Energy level leakage suppression method, system, device and storage medium thereof

Abstract

This invention discloses a method, system, device, and storage medium for suppressing energy level leakage, relating to the field of quantum information processing. The method applies parametric modulation to qubits to establish and activate effective exchange coupling between qubits under dispersive coupling conditions, thereby performing a two-qubit entanglement gate operation. During the gate operation, a computational subspace control model and an energy level leakage model are constructed by performing representational and unitary transformations on the system's Hamiltonian. Based on these models, the entanglement gate control pulse is optimized. The energy level correction introduced by the parametric driving is dynamically compensated through modulation of the effective Rabi frequency of time-shaping and time-dependent detuning parameters, thus suppressing energy level leakage from the computational subspace to higher energy levels. Compared with existing technologies, this invention improves the controllability and fidelity of entanglement gate operations under complex energy level structures and is applicable to quantum operations in modular quantum systems.

Description

Technical Field

[0001] This invention relates to the field of quantum information processing, specifically to a method, system, device, and storage medium for suppressing energy level leakage. Background Technology

[0002] In the field of quantum information processing, achieving scalable and high-fidelity multi-qubit manipulation is one of the core research challenges. Hybrid quantum systems composed of semiconductor spin qubits and superconducting resonant cavities are considered an important technological path for realizing modular and scalable quantum information processing due to their ability to combine long coherence times with flexible qubit interconnection capabilities. In such hybrid quantum systems, spin qubits typically possess long coherence times and high-fidelity manipulation and readout characteristics, making them suitable as quantum information processing or storage units. Meanwhile, microwave photons in the superconducting resonant cavity can coherently connect multiple qubits in space, thereby achieving effective coupling between distant qubits and providing a technological foundation for constructing fully interconnected or modular quantum architectures.

[0003] Currently, the main schemes for realizing qubit entanglement gates in spin-cavity hybrid quantum systems include the following: (1) By adjusting the frequency of the qubits, the qubits can switch between resonant and detuned states, thereby controlling the effective exchange coupling between the qubits and realizing entanglement gate operations such as iSWAP. This method can achieve a relatively fast gate operation speed, but large-scale adjustment of the qubit frequency can easily introduce frequency congestion problems and may generate undesired resonances with other qubits or system modes, resulting in additional energy loss and a decrease in gate fidelity. (2) The all-microwave control scheme applies microwave driving pulses to the qubits or resonant cavities while keeping the intrinsic frequency of the qubits fixed, so that the qubits always work near the "sweet spot" where they are relatively insensitive to noise. This type of scheme is beneficial to suppressing low-frequency noise to some extent, but it usually requires a long gate operation time. During this process, the accumulation of decoherence effects will significantly limit the achievable gate operation fidelity.

[0004] Furthermore, parametric quantum gates have attracted widespread attention as an alternative quantum manipulation scheme. The core idea of ​​this scheme is to activate interactions that are normally suppressed due to detuning by modulating the qubit parameters at appropriate frequencies. This method can achieve faster gate operation speeds while maintaining the stability of the qubit's operating point, and to some extent alleviates problems such as frequency congestion, addressability errors, and crosstalk. However, realizing high-fidelity parametric entanglement gates in hybrid quantum systems composed of spin qubits and resonant cavities still faces many technical challenges: (1) Complex energy level structure: Hybrid systems usually have a relatively complex multi-level structure, which makes parameter selection and parametric modulation scheme design difficult, and makes it difficult to enhance the coupling between spin qubits and resonant cavity under optimal conditions.

[0005] (2) Difficulty in error suppression: How to suppress and balance the effects of decoherence, leakage error and control imperfection during gate operation still needs further research. Existing methods have limited effectiveness in suppressing leakage error, resulting in the gate fidelity failing to reach the fault tolerance threshold required for quantum error correction, which seriously restricts the development of modular quantum architecture.

[0006] Therefore, there is an urgent need for a technical solution that can effectively suppress energy level leakage during parametric entanglement gate operation in hybrid quantum systems and improve the fidelity of gate operation, so as to meet the actual needs of scalable quantum information processing for high-fidelity quantum gates. Summary of the Invention

[0007] The purpose of this invention is to provide a method, system, electronic device, and computer-readable storage medium for suppressing energy level leakage in hybrid quantum systems composed of spin qubits and resonant cavities. This invention aims to solve the problems of complex energy level structure and difficulty in suppressing leakage errors in the implementation of high-fidelity entangled gates in existing technologies, improve the fidelity of gate operation, and provide strong support for the development of modular quantum architecture.

[0008] Specifically, the technical solution provided by this invention is: a method for suppressing energy level leakage, comprising: Step 1: In a quantum system including at least two qubits and an intermediary system coupled to the qubits, by applying parametric modulation to the qubits, an effective exchange coupling between the qubits is established under the condition of dispersion coupling between the qubits and the intermediary system, and the effective exchange coupling is activated by parametric modulation to perform a two-qubit parametric entanglement gate operation. Step 2: During the parametric entanglement gate operation, the quantum system is effectively modeled dynamically. By applying representational transformation and unitary transformation to the Hamiltonian of the hybrid system, the effective exchange interaction between qubits activated by parametric modulation is extracted. After eliminating the fast oscillation term, the separate computational subspace control model and energy level leakage model are obtained to characterize the energy level correction of the computational subspace and the coupling effect between the computational subspace and the high-energy-level state during the parametric entanglement gate operation. Step 3: Based on the effective control model and effective leakage model of the computational subspace established during the parametric entanglement gate operation, the entanglement gate control pulse is jointly optimized. By time-shaping the effective Rabi frequency and introducing time-dependent detuning parameter modulation, the energy level correction introduced by parametric modulation is dynamically compensated, thereby suppressing energy level leakage of the computational subspace to higher energy levels while completing the two-qubit entanglement gate operation.

[0009] Preferably, step 1 further includes: Step 1.1: Apply a driving pulse to one of the at least two qubits to parametrically modulate the frequency parameter of that qubit. The driving Hamiltonian corresponding to the driving pulse contains a diagonal term related to the calculation of the ground state of the qubit, specifically in the form of...

[0010] in, Represents the modulation frequency that varies with time; select a modulation frequency such that its time integral satisfies...

[0011] in, and Let represent the time-varying amplitude and phase of the parametric modulation driving pulse, respectively. Under the action of the parametric modulation driving pulse, the dynamics of the hybrid quantum system is described by the total Hamiltonian including the driving term, which has the form:

[0012] in, For qubits At energy level The corresponding energy level frequency, The frequency of the resonant cavity, Representing the quantum bit subspace The coupling strength between the resonant cavity and the resonant cavity. and These represent the photon generation operator and annihilation operator of the resonant cavity, respectively. The subscript represents the transition operator of a quantum bit. Representing a quantum bit and quantum bits .

[0013] Step 1.2: Under the action of the parametric modulation driving pulse, the qubit and the resonant cavity are positioned in the dispersion region, such that the frequency detuning between the qubit and the resonant cavity is greater than their coupling strength, and the resonant cavity is placed in a vacuum or near-vacuum state, i.e., satisfying... Under the above conditions, the hybrid quantum system is effectively decoupled at a predetermined approximate order through the Schrieffer-Wolf transformation, eliminating the resonant cavity degree of freedom, and obtaining the dispersive Hamiltonian describing the effective dynamics of the qubit.

[0014] in, Representing a quantum bit In The corrected transition frequency at state is taken as ,but

[0015] The effective exchange coupling strength between at least two qubits is

[0016] In this process, effective exchange coupling is activated under parametric modulation and used to realize the two-qubit parametric entanglement gate operation.

[0017] Preferably, step 2 further includes: Step 2.1: During the parametric entanglement gate operation, in order to extract the effective exchange interactions activated by parametric modulation, the dispersive Hamiltonian is... Perform a representational transformation and apply the first unitary transformation to it:

[0018] To eliminate the fast oscillation factor introduced by the energy level correction term and parametric modulation, the Hamiltonian under the interaction representation is obtained:

[0019] The interaction Hamiltonian is expressed by the Jacobi–Anger expansion.

[0020] get, It is a first-order Bessel function. The phase parameter represents the detuning between two spin qubits and the driving pulse, and is taken as the phase parameter of parametric modulation. In state In the notation, the first and second indices represent qubits, respectively. and quantum bits The state.

[0021] Step 2.2: To further obtain an effective control model within the computational subspace and to clarify the energy level leakage channels that may be introduced during the parametric entanglement gate operation, a second unitary transformation is applied to the Hamiltonian under the interaction representation:

[0022] To eliminate the explicit time dependence caused by detuning in the computational subspace, the effective Hamiltonian of the hybrid quantum system in the transformed reference frame can be written as:

[0023] Among them, the limitation is in the computational subspace The effective control Hamiltonian within is:

[0024] The effective leakage Hamiltonian acting outside the computational subspace is:

[0025] in, Indicates the effective mistuning parameter. The effective Rabi frequency generated by parametric modulation is a parameter characterizing the anharmonicity of the qubit. Used to characterize the relative coupling strength between the computational subspace and the higher-level states.

[0026] Preferably, step 3 further includes: Step 3.1: When implementing the two-qubit parametric entanglement gate operation, first set the effective detuning parameter under the baseline condition of ignoring leakage compensation. And by measuring the effective Rabi frequency Time-shaping is performed to achieve the target entanglement gate operation, where the effective pull ratio frequency satisfies a predetermined pulse area condition:

[0027] This ensures that the two-qubit entanglement gate operation is completed within the computational subspace. Preferably, the effective Rabi frequency... It adopts a time-dependent pulse form with smooth start and end characteristics, and its envelope function is a Gaussian function, specifically as follows:

[0028] in, The maximum amplitude of the effective radius frequency. Total door operation time. To determine the standard deviation of the effective pulse width, the above pulse shaping is used to smoothly reduce the effective Rabi frequency to zero at the beginning and end of the gate operation, thereby reducing the high-spectral components of the driving pulse, suppressing spectral leakage, and reducing the probability of unwanted transitions to non-computational states. Step 3.2: Considering the existence of multiple energy level leakage channels during the parametric entanglement gate operation, based on the effective leakage model established in Step 2, the effective detuning parameters are... Time-dependent modulation is introduced to dynamically compensate for the energy level shift introduced by parametric modulation. In one embodiment, the time-dependent form of the effective detuning parameter is related to the square of the effective Rabi frequency, and its specific form is as follows:

[0029] in, and These represent the anharmonicity parameters of the corresponding qubits. and This is used to characterize the relative coupling strength between the leakage channels of each energy level and the computational subspace. By synchronously modulating the effective detuning parameter with the change of the effective Rabi frequency, the dynamic energy level correction introduced during the parametric entanglement gate operation can be compensated without significantly increasing the gate operation time, thereby suppressing undesirable transitions of the computational subspace to higher energy levels and reducing energy level leakage errors.

[0030] Preferably, an energy level leakage suppression system is also provided, which mainly includes a parametric modulation and entanglement gate execution module, an effective dynamics modeling module, a pulse optimization and leakage suppression module, a system control and monitoring module, and a data storage and analysis module. The modules work together through control signals and data interfaces.

[0031] The parametric modulation and entanglement gate execution module is used to apply time-dependent driving pulses to at least one qubit in the quantum system, thereby realizing parametric modulation of the qubit frequency parameters. By selecting the driving frequency, amplitude, and phase parameters, the module enables the driving signal to generate effective energy level modulation in the qubit computational state subspace. Under the driving action, the qubit and the intermediate system are in the dispersion coupling region, which can effectively eliminate the resonant cavity degree of freedom and induce equivalent exchange coupling between qubits. By adjusting the parametric modulation parameters, the system can activate the interaction between qubits that were originally in a detuned state, thereby realizing two-qubit parametric entanglement gate operation. The module preferably includes a microwave driving source, a pulse modulation unit, and a quantum control interface for generating and outputting high-precision driving signals.

[0032] The effective dynamics modeling module is used to perform effective Hamiltonian modeling of the quantum system during the execution of the parametric entanglement gate, in order to obtain the dynamic coupling relationship between the computational subspace and the leakage subspace. Specifically, this module first transforms the system description into an interaction representation based on the dispersive Hamiltonian model through unitary representation transformation to extract the effective exchange coupling term activated by parametric modulation. Subsequently, through further reference frame transformation, the system dynamics are decomposed into a control Hamiltonian confined within the computational subspace and a leakage Hamiltonian describing the transitions of higher energy levels. Through this modeling process, the following key control parameters can be obtained: the effective Rabi frequency describing coherent transitions within the computational subspace; the effective detuning parameter characterizing the energy level difference between computational states; the weighting parameter describing the coupling strength of the leakage channel; and the energy level structure parameter characterizing the anharmonicity of the qubit. The effective dynamics modeling module provides the theoretical model and parameter basis for subsequent pulse optimization.

[0033] The pulse optimization and leakage suppression module is used to dynamically optimize the entanglement gate control pulse based on the effective dynamic modeling results, so as to reduce the undesired transitions between the computational subspace and the high-energy leakage state. In one embodiment, the module constructs an effective Rabi frequency that satisfies the predetermined pulse area condition to achieve the target entanglement gate operation. Preferably, a Gaussian envelope pulse with smooth start and end characteristics is used to reduce the high-spectral components of the driving signal and suppress spectral leakage. In the further optimization process, the module introduces time-dependent modulation of the detuning parameter based on the effective leakage model, so that the detuning parameter is dynamically adjusted with the change of Rabi frequency, thereby compensating for the transient energy level shift generated during parametric driving. This dynamic compensation mechanism can effectively suppress the excitation of multiple leakage channels and improve the overall fidelity of the entanglement gate operation.

[0034] The system control and monitoring module is used for unified scheduling and operation management of the entire energy level leakage suppression system. This module can coordinate the workflow between the parametric modulation and entanglement gate execution module, the effective dynamics modeling module, and the pulse optimization and leakage suppression module according to the preset quantum control strategy. At the same time, this module monitors the operating status of the quantum system in real time, including operating data such as driving parameters, quantum state evolution information, and gate operation results, and dynamically adjusts the control parameters according to the monitoring results to ensure stable system operation. The system control and monitoring module preferably consists of a quantum control processing unit and a data acquisition interface.

[0035] The data storage and analysis module is used to centrally store and process the data collected during system operation. This module establishes a quantum control database to securely store experimental parameters, quantum state measurement results, and gate operation performance indicators. During data analysis, this module can perform statistical analysis, error source identification, and performance evaluation on system operation data, and generate system operation reports and optimization suggestions to support the continuous improvement of quantum control strategies.

[0036] The system has a collaborative working mechanism. During system operation, each module works collaboratively according to the following process: (1) The parametric modulation and entanglement gate execution module generates driving pulses and executes entanglement gate operations; (2) The effective dynamics modeling module calculates the effective control model and leakage model of the system in real time; (3) The pulse optimization and leakage suppression module optimizes the control pulse parameters based on the modeling results; (4) The system control and monitoring module schedules and monitors the overall control process; (5) The data storage and analysis module stores the system operation data and evaluates its performance. Through the above collaborative control mechanism, this invention can effectively suppress energy level leakage in hybrid quantum systems with complex energy level structures, improve the operational fidelity of the two-qubit entanglement gate, and enhance the system's scalability and stability.

[0037] Preferably, 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. The memory stores program instructions, parameter configurations, and intermediate and result data generated during system operation. The processor calls and executes the computer program to perform corresponding data processing and control operations. In specific implementations, when the processor executes the computer program, it can implement the steps of the energy level leakage suppression method as described in any one of claims 1 to 4, including but not limited to: applying time-dependent parametric modulation drive to the qubits according to a preset parametric modulation strategy to activate effective exchange coupling between qubits and perform a two-qubit parametric entanglement gate operation; performing effective dynamic modeling of the quantum system during the parametric entanglement gate operation to characterize the energy level correction of the computational subspace introduced by parametric modulation and the coupling effect between the computational subspace and the leakage subspace; and optimizing the entanglement gate control pulse based on the modeling results, compensating for the energy level shift generated during the parametric entanglement gate operation by introducing time-dependent detuning parameter modulation, thereby suppressing energy level leakage and improving the fidelity of the entanglement gate operation.

[0038] Preferably, the present invention also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program is used to implement the steps of the energy level leakage suppression method as described in any one of claims 1 to 4. Specifically, the computer program includes program instructions for implementing the following functions: generating and loading a control parameter modulation driving signal to achieve time-dependent modulation of the qubit parameters; constructing an effective dynamic model of the quantum system to characterize the effective control behavior of the computational subspace and the coupling effects related to the leakage subspace; and calculating and optimizing the parameters of the entanglement gate control pulse based on the dynamic model to generate a control pulse sequence for suppressing energy level leakage.

[0039] Compared with the prior art, the advantages of this invention are: (1) Effective suppression of leakage error of parametric entanglement gate: This invention addresses the unavoidable coupling problem between the computational subspace and the high-energy state during the operation of parametric entanglement gate. It establishes an effective dynamic model to clearly characterize the generation mechanism of the leakage channel, and on this basis, it optimizes the control pulse of the entanglement gate. Specifically, by adopting a pulse shaping method with a Gaussian envelope for the effective Rabi frequency and introducing time-dependent detuning parameter modulation to compensate for the energy level shift introduced by parametric modulation, the probability of undesired transitions to non-computational states is significantly reduced during the gate operation, effectively suppressing energy level leakage error and improving the operational fidelity of the two-qubit entanglement gate. (2) Stable entanglement gate implementation without large frequency adjustment: The present invention adopts a parametric entanglement gate scheme, which activates the effective exchange coupling between qubits by applying time-dependent parametric modulation to at least one qubit, without large frequency adjustment of the qubits during the gate operation, so that the qubits can always work near a relatively stable operating point. This technical solution effectively alleviates the frequency congestion problem introduced by frequency adjustment, such as addressability error and crosstalk, thereby improving the stability and reliability of the hybrid quantum system under multi-qubit conditions. (3) Analyzable entanglement gate design in complex multi-level systems: For the complex multi-level structure inherent in the spin-resonant cavity hybrid quantum system, the present invention systematically decouples the computational subspace from other energy level subspaces at a predetermined approximate order through Schriever-Wolf transformation to obtain the dispersive Hamiltonian describing the low-energy dynamic behavior of the system, and further transforms the system Hamiltonian to the interaction picture through unitary transformation, thereby extracting a clear qubit-qubit effective exchange coupling form in the complex energy level background. This method gives the physical mechanism and control parameters of the entanglement gate a clear physical meaning, avoiding the dependence on empirical parameter tuning or pure numerical optimization. (4) Leakage compensation mechanism that takes into account both gate speed and fidelity: Compared with the traditional method of reducing leakage error by extending the gate operation time, this invention introduces time-dependent detuning compensation during the gate operation process, so that the energy level correction is dynamically adjusted with the control pulse, thereby suppressing the excitation of multiple leakage channels while maintaining the speed advantage of parametric entanglement gate operation, effectively alleviating the inherent contradiction between high-speed operation and high fidelity. (5) Good scalability for modular quantum systems: The energy level leakage suppression method proposed in this invention does not depend on a specific energy level configuration or a single leakage transition channel. Its control strategy can be naturally extended to quantum systems with multiple leakage channels and more complex energy level structures. This method is not only applicable to two-qubit entanglement gate operation, but can also be directly applied to high-fidelity quantum state transmission and the preparation of remote entangled states. It can also be easily extended to other qubit-resonant cavity hybrid platforms, providing strong support for building a high-fidelity, scalable modular quantum system architecture. Attached Figure Description

[0040] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0041] Figure 1 This is a flowchart illustrating the method of the present invention.

[0042] Figure 2 This is a schematic diagram of the system structure of the present invention.

[0043] Figure 3 This is a schematic diagram of the semiconductor spin quantum bit-superconducting resonant cavity hybrid system of the present invention.

[0044] Figure 4 This is a test diagram of the entanglement gate fidelity related parameters of the present invention.

[0045] Figure 5 This is a test diagram of the parameters related to quantum state transmission and remote entanglement of the present invention. Detailed Implementation

[0046] Example 1 like Figure 1 As shown, this embodiment discloses an energy level leakage suppression method, applicable to hybrid quantum systems containing at least two qubits and an intermediate system coupled to the qubits. The implementation process of the energy level leakage suppression method of the present invention will be described in detail below with reference to a specific physical model.

[0047] In this embodiment, the hybrid quantum system includes qubit A, qubit B, and an intermediary system simultaneously coupled to qubit A and qubit B. The intermediary system is preferably a superconducting microwave resonant cavity, and the qubits are semiconductor spin singlet-tritt qubits with a multi-level structure, wherein the lowest two levels... and Constructing computational subspaces, higher energy levels (such as...) The leaky subspace is formed by the qubits, which are coupled to the resonant cavity via capacitance. A schematic diagram of the corresponding spin-resonant cavity hybrid quantum system is shown below. Figure 3 In the absence of external driving forces, the dynamics of the hybrid quantum system are described by the following total Hamiltonian:

[0048] in, Representing a quantum bit At energy level The corresponding transition frequency, The resonant cavity frequency, and These are the photon generation and annihilation operators for the resonant cavity, respectively. Representing the quantum bit subspace The coupling strength between the resonant cavity and the resonant cavity. This is a transition operator.

[0049] Step 1.1: In this embodiment, a parametric modulation drive pulse is applied to one of the at least two qubits (e.g., qubit A) to time-dependently modulate its frequency parameters. The drive Hamiltonian corresponding to the drive pulse is:

[0050] in, Let be the modulation frequency that varies with time. The modulation frequency is selected such that its time integral satisfies the following form:

[0051] in, and These represent the time-varying amplitude and phase of the parametric modulation driving pulse, respectively. Under parametric modulation driving, the total Hamiltonian of the hybrid quantum system can be expressed as:

[0052] Step 1.2: In this embodiment, the qubit and the resonant cavity are set to operate in the dispersive coupling region, such that the frequency detuning between the qubit and the resonant cavity is greater than their coupling strength, and the resonant cavity is in a vacuum or near-vacuum state, i.e., satisfying... Under the above conditions, by applying the Schrieffer-Wolf transform to the total Hamiltonian, the degrees of freedom of the resonant cavity are eliminated at a predetermined approximate order, yielding the dispersive Hamiltonian describing the effective dynamics of the qubit:

[0053] in, The dispersion correction frequency of the qubit energy level is given by: The effective exchange coupling strength is:

[0054] The effective exchange coupling is activated under parametric modulation to realize the two-qubit parametric entanglement gate operation.

[0055] Step 2.1: To extract the effective exchange interactions activated by parametric modulation, the dispersive Hamiltonian is... Apply the first unitary transformation:

[0056] Under this transformation, the system Hamiltonian is transformed to the interaction representation, and the first-order resonance term is extracted using the Jacobi-Anger expansion, yielding:

[0057] in, This represents the effective detuning between qubits related to the drive.

[0058] Step 2.2: Further apply a second unitary transformation to the interacting Hamiltonian:

[0059] In the aforementioned reference frame, the effective Hamiltonian of the system can be decomposed into:

[0060] The effective control Hamiltonian within the computational subspace is:

[0061] The Hamiltonian of energy level leakage is:

[0062] Step 3.1: Under the baseline condition of ignoring leakage compensation, set... By measuring the effective Rabi frequency Time-shaping is performed to achieve the target entanglement gate operation and satisfy the pulse area condition:

[0063] Preferably, Using Gaussian envelope form:

[0064] Step 3.2: Considering multiple leakage paths, introduce time-dependent mistuning compensation:

[0065] The effective detuning parameter is made to change synchronously with the effective Rabi frequency, thereby compensating for the dynamic energy level correction introduced by parametric modulation and suppressing undesirable transitions from the computational subspace to higher energy levels.

[0066] Example 2 Based on the energy level leakage suppression method described in Example 1, this example further conducts numerical tests and evaluations on the performance of the method in actual quantum gate operations, focusing on the effectiveness of the proposed optimized pulse shaping and time-dependent detuning compensation scheme in suppressing energy level leakage errors and improving the fidelity of two-qubit entanglement gates.

[0067] To quantitatively evaluate the effect of the energy level leakage suppression method on the performance improvement of entanglement gates, this embodiment uses the average gate fidelity. As an evaluation metric, specifically, for any initial pure state, the final quantum state of the system at the end of the gate operation is obtained by solving the master equation, which includes decoherence and dissipation effects, and then compared with the quantum state after the ideal target entanglement gate is applied. In one embodiment, the average gate fidelity is defined as:

[0068] in, This represents the actual quantum evolution process. For the ideal target two-qubit entanglement gate operator, and Let A and B represent the Pauli operators acting on qubit A and qubit B, respectively. In this way, the performance of entanglement gates under different control pulse parameters and different noise conditions can be compared in a unified manner.

[0069] In one embodiment, firstly, under noise-free conditions, numerical tests are performed to investigate the relationship between the fidelity of the entanglement gate and the gate operation time. Then, the optimized pulse scheme employing the energy level leakage suppression method is compared with a baseline pulse scheme without leakage compensation. The relevant pulse parameters of the baseline and optimized pulse schemes are as follows: Figure 4 As shown in (a) and (b), the test results demonstrate that, compared to the baseline pulse scheme, the optimized pulse scheme significantly reduces the probability of the system occupying higher energy levels outside the computational subspace during gate operation, thereby effectively suppressing energy level leakage and improving the average fidelity of the entanglement gate. With increasing gate operation time, the overall fidelity of the entanglement gate shows an upward trend and gradually stabilizes. Fidelity-related test results are shown in (a) and (b). Figure 4 As shown in (c). This result demonstrates that by time-shaping the effective Rabi frequency and introducing a compensation mechanism for leakage channels, the operational performance of the parametric entanglement gate under ideal conditions can be effectively improved without changing the gate type.

[0070] In another embodiment, practical noise factors such as qubit decoherence and mediator system dissipation are further considered, and the relationship between entanglement gate fidelity and control parameters is tested. Test results show that, under noisy conditions, entanglement gate fidelity exhibits a trend of first increasing and then decreasing with gate operation time, reflecting the competitive relationship between energy level leakage error and decoherence error. Compared to the control scheme without leakage compensation, the optimized pulse scheme using the described energy level leakage suppression method achieves higher gate fidelity over a wider parameter range, indicating that it still has significant performance advantages in practical noisy environments. Fidelity-related test results are as follows: Figure 4 As shown in (d).

[0071] As can be seen from the above embodiments, the energy level leakage suppression method proposed in this invention not only effectively suppresses the leakage error introduced by the high energy level during the parametric entanglement gate operation in theory, but also, under the condition of considering real noise, can still achieve high-fidelity two-qubit entanglement gate operation within a reasonable parameter window, and has good engineering feasibility and application prospects.

[0072] Example 3 Based on the energy level leakage suppression methods described in Examples 1 and 2, this embodiment further applies the high-fidelity two-qubit parametric entanglement gate to the quantum state transmission and remote entanglement state preparation process in a modular hybrid quantum system to verify the applicability and reliability of the method in key tasks of quantum networks.

[0073] In one embodiment, a hybrid quantum system consisting of at least two spin qubits and a resonant cavity coupled thereto is considered. First, spin qubit A is initialized to an arbitrary superposition state, which takes the form:

[0074] in, This represents the initial phase. Subsequently, while maintaining the intermediate system under dispersive coupling conditions, a control pulse obtained through joint optimization in step 3 is applied to the qubits to activate effective exchange coupling between them, causing the system to perform a parametric iSWAP-type entanglement gate operation. Through this operation, the quantum state on qubit A is coherently mapped to qubit B, resulting in the final state of qubit B being...

[0075] in, The final phase, and satisfies the condition of the initial phase. To verify the preservation of phase information during quantum state transmission, the actual obtained quantum state is compared with the ideal target state, and the quantum state transmission fidelity is calculated.

[0076] in, and The values ​​represent the actual quantum state and the target quantum state, respectively. The results show that the quantum state transmission process maintains high fidelity under different initial phase conditions, demonstrating the excellent performance of the energy level leakage suppression method in quantum state transmission tasks. The test results related to the quantum state transmission fidelity are as follows: Figure 5 As shown in (a).

[0077] In another embodiment, the energy level leakage suppression method is used to prepare a long-range entangled state between two spin qubits. Specifically, qubit A and qubit B are initialized to state A and B respectively. and Then, a jointly optimized control pulse is applied to cause the system to execute once. Bell-type parametric entanglement gate operation. This operation generates the following Bell-type entangled state between two qubits:

[0078] To evaluate the quality of the prepared entangled state, quantum state tomography reconstruction was performed on the final quantum state, and the resulting density matrix was compared with the density matrix corresponding to the ideal Bell state. The fidelity of the entangled state was calculated.

[0079] in, and The values ​​represent the actual density matrix and the density matrix corresponding to the ideal Bell state, respectively. The results show that the prepared entangled state has high fidelity and can meet the entanglement quality requirements of various quantum communication and quantum network protocols. The density matrix results of the prepared long-range entangled state are shown in the figure below. Figure 5 As shown in (b).

[0080] The results of the above implementation of quantum state transmission and remote entanglement preparation demonstrate that the parametric entanglement gate constructed based on the energy level leakage suppression method described in this invention can not only achieve high-fidelity operations between local qubits, but can also be directly used for key quantum network tasks in modular hybrid quantum systems. The method effectively suppresses leakage from the computational subspace to higher energy levels during quantum state transmission, maintaining the phase coherence of the quantum state; and during remote entanglement preparation, it can stably generate high-quality entangled states, thus providing a reliable physical implementation scheme for applications such as quantum state distribution, quantum repeaters, and distributed quantum computing.

[0081] In summary, modular quantum architectures, by interconnecting multiple relatively independent quantum nodes via photonic or microwave links, can be used to realize remote quantum operations and distributed quantum information processing. Addressing the need for high-fidelity quantum operations in this type of architecture, this paper proposes and studies a hybrid quantum system based on the coupling of spin qubits and a superconducting microwave resonant cavity. In this system, spin qubits are used for quantum information storage and processing, while the microwave resonant cavity mediates the coherent interaction between spatially separated qubits. By introducing a parametric modulation mechanism and combining it with a control pulse optimization method targeting energy level leakage, parameter-driven exchange-entanglement gates, quantum state transfer, and remote entanglement state preparation quantum operations are realized. Numerical test results show that, under preset system parameters and noise model conditions, the above quantum operations can achieve high operational fidelity, and the results meet or exceed the performance requirements of various quantum error correction schemes for basic gate operations. This demonstrates that, in the proposed spin-resonant cavity hybrid system, through reasonable parameter selection and pulse design, stable multi-qubit quantum operations can be achieved while suppressing energy level leakage and decoherence effects. Therefore, the technical solution described in this paper provides a way to realize coherent operation between modular quantum nodes on a spin-resonant cavity hybrid platform, which can be used to build a quantum information processing system that supports long-range quantum state transmission and entanglement generation.

[0082] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for suppressing energy level leakage, characterized in that, include: Step 1: In a quantum system including at least two qubits and an intermediary system coupled to the qubits, by applying parametric modulation to the qubits, an effective exchange coupling between the qubits and the intermediary system is established under the condition of dispersion coupling, and the effective exchange coupling is activated by the parametric modulation to perform a two-qubit parametric entanglement gate operation. Step 2: During the parametric entanglement gate operation, the quantum system is effectively modeled. By applying representational transformation and unitary transformation to the Hamiltonian of the hybrid system, the effective exchange interaction between qubits activated by parametric modulation is extracted. After eliminating the fast oscillation term, the separate computational subspace control model and energy level leakage model are obtained to characterize the energy level correction of the computational subspace and the coupling effect between the computational subspace and the high-energy-level state during the parametric entanglement gate operation. Step 3: Based on the effective control model and effective leakage model of the computational subspace established during the parametric entanglement gate operation, the entanglement gate control pulse is jointly optimized. By time-shaping the effective Rabi frequency and introducing time-dependent detuning parameter modulation, the energy level correction introduced by parametric modulation is dynamically compensated, thereby suppressing energy level leakage of the computational subspace to higher energy levels while completing the two-qubit entanglement gate operation.

2. The method for suppressing energy level leakage according to claim 1, characterized in that, Step 1 further includes: Step 1.1: Apply a parametric modulation drive pulse to one of the at least two qubits to parametrically modulate the frequency parameters of that qubit, wherein the driving Hamiltonian corresponding to the parametric modulation drive pulse contains a diagonal term acting on the qubit to calculate its ground state, and its form is: in, The modulation frequency varies with time, and the modulation frequency is selected such that its time integral satisfies a sinusoidal form: in, and These represent the time-varying amplitude and phase of the parametric modulation drive pulse, respectively. Step 1.2: Under the action of the parametric modulation driving pulse, the qubit and the intermediary system are made to operate in the dispersive coupling region, that is, the frequency detuning between the qubit and the intermediary system is greater than its coupling strength, and the intermediary system is placed in a vacuum or near-vacuum state; under this condition, the degrees of freedom of the intermediary system are eliminated at a predetermined approximate order by the Schrieffer-Wolf transformation to obtain the dispersive Hamiltonian describing the effective dynamics of the qubit, thereby generating effective exchange coupling between the at least two qubits, wherein the effective exchange coupling is activated by the parametric modulation and is used to realize the two-qubit parametric entanglement gate operation.

3. The method for suppressing energy level leakage according to claim 1, characterized in that, Step 2 also includes: Step 2.1: During the parametric entanglement gate operation, a first unitary transformation is applied to the dispersive Hamiltonian to transform the quantum system to the interaction representation, thereby eliminating the fast oscillation term introduced by the energy level correction term and the parametric modulation drive, thus obtaining the interaction Hamiltonian describing the effective exchange coupling between the qubits activated by the parametric modulation, wherein the strength of the effective exchange coupling is determined by the parametric modulation parameters. Step 2.2: Under the interaction representation, apply a second unitary transformation to the interaction Hamiltonian to eliminate the explicit time dependence caused by detuning in the computational subspace. In the transformed reference frame, decompose the effective Hamiltonian of the quantum system into a control Hamiltonian confined within the computational subspace and a leakage Hamiltonian acting outside the computational subspace, wherein the leakage Hamiltonian is used to characterize the coupling relationship between the computational subspace and the high-level state.

4. The method for suppressing energy level leakage according to claim 1, characterized in that, Step 3 also includes: Step 3.1: When implementing the two-qubit parametric entanglement gate operation, the effective detuning parameter is set to zero, and the target entanglement gate operation is achieved by time-shaping the effective Rabi frequency, wherein the effective Rabi frequency satisfies a predetermined pulse area condition: The entanglement gate operation is performed within the computational subspace; the effective Rabi frequency adopts a Gaussian envelope form with smooth start and end characteristics, so that the control pulse smoothly returns to zero at the beginning and end of the gate operation, thereby reducing the high-spectral components of the driving pulse, suppressing spectral leakage and reducing undesirable transitions to non-computational states. Step 3.2: During the parametric entanglement gate operation, for cases with multiple energy level leakage channels, based on the effective leakage model established in Step 2, time-dependent modulation is introduced into the effective detuning parameter. This allows the effective detuning parameter to dynamically adjust with changes in the effective Rabi frequency, compensating for transient energy level shifts introduced by parametric modulation and suppressing leakage coupling between the computational subspace and higher energy level states. The time-dependent form of the effective detuning parameter is related to the square of the effective Rabi frequency, and its proportionality coefficient is jointly determined by the qubit anharmonicity parameter corresponding to each leakage channel and the coupling weight between the leakage channel and the computational subspace. Through this time-dependent detuning parameter modulation, dynamic energy level corrections introduced by multiple energy level leakage channels are compensated simultaneously without significantly increasing the entanglement gate operation time, thereby improving the overall fidelity of the two-qubit entanglement gate operation.

5. An energy level leakage suppression system, applied to a quantum system comprising at least two qubits and an intermediate system coupled to the qubits, characterized in that, The system includes: The parametric modulation and entanglement gate execution module is used to apply parametric modulation drive to at least one qubit to activate effective exchange coupling between qubits, thereby performing two-qubit parametric entanglement gate operation; An effective dynamics modeling module is used to perform effective dynamics modeling of the quantum system during the parametric entanglement gate operation, so as to characterize the energy level correction of the computational subspace introduced by parametric modulation, as well as the coupling effect between the computational subspace and the leakage subspace. The pulse optimization and leakage suppression module is used to optimize the entanglement gate control pulse based on the energy level correction result. By introducing time-dependent detuning parameter modulation, it compensates for the energy level shift generated during the parametric entanglement gate operation, thereby suppressing energy level leakage during the entanglement gate operation. The system control and monitoring module is used to perform overall control and operation monitoring of the energy level leakage suppression system, coordinate the parametric modulation and entanglement gate execution module, the effective dynamics modeling module, and the pulse optimization and leakage suppression module to work together according to preset parameters and processes, and collect system operation data in real time for system performance evaluation and optimization. The data storage and analysis module is used to store the operational data collected by the system control and monitoring module to ensure the security and integrity of the data, and to analyze and process the operational data to generate system operation status and performance evaluation information based on the analysis results, so as to provide feedback on system operation status and optimization suggestions to system operators and managers.

6. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor, when executing the computer program, implements the energy level leakage suppression method as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, wherein, when executed by a processor, the computer program is used to implement the energy level leakage suppression method as described in any one of claims 1 to 4.

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