigenvalue, diag means taking the diagonal elements of the corresponding matrix.

[0095] The steps to calculate entanglement are:

[0096] For the quantum state |ψ f (t,θ1,θ2)> is processed to obtain the intermediate matrix EM=|ψ f (t,θ1,θ2)><ψ f (t,θ1,θ2)|;

[0097] The eigenvalues ​​of the intermediate matrix EM are obtained to obtain multiple eigenvalues ​​{λ1,λ2,λ3,...,λ E};

[0098] Processing the eigenvalues ​​yields a measure of quantum entanglement for a period

[0099] To find the coherence and entanglement of the quantum state of the web page in the last cycle, first calculate the quantum state |ψ f (t)> is processed to obtain the coherence C(θ1,θ2): in Then the quantum state |ψ f (t)> is processed to obtain the entanglement En(θ1,θ2,t,j): En(θ1,θ2,t,j)=-λ j log(λ j ), λ j for |ψ f (t)><ψ f (t)| has a total of E eigenvalues, for the quantum state |ψ f (t)<Processing to obtain the intermediate matrix EMEM=|ψ f (t)><ψ f (t)|, and obtain E eigenvalues ​​{λ1,λ2,λ3,...,λ E}, and finally process the eigenvalues ​​to get the result under one cycle:

[0100] In the entanglement calculation, an intermediate matrix is ​​first constructed. Starting from a given quantum state, an intermediate matrix is ​​obtained through a specific linear transformation or contract mapping. Then, eigenvalue analysis is performed to decompose the intermediate matrix to obtain a series of eigenvalues. These eigenvalues ​​carry important information about the entanglement properties of the quantum state. Finally, entanglement metric extraction is performed. According to a specific entanglement metric scheme, such as von Neumann entropy, entanglement entropy or other entanglement metrics, the eigenvalues ​​are further processed to obtain a quantum entanglement metric of one or more cycles.

[0101] Step S5, changing the rotation phase of the variable sub-initial state, repeating steps S2 to S4 to obtain the variance, power law, correlation and entanglement of different rotation phases.

[0102] Change the rotation phases θ1 and θ2 of the quantum initial state, set θ1 and θ2 to take uniform values ​​in the interval [0,2π), repeat the above steps, and calculate the variance, power law, correlation and entanglement under the corresponding rotation phases.

[0103] Step S6: cluster the variances of different rotation phases using the k-means algorithm to obtain a clustering result.

[0104] The k-means algorithm is used to cluster the probability variance of web pages in different phases. Figure 3 The clustering results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown. Figure 8 The clustering results of the unitary matrix W2 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown. Fig. 9 The clustering results of the unitary matrix W3 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown. Fig.10 The clustering results of the unitary matrix W4 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown. The clustering results are all 3D distribution diagrams, and it is shown that the quantum adjustable phase parameters θ1 and θ2 have a clustering effect on the importance of network nodes given by the final quantum web page sorting, and thus the relative importance of individual nodes can be mined from different angles.

[0105] The k-means algorithm is used to perform cluster analysis on the probability variance of web pages calculated under different rotation phases. The goal is to find out whether there are patterns or regularities in the probability distribution characteristics of web pages under different phase settings, that is, whether different phase configurations can be classified into clusters that express differences in the importance of network nodes. First, all web page probability variance data calculated under different rotation phases are collected, and the appropriate k value (number of clusters) is selected. The k-means algorithm is run to allow the algorithm to automatically assign these variance values ​​to k clusters. Each cluster represents a class of similar probability variance behaviors. The clustering results obtained show the influence pattern of the phase parameter on the variance distribution.

[0106] Step S7: Based on the clustering results, the probability variance, power law, correlation and entanglement of web pages in different phases are analyzed to obtain positive correlation and negative correlation.

[0107] The variance, power law, correlation and entanglement of web page probabilities under different rotation phases based on clustering results are analyzed to determine the positive or negative correlation between them.

[0108] Variance vs. Phase: Examine how variance varies within and across clusters to understand which phase ranges tend to produce higher or lower variance.

[0109] Power-law properties: Examine the power-law distribution characteristics of web page probabilities within each cluster, analyze how the phase affects the distribution of the power-law exponent, and reveal how phase modulation changes the power-law properties of the network structure.

[0110] Correlation analysis: Evaluate the change in the strength of the association between the probability distribution and the eigenvalue (part of the correlation calculation) for different phases to explore how the phase modulates this relationship.

[0111] Entanglement exploration: Analyze the trend of quantum entanglement measurement with phase change, explore how phase affects the entanglement characteristics of the system, and its potential impact on the significance of network ordering.

[0112] By analyzing the probability variance and power law of web pages at different phases, the correlation and entanglement at different phases, we can obtain the characteristics of positive correlation and negative correlation. Figure 4 The variance results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown. Figure 5 The power law results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown. Figure 6 The coherence results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown. Figure 7 The entanglement results of the unitary matrix W1 (θ1, θ2) proposed in the embodiment of the present application after quantum web page sorting at different phases are shown. Fig.11 The reverse tracing diagram of the unitary matrix W4 (θ1, θ2) proposed in the embodiment of the present application is the clustering result after quantum web page sorting at different phases. The above are all 3D distribution diagrams, and the power law and entanglement are positively correlated.

[0113] The embodiment of the present application introduces an adjustable phase parameter in the Szegedy quantum walk operator, so that the result of the corresponding quantum web page sorting algorithm presents a clustering effect in the parameter space. The introduction of the adjustable phase parameter provides an effective way to explore the importance of web page nodes in complex web page sorting. The clustering of web page sorting results is consistent with the coherence of the corresponding quantum state, the clustering of entangled rows, and the clustering of the key power law coefficients of the scale-free graph, reflecting the scientific nature of this solution.

[0114] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A web page sorting method based on quantum walk, characterized in that: The method comprises: Step S1, obtaining a directed unweighted graph of web page jump relations according to the jump relations between multiple web pages; Step S2, processing the directed unweighted graph to obtain a quantum web page sorting operator; Step S3, using the quantum webpage sorting operator to calculate the quantum initial states of multiple webpage nodes, and using the evolution operator to iterate the quantum initial states to obtain the iteration probability of each webpage; Step S4, calculating the variance, power law, correlation and entanglement of the iterative probability of the last cycle; Step S5, changing the rotation phase of the variable sub-initial state, repeating steps S2 to S4 to obtain the variance, power law, correlation and entanglement of different rotation phases; Step S6, clustering the variances of different rotation phases using a k-means algorithm to obtain a clustering result; Step S7: Based on the clustering results, the probability variance, power law, correlation and entanglement of web pages in different phases are analyzed to obtain positive correlation and negative correlation.

2. The web page ranking method according to claim 1, characterized in that: Step S2, the step of processing the directed unweighted graph to obtain a quantum web page sorting operator, comprises: Normalizing the directed unweighted graph to obtain a coherent connectivity matrix; Matrix operations on the coherent connectivity matrix give the quantum web page sorting operator.

3. The web page ranking method according to claim 2, characterized in that: The step of performing matrix operations on the coherent connectivity matrix to obtain a quantum web page sorting operator comprises: Assign values ​​to the elements in the coherent connectivity matrix to obtain the Google matrix; Perform matrix operations on the Google matrix to obtain the quantum web page sorting operator; The assignment process is: H is the Google matrix, P j is a web page node, outdeg(P j ) is the out-degree of the web page node, B i are all nodes linked to the web page node, and N is the number of nodes.

4. The web page ranking method according to claim 3, characterized in that: The quantum web page sorting operator G is: Where α is the damping parameter, N is the number of nodes, and H is the Google matrix.

5. The web page ranking method according to claim 1, characterized in that: Step S3, using a quantum webpage sorting operator to calculate the quantum initial states of multiple webpage nodes, and using an evolution operator to iterate the quantum initial states to obtain the iteration probability of each webpage, comprises: The quantum web page sorting operator uses the tensor calculation formula to calculate the intermediate tensor |ψ i >, the tensor calculation formula is: Where i is the symbol of the graph node in the original graph in the Szegedy quantum walk algorithm, k is the symbol of the graph node in the replica graph in the Szegedy quantum walk algorithm, |>1 is the quantum state of the original graph in the quantum walk algorithm, |>2 is the quantum state of the replica graph in the quantum walk algorithm, is a tensor operator; The quantum initial state |ψ0> of multiple web page nodes is calculated by using the intermediate tensor in a normalized manner. The calculation formula of the quantum initial state |ψ0> is: Where N is the number of nodes; The iterative formula is used to iterate the quantum initial state |ψ0> to obtain the iterative result. The iterative formula is: |ψ f (t,θ1,θ2)>=W t |ψ0>, t is the number of iterations, θ1 and θ2 are both rotation phases, and W is the evolution operator of the quantum web page sorting operator; Perform quantum observation on the iteration results to obtain the iteration probability I of each web page q (P i ,t,θ1,θ2), where the iteration probability I q (P i ,t,θ1,θ2)=||2 <i|ψ f (t,θ1,θ2)>|| 2 , P i Represents the probability of the i-th web page node.

6. The web page ranking method according to claim 5, characterized in that: The steps for calculating the variance of the iterative probability of the last cycle are: Calculate the probability mean of the last period Where T is the period, t is the number of iterations, and I q (P i ,t,θ1,θ2) is the iteration probability; Calculate the variance σ(θ1,θ2) based on the probability mean:

7. The web page ranking method according to claim 6, characterized in that: The steps to find the power law of the iterative probability of the last cycle are: By using the least squares method, I q (P i ,θ1,θ2)=i -β The slope of is fitted, where β is the slope obtained by fitting, i represents the corresponding i-th ordinal number in the probability vector obtained by web page ranking, and N represents the total number of web page nodes in the web page ranking.

8. The web page ranking method according to claim 7, characterized in that: The calculation formula of correlation C(θ1,θ2) is: where λ j for |ψ f (t,θ1,θ2)><ψ f (t,θ1,θ2)||ψ f (t)><ψ f (t)|eigenvalue, diag means taking the diagonal elements of the corresponding matrix.

9. The web page ranking method according to claim 8, characterized in that: The steps to calculate entanglement are: For the quantum state |ψ f (t,θ1,θ2)> is processed to obtain the intermediate matrix EM=|ψ f (t,θ1,θ2)><ψ f (t,θ1,θ2)|; find the eigenvalues ​​of the intermediate matrix EM and obtain multiple eigenvalues ​​{λ1,λ2,λ3,...,λ E }; Processing the eigenvalues ​​yields a measure of quantum entanglement for a period

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