Method and system for solving a quantum many-body model of a ferrimagnetic-like based on a fractional matching

Abstract

The application discloses a kind of based on the solution method and system of ferromagnetic quantum many-body model of fractional matching, based on the solution method of ferromagnetic quantum many-body model of fractional matching includes: obtaining and according to the Hamiltonian of ferromagnetic quantum many-body model, the corresponding undirected graph is generated;For all edges in undirected graph, angle parameter is introduced, and first parametric formula is obtained;According to first parametric formula and Hamiltonian, the second parametric formula of system energy is obtained;According to undirected graph, and by quasi-uniform fractional matching strategy, determine fractional matching scheme;According to the second parametric formula and fractional matching scheme, the entanglement degree control parameter that makes system energy maximum or minimum is output;According to entanglement degree control parameter, first parametric formula and second parametric formula, the approximate ground state and approximate energy of model are obtained.The application is distributed to a certain proportion of entanglement by quasi-uniform fractional matching strategy, so that each pair of adjacent particles is distributed, so that higher approximation ratio is realized.

Description

Technical Field

[0001] This invention relates to the field of quantum technology, and in particular to a solution method for a ferromagnetic quantum many-body model based on fractional matching, a solution system for a ferromagnetic quantum many-body model based on fractional matching, and an electronic device. Background Technology

[0002] Quantum many-body models characterize the interactions between multiple particles (such as qubits, atoms, and molecules). They use the Hamiltonian to describe the total energy of the system, and solve for the eigenvalues ​​of the Hamiltonian (i.e., the system energy) and the corresponding eigenstates to understand the physical properties of the system. These models have wide applications in materials science, condensed matter physics, quantum chemistry, quantum information, and quantum computing. Ferromagnetic quantum many-body models are a class of quantum many-body models with ferromagnetic-like characteristics. Solving their Hamiltonian problems is one of the core tasks in research directions such as quantum materials simulation and quantum computing, and has significant application value. For example, solving for the maximum energy and corresponding state of ferromagnetic EPR models can help engineers constrain entanglement behavior in the system, thereby designing quantum algorithms to achieve entanglement optimization. However, current solution methods have significant errors in obtaining the approximate ground state and approximate energy of ferromagnetic quantum many-body models. Therefore, how to more accurately solve for the approximate ground state and approximate energy of ferromagnetic quantum many-body models is a problem that urgently needs to be solved. Summary of the Invention

[0003] The present invention is proposed to solve at least one of the above-mentioned problems. According to a first aspect of the present invention, a method for solving a ferromagnetic quantum many-body model based on fractional matching is provided, the method comprising:

[0004] Obtain the Hamiltonian of the ferromagnetic quantum many-body model and generate the corresponding undirected graph.

[0005] By introducing angle parameters to all edges in the undirected graph, the first parameterized general formula of the magic graph state corresponding to the undirected graph is obtained.

[0006] Based on the first parameterized general formula and the Hamiltonian, the second parameterized general formula for the system energy of the ferromagnetic quantum many-body model is obtained.

[0007] Based on the undirected graph, a fraction matching scheme is determined using a quasi-uniform fraction matching strategy.

[0008] Based on the second parameterized general formula and the fractional matching scheme, output the entanglement degree control parameter that maximizes or minimizes the energy of the system.

[0009] Based on the entanglement degree control parameters, calculate each of the angle parameters and their corresponding trigonometric function values.

[0010] Based on the angle parameters, the trigonometric function values, the first parameterized general formula, and the second parameterized general formula, the approximate ground state and approximate energy of the ferromagnetic quantum many-body model are obtained.

[0011] In one embodiment of the present invention, the step of obtaining and generating a corresponding undirected graph based on the Hamiltonian of a ferromagnetic quantum many-body model includes:

[0012] Each particle in the Hamiltonian is assigned a vertex, forming a vertex set V.

[0013] Determine whether the Hamiltonian contains two-body terms and / or single-body terms.

[0014] If the two-body term exists between two particles in the Hamiltonian, then an edge is connected between the two particles to obtain the first weight coefficient of each edge. All the edges constitute the edge set E, and all the first weight coefficients constitute the weight set w.

[0015] If the Hamiltonian contains the single-entity term, then the vertex corresponding to the single-entity term is assigned a second weight coefficient, and the second weight coefficient is updated to the weight set w.

[0016] Determine whether there are non-integer weights in the weight set w.

[0017] If it exists, multiply the weight coefficients in the weight set w by 10, and return to the step of determining whether there are non-integer weights in the weight set w.

[0018] If it does not exist, then the undirected graph is constructed based on the vertex set V, the edge set E, and the weight set w. .

[0019] In one embodiment of the present invention, the Hamiltonian is represented as:

[0020]

[0021] The step of introducing angle parameters to all edges in the undirected graph to obtain the first parameterized generalized expression of the magic graph state corresponding to the undirected graph includes:

[0022] For the undirected graph Define angle parameters for all adjacent vertices i and j. .

[0023] According to the angle parameters Thus, the first parameterized general formula is obtained:

[0024]

[0025] Where i and j represent vertex indices, This represents the first weight coefficient of the edge between the i-th vertex and the j-th vertex. This represents the second weight coefficient of the i-th vertex single item. , , , Indicates the preset coefficient. This represents the angle parameter between the i-th vertex and the j-th vertex. , This represents the I-gate of the i-th vertex. This represents the Z-gate of the i-th vertex. This represents the X-gate of the i-th vertex. This represents the Y-gate of the i-th vertex. Let P represent the P-gate of the i-th vertex, and n represent the total number of vertices in the vertex set V. This represents the edge between the i-th vertex and the j-th vertex. Represents the imaginary unit. .

[0026] In one embodiment of the present invention, the construction process of the second parameterized formula includes:

[0027] The two-body term in the Hamiltonian Replace with: and the two-body terms in the Hamiltonian Replace with: The replaced Hamiltonian is obtained as follows: .

[0028] Transform the replaced Hamiltonian into the second parameterized general formula: .

[0029] in, , , , , , , , Let Q represent the Q-gate of the i-th vertex, K represent the set of all neighbors of the i-th vertex except the j-th vertex, k represent the k-th vertex in set K, L represent the set of all neighbors of the j-th vertex except the i-th vertex, l represent the l-th vertex in set L, T represent the set of the common neighbors of the i-th and j-th vertices, S represent a subset of T, s represent the s-th vertex in set S, |S| even represents the set S has an even number of elements, and |S| odd represents the set S has an odd number of elements. This means removing all elements from set S from set K. Let k represent all neighboring vertices of vertex i.

[0030] In one embodiment of the present invention, the step of determining a score matching scheme based on the undirected graph and using a quasi-uniform score matching strategy includes:

[0031] The weighted degree of each vertex in the undirected graph is calculated based on the first weight coefficient.

[0032] The matching score of each edge is calculated based on the first weight coefficient and the weighting degree.

[0033] In one embodiment of the present invention, the weighted degree of the i-th vertex is calculated using the following formula:

[0034]

[0035] The edge is calculated using the following formula. Match score:

[0036]

[0037] in, This represents the weighted degree of the i-th vertex. This represents the weighted degree of the j-th vertex. This represents the first weight coefficient of the edge between the i-th vertex and the k-th vertex. Representing an edge The matching score.

[0038] In one embodiment of the present invention, the step of outputting entanglement degree control parameters that maximize or minimize the system energy based on the second parameterized general formula and the fractional matching scheme includes:

[0039] according to , , , and The lower bound of energy is obtained from the boundary. energy lower bound ,in, .

[0040] Based on the lower bound of the matching score and the Upper Realm Define optimization variables .

[0041] Will In Replace with and according to Define the extreme values ​​of the interval .

[0042] Make Maximize as the goal, In Optimize and determine The value of .

[0043] in, This indicates the parameter controlling the degree of entanglement. The lower bound of energy is , The lower bound of energy is , The lower bound of energy is , The lower bound of energy is , , .

[0044] In one embodiment of the present invention, the trigonometric function values ​​are double-angle cosine and double-angle sine;

[0045] Calculate the angle parameter using the following formula. The double-angle cosine value:

[0046]

[0047] Calculate the corresponding angle parameters based on the double-angle cosine value. And the sine value of a double angle.

[0048] According to a second aspect of the present invention, a solution system for a ferromagnetic quantum many-body model based on fractional matching is provided. The solution system for the ferromagnetic quantum many-body model based on fractional matching includes: a preprocessing module, a ground state simulation module, an energy simulation module, a fractional matching module, a parameter optimization module, an angle calculation module, and a result processing module.

[0049] The preprocessing module is used to obtain and generate the corresponding undirected graph based on the Hamiltonian of the ferromagnetic quantum many-body model.

[0050] The ground state simulation module is used to introduce angle parameters into all edges of the undirected graph to obtain the first parameterized general formula of the magic graph state corresponding to the undirected graph.

[0051] The energy simulation module is used to obtain a second parameterized formula for the system energy of the ferromagnetic quantum many-body model based on the first parameterized formula and the Hamiltonian.

[0052] The score matching module is used to determine a score matching scheme based on the undirected graph and through a quasi-uniform score matching strategy.

[0053] The parameter optimization module is used to output entanglement control parameters that maximize or minimize the energy of the system, based on the second parameterized general formula and the fractional matching scheme.

[0054] The angle calculation module is used to calculate each angle parameter and its corresponding trigonometric function value according to the entanglement degree control parameter.

[0055] The result processing module is used to obtain the approximate ground state and approximate energy of the ferromagnetic quantum many-body model based on the angle parameter, the trigonometric function value, the first parameterized general formula and the second parameterized general formula.

[0056] According to a third aspect of the present invention, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory, wherein when the computer program is executed by the processor, it implements any of the above-described methods for solving the fractional matching-based ferromagnetic quantum many-body model.

[0057] According to embodiments of the present invention, the solution method, system, and electronic device for a ferromagnetic quantum many-body model based on fractional matching achieves a higher approximation ratio by employing a quasi-uniform fractional matching strategy to ensure that each pair of adjacent particles is assigned a certain proportion of entanglement. Therefore, the target eigenvalues ​​and corresponding states of the model can be obtained more accurately, providing a higher accuracy guarantee for solving more practical engineering problems. Furthermore, the solution method for a ferromagnetic quantum many-body model based on fractional matching is applicable not only to the EPR model but also to commonly used ferromagnetic or ferromagnetic models, including the transverse-field Ising model and the anisotropic XY model, thus possessing higher practical value and better scalability. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart illustrating a solution method for a ferromagnetic quantum many-body model based on fractional matching, provided in an embodiment of the present invention.

[0060] Figure 2 This is a schematic diagram of an undirected graph provided in an embodiment of the present invention;

[0061] Figure 3 This is a schematic diagram of the structure of a solution system for a ferromagnetic quantum many-body model based on fractional matching, provided in an embodiment of the present invention.

[0062] Figure 4 The hardware structure block diagram of a computer terminal for solving a ferromagnetic quantum many-body model based on fractional matching, as provided in an embodiment of the present invention. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the present invention more apparent, exemplary embodiments according to the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely a part of the embodiments of the present invention, and not all of the embodiments of the present invention. It should be understood that the present invention is not limited to the exemplary embodiments described herein. Based on the embodiments of the present invention described herein, all other embodiments obtained by those skilled in the art without inventive effort should fall within the protection scope of the present invention.

[0064] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0065] It should be understood that the invention can be embodied in various forms and should not be construed as being limited to the embodiments set forth herein. Rather, providing these embodiments will make the disclosure thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0066] To fully understand this invention, a detailed structure will be presented in the following description to illustrate the technical solution proposed by this invention. Optional embodiments of the invention are described in detail below; however, in addition to these detailed descriptions, the invention may have other embodiments.

[0067] The following detailed description of some embodiments of the present invention is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0068] The general form of the Hamiltonian for all ferromagnetic models can be expressed as:

[0069]

[0070] Among them, the shape is like The term represents the two-body interaction between particles i and j. I, Z, X, and Y are commonly used quantum gates. These are the weighting coefficients of the two-body term between particles i and j. Non-negative, , , , , These are preset coefficients. They are usually small to avoid single items becoming dominant.

[0071] Specifically, the general form of the Hamiltonian in the EPR model is:

[0072]

[0073] Solving for the maximum energy and corresponding state of the EPR model is equivalent to solving for the maximum eigenvalue and corresponding eigenstate of the Hamiltonian.

[0074] In related technologies, when solving the EPR model, the maximum fractional matching method in graph theory is usually used. The matching value of the edges determines the specific value of the angle parameter, thereby constraining the entanglement behavior of the EPR model. However, the quantum entanglement corresponding to the maximum fractional matching is often extremely non-uniform. It usually concentrates the maximum matching on a very small number of edges. From a physical point of view, this means that some particles have almost no entanglement. While gaining quantum contributions from some edges, they lose quantum contributions from other edges, making it difficult to obtain the maximum possible energy.

[0075] Therefore, in order to obtain the target eigenvalues ​​and corresponding states of the ferromagnetic quantum many-body model more accurately, the first aspect of this invention provides a solution method for the ferromagnetic quantum many-body model based on fractional matching, such as... Figure 1 As shown, the solution methods for the ferromagnetic quantum many-body model based on fractional matching include:

[0076] S1, obtain the Hamiltonian of the ferromagnetic quantum many-body model and generate the corresponding undirected graph.

[0077] It should be noted that an undirected graph is a structure that uses graph theory to represent the state or relationships of a quantum system. Its edges are not directional and are usually used to describe the symmetric interactions or entanglement between particles.

[0078] S2 introduces angle parameters to all edges in the undirected graph, resulting in the first parameterized general form of the magic graph state corresponding to the undirected graph.

[0079] S3. Based on the first parameterized general formula and the Hamiltonian, the second parameterized general formula for the system energy of the ferromagnetic quantum many-body model is obtained.

[0080] It should be noted that the second parameterized general formula makes the system energy a function that can be adjusted by the angle parameter, so as to facilitate the subsequent solution of the system energy extremum.

[0081] S4. Based on the undirected graph, determine the fraction matching scheme using a quasi-uniform fraction matching strategy.

[0082] It should be noted that in the quantum realm, the quasi-uniform fractional matching strategy is an entangled resource allocation strategy.

[0083] Accordingly, the lower bound of all matching scores can be denoted as The Upper Realm records it as .

[0084] S5, based on the second parameterized general formula and fractional matching scheme, outputs the entanglement degree control parameter that maximizes or minimizes the system energy.

[0085] As an example, an entanglement degree control parameter can be introduced. Matching results with quasi-uniform fractions, defining interval extrema. By optimizing parameters Solving for the extreme values ​​of an interval Thus, the parameters are determined. The value of .

[0086] S6, based on the entanglement degree control parameter, calculate each angle parameter and its corresponding trigonometric function value.

[0087] As an example, parameters can be substituted. Based on the quasi-uniform fractional matching results, calculate all angle parameters and their double-angle cosine and double-angle sine values.

[0088] S7. Based on the angle parameters, trigonometric function values, the first parameterized general formula and the second parameterized general formula, the approximate ground state and approximate energy of the ferromagnetic quantum many-body model are obtained.

[0089] The fractional matching-based solution method for ferromagnetic quantum many-body models in this invention employs a quasi-uniform fractional matching strategy, ensuring that each pair of adjacent particles is assigned a certain proportion of entanglement, thereby achieving a higher approximation ratio. Therefore, it can more accurately obtain the target eigenvalues ​​and corresponding states of the model, providing a higher accuracy guarantee for solving more engineering problems. Furthermore, the fractional matching-based solution method for ferromagnetic quantum many-body models of this invention is applicable not only to the EPR model but also to commonly used ferromagnetic or ferromagnetic models, including the transverse-field Ising model and the anisotropic XY model, demonstrating higher practical value and better scalability.

[0090] In some embodiments, the step of obtaining and generating a corresponding undirected graph based on the Hamiltonian of a ferromagnetic quantum many-body model includes:

[0091] S11 assigns a vertex to each particle in the Hamiltonian, forming the vertex set V.

[0092] As an example, the Hamiltonian of a ferromagnetic quantum many-body model describes the states of n particles, assigning each particle a unique vertex (which can be labeled as...). The set of all vertices is called the vertex set. .

[0093] S12, determine whether there are two-body terms and / or single-body terms in the Hamiltonian.

[0094] S13. If there is a two-body term between two particles in the Hamiltonian, then connect an edge between the two particles to obtain the first weight coefficient of each edge. All edges constitute the edge set E, and all first weight coefficients constitute the weight set w.

[0095] As an example, if there is a two-body term between particle i and particle j, then at the corresponding vertex and Connect them with an undirected edge.

[0096] S14. If there is a single term in the Hamiltonian, then assign a second weight coefficient to the vertex corresponding to the single term and update the second weight coefficient to the weight set w.

[0097] S15, determine whether there are non-integer weights in the weight set w.

[0098] It should be noted that in graph theory algorithms, integer weights are more favorable. By eliminating decimals through integerization, problems such as calculation errors can be avoided.

[0099] S16, if it exists, multiply the weight coefficients in the weight set w by 10 and return to step S15.

[0100] It should be noted that by multiplying by 10 each time, one decimal place can be eliminated, and after multiple iterations, a finite decimal can be converted into an integer.

[0101] S17, if it does not exist, then construct an undirected graph based on the vertex set V, edge set E, and weight set w. .

[0102] In this embodiment, by transforming the abstract Hamiltonian into an intuitive undirected graph structure, conditions are provided for subsequent solutions to quantum problems using graph theory tools, enabling quantum models to be directly processed using graph theory methods. Simultaneously, by designing edges to correspond to two-body terms and vertex weights to correspond to single-body terms, the core information of inter-particle interactions and individual particle energies in the Hamiltonian can be fully preserved, ensuring that the transformation process does not lose key physical meaning. Furthermore, the integerization of weights not only adapts to the computational requirements of subsequent graph theory algorithms such as fraction matching but also reduces errors caused by decimal operations, improving the stability and accuracy of the subsequent solution process.

[0103] In some embodiments, the Hamiltonian is represented as:

[0104]

[0105] By introducing angle parameters to all edges in an undirected graph, we obtain the magic graph state corresponding to the undirected graph. The first step involving a parameterized general formula includes:

[0106] S21 is an undirected graph. Define angle parameters for all adjacent vertices i and j. .

[0107] S22, based on angle parameters We obtain the first general formula containing parameters:

[0108]

[0109] Where i and j represent vertex indices, This represents the first weight coefficient of the edge between the i-th vertex and the j-th vertex. This represents the second weight coefficient of the i-th vertex single item. , , , Indicates the preset coefficient. This represents the angle parameter between the i-th vertex and the j-th vertex. , This represents the I-gate of the i-th vertex. This represents the Z-gate of the i-th vertex. This represents the X-gate of the i-th vertex. This represents the Y-gate of the i-th vertex. Let P represent the P-gate of the i-th vertex, and n represent the total number of vertices in the vertex set V. This represents the edge between the i-th vertex and the j-th vertex. Represents the imaginary unit. .

[0110] It should be noted that the function of the P door is equivalent to the combination of the X door and the Y door, that is: .

[0111] It should also be noted that, This represents the initial state of the system, which is the ground state of n particles. The product state.

[0112] In this embodiment, an angle parameter is defined for each edge of the undirected graph. This method transforms the structural information of a graph into adjustable quantum state parameters, achieving a precise correspondence between graph-theoretical structures and quantum entangled states. Furthermore, the first parameterized general formula not only preserves the connectivity between vertices in the undirected graph but also endows the quantum state with adjustable degrees of freedom through angle parameters. This provides a quantum state formal basis for subsequently obtaining the parameterized expression of the system energy by combining it with the Hamiltonian. At the same time, the constraint of the angle parameter's value range also limits the parameter space for subsequent optimization.

[0113] In some embodiments, the construction process of the second parameterized expression includes:

[0114] S31, the two-body terms in the Hamiltonian Replace with: and the two-body terms in the Hamiltonian Replace with: The replaced Hamiltonian is obtained as follows: .

[0115] Therefore, if the Hamiltonian contains a two-body term... If the Hamiltonian contains a two-body term, it can be equivalently replaced by a combination of P-gates and Q-gates. It can also be replaced by an equivalent combination of P-gate and Q-gate.

[0116] S32, transforms the replaced Hamiltonian into the second parameterized general formula: .

[0117] In summary, the system energy is equal to the weighted sum of the energies of all single-unit or two-unit terms in the Hamiltonian.

[0118] in, , , , , , , , Let Q represent the Q-gate of the i-th vertex, K represent the set of all neighbors of the i-th vertex except the j-th vertex, k represent the k-th vertex in set K, L represent the set of all neighbors of the j-th vertex except the i-th vertex, l represent the l-th vertex in set L, T represent the set of the common neighbors of the i-th and j-th vertices, S represent a subset of T, s represent the s-th vertex in set S, |S| even represents the set S has an even number of elements, and |S| odd represents the set S has an odd number of elements. This means removing all elements from set S from set K. Let k represent all neighboring vertices of vertex i.

[0119] It should be noted that the function of the Q door is equivalent to the combination of the X door and the Y door, that is: .

[0120] In this embodiment, by uniformly replacing the two-body terms in the Hamiltonian with a combination of P-gate and Q-gate, the formal differences between different interaction terms are eliminated, achieving adaptation to P-gate operations in magic graphs. Simultaneously, the replaced Hamiltonian is transformed into an angular parameter... The second parameterized general formula is the core variable, and the expected values ​​are clearly defined. The correlation of trigonometric functions transforms the abstract calculation of quantum system energy into a quantifiable and operable concrete expression, thus fully preserving the weight information in the original Hamiltonian.

[0121] In some embodiments, the step of determining a score matching scheme based on an undirected graph and using a quasi-uniform score matching strategy includes:

[0122] S41, Calculate the weighted degree of each vertex in the undirected graph based on the first weight coefficient.

[0123] Specifically, the weighted degree of the i-th vertex is calculated using the following formula:

[0124]

[0125] S42, calculate the matching score for each edge based on the first weight coefficient and the weighted degree.

[0126] Specifically, the edge is calculated using the following formula. Match score:

[0127]

[0128] in, This represents the weighted degree of the i-th vertex. This represents the weighted degree of the j-th vertex. This represents the first weight coefficient of the edge between the i-th vertex and the k-th vertex. Representing an edge The matching score.

[0129] In this embodiment, the weighted degree of each vertex is calculated to avoid local judgment bias caused by relying solely on edge weights in subsequent steps. At the same time, the matching score is calculated by dividing the edge weight by the maximum value of the weighted degrees of the two vertices, which can effectively balance the edge weight ratio between vertices with different loads. This preserves the differences in the magnitude of the edge weights themselves and avoids edges of high-load vertices occupying an unreasonable matching share due to excessively high vertex weights.

[0130] In some embodiments, the step of outputting entanglement control parameters that maximize or minimize system energy according to a second parametric generalization and fractional matching scheme includes:

[0131] S51, according to , , , and The lower bound of energy is obtained from the boundary. energy lower bound ,in, .

[0132] It should be noted that the edge energy lower bound This represents the lower bound of the weighted energy of the two-body terms associated with vertex i in the Hamiltonian, with the weights being coefficients. , , or .

[0133] S52, based on the lower bound in the matching score and the Upper Realm Define optimization variables .

[0134] S53, In Replace with and according to Define the extreme values ​​of the interval .

[0135] S54, so that Maximize as the goal, In Optimize and determine The value of .

[0136] in, This indicates the parameter controlling the degree of entanglement. The lower bound of energy is , The lower bound of energy is , The lower bound of energy is , The lower bound of energy is , , .

[0137] It should be noted that the lower bound of the energy of a single-unit or two-unit term with constant energy is the corresponding constant value.

[0138] In this embodiment, by defining interval extrema, it is not necessary to process each edge individually, thus improving the efficiency of optimization.

[0139] In some embodiments, the trigonometric function values ​​are double-angle cosine and double-angle sine.

[0140] Calculate the angle parameter using the following formula. The double-angle cosine value:

[0141]

[0142] Calculate the corresponding angle parameters based on the double-angle cosine value. And the sine value of a double angle.

[0143] Specifically, this can be achieved by solving... arccosine value ,Sure The value of is then used to determine its double angle sine value. .

[0144] Next, this application will specifically illustrate the method of this application by taking the approximate solution of the maximum energy and corresponding state of the Hamiltonian of the ferromagnetic EPR model as an example.

[0145] Assuming the EPR model, its Hamiltonian is:

[0146]

[0147] in, , There are no binary terms among the other particles.

[0148] A1, the Hamiltonian of the target-type ferromagnetic quantum many-body model:

[0149]

[0150] Generate the corresponding undirected graph Specifically:

[0151] A11 assigns a vertex to each of the particles involved in the Hamiltonian H, forming a vertex set. .

[0152] A12. If there is a two-body interaction term between two particles in the Hamiltonian H, then an edge is connected between the corresponding two vertices, and the weight of the edge is a coefficient. All edges form an edge set. All weights constitute the weight set .

[0153] A13, There is no singleton term in Hamiltonian H, skip.

[0154] A14, There are no non-integer weights in the weight set w, skip.

[0155] A15 is an undirected graph consisting of vertex set V, edge set E, and weight set w. See Figure 2 .

[0156] A2, for Define angle parameters for all adjacent vertices i and j. Output magic graph The first general formula containing parameters:

[0157]

[0158] A3, based on the target Hamiltonian H and the magic diagram The first parameterized equation outputs the system energy. The second parameterized general formula is as follows:

[0159] A31, The Hamiltonian H contains a two-body term. Replace it with an equivalent combination of P-gate and Q-gate:

[0160]

[0161] get:

[0162]

[0163] A32, The Hamiltonian H contains a two-body term. Replace it with an equivalent combination of P-gate and Q-gate:

[0164]

[0165] After simplification, we get:

[0166]

[0167] A33, System Energy It equals the weighted sum of the energy of all two-body terms in the Hamiltonian H:

[0168]

[0169] in,

[0170]

[0171]

[0172]

[0173]

[0174] A4, Access Diagram Based on the quasi-uniform score matching strategy, the matching scores of all edges are determined as follows:

[0175] A41, calculate the weighted degree of all vertices. The weighted degree of vertex i is the sum of the weights of all its neighboring edges, i.e. Where k~i represents all neighboring vertices k of vertex i, we get:

[0176]

[0177]

[0178]

[0179]

[0180]

[0181] A42, calculate the matching score for all edges, edges The matching score is the ratio of its weight to the larger of the weighted degrees of vertices i and j, i.e. ,get:

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189]

[0190] Let the lower bound of all matching scores be denoted as . The Upper Realm records it as .

[0191] A5, introducing entanglement degree control parameters. Matching results with quasi-uniform fractions, defining interval extrema. By optimizing parameters Find the maximum and minimum values. Thus, the parameters are determined. The specific values ​​for are:

[0192] A51, Define the edge Energy lower bound function That is, the weighted lower bound of the bibody term between vertices i and j in the Hamiltonian H, where the weight is the coefficient of the bibody term. In this context, the lower bound of the energy of the two-body term with constant energy is the corresponding constant value:

[0193]

[0194] The lower bound of the energy for the two-body terms containing the parameterized formula can be simplified as follows:

[0195]

[0196]

[0197]

[0198] We obtain the weighted energy lower bound: .

[0199] A52, Introducing Variables Define the extreme values ​​of the interval :

[0200]

[0201] A53, through parameter optimization , making Make it as large as possible to determine the parameters. The value of is easily determined using a classic optimizer. .

[0202] A6, Substitute parameters Based on the matching results with the quasi-uniform fraction, calculate all angular parameters and their double-angle cosine and sine values, specifically:

[0203] A61, Substitute parameters and matching score Calculate the rotation angle The double-angle cosine value:

[0204]

[0205] get:

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212]

[0213]

[0214] A62, please solve. arccosine value That will confirm The value of is obtained as follows:

[0215]

[0216]

[0217]

[0218]

[0219]

[0220]

[0221]

[0222]

[0223] Then determine its double angle sine value ,get:

[0224]

[0225]

[0226]

[0227]

[0228]

[0229]

[0230]

[0231]

[0232] A7, substitute the angle parameters and trigonometric function values ​​into the magic graph. and system energy The general formula for outputting the approximate ground state. and approximate energy ,get:

[0233]

[0234] For the edge :

[0235]

[0236]

[0237] in, or ,so,

[0238]

[0239]

[0240]

[0241] Therefore, the edge The weighted sum of energy is:

[0242]

[0243] Similarly, by obtaining the weighted sum of the energies of all edges, the final summation yields an approximate maximum energy. .

[0244] According to the upper bound theorem for the maximum energy of the EPR model, the upper bound in this example is 32.5. Therefore, the approximation ratio of the method in this application is approximately 0.88026. However, applying methods from related technologies, such as the maximum energy approximation method for the EPR model proposed by Apte et al. (Anuj Apte, Eunou Lee, Kunal Marwaha, etc. Improved Algorithms for QuantumMaxCut via Partially Entangled Matchings[J]. arXiv preprint arXiv:2504.15276,2025.), yields an approximate energy of approximately 27.09919, with an approximation ratio of approximately 0.83382. Clearly, the method in this application significantly improves the approximation ratio of the maximum energy of the EPR model.

[0245] In addition, this invention also provides a solution system for a ferromagnetic quantum many-body model based on fractional matching, such as... Figure 3As shown, the solution system for the ferromagnetic quantum many-body model based on fractional matching includes: a preprocessing module 10, a ground state simulation module 20, an energy simulation module 30, a fractional matching module 40, a parameter optimization module 50, an angle calculation module 60, and a result processing module 70.

[0246] The preprocessing module 10 is used to obtain and generate the corresponding undirected graph based on the Hamiltonian of the ferromagnetic quantum many-body model.

[0247] The ground state simulation module 20 is used to introduce angle parameters to all edges in the undirected graph to obtain the first parameterized general formula of the magic graph state corresponding to the undirected graph.

[0248] The energy simulation module 30 is used to obtain the second parameterized formula of the system energy of the ferromagnetic quantum many-body model based on the first parameterized formula and the Hamiltonian.

[0249] The fraction matching module 40 is used to determine the fraction matching scheme based on the undirected graph and through a quasi-uniform fraction matching strategy.

[0250] The parameter optimization module 50 is used to output entanglement control parameters that maximize or minimize the system energy based on the second parameterized general formula and fractional matching scheme.

[0251] The angle calculation module 60 is used to calculate various angle parameters and their corresponding trigonometric function values ​​based on the entanglement degree control parameters.

[0252] The result processing module 70 is used to obtain the approximate ground state and approximate energy of the ferromagnetic quantum many-body model based on the angle parameters, trigonometric function values, the first parameterized formula and the second parameterized formula.

[0253] For other specific implementations of the solution system for the ferromagnetic quantum many-body model based on fractional matching in the embodiments of the present invention, please refer to the specific implementations of the solution method for the ferromagnetic quantum many-body model based on fractional matching in the above embodiments of the present invention.

[0254] The solution system for the ferromagnetic quantum many-body model based on fractional matching in this invention employs a quasi-uniform fractional matching strategy, ensuring that each pair of adjacent particles is assigned a certain proportion of entanglement, thereby achieving a higher approximation ratio. Therefore, it can more accurately obtain the target eigenvalues ​​and corresponding states of the model, providing a higher accuracy guarantee for solving more practical engineering problems. Furthermore, the solution system for the ferromagnetic quantum many-body model based on fractional matching is applicable not only to the EPR model but also to commonly used ferromagnetic or ferromagnetic models, including the transverse-field Ising model and the anisotropic XY model, demonstrating higher practical value and better scalability.

[0255] The following detailed explanation uses a computer terminal as an example. Figure 4This is a hardware block diagram of a computer terminal for a solution method of a ferromagnetic quantum many-body model based on fractional matching, provided in an embodiment of the present invention. Figure 4 As shown, a computer terminal may include one or more ( Figure 4 Only one is shown in the diagram. A processor 401 (processor 401 may include, but is not limited to, a microprocessor MCU or a programmable logic device FPGA, etc.) and a memory 402 for storing data are also shown. Optionally, the computer terminal may further include a transmission device 403 for communication functions and an input / output device 404. Those skilled in the art will understand that... Figure 4 The structure shown is for illustrative purposes only and does not limit the structure of the computer terminal described above. For example, the computer terminal may also include components that are more complex than those described above. Figure 4 The more or fewer components shown, or having the same Figure 4 The different configurations shown.

[0256] The memory 402 can be used to store software programs and modules for application software, such as the program instructions / modules corresponding to the solution method of the fractional matching-based ferromagnetic quantum many-body model in this embodiment. The processor 401 executes various functional applications and data processing by running the software programs and modules stored in the memory 402, thereby implementing the above-described method. The memory 402 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory 402 may further include memory remotely located relative to the processor 401, and these remote memories can be connected to a computer terminal via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0257] The transmission device 403 is used to receive or send data via a network. Specific examples of the network described above may include a wireless network provided by a communication provider of the computer terminal. In one example, the transmission device 403 includes a Network Interface Controller (NIC), which can connect to other network devices via a base station to communicate with the Internet. In another example, the transmission device 403 may be a Radio Frequency (RF) module, used for wireless communication with the Internet. Embodiments of this application also provide a computer-readable storage medium storing a computer program for electronic data interchange, which causes a computer to perform some or all of the steps of any of the methods described in the above method embodiments, wherein the computer includes an electronic device.

[0258] This application also provides a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program operable to cause a computer to perform some or all of the steps of any of the methods described in the above method embodiments. The computer program product may be a software installation package, and the computer may include an electronic device.

[0259] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for solving a quantum many-body model of a ferrimagnetic-like class based on fractional matching, characterized by, The method comprises: acquiring and generating a corresponding undirected graph according to a Hamiltonian of a ferromagnetic quantum many-body model; introducing an angle parameter for all edges in the undirected graph to obtain a first parametric formula of a magic graph state corresponding to the undirected graph; obtaining a second parametric formula of system energy of the ferromagnetic quantum many-body model according to the first parametric formula and the Hamiltonian; determining a fraction matching scheme according to the undirected graph and through a quasi-uniform fraction matching strategy; outputting an entanglement degree control parameter that makes the system energy maximum or minimum according to the second parametric formula and the fraction matching scheme; calculating each angle parameter and a corresponding trigonometric function value according to the entanglement degree control parameter; obtaining an approximate ground state and an approximate energy of the ferromagnetic quantum many-body model according to the angle parameter, the trigonometric function value, the first parametric formula and the second parametric formula.

2. The method of claim 1, wherein, The step of acquiring and generating a corresponding undirected graph according to a Hamiltonian of a ferromagnetic quantum many-body model comprises: allocating a vertex for each particle in the Hamiltonian to form a vertex set V; judging whether there is a two-body term and / or a single-body term in the Hamiltonian; if there is the two-body term between two particles in the Hamiltonian, connecting an edge between the two particles to obtain a first weight coefficient of each edge, and all the edges form an edge set E, and all the first weight coefficients form a weight set w; if there is the single-body term in the Hamiltonian, assigning a second weight coefficient to the vertex corresponding to the single-body term, and updating the second weight coefficient to the weight set w; judging whether there is a non-integer weight in the weight set w; if there is, multiplying the weight coefficient in the weight set w by 10, and returning to the step of judging whether there is a non-integer weight in the weight set w; if not, then construct the undirected graph G = (V, E, w) from the vertex set V, the edge set E, and the weight set w .

3. The method of claim 2, wherein, the Hamiltonian is expressed as: ； The step of introducing an angle parameter for all edges in the undirected graph to obtain a first parametric formula of a magic graph state corresponding to the undirected graph comprises: For each of the vertices i and j of the undirected graph G define an angle parameter ; According to the angle parameter , the first containing parameter formula is obtained: ； wherein i and j represent vertex serial numbers, represents a first weight coefficient of an edge between the i-th vertex and the j-th vertex, represents a second weight coefficient of the i-th vertex monomer item, , , , represents a preset coefficient, represents an angle parameter between the i-th vertex and the j-th vertex, , represents an I gate of the i-th vertex, represents a Z gate of the i-th vertex, represents an X gate of the i-th vertex, represents a Y gate of the i-th vertex, represents a P gate of the i-th vertex, and n represents a total number of vertices in the vertex set V, represents an edge between the i-th vertex and the j-th vertex, represents an imaginary unit, .

4. The method of claim 3, wherein, The construction process of the second parametric formula comprises: replacing the two-body term in the Hamiltonian with and replacing the two-body term in the Hamiltonian with to obtain the replaced Hamiltonian ; The replaced Hamiltonian is converted into a second parametric formula: ; wherein, , , , , , , , Qij represents a Q gate for the ith vertex, K represents a set of other neighboring vertices of the ith vertex except for the jth vertex, k represents the kth vertex in the set K, L represents a set of other neighboring vertices of the jth vertex except for the ith vertex, 1 represents the 1th vertex in the set L, T represents a set of common neighboring vertices of the ith vertex and the jth vertex, S represents a subset of T, s represents the sth vertex in the set S, |S| even represents that the number of elements of the set S is even, |S| odd represents that the number of elements of the set S is odd, represents removing all elements in the set S from the set K, represents all neighboring vertices k of the vertex i.

5. The method of claim 2, wherein, The step of determining a fraction matching scheme according to the undirected graph and through a quasi-uniform fraction matching strategy comprises: calculating a weighted degree of each vertex in the undirected graph according to the first weight coefficient; calculating a matching fraction of each edge according to the first weight coefficient and the weighted degree.

6. The method of claim 5, wherein, The weighted degree of the i-th vertex is calculated through the following formula: ； The matching score of the edge is calculated by the following equation: ； wherein, denotes the weighted degree of the i-th vertex, denotes the weighted degree of the j-th vertex, denotes the first weight coefficient of the edge between the i-th vertex and the k-th vertex, denotes the matching score of the edge .

7. The method of solving a fractionally matched, ferrimagnetic quantum many-body model according to claim 6, wherein, The step of outputting an entanglement degree control parameter that makes the system energy maximum or minimum according to the second parametric formula and the fraction matching scheme comprises: According to , , , and the lower bound of the energy of the edge is obtained where ; According to a lower bound in the matching score and an upper bound , define optimization variables ; Replace with in and define interval extrema according to ; To make maximization as the goal, the optimization is performed on in to determine the value of ; wherein denotes the entanglement degree control parameter, the lower bound of the energy of , the lower bound of the energy of , the lower bound of the energy of , the lower bound of the energy of , , .

8. The method of claim 7, wherein, The trigonometric function value is a double-angle cosine value and a double-angle sine value; The angle parameter is calculated by the following equation the double angle cosine value of ； According to the double-angle cosine value, a corresponding angle parameter is calculated and a double-angle sine value.

9. A system for solving a quantum many-body model of a ferrimagnetic-like based on fractional matching, characterized in that, The system comprises: a preprocessing module configured to acquire and generate a corresponding undirected graph according to a Hamiltonian of a ferromagnetic quantum many-body model; a ground state simulation module configured to introduce an angle parameter for all edges in the undirected graph to obtain a first parametric formula of a magic graph state corresponding to the undirected graph; an energy simulation module configured to obtain a second parametric formula of system energy of the ferromagnetic quantum many-body model according to the first parametric formula and the Hamiltonian; a fraction matching module configured to determine a fraction matching scheme according to the undirected graph and by a quasi-uniform fraction matching strategy; a parameter optimization module configured to output a degree-of-entanglement control parameter that enables the system to have maximum or minimum energy according to the second parametric general formula and the fraction matching scheme; an angle calculation module configured to calculate each of the angle parameters and a corresponding trigonometric function value according to the degree-of-entanglement control parameter; a result processing module configured to obtain an approximate ground state and an approximate energy of the ferromagnetic-like quantum many-body model according to the angle parameters, the trigonometric function values, the first parametric general formula and the second parametric general formula.

10. An electronic device comprising a memory, a processor, and a computer program stored on the memory, characterized in that, The computer program is executed by the processor to implement the solving method of the ferromagnetic-like quantum many-body model based on fraction matching according to any one of claims 1-8.

Images