A quantum algorithm and system utilizing noise-induced spectral filtering effect

Abstract

This invention provides a quantum algorithm utilizing noise-induced spectral filtering to optimize a target quantum circuit and obtain its global optimal solution. The algorithm includes: S1, constructing a noisy proxy model with added quantum noise for the target quantum circuit to be optimized, used to proxy the evolution of quantum states affected by noise after each quantum logic gate operation; S2, performing a first gradient descent optimization on the noisy proxy model to obtain pre-trained circuit parameters for the target quantum circuit; S3, loading the pre-trained circuit parameters into a noise-free or low-noise environment simulating the target quantum circuit to complete parameter transfer; S4, in the environment simulating the target quantum circuit after parameter transfer, performing a second gradient descent on the circuit parameters based on the loss function of the target quantum circuit until convergence to obtain the global optimal solution for the target quantum circuit.

Description

Technical Field

[0001] This invention relates to the fields of quantum computing and quantum machine learning, specifically to parameter optimization techniques in variable quantum algorithms, and more specifically to a quantum algorithm and system utilizing noise-induced spectral filtering effects. Background Technology

[0002] With the advancement of science and technology and the continuous development of quantum technology, Variable Quantum Algorithm (VQA) is one of the most promising application directions in the current era of Noisy Mesoscale Quantum (NISQ), especially in the fields of quantum chemistry and condensed matter physics. During VQA training, trainable parameters on the variable quantum circuit are adjusted through gradient descent to minimize the loss function for a specific task. However, the training process of VQA faces significant challenges, primarily due to the extremely rugged optimization landscape, the presence of numerous local minima, and the Barren Plateau phenomenon where gradients vanish exponentially with the number of qubits. These phenomena make it difficult for VQA to converge to the optimal result, thus affecting the capabilities of the quantum algorithm.

[0003] Existing methods for initializing quantum circuit parameters mainly include the following three types:

[0004] 1. Random initialization: The parameters of the quantum algorithm are initialized in a random manner. This method is the simplest and starts optimization directly from random points on a precise and noise-free terrain. However, it is very easy to encounter barren plateaus in deep routes, which will cause the gradient to vanish and make training impossible.

[0005] 2. Near-identical initialization: Initializes parameters near the unit operator constituting the entire circuit. While this method can alleviate low-energy plateaus, it is prone to getting trapped in high-energy local minima when dealing with complex entangled circuits, i.e., getting trapped in a large number of high-frequency local minima, leading to optimization failure.

[0006] 3. Pre-optimization based on classical simulation (e.g., LWPP): This method uses a customized classical algorithm to approximate energy through hard truncation (discarding high-weight Pauli terms). For example, some studies (e.g., Low-Weight Pauli Propagation, LWPP) propose using classical algorithms to simulate quantum circuits, classically approximating energy by truncating high-weight Pauli operators. Through several rounds of gradient descent in classical simulation, a suitable set of parameters is found to provide to the quantum circuit for precise gradient descent optimization, thus performing pre-optimization. The LWPP method uses a "hard truncation" approach based on Hamming weights, meaning that once an operator becomes sufficiently complex, its contribution is directly set to zero. While this discontinuous and crude truncation smooths the terrain, it can cause a shift in the location of terrain minima. Even if computational complexity is reduced, it can distort the topological structure of the optimized terrain, causing the "optimal solution" found by pre-optimization to deviate from the center of the global attraction domain of the real terrain. Furthermore, LWPP requires complex classical algorithm implementations, is limited to classical simulations, and cannot directly utilize existing noisy quantum hardware.

[0007] It is evident that existing quantum circuit parameter initialization methods still have many problems and cannot quickly, simply, and efficiently complete VQA training.

[0008] It should be noted that the background information presented here is only for illustrating relevant information about the present invention to aid in understanding the technical solution of the present invention, and does not imply that the relevant information is necessarily prior art. The relevant information was submitted and disclosed together with the present invention, and should not be considered prior art unless there is evidence that the relevant information was disclosed before the filing date of the present invention. Summary of the Invention

[0009] Therefore, the purpose of this invention is to overcome the shortcomings of the prior art and provide a quantum algorithm and system that utilizes the noise-induced spectral filtering effect.

[0010] The objective of this invention is achieved through the following technical solution:

[0011] According to a first aspect of the present invention, a quantum algorithm utilizing noise-induced spectral filtering effect is provided for optimizing a target quantum circuit to obtain the global optimal solution of the target quantum circuit, comprising: S1, constructing a noisy proxy model with added quantum noise for the target quantum circuit to be optimized, so as to proxy the evolution process of the quantum state affected by noise after each quantum logic gate operation; S2, performing a first gradient descent optimization process on the proxy model containing quantum noise to obtain pre-trained circuit parameters of the target quantum circuit; S3, loading the pre-trained circuit parameters into a noise-free or low-noise environment simulating the target quantum circuit to complete parameter transfer; S4, in the environment of the simulated target quantum circuit after parameter transfer, performing a second gradient descent on the circuit parameters based on the loss function of the target quantum circuit until convergence to obtain the global optimal solution of the target quantum circuit.

[0012] Preferably, the evolution process of the quantum state affected by noise after each quantum logic gate operation is as follows:

[0013]

[0014] in, It is a quantum state. The quantum state after evolution under the influence of noise. Indicates the noise channel. Representing quantum logic gates, express Hermitian conjugate, Indicates the first A Kraus operator, express Hermitian conjugation, all operators satisfy the completeness condition. ,in, Unit operator.

[0015] Preferably, the quantum noise added to the noisy surrogate model is depolarization noise or decoherent phase damping noise; the noisy surrogate model is implemented based on a classical quantum simulator or noisy mesoscale quantum hardware.

[0016] Preferably, in step S2, the Adam optimizer, gradient-based optimizer, gradient-free optimizer, or zero-order optimizer is used to perform a first gradient descent optimization process on the surrogate model containing quantum noise; in step S4, the Adam optimizer, gradient-based optimizer, gradient-free optimizer, or zero-order optimizer is used in the environment of the simulated target quantum circuit after parameter transfer, and a second gradient descent is performed on the circuit parameters based on the loss function of the target quantum circuit until convergence.

[0017] Preferably, the noise-free or low-noise environment is: a high-precision classical simulator environment, quantum error-corrected logic bits, or a high-precision real machine environment with increased sampling number and quantum error mitigation technology.

[0018] Preferably, the target quantum circuit is a variable quantum eigenvalue solver, quantum machine learning, quantum neural network, or quantum approximation optimization algorithm.

[0019] According to a second aspect of the present invention, a quantum system utilizing the noise-induced spectral filtering effect based on the algorithm described in the first aspect of the present invention is provided. The system comprises: a model building module for building a noisy proxy model with added quantum noise for a target quantum circuit to be optimized, so as to proxy the evolution process of the quantum state affected by noise after each quantum logic gate operation; a pre-optimization module for performing a first gradient descent optimization process on the proxy model containing quantum noise to obtain pre-trained circuit parameters of the target quantum circuit; a parameter transfer module for loading the pre-trained circuit parameters into a noise-free or low-noise environment simulating the target quantum circuit to complete the parameter transfer; and a fine optimization module for performing a second gradient descent on the circuit parameters based on the loss function of the target quantum circuit in the environment of the simulated target quantum circuit after parameter transfer until convergence to obtain the global optimal solution of the target quantum circuit.

[0020] Compared with existing technologies, the advantages of this invention are as follows: This invention proposes to utilize noise for "coarse-grained navigation," enabling existing quantum devices, previously considered "too noisy," to undertake critical pre-training tasks. This significantly improves the commercial utilization and computing power value of NISQ devices, unlocks the potential of NISQ hardware, and significantly reduces the cost of quantum computing. Furthermore, the "soft filtering" initialization strategy provided by this method outperforms existing classical approximation algorithms (such as LWPP) in complex terrains (such as 2D strongly correlated systems). This means that this invention has the potential to help researchers and companies study larger-scale chemical molecule simulations or complex financial optimization problems, driving breakthroughs in materials design and drug development. This invention does not require modification of the underlying quantum chip architecture or complex classical algorithm reconstruction. It is very easy to integrate into existing quantum cloud platforms or quantum software development frameworks, providing end users with a standard "one-click initialization" functional module, facilitating integration and standardization. Attached Figure Description

[0021] The embodiments of the present invention will be further described below with reference to the accompanying drawings, wherein:

[0022] Figure 1 This is a schematic diagram of a quantum algorithm I utilizing the noise-induced spectral filtering effect according to an embodiment of the present invention;

[0023] Figure 2This is a schematic diagram illustrating the noise-induced spectrum filtering principle and optimized landform according to an embodiment of the present invention.

[0024] Figure 3 This is a schematic diagram of the optimized trajectory of the variable quantum algorithm on the 2D Heisenberg XYZ model under three initialization schemes according to an embodiment of the present invention.

[0025] Figure 4 This is a schematic diagram of the optimization trajectory of the variational quantum algorithm on the 1D Heisenberg XYZ model according to an embodiment of the present invention, under direct optimization and initialization under different noise intensities. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the invention.

[0027] As described in the background section, existing quantum algorithm optimization suffers from numerous problems. The purpose of this invention is to address the issues of existing VQA optimization methods being prone to getting trapped in local minima and existing approximate optimization methods (such as LWPP) causing insufficient alignment and offset of the optimized terrain due to hard truncation. To this end, this invention proposes a scheme utilizing quantum noise as a natural spectral filter. By injecting specific noise into classical simulations or directly utilizing the inherent noise of NISQ hardware, a "soft-filtered" surrogate optimized terrain is constructed. This terrain can exponentially suppress high-frequency oscillations (corresponding to local minima) while preserving low-frequency overall trends (corresponding to global attraction domains), thereby providing more accurate and robust initial parameters for precise optimization and avoiding the negative impact of gradient vanishing plateaus and numerous low-quality local minima on optimization.

[0028] In summary, such as Figure 1 As shown, the scheme of this invention begins by inputting the target quantum circuit and Hamiltonian, and then performs the following steps: Step 1: Construct a noisy surrogate model (introducing spectral filtering noise, such as depolarization noise or decoherence noise), that is, constructing a noisy surrogate model with added quantum noise for the target quantum circuit to be optimized, so as to surrogate the evolution process of the quantum state affected by noise after each quantum logic gate operation; Step 2: Noise-induced pre-optimization (coarse-grained optimization to obtain parameters in the global attraction domain). Step 1: Perform the first gradient descent optimization on the surrogate model containing quantum noise to obtain the pre-trained circuit parameters of the target quantum circuit; Step 2: Parameter transfer (transferring...) As the initial point for precise optimization, the pre-trained circuit parameters are loaded into a noiseless or low-noise environment simulating the target quantum circuit to complete parameter transfer; Step 4: Precise optimization (noiseless simulator or error-correcting quantum hardware fine-tuning), that is, in the environment of the simulated target quantum circuit after parameter transfer, gradient descent is performed on the circuit parameters for the second time based on the loss function of the target quantum circuit until convergence is obtained to obtain the global optimal solution of the target quantum circuit; finally, the optimal parameters are output.

[0029] Each stage is described in detail below.

[0030] I. Constructing a Noisy Proxy Model

[0031] This invention constructs a proxy evolution process that incorporates a specific quantum noise model for the target quantum circuit to be optimized.

[0032] The technical principle of the proxy evolution process is as follows: the quantum circuit outputs information about the circuit parameters. The function can be analytically expanded into a Fourier series. This invention utilizes the exponential decay characteristic of high-frequency Fourier coefficients caused by specific noise (such as depolarization noise or decoherent noise along the rotation axis). For example, under a specific Pauli channel noise model, the amplitude of the component at frequency ω will increase exponentially. The noise is attenuated in the form of γ (where γ is the noise rate). By introducing noise, a soft filtering mechanism is achieved. Unlike the hard truncation of the loss function approximated by LWPP, noise injection preserves the phase information of the high-frequency terms, only reducing their amplitude. This "soft filtering" not only smooths the optimized terrain but also preserves the topological structure of the terrain to the greatest extent, making the alignment between the base of attraction of the global minimum and the location of the minimum of the exact loss function more accurate.

[0033] In quantum information theory, the evolution of open quantum systems is typically described using operators and forms. For the "noisy surrogate model" involved in this invention, it is assumed that in each quantum logic gate operation... After that, quantum state They will all be affected by the noise channel The impact of this process can be represented as:

[0034]

[0035] in It is a set that satisfies the completeness condition Kraus operators, It is a quantum state. The quantum state after evolution under the influence of noise. Indicates the noise channel. Representing quantum logic gates, express Hermitian conjugate, Indicates the first A Kraus operator, express Hermitian conjugate, This is a unit operator. The two typical noise models primarily used in this invention that can produce a spectral filtering effect (i.e., suppress high-frequency components) are as follows:

[0036] The first type is depolarizing noise.

[0037] Depolarization noise is an isotropic noise, which intuitively represents the probability that a quantum bit will depolarize. Complete mixing occurs (loss of all information), or... The probability remains unchanged. This is a very effective way to "smooth" noise.

[0038] The single-bit Kraus operator group is:

[0039]

[0040]

[0041]

[0042]

[0043] in, For Pauli matrices, This represents the depolarization rate.

[0044] The physical significance of introducing depolarization noise is that, on the Bloch sphere, depolarization noise manifests as a uniform contraction of the entire sphere towards the center. In optimizing the terrain, it can uniformly reduce the amplitude of high-frequency oscillations in all directions.

[0045] The second method is to dephasing / phase-damping noise.

[0046] This invention can also introduce "decoherent noise along the rotation axis" when constructing a noisy proxy model. This usually refers to noise that only affects the phase information of the quantum state without changing the energy (diagonal element).

[0047] Its single-bit Kraus operator set is as follows:

[0048]

[0049]

[0050] Here, it is assumed that the quantum gate is a Pauli rotation in the Z direction, so coherence is performed along the Z-axis. This represents the probability of a phase flip occurring.

[0051] In this invention, the physical significance of introducing this type of noise is that, on the Bloch sphere, it manifests as the state on the equatorial plane contracting towards the Z-axis, becoming an ellipsoid. This noise mainly filters out high-frequency terms related to phase interference, while retaining the low-frequency profile along the eigenvalues.

[0052] According to one embodiment of the present invention, the noisy proxy model can be constructed based on a classical quantum simulator or noisy mesoscale quantum hardware. The classical quantum simulator refers to classical simulation software applicable to various tensor networks or state vectors; this method can be implemented simply by enabling the noise model at the software level. The noisy mesoscale quantum (NISQ) hardware refers to the present invention's ability to directly utilize uncorrected physical quantum processors (such as superconductors, ion traps, photonic quantum systems, and neutral atom platforms) for "pre-optimization," leveraging the inherent decoherence noise of the hardware as a natural filter without requiring additional error correction overhead.

[0053] II. Noise-Induced Pre-optimization:

[0054] On the noisy surrogate model, the variational parameters are coarse-grained optimized using gradient descent (e.g., using the Adam optimizer) with a classical optimizer.

[0055] Because the high-frequency components (which cause the "potholes" in the terrain) are suppressed by noise exponentially, the optimizer can quickly overcome local obstacles on this smooth, noisy terrain and converge to the broad attraction domain where the global optimum is located, thus obtaining a set of high-quality pre-trained line parameters.

[0056] According to one embodiment of the present invention, the Adam (Adaptive Moment Estimation) optimizer is used for pre-optimization. Furthermore, when constructing the "noise-induced pre-optimization," the following types of optimizers can also be used for different terrain features and computational resources:

[0057] For noisy proxy models based on classic simulator environments, gradient-based optimizers such as SGD (Stochastic Gradient Descent), RMSprop, or L-BFGS-B can be used, and the gradient can be accurately calculated through adjoint differentiation or backpropagation.

[0058] For noisy surrogate models built on real quantum hardware (NISQ), i.e., real machine environments, gradient-free / zeroth-order optimizers can be used: SPSA (Simultaneous Perturbation Stochastic Approximation), COBYLA (Constrained Optimization BY Linear Approximation), or Nelder-Mead. This is because calculating gradients on real machines requires a large number of measurement shots and is greatly affected by statistical noise, while gradient-free methods are more robust.

[0059] Specifically, SPSA is a simultaneous perturbation stochastic approximation algorithm that requires only two measurements per iteration to estimate the gradient direction, and the number of measurements does not increase with the number of parameters. COBYLA is a linear approximation constrained optimization algorithm, a deterministic algorithm based on the simplex, which does not require gradient calculation and is suitable for shallow circuits with low noise and few parameters. Nelder-Mead is another commonly used simplex method, used to find local minima in multidimensional space, and has a certain tolerance for noise.

[0060] III. Parameter Migration

[0061] This invention uses the trained parameters as an initial point and loads them into the "noise-free" or "low-noise" environment of the target quantum circuit (including a high-precision classical simulator, quantum-corrected logic bits, or a high-precision real machine operation mode with increased sampling number and quantum error mitigation technology).

[0062] IV. Precision Optimization

[0063] Based on the completed parameter transfer, a secondary optimization is performed. The loss function given by the precise quantum circuit is subjected to gradient descent with respect to the circuit parameters. Since the initial point is already deep in the globally optimal attraction domain, the optimization process can quickly converge to a high-precision globally optimal solution.

[0064] Precise optimization is similar to pre-optimization, where an appropriate optimizer is selected based on the environment to perform gradient descent, which will not be elaborated on here.

[0065] Through precise optimization, the global optimal solution for the target quantum circuit can be obtained.

[0066] The parameter initialization method based on noise-induced spectral filtering proposed in this invention has extremely high versatility and is applicable to a wide range of quantum computing application scenarios and hardware environments, including but not limited to:

[0067] The first type is the Variable Quantum Eigenvalue Solver (VQE): used to solve for the ground-state energy of molecular Hamiltonians or condensed matter physics models, especially for strongly correlated systems with rugged energy landscapes and numerous local traps (such as the Heisenberg model in the examples). It is primarily used in quantum chemistry and condensed matter physics. Wavefunctions are prepared by adjusting parameterized quantum circuits (PQC). ,in The parameters to be optimized aim to find the Hamiltonian for a given problem. The minimum expected value. Its corresponding loss function is: Expected system energy. The globally optimal solution here means that the ground state energy and corresponding ground state wave function of the system have been found physically. In applications, this corresponds to the most stable structure of a molecule, the potential barrier height of a chemical reaction, or the ground state magnetic configuration of a new material (such as a superconductor). These are the most crucial parameters in drug discovery and materials design.

[0068] The second method is quantum machine learning (QML) / quantum neural network (QNN). When training quantum classifiers or generative models, this method can be used for pre-training to solve the "vanishing gradient" problem and improve the training efficiency and generalization ability of the model.

[0069] This method utilizes quantum circuits as feature extractors or classifiers to process classical or quantum data, and is commonly used for image classification, generative models, or anomaly detection. Its loss function is typically the error between the predicted value and the true label, such as mean squared error (MSE) or cross-entropy loss. The global optimal solution here means finding a set of parameters that minimizes the prediction error on the training data, resulting in an AI model with the strongest generalization ability and highest accuracy. In the context of this invention, this means the model successfully avoids the "vanishing gradient" problem and can truly learn complex feature distributions from the data.

[0070] The third method is the Quantum Approximate Optimization Algorithm (QAOA), used to solve combinatorial optimization problems (such as Max-Cut, Traveling Salesman Problem, and logistics scheduling). This method helps QAOA avoid barren plateaus in deep routes and quickly find high-quality initial parameters.

[0071] It evolves the quantum state by alternately applying the problem Hamiltonian and the hybrid Hamiltonian. Its loss function is the negative expected value of the objective function (e.g., maximizing the number of cut edges is equivalent to minimizing the negative number of cut edges). Here, the global optimal solution means finding the classical bit string corresponding to the optimal solution in the computation; in logistics scheduling, it means the shortest transportation path; in financial portfolios, it means the asset allocation scheme that minimizes risk or maximizes return.

[0072] Furthermore, the method of this invention can also be used in quantum control and variable quantum compilation to find optimal control pulses or compile quantum circuit parameters.

[0073] The schemes employed in this invention can all quickly converge to obtain the global optimal solution for various VQAs. Compared with existing technologies, the noise initialization strategy of this invention, compared with the hard truncation of LWPP, can find an initial point with lower energy and faster convergence. This is because the "soft filtering" characteristic of noise better preserves the global topological structure of the terrain, avoiding the minimum drift caused by hard truncation. For general random initialization and near-identical initialization, this scheme has more obvious advantages, and the quality of the solution found and the iteration speed are better. Secondly, this invention rewrites the traditional understanding that quantum noise is harmful, transforming the noise of NISQ devices into computational resources for finding the global optimal solution. This means that this method can be directly run for pre-optimization on uncorrected quantum chips with high noise, greatly reducing the requirements for hardware quality. Furthermore, compared with LWPP, which requires rewriting the underlying simulation algorithm, this invention only needs to enable the noise channel in the existing simulator or run on a noisy real machine, applicable to variational circuits of various structures, simple to implement, and highly universal.

[0074] This invention addresses the core challenge of training variational quantum algorithms by counterintuitively utilizing noise as a computational resource. Current quantum computers generally suffer from high noise levels, making it difficult to directly run high-precision, long-line algorithms. This invention proposes using noise for "coarse-grained navigation," enabling existing quantum devices, previously considered "too noisy," to undertake critical pre-training tasks. This significantly improves the commercial utilization and computational value of NISQ devices, unlocks the potential of NISQ hardware, and substantially reduces the cost of quantum computing. Furthermore, the "soft filtering" initialization strategy provided by this method outperforms existing classical approximation algorithms (such as LWPP) in complex terrains (e.g., 2D strongly correlated systems). This means that this invention has the potential to help researchers and companies study larger-scale chemical molecule simulations or complex financial optimization problems, driving breakthroughs in materials design and drug development. This invention does not require modification of the underlying quantum chip architecture or complex classical algorithm reconstruction. It is easily integrated into existing quantum cloud platforms or quantum software development frameworks, providing end users with a standard "one-click initialization" module, facilitating integration and standardization. In summary, this invention not only reveals the positive role of noise in optimization, but also provides a low-cost, high-efficiency, and noise-resistant general solution for engineering practice. It serves as a key technological bridge connecting current noisy hardware with future practical quantum advantages.

[0075] It should be noted that the present invention also provides a quantum system utilizing the noise-induced spectral filtering effect. The system includes: a model building module for building a noisy proxy model with added quantum noise for the target quantum circuit to be optimized, so as to proxy the evolution process of the quantum state affected by noise after each quantum logic gate operation; a pre-optimization module for performing a first gradient descent optimization process on the proxy model containing quantum noise to obtain the pre-trained circuit parameters of the target quantum circuit; a parameter transfer module for loading the pre-trained circuit parameters into a noise-free or low-noise environment simulating the target quantum circuit to complete the parameter transfer; and a fine optimization module for performing a second gradient descent on the circuit parameters based on the loss function of the target quantum circuit in the environment of the simulated target quantum circuit after parameter transfer until convergence to obtain the global optimal solution of the target quantum circuit.

[0076] To better understand the effects of the present invention, several specific examples are provided below to further illustrate the solution of the present invention.

[0077] like Figure 2 As shown, it illustrates the principle of noise-induced spectral filtering and a comparison diagram of optimized landforms with other optimization schemes. In this diagram, label 1 represents the original / precise landform, which is a thin solid line with violent oscillations and an overall parabolic trend (large valley), but it is covered with dense spikes (local minima).

[0078] Label 2 represents the noise terrain based on this invention, a smooth, thick solid line that perfectly passes through the center of the original curve, resembling a smooth envelope. Its lowest point is aligned with the global minimum of the original curve on the horizontal axis. Label 3 represents the LWPP / truncated terrain, a dashed line that is also smooth, but its shape is slightly distorted, and its lowest point is significantly offset from the lowest point of the original curve on the horizontal axis. It can be seen that the solution of this invention can smooth the loss function terrain, facilitating global optimization, without causing significant deviations or errors in the estimation of the location of the global minimum.

[0079] According to an example of the present invention, the VQE optimization based on the two-dimensional Heisenberg model of the present invention (the scenario is: solving the ground state energy of the Heisenberg XYZ model on a 3*3 square grid (the coupling coefficients in the three directions of the model are 1.0, 0.8, and 0.5, respectively), and the variable quantum line depth d=6) process is as follows: In the classical simulator, depolarizing noise is injected after each rotating door, and the noise rate is set to γ=1e-5; the Adam optimizer is used to perform 500 optimization steps on the noisy model to obtain the parameter θ_noise; θ_noise is used as the initial value, and subsequent optimization steps are performed on the noiseless simulator for 1000 steps. Figure 3The optimized trajectories of the variational quantum algorithm on the 2D Heisenberg XYZ model under three initialization schemes are shown. Figure 3 In this context, (a) represents direct optimization. Figure 3 (b) in the text represents the noise initialization optimization scheme of this patent. Figure 3 In the diagram, (c) represents the LWPP initialization optimization scheme. It can be seen that direct optimization can trap in a local minimum (relative error). (Level); While LWPP initialization improves the results, the quality of the results and the results given by different initial parameters are still worse than the *noise initialization scheme of this invention. The scheme of this invention rapidly reduces the relative error to The following results show that the convergence curve is the smoothest, the noise-induced spectrum filtering scheme of this invention has the fewest trajectories that stagnate in local minima, the highest energy accuracy, and the lowest energy corresponding to the initial parameters.

[0080] According to an example of the present invention, the VQE optimization scenario based on the one-dimensional Heisenberg model of the present invention is as follows: 1000 steps of direct optimization and 500 steps of pre-optimization under different noise intensities plus 500 steps of precise optimization are used for comparison. The variational circuit depth d=4, and a one-dimensional ladder-arranged quantum circuit structure with two-qubit gates is used. A one-dimensional Heisenberg XYZ model is used (the coupling coefficients in the three directions of the model are 1.0, 0.8, and 0.5, respectively). Adam gradient descent is employed. The first 500 steps are the results of evaluating the noisy pre-optimization loss function. It can be seen that the pre-optimization under different noise intensities plus 500 steps of precise optimization is more accurate than 1000 steps of direct optimization. Within a certain range, the greater the noise intensity, the better the final optimization effect, which is consistent with the theory of smoothing out high-frequency optimization terrain. Figure 4 The optimization trajectories of the variational quantum algorithm on the 1D Heisenberg XYZ model are shown in both direct optimization and initialization under different noise intensities. Figure 4 (a) in the figure shows noiseless optimization. Figure 4 (b) Noise initialization with a noise intensity of 0.0001. Figure 4 (c) shows the noise initialization with a noise intensity of 0.0003. Figure 4 (d) in the figure shows the noise initialization with a noise intensity of 0.001. It can be seen that the advantage of noise initialization over direct initialization without noise is that the final convergence energy is lower.

[0081] This invention utilizes the suppression properties of quantum noise on high-frequency components of the quantum circuit output function to construct a smooth, noisy surrogate optimized terrain. Unlike existing hard-truncation approximation methods, the noise injection method in this invention is a soft filter, which can more accurately preserve the global topological structure of the terrain. By pre-optimizing on the noisy terrain, the parameters are guided into the attraction domain of the global optimum, and then fine-tuned in the exact model. This method effectively avoids local minima, significantly improves the convergence speed and final accuracy of the variational quantum algorithm, and can be directly implemented using noisy quantum hardware.

[0082] It should be noted that although the steps are described in a specific order above, it does not mean that the steps must be executed in the above specific order. In fact, some of these steps can be executed concurrently, or even in a different order, as long as the required function can be achieved.

[0083] This invention can be a system, method, electronic device, computing device, computer-readable medium, and / or computer program product. A computer program product primarily refers to a software product that implements this solution through a computer program.

[0084] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. Computer-readable storage media can include, for example, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof.

[0085] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A quantum algorithm utilizing noise-induced spectral filtering effect to optimize a target quantum circuit to obtain the global optimal solution of the target quantum circuit, characterized in that, include: S1. Construct a noisy proxy model with added quantum noise for the target quantum circuit to be optimized, so as to proxy the evolution process of the quantum state affected by noise after each quantum logic gate operation; S2. Perform the first gradient descent optimization on the surrogate model containing quantum noise to obtain the pre-trained circuit parameters of the target quantum circuit. S3. Load the pre-trained circuit parameters into the noise-free or low-noise environment of the simulated target quantum circuit to complete the parameter transfer. S4. In the environment of the simulated target quantum circuit after parameter transfer, gradient descent is performed on the second circuit parameters based on the loss function of the target quantum circuit until convergence is obtained to obtain the global optimal solution of the target quantum circuit.

2. The quantum algorithm utilizing noise-induced spectral filtering effect according to claim 1, characterized in that, The evolution of the quantum state under the influence of noise after each quantum logic gate operation is as follows: in, It is a quantum state. The quantum state after evolution under the influence of noise. Indicates the noise channel. Representing quantum logic gates, express Hermitian conjugate, Indicates the first A Kraus operator, express Hermitian conjugation, all operators satisfy the completeness condition. ,in, Unit operator.

3. The quantum algorithm utilizing noise-induced spectral filtering effect according to claim 2, characterized in that: The quantum noise added to the noisy surrogate model is either depolarization noise or decoherent phase damping noise; The noisy surrogate model is implemented based on a classical quantum simulator or noisy mesoscale quantum hardware.

4. The quantum algorithm utilizing noise-induced spectral filtering effect according to claim 3, characterized in that: In step S2, the Adam optimizer, gradient-based optimizer, gradient-free optimizer, or zero-order optimizer are used to perform the first gradient descent optimization process on the surrogate model containing quantum noise. In step S4, the Adam optimizer, gradient-based optimizer, gradient-free optimizer, or zero-order optimizer are used in the environment of the simulated target quantum circuit after parameter transfer. The second gradient descent is performed on the circuit parameters based on the loss function of the target quantum circuit until convergence.

5. A quantum algorithm utilizing noise-induced spectral filtering effect according to claim 4, characterized in that, Noise-free or low-noise environments include: high-precision classical simulator environments, quantum-corrected logic bits, or high-precision real machine environments with increased sampling numbers and quantum error mitigation technology.

6. A quantum algorithm utilizing noise-induced spectral filtering effect according to claim 5, characterized in that, The target quantum circuit is a variable quantum eigenvalue solver, quantum machine learning, quantum neural network, or quantum approximation optimization algorithm.

7. A quantum system utilizing the noise-induced spectral filtering effect based on the algorithm described in any one of claims 1-6, characterized in that, The system includes: The model building module is used to build a noisy proxy model with added quantum noise for the target quantum circuit to be optimized, so as to proxy the evolution process of the quantum state affected by noise after each quantum logic gate operation; The pre-optimization module is used to perform the first gradient descent optimization on the surrogate model containing quantum noise in order to obtain the pre-trained circuit parameters of the target quantum circuit. The parameter transfer module is used to load pre-trained circuit parameters into a noise-free or low-noise environment simulating the target quantum circuit to complete the parameter transfer. The fine optimization module is used to perform gradient descent on the second circuit parameters based on the loss function of the target quantum circuit in the environment of the simulated target quantum circuit after parameter migration is completed, until convergence, to obtain the global optimal solution of the target quantum circuit.

8. A computer device / equipment / system, comprising a memory, a processor, and computer programs / instructions stored in the memory, characterized in that, The processor executes the computer program / instructions to implement the steps of the algorithm according to any one of claims 1-6.

9. A computer program product comprising a computer program / instructions that, when executed by a processor, implement the steps of the algorithm as claimed in any one of claims 1-6.

10. A computer-readable storage medium, characterized in that, It stores a computer program / instruction thereon, which is executed by a processor to implement the steps of the algorithm described in any one of claims 1-6.

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