Quantum evidence theory-based evidence fusion reasoning method, system, device and storage medium

Abstract

The present application relates to the technical field of uncertainty reasoning and quantum computing, and particularly relates to an evidence fusion reasoning method, system and device based on quantum evidence theory and a storage medium, which comprises the following steps: obtaining a first evidence source and a second evidence source to be combined, and constructing a first generalized quantum basic probability amplitude and a second generalized quantum basic probability amplitude; generating a first quantum superposition state according to the first generalized quantum basic probability amplitude, and generating a second quantum superposition state according to the second generalized quantum basic probability amplitude; constructing an initial global quantum state based on the first quantum superposition state and the second quantum superposition state, and obtaining a final system state through quantum evidence combination rules evolution; performing quantum measurement on the final system state generalized quantum using a basic probability measurement operator to extract a generalized quantum basic probability distribution, and obtaining an evidence fusion reasoning result based on the generalized quantum basic probability distribution. The present application can realize the technical effect of efficient and robust pattern classification decision-making in a high-dimensional and complex data set scenario.

Description

Technical Field

[0001] This invention relates to the fields of uncertainty reasoning and quantum computing technology, specifically to evidence fusion reasoning methods, systems, devices, and storage media based on quantum evidence theory. Background Technology

[0002] Quantum Evidence Theory (QET), as a powerful tool for uncertainty reasoning, has demonstrated significant advantages in handling the fusion of conflicting information in open environments. However, in practical engineering and pattern classification applications, the data sources to be processed often do not involve complex quantum interference effects; that is, the evidence sources are physically or statistically independent and have no coherent relationship. Under this non-interference assumption, the interference terms in the combination rules of quantum evidence theory naturally dissolve, and the entire theoretical system degenerates into the generalized combination rule (GCR) of classical generalized evidence theory (GET). Under non-interference conditions, this rule can be implemented in a quantum computing architecture, usually denoted as the generalized non-coherent quantum evidence combination rule (GCR). ).

[0003] Although the generalized incoherent quantum evidence combination rules strip away complex complex phase operations, their underlying combinational logic still inevitably relies on the power set of the identification framework. The algorithm involves exhaustive traversal and set intersection operations. In the generalized incoherent quantum evidence combination rule algorithm, solving the generalized basic probability assignment function (GBPA) for any single proposition requires a large number of intersection and multiplication operations in the worst case. Assume the identification frame size is... Solve When dealing with a single proposition, the overall computational complexity of this classic algorithm is as high as [missing information]. .

[0004] As the dimensions of the identification framework increase or the amount of fused evidence grows, the computational complexity of this combinatorial rule based on classical computing architecture explodes exponentially. This extremely high computational cost constitutes the curse of dimensionality in classical evidence theory, severely limiting its practical deployment and application in massive datasets, complex multimodal fusion, and large-scale pattern classification tasks with high real-time requirements.

[0005] Therefore, how to fundamentally break through this computing power bottleneck and significantly reduce the computational complexity of multi-source incoherent evidence fusion under the high-dimensional identification framework while ensuring the rigor of evidence reasoning has become a key technical problem that urgently needs to be solved in the field of uncertainty artificial intelligence and pattern recognition. Summary of the Invention

[0006] The purpose of this invention is to provide a method, system, device, and storage medium for evidence fusion reasoning based on quantum evidence theory, so as to solve the technical problem that existing evidence theories cannot simultaneously take into account the rigor of evidence reasoning and the computational complexity of multi-source incoherent evidence fusion under a high-dimensional identification framework.

[0007] In a first aspect, the present invention provides an evidence fusion reasoning method based on quantum evidence theory, comprising the following steps: Obtain a first source of evidence and a second source of evidence to be combined. The first source of evidence and the second source of evidence are independent of each other. The first source of evidence and the second source of evidence are one of the following: equipment observation features, physical observation features, and conflict information to be fused. A first generalized quantum fundamental probability amplitude is constructed based on the first source of evidence, and a second generalized quantum fundamental probability amplitude is constructed based on the second source of evidence. The first quantum superposition state is generated according to the first generalized quantum fundamental probability amplitude, and the second quantum superposition state is generated according to the second generalized quantum fundamental probability amplitude; An initial global quantum state is constructed based on the first and second quantum superposition states, and the final system state is obtained by evolution through the quantum evidence combination rule based on the initial global quantum state. The generalized quantum state of the final system is measured using the fundamental probability measurement operator to extract the generalized quantum fundamental probability distribution, and the evidence fusion reasoning result is obtained based on the generalized quantum fundamental probability distribution.

[0008] The significant advantages of this invention are as follows: This solution leverages the inherent advantages of quantum computing in handling high-dimensional tensor spaces, namely state superposition and parallel processing. It constructs an initial global quantum state from the first and second quantum superposition states, and then evolves the final system state based on this initial global quantum state using quantum evidence combination rules. This maps the underlying combinatorial logic to a high-dimensional quantum Hilbert space. Compared to the high time overhead of classical non-interference combinatorial methods, this invention combines quantum gate evolution with the extremely lightweight post-processing overhead of classical methods, significantly compressing the overall computational complexity. This removes the computational power barrier to efficiently deploying evidence theory on large-scale, high-dimensional real-world datasets, and reduces the time complexity of evidence fusion reasoning in attribute-free scenarios from exponential to linear levels. It effectively overcomes the computational power limitations of traditional computing architectures, thus achieving efficient and robust pattern classification decisions in high-dimensional, complex dataset scenarios.

[0009] Furthermore, this invention, through customized quantum circuit design, perfectly replicates the set cross-multiplication and joint normalization computation in classical generalized evidence theory at the physical level. The statistical properties of quantum measurement ensure the strict equivalence of the fusion result with classical theory, and by reasonably configuring the number of measurement samplings, the statistical fluctuation error caused by quantum state collapse can be effectively suppressed.

[0010] Furthermore, the steps of constructing the first generalized quantum fundamental probability amplitude and the second generalized quantum fundamental probability amplitude based on the first evidence source and the second evidence source respectively include: The first classical generalized basic probability assignment function is obtained based on the first source of evidence, and the second classical generalized basic probability assignment function is obtained based on the second source of evidence. The first complex probability amplitude is obtained by transformation based on the first classical generalized basic probability assignment function, and the second complex probability amplitude is obtained by transformation based on the second classical generalized basic probability assignment function. The first generalized quantum fundamental probability amplitude is generated based on the first complex probability amplitude, and the second generalized quantum fundamental probability amplitude is generated based on the second complex probability amplitude.

[0011] Furthermore, when constructing the initial global quantum state based on the first quantum superposition state and the second quantum superposition state, a target register is constructed, and the initial global quantum state is obtained by combining the first quantum superposition state, the second quantum superposition state, the target register, and the auxiliary bit input line.

[0012] Furthermore, the step of evolving the final system state based on the initial global quantum state through the quantum evidence combination rule includes: The mass assignment of the empty set is computed by applying operators to the initial global quantum state, and a first system evolution state containing the target value and intermediate computational data is generated based on the mass assignment of the empty set. The first system evolution state contains... The quantum state of a qubit; By applying a controlled NOT gate in the first system evolution state, the first system evolution state is... The computation results on the i-th qubit are copied and temporarily stored in the i-th qubit. Each qubit yields the second system evolution state. , It is a positive integer greater than 1; The third system evolution state is obtained by applying an inverse operator to the second system evolution state to revoke state entanglement and clear intermediate computation data; The final system state is obtained by applying an intersection simulation operator to the third system evolution state and performing intersection operations through bitwise operation logic.

[0013] The beneficial effects of the above technical solution are: it uses a quantum process to replace the classical fusion process of generalized quantum probabilistic basic assignment. Through the parallelism of quantum mechanics, the computational complexity of this fusion process is reduced exponentially.

[0014] Furthermore, the operator is constructed based on the standard Toveley function, which is to apply a Pauli X-gate to the target bit when both control bits are in an excited state; The controlled NOT gate applies a Pauli X gate to the target bit when a single control bit is in an excited state.

[0015] Furthermore, the step of extracting the generalized quantum fundamental probability distribution by performing quantum measurement on the generalized quantum of the final system state using the fundamental probability measurement operator, and obtaining the evidence fusion reasoning result based on the generalized quantum fundamental probability distribution includes: Constructing a set of generalized quantum fundamental probability measurement operators; The generalized quantum fundamental probability distribution is obtained by performing quantum measurements based on the final system state and the set of generalized quantum fundamental probability measurement operators. The evidence fusion reasoning results are obtained based on the selection of the classical generalized basic probability assignment function.

[0016] The beneficial effects of the above technical solution are: it transforms the quantum superposition state containing the fusion result into a classical fusion result that can be processed by a classical system. The complete process of the quantum circuit can exponentially reduce the computational complexity of fusing two generalized quantum fundamental probability assignments to obtain a complete generalized fundamental probability assignment.

[0017] Furthermore, the step of obtaining the generalized quantum fundamental probability distribution by performing a generalized quantum fundamental probability measurement on the final system state includes: Perform a partial trace operation on the final system state to obtain a reduced density operator containing fused information; Calculate the conflict coefficient based on the set of reduced density operators and generalized quantum fundamental probability measurement operators; Probability distributions are calculated based on the conflict coefficient.

[0018] The beneficial effects of the above technical solution are: it transforms the quantum superposition state containing the classification result after fusion into a classical classification result that can be processed by a classical system. The complete process of the quantum circuit can exponentially reduce the computational complexity of fusing the classification result from the probability assignment of two generalized quantum fundamentals.

[0019] Secondly, the present invention provides an evidence fusion reasoning system based on quantum evidence theory, applicable to the aforementioned evidence fusion reasoning method based on quantum evidence theory, including: The evidence source acquisition module is used to acquire the first and second evidence sources for the fusion reasoning; A generalized quantum fundamental probability amplitude construction module is used to construct a first generalized quantum fundamental probability amplitude based on a first source of evidence and a second generalized quantum fundamental probability amplitude based on a second source of evidence. A quantum superposition state generation module is used to generate a first quantum superposition state based on a first generalized quantum fundamental probability amplitude and a second quantum superposition state based on a second generalized quantum fundamental probability amplitude. The quantum state evolution module is used to construct an initial global quantum state based on the first quantum superposition state and the second quantum superposition state, and to obtain the final system state based on the initial global quantum state through the quantum evidence combination rule. The evidence fusion reasoning module is used to extract the generalized quantum fundamental probability distribution based on the final system state and obtain the evidence fusion reasoning result based on the generalized quantum fundamental probability distribution.

[0020] Thirdly, the present invention provides an evidence fusion reasoning device based on quantum evidence theory, including a memory, a processor, and a computer program stored in the memory, characterized in that the processor executes the computer program to implement the steps of the above-mentioned evidence fusion reasoning method based on quantum evidence theory.

[0021] Fourthly, the present invention provides a computer-readable storage medium containing a computer program, wherein the computer program is stored thereon, characterized in that, when the computer program is executed by one or more processors, it implements the steps of the above-described evidence fusion reasoning method based on quantum evidence theory. Attached Figure Description

[0022] Figure 1 This is a flowchart of the evidence fusion reasoning method based on quantum evidence theory in an embodiment of the present invention; Figure 2 This is a schematic diagram of the quantum state evolution circuit structure in an embodiment of the present invention; Figure 3 This is a detailed structural diagram of each operator in the quantum state evolution circuit structure diagram in the embodiment of the present invention; Figure 4 This is a three-dimensional mapping diagram showing the mean absolute percentage error, number of measurements, and frame size of the quantum and classical results of the evidence fusion reasoning method in this embodiment of the invention. Figure 5 This is a graph showing the relationship between the average absolute percentage error of the quantum and classical results of the evidence fusion reasoning method in this embodiment of the invention and the number of measurements. Figure 6 This is a graph showing the relationship between the mean absolute percentage error of the quantum and classical results of the evidence fusion reasoning method in this embodiment of the invention and the frame size. Figure 7This is a graph showing the relationship between the number of measurements and the frame size for the quantum and classical results of the evidence fusion reasoning method in this embodiment of the invention. Figure 8 The similarity between the evidence fusion reasoning method and the classic combination rule in the classification accuracy of the Iris dataset in the embodiments of the present invention ( ) Analysis chart; Figure 9 The similarity between the quantum results, classical results, and classical combination rules of the evidence fusion reasoning method in this embodiment of the invention in terms of classification accuracy on the Penguin dataset is ( ). ) Analysis chart; Figure 10 The similarity between the quantum results, classical results, and classical combination rules of the evidence fusion reasoning method in this embodiment of the invention in terms of classification accuracy on the Star dataset. ) Analysis chart; Figure 11 The similarity between the quantum results, classical results, and classical combination rules of the evidence fusion reasoning method in this embodiment of the invention in terms of classification accuracy on the wheat-seed dataset. Analysis diagram. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, a clear and complete description will be provided below in conjunction with the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0024] See appendix Figure 1 The evidence fusion reasoning method based on quantum evidence theory, as shown, includes the following steps: S1. Obtain the first and second sources of evidence to be combined, where the first and second sources of evidence are independent of each other; A first generalized quantum fundamental probability amplitude is constructed based on a first evidence source, and a second generalized quantum fundamental probability amplitude is constructed based on a second evidence source. Specifically, the first and second evidence sources are two independent combined evidence sources to be verified in a specific pattern classification or actual physical observation task. The first and second evidence sources are one of three independent types: device observation features, physical observation features, or conflicting information to be fused. Specifically, in this embodiment, the first and second evidence sources come from medical auxiliary diagnosis scenarios, multi-sensor target recognition scenarios, or other actual industrial and daily life application scenarios that require processing and fusion of high-dimensional conflicting information. For example, in a medical auxiliary diagnosis scenario, the first and second evidence sources represent independent physical observation features from different medical testing devices (such as high-dimensional physiological features extracted from MRI images and routine blood test results), used for pattern classification and diagnostic inference of the probability of a specific disease (such as a tumor lesion); in a multi-sensor target recognition scenario, the first and second evidence sources describe continuous physical observation features of the same unknown target from different radar or optical sensors. To verify the underlying core logic of this invention, specifically in the algorithm performance testing phase of this embodiment, the first and second evidence sources are continuous physical observation features from standard datasets such as irises, penguins, or stars, in order to verify the technical effect of this invention in balancing computational complexity and reasoning rigor when processing complex data with different dimensions and distribution characteristics.

[0025] The specific steps involved in constructing the first and second generalized quantum fundamental probability amplitudes are as follows: S101. Obtain the first classical generalized basic probability assignment function based on the first evidence source, and obtain the second classical generalized basic probability assignment function based on the second evidence source. The first classical generalized basic probability assignment function and the second classical generalized basic probability assignment function quantify the degree of trust of each observation feature in different pattern category propositions within the identification framework.

[0026] S102. The first complex probability amplitude is obtained based on the first classical generalized fundamental probability assignment function, and the second complex probability amplitude is obtained based on the second classical generalized fundamental probability assignment function. The classical real probability assignment is converted into the generalized quantum fundamental probability amplitude in quantum mechanics. Specifically, a generalized fundamental probability assignment determination algorithm based on the Triangular Fuzzy Number (TFN) model is adopted. The specific conversion steps include: First, based on the feature distribution of the training data for each pattern category, a corresponding triangular fuzzy number model is constructed for each known category within the identification framework using the statistical properties of the features (such as mean and standard deviation) to characterize the uncertainty distribution of feature values; then, the similarity between the normalized feature values ​​of the sample to be classified and the model center values ​​of each category is calculated, that is, the probability of the sample feature falling into each category interval or belonging to that category is calculated using the membership function; finally, the calculated similarity results are mapped and normalized to generate the classical generalized fundamental probability assignment (GBPA) function values ​​corresponding to each data feature, completing the feature conversion from original physical observations to the quantum evidence theory trust space. The specific details of the algorithm for determining the generalized basic probability assignment of the triangular fuzzy number model, which calculates the first and second complex probability amplitudes, are existing technologies and will not be elaborated here.

[0027] S103. Based on the assumption of no interference (incoherence), the first generalized quantum fundamental probability amplitude in quantum evidence theory is generated according to the first complex probability amplitude, and its expression is:

[0028]

[0029] In the formula, The first generalized quantum fundamental probability amplitude, To identify the first in the framework A subset proposition, that is, a specific pattern category or combination of categories. An index for a subset of propositions of the first generalized quantum fundamental probability amplitude. Let be the modulus of the first complex probability amplitude, where the modulus of the first complex probability amplitude is strictly equal to the square root of the first classical generalized basic probability assignment. The complex phase factor characterizing the coherence of quantum states in the first generalized quantum fundamental probability amplitude. The initial phase angle is the first generalized quantum fundamental probability amplitude. This is the first classical generalized basic probability assignment function.

[0030] The expression for the second generalized quantum fundamental probability amplitude in quantum evidence theory, based on the second complex probability amplitude, is as follows:

[0031]

[0032] In the formula, This represents the second generalized quantum fundamental probability amplitude. To identify the first in the framework A subset proposition, that is, a specific pattern category or combination of categories. An index for a subset of propositions of the second generalized quantum fundamental probability amplitude. Let be the modulus of the second complex probability amplitude, where the modulus of the second complex probability amplitude is strictly equal to the square root of the second classical generalized basic probability assignment. The complex phase factor characterizing the coherence of quantum states in the second generalized quantum fundamental probability amplitude. The initial phase angle is the second generalized quantum fundamental probability amplitude. This is the second classical generalized basic probability assignment function.

[0033] The form of the identification framework is as follows: .and and These are all subset propositions for identifying the power set of the frame. The proposition itself is an index, i.e. and They are all a series of values, and each of these values ​​represents a specific value for each proposition.

[0034] Under the condition of generalized incoherence, it is assumed that the sources of evidence are incoherent and therefore do not produce interference terms. That is, each source of evidence is independent at the physical or statistical level. The initial phase angles of the first and second generalized quantum fundamental probability amplitudes can both be uniformly set to zero. At this point, the generalized quantum fundamental probability amplitude is completely determined by its modulus, realizing the simplest mapping from classical real probability assignment to quantum complex probability amplitude.

[0035] S2. Generate a first quantum superposition state based on the first generalized quantum fundamental probability amplitude, and a second quantum superposition state based on the second generalized quantum fundamental probability amplitude; that is, isomorphically map the first and second generalized quantum fundamental probability amplitudes to a higher-dimensional Hilbert space using quantum amplitude encoding technology. Specifically, the two generated independent first and second generalized quantum fundamental probability amplitudes are encoded separately, and these two discrete generalized fundamental probability amplitudes are encoded as quantum state amplitudes and embedded into a register with n qubits (where n equals the identification frame). The number of elements is determined, thus generating two independent first quantum superposition states and a second quantum superposition state. These two superposition states are the initial input parameters for subsequent quantum circuit combination evolution. The expression for the first quantum superposition state is:

[0036] In the formula, It is the first quantum superposition state. The first generalized quantum fundamental probability amplitude, The computational ground state of the first generalized quantum is composed of the tensor product of n single-qubit states and is used to characterize the corresponding proposition. To identify frames, a non-empty set consisting of n mutually exclusive and complete elements (i.e., all possible basic pattern categories or independent hypothetical targets) is denoted as . .

[0037] The expression for the second quantum superposition state is:

[0038] In the formula, It is the second quantum superposition state. This represents the second generalized quantum fundamental probability amplitude. This is the computational ground state of the second generalized quantum.

[0039] S3. Construct an initial global quantum state based on the first quantum superposition state and the second quantum superposition state, and then evolve the final system state based on the initial global quantum state through the quantum evidence combination rule.

[0040] The specific steps include: S301, Build initialization Ground state target register The first quantum superposition state, the second quantum superposition state, the target register, and the auxiliary bits are combined. As inputs to the circuit, these superposition states naturally yield the initial global quantum state of the tensor throughout the system:

[0041] In the formula, For the initial global quantum state, For auxiliary bits, For the target register of the ground state, To identify the first in the framework subset propositions To identify the first in the framework subset propositions, among which and Independent of each other For the proposition in the first quantum superposition state The magnitude of the corresponding probability amplitude, For the proposition in the second quantum superposition state The magnitude of the corresponding probability amplitude, For the proposition in the first quantum superposition state The corresponding quantum ground state and the proposition in the second quantum superposition state The corresponding quantum ground state.

[0042] S302, as attached Figure 2 and attached Figure 3 As shown, the first system evolution state is obtained by evolving from the initial global quantum state through the quantum evidence combination rule. Specifically, when evolving the initial global quantum state, the operator is used. Identify and label the quality assignments of the empty set, generate the first system evolution state containing the target value and unknown computational intermediate data, in order to accurately define the operators. First, we need to accurately define the quantum gate that constitutes this operator. The definition process is as follows: Standard Toffoli Gate: We define the generalized standard Toveley function. If and only if two control bits and All are in excited state Only when the target bit t is reached is a Pauli-X gate applied. Considering that the target bit is always below the control bits in the circuit, the mathematical definition of this gate, acting on the global space, is:

[0043]

[0044] In the formula, For the generalized standard Toveley function, To apply to all identity matrices without specified bits, in order to maintain dimensional consistency, In quantum mechanics, the tensor product operator is used to combine multiple single-qubit states into a many-body composite quantum state. To control the projection operator of the bits, For the first control bit, For the second control bit, For the target bit, To apply to the target bit Pauli-X matrix on To apply to the target bit The identity matrix on, To be applied to the first control bit Second control bit The identity matrix on, First control bit Second control bit All in The projection operator will only perform subsequent operations on the target bit when the projection operator is active.

[0045] The generalized standard Toveli operator is a Hermitian operator that satisfies... ,in For generalized standard Toveley operators, It is the conjugate transpose of the generalized standard Toveli operator.

[0046] Operators are constructed based on the generalized standard Toveley function. Its expression is:

[0047]

[0048] In the formula, For continuous product operation, To identify the size of the frame, The cyclic part of the operator consists of three Toffoli gates. The first qubit that stores the first quantum superposition state. The first qubit is the qubit that stores the second quantum superposition state. For the first qubit of the target quantum register, The identity matrix applied to the auxiliary bits. To assist the qubit, For the target quantum register's first 1 qubit The identity matrix applied to the target quantum register. The Pauli-X matrix is ​​applied to the qubits storing the second quantum superposition state. Let be the Pauli-X matrix applied to the qubit storing the first quantum superposition state.

[0049] The expression for the evolution state of the first system is:

[0050] In the formula, This represents the first system evolution state. The excited state of the auxiliary flag bit is used here to indicate that the condition for the union operation of propositional combinations to result in an empty set is met. To calculate intermediate data, For Pauli Door( Door), To perform the union operation, It is an empty set; The intermediate computation data refers to the superposition state generated during quantum logic operations, which is entangled with the target information and no longer needed in subsequent calculations, due to the use of auxiliary bits to store intermediate operation results. The intermediate computation data is the entangled intermediate state data generated by introducing auxiliary bits to achieve reversible set operation logic; the expression for the intermediate computation data is:

[0051] In the formula, For the first A state in the ground state The tensor product of a single quantum bit, For the first A state in an excited state The tensor product of a single quantum bit, In quantum mechanics, the tensor product operator is used to combine multiple single-qubit states into a many-body composite quantum state. To identify the size of the frame, i.e., the total number of basic elements in the frame, corresponding to the total number of qubits in the target data register, Here is the position index of the qubit currently participating in the logic operation, where .

[0052] The first system evolutionary state includes The quantum states of qubits; where the first system evolution state is the _th qubit The values ​​on the qubits are needed for subsequent steps, while the values ​​on the other bits in the first system evolution state are intermediate data for computation.

[0053] S303. Obtain the second system evolution state based on the first system evolution state. Specifically, use a controlled NOT gate (CNOT) to convert the first system evolution state into its second evolution state. The efficient computation results on each of the qubits are securely copied and temporarily stored to the qubit. Of the qubits, , For positive integers greater than 1, the second system evolution state is obtained, where the controlled NOT gate (CNOT) function... If and only if a single control bit c is in the excited state Only when the target bit t is reached is a Pauli-X gate applied. Assuming the target bit in the continuation circuit is typically located below the control bits, the mathematical definition of a controlled NOT gate acting on the global space is:

[0054]

[0055] In the formula, To control the projection operator of the bits, The identity matrix applied to the control bits. To control bits In The projection operator will only perform subsequent operations on the target bit when the projection operator is active.

[0056] The expression for the evolution state of the second system is:

[0057] In the formula, This represents the second system evolution state. For the target quantum register's first 1 qubit The composite quantum state, where the nth qubit and the (n+1)th auxiliary qubit are simultaneously in an excited state, signifies that the result of determining that the target intersection is an empty set has been successfully copied and temporarily stored by the controlled NOT gate. It is a composite quantum state in which the nth qubit and the (n+1)th auxiliary qubit are simultaneously in the ground state.

[0058] S304. Obtain the third system evolution state based on the second system evolution state, specifically by applying an inverse operator to the second system evolution state. The evolution process yields the third system evolution state, where the inverse operator, serving as the inverse operator of the operator in step S302, is specifically used to undo state entanglement and clear the aforementioned intermediate computational data, thereby ensuring the... The target information is preserved. The expression for the evolutionary state of the third system after evolution is:

[0059]

[0060] In the formula, This represents the third system's evolutionary state. For inverse operators, The (n+1)th auxiliary bit (flag bit) is in the excited state. And the computation register is restored to the ground state. The composite quantum state indicates that the empty set condition is met and the intermediate states have been cleared. The (n+1)th auxiliary bit (flag bit) is in the ground state. And the computation register is restored to the ground state. The composite quantum state indicates that the empty set determination condition is not met and the intermediate state has been cleared.

[0061] S305. Obtain the final system state based on the evolution of the third system state, specifically by applying the intersection simulation operator to the third system evolution state. The evolution process yields the final system state, where the intersection simulation operator consists of multiple parallel Toffoli gates. Bitwise operations are used to simulate the process of finding the intersection of two propositions in classical evidence theory. The expression for the final system state is:

[0062]

[0063]

[0064] In the formula, For the final system state, For intersection simulation operators, Let the quantum ground state in the target register be the proposition used to characterize the result of evidence fusion reasoning, which is composed of a subset of propositions from the first source of evidence. The proposition of a subset of the second source of evidence The result of performing the intersection operation is the propositional mapping. To perform intersection operations.

[0065] For ease of explanation of subsequent measurement processes, the final system state can be more simply and clearly described using the density operator. The expression for the density operator of the final system state is as follows:

[0066] In the formula, For the density operator of the final system state, The square of the modulus, For the right vector of the composite quantum state containing the intersection result and the original double-evidence proposition, The left-hand conjugate of the composite quantum state is formed by combining the right-hand conjugate of the left-hand conjugate of the composite quantum state. It is the basic operator unit for calculating the global pure state density matrix.

[0067] S4. Use the fundamental probability measurement operator to perform quantum measurement on the generalized quantum of the final system state to extract the generalized quantum fundamental probability distribution, and obtain the evidence fusion reasoning result based on the generalized quantum fundamental probability distribution.

[0068] Specifically, the trace operation in quantum mechanics is used to extract the reduced density operator containing fused information from the density operator of the final system state, and from this, the classical generalized quantum fundamental probability distribution is obtained. The specific steps include: S401. Extract the reduced density operator from the density operator of the final system state and construct a set of generalized quantum fundamental probability measurement operators. When extracting the reduced density operator, a bias operation is performed on the density operator of the final system state to remove redundant information from the data quantum register, thereby extracting the reduced density operator containing fusion information from the target quantum register. The calculation formula is as follows:

[0069] In the formula, To reduce the density operator, This is a partial trace operation used to sum or integrate the degrees of freedom of the data register in order to remove redundant information. For data quantum registers, Let be the conjugate transpose left vector corresponding to the composite data quantum state containing the original subset propositions of the second and first evidence sources. The right vector of the composite data quantum state containing propositions from the original subsets of the second and first evidence sources. The quantum ground state is the proposition for the target result. The left-hand conjugate of the quantum ground state of the propositional result is formed by combining it with the corresponding right-hand conjugate. It is the projection operator representing the effective fusion information in the extracted reduced density operator.

[0070] The set of generalized quantum fundamental probability measurement operators is defined based on the target quantum register:

[0071] In the formula, For the set of generalized quantum fundamental probability measurement operators, For projection measurement operators corresponding to a specific measurement substrate, To measure the right vector of the composite quantum state of the basis, the auxiliary qubit ground state is used to indicate the validity of the computation. Ground state of the proposition of target outcome The tensor product is composed of, To measure the left vector of the composite quantum state of the basis, it is expressed as an outer product with the right vector of the composite quantum state. Together they form the complete projection operator matrix.

[0072] S402. The generalized quantum fundamental probability distribution is obtained by performing quantum measurements on the final system state using the generalized quantum fundamental probability measurement operators from the set of generalized quantum fundamental probability measurement operators. Specifically, the conflict coefficient is calculated based on the reduced density operator and the set of generalized quantum fundamental probability measurement operators, and the probability distribution is calculated based on the conflict coefficient. Specifically, a quantum measurement evaluation operation is performed on the reduced density operator and the set of generalized quantum fundamental probability measurement operators, where the conflict coefficient is calculated as follows:

[0073] In the formula, The conflict coefficient, The trace operation is used to calculate the expected value of the reduced density operator under a specific measurement basis, i.e., the probability of the corresponding state occurring. For measurement operators The conjugate transpose of . For measurement operators The conjugate transpose of . The system auxiliary flag bit is in the excited state. Furthermore, the objective outcome proposition collapses into the ground state. The projection measurement operator, The system auxiliary flag bit is in the ground state. Furthermore, the objective outcome proposition collapses into the ground state. Projection measurement operator.

[0074] The formula for calculating the probability distribution is:

[0075]

[0076] In the formula, The value of the generalized quantum fundamental probability distribution of the empty set is obtained by quantum measurement from the final system state. To identify empty set propositions within the frame, The normalized value of the generalized quantum fundamental probability distribution of the non-empty subset proposition represents the degree of support the fusion system has for this specific hypothetical proposition. To identify the first in the power set of the frame The proposition of subsets of each.

[0077] S403. The probability distribution is transformed to obtain the fused classical generalized fundamental probability assignment function to eliminate the probability quality loss caused by quantum measurement. The formula for calculating the fused classical generalized fundamental probability assignment function is as follows:

[0078]

[0079] In the formula, Assign the empty set proposition to the merged classical generalized basic probability assignment function. The basic probability quality is used to quantify the overall degree of conflict in a system at the classical pattern classification decision level. Assign a specific non-empty subset proposition to the merged classical generalized basic probability assignment function. The fundamental probability quality represents the final overall confidence level of multi-source evidence in the target hypothesis category or pattern combination after quantum circuit evolution and equivalent measurement.

[0080] S404. Based on the selection of evidence fusion inference results using the fusion of classical generalized basic probability assignment functions, the confidence level of subset propositions in the identification framework is calculated according to the fusion of classical generalized basic probability assignment functions. The subset hypothesis category corresponding to the maximum confidence level is selected as the final inference and pattern recognition output. The specific decision classification logic can be expressed by the following formula:

[0081] In the formula, The final output reasoning and recognition decision results are obtained by assessing the confidence levels of all single hypothesis categories within the recognition framework. Perform traversal and comparison, and select the category corresponding to the largest value. As the final classification assignment of the target sample; The function for maximizing the independent variable for the target variable is, in other words, finding the mathematical operator of the input independent variable that makes a given function achieve its global maximum. In this invention, this function is specifically used in the identification framework. Perform a global traversal within the function to find and return the function that evaluates the confidence of a subset. Specific mode categories for reaching the maximum value , To identify the frame A subset of propositions within a single set, that is, a specific single category of assumptions. For a specific pattern recognition or physical observation task, the identification framework includes the set of all possible classification results. propositions for monosets The confidence score is calculated strictly based on the fusion classical generalized basic probability assignment function obtained in step S403, and represents the overall support for the hypothesis category after the fusion of current multi-source evidence.

[0082] To verify the evidence fusion reasoning method based on quantum evidence theory proposed in this invention To demonstrate the effectiveness and superiority of the algorithm, comparative analysis experiments on statistical error and computational complexity, as well as application testing experiments on pattern classification, were conducted. These included analysis of the evolution of inherent statistical error, comparative analysis of algorithm computational complexity, and performance testing of pattern classification on public multi-class datasets.

[0083] In the comparative analysis of statistical error and computational complexity, the inherent statistical error introduced by quantum state collapse and measurement mechanisms was quantitatively examined by first constructing a uniformly distributed initial generalized fundamental probability assignment function and performing a self-fusion test. The mean absolute percentage error (MAPE) evaluation results of the quantum and classical results calculated by this scheme under different identification frame sizes are attached. Figure 4 To be continued Figure 7 As shown. Experimental results show that, despite the classic non-interference combination rules And the algorithm of this invention The calculated results are highly accurate, but small errors remain due to the randomness of quantum measurements. Specifically, as the size of the identification frame increases, the number of approximate probability states (quantum ground states) that need to be statistically analyzed in the target register increases exponentially, leading to a corresponding increase in the mean absolute percentage error (MAPE). However, by adaptively increasing the number of quantum measurements (e.g., from...), the error can be mitigated. Increase to This method can effectively suppress statistical fluctuations and significantly reduce MAPE, thereby obtaining a probability distribution that is closer to the theoretical true value.

[0084] Secondly, the computational overhead of the underlying algorithm was compared. For a size of... The identification framework and solution The task of a specific proposition, classic The algorithm needs to traverse the entire power set space, and its worst-case computational complexity is as high as [missing value]. It exhibits exponential explosive growth; in contrast, the invention proposed... The algorithm cleverly utilizes the superposition and parallel evolution characteristics of quantum circuits (the system only needs...). (Number of qubits), combining operator evolution with extremely lightweight classical post-processing overhead, significantly compressing the total computational complexity to Both experimental data and theoretical derivation demonstrate that this method achieves a leap in computational cost from exponential to linear levels, successfully overcoming the curse of dimensionality when processing high-dimensional information fusion.

[0085] In conducting pattern classification application testing experiments, to evaluate the actual inference performance of this invention under complex data distributions in the real physical world, four classic multi-class datasets from open-source data platforms were selected: Iris, Penguin, Star, and Wheat-seed datasets. The experiments uniformly employed 5-fold cross-validation. The strategy transforms continuous physical observation features into GBPA for processing and comprehensively records classical data. Algorithms and Quantum Measurements at Different Numbers The classification accuracy of the algorithm.

[0086] The similarity between the quantum and classical classification accuracy rates obtained by this method on different open-source multi-class datasets ( The analysis results are attached. Figure 8 To be continued Figure 11 As shown in the figure; experimental results demonstrate that, in terms of test set accuracy on various datasets, this invention exhibits superior overall performance and extremely strong approximation ability. For example, on the Iris dataset, the average accuracy of the classical method is 0.947, while the method of this invention achieves significantly lower accuracy with fewer sampling times. The accuracy reached 0.927; on the Penguin dataset, the classic method achieved 0.919, while this invention achieved [a higher accuracy]. The accuracy is also as high as 0.919; on the Wheat-seed dataset, the classic method achieves 0.906, while this invention achieves... and The average value reached 0.894.

[0087] To further quantify the performance similarity between the two, the experiment introduced a classification result similarity evaluation function ( Data analysis clearly shows that when the number of quantum measurements is small, the classification accuracy of this invention is usually low and prone to fluctuations due to the statistical fluctuation effect of state collapse; however, as the number of measurements increases, the discrimination ability of the quantum algorithm is significantly improved, and its classification accuracy is comparable to that of classical quantum ... The algorithm's judgment results are becoming increasingly consistent. (Approaching 1). This fully demonstrates that, given sufficient sampling times for the system, the slight inference error caused by the inherent probabilistic properties of the algorithm of this invention will not have a substantial negative impact on the overall performance of pattern classification, and it fully possesses the same level of decision-making ability and engineering application robustness as classical theory.

[0088] This invention also aims to provide an evidence fusion reasoning system based on quantum evidence theory, applicable to the aforementioned evidence fusion reasoning method based on quantum evidence theory, including: The evidence source acquisition module is used to acquire the first and second evidence sources for the fusion reasoning; A generalized quantum fundamental probability amplitude construction module is used to construct a first generalized quantum fundamental probability amplitude based on a first source of evidence and a second generalized quantum fundamental probability amplitude based on a second source of evidence. A quantum superposition state generation module is used to generate a first quantum superposition state based on a first generalized quantum fundamental probability amplitude and a second quantum superposition state based on a second generalized quantum fundamental probability amplitude. The quantum state evolution module is used to construct an initial global quantum state based on the first quantum superposition state and the second quantum superposition state, and to obtain the final system state based on the initial global quantum state through the quantum evidence combination rule. The evidence fusion reasoning module is used to perform quantum measurements using the generalized quantum fundamental probability measurement operator based on the final system state, extract the generalized quantum fundamental probability distribution, and obtain the evidence fusion reasoning result based on the generalized quantum fundamental probability distribution.

[0089] The present invention also aims to provide an evidence fusion reasoning device based on quantum evidence theory, including a memory, a processor, and a computer program stored in the memory, characterized in that the processor executes the computer program to implement the steps of the above-described evidence fusion reasoning method based on quantum evidence theory.

[0090] The present invention also aims to provide a computer-readable storage medium containing a computer program, wherein the computer program is stored thereon, characterized in that, when the computer program is executed by one or more processors, it implements the steps of the above-described evidence fusion reasoning method based on quantum evidence theory.

[0091] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the scope of the present invention should be included within the protection scope of the present invention.

Claims

1. An evidence fusion reasoning method based on quantum evidence theory, characterized in that, Includes the following steps: Obtain a first source of evidence and a second source of evidence to be combined. The first source of evidence and the second source of evidence are independent of each other. The first source of evidence and the second source of evidence are either equipment observation features or physical observation features. A first generalized quantum fundamental probability amplitude is constructed based on the first source of evidence, and a second generalized quantum fundamental probability amplitude is constructed based on the second source of evidence. The first quantum superposition state is generated according to the first generalized quantum fundamental probability amplitude, and the second quantum superposition state is generated according to the second generalized quantum fundamental probability amplitude; An initial global quantum state is constructed based on the first quantum superposition state and the second quantum superposition state. The final system state is obtained by evolution based on the initial global quantum state through the quantum evidence combination rule. When constructing the initial global quantum state based on the first quantum superposition state and the second quantum superposition state, a target register is constructed, and the initial global quantum state is obtained by inputting the first quantum superposition state, the second quantum superposition state, the target register, and the auxiliary bit input line. The steps for obtaining the final system state based on the initial global quantum state through the quantum evidence combination rule include: The mass assignment of the empty set is computed by applying operators to the initial global quantum state, and a first system evolution state containing the mass assignment of the empty set and computational intermediate data is generated based on the mass assignment of the empty set. The first system evolution state contains... The quantum state of a qubit; By applying a controlled NOT gate to the first system evolution state, the first system evolution state is... The computation results on the i-th qubit are copied and temporarily stored in the i-th qubit. Each qubit yields the second system evolution state, where , It is a positive integer greater than 1; The third system evolution state is obtained by applying an inverse operator to the second system evolution state to revoke state entanglement and clear intermediate computation data; The final system state is obtained by applying an intersection simulation operator to the third system evolution state and performing intersection operations through bitwise logic. The generalized quantum state of the final system is measured using the fundamental probability measurement operator to extract the generalized quantum fundamental probability distribution, and the evidence fusion reasoning result is obtained based on the generalized quantum fundamental probability distribution.

2. The evidence fusion reasoning method based on quantum evidence theory according to claim 1, characterized in that, The steps for constructing the first generalized quantum fundamental probability amplitude and the second generalized quantum fundamental probability amplitude based on the first evidence source and the second evidence source, respectively, include: The first classical generalized basic probability assignment function is obtained based on the first source of evidence, and the second classical generalized basic probability assignment function is obtained based on the second source of evidence. The first complex probability amplitude is obtained by transformation based on the first classical generalized basic probability assignment function, and the second complex probability amplitude is obtained by transformation based on the second classical generalized basic probability assignment function. The first generalized quantum fundamental probability amplitude is generated based on the first complex probability amplitude, and the second generalized quantum fundamental probability amplitude is generated based on the second complex probability amplitude.

3. The evidence fusion reasoning method based on quantum evidence theory according to claim 1, characterized in that, The operator is constructed based on the standard Toveley function, which is to apply a Pauli X-gate to the target bit when both control bits are in an excited state.

4. The evidence fusion reasoning method based on quantum evidence theory according to claim 1, characterized in that, The steps of extracting the generalized quantum fundamental probability distribution by performing quantum measurement using the fundamental probability measurement operator on the generalized quantum of the final system state, and obtaining the evidence fusion inference result based on the generalized quantum fundamental probability distribution include: Constructing a set of generalized quantum fundamental probability measurement operators; The generalized quantum fundamental probability distribution is obtained by performing quantum measurements based on the final system state and the set of generalized quantum fundamental probability measurement operators. The probability distribution is transformed to obtain a fusion of classical generalized basic probability assignment functions; The confidence level of a subset proposition in the identification framework is calculated using a fusion of classical generalized basic probability assignment functions. Based on the confidence level, the subset hypothesis category is selected to obtain the evidence fusion reasoning result.

5. The evidence fusion reasoning method based on quantum evidence theory according to claim 4, characterized in that, The steps for obtaining the generalized quantum fundamental probability distribution by performing quantum measurements based on the final system state and the set of generalized quantum fundamental probability measurement operators include: Perform a partial trace operation on the final system state to obtain a reduced density operator containing fused information; Calculate the conflict coefficient based on the set of reduced density operators and generalized quantum fundamental probability measurement operators; Probability distributions are calculated based on the conflict coefficient.

6. An evidence fusion reasoning system based on quantum evidence theory, used to implement the evidence fusion reasoning method based on quantum evidence theory as described in any one of claims 1-5, characterized in that, include: The evidence source acquisition module is used to acquire the first and second evidence sources for the fusion reasoning; A generalized quantum fundamental probability amplitude construction module is used to construct a first generalized quantum fundamental probability amplitude based on a first source of evidence and a second generalized quantum fundamental probability amplitude based on a second source of evidence. A quantum superposition state generation module is used to generate a first quantum superposition state based on a first generalized quantum fundamental probability amplitude and a second quantum superposition state based on a second generalized quantum fundamental probability amplitude. The quantum state evolution module is used to construct an initial global quantum state based on the first quantum superposition state and the second quantum superposition state, and to obtain the final system state based on the initial global quantum state through the quantum evidence combination rule. The evidence fusion reasoning module is used to extract the generalized quantum fundamental probability distribution based on the final system state, and to obtain the evidence fusion reasoning result based on the generalized quantum fundamental probability distribution.

7. An evidence fusion reasoning device based on quantum evidence theory, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the evidence fusion reasoning method based on quantum evidence theory as described in any one of claims 1-5.

8. A computer-readable storage medium containing a computer program, wherein the computer program is stored thereon, characterized in that, When the computer program is executed by one or more processors, it implements the steps of the evidence fusion reasoning method based on quantum evidence theory as described in any one of claims 1-5.

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