Universal denoising framework and training method and device thereof

Abstract

The invention discloses a general denoising framework and a training method and device thereof, and the general denoising framework comprises a quantum state input unit which comprises a first register used for receiving a source time step coding quantum state; the second register is used for receiving the target time step coding quantum state; the third register is used for receiving a source quantum state corresponding to the source time step; the quantum state input unit is used for obtaining a first composite quantum state based on the first register, the second register and the third register; the parameterized quantum denoising unit is used for generating a second composite quantum state based on the first composite quantum state; the measuring unit is used for generating a target quantum state based on the second composite quantum state; wherein the parameterized quantum denoising unit adopts any denoising circuit of a quantum diffusion model for quantum state generation and carries training parameters, mapping from any source time step to a target time step is realized, the reasoning time is remarkably shortened, and the framework universality and the sampling efficiency are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of quantum machine learning, and particularly relates to a general denoising framework and a training method and device thereof. BACKGROUND

[0002] The advent of the noisy intermediate-scale quantum (NISQ) era has greatly promoted the in-depth research of quantum machine learning (QML), which is committed to realizing the quantum advantage in computation. In the field of QML, quantum generative model (QGM) is a key research direction, which focuses on learning data distribution to generate new high-fidelity samples. Among them, quantum diffusion model (QDM) shows wide applicability and has been successfully applied to image generation, classical discrete data generation and quantum state generation.

[0003] However, the existing QDM is still hindered by a key limitation: its inherent slow and iterative sampling process hinders its practical application. This process requires a large number of consecutive denoising steps, which creates a major bottleneck for model expansion and deployment. SUMMARY

[0004] The present application provides a general denoising framework and a training method and device thereof, which solves the defects of slow and iterative sampling of the quantum state generation process in the prior art, and realizes the acceleration of general and efficient quantum state generation.

[0005] The present application provides a general denoising framework for few-step generation, which comprises:

[0006] a quantum state input unit, a parameterized quantum denoising unit and a measurement unit connected in sequence;

[0007] The quantum state input unit comprises:

[0008] a first register for receiving a source time step encoding quantum state;

[0009] a second register for receiving a target time step encoding quantum state;

[0010] a third register for receiving a source quantum state corresponding to the source time step;

[0011] The quantum state input unit is configured to obtain a first composite quantum state based on the first register, the second register and the third register;

[0012] The parameterized quantum denoising unit is used to generate a denoised second composite quantum state based on the first composite quantum state.

[0013] The measurement unit is used to generate a target quantum state corresponding to the target time step based on the second composite quantum state;

[0014] The parameterized quantum denoising unit employs any denoising circuit for the quantum diffusion model used for quantum state generation and carries training parameters.

[0015] According to a general denoising framework for few-step generation provided by the present invention, the quantum state input unit further includes: a fourth register for receiving auxiliary noise states; then, the quantum state input unit is used to obtain the first composite quantum state based on the first register, the second register, the third register, and the fourth register.

[0016] According to the present invention, a general denoising framework for few-step generation is provided, wherein both the source time-step encoded quantum state and the target time-step encoded quantum state are obtained through a learnable decoupled qubit encoding circuit, the learnable decoupled qubit encoding circuit comprising:

[0017] n qubits arranged from least significant bit to most significant bit, where n is an integer greater than or equal to 1;

[0018] The first operation column includes n controlled Rs. y The gates are set on n qubits respectively;

[0019] The second operation column includes n controlled Rs. z The gates are set on n qubits respectively;

[0020] The output of the first operation column serves as the input of the second operation column; the output of the second operation column is either the source time-step encoded quantum state or the target time-step encoded quantum state; the controlled R y Gate and the controlled R z The gate carries training parameters related to the time step.

[0021] This invention also provides a training method for a general denoising framework, based on the general denoising framework for few-step generation provided by this invention, comprising:

[0022] Obtain the initial set of quantum states;

[0023] Obtain time step pairs (source time step s, target time step t), where and

[0024] Based on the initial set of quantum states, a source set of quantum states corresponding to time step s and a target set of quantum states corresponding to time step t are generated through a forward diffusion process.

[0025] Based on the source quantum state set and the time step pair, a predicted quantum state set is generated using the general denoising framework for few-step generation;

[0026] Calculate the loss between the predicted quantum state set and the target quantum state set;

[0027] Based on the loss, the training parameters of the general denoising framework for few-step generation are optimized until the number of training iterations or the loss converges to a set threshold.

[0028] According to the training method of the general denoising framework provided by the present invention, the method for calculating the loss between the predicted quantum state set and the target quantum state set includes:

[0029] The following loss function is used:

[0030]

[0031] Among them, |ψ t > represents the target quantum state; |ψ s > Represents the source quantum state; q represents a uniform distribution over integers from 1 to T; D represents a general metric for comparing quantum state distributions; s and q t These represent the baseline true distributions of the source time step and the target time step, respectively.

[0032] The present invention also provides a method for generating quantum states, comprising:

[0033] Obtain the initial noisy quantum state;

[0034] Get the time step pair (source time step s, target time step t);

[0035] Based on the initial noisy quantum state and the time step pair, a predicted quantum state is generated as the target quantum state through the general denoising framework for few-step generation;

[0036] The general denoising framework for few-step generation is trained by the method provided in this invention.

[0037] The quantum state generation method provided by the present invention further includes:

[0038] The time steps are taken evenly to construct K+1 time step sequences {n0, n1, ..., n}. K}, where n0=T and n K =0;

[0039] Based on the initial noisy quantum state and the time step sequence, a predicted quantum state is generated using the general denoising framework for few-step generation; this step is repeated until a predicted quantum state is generated corresponding to time step n. K The corresponding predicted quantum state is used as the target quantum state.

[0040] The present invention also provides a training device for a general denoising framework, comprising:

[0041] The first acquisition module is used to acquire the initial quantum state set;

[0042] The second acquisition module acquires time step pairs (source time step s, target time step t), where and

[0043] The first generation module is used to generate, based on the initial quantum state set, a source quantum state set corresponding to time step s and a target quantum state set corresponding to time step t through a forward diffusion process;

[0044] The second generation module generates a predicted quantum state set based on the source quantum state set and the time step pair, using the general denoising framework for few-step generation.

[0045] The calculation module is used to calculate the loss between the predicted quantum state set and the target quantum state set;

[0046] An optimization module is used to optimize the training parameters of the general denoising framework for few-step generation based on the loss, until the number of training iterations or the loss converges to a set threshold.

[0047] 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 a training method of any of the general denoising frameworks described above, or a quantum state generation method.

[0048] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a training method for the general denoising framework described above, or a quantum state generation method.

[0049] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements a training method or a quantum state generation method of any of the general denoising frameworks described above.

[0050] Compared with the prior art, the beneficial effects of the present invention are:

[0051] (1) This invention encodes the source time step and the target time step into the quantum state, and applies the parameterized quantum denoising unit to any denoising circuit used for quantum diffusion modeling quantum state generation. The denoising process is modeled as a conditional probability dependent on the source time step, the target time step and the noisy source quantum state, thereby realizing the mapping from any source time step to the target time step. This significantly reduces inference time and improves the framework's versatility and sampling efficiency.

[0052] (2) This invention achieves powerful expressive power while maintaining linear parameter complexity through a learnable decoupled quantum bit encoding circuit, improves friendliness to NISQ devices, and further enhances the efficiency of the general denoising framework. Attached Figure Description

[0053] 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.

[0054] Figure 1 This is a schematic diagram comparing sampling strategies according to embodiments of the present invention.

[0055] Figure 2 This is a schematic diagram of a general denoising framework for few-step generation according to an embodiment of the present invention.

[0056] Figure 3 This is an N-type learnable decoupled quantum bit encoding method according to an embodiment of the present invention. t A schematic diagram of a quantum bit circuit architecture.

[0057] Figure 4 This is a flowchart illustrating the training method of a general denoising framework according to an embodiment of the present invention.

[0058] Figure 5 This is a schematic diagram of the circuit architecture of a general noise reduction framework example according to an embodiment of the present invention.

[0059] Figure 6 This is a schematic diagram of the modular architecture of the noise reduction circuit U according to an embodiment of the present invention.

[0060] Figure 7 This is a schematic flowchart of a quantum state generation method according to an embodiment of the present invention.

[0061] Figure 8 The average Pauli-Y expectation value of all models in the ring state generation task according to an embodiment of the present invention. A diagram illustrating the relationship between the number of function evaluations (NFE) and the function evaluation number.

[0062] Figure 9 This refers to the leakage fidelity of all models in a coherent noise task according to an embodiment of the present invention. A schematic diagram illustrating the relationship with NFE.

[0063] Figure 10 This refers to the average fidelity of all models in the clustered state generation task according to an embodiment of the present invention. A schematic diagram illustrating the relationship with NFE.

[0064] Figure 11 This is a schematic diagram showing the relationship between the average magnetization p(M) and NFE for all models in a multi-body phase mission according to an embodiment of the present invention.

[0065] Figure 12 This is a schematic diagram of the structure of a training device for a universal denoising framework implemented according to the present invention;

[0066] Figure 13 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0067] 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.

[0068] Quantum state generation is a crucial application where QDM excels. Compared to earlier methods such as Quantum Generative Adversarial Networks (QuGAN), QDM offers a more powerful and robust alternative, as QuGAN often suffers from training instability and convergence difficulties. The effectiveness of QDM lies in its ability to generate a wide variety of quantum data, including pure states, mixed states, and even continuous-variable quantum states.

[0069] Despite their success, these QDMs are hampered by a key limitation: their inherently slow, iterative sampling process. This slowness stems from the underlying Markov assumption of the generation process, which states that generating a pure quantum state from noise requires sequential execution along a denoised trajectory containing T discrete steps. Figure 1The standard procedure (shown by solid green arrows) represents the forward diffusion process, while the dashed black arrows represent the forward diffusion process. This standard procedure requires T distinct calls to a trained quantum circuit, resulting in significant inference latency. This challenge is exacerbated for difficult generation tasks that require a large T to guarantee high-quality results. This substantial time overhead has become a major bottleneck, hindering the scalability and practical deployment of QDM.

[0070] Before delving into the specific implementation of the embodiments of the present invention, a brief introduction to the relevant technologies and terminology of the present invention will be given in order to better understand its working principle and innovation.

[0071] 1) Quantum states and evolution. In quantum computing, the state of an N-qubit system is determined by a single dimension d = 2. N Hilbert space The state is described by a unit vector in the vector. This state is typically represented by a right-hand vector, denoted as . For a single qubit (N=1), its state is a superposition of two ground states |0> and |1>: The complex numbers α and β are called probability amplitudes. They are subject to the normalization condition |α| 2 +|β| 2 The constraint = 1 is used to ensure that the total probability is 1. Its corresponding left vector <ψ| is the conjugate transpose of the right vector: <ψ| = a * <0|+β * <1|=[a * β * The evolution of a quantum state from |ψ> to |ψ′> is governed by a unitary operator u: |ψ′> = U|ψ>. The unitary operator satisfies the condition... (where I is the identity matrix), which ensures that the quantum state remains normalized throughout the evolution process.

[0072] 2) Composite quantum systems. When a system consists of multiple subsystems, its total Hilbert space is the tensor product of the spaces of each subsystem. For example, if two subsystems are in pure states |ψ... A > and |ψ B Then the combined state of the entire system is their tensor product:

[0073] 3) Quantum Measurement. Quantum measurement is an irreversible process of extracting classical information from a quantum state, which leads to the probabilistic collapse of the quantum state. Quantum measurement consists of a set of measurement operators {M}. m By definition, each operator corresponds to a measurement result m, and they must satisfy the completeness relation: For an initial state |ψ>, the probability of measuring the result m is given by the Born rule, After measurement, the quantum state becomes: In the case of common projective measurements, the measurement operator is a projection operator, such as M x = |x><x|, and the probability is simplified to p(x) = |<x|ψ>| 2 , and the quantum state directly collapses to the basis state |x>.

[0074] 4) Quantum Denoising Diffusion Probabilistic Model

[0075] The Quantum Denoising Diffusion Probabilistic Model (QuDDPM) provides a framework to learn an unknown probability distribution p0 by training on a finite set of sample quantum states .

[0076] The diffusion process of QuDDPM is based on the fast scrambling model, which systematically introduces noise by applying a series of random circuits . Although each circuit in the sequence shares the same ansatz structure, its parameters are randomly sampled, and this process can effectively diffuse the quantum state throughout the Hilbert space. Therefore, the state at time step m is:

[0077]

[0078] This transformation defines the distribution q of the noisy state m . After a total of T steps, this process transforms the initial data distribution into a maximally mixed noise distribution p T , which corresponds to the Haar distribution.

[0079] Conversely, the denoising reverse process generates states by starting from a set of fully noise-corrupted states . This generation process is driven by a series of trainable parameterized quantum circuits , where U is the denoising circuit and θ m is the trainable parameter in the denoising circuit at the m-th moment, and T is the total number of denoising steps. At each step m, a circuit acts on the current state |ψ m > and an auxiliary state Measuring the auxiliary qubit gives a result |z> and the predicted denoised state

[0080]

[0081] The auxiliary state |z> is discarded, while The denoised output is retained. This process can be described as a Markov conditional probability distribution. By repeating this process T times, the model generates the final set of states. The aim is to reproduce the target distribution p0.

[0082] To train the model, QuDDPM employs a stepwise optimization strategy. Training begins at the last time step T and proceeds sequentially, optimizing each parameterized circuit U(θ) independently. m At each stage, the objective is to minimize the maximum mean difference (MMD) between the distribution generated by the circuit and the target distribution corresponding to the diffusion stage.

[0083]

[0084] q m Represents the distribution of noisy states. This represents the distribution of the generated denoised states.

[0085] MMD calculates the average fidelity between two quantum state ensembles. What was obtained:

[0086]

[0087] Based on this, such as Figure 2 As shown, the present invention provides a general denoising framework for few-step generation, comprising the following units:

[0088] A quantum state input unit 200, a parameterized quantum denoising unit 210, and a measurement unit 220 are connected in sequence.

[0089] The quantum state input unit 200 includes: a first register for receiving a source time step encoded state; a second register for receiving a target time step encoded state; and a third register for receiving a noisy source quantum state corresponding to the source time step. The quantum state input unit 200 is used to obtain a first composite quantum state based on the first register, the second register, and the third register. The parameterized quantum denoising unit 210 is used to generate a denoised second composite quantum state based on the first composite quantum state. The measurement unit 220 is used to generate a denoised target quantum state corresponding to the target time step based on the second composite quantum state. The parameterized quantum denoising unit employs any denoising circuit for a quantum diffusion model used for quantum state generation and carries training parameters.

[0090] Specifically, to achieve accelerated, fewer-step denoising, the key lies in learning a direct denoising mapping from any source time step s to the target time step t. Formally, this corresponds to learning a conditional probability distribution. Where |ψ s > represents the noisy source quantum state corresponding to the source time step s. Let represent the predicted target quantum state corresponding to the target time step t, where the distribution is explicitly conditioned on the source quantum state, the source time step, and the target time step. Therefore, by means of... Figure 2 The general denoising framework shown implements this mapping and can serve as a multifunctional denoiser applicable to any QDM used for quantum state generation.

[0091] The quantum state input unit 200 includes multiple registers that can receive quantum states or prepare quantum states, for example, the first register |τ s >: An N s The state of the qubit is used to encode the source time step s; the second register |τ s >: An N t The state of the qubit is used to encode the target time step t; the third register |ψ s >: The noisy source quantum state at time step s. |τ s >|、|τ t >and|ψ s They can be combined into a composite system, for example, by tensor product, to obtain the first composite quantum state.

[0092] After obtaining the first composite quantum state, the parameterized quantum denoising unit 210 acts on the first composite quantum state, combining the source time step and target time step information, to denoise |ψ s Denoising is performed. It should be noted that the parameterized quantum denoising unit can employ any denoising circuit used for quantum state generation (QDM), such as a denoising circuit based on the Quantum Denoising Diffusion Probabilistic Model (QuDDPM) or a denoising circuit based on the Temporal-aware QuDDPM (TQuDDPM). This lack of restriction fully reflects the framework's versatility. Furthermore, the parameterized quantum denoising unit carries training parameters, allowing for optimization of the denoising effect through training. Source quantum state | ψ s After denoising, the second composite quantum state is obtained.

[0093] Next, the measurement unit also needs to perform a measurement or traceout operation on the second composite quantum state, that is, on |τ. s >、|τt >and|ψ s The register is used for measurement (e.g., Pauli Z measurement) or to perform a trace-out operation. The final result in the register being the denoised, predicted target quantum state. The predicted target quantum state obtained by the trained general denoising framework This is the ultimate target quantum state.

[0094] Through the above denoising process, a general conditional probability distribution is constructed. The proposed denoising framework enables QDM to perform skip sampling after training. It is worth noting that the general denoising framework in this embodiment does not require any changes to the forward diffusion process of the original QDM; modifications are limited to the denoising process and the training algorithm.

[0095] This invention encodes the source time step and the target time step into the quantum state. By using a parameterized quantum denoising unit to apply any denoising circuit for the quantum diffusion model used for quantum state generation, the denoising process is modeled as a conditional probability dependent on the source time step, the target time step, and the noisy source quantum state. This achieves a mapping from any source time step to the target time step, thereby significantly reducing inference time and improving the framework's versatility and sampling efficiency.

[0096] Optionally, the quantum state input unit further includes a fourth register for receiving an auxiliary noise state; then, the quantum state input unit is used to obtain the first composite quantum state based on the first register, the second register, the third register, and the fourth register.

[0097] Specifically, the fourth register |∈> is an optional noise register used to introduce randomness. This is crucial for models like Mixed-State Quantum Denoising Diffusion Probabilistic Models (MSQuDDPM), where the initial noise state at step t is fixed, and introducing randomness prevents a lack of diversity in the generated outputs. If the quantum diffusion model already has random noise, no additional noise is needed, and the fourth register is unnecessary.

[0098] Optionally, both the source time-step encoded quantum state and the target time-step encoded quantum state are obtained through a learnable decoupled qubit encoding circuit, which includes:

[0099] n qubits arranged from least significant bit to most significant bit, where n is an integer greater than or equal to 1;

[0100] The first operation column includes n controlled Rs. y The gates are set on n qubits respectively;

[0101] The second operation column includes n controlled Rs. z The gates are set on n qubits respectively;

[0102] The output of the first operation column serves as the input of the second operation column; the output of the second operation column is the encoded time-step quantum state; the controlled R y Gate and the controlled R z The gate carries training parameters related to the time step.

[0103] Specifically, the design of the time-encoded circuit is a crucial component of the denoising process, constrained by three key factors: expressive power, compatibility with NISQ devices, and scalability. Common methods include qubit encoding (QE) and amplitude encoding (AE). While QE offers compatibility with NISQ devices and scalability, its limited expressive power results in inferior performance compared to AE in quantum diffusion models. Conversely, AE, despite its strong expressive power, suffers from significant drawbacks: it requires an exponential number of quantum gates to encode arbitrary states, making it unsuitable for current NISQ hardware, and its parameter count also expands exponentially, hindering its scalability.

[0104] To address these shortcomings, this invention provides a novel time-based coding method, Learnable Decoupled Qubit Encoding (LDQE), which aims to simultaneously achieve high expressive power and scalability. The LDQE method utilizes methods such as... Figure 3 The circuit shown is implemented to obtain an LDQE circuit. The LDQE circuit carries training parameters, such as the rotation angle parameters of the Ry and Rz gates. For example, n in the target time-step encoding circuit can take the value N. t The training parameters it carries can be It is understandable that n in the source time-step encoding circuit can take the value N. s The training parameters it carries can be Where, N s N t The values ​​can be the same or different, depending on individual needs. It should be noted that the training parameters for each time step are independent of each other, which decouples the quantum states at different time steps, thereby maximizing the ability to explore the entire Hilbert space.

[0105] This design also endows the embodiments of the present invention with excellent scalability. The number of trainable parameters increases with the total time steps T and the number of qubits (N). s N t)Linear growth, specifically This has a significant advantage compared to methods such as AE, because AE relies on classical neural networks to learn quantum states. The parameter complexity of the AE method grows exponentially, which is This makes it impractical in larger systems. Table 1 provides a detailed comparison of these three methods, outlining their respective advantages and disadvantages.

[0106] Table 1 Comparison of three time embedding methods

[0107]

[0108] Embodiments of the present invention achieve powerful expressive ability while maintaining linear parameter complexity through a learnable decoupled qubit encoding circuit, improving the friendliness to NISQ devices and further enhancing the efficiency of the general denoising framework.

[0109] As Figure 4 shown, the present invention also provides a training method for a general denoising framework. This method is based on the above-mentioned general denoising framework for few-step generation and includes the following steps:

[0110] Step 400, obtain an initial set of quantum states.

[0111] Step 401, obtain a time step pair (source time step s, target time step t), where and

[0112] Step 402, based on the initial set of quantum states, generate a set of source quantum states corresponding to the time step s and a set of target quantum states corresponding to the time step t through a forward diffusion process;

[0113] Step 403, based on the set of source quantum states and the time step pair, generate a set of predicted quantum states through the general denoising framework for few-step generation;

[0114] Step 404, calculate the loss between the set of predicted quantum states and the set of target quantum states;

[0115] Step 405, based on the loss, optimize the training parameters of the general denoising framework for few-step generation until the number of training iterations or the loss converges to a set threshold.

[0116] Specifically, the training objective is to ensure that the denoising circuit can generalize over all possible time step pairs (source time step s, target time step t) (where 0 ≤ s < t ≤ T). The training parameters can include the rotation angle parameters of the Ry and Rz gates of the LDQE circuit, as well as the training parameters carried by the parameterized quantum denoising unit.

[0117] In step 400 above, the initial quantum state set is obtained from the training data distribution. For example, a small batch of initial quantum states can be sampled from the training data distribution. The training data distribution can be a single-qubit ring state distribution, a cluster distribution, etc., and there are no restrictions here.

[0118] In step 401 above, from a uniform distribution At any time, a source time step s is selected, and a target time step t is randomly selected from a uniform distribution (0, s-1) to ensure that t is less than s.

[0119] In step 402 above, the forward diffusion process can be performed using formula (1) to generate each quantum state in the source quantum state set and the target quantum state set.

[0120] In step 403 above, each predicted quantum state in the set of predicted quantum states generated by the general denoising framework can satisfy the conditional probability. in To predict quantum states, |ψ s > is the source quantum state.

[0121] In steps 404 and 405 above, optionally, the loss between the predicted quantum state set and the target quantum state set can be calculated using the following loss function:

[0122]

[0123] in, Represents the predicted quantum state; |ψ s > Represents the source quantum state; q represents a uniform distribution over integers from 1 to T; D represents a general metric for comparing quantum state distributions; s and q t represents the baseline true distributions of the source and target time steps, respectively. It should be noted that D can be customized according to the task (e.g., MMD loss (Equation 4) or Wasserstein distance).

[0124] The general denoising framework of this invention is trained by minimizing the above-mentioned loss function averaged over all effective time steps and the initial state from the data distribution. The general denoising framework is trained when the number of training iterations reaches a specified threshold or the calculated loss value converges to a set threshold.

[0125] The implementation methods and advantages of the embodiments of the present invention have been described above through multiple examples. The specific reasoning process of the present invention will be described in detail below with specific examples.

[0126] like Figure 5The diagram shows the structure of Skip QuDDPM, which serves as a specific implementation of a general denoising framework for few-step generation in this invention. The parameterized quantum denoising unit employs the following... Figure 6 The QuDDPM denoising circuit shown has its circuit modules within the dashed box repeated L times, with each repetition having independent trainable parameters. Therefore, the total number of parameters in the denoising circuit is 2(N). s +N t +N)L.

[0127] The aforementioned parameterized quantum denoising unit, combining the source time step and the target time step, models the denoising process as follows: Conditional probability in the form of...

[0128] Since the quantum state at step T in the original QuDDPM follows a Haar random distribution, it is inherently random. Figure 2 The auxiliary noise state |∈> in the equation is not needed here. The denoising process begins from the initial state:

[0129]

[0130] First, the time encoding circuit and Acting on the first N respectively s and N t On each qubit, time steps t and s are encoded into a quantum state. Therefore, the first composite quantum state is obtained:

[0131]

[0132] Where u and v are respectively and The trainable parameters in. and The same circuit design is used, but each instance is configured for a specific number of qubits and has its own independent, non-shared set of trainable parameters, thereby decoupling quantum states at different time steps and improving sampling efficiency. Next, the parameterized quantum circuit U(w) in the parameterized quantum denoising unit is applied to the composite state |φ2> to obtain the state before measurement, i.e., the second composite quantum state:

[0133]

[0134] Finally, for the first two registers |τ s and |τ t The measurement is performed on the observable Z. The state after the measurement is as follows:

[0135]

[0136] where |z s > and |z t > are measurement results. Regardless of these results, the output state of the |ψ s > register is retained as the denoised state (target quantum state) predicted at time step t. Thus, a single-step jump denoising step from time s to t is completed. Therefore, the denoising process is modeled as a conditional probability distribution parameterized by a set of trainable parameters θ = {u, v, w}.

[0137] This process effectively defines a shortcut that enables the general denoising framework to bypass the incremental steps of the standard diffusion trajectory. This ability is key to accelerating inference as it enables few-step or even single-step generation by directly mapping from the source time s to the target time t (e.g., from s = T to t = 0). The result is a significant reduction in the number of quantum circuit calls, leading to a notable improvement in sampling efficiency.

[0138] The SQuDDPM training steps are exemplified below by the algorithm in Table 2, which learns to predict the state (where t < s) from a noisy state, i.e., the source quantum state<00,00450>which is the target quantum state.

[0139] Table 2 SQuDDPM Training

[0140] [[ID=,000456>

[0141] As Figure 7 shown, the present invention also provides a method for generating a quantum state, comprising the following steps:

[0142] Step 700, obtaining an initial noisy quantum state;

[0143] Step 701, obtaining a time step pair (source time step s, target time step t);

[0144] Step 702, based on the initial noisy quantum state and the time step pair, generating a predicted quantum state as the target quantum state through the general denoising framework for few-step generation;

[0145] where the general denoising framework for few-step generation is trained by the method of the above steps 400 to 405.

[0146] Specifically, since the general denoising framework has been trained, single-step sampling from any source time step to the target time can be achieved. The single-step sampling process is exemplified below by Table 3:

[0147] Table 3 Single-step Sampling Using SQuDDPM

[0148]

[0149] Optionally, the quantum state generation method also includes:

[0150] The time steps are taken evenly to construct K+1 time step sequences {n0, n1, ..., n}. K}, where n0=T and n K =0;

[0151] Based on the initial noisy quantum state and the time step sequence, a predicted quantum state is generated using the general denoising framework for few-step generation; this step is repeated until a predicted quantum state is generated corresponding to time step n. K The corresponding predicted quantum state is used as the target quantum state.

[0152] Specifically, by uniformly sampling the time steps, K-step sampling can be achieved, providing multiple options for the generation process. Table 4 provides an example of the K-step sampling process:

[0153] Table 4 shows the K-step sampling using SQuDDPM.

[0154]

[0155]

[0156] The quantum state generation method of this invention overcomes the inherent slow, iterative sampling problem in quantum diffusion models (QDM). By using a single, time-conditional network—a general framework for few-step generation—the standard generation process is reconstructed into direct, non-sequential, denoised jumps, greatly improving sampling efficiency.

[0157] The following experimental results and analysis of the embodiments of the present invention further verify the beneficial effects of the embodiments of the present invention.

[0158] Before conducting the experiment, the experimental simulation was set up as follows:

[0159] Quantum circuit simulations were implemented using the TensorCircuit framework, with parameter optimization handled by TensorFlow and the Adam optimizer. To ensure statistical robustness, all experiments were run five times using different random seeds. The implementations of SQuDDPM, QuGAN, and Quantum Direct Transport (QuDT) were all adapted from the original open-source code of QuDDPM to ensure fair comparison.

[0160] The experimental parameters for SQuDDPM are detailed in Table 5. For some tasks, the Wasserstein distance is used to evaluate the dissimilarity between the two distributions, defined as:

[0161] In the experiment of generating multibody phases, the magnetization is calculated for each generated state. The final metric of this invention is the average magnetization of all generated samples. In each training iteration, a uniform random sampling strategy is used to select four time steps from a total of T time steps to update the model parameters.

[0162] To ensure fairness, each QuDT and QuGAN experiment used the same number of layers (L) and auxiliary qubits (N) as SQuDDPM. a And batch size. Please refer to Tables 6 and 7 for specific hyperparameter settings.

[0163] Table 5 shows the hyperparameters of the proposed SQuDDPM.

[0164]

[0165]

[0166] Table 6 shows the hyperparameters of QuGAN.

[0167] Task N <![CDATA[N a ]]> Batch size L Learning rate Ring state 1 2 500 12 0.0005 Coherent noise 2 1 100 22 0.0005 Cluster state 2 1 100 18 0.0005 Multi-body phase 4 2 100 19 0.0005

[0168] Table 7 Hyperparameters of QuDT

[0169]

[0170] SQuDDPM was compared to four leading benchmark models on four quantum state generation tasks: QuGAN, QuDT, the original QuDDPM, and TQuDDPM. To demonstrate the effectiveness of the time-encoding strategy, it was also benchmarked against a variant of the QE method, SQuDDPM-QE. The AE method was not included in the comparison due to its incompatibility with NISQ devices. This invention evaluates the performance of SQuDDPM across a range of Number of Function Evaluations (NFEs) from 1 to 10. The following table shows the performance at NFE of 1, the minimum NFE required to outperform competing models, and the optimal NFE for achieving the best results.

[0171] 1) Learning circular states

[0172] The first task evaluates the model's ability to learn the ring state distribution of a single qubit. These states are formed by... Define, where the rotation angle x i Uniform sampling from [0, 2π) forms a continuous loop on the XZ plane of the Bloch sphere. Performance is expressed by the average Pauli-Y expectation. To assess this, a lower value indicates a more accurate distribution.

[0173] As shown in Table 8 and Figure 8 As described, the SQuDDPM model exhibits a significant advantage across all sampling steps. With only NFE=2, its performance is [missing information]. This surpasses all competing models, including those with 40 steps. This result decisively outperforms the SQuDDPM-QE variant, which is limited and begins to decline after NFE=6. The general denoising framework of this invention continues to improve, reaching its best performance of 0.0002±0.0001 at NFE=10, an order of magnitude better than the suboptimal model. This strongly demonstrates that the enhanced expressive power of the LDQE encoder directly translates into higher generation quality and superior sampling efficiency.

[0174] Table 8. Performance comparison of different models on the tasks of ring state and coherent noise generation.

[0175]

[0176] 2) Learning coherent noise

[0177] This task aims to evaluate the model's ability to capture coherent noise in a 2-qubit system. The goal is to generate a target state, a superposition of |00>, |01>, and |11>, which has been corrupted by a simulated noisy channel. This channel contains two unitary rotation operations. and The angles δ are applied with probabilities p and 1-p, respectively, where the angle δ is uniformly sampled from [-δ0, δ0]. The average value leaked into the orthogonal error subspace is used. To evaluate performance, a lower value indicates better performance.

[0178] like Figure 9 As shown in Table 8, the results of this task reveal the trade-off between encoder complexity and task requirements: the SQuDDPM-QE variant, employing a simpler encoder, achieves peak performance... Slightly outperforms the full LDQE-based model. This suggests that the specific noise distribution does not require particularly high expressive power, allowing the simpler QE method to converge to a more efficient solution. This task-dependent behavior is consistent with similar conclusions in the references. Nevertheless, the SQuDDPM model exhibits excellent overall efficiency, surpassing the 20-step baseline model at NFE=8 and achieving a superior best score of 0.1270±0.0154.

[0179] 3) Learning clustered states

[0180] This task involves generating a 2-qubit state distribution centered on the |00> state. These states are mathematically defined as... in And ∈ = 0.08. Using the average fidelity of the ideal |00> state. This is used to measure performance; a higher value indicates better quality.

[0181] like Figure 10 As shown in Table 9, the results highlight the powerful capabilities of the LDQE encoder in handling more complex distributions. At NFE=3, SQuDDPM's fidelity (0.9707±0.0058) surpasses all competing models, including the 20-step TQuDDPM-AE. This is a significant improvement over the SQuDDPM-QE variant, which struggles to achieve comparable fidelity at any NFE. SQuDDPM achieves a peak fidelity of 0.9838±0.0026 at NFE=10, confirming that the enhanced expressive power of LDQE is crucial for capturing the complex features of clustered state distributions.

[0182] Table 9. Performance comparison of different models on clustered state and multi-body phase generation tasks.

[0183]

[0184]

[0185] 4) Learning multi-body phase

[0186] In the final task, the model was trained to generate the ground state of the 4-qubit Transverse-Field Ising Model (TFIM), a classic problem in condensed matter physics. The experiment focused on a ferromagnetic phase with a Hamiltonian of H. TFIM =-∑ i Z i Z i+1 -g∑ i X i The field strength g is sampled from [0.2, 0.4]. Performance is evaluated using a key physical observable—the average magnetization p(M).

[0187] like Figure 11As shown in Table 9, in this physically motivated task, the SQuDDPM performance curve rises rapidly, surpassing the baseline model for all 30 steps at NFE = 3 (p(M) = 0.9758 ± 0.0036). The necessity of the LDQE encoder is evident compared to the SQuDDPM-QE variant, whose performance is significantly lower at all NFE values. SQuDDPM achieves an optimal magnetization of 0.9763 ± 0.0035 at NFE = 6, decisively demonstrating its ability to capture complex physical properties at a much lower computational cost than previous methods.

[0188] SQuDDPM demonstrates the framework's power on four different generation tasks, achieving performance comparable to or even better than the original QuDDPM, while achieving up to 20x sampling speedup. This successfully addresses the key trade-off between generation quality and inference speed.

[0189] The main advantage of the general denoising framework in this invention lies in its versatility. This framework is not limited to a single case study but can be easily extended to accelerate other quantum diffusion architectures, including TQuDDPM, MSQuDDPM, and even continuous variable models. Validating this adaptability across various models is crucial for establishing new efficiency standards in the field of quantum generation models.

[0190] The following describes a training device for a general denoising framework provided by the present invention. The training device for a general denoising framework described below and the training method for a general denoising framework described above can be referred to in correspondence.

[0191] like Figure 12 As shown, the present invention also provides a training device for a general denoising framework, comprising the following modules:

[0192] The first acquisition module 1200 is used to acquire the initial quantum state set;

[0193] The second acquisition module 1210 acquires time step pairs (source time step s, target time step t), where and

[0194] The first generation module 1220 is used to generate a source quantum state set corresponding to time step s and a target quantum state set corresponding to time step t based on the initial quantum state set through a forward diffusion process.

[0195] The second generation module 1230 generates a predicted quantum state set based on the source quantum state set and the time step pair, using the general denoising framework for few-step generation.

[0196] Calculation module 1240 is used to calculate the loss between the predicted quantum state set and the target quantum state set;

[0197] The optimization module 1250 is used to optimize the training parameters of the general denoising framework for few-step generation based on the loss, until the number of training iterations or the loss converges to a set threshold.

[0198] Figure 13 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 13 As shown, the electronic device may include a processor 1310, a communications interface 1320, a memory 1330, and a communication bus 1340. The processor 1310, communications interface 1320, and memory 1330 communicate with each other via the communication bus 1340. The processor 1310 can call logic instructions from the memory 1330 to execute a training method for a general denoising framework or a quantum state generation method.

[0199] Furthermore, the logical instructions in the aforementioned memory 1330 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, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0200] 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, implements a training method for the general denoising framework provided by the above methods, or a quantum state generation method.

[0201] In another aspect, the present invention also provides a computer program product comprising 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 training method of the general denoising framework provided by the above methods, or the quantum state generation method.

[0202] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. 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.

[0203] 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.

[0204] 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 general denoising framework for few-step generation, characterized in that, The general denoising framework includes: The quantum state input unit, the parameterized quantum denoising unit, and the measurement unit are arranged and connected in sequence. The quantum state input unit includes: The first register is used to receive the source time-step encoded quantum state; The second register is used to receive the quantum state encoded at the target time step; The third register is used to receive the source quantum state corresponding to the source time step; The quantum state input unit is used to obtain a first composite quantum state based on the first register, the second register, and the third register; The parameterized quantum denoising unit is used to generate a denoised second composite quantum state based on the first composite quantum state. The measurement unit is used to generate a target quantum state corresponding to the target time step based on the second composite quantum state; The parameterized quantum denoising unit employs any denoising circuit for the quantum diffusion model used for quantum state generation and carries training parameters.

2. The general denoising framework for few-step generation according to claim 1, characterized in that, The quantum state input unit further includes a fourth register for receiving an auxiliary noise state; then, the quantum state input unit is used to obtain the first composite quantum state based on the first register, the second register, the third register, and the fourth register.

3. The general denoising framework for few-step generation according to claim 1, characterized in that, Both the source time-step encoded quantum state and the target time-step encoded quantum state are obtained through a learnable decoupled qubit encoding circuit, which includes: n qubits arranged from least significant bit to most significant bit, where n is an integer greater than or equal to 1; The first operation column includes n controlled Rs. y The gates are set on n qubits respectively; The second operation column includes n controlled Rs. z The gates are set on n qubits respectively; The output of the first operation column serves as the input of the second operation column; the output of the second operation column is either the source time-step encoded quantum state or the target time-step encoded quantum state; the controlled R y Gate and the controlled R z The gate carries training parameters related to the time step.

4. A training method for a general denoising framework, characterized in that, Based on the general denoising framework for few-step generation as described in any one of claims 1 to 3, comprising: Obtain the initial set of quantum states; Obtain time step pairs (source time step s, target time step t), where and Based on the initial set of quantum states, a source set of quantum states corresponding to time step s and a target set of quantum states corresponding to time step t are generated through a forward diffusion process. Based on the source quantum state set and the time step pair, a predicted quantum state set is generated using the general denoising framework for few-step generation; Calculate the loss between the predicted quantum state set and the target quantum state set; Based on the loss, the training parameters of the general denoising framework for few-step generation are optimized until the number of training iterations or the loss converges to a set threshold.

5. The training method for the general denoising framework according to claim 4, characterized in that, The method for calculating the loss between the predicted quantum state set and the target quantum state set includes: The following loss function is used: Among them, |ψ t > represents the target quantum state; |ψ s > Represents the source quantum state; q represents a uniform distribution over integers from 1 to T; D represents a general metric for comparing quantum state distributions; s and q t These represent the baseline true distributions of the source time step and the target time step, respectively.

6. A method for generating quantum states, characterized in that, include: Obtain the initial noisy quantum state; Get the time step pair (source time step s, target time step t); Based on the initial noisy quantum state and the time step pair, a predicted quantum state is generated as the target quantum state through the general denoising framework for few-step generation; The general denoising framework for few-step generation is trained by the method described in any one of claims 4 to 5.

7. The quantum state generation method according to claim 6, characterized in that, include: The time steps are taken evenly to construct K+1 time step sequences {n0, n1, ..., n}. K }, where n0=T and n K =0; Based on the initial noisy quantum state and the time step sequence, a predicted quantum state is generated using the general denoising framework for few-step generation; this step is repeated until a predicted quantum state is generated corresponding to time step n. K The corresponding predicted quantum state is used as the target quantum state.

8. A training device for a universal denoising framework, characterized in that, include: The first acquisition module is used to acquire the initial quantum state set; The second acquisition module acquires time step pairs (source time step s, target time step t), where And t~ The first generation module is used to generate, based on the initial quantum state set, a source quantum state set corresponding to time step s and a target quantum state set corresponding to time step t through a forward diffusion process; The second generation module generates a predicted quantum state set based on the source quantum state set and the time step pair, using the general denoising framework for few-step generation. The calculation module is used to calculate the loss between the predicted quantum state set and the target quantum state set; An optimization module is used to optimize the training parameters of the general denoising framework for few-step generation based on the loss, until the number of training iterations or the loss converges to a set threshold.

9. 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 4 to 5, or the method as described in any one of claims 6 to 7.

10. 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 4 to 5, or the method as described in any one of claims 6 to 7.

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