Quantum state tomography measurement method based on pre-learning physical neural network
Through the quantum state tomography measurement method based on pre-learning physical neural network, the density matrix of high-dimensional OAM entangled states is reconstructed using the PTPINN model, solving the complexity and time-consuming problem of characterizing the angular momentum entangled states of high-dimensional orbits, and achieving fast and accurate quantum state tomography.
Patent Information
- Application Number
- CN202510187134.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-20
- Publication Date
- 2025-06-10
AI Technical Summary
Characterizing the angular momentum entangled state of high-dimensional orbits has problems such as large measurement volume, complex data processing and time-consuming.
The quantum state tomography measurement method based on pre-learning physical neural network is adopted, and signal photons and idle frequency photons are generated by spontaneous parameter downconversion, and the probability distribution data of idle frequency photons is obtained by using an enhanced charge coupler. It is input to the PTPINN model for iteration to reconstruct the density matrix of the entangled state.
It realizes efficient and accurate characterization of high-dimensional OAM entangled states, and can quickly reconstruct the density matrix in just two measurements, improving the efficiency and flexibility of quantum state tomography.
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Figure CN120124765A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the technical field of quantum state tomography of orbital angular momentum entanglement, and particularly to a quantum state tomography measurement method based on a pre-trained physical neural network. Background Art
[0002] Quantum entanglement based on orbital angular momentum (OAM) not only expands the dimension of the Hilbert space to encode more information, but also significantly enhances the anti-noise ability and robustness of the quantum information system. However, characterizing high-dimensional OAM entanglement still faces many challenges, including a large number of measurements, complex data processing, and time-consuming processes. Summary of the Invention
[0003] The purpose of this application is to provide a quantum state tomography measurement method based on a pre-trained physical neural network, which can effectively and accurately characterize high-dimensional OAM entangled states.
[0004] To achieve the above purpose, this application provides the following solutions:
[0005] This application provides a quantum state tomography measurement method based on a pre-trained physical neural network, including:
[0006] Generating a signal photon and an idler photon based on the spontaneous parametric down-conversion process; the signal photon and the idler photon are a pair of high-dimensional orbital angular momentum entangled state photons;
[0007] Based on the pair of high-dimensional orbital angular momentum entangled state photons, performing two projection measurements on the signal photon to collapse the corresponding idler photon, and using an intensified charge-coupled device to measure the probability distribution data of the two collapses of the idler photon;
[0008] Inputting the probability distribution data of the two collapses of the idler photon into a preset OAM entangled state reconstruction model for iteration to obtain predicted entanglement parameters, and reconstructing the density matrix of the target entangled state according to the predicted entanglement parameters;
[0009] Wherein, the preset OAM entangled state reconstruction model is a PTPINN model, including a neural network sub-model and a physical sub-model; the neural network sub-model is obtained by parameter transfer based on a pre-trained convolutional neural network model, and is used to learn the relationship between the probability distribution data of the idler photon and the entanglement parameters; the physical sub-model is used to simulate and generate the probability distribution data of the idler photon according to the entanglement parameters.
[0010] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method for quantum state tomography measurement based on a pre-learned physical neural network. The PTPINN model used therein includes a neural network sub-model and a physical sub-model, and the neural network sub-model is obtained by parameter transfer based on a pre-trained convolutional neural network model, realizing the combination of the data-driven feature extraction ability of the convolutional neural network model and the physical model, enabling the PTPINN model to be used for the effective characterization of high-dimensional OAM entanglement, and the density matrix can be quickly reconstructed with only two measurements. In addition, PTPINN can transfer the features learned from pre-training to high-dimensional tasks, ensuring its adaptability to any dimension and highlighting its flexibility and scalability. Since the neural network sub-model is obtained by parameter transfer based on a pre-trained convolutional neural network model, the time required for each prediction is very short, improving the efficiency of quantum state tomography. In practical applications, after obtaining the probability distribution data of the two collapses of the idler photons, input it into the PTPINN model (i.e., the preset OAM entanglement state reconstruction model) for iteration, and the predicted entanglement parameters can be quickly and accurately obtained, and the density matrix of the target entanglement state can be reconstructed. BRIEF DESCRIPTION OF THE DRAWINGS
[0011] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.
[0012] Figure 1 It is a schematic flowchart of a method for quantum state tomography measurement based on a pre-learned physical neural network provided by an embodiment of the present application.
[0013] Figure 2 It is a schematic structural diagram of the PTPINN model provided by an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0014] The following will clearly and completely describe the technical solutions in the embodiments of the present application in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, rather than all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present application.
[0015] To make the purpose, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the drawings and specific embodiments.
[0016] In an exemplary embodiment, as Figure 1As shown, a quantum state tomography measurement method based on a pre-trained physical neural network is provided, including the following steps 101 - 103.
[0017] Step 101, generating a signal photon and an idler photon based on the spontaneous parametric down-conversion (SPDC) process; the signal photon and the idler photon are a pair of high-dimensional orbital angular momentum entangled state photons.
[0018] The spontaneous parametric down-conversion process is the main mechanism for generating OAM entanglement: usually, a Gaussian beam pumps a second-order nonlinear crystal, such as PPKTP, BBO, etc. The generation process of the signal photon and the idler photon is represented by the following function formula:
[0019]
[0020] where, |l> s represents the s orbital angular momentum state of the signal photon with quantum number l generated by the spontaneous parametric down-conversion process, and |l> i represents the i orbital angular momentum state of the idler photon with quantum number l generated by the spontaneous parametric down-conversion process; |l> represents the Laguerre-Gaussian mode with topological charge l and radial index 0, and the entanglement dimension is D = 2d + 1, where d is an integer; α l represents the amplitude, and φ l represents the phase. The amplitude and the phase constitute the entanglement parameters, that is, the amplitude α l and the phase φ l are the unknown entanglement parameters required to fully characterize the system. The amplitude α l satisfies the normalization condition The condition satisfied by the phase is that φ l ∈[0, 2π) and φ 0 = 0; |Ψ> represents the high-dimensional orbital angular momentum entangled state, and j represents the imaginary unit.
[0021] Step 102, based on the pair of high-dimensional orbital angular momentum entangled state photons, performing two projection measurements on the signal photon to collapse the corresponding idler photon, and using an intensified charge-coupled device (ICCD) to measure the probability distribution data of the two collapses of the idler photon.
[0022] In a specific application, based on the pair of high-dimensional orbital angular momentum entangled state photons, performing two projection measurements on the signal photon to collapse the corresponding idler photon, including: for two-photon OAM entanglement, successively projecting the signal photon onto the first superposition state basis vector and the second superposition state basis vector above, such that the corresponding idler photons collapse to the following state:
[0023]
[0024] wherein, represents the superposition state of the idler photons when the signal photons are projected onto the first superposition state basis vectors, represents the superposition state of the idler photons when the signal photons are projected onto the second superposition state basis vectors. In other words, for high-dimensional orbital angular momentum entangled photon pairs, if the signal photons are in the first superposition state basis vectors or the second superposition state basis vectors, the associated idler photons will collapse to or
[0025] The above-mentioned projection process is as follows: By loading a specific holographic grating on a spatial light modulator, the signal photons are projected onto the first superposition state basis vectors or the second superposition state basis vectors.
[0026] In a specific application, the probability distribution data of the two collapses of the idler photons measured by an intensified charge-coupled device is and
[0027] Step 103, input the probability distribution data of the two collapses of the idler photons into a preset OAM entanglement state reconstruction model for iteration to obtain predicted entanglement parameters, and reconstruct the density matrix of the target entanglement state according to the predicted entanglement parameters.
[0028] Wherein, the preset OAM entanglement state reconstruction model is an integrated and optimized PTPINN (pre-trained physics-informed neural network) model; the PTPINN model includes a neural network sub-model and a physics sub-model; the neural network sub-model is obtained by parameter transfer based on a pre-trained convolutional neural network model, and is used to learn the relationship between the probability distribution data of the idler photons and the entanglement parameters; the physics sub-model is used to simulate and generate the probability distribution data of the idler photons according to the entanglement parameters. The above-mentioned PTPINN model integrating pre-trained parameters and a physics sub-model does not need to train on multiple data sets, but can directly iterate on the probability distribution data of the two collapses of the idler photons measured by an ICCD, so as to extract the entanglement parameters, and then realize the reconstruction of the OAM entanglement state.
[0029] Such as Figure 2As shown, the neural network sub-model includes a convolutional block, a fully connected block, and a sigmoid function layer arranged in sequence; the convolutional block includes a plurality of convolutional sub-blocks arranged in sequence, and each convolutional sub-block includes a convolutional layer, a regularization layer (BatchNormalization), and a linear activation function layer (ReLU) arranged in sequence; the fully connected block includes a plurality of fully connected layers arranged in sequence. In the subsequent training process, the parameters of the convolutional block are introduced by pre-trained CNN parameters and remain unchanged, and the parameters of the fully connected layer are continuously updated during the iteration process. In addition, the sigmoid function constrains the entanglement parameters α l and φ l whose ranges are in [0, 1] and [0, 2π) respectively.
[0030] In an application example, the number of convolutional sub-blocks and the number of fully connected layers are determined according to the preset model requirements. For example: the number of convolutional sub-blocks is 3, namely convolutional block 1, convolutional block 2, and convolutional block 3. The dimension of convolutional block 1 is 24×24×16, the dimension of convolutional block 2 is 12×12×32, and the dimension of convolutional block 3 is 6×6×64. The number of fully connected layers is 3, namely fully connected layer 4, fully connected layer 5, and fully connected layer 6. The dimension of fully connected layer 4 is 1×1×500, the dimension of fully connected layer 5 is 1×1×50, and the dimension of fully connected layer 6 is 1×1×D.
[0031] The structure of the convolutional neural network model is similar to that of the neural network sub-model. The differences are: the fully connected layers of the convolutional neural network model are: fully connected layer 1, fully connected layer 2, and fully connected layer 3. The dimension of fully connected layer 1 is 1×1×500, the dimension of fully connected layer 2 is 1×1×50, and the dimension of fully connected layer 3 is 1×1×3. In a specific application, the dimension of fully connected layer 3 depends on the dimension D of the entangled state of the pre-trained sample set, so it is also 1×1×D, Figure 2 In the example, it is pre-trained with a sample set of three-dimensional entangled states, so the dimension of fully connected layer 3 is 3.
[0032] In another application example, the pre-training process of the convolutional neural network model includes: (1) determining the probability distribution data of the two collapses of an idler photon through simulation and determining the corresponding entanglement parameter labels to form a pre-training sample; a plurality of the pre-training samples form a pre-training sample set; (2) using the pre-training sample set to pre-train the convolutional neural network model so that the network learns the relationship between the probability distribution data of the idler photon and the entanglement parameters to obtain a pre-trained convolutional neural network model.
[0033] In another application example, the process of inputting the probability distribution data of the two collapses of the idler photon into a preset OAM entanglement state reconstruction model for iteration includes:
[0034] (1) Obtain the model parameters of the pre-trained convolutional neural network model and transfer them to the convolutional block to obtain an updated neural network sub-model. Specifically, transfer the parameters of the pre-trained convolutional neural network model to the PTPINN model and use code to keep them frozen, that is, do not update the convolutional parameters during subsequent iterative training. This adjustment enables the PTPINN model to only update the parameters in the fully connected layer during the iterative process, significantly reducing the training time compared to traditional neural networks that randomly initialize all parameters.
[0035] (2) In one iteration, input the probability distribution data of the two collapses of the idler photons into the updated neural network sub-model to obtain a preliminary predicted entanglement parameter; use the physical sub-model to generate the probability distribution prediction data of the two collapses of the sample idler photons according to the preliminary predicted entanglement parameter (i.e., the predicted amplitude and the predicted phase ). Calculate the loss function value based on the probability distribution prediction data of the two collapses of the sample idler photons and the corresponding training sample I(α, φ), and use the loss function value to represent the error between the two. Based on the probability distribution prediction data of the two collapses of the sample idler photons and the corresponding training sample I(α, φ), calculate the loss function value, and use the loss function value to represent the error between the two.
[0036] (3) If the preset stop condition is not met, optimize the parameters of the fully connected block in the updated neural network sub-model using the gradient descent method based on the loss function value, and then enter the next iteration; as the error decreases, the output of the network converges to the ideal entanglement parameter.
[0037] (4) If the preset stop condition is met, stop the iteration and output the preliminary predicted entanglement parameter as the final predicted entanglement parameter.
[0038] In a specific practical application, during the iteration using the preset OAM entanglement state reconstruction model, the initial learning rate is set to 1×10 -4When using the Adam optimizer to minimize the loss function value, the mean square error (MSE) and the Negative Pearson Correlation Coefficient (NPCC) can be adopted. MSE measures the average squared difference between the predicted value and the label value to ensure accurate prediction. NPCC evaluates the linear correlation between the predicted value and the label value to promote the consistency of their overall trends. The above training process is implemented using PyTorch 1.13.1 and Python 3.9.7. The hardware settings include an Intel(R) Xeon(R) Platinum 8378C CPU (3.60 GHz), 512 GB of RAM, and an NVIDIA GeForce RTX 4070 GPU.
[0039] In summary, this application combines the data-driven feature extraction ability of the convolutional neural network model with the physical model. The PTPINN model can be used for the effective characterization of high-dimensional OAM entanglement, and the density matrix can be quickly reconstructed with only two measurements. Moreover, since the PTPINN model utilizes the parameters of the pre-trained convolutional neural network, the time required for each prediction is very short, improving the efficiency of quantum state tomography. The PTPINN model can transfer the features learned from pre-training to high-dimensional tasks, ensuring its adaptability to any dimension and highlighting its flexibility and scalability.
[0040] In an exemplary embodiment, a computer device is provided, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.
[0041] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.
[0042] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.
[0043] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.
[0044] In this text, specific examples are used to illustrate the principles and implementation manners of the present application. The description of the above embodiments is only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation on the present application.
Claims
1. A quantum state tomography measurement method based on pre-learning physical neural network, characterized in that: The quantum state tomography measurement method based on pre-learning physical neural network includes: Generate a signal photon and an idler photon based on a spontaneous parametric down-conversion process; the signal photon and the idler photon are a high-dimensional orbital angular momentum entangled state photon pair; Based on the high-dimensional orbital angular momentum entangled state photon pair, the signal photon is projected twice to cause the corresponding idler photon to collapse, and an enhanced charge coupled device is used to measure and obtain probability distribution data of the two collapses of the idler photon; The probability distribution data of the two collapses of the idler photon is input into a preset OAM entangled state reconstruction model for iteration to obtain predicted entanglement parameters, and the density matrix of the target entangled state is reconstructed according to the predicted entanglement parameters; Among them, the preset OAM entangled state reconstruction model is a PTPINN model, which includes a neural network sub-model and a physical sub-model; the neural network sub-model is obtained by parameter migration based on a pre-trained convolutional neural network model, and is used to learn the relationship between the probability distribution data of idle photons and entanglement parameters; the physical sub-model is used to simulate and generate the probability distribution data of idle photons based on the entanglement parameters.
2. The quantum state tomography measurement method based on pre-learning physical neural network according to claim 1 is characterized in that: The pre-training process of the convolutional neural network model includes: Determine the probability distribution data of the double collapse of an idler photon by simulation, and determine the corresponding entanglement parameter label to form a pre-training sample; a plurality of the pre-training samples constitute a pre-training sample set; The pre-training sample set is used to pre-train the convolutional neural network model, so that the network learns the relationship between the probability distribution data of the idle photons and the entanglement parameters, and obtains the pre-trained convolutional neural network model.
3. The quantum state tomography measurement method based on pre-learning physical neural network according to claim 1 is characterized in that: The neural network sub-model includes a convolution block, a fully connected block and a sigmoid function layer arranged in sequence; The convolution block includes a plurality of convolution sub-blocks arranged in sequence, and each of the convolution sub-blocks includes a convolution layer, a regularization layer, and a linear activation function layer arranged in sequence; The fully connected block includes a plurality of fully connected layers arranged in sequence.
4. The quantum state tomography measurement method based on pre-learning physical neural network according to claim 3 is characterized in that: The number of the convolution sub-blocks and the number of the fully connected layers are determined according to preset model requirements.
5. The quantum state tomography measurement method based on pre-learning physical neural network according to claim 3 is characterized in that: The process of inputting the probability distribution data of the two collapses of the idler photon into a preset OAM entangled state reconstruction model for iteration includes: Obtaining model parameters of a pre-trained convolutional neural network model and migrating them to the convolution block to obtain an updated neural network sub-model; In one iteration, the probability distribution data of the two collapses of the idler photon is input into the updated neural network sub-model to obtain a preliminary predicted entanglement parameter; Using the physical sub-model, generating probability distribution prediction data of the double collapse of the sample idler photon according to the preliminary predicted entanglement parameters; Calculating a loss function value based on the probability distribution prediction data of the two collapses of the sample idler photons and the corresponding training samples; If the preset stop condition is not met, the parameters of the fully connected blocks in the updated neural network sub-model are optimized using a gradient descent method based on the loss function value, and then the next iteration is entered; If the preset stop condition is met, the iteration is stopped and the preliminary predicted entanglement parameters are output as the final predicted entanglement parameters.
6. The quantum state tomography measurement method based on pre-learning physical neural network according to claim 1 is characterized in that: The generation process of the signal photon and the idler photon is expressed by the following function formula: Among them, |l> s represents the orbital angular momentum state of the signal photon s with quantum number l generated by the spontaneous parametric down-conversion process, |l> i represents the orbital angular momentum state of idler photon i with quantum number l generated by the spontaneous parametric down-conversion process; |l> represents a Laguerre-Gaussian mode with topological charge l and radial index 0, and the entanglement dimension is D = 2d + 1, where d is an integer; α l represents the amplitude, φ l represents the phase, the amplitude and the phase constitute the entanglement parameter; |Ψ> represents the high-dimensional orbital angular momentum entangled state, and j represents the imaginary unit.
7. The quantum state tomography measurement method based on pre-learning physical neural network according to claim 6 is characterized in that: Based on the high-dimensional orbital angular momentum entangled state photon pair, the signal photon is projected and measured twice to collapse the corresponding idler photon, including: Project the signal photons onto the first superposition state basis vectors in sequence and the second superposition state basis vector So that the corresponding idler photon collapses to the following state: in, represents the superposition state of the idler photon when the signal photon is projected onto the first superposition state basis vector, It represents the superposition state of the idler photon when the signal photon is projected onto the second superposition state basis vector.
8. The quantum state tomography measurement method based on pre-learning physical neural network according to claim 5 is characterized in that: In the iterative process of reconstructing the model using the preset OAM entangled state, the Adam optimizer is used to minimize the loss function value.