Continuous variable quantum state generation, recovery and training method and model

Abstract

The invention discloses a continuous variable quantum state generation, recovery and training method and model, and the method comprises the steps: converting an input quantum state into a thermal state through a forward diffusion process of thermal loss channel modeling; generating the thermal state into a target quantum state through a trainable reverse denoising process; constructing a coherent state data set; obtaining a diffusion quantum state according to a sample quantum state in the coherent state data set; based on the diffusion quantum state, recovering the sample quantum state to obtain an output coherent state; and training the continuous variable quantum state recovery model according to the sample quantum state and the output coherent state. According to the method, the common environmental noise effect in continuous variable quantum communication is effectively simulated, so that the generation method is more flexible, the fidelity of generation and recovery results, the response speed to unpredictable noise and the robustness of quantum state recovery are improved, and the blank left by a model taking generation as a center is filled.

Description

Technical Field

[0001] This invention relates to the field of quantum machine learning technology, and in particular to a method and model for generating, recovering and training continuous variable quantum states. Background Technology

[0002] Quantum engineering leverages the principles of quantum mechanics to advance technologies such as communication, computing, and sensing. In these systems, the processing of quantum information typically follows one of two main paradigms: discrete-variable (DV) systems, which use qubits with finite-dimensional Hilbert spaces; and continuous-variable (CV) systems, which operate on observables with continuous spectra in infinite-dimensional Hilbert spaces. The latter forms the basis of CV quantum computing, a method that utilizes continuous degrees of freedom.

[0003] Existing quantum machine learning methods for CV systems include Continuous-Variable Quantum Neural Networks (CVQNNs), CV Boltzmann Machines, CV Born Machines, and Generative Adversarial Networks (GANs). While these existing techniques demonstrate the ability to generate complex quantum states, they generally face limitations: 1) they primarily focus on the state generation task, neglecting the equally crucial problem of recovering damaged states from noise; 2) existing methods typically employ rigid frameworks that rely on fixed transformations. Summary of the Invention

[0004] This invention provides a method and model for generating, recovering, and training continuous variable quantum states, which solves the problems of rigidity in operation and inability to generate and recover quantum states simultaneously in existing technologies. It achieves flexible and diverse high-fidelity generation and robust recovery of continuous variable quantum states.

[0005] This invention provides a method for generating continuous variable quantum states, comprising:

[0006] The forward diffusion process, modeled through thermal loss channels, converts the input quantum state into a thermal state.

[0007] The thermal state is generated into the target quantum state through a trainable reverse denoising process.

[0008] According to a continuous-variable quantum state generation method provided by the present invention, the forward diffusion process of the heat loss channel modeling includes:

[0009] At each time step t, the input quantum state ρ t-1The heat loss channel, characterized by the following formula, is converted into a hot state ρ. t :

[0010]

[0011] in, Characterizing the heat loss path, η t ∈[0,1] is a time-step dependent transmittance parameter; The average number of photons is Environmental thermal state; U BS (η t ) is the beam splitter operator; It's U BS (η t The conjugate transpose of ); operation Tr E This indicates the elimination of traces in the environmental degrees of freedom.

[0012] According to a continuous-variable quantum state generation method provided by the present invention, the forward diffusion process modeled by the heat loss channel further includes:

[0013] At any time step t, the initial input quantum state ρ0 is transformed into the thermal state ρ through the thermal loss channel characterized by the following formula. t :

[0014]

[0015] in Indicates transmittance The unitary operator of the bundle splitter, η represents the cumulative transmittance. i ∈[0,1] is a time-step dependent transmittance parameter; express The conjugate transpose of; The average number of photons is The environment is hot; operation Tr E This indicates the elimination of traces in the environmental degrees of freedom.

[0016] A continuous-variable quantum state generation method according to the present invention further includes:

[0017] At each time step t, for the η t Linear scheduling is used:

[0018]

[0019] Where η0 and η T It is a hyperparameter that defines the start and end points of the T-step linear interpolation.

[0020] According to a continuous-variable quantum state generation method provided by the present invention, the trainable inverse denoising process includes:

[0021] The time quantum state is obtained by using a time-embedded circuit;

[0022] The composite system constructed from the time quantum state and the thermal state is denoised using a denoising circuit to generate the target quantum state.

[0023] The denoising circuit is obtained based on the denoising circuit parameters trained.

[0024] According to the present invention, a method for generating a continuous-variable quantum state is provided, wherein a time quantum state is obtained through a time-embedding circuit, the method comprising:

[0025] For any non-zero coherent state |α>, the time step information is encoded by the following phase evolution:

[0026] α(t)=e -iωt α;

[0027] Here, α represents the complex parameter of the coherent state, and ω represents the angular frequency, which controls the rate of phase evolution.

[0028] According to a continuous variable quantum state generation method provided by the present invention, the denoising circuit is obtained based on denoising circuit parameters, and the method includes:

[0029] The loss is determined based on the input quantum state and the target quantum state;

[0030] The parameters of the denoising circuit are adjusted based on the loss.

[0031] This invention also provides a training method for a continuous-variable quantum state recovery model, comprising:

[0032] Construct a coherent state dataset;

[0033] Based on the sample quantum states in the coherent state dataset, the diffused quantum states are obtained;

[0034] Based on the diffused quantum state, the sample quantum state is recovered to obtain the output coherent state; and

[0035] The continuous variable quantum state recovery model is trained based on the sample quantum state and the output coherent state.

[0036] According to a training method for a continuous-variable quantum state recovery model provided by the present invention, the construction of a coherent state dataset includes:

[0037] Sample coherent states {|α} from a uniform disk of radius D. tr >}Construct;

[0038] Here, parameter D defines the high-probability operating range of the transmitter signal; signal parameter α in =x+ip is composed of independently sampled orthogonal components Build.

[0039] The present invention also provides a method for restoring a continuous variable quantum state, comprising:

[0040] Obtain the quantum state to be recovered;

[0041] The quantum state to be recovered is input into the continuous variable quantum state recovery model to obtain the target quantum state;

[0042] The continuous variable quantum state recovery model is trained by the method described in any one of claims 8 to 9.

[0043] The present invention also provides a continuous variable quantum state generation model, comprising:

[0044] The forward diffusion module is used to convert the input quantum state into a thermal state through the forward diffusion process modeled by the thermal loss channel;

[0045] A reverse denoising module is used to generate the thermal state into a target quantum state through a trainable reverse denoising process.

[0046] The present invention also provides a training device for a continuous variable quantum state recovery model, comprising:

[0047] Build modules are used to construct coherent state datasets;

[0048] The acquisition module is used to obtain the diffused quantum state based on the sample quantum states in the coherent state dataset;

[0049] A recovery module is used to recover the sample quantum state based on the diffused quantum state to obtain the input coherent state; and

[0050] The training module is used to train the continuous variable quantum state recovery model based on the sample quantum state and the input coherent state.

[0051] According to the present invention, a training apparatus for a continuous-variable quantum state recovery model is provided, wherein constructing a coherent state dataset includes:

[0052] Sample coherent states {|α} from a uniform disk of radius D. tr >}Construct;

[0053] Here, parameter D defines the high-probability operating range of the transmitter signal; signal parameter α in =x+ip is composed of independently sampled orthogonal components Build.

[0054] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement any of the continuous variable quantum state generation methods or training methods of the continuous variable quantum state recovery model described above.

[0055] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the continuous variable quantum state generation method or the training method of the continuous variable quantum state recovery model as described above.

[0056] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the continuous variable quantum state generation method or the training method of the continuous variable quantum state recovery model as described above.

[0057] Compared with the prior art, the beneficial effects of the present invention are:

[0058] (1) This invention converts the input quantum state into a thermal state by modeling the thermal loss channel, effectively simulating the environmental noise effects commonly found in continuous variable quantum communication. The thermal state is restored to a diverse target quantum state through a trainable reverse denoising process, breaking through the limitation of fixed input-output mapping, thereby improving the fidelity of the generation and restoration results, the response speed to unpredictable noise, and the robustness of quantum state restoration.

[0059] (2) By constructing a diverse training dataset, the continuous variable quantum state recovery model trained in this invention can recover any coherent state from a predefined operating range, achieving blind recovery and avoiding the problem of prior knowledge required by existing technologies. At the same time, it is integrated with the continuous variable quantum state generation model, thereby realizing quantum state generation and recovery within a unified framework, filling the gap left by the generation-centered model. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0061] Figure 1 This is a flowchart illustrating a continuous variable quantum state generation method according to an embodiment of the present invention.

[0062] Figure 2 This is a schematic diagram of a general continuous variable quantum diffusion framework according to an embodiment of the present invention.

[0063] Figure 3 This is a schematic diagram of a continuous variable quantum diffusion process according to an embodiment of the present invention.

[0064] Figure 4 This is a schematic diagram of the CVQD-G denoising framework according to an embodiment of the present invention.

[0065] Figure 5 This is a schematic diagram of the training method for a continuous variable quantum state recovery model according to an embodiment of the present invention.

[0066] Figure 6 The generative model according to an embodiment of the present invention is used in a pure loss channel. A schematic diagram of generating coherent states |α=1.0> is shown, where (a) is the training loss, (b) is the forward diffusion fidelity, and (c) is the reverse denoising fidelity starting from an initial state with different noise levels η.

[0067] Figure 7 The fidelity of the generated quantum state is a function of the key state parameters according to the embodiments of the present invention, wherein (a) the relationship between the fidelity of the coherent state and the amplitude α, and (b) the relationship between the fidelity of the compressed vacuum state and the compression parameter r.

[0068] Figure 8 The generative model according to an embodiment of the present invention is used in a pure loss channel. A schematic diagram of generating a compressed vacuum state S(r=0.5)|0> is shown, where (a) is the training loss, (b) is the forward diffusion fidelity, and (c) is the reverse denoising fidelity starting from an initial state with different noise levels η.

[0069] Figure 9 The generative model according to an embodiment of the present invention is used in a pure loss channel. A schematic diagram of generating Fock state |1> is shown, where (a) is the training loss, (b) is the forward diffusion fidelity, and (c) is the reverse denoising fidelity starting from an initial state with different noise levels η.

[0070] Figure 10 The generative model according to an embodiment of the present invention is used in a pure loss channel. A schematic diagram of the generated even cat state |cat(1)> is shown, where (a) is the training loss, (b) is the forward diffusion fidelity and (c) is the reverse denoising fidelity starting from the initial state with different noise levels η.

[0071] Figure 11 This is a schematic diagram showing the relationship between the average recovery fidelity of the coherent states generated by different X-gate parameters (s = 0.3, 0.5, 0.7) of the recovery model according to an embodiment of the present invention and the recovery time step.

[0072] Figure 12The fixed initial coherence state (X-gate parameter s = 0.5, R-gate parameter π / 4) of the recovery model according to an embodiment of the present invention is subjected to different effective transmittances η (e.g., η ∈ {0.25, 0.50, 0.75}, environmental conditions). A schematic diagram illustrating the relationship between recovery fidelity and recovery time step after thermal loss channel damage.

[0073] Figure 13 The generative model according to the embodiments of the present invention is in Under the given conditions, using general hyperparameters, the training loss and fidelity of the coherent states |α> generated for amplitudes α = 0.5, 1.0, 1.5, 2.0, and 2.5 are illustrated.

[0074] Figure 14 The generative model according to the embodiments of the present invention is in Under the given conditions, using general hyperparameters, the training loss and fidelity diagrams for the compressed vacuum state S(r)|0> generated for compression parameters r = 0.25, 0.5, 0.75, and 1.0 are shown respectively.

[0075] Figure 15 These are the generative models according to embodiments of the present invention. and Under the given conditions, the training loss and fidelity diagrams for the following states are generated: coherent state (|α=1.0>), compressed state (S(r=0.5)|0>), Fock state (|1>), and Cat state (|cat(1)>).

[0076] Figure 16 The generative model according to embodiments of the present invention uses tuned hyperparameters in... Performance of generating coherent states |α=2.5> under the condition, where (a) the relationship between training loss and epoch, and (b) the forward diffusion fidelity F(ρ0,ρ t (c) Schematic diagram of the relationship between (a) and (b) time step and (c) the relationship between inverse denoising fidelity and denoising time step.

[0077] Figure 17 This is a schematic flowchart of a continuous variable quantum state recovery method according to an embodiment of the present invention.

[0078] Figure 18 This is a schematic diagram of the quantum state generation model implemented according to the present invention.

[0079] Figure 19 This is a schematic diagram of the structure of a training device for a quantum state recovery model implemented according to the present invention.

[0080] Figure 20 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0082] Environmental thermal noise poses a significant threat during the transmission of quantum states through physical channels such as optical fibers or free space. Addressing the detrimental effects of this noise is therefore a critical challenge for practical quantum computing systems that heavily rely on such optical channels. This noise causes decoherence, transforming the initial pure quantum state into a mixed state and reducing the encoded quantum information. This degradation impairs the accuracy of quantum computing and the efficiency of quantum communication. Therefore, developing robust methods for high-fidelity quantum state generation (the initial preparation of desired states) and efficient quantum state recovery (the recovery of states after noise-induced damage) has become essential for the continued development and practical realization of quantum computing in the field of quantum computing.

[0083] In existing technical frameworks, gate parameters are typically trained to map a specific, predefined initial state (such as a vacuum state) to a desired target output. Since the final transformation and its parameters are optimized only along this fixed path, changing the initial state or target output usually requires retraining the model, leading to operational rigidity in the framework. This inherent lack of adaptability makes it unsuitable for dynamic scenarios such as quantum communication, where unpredictable noise requires responsive rather than fixed processing strategies.

[0084] The symbols used in the embodiments of this invention are summarized in Table 1.

[0085] Table 1 Symbol Table

[0086]

[0087]

[0088] Before delving into the embodiments of the present invention, a brief introduction to the basic concepts of continuous variable quantum computing in the present invention will be given first, so as to better understand its principles and innovations.

[0089] 1) Qumode as a basic information carrier

[0090] CV quantum computing utilizes continuous physical observables, such as position. and momentum This contrasts with discrete-variable quantum computing. In CV quantum computing, quantum information is encoded in optical modes called qumodes, which serve as the basic building blocks of quantum circuits.

[0091] A qumode state can be represented by two complementary frames: Fok space and phase space.

[0092] Fokker space representation directly describes the energy distribution in a light field. In this representation, a qumode state is defined by its infinite basis. The energy distribution in the image is used to describe the state, where |n> represents a state with n photons.

[0093] Phase space representation provides an intuitive alternative, using position x and momentum p as conjugate coordinates to map a qumode state to... The quantum state is characterized by the Wigner function:

[0094]

[0095] Where ρ is the density matrix. is the reduced Planck constant, and y is the integration variable. This function completely describes the quantum states in phase space.

[0096] 2) Gaussian states as practical building blocks for CV quantum computing

[0097] Gaussian states are the cornerstone of continuous-variable (CV) quantum information, defined as quantum states whose Wigner functions exhibit a Gaussian distribution in phase space. Using ρ... G (μ,Σ) represents a Gaussian state, where the state is completely characterized by the mean vector μ and covariance matrix Σ of its corresponding Wigner distribution. Because they are relatively easy to prepare and manipulate, they have become practical building blocks for many quantum protocols.

[0098] Vacuum state: The vacuum state is the simplest and most fundamental Gaussian state, representing the ground state of a quantum harmonic oscillator, and contains no photons. In Fokker space, it is represented as the zero-photon state |0>. In phase space, it corresponds to a minimum uncertainty Gaussian distribution centered at the origin, described as... Where I2 is a two-dimensional identity matrix.

[0099] Hot states: Hot states are crucial for realistically simulating ambient noise because they represent quantum systems in thermal equilibrium at finite temperatures. In Fok space, a hot state is a statistical mixture of photon number states whose occupancy probabilities follow a Boltzmann distribution. In phase space, it is a Gaussian distribution centered at the origin, but with increasing, symmetric noise, formally represented as… here, It is the average number of photons in the environment.

[0100] Coherent state: A coherent state, denoted as |α>, is the quantum mechanical counterpart of a classical laser beam and is uniquely defined as an annihilation operator. Eigenstates: The complex eigenvalue α directly corresponds to the displacement of this state in phase space. This displacement defines the mean vector of its Gaussian representation. As a vacuum state under displacement, its complete phase space description is therefore This maintains the minimum uncertainty of the vacuum. In Fockeky, this state is given by superposition:

[0101] Compressed vacuum states: Compressed vacuum states are a unique non-classical resource crucial for applications requiring ultra-high precision measurements. In phase space, a compressed vacuum state is also a minimal uncertainty Gaussian distribution centered at the origin (μ = 0). However, its noise distribution is asymmetric, exhibiting an ellipse rather than a circle. This indicates that the noise in one orthogonal component has been reduced ("compressed") below the vacuum level, at the cost of increased noise in the conjugate orthogonal components.

[0102] 3) Gaussian operator

[0103] Gaussian operations are transformations that map one Gaussian state to another. In quantum optics implementations, these operators correspond to physical processes that can be implemented using linear optical elements, parametric processes, and zero-step measurements. The following are the basic Gaussian operators that form the building blocks of CV quantum computing:

[0104] Displacement operator: A displacement operator translates a quantum state in phase space without altering its shape or uncertainty properties. For complex parameters α∈C, the displacement operator transforms the phase space coordinates as follows:

[0105]

[0106] When applied to a vacuum state, the displacement operator produces a coherent state: D(α)|0>=|α>.

[0107] Phase shift operator: The phase shift operator rotates a quantum state around the origin of phase space. For a phase angle φ∈[0,2π], the transformation is:

[0108] Squeezing operators: Squeezing operators reshape the uncertainty distribution of quantum states, reducing noise in one orthogonal component while increasing noise in the conjugate orthogonal component. For the squeezing parameter r∈R, the transformation is:

[0109]

[0110] Beam splitter operator: The beam splitter operator acts simultaneously on two qumodes, creating a linear combination of their orthogonal components. It transforms the input qumodes into a weighted superposition, where each output mode contains components from both input qumodes. For two qumodes... The transformation of the transmittance parameter η is:

[0111]

[0112] Based on this, the present invention provides a method for generating continuous variable quantum states, such as... Figure 1 The method shown includes the following steps:

[0113] Step 100: The input quantum state is converted into a thermal state through a forward diffusion process modeled by a thermal loss channel.

[0114] Step 101: Generate the thermal state into the target quantum state through a trainable reverse denoising process.

[0115] Specifically, in step 100 above, a forward (diffusion) process is modeled as a non-unitary thermal loss channel, physically modeled as a beam splitter mixing the system's quantum modes with the thermal environment. The thermal loss channel introduces both signal attenuation and additional thermal noise. A target quantum state (which serves as the input quantum state at this point), for example, the non-classical Fock state |n> used to realize a non-Gaussian gate, gradually degenerates into a simple thermal state by repeatedly applying this thermal loss channel.

[0116] In step 101 above, the trainable inverse denoising process can be modeled as an operation function that can generate an output quantum state that is closer to the original quantum state through a trainable quantum neural network. This original quantum state is the target quantum state in step 100 above. It should be noted that the training of the quantum neural network can continuously optimize the trainable parameters of the quantum neural network by considering the differences between the output quantum state and the target quantum state, such as fidelity or other quantities representing the differences. After the quantum neural network is trained, by applying the trained quantum neural network multiple times, the output quantum state becomes sufficiently close to the target quantum state, and the target quantum state is gradually recovered.

[0117] The generation method can be made more flexible and diverse by designing appropriate transmittance parameters for the heat loss channel, or other parameters that can achieve different noise levels.

[0118] like Figure 2 The following is an example of an embodiment of the present invention, the generation method being based on a continuous variable quantum diffusion model.

[0119] The Continuous-Variable Quantum Diffusion Model-Generator (CVQD-G) for generating continuous-variable quantum states operates through a learnable bidirectional process, and its general framework is as follows: Figure 2 As shown. The framework comprises two main stages: a forward (diffusion) process. And a learnable inverse (denoising) process f θ (ρ t ,t).

[0120] During the forward diffusion process, environmental thermal noise is gradually added to the original state ρ0 over multiple time steps t. This process is facilitated by a heat loss channel (in... Figure 3 The model is visualized as a virtual beam splitter, with the input state being ρ. t-1 The loss parameter is η t When t = 0, ρ0 represents the target state, while when t = T, ρ T The number of photons depends on the ambient average. The hot state.

[0121] The reverse denoising process uses a model f with trainable parameters θ and temporal embeddings. θ (ρ t ,t). The noisy quantum state ρ at a given time step t. t This trainable circuit generates a quantum state that is closer to the original state ρ0. During training, by comparing the predicted states Compared with the actual ρ obtained from the forward process t-1 To optimize the model parameters θ. By using the trained function f θ (·,·) are applied sequentially to ρ T The target quantum state is gradually recovered through a total of T iterations.

[0122] This invention converts the input quantum state into a thermal state by modeling a thermal loss channel, effectively simulating the environmental noise effects commonly found in continuous variable quantum communication. Through a trainable reverse denoising process, the thermal state is restored to a diverse target quantum state, breaking through the limitation of fixed input-output mapping. This improves the fidelity of the generation and restoration results, the response speed to unpredictable noise, and the robustness of quantum state restoration.

[0123] Optionally, the forward diffusion process modeled by the heat loss channel includes: at each time step t, input quantum state ρ t-1 The heat loss channel, characterized by the following formula, is converted into a hot state ρ. t :

[0124]

[0125] in, Characterizing the heat loss path, η t ∈[0,1] is a time-step dependent transmittance parameter; The average number of photons is Environmental thermal state; U BS (η t ) is the beam splitter operator; the operation Tr E This indicates the elimination of traces in the environmental degrees of freedom.

[0126] Specifically, to fully describe this physical process, two complementary mathematical forms are utilized. The Heisenberg picture, which focuses on operator transformations, provides an elegant framework for understanding the underlying physical interactions. Meanwhile, the Schrödinger picture directly describes the evolution of the density matrix, making it particularly suitable for implementation in subsequent equations and numerical simulations.

[0127] In Heisenberg's picture, the heat loss channel can be intuitively understood as the beam splitter interaction between the quantum system and the thermal environment (e.g., Figure 3 (As shown). When an optical mode With a thermal environment model During the interaction, the transformation of time step t is given by the following equation:

[0128]

[0129] Where η t ∈[0,1] is a time-step-dependent transmittance parameter. This formula clearly illustrates how the output mode becomes a weighted combination of the input quantum state and thermal noise.

[0130] Transmittance parameter η t The intensity of the interaction between the control and the thermal environment: when η t When η = 1, the quantum state remains unchanged, while when η = 1, the quantum state remains unchanged. t When = 0, the output becomes completely thermal. For intermediate values, the channel generates a partial mixture of the input state and thermal noise. This non-unitary process increases the entropy of the system, gradually transforming a potentially low-entropy state (e.g., a pure state) into a higher-entropy state (e.g., a mixed state) as energy and coherence are lost to the environment.

[0131] Equivalently, the forward diffusion process can be represented by a density operator in a Schrödinger picture. At each time step t, the thermal loss channel transforms into the quantum state ρ. t-1 as follows:

[0132]

[0133] Operation Tr EThis indicates that trace elimination of the environmental degrees of freedom captures the non-unitary nature of the evolution of this open quantum system.

[0134] By designing a suitable sequence {η t The heat loss channel gradually transforms the original state ρ0 into a hot state, and when T is large enough, it eventually yields... This controlled degradation toward thermal equilibrium forms the physical basis of the forward diffusion process.

[0135] A thermal dissipation channel is used to gradually transform the target quantum state into a thermal equilibrium state. This method effectively simulates the environmental noise effects commonly found in quantum communication, providing theoretical elegance and practical relevance for real-world quantum systems.

[0136] Optionally, the forward diffusion process modeled by the heat loss channel further includes: at any time step t, the initial input quantum state ρ0 is transformed into the thermal state ρ by the heat loss channel characterized by the following formula. t :

[0137]

[0138] in Indicates transmittance The unitary operator of the bundle splitter, η represents the cumulative transmittance. i ∈[0,1] is a time-step dependent transmittance parameter; express The conjugate transpose of; The average number of photons is The environment is hot; operation Tr E This indicates the elimination of traces in the environmental degrees of freedom.

[0139] Specifically, the transition from the initial state ρ0 to any arbitrary time step state ρ t Traditionally, this method requires iteratively applying the thermal loss channel a total of t times. This sequential approach becomes computationally expensive and inefficient as t increases, creating significant bottlenecks in both the training and sampling phases.

[0140] To overcome this limitation, embodiments of the present invention provide a direct conversion method that can directly calculate the state ρ at any time step from ρ0 in a single step. t This enables efficient quantum state transitions to any time step. Theorem 1 theoretically establishes that the cumulative effect of t sequential heat loss channels is equivalent to a single effective heat loss channel. The proof of Theorem 1 will be discussed later and will not be elaborated here.

[0141] Theorem 1: In CVQD-G, it is assumed that the forward diffusion process is associated with an average photon number at each step. Constant environmental interactions. The system state at time step t (represented in Heisenberg's panorama as...) In Schrödinger's painting, it is represented as ρ t ) can be directly obtained from the corresponding initial system state ( Or ρ0) is obtained through a single effective heat loss channel with appropriately modified parameters:

[0142] 1) In the Heisenberg picture, the annihilation operator at time step t is directly related to the initial operator at t=0, as shown below: in This is the effective cumulative transmittance. Operator Represents all individual environment modes The combination produces an effective environmental model. As demonstrated in Appendix A, in the environment Under constant assumptions, It also has the same average number of photons Effective thermal mode.

[0143] 2) In the Schrödinger picture, the system density matrix at time step t is directly related to the initial operator at t=0, as shown below: in, Indicates transmittance The unitary operator of the bundle splitter, It is the thermal state of the auxiliary environment mode (with the said average photon number) ), Tr E It is a deviation from the environment.

[0144] This direct transformation significantly improves computational efficiency by eliminating the need to sequentially compute all intermediate states. Quantum states at any time step can be accessed instantaneously during training and sampling, which is particularly valuable when dealing with long diffusion lengths.

[0145] Optionally, at each time step t, for the η t Linear scheduling is used:

[0146]

[0147] Where η0 and η T It is a hyperparameter that defines the start and end points of the T-step linear interpolation.

[0148] Specifically, the forward diffusion process is controlled by a carefully defined noise schedule that determines the rate at which the quantum state degrades over time. This schedule is determined by a single-step transmittance sequence. Definition. Each η t It must be within the range of [0,1], and the scheduling design must ensure cumulative transmittance. The fact that it becomes very small indicates that significant diffusion has occurred.

[0149] By using η t Linear scheduling is used, and the hyperparameter values ​​are selected to ensure η t To remain physically valid, and

[0150] By using noise scheduling, the degradation rate of quantum states can be controlled and predicted, reducing the loss of quantum information caused by sudden decoherence.

[0151] Optionally, the trainable reverse denoising process includes: obtaining a temporal quantum state through a time embedding circuit; and denoising the composite system constructed from the temporal quantum state and the thermal state through a denoising circuit to generate a target quantum state; wherein the denoising circuit is trained based on denoising circuit parameters.

[0152] Specifically, the reverse denoising process aims to remove noise from the thermal state ρ of the environment. T The original quantum state ρ0 is systematically recovered. This recovery process faces two fundamental theoretical challenges: the first challenge involves parameter efficiency: although the forward diffusion process utilizes thermal loss channels with known parameters... and Directly calculate any ρ t However, the reverse process is essentially a training process. Unlike the forward process, the quantum channel model cannot directly obtain the state at any time step; instead, it requires training T time-step-specific denoising functions. The first challenge is the imposition of excessive computational demands; the second challenge stems from the inherent non-unitary forward diffusion process: since quantum information is irreversibly dissipated into the environment, the reverse process must employ non-unitary operations.

[0153] like Figure 3 As shown, the trainable inverse denoising process in this embodiment is modeled as an operation function f. θ (ρ t The operation function (t) addresses both challenges. This operation function can be implemented using quantum circuits, including time-embedded circuits. and a parameterized noise reduction circuit For parameter efficiency, By generating a time-step-dependent state by using t as an explicit input to the operation function, a time-quantum state τ is obtained. t This allows the denoising method to be modified from having T sets of independent parameters. The set is transformed into a single shared parameter set conditional on time steps. To achieve non-unitary operations, auxiliary qumodes beyond the master quantum system are introduced. The denoising process involves preparing a composite system. application The predicted state is obtained by performing trace removal on the auxiliary qumode B while preserving qumode A. This enables non-unitary transformation.

[0154] To address the first challenge—parameter efficiency—a temporal embedding mechanism is developed that leverages the natural phase evolution of coherent states. This approach allows for the conditioning of a single model at different time steps, rather than training a separate model for each time step. The coherent states evolve according to the following formula:

[0155] α(t)=e -iωt α;

[0156] Where α represents the complex parameter of the coherent state, describing the characteristics of the coherent state such as its "position"; ω represents the angular frequency, which controls the rate of phase evolution;

[0157] For any non-zero coherent state |α>, this phase evolution provides an elegant way to encode time step information. For example... Figure 3 of As shown in the component, this is achieved through two operations: First, a displacement gate D(α) with fixed parameters α∈R. + The vacuum state is moved along the x-axis of the phase space; then, a rotating gate R(φ(t)) applies a phase that depends on the time step. The discrete time step t is linearly mapped to the phase angle φ∈[0,π]. This method effectively embeds time step information directly into the quantum state itself, thereby improving parameter efficiency.

[0158] To address the second challenge—the non-unitary operation challenge—a denoising circuit operating in the extended Hilbert space can be designed. (Denoising circuit) Acting on composite systems A dual-qumode system. After applying this circuit, the predicted output is obtained by trace cancellation of subsystem B.

[0159]

[0160] Among them, the operation tr B This indicates trace elimination of the environmental degrees of freedom. Although for the input ρ... t and output Using the same qumode seems intuitive, but this approach may have problems. Due to the state ρ t and ρ t-1 The differences between them may be small, and the circuit may simply default to copying its input instead of generating an appropriate denoised output. For example... Figure 3 of As shown in the component diagram, the denoising circuit consists of an L-layer dual-qumode CVQNN circuit. Each CVQNN layer comprises two distinct parts, similar to how classic neural networks require linear and non-linear components:

[0161] A linear component utilizing Gaussian operators, comprising a displacement gate D, a rotation gate R, a compression gate S, and a beam splitter gate BS.

[0162] A nonlinear component implemented using Kelman K is defined as: Where κ is the gate parameter. It is a particle number operator used to measure the number of particles in a quantum state (e.g., the number of photons in a light field).

[0163] The method described above combines linear operations with a single nonlinear operation, enabling universal CV quantum computing with polynomial overhead. Gaussian operators alone are limited to generating only quadratic Hamiltonians, hindering complex higher-order computations and restricting computational expressiveness. Kermen provides the necessary nonlinearity to construct higher-order Hamiltonians, thus enabling universal quantum computing that transcends the Gaussian limitation. Furthermore, due to their diagonal nature in Fockeki, Kermen facilitates faster and more reliable numerical simulations.

[0164] Optionally, the denoising circuit is obtained by training based on denoising circuit parameters, and the method includes: determining a loss based on the input quantum state and the target quantum state; and adjusting the denoising circuit parameters based on the loss.

[0165] Specifically, the quantum state entering the denoising circuit is the input quantum state, and the output of the denoising circuit is the target quantum state. By comparing the difference between the two, the loss can be determined, or the loss can be calculated using the loss function. The parameters of the denoising circuit can then be adjusted based on the calculated loss.

[0166] For example, the basic goal of training CVQD-G is to optimize the parameters of the denoising circuit. Make the predicted state Closely approximating the actual state ρ t-1 This can be achieved by maximizing the quantum fidelity between these states. The total loss function is defined as:

[0167] This corresponds to the final and most important denoising step (t=1) and serves as a key anchor point in the training process. By directly penalizing errors in the reconstruction of the target state ρ0, it ensures that the main objective remains to accurately form a valid, physical quantum state. The hyperparameter λ balances the loss in this final step. Expected loss compared to other steps . contributions.

[0168] Component loss at any given step The calculation is as follows:

[0169]

[0170] Where F(·,·) is the quantum fidelity function, which measures the similarity between quantum states. The closer the fidelity is to 1, the more similar the quantum states are. γ represents the penalty parameter.

[0171]

[0172] Here, tr represents the trace operation. For numerical implementation, the Fock backend in Strawberry Fields can be used, which inevitably truncates the infinite-dimensional Hilbert space. This truncation can lead to circuit operations pushing states outside the computational basis, resulting in a non-normalized density matrix. To address this challenge, a penalty term is added to the loss function.

[0173]

[0174] This ensures that the trace of the output density matrix remains close to 1.

[0175] The specific training algorithm can be implemented as shown in Table 2 below:

[0176] In each iteration, calculate Then, gradient-based optimization is used to update the gate parameters until convergence or the maximum number of iterations is reached.

[0177] Table 2 CVQD-G Training

[0178]

[0179]

[0180] Once the model is trained, the optimized parameters can be used. Quantum state generation occurs. From the thermal state ρ T Initially, the reverse process sequentially applies a denoising circuit to recover the initial state ρ0, and its algorithm 2 is detailed in Table 3.

[0181] Table 3 CVQD-G Generation

[0182]

[0183] The training method for the continuous-variable quantum state recovery model will be described in detail below, such as... Figure 5 As shown, the method includes the following steps:

[0184] Step 500: Construct a coherent state dataset.

[0185] Step 501: Obtain the diffused quantum state based on the sample quantum states in the coherent state dataset;

[0186] Step 502: Based on the diffused quantum state, recover the sample quantum state to obtain the input coherent state; and

[0187] Step 503: Train the continuous variable quantum state recovery model based on the sample quantum state and the input coherent state.

[0188] Specifically, the continuous-variable quantum state recovery model addresses the problem of recovering a quantum state with unknown parameters from unknown levels of environmental noise. To more clearly illustrate the principle of the method in this embodiment, a brief introduction to relevant knowledge is provided first.

[0189] 1) Challenges of State Recovery in Noisy Channels

[0190] In practical quantum communication, the state transmitted by the sender (Alice) is inevitably corrupted by environmental noise before reaching the receiver (Bob). Consider a scenario where Alice transmits a coherent state ρ. in =|α in ><α in It passes through a noisy quantum channel, typically modeled as a thermally depleted channel, and degenerates into a damaged state ρ. out :

[0191]

[0192] Among them U BS It is related to the thermal state of the environment The interaction between the beam splitters, Tr E This represents the bias towards the environment. Bob's task is to process the received state ρ. out The goal is to restore the original state and retrieve Alice's information. This presents a significant challenge because it requires the model to operate "blindly" with very little knowledge of several key parameters. Specifically, the model is unaware of the initial state parameter α that encodes the information. in ; Channel transmittance η of quantized signal loss ch ; and the environmental noise level of the increased thermal noise. This situation is fundamentally different from the quantum state generation task of CVQD-G, as shown in Table 4. In the latter task, the parameters of the target state are known by definition, such as the average number of photons. Transmittance parameters, etc. Therefore, it is necessary to effectively process the received, damaged state ρ. out This will help to recover the potential quantum state and thus solve this practical challenge.

[0193] As can be understood, the differences between CVQD-R and CVQD-G are shown in Table 4:

[0194] Table 4 Comparison of CVQD-G and CVQD-R

[0195]

[0196] 2) Theoretical basis of restoration

[0197] The Continuous-Variable Quantum Diffusion Model-Restorer (CVQD-R), based on the continuous-variable quantum diffusion model, trains a quantum neural network to identify and reverse the systematic effects of thermal environmental noise on quantum states. Instead of being given noise parameters, the model learns to infer the degree of damage by analyzing the orthogonal variance of the received states, enabling it to apply appropriate learned recovery operations.

[0198] Understanding how the variance of a quantum state is affected when it traverses a thermally dissipated channel is crucial. When a coherent state passes through such a channel, the variance is determined by the transmittance η and the average photon number. When the environment characterization of the channel is used, its output orthogonal variance Essentially, it is a weighted combination of the intrinsic variance of the initial coherent state and the variance contributed by the thermal environment. This dominant relationship is given by the following equation:

[0199]

[0200] To make this expression specific, first examine the component variances. This represents the variance of the initial coherent state (|αin>). Coherent states are the fundamental states in a CV quantum system, embodying the minimum uncertainty state according to the saturated Heisenberg uncertainty principle. Their eigenorthogonal variance, for example, in the X-orthogonal components, is the minimum shot noise variance:

[0201]

[0202] This value quantifies the minimum expansion of the state's Gaussian distribution in phase space.

[0203] item This involves the variance of the thermal states of the simulated environment. These states are also Gaussian, and their variance increases with the average number of photons. Increased with the increase:

[0204]

[0205] This increased variance reflects a wider and more mixed phase space distribution compared to coherent or vacuum states.

[0206] Substituting the specific expressions for the coherent state variance and the thermal state variance into the general combination formula, the final explicit form of the formula for the total output variance is derived:

[0207]

[0208] This variance-noise relationship is key to the “blind” recovery strategy because it establishes the orthogonal variance of the state as a measurable proxy for the degree of corruption. The CVQD-R model is trained to exploit this by treating the entire corrupted quantum state as a coherent, measurement-free input. The quantum neural network learns a single, global transformation implicitly conditioned on the intrinsic properties of the input state, such as its variance. This allows the model to effectively reverse the noise without explicitly knowing the channel parameters η or ...

[0209] In step 500 above, in order to perform blind recovery: to recover arbitrary coherent states from a predefined operating range without prior knowledge, regardless of their encoding parameters or the specific thermal noise they experience. The continuous-variable quantum state recovery model needs to be trained again on a diverse dataset. Optionally, this dataset can be obtained by sampling "clean" coherent states {|α} from a uniform disk of radius D. tr >} Created. This parameter D defines the high-probability operating range of the Alice signal, approximated by a practical Gaussian modulation scheme, where the signal parameter α in =x+ip is composed of independently sampled orthogonal components Build it up. Setting the boundary to D = 3σ ensures that the range covers more than 99.9% of all possible transmissions.

[0210] In step 501 above, for each training instance, an efficient single-step diffusion method can be applied to a clean state ρ0, and a time step t can be randomly selected to dynamically generate the corresponding noise-damaged state ρ. t A gradual diffusion approach can also be adopted, and there are no restrictions on this.

[0211] In step 502 above, during the denoising process of the diffused quantum state entering the recovery model, it should be noted that this denoising process is the same as the trainable inverse denoising process in the continuous variable quantum state generation method described above, and they can be referenced interchangeably. This can be achieved through the operation function f. θ (ρ t Modeling for ,t) will not be elaborated here.

[0212] In step 503 above, the parameters of the recovery model are trained by comparing the differences between the input sample quantum states and the output coherent states of the recovery model. It's important to note that, due to training on a varying dataset, the quantum neural network of the recovery model learns a powerful, generalized denoising function, not just a memory of the recovery path. Crucially, it learns to interpret the intrinsic properties of the states—primarily their variance, according to the formula—as an implicit signature of their noise level. This learning is driven by a training loop, in which the model receives a diffused state in each iteration. It is then optimized to produce an estimate of the baseline state from the previous step. Optimize to minimize single-step loss:

[0213]

[0214] Where F is the quantum fidelity, P is the trace-one penalty term, and γ is the penalty parameter. Total loss The calculation, as defined, is consistent with the continuous variable quantum state generation method described above, and will not be repeated here.

[0215] Once training is complete, CVQD-R is used to recover unknown, noise-damaged coherent states through a fixed-time-step sequential inference process. This process begins by taking the received state as input for the last time step t = T. The model then sequentially applies its learned single-step denoising transform from T to 1. In this reverse process, the output state at step t is used as input for step t-1. This fixed-step sequence reconstructs an estimate of the original clean state. Finish.

[0216] This invention, through the construction of diverse training datasets, enables the trained continuous-variable quantum state recovery model to recover any coherent state from a predefined operating range, achieving blind recovery and avoiding the problem of prior knowledge required in existing technologies. Furthermore, by integrating with the continuous-variable quantum state generation model, quantum state generation and recovery are realized within a unified framework, filling the gap left by generation-centered models.

[0217] like Figure 17 As shown, the present invention also provides a method for restoring a continuous variable quantum state, comprising the following steps:

[0218] Step 1700: Obtain the quantum state to be recovered.

[0219] Step 1701: Input the quantum state to be recovered into the continuous variable quantum state recovery model to obtain the target quantum state; wherein, the continuous variable quantum state recovery model is obtained through the above-described... Figure 5 The method shown is used for training.

[0220] Specifically, in step 1700 above, the quantum state to be recovered can be a quantum state generated by the continuous variable quantum state generation model described above, or it can be any coherent state within a predefined operating range.

[0221] In step 1701 above, the continuous variable quantum state recovery model can be achieved through, for example... Figure 5 The method shown is used for training, for example, to construct a denoising circuit using the trained quantum neural network described above. The received quantum state is used as the input for the final time step t = T. Then, the model sequentially applies its learned single-step denoising transform from T to 1. In this reverse process, the output state at time step t is used as the input for time step t-1. This continues until a clean quantum state is recovered. Obtain the target quantum state.

[0222] To better understand the technical effects of the embodiments of the present invention, the complexity of the embodiments of the present invention will now be analyzed and compared with other continuous variable quantum generation methods.

[0223] 1) Reasoning and parameter complexity

[0224] The computational cost of generating a single quantum state is determined by the number of diffusion steps T and the number of layers L in the denoising circuit. The generation process is iterative: for each of the T denoising steps, a parameterized quantum circuit with L layers must be applied sequentially. This results in a total generation complexity of: A key feature of this invention is its superior parameter efficiency. By using time-step embedding, a set of trainable parameters can be achieved. This is shared across all T steps. This results in a highly scalable parameter complexity: This efficiency makes the model practical and scalable, especially when a large number of diffusion steps are required to achieve a smooth generation process.

[0225] 2) Training complexity

[0226] A key to the training efficiency of this invention is the use of efficient single-step state transitions. This method avoids the need for sequential, step-by-step computations to generate training data. Instead, the quantum state at any arbitrary time step t is directly generated from the initial state ρ0 through a single operation. This results in a total training complexity of: Where I is the number of training iterations and B is the batch size. This independence from the total diffusion length T is a significant advantage, allowing for a large number of diffusion steps without incurring excessive training costs.

[0227] 3) Comparative analysis with other continuous variable quantum generation methods

[0228] This invention provides a unique computational tradeoff. While single-shot models like OpticalGANs have varying generative complexity profiles, the models of this invention offer significant advantages in other key areas. Specifically, the models of this invention avoid the high measurement and classical post-processing overhead inherent in OpticalGAN architectures, which require a zero-beat measurement for each discriminator evaluation. Furthermore, the diffusion framework-stable, non-adversarial training objective aims to mitigate common challenges such as mode collapse and training instability that can affect adversarial frameworks. Table 5 provides a summary of this comparison.

[0229] Table 5. Comparison of the complexity of CVQD and Optical GAN

[0230]

[0231] Where L g and L d These represent the number of layers in the generator and discriminator of the Optical GAN, respectively.

[0232] This complexity profile provides crucial insights into hardware implementation and identifies optimization opportunities for resource-constrained quantum systems.

[0233] The experimental results of the embodiments of the present invention are analyzed below:

[0234] The high-fidelity state generation capability of the CVQD-G model and the robust quantum state recovery capability of the CVQD-R model were tested. The experiment aims to demonstrate the generative diversity of the framework through CVQD-G and its practical value in noise suppression through CVQD-R, addressing key challenges in real-world quantum information processing.

[0235] The experimental setup is as follows: All numerical simulations were performed using Strawberry Fields as the quantum circuit simulation engine, specifically utilizing its Fock backend. This backend requires setting a finite cutoff dimension for the Fock basis representation. While this is crucial for the simulation, this cutoff is not a fundamental limitation of physical CV quantum devices, which naturally operate in an infinite-dimensional Hilbert space. The optimization of the CVQNN parameters in this embodiment was performed using TensorFlow and the Adam optimizer, enhanced with an exponential learning rate decay scheme to achieve stable and efficient convergence. The systematic search and fine-tuning of these optimization settings and other key model hyperparameters were performed using the Optuna hyperparameter optimization framework.

[0236] (1) Test results of quantum state generation

[0237] This invention systematically evaluates the ability of the CVQD-G model to generate a diverse range of target quantum states. To provide a comprehensive evaluation, the evaluation protocol considers two different and physically related forward diffusion process scenarios: a purely lossy channel... This represents the loss in a vacuum environment and the thermal loss channel. This represents a more realistic noisy environment. Furthermore, in addition to standard generation from noise priors, the robustness of the model is evaluated by initiating a reverse denoising process from various partially noise-damaged states. This test primarily verifies the robustness of the denoising mechanism itself and its ability to converge to its predefined target from any point on the diffusion trajectory, which differs from the general recovery task of restoring unknown states performed by CVQD-R. The core hyperparameters of the generation task are shown in Table 6:

[0238] Table 6 General hyperparameters of the CVQD-G experiment

[0239]

[0240]

[0241] The detailed results for each state and scenario are as follows:

[0242] Gaussian state generation: The performance of the CVQD-G model was evaluated by testing its performance on two key types: coherent states and compressed vacuum states.

[0243] Coherent state (|α>): Figure 6 Demonstrates the use of pure loss channels A representative coherent state |α=1.0> is generated in the middle. Figure 6 (a) shows the training loss, which drops sharply and stabilizes after about 40 epochs. The initial oscillations indicate a dynamic learning phase before the model stabilizes to a stable convergence trajectory, suggesting that the model is highly trainable and can effectively learn features of the target state. Figure 6 (b) shows the fidelity of forward diffusion; as noise gradually increases, the fidelity smoothly decreases, effectively erasing information from the initial state. Conversely, Figure 6 (c) illustrates the inverse denoising process, in which the fidelity of the generated states steadily increases, converging to a final value of 99.95%. Crucially, the process exhibits consistently high-fidelity convergence even when starting from partially corrupted states (different η), demonstrating that the learned denoising function is robust and independent of a fixed starting point.

[0244] To further evaluate the model's capabilities and limitations, Figure 7 The performance was evaluated under different coherent state amplitudes α and different noise environments, such as Figure 7As shown in (a). This figure shows that for smaller amplitudes (α≤1.5), the model performs better in pure loss mode. and heat loss Near-perfect fidelity (>99.8%) was consistently achieved in the environment. However, a significant decrease in fidelity was observed as the amplitude increased further (e.g., to α = 2.5). This performance degradation at larger amplitudes is expected in simulations using a fixed Fock space cutoff dimension (15); states with larger amplitudes occupy a larger phase space volume, and their high-energy components may be truncated by the finite basis. This result highlights the practical trade-off between computational resources and the reachable parameter range. Detailed results of this parameter scan and individual generated curves are shown in Figure 1. Figure 13 As shown. Nevertheless, this limitation can be mitigated through targeted hyperparameter tuning, which can restore high fidelity for the case of α = 2.5, as... Figure 16 As shown.

[0245] Compressed vacuum state (S(r)|0>): Figure 8 Demonstrates the use of pure loss channels A compressed vacuum state with a compression parameter of r = 0.5 is generated. Compared to the coherent state, its training process exhibits different characteristics. The training loss, such as... Figure 8 As shown in (a), it exhibits very smooth and rapid convergence, stabilizing within approximately 20 epochs without initial oscillations in the coherent states. This enhanced stability is likely due to the target compressed vacuum state and the noisy prior ρ. T All are centered at the origin in phase space. Therefore, the learning task focuses on reshaping the uncertainty distribution of the state, rather than learning the displacement from the origin, which simplifies the optimization landscape. The inverse denoising process, such as... Figure 8 As shown in (c), the target state was successfully restored to 99.56% high fidelity. A significant difference was observed at the beginning of the restoration process. State fidelity after the first denoising step. As indicated by the notation, the value is significantly higher for the compressed vacuum state (approximately 0.6) than for the coherent state (approximately 0.45). This can be explained by the initial overlap between the target state and the vacuum state |0>, the latter being structurally similar to the thermal prior ρ. T Similarities exist. The fidelity between the compressed vacuum target and the vacuum state is high (F(S(r=0.5)|0>,|0>)≈88.6%), while the fidelity of the coherent state target is low (F(|α=1.0>,|0>)≈36.8%). The higher initial overlap of the compressed vacuum state provides a more favorable starting point for the denoising process, leading to higher fidelity even after the first recovery step. Despite these different initial dynamics, the model consistently converges to the target from various partially damaged states, demonstrating its robustness.

[0246] To investigate the performance limits of the model for these types of states, a parameter scan was performed on the compression parameter r∈{0.25,0.5,0.75,1.0}, and the results are summarized in... Figure 7 (b) shows that the model performs well in pure loss mode. and heat loss In this environment, high fidelity was maintained within this range, although a slight, gradual decrease in fidelity occurred with increasing compression parameter r. This trend is expected, as states with stronger compression exhibit more pronounced non-classical characteristics and are more vulnerable to losses, making their perfect generation more challenging. Detailed results of this parameter scan and individual generation curves are shown below. Figure 14 As shown.

[0247] Non-Gaussian state generation: The expressive power of the embodiments of the invention is tested by demonstrating high-fidelity generation of two well-known examples: the Fock state and the cat state.

[0248] Fock state (|n>): through a pure loss channel The ability of the model in this embodiment of the invention to generate the first excited Fock state |1> is demonstrated, and the result is as follows. Figure 9 As shown. A comparison of the training processes reveals that generating non-Gaussian states is a more demanding learning task. The training loss for Fock states, as... Figure 9 As shown in (a), the convergence rate is significantly slower than that of the Gaussian state (and). Figure 6 (a) and Figure 8 (a) Comparison). This is expected because the model must learn to reverse the forward diffusion, which transforms the highly non-Gaussian Fock state into a simple, Gaussian distributed hot state (ρ). T The process of learning to perform this non-Gaussian to Gaussian inverse transformation is inherently a more challenging optimization problem than the simpler Gaussian to Gaussian transformation required for coherent states or squeezed vacuum states, which explains the slower convergence speed.

[0249] Forward diffusion process, such as Figure 9 As shown in (b), the erasure of information is clearly demonstrated. Fidelity It gradually decreases, eventually decaying to a value close to zero. In this purely lossy channel condition, the final diffusion state is a vacuum state. Due to the target state and vacuum state These are orthogonal basis vectors in the Fock space, with a theoretical fidelity of exactly zero. Despite facing the dual challenges of a more demanding training task and an initial prior orthogonal to the target, the reverse process ( Figure 9 (c) The model demonstrates its powerful expressive ability by successfully reconstructing the state to an excellent final fidelity of 99.85%. (Regarding heat loss...) Similar high-fidelity generation performance was also observed in the environment.

[0250] cat state (|cat(α)): Figure 10 Demonstrates the use of pure loss channels An even cat state |cat(1)> is generated. The training dynamics of the cat state reveal a unique learning process. The loss curve, as shown... Figure 10 As shown in (a), after an initial sharp decline, a distinct “plateau” phase is observed between approximately epochs 10 and 20. This behavior, unlike all other test states, likely reflects the unique multi-component structure of the cat state. It is assumed that the model first learns the general Gaussian envelope of the two coherent state components, then enters a more challenging optimization phase, learning the subtle interference fringes and quantum superposition between them, leading to a temporary plateau in the loss curve. Despite the complexity of the training landscape, the reverse process is highly successful. Forward diffusion ( Figure 10 (b) reduces the fidelity to approximately 0.65, a level comparable to that of a Gaussian state, reflecting the potential coherent state components of the cat state. From this starting point, the inverse denoising process ( Figure 10 (c) The target was continuously reconstructed, achieving an excellent final fidelity of 99.61%. The successful generation of this state with subtle superposition characteristics strongly demonstrates the model's ability to create complex non-Gaussian quantum states. (Regarding thermal losses...) For performance details in the environment, please refer to [link / reference]. Figure 15 .

[0251] Performance comparison with Optical GANs:

[0252] To benchmark the model's performance against existing methods, a direct comparison was made with Optical Generative Adversarial Networks (OpticalGANs). For a robust and fair comparison, the results for Optical GANs were obtained by implementing its publicly available source code. To ensure maximum performance under the experimental conditions of this embodiment, an extensive hyperparameter search was also performed on the Optuna optimization framework for the Optical GAN ​​model.

[0253] Table 7 summarizes the state generation fidelity achieved by the two models. The results clearly demonstrate that the CVQD-G of the present invention consistently and significantly outperforms Optical GAN ​​on all tested quantum states. The performance gap is particularly significant on non-Gaussian states. For example, in generating the Fock state |1>, CVQD-G achieves 99.85% fidelity, a 36.3% improvement over Optical GAN's 73.27% fidelity. Similarly, for the Cat state |cat(1)>, the model of the present invention achieves 99.61% fidelity, a 26.4% improvement over the 78.82% result. Even for Gaussian states, such as the coherent state |α=1.0>, CVQD-G shows a significant advantage, with its 99.95% fidelity being approximately 19.8% higher than Optical GAN's 83.43%.

[0254] CVQD-G’s superior performance can be attributed to several fundamental architectural and procedural advantages over adversarial GAN ​​frameworks.

[0255] Stable training objective: Unlike GANs, which are known for their challenging adversarial training dynamics that can lead to instability or pattern collapse, diffusion models possess a more stable, well-defined loss function. This allows for more reliable and consistent convergence to the target state distribution.

[0256] Iterative Refinement Process: The stepwise nature of the diffusion model's reverse process is a key advantage. It decomposes the complex task of generating states into a series of simpler denoising steps. This iterative refinement can capture the subtle, non-classical features of quantum states more effectively than a single-shot generator in a GAN, which must learn the entire complex mapping at once.

[0257] No discriminator overhead: The CVQD-G framework does not require an adversarial discriminator network. This not only simplifies the overall architecture and training dynamics, but also avoids the significant computational and measurement overhead introduced by quantum or classical discriminators.

[0258] While comprehensive numerical benchmarking against the full spectrum of CV quantum generation models remains an important area for future research, the CVQD-G framework has clear and principled advantages. Its unique architecture, which avoids adversarial training and incorporates an iterative refinement process, coupled with its proven robust generation and recovery capabilities, makes it a flexible and powerful alternative, particularly suitable for applications requiring both noise recovery and state recovery.

[0259] In summary, the state generation experiments strongly demonstrate the versatility and effectiveness of the CVQD-G model. It not only achieves high-fidelity generation of basic Gaussian and complex non-Gaussian states—outperforming previous benchmarks like Optical GANs—but also exhibits significant robustness to varying environmental noise conditions and different starting points during the inversion process. Detailed analysis of the training and diffusion dynamics for each state reveals the model's powerful expressive capabilities, enabling it to learn and construct complex non-classical features from simple noisy priors, making it a powerful tool for quantum state engineering.

[0260] Table 7 shows the pure loss channel Below is a comparison of the state generation fidelity (%) of CVQD-G and Optical GAN.

[0261]

[0262] Having demonstrated the quantum state generation capability using the CVQD-G model, we now demonstrate the recovery capability of the model of this invention from quantum states damaged by environmental noise, performed using the continuous variable quantum diffusion recovery model (CVQD-R).

[0263] Training Methods and Setup for Recovery: To enable CVQD-R to generalize and recover arbitrary coherent states, its training strategy differs fundamentally from that of CVQD-G. Instead of focusing on a single objective, the training process for CVQD-R involves generating a diverse ensemble of initial clean coherent states. Specifically, this ensemble is created by applying a shift operator (X-gate) whose parameters are randomly sampled from a given amplitude range (e.g., [0,1] in the experiments of this embodiment) and combining it with a phase rotation operator (R-gate) whose parameters are randomly sampled from 0 to 2π. Each of these clean states is then subjected to simulated noise through thermally depleted channels with varying levels of corruption, corresponding to different time steps in the diffusion process. The model is then trained on this rich dataset to learn how to reverse these noise effects. The core hyperparameters used in these recovery-focused experiments are summarized in Table 8.

[0264] Table 8 Hyperparameters of the CVQD-R state recovery experiment

[0265] Hyperparameters value Cutoff dimension 15 Number of layers (per diffusion step in CVQNN) 30 Batch size 48 Epochs 112 Total time steps T (diffusion / recovery) 150 <![CDATA[Initial noise schedule β start > <![CDATA[1.0×10 -4 ]]> <![CDATA[Final noise schedule β end > 0.05 Initial learning rate 0.00045 Decay steps (learning rate) 24 Decay rate (learning rate) 0.906 Normalized penalty weight (γ) 100 Time step loss weight (λ) 0.16

[0266] Recovery in thermally dissipated channels: using a... The environmental environment is used as a representative thermal noise level to demonstrate the model's resilience.

[0267] Recovering coherent states of different amplitudes from fixed noise: First, evaluate the model under fixed noise channel conditions (transmittance η = 0.5 and ambient noise). The ability to recover coherent states with different initial amplitudes when affected by X gate parameters is investigated. To this end, a test set was created using initial clean coherent states with different displacement amplitudes, corresponding to X gate parameters s∈{0.3,0.5,0.7}, with each amplitude group containing eight different initial phase states.

[0268] Figure 11 This illustrates the average recovery fidelity of these three amplitude groups. The average is taken over eight initial phases. The thermally dissipated channel with a fixed state (e.g., η = 0.5) is used. Damage. The shaded area may represent the standard deviation of the phase.

[0269] The figure clearly shows a performance trend: while the final fidelity is high, it decreases with increasing initial amplitude s (from approximately 98% for s = 0.3 to 89% for s = 0.7). This trend can be attributed to the challenge of simulating the learned denoising circuit within a truncated Fock space. Although the cutoff dimension (15) is sufficient for the input and the final target state, the learnable denoising unit at each step... Transient quantum states generated within a layer are not guaranteed to remain within this basis. For targets with larger amplitudes, the circuit is more likely to instantaneously generate states with high photon number components, which are truncated during internal computation. These intermediate truncation errors can accumulate during iterative recovery, ultimately limiting the final fidelity achievable for high-energy states. Therefore, the observed decrease in high-energy state fidelity is not a limitation of the model's learning ability, but a direct reflection of the actual trade-off between simulation accuracy and computational cost (i.e., the cutoff dimension of the Fock space). Nevertheless, the high fidelity achieved for all three different initial radii confirms that the model does not converge to a single, trivial state. Instead, it successfully learns to recover each corrupted input to its unique original amplitude, demonstrating robustness within this parameter range.

[0270] Recovering a fixed coherent state from variable noise levels: Another key scenario is evaluating the model's ability to recover a specific initial state after being subjected to varying degrees of noise. For this test, a fixed coherent state (prepared with phases of s = 0.5 and π / 4) is passed through a thermally dissipated channel with different transmittances η ∈ {0.25, 0.50, 0.75}. Therefore, the initial state damaged by noise has a significantly different fidelity compared to the original clean state.

[0271] Figure 12The resulting recovery fidelity curves are shown. Notably, after the first denoising step, the fidelity of the states has been brought very close, significantly reducing the initial fidelity gap. The enlarged inset reveals a subtle dynamic where the initial steps show a slight dependence on the noise level η. However, immediately following this transient phase, the fidelity trajectories of all three cases merge into a single, indistinguishable path. This universal recovery curve not only converges to the same high final fidelity of approximately 96%, but also completely coincides with the trajectory observed in the previous experiment for s=0.5. Figure 11 The perfect overlap of the recovery paths provides profound insights into the model's robustness. It shows that the learned reverse process not only defines a general recovery trajectory but also exhibits a strong "attractor" dynamic. Even starting from input states with significantly different levels of corruption and fidelity, the model's initial steps are sufficient to correct these large initial biases and guide all evolutionary paths onto a single, general recovery trajectory.

[0272] The comprehensive numerical simulations of this invention powerfully demonstrate the effectiveness and versatility of the continuous variable quantum diffusion (CVQD) model. The results confirm that models CVQD-G and CVQD-R not only achieve their respective goals of high-fidelity state generation and robust state recovery, but also exhibit significant advantages in performance and adaptability.

[0273] In state generation, CVQD-G successfully produces diverse Gaussian and non-Gaussian states with fidelity typically exceeding 99%, significantly outperforming Optical GAN ​​benchmarks, especially for complex non-Gaussian targets. The framework's robustness is a standout feature. During generation, the model is resilient to environmental noise and variations in the initial state during the reverse process. This robustness is even more pronounced in state recovery, where the CVQD-R model exhibits a powerful "attractor" dynamic: it consistently guides states with vastly different initial corruption levels to a single, universal recovery trajectory, demonstrating remarkable generalization ability.

[0274] These strong results are attributed to the fundamental advantages of the diffusion-based architecture. By implementing a physically plausible forward diffusion process (thermal loss) and avoiding complex adversarial training dynamics, the models in this embodiment benefit from a more stable and direct learning objective than GANs. Furthermore, the inherent iterative refinement of the reverse process is naturally suited to progressively building the complexity of generated states and progressively removing noise from damaged states. This stepwise approach, combined with parameter-efficient design, provides a powerful and scalable alternative for quantum state engineering.

[0275] These fundamental advantages in architecture and training dynamics, combined with proven robust generation and recovery capabilities, establish the CVQD framework as a powerful and promising paradigm. It provides a unified, efficient, and highly adaptive solution to the key challenges of state generation and noise suppression in real-world continuous-variable quantum systems.

[0276] In this invention, a novel framework is introduced and fully validated that utilizes continuous-variable (CV) quantum diffusion processes to accomplish the dual tasks of high-fidelity state generation and robust state recovery. This single, unified approach has been demonstrated to successfully generate two powerful, specialized models: the continuous-variable quantum diffusion generation model (CVQD-G) and the continuous-variable quantum diffusion recovery model (CVQD-R). The method of this invention combines a physically plausible thermally dissipated channel for forward diffusion with a parametrically efficient, learnable CVQNN for the reverse process, overcoming the operational rigidity of many previous CV generation models.

[0277] Numerical simulations of these embodiments provide strong evidence for the capabilities of this framework. In state (quantum state) generation, CVQD-G consistently produces a diverse range of Gaussian and highly nonclassical states with fidelity exceeding 99%, significantly outperforming established benchmarks like Optical GANs, and achieving a performance improvement of over 36% for challenging states such as Fock states. In state recovery, the dedicated CVQD-R model exhibits remarkable robustness. It successfully recovers coherent states from unknown levels of thermal noise, demonstrating a strong “attractor” dynamic where different initial corruption levels converge to a single, universal recovery trajectory. This confirms its ability to generalize and adapt—a key feature for practical applications in noisy environments.

[0278] These powerful results are rooted in the fundamental advantages of diffusion-based architectures, which provide a stable training objective and an iterative refinement process well-suited for capturing the subtle characteristics of quantum states. Ultimately, this work establishes the CV quantum diffusion process as an effective and practical paradigm for quantum state engineering. It offers a flexible, efficient, and unified solution for creating and protecting quantum states, paving the way for more robust and capable CV quantum information processing systems.

[0279] It is understood that the performance of the generation model and recovery model of the present invention embodiments and their comparison with existing continuous variable quantum state generation models have been analyzed above. The following text provides supplementary explanations for some of the conclusions in the above analysis.

[0280] 1) Proof of Theorem 1

[0281] The proof is presented in two parts. First, the transformation in the Heisenberg picture is derived by recursively applying the heat loss path. Then, the equivalent representation in the Schrödinger picture is established.

[0282] Part 1: Heisenberg's Derivation of Landscape Painting

[0283] First, we study the transformation of the annihilation operator in a single thermal loss channel at time step $i$:

[0284]

[0285] Each of them Represents a state with an average photon number of The hot environment mode.

[0286] Recursively apply this transformation in the first two steps:

[0287]

[0288] To simplify this expression, define a valid environment operator. Make:

[0289]

[0290] Verifiable It is a commutative relation Regular boson operators:

[0291]

[0292] Furthermore, when all environmental modes have the same average photon number hour, Also maintain this average photon number:

[0293]

[0294] This indicates Corresponding to a pattern with the same average photon number as the original environment. The hot state. Therefore, it can be To be compactly represented as:

[0295]

[0296] Using induction, The general form for obtaining any time step $t$ is:

[0297]

[0298] in It is still an average photon number of Thermal environment mode.

[0299] Part Two: Schrödinger's Pictographic Representation

[0300] To transition to the Schrödinger picture, it is understood that this transformation occurs precisely when beam splitters are applied between the system and the thermal environment. Based on the beam splitter transformation:

[0301]

[0302] When this transformation is expressed in terms of transmittance Applied to the initial system mode and a state of heat Environment mode At that time, the transformation of the system mode is completely consistent with the expression derived above. In the Schrödinger picture, this corresponds to:

[0303]

[0304] Therefore, a transmittance can be used. The heat loss path directly obtains ρ from ρ0 in a single step. t It does not require t sequential applications.

[0305] 2) Detailed introduction to CVQD-G using the general hyperparameters and pure losses listed in Table 5 above. The performance of generating Gaussian states with different characteristic parameters in the environment.

[0306] Figure 13 The generation results of coherent states |α> with amplitudes α∈{0.5,1.0,1.5,2.0,2.5} are shown. For α=2.5, as discussed above, the fidelity achieved using the general hyperparameters is affected by the fixed Fock cutoff dimension. The results of the hyperparameter tuning for α=2.5 are described below. Figure 13 Each pair of graphs shows the training loss (left) and fidelity (right).

[0307] Figure 14 The results of generating the compressed vacuum state S(r)|0> using generalized hyperparameters for the compression parameters r∈{0.25,0.5,0.75,1.0} are presented. For larger r values, a slight decrease in fidelity is observed.

[0308] 3) Generation of diverse quantum states

[0309] CVQD-G, using the general hyperparameters in Table 5, achieves high performance in pure loss. and heat loss The performance of generating multiple quantum states (coherent state, squeezed state, Fock state, and Cat state) under two environments. These results support the performance analysis and discussion above.

[0310] Figure 15 This indicates that these diverse states all achieve high fidelity. For heat loss... Under Gaussian states (coherent states, squeezed states), the model maintains robust performance. For information on the fidelity of parameter scans under thermal loss, please refer to the main text. Figure 5 For non-Gaussian states (Fock state, Cat state), high fidelity was achieved under pure loss conditions (e.g., Fock state |1>>99.8%, Cat state |cat(1)>>99.6%, as described above). Performance remained robust under thermal noise. The low forward diffusion fidelity characteristic of the Fock state was also evident.

[0311] 4) Optimization of specific hyperparameters for coherent states |α=2.5>

[0312] Due to the fixed Fock cutoff dimension (15), generating large-amplitude coherent states (e.g., |α=2.5>) using general hyperparameters can be challenging. To achieve this in pure loss... To achieve higher fidelity in the environment where |α=2.5>, a specific set of hyperparameters was used. These dedicated hyperparameters (which may differ from or be the same as the general parameters in Table 6, are noted) are summarized in Table 9.

[0313] Table 9. Coherent states α = 2.5 Dedicated hyperparameters

[0314] Hyperparameters value Batch size 30 Epochs 78 Total time steps T 117 Initial learning rate 0.002605 Decay steps (learning rate) 15 Decay rate (learning rate) 0.8394 Time step loss weight λ <![CDATA[2.3236×10 -3 ]]> Normalized penalty weight γ 10.358 <![CDATA[Initial noise schedule β start > <![CDATA[1.0×10 -4 (Same as general)]]> <![CDATA[Final noise schedule β end > 0.05 (same as general)

[0315] Figure 16 The training loss, forward diffusion fidelity, and reverse denoising fidelity of the coherent state |α=2.5> generated using these tuned hyperparameters are shown, with the final fidelity exceeding 97%.

[0316] The following describes a continuous variable quantum state generation model provided by the present invention. The continuous variable quantum state generation model described below and the continuous variable quantum state generation method described above can be referred to and correspond to each other.

[0317] like Figure 18 As shown, this invention provides a continuous variable quantum state generation model, comprising the following modules:

[0318] The forward diffusion module 1800 is used to convert the input quantum state into a thermal state through a forward diffusion process modeled by a thermal loss channel.

[0319] The inverse denoising module 1810 is used to generate the thermal state into a target quantum state through a trainable inverse denoising process.

[0320] According to the continuous-variable quantum state generation model provided by the present invention, the forward diffusion process modeled by the heat loss channel includes:

[0321] At each time step t, the input quantum state ρ t-1 The heat loss channel, characterized by the following formula, is converted into a hot state ρ. t :

[0322]

[0323] in, Characterizing the heat loss path, η t ∈[0,1] is a time-step dependent transmittance parameter; The average number of photons is Environmental thermal state; U BS (η t ) is the beam splitter operator; It's U BS (η t The conjugate transpose of ); operation Tr E This indicates the elimination of traces in the environmental degrees of freedom.

[0324] According to the continuous variable quantum state generation model provided by the present invention, the forward diffusion process modeled by the heat loss channel further includes:

[0325] At any time step t, the initial input quantum state ρ0 is transformed into the thermal state ρ through the thermal loss channel characterized by the following formula. t :

[0326]

[0327] in Indicates transmittance The unitary operator of the bundle splitter, η represents the cumulative transmittance. i ∈[0,1] is a time-step dependent transmittance parameter; express The conjugate transpose of; The average number of photons is The environment is hot; operation Tr E This indicates the elimination of traces in the environmental degrees of freedom.

[0328] According to the continuous variable quantum state generation model provided by the present invention, the operation further includes:

[0329] At each time step t, for the η t Linear scheduling is used:

[0330]

[0331] Where η0 and η T It is a hyperparameter that defines the start and end points of the T-step linear interpolation.

[0332] According to the continuous variable quantum state generation model provided by the present invention, the trainable inverse denoising process includes:

[0333] The time quantum state is obtained by using a time-embedded circuit;

[0334] The composite system constructed from the time quantum state and the thermal state is denoised using a denoising circuit to generate the target quantum state.

[0335] The denoising circuit is obtained based on the denoising circuit parameters trained.

[0336] According to the continuous variable quantum state generation model provided by the present invention, the operation of obtaining a time quantum state through a time embedding circuit includes:

[0337] For any non-zero coherent state |α>, the time step information is encoded by the following phase evolution:

[0338] α(t)=e -iωt α;

[0339] Here, α represents the complex parameter of the coherent state, and ω represents the angular frequency, which controls the rate of phase evolution.

[0340] According to the continuous variable quantum state generation model provided by the present invention, the denoising circuit is obtained based on the denoising circuit parameters trained, and the operation includes:

[0341] The loss is determined based on the input quantum state and the target quantum state;

[0342] The parameters of the denoising circuit are adjusted based on the loss.

[0343] The following describes a training device for a continuous variable quantum state recovery model provided by the present invention. The training device for a continuous variable quantum state recovery model described below and the training method for a continuous variable quantum state recovery model described above can be referred to in correspondence.

[0344] like Figure 19 As shown, the present invention also provides a training device for a continuous variable quantum state recovery model, comprising the following modules:

[0345] Module 1900 is used to build coherent state datasets;

[0346] The module 1910 is used to obtain the diffused quantum state based on the sample quantum states in the coherent state dataset;

[0347] Recovery module 1920 is used to recover the sample quantum state based on the diffused quantum state to obtain the input coherent state; and

[0348] Training module 1930 is used to train the continuous variable quantum state recovery model based on the sample quantum state and the input coherent state.

[0349] According to the training apparatus for the continuous variable quantum state recovery model provided by the present invention, the operation of constructing the coherent state dataset includes:

[0350] Sample coherent states {|α} from a uniform disk of radius D. tr >}Construct;

[0351] Here, parameter D defines the high-probability operating range of the transmitter signal; signal parameter α in =x+ip is composed of independently sampled orthogonal components Build.

[0352] Figure 20 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 20 As shown, the electronic device may include a processor 2010, a communications interface 2020, a memory 2030, and a communication bus 2040. The processor 2010, communications interface 2020, and memory 2030 communicate with each other via the communication bus 2040. The processor 2010 can call logic instructions from the memory 2030 to execute continuous-variable quantum state generation methods or training methods for continuous-variable quantum state recovery models.

[0353] Furthermore, the logical instructions in the aforementioned memory 2030 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, external hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0354] On the other hand, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the training method for the continuous variable quantum state generation method or the continuous variable quantum state recovery model provided by the above methods.

[0355] In another aspect, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the continuous variable quantum state generation method or the continuous variable quantum state recovery model training method provided by the above methods.

[0356] The apparatus and model embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0357] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0358] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for generating continuous-variable quantum states, characterized in that, include: The forward diffusion process, modeled through thermal loss channels, converts the input quantum state into a thermal state. The thermal state is generated into the target quantum state through a trainable reverse denoising process.

2. The method for generating continuous variable quantum states according to claim 1, characterized in that, The forward diffusion process of the heat loss channel modeling includes: At each time step t, the input quantum state ρ t-1 The heat loss channel, characterized by the following formula, is converted into a hot state ρ. t : in, Characterizing the heat loss path, η t ∈[0,1] is a time-step dependent transmittance parameter; The average number of photons is Environmental thermal state; U BS (η t ) is the beam splitter operator; It's U BS (η t The conjugate transpose of ); operation Tr E This indicates the elimination of traces in the environmental degrees of freedom.

3. The continuous variable quantum state generation method according to claim 1, characterized in that, The forward diffusion process in the heat loss channel modeling also includes: At any time step t, the initial input quantum state ρ0 is transformed into the thermal state ρ through the thermal loss channel characterized by the following formula. t : in Indicates transmittance The unitary operator of the bundle splitter, η represents the cumulative transmittance. i ∈[0,1] is a time-step dependent transmittance parameter; express The conjugate transpose of; The average number of photons is The environment is hot; operation Tr E This indicates the elimination of traces in the environmental degrees of freedom.

4. The method for generating continuous variable quantum states according to claim 2, characterized in that, The method also includes: At each time step t, for the η t Linear scheduling is used: Where η0 and η T It is a hyperparameter that defines the start and end points of the T-step linear interpolation.

5. The method for generating continuous variable quantum states according to claim 1, characterized in that, The trainable inverse denoising process includes: The time quantum state is obtained by using a time-embedded circuit; The composite system constructed from the time quantum state and the thermal state is denoised using a denoising circuit to generate the target quantum state. The denoising circuit is obtained based on the denoising circuit parameters trained.

6. The method for generating continuous variable quantum states according to claim 5, characterized in that, The method for obtaining a time quantum state through a time embedding circuit includes: For any non-zero coherent state |α>, the time step information is encoded by the following phase evolution: α(t)=e -iωt a; Here, α represents the complex parameter of the coherent state, and ω represents the angular frequency, which controls the rate of phase evolution.

7. The method for generating continuous variable quantum states according to claim 5, characterized in that, The denoising circuit is obtained based on denoising circuit parameters through training, and the method includes: The loss is determined based on the input quantum state and the target quantum state; The parameters of the denoising circuit are adjusted based on the loss.

8. A training method for a continuous-variable quantum state recovery model, characterized in that, include: Construct a coherent state dataset; Based on the sample quantum states in the coherent state dataset, the diffused quantum states are obtained; Based on the diffused quantum state, the sample quantum state is recovered to obtain the output coherent state; as well as The continuous variable quantum state recovery model is trained based on the sample quantum state and the output coherent state.

9. The training method for the continuous variable quantum state recovery model according to claim 8, characterized in that, The construction of the coherent state dataset includes: Sample coherent states {|α} from a uniform disk of radius D. tr >}Construct; Here, parameter D defines the high-probability operating range of the transmitter signal; signal parameter α in =x+ip is composed of independently sampled orthogonal components Build.

10. A method for recovering a continuous-variable quantum state, characterized in that, include: Obtain the quantum state to be recovered; The quantum state to be recovered is input into the continuous variable quantum state recovery model to obtain the target quantum state; The continuous variable quantum state recovery model is trained by the method described in any one of claims 8 to 9.

11. A continuous-variable quantum state generation model, characterized in that, include: The forward diffusion module is used to convert the input quantum state into a thermal state through the forward diffusion process modeled by the thermal loss channel; A reverse denoising module is used to generate the thermal state into the target quantum state through a trainable reverse denoising process.

12. A training device for a continuous-variable quantum state recovery model, characterized in that, include: Build modules are used to construct coherent state datasets; The acquisition module is used to obtain the diffused quantum state based on the sample quantum states in the coherent state dataset; The recovery module is used to recover the sample quantum state based on the diffused quantum state to obtain the input coherent state; as well as The training module is used to train the continuous variable quantum state recovery model based on the sample quantum state and the input coherent state.

13. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 7, or the method as described in any one of claims 8 to 9.

14. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7, or the method as described in any one of claims 8 to 9.

15. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7, or the method as described in any one of claims 8 to 9.

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