Method for realizing high-fidelity two-bit quantum gate

Abstract

The invention provides a method for realizing a high-fidelity two-bit quantum gate. The method comprises the following steps: generating a compensation pulse group according to a pre-modified coupler magnetic flux bias pulse and a frequency adjustment pulse of a quantum bit pair; performing excitation quantum state configuration and frequency detuning configuration on the quantum bit pairs, and updating the compensation pulse group based on a minimum state leakage optimization method to obtain a low-leakage pulse group; extracting a phase factor group in a non-adiabatic interaction evolution process by using the low-leakage pulse group, calculating an offset corresponding to the phase factor group based on a phase matching condition, and performing single-bit trivial phase compensation to obtain a pre-calibration pulse group; constructing a global optimization parameter group according to the pre-calibration pulse group and a to-be-compensated single-bit phase, and performing iterative optimization on the global optimization parameter group by taking the fidelity of the random reference sequence as a target function to obtain a high-fidelity global parameter group; and executing quantum gate operation based on the high-fidelity global parameter group to obtain a high-fidelity quantum gate.

Description

Technical Field

[0001] This invention relates to the field of quantum computing technology, and in particular to a method for realizing a high-fidelity two-qubit quantum gate. Background Technology

[0002] High-fidelity two-qubit quantum gates are core components for realizing fault-tolerant quantum computing, and their performance directly determines the execution efficiency and reliability of quantum algorithms. In superconducting quantum computing systems, architectures based on tunable couplers can achieve two-qubit entanglement operations through dynamic frequency tuning, but this process faces several physical challenges. First, traditional fixed-frequency qubit schemes lack flexible control over coupling strength, rely on fabrication precision, and are difficult to adapt to multi-qubit expansion requirements. Second, non-adiabatic interactions can easily lead to quantum state leakage into non-computational spaces, and the high-frequency components of pulse waveforms are limited by the bandwidth of the control system, resulting in waveform distortion and timing crosstalk. Furthermore, two-qubit gate operations accumulate unpredictable dynamic phase errors, and existing calibration methods mostly rely on local parameter optimization, lacking global collaborative optimization of parameters such as amplitude and phase, making it difficult to further improve fidelity. Summary of the Invention

[0003] (a) Technical problems to be solved To address the shortcomings of existing technologies, this invention provides a method for realizing a high-fidelity two-qubit quantum gate, which has advantages such as high fidelity, high calibration efficiency, and strong robustness. It solves the problem of low quantum gate fidelity caused by conditional leakage, pulse distortion, phase error, and insufficient parameter optimization in the two-qubit quantum gate scenario.

[0004] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: This invention provides a method for realizing a high-fidelity two-qubit quantum gate, comprising the following steps: A quantum-gated pulse group is generated based on a pre-modified coupler flux bias pulse and a frequency adjustment pulse for the quantum bit pair. The quantum-gated pulse group is then smoothed and a buffer period is compensated to obtain a compensated pulse group. The quantum bit pairs are configured with excited quantum states and frequency detuning respectively. The target amplitude parameters of the compensation pulse group are extracted based on the quantum bit pairs using a minimum state leakage optimization method. The compensation pulse group is then updated based on the target amplitude parameters to obtain a low leakage pulse group. The low-leakage pulse group is used to trigger the non-adiabatic interaction between the qubit pairs, and the phase factor group in the evolution process of the non-adiabatic interaction is extracted. Based on the phase matching condition and the phase factor group, single-bit trivial phase compensation is performed on the low-leakage pulse group to obtain the pre-calibrated pulse group. A global optimization parameter set is constructed based on the pre-calibrated pulse set. The global optimization parameter set is iteratively searched and fine-tuned globally with the fidelity of the random reference sequence as the objective function to obtain a high-fidelity global parameter set. Based on the high-fidelity global parameter set, quantum gate operations are performed on the qubit pair, and the residual single-bit phase is compensated by software to obtain a high-fidelity quantum gate.

[0005] According to a preferred embodiment of the present invention, a quantum-gated pulse group is generated based on a pre-modified coupler flux bias pulse and a frequency adjustment pulse for the qubit pair, comprising: The adjustable coupler is modified by a square wave with sinusoidal modification to obtain the coupler flux bias pulse. The frequency adjustment pulse of the quantum bit pair is defined based on the time reference of the coupler magnetic flux bias pulse; A quantum-gated pulse group is generated based on the coupler flux bias pulse and the frequency adjustment pulse.

[0006] According to another preferred embodiment of the present invention, waveform smoothing and buffer period compensation are performed on the quantum-gated pulse group to obtain a compensated pulse group, including: Based on the bandwidth limitation of the tunable coupler and the anharmonicity of the qubit pair, the standard deviation parameter and effective range of the Gaussian filter are determined, and the Gaussian kernel parameter is obtained. Based on the Gaussian kernel parameters, the quantum-gated pulse group is subjected to Gaussian smoothing filtering to obtain a smooth pulse group; The waveform tail duration introduced by the convolution effect after Gaussian smoothing filtering of the smoothed pulse group is calculated based on the attenuation characteristics of the Gaussian kernel parameter under the preset truncation error. Fill the waiting bits corresponding to the waveform tail duration at both ends of the smooth pulse group to obtain the envelope pulse group; The envelope pulse group is time-series marked and integrated to obtain the compensation pulse group.

[0007] According to another preferred embodiment of the present invention, the excited quantum state configuration and frequency detuning configuration of the qubit pair are respectively performed, including: The qubit pair is reset to the ground state, and each qubit in the qubit pair is excited to the first excited state; Obtain the initial operating frequency of the quantum bit pair, and calculate the frequency offset corresponding to the initial operating frequency based on the preset operating frequency point; The operating frequency of the qubit pair is tuned to the operating frequency point according to the frequency offset.

[0008] According to another preferred embodiment of the present invention, before calculating the frequency offset corresponding to the initial operating frequency based on a preset operating frequency point, the method further includes: The transition frequencies of each qubit pair from the ground state to the first excited state and from the first excited state to the second excited state are measured to obtain a set of transition frequencies, and the Hamiltonian model of the qubit pair is established based on the set of transition frequencies. The operating frequency parameter space of the qubit pair is determined based on the Hamiltonian model and the adjustable frequency range of the adjustable coupler. The working frequency parameter space is scanned to obtain the energy difference between the first excited state and the second excited state of the quantum bit pair as a function of the working frequency parameter. The coherent resonance trajectory corresponding to the energy level degeneracy is identified based on the energy difference-frequency relationship. On the coherent resonance trajectory, coordinate points with effective coupling strength greater than a preset strength threshold and without parasitic energy level crossover are selected as operating frequency points.

[0009] According to another preferred embodiment of the present invention, the method based on minimum-state leakage optimization extracts the target amplitude parameters of the compensation pulse group according to the qubit pair, including: The initial amplitude parameter is determined based on the frequency-flux mapping relationship between the operating frequency point and the adjustable coupler, and the amplitude parameter range is configured with the initial amplitude parameter as the midpoint. Amplitude parameters within the range of amplitude parameters are selected one by one, and the compensation pulse group is updated using the amplitude parameters to obtain the updated compensation pulse group; The qubit pair is coherently evolved using the update compensation pulse group, and the state of the coherently evolved qubit pair is measured to obtain the occupancy probability of the first excited state; The occupancy probabilities of the first excited state corresponding to all amplitude parameters within the amplitude parameter range are aggregated into an occupancy probability set, and the maximum value in the occupancy probability set is selected as the target occupancy probability. The amplitude parameter corresponding to the target occupancy probability is used as the target amplitude parameter.

[0010] According to another preferred embodiment of the present invention, the phase factor set in the non-adiabatic interaction evolution process is extracted, including: Three initial computational ground states are set for the quantum bit pair respectively, and the reference interference fringe phase groups corresponding to the three initial computational ground states are obtained without applying the low leakage pulse group. The three initial computational ground states include the 01 state, the 10 state and the 11 state. Apply to one of the qubits in the qubit pair / 2 pulses are used to obtain qubits in a coherent superposition state, and the low-leakage pulse group is applied to the qubits in the coherent superposition state to obtain qubits in an evolved quantum state; Applying to the qubits of the evolved quantum state / 2 pulses are used to obtain the qubit of the measurement state, and the occupancy probability of the excited state of the qubit of the measurement state in the computing basis is measured to obtain the oscillating interference fringe phase group corresponding to the occupancy probability of the excited state. The phase factor set in the non-adiabatic interaction evolution process is extracted based on the phase difference between the oscillating interference fringe phase set and the initial interference fringe phase set.

[0011] According to another preferred embodiment of the present invention, a pre-calibrated pulse group is obtained by performing single-bit trivial phase compensation on the low-leakage pulse group based on the phase matching condition and the phase factor group, including: The phase offset corresponding to the phase factor group is calculated based on the phase matching condition; The phase offset is allocated to each qubit of the qubit pair to obtain a first phase compensation amount and a second phase compensation amount; A virtual Z-gate compensation operator is constructed based on the first phase compensation amount and the second phase compensation amount to obtain a set of compensation parameters. A virtual Z-gate compensation instruction is generated based on the compensation parameter set, and the low-leakage pulse set is bound to the virtual Z-gate compensation instruction to obtain a pre-calibration pulse set.

[0012] According to another preferred embodiment of the present invention, the global optimization parameter set is iteratively searched and globally fine-tuned using the fidelity of the random reference sequence as the objective function to obtain a high-fidelity global parameter set, including: The global optimization parameter set is compiled into a global optimization parameter vector, and a random reference sequence is constructed based on the pre-calibrated pulse set; An objective function is constructed based on the fidelity of the random benchmark sequence, and an initial simplex is constructed with the global optimization parameter vector as the center. The fidelity of each vertex in the initial simplex is calculated based on the objective function, and the fidelities are sorted from high to low according to their numerical values ​​to obtain a fidelity sequence. The last fidelity in the fidelity sequence is taken as the worst fidelity, and the vertex corresponding to the worst fidelity in the initial simplex is taken as the worst vertex; the first fidelity in the fidelity sequence is taken as the best fidelity, and the vertex corresponding to the best fidelity in the initial simplex is taken as the best vertex. Calculate the geometric center of each vertex of the initial simplex except for the worst vertex to obtain the simplex centroid. Perform symmetrical reflection of the worst vertex about the simplex centroid to obtain the reflection vertex. Calculate the fidelity of the reflection vertex using the objective function as the reflection fidelity. The initial simplex is updated based on the reflection fidelity to obtain an updated simplex, and the distance from each vertex in the updated simplex to the optimal vertex is calculated to obtain a set of vertex distances. The vertex distance with the largest value in the vertex distance group is selected as the target vertex distance, and it is determined whether the target vertex distance is greater than a preset distance threshold. If so, the updated simplex is used to replace the initial simplex, and the step of calculating the fidelity of each vertex in the initial simplex according to the objective function is returned; If not, then the updated simplex is optimized by parameter mapping to obtain a high-fidelity global parameter set.

[0013] To achieve at least one of the above-mentioned objectives, the present invention further provides a system for implementing a high-fidelity two-qubit quantum gate, the system comprising a pulse construction module, an amplitude correction module, a logic calibration module, a global optimization module, and a gate operation module, wherein: The pulse construction module generates a quantum-gated pulse group based on the pre-modified coupler flux bias pulse and the frequency adjustment pulse of the quantum bit pair, and performs waveform smoothing and buffer compensation on the quantum-gated pulse group to obtain a compensated pulse group. The amplitude correction module configures the excited quantum state and frequency detuning of the qubit pair respectively. Based on the minimum state leakage optimization method, it extracts the target amplitude parameter of the compensation pulse group according to the qubit pair and updates the compensation pulse group according to the target amplitude parameter to obtain a low leakage pulse group. The logic calibration module uses the low-leakage pulse group to trigger the non-adiabatic interaction between the quantum bit pairs, extracts the phase factor group in the evolution process of the non-adiabatic interaction, and performs single-bit trivial phase compensation on the low-leakage pulse group based on the phase matching condition and the phase factor group to obtain the pre-calibration pulse group. The global optimization module constructs a global optimization parameter set based on the pre-calibrated pulse group, and performs iterative search and global fine-tuning on the global optimization parameter set with the fidelity of the random reference sequence as the objective function to obtain a high-fidelity global parameter set. The gate operation module performs quantum gate operations on the qubit pair based on the high-fidelity global parameter set and performs software compensation on the residual single-bit phase to obtain a high-fidelity quantum gate.

[0014] The present invention further provides a computer-readable storage medium storing a computer program, which is executed by a processor to implement the above-described method for implementing a high-fidelity two-qubit quantum gate.

[0015] (III) Beneficial Effects Compared with existing technologies, the present invention provides a method and system for realizing a high-fidelity two-qubit quantum gate, which has the following beneficial effects: This method for achieving a high-fidelity two-qubit quantum gate generates smooth pulse edges through sinusoidal modification, effectively reducing high-frequency harmonics in the control pulse. This significantly reduces quantum state leakage caused by rapid changes in frequency components during operation. By employing a series of waveform engineering techniques, such as bandwidth constraint, Gaussian smoothing, and tail compensation, the pulse shape is ensured to conform to the controller's finite bandwidth, preventing waveform distortion. Tail compensation accommodates the finite rise and fall times of the pulse, avoiding timing crosstalk errors caused by pulse tail truncation. This ensures the execution quality of the pulse in the real world, transforming the ideal gated waveform into a compensated pulse group that can be accurately executed by actual hardware, significantly reducing the impact of hardware non-ideals on quantum gate fidelity.

[0016] This method for achieving high-fidelity two-qubit quantum gates introduces a working frequency selection mechanism based on the Hamiltonian model before quantum gate operation. This ensures that the quantum bit pair is in structurally optimal energy level configuration before entering non-adiabatic interaction, thus avoiding unavoidable state leakage and parasitic energy level interference caused by improper frequency selection in the subsequent pulse optimization stage. By introducing an amplitude scanning optimization method targeting the occupancy probability of the first excited state, the state leakage problem is transformed into a directly measurable experimental index, enabling precise calibration of the coupler pulse amplitude parameters. This not only effectively suppresses state leakage caused by non-ideal coupling but also provides a stable and low-noise pulse foundation for subsequent phase compensation and global fidelity optimization.

[0017] This method for achieving a high-fidelity two-qubit quantum gate introduces a gradient-free optimization mechanism with the fidelity of a random benchmark sequence as the objective function, enabling global joint fine-tuning of key control parameters of the two-qubit quantum gate. Unlike model- or gradient-based methods, this method directly uses the experimentally measured random benchmark fidelity as optimization feedback, effectively avoiding the influence of unavoidable modeling errors and measurement noise in quantum hardware. Through geometric search operators such as simplex reflection, expansion, and contraction, stable search and fast convergence in the multi-parameter space are achieved without relying on gradient information, thereby simultaneously optimizing the coupler amplitude, qubit frequency adjustment amplitude, and single-qubit phase compensation parameters, significantly improving the overall fidelity and consistency of the two-qubit quantum gate under actual operating conditions. Attached Figure Description

[0018] Figure 1 The diagram shown is a flowchart of a method for realizing a high-fidelity two-qubit quantum gate according to the present invention. Detailed Implementation

[0019] The following description is intended to disclose the present invention and enable those skilled in the art to implement it. The preferred embodiments described below are merely examples, and other obvious modifications will occur to those skilled in the art. The basic principles of the invention defined in the following description can be applied to other embodiments, modifications, improvements, equivalents, and other technical solutions that do not depart from the spirit and scope of the invention.

[0020] It is understood that the term "a" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "a" should not be understood as a limitation on the number.

[0021] Example 1: Please combine Figure 1 This invention discloses a method for realizing a high-fidelity two-qubit quantum gate, the method comprising the following steps: A quantum-gated pulse group is generated based on a pre-modified coupler flux bias pulse and a frequency adjustment pulse for the quantum bit pair. The quantum-gated pulse group is then smoothed and buffered to obtain a compensated pulse group.

[0022] In detail, a quantum-gated pulse group is generated based on a pre-modified coupler flux bias pulse and a frequency adjustment pulse for the qubit pair, including: The adjustable coupler is modified by a square wave with sinusoidal modification to obtain the coupler flux bias pulse. The frequency adjustment pulse of the quantum bit pair is defined based on the time reference of the coupler magnetic flux bias pulse; A quantum-gated pulse group is generated based on the coupler flux bias pulse and the frequency adjustment pulse.

[0023] A tunable coupler is a circuit element used in superconducting quantum computing to dynamically control the coupling strength between two or more qubits. Sine modulation refers to modulating the amplitude of the pulses of the tunable coupler using the following sine wave function: in, It is the coupler flux bias pulse at The range of time, This refers to the amplitude parameter of the sine wave function. This refers to the sine-modified weight. It is a time index. It is the quantum gate duration corresponding to the qubit pair. In this embodiment of the invention, It is 0.3. It is 30ns; The coupler flux bias pulse enables the frequency of the adjustable coupler to be tuned along the trajectory of 10.5 GHz → 7.3 GHz → 10.5 GHz. The defined frequency adjustment pulse refers to defining a frequency adjustment pulse that is time-synchronized with the coupler flux bias pulse according to the time base of the coupler flux bias pulse. The quantum gated pulse group consists of the coupler flux bias pulse and the frequency adjustment pulse.

[0024] Specifically, waveform smoothing and buffer period compensation are performed on the quantum-gated pulse group to obtain a compensated pulse group, including: Based on the bandwidth limitation of the tunable coupler and the anharmonicity of the qubit pair, the standard deviation parameter and effective range of the Gaussian filter are determined, and the Gaussian kernel parameter is obtained. Based on the Gaussian kernel parameters, the quantum-gated pulse group is subjected to Gaussian smoothing filtering to obtain a smooth pulse group; The waveform tail duration introduced by the convolution effect after Gaussian smoothing filtering of the smoothed pulse group is calculated based on the attenuation characteristics of the Gaussian kernel parameter under the preset truncation error. Fill the waiting bits corresponding to the waveform tail duration at both ends of the smooth pulse group to obtain the envelope pulse group; The envelope pulse group is time-series marked and integrated to obtain the compensation pulse group.

[0025] Specifically, determining the standard deviation parameter and the effective range means ensuring, through Fourier transform, that the energy component at the second excited state of the pulse spectrum is below a preset energy component threshold. Simultaneously, combined with the sampling frequency of the adjustable coupler, it ensures that the Gaussian kernel parameter covers a sufficient number of sampling points in the quantum-gated pulse group. The energy component threshold can be -40 dB, and the standard deviation parameter can be... =2ns; The calculated waveform tail duration refers to the time distance from the center point to the cutoff point calculated based on the Gaussian function, using this time distance as the waveform tail duration, and calculating the waveform tail duration based on the time distance and the Gaussian kernel parameters, for example, according to... ,in, For time distance, It is the standard deviation parameter. It is the truncation error, when The value is 2ns, and the cutoff position is 2.5. hour, Approximately 0.012, Approximately 5ns; after filling the beginning and end of the smooth pulse group with 5ns of waiting bits, the duration of the envelope pulse group changes from 30ns for the smooth pulse group to 40ns; timing mark integration refers to marking the start time and duration of each pulse segment and aligning the time axis.

[0026] By performing sinusoidal modification, smooth pulse edges can be generated, effectively reducing high-frequency harmonics in the control pulse. This significantly reduces quantum state leakage caused by rapid changes in frequency components during operation. Through a series of waveform engineering techniques, such as bandwidth constraint, Gaussian smoothing, and tail compensation, the pulse shape is ensured to conform to the controller's finite bandwidth, preventing waveform distortion. Tail compensation accommodates the finite rise and fall times of the pulse, avoiding timing crosstalk errors caused by pulse tail truncation. This ensures the execution quality of the pulse in the real world, transforming the ideal gated waveform into a compensated pulse group that can be accurately executed by actual hardware, significantly reducing the impact of hardware non-ideals on quantum gate fidelity.

[0027] The quantum bit pairs are configured with excited quantum states and frequency detuning respectively. The target amplitude parameters of the compensation pulse group are extracted from the quantum bit pairs based on the minimum state leakage optimization method, and the compensation pulse group is updated according to the target amplitude parameters to obtain a low leakage pulse group.

[0028] In detail, the excited quantum state configuration and frequency detuning configuration of the qubit pair are performed respectively, including: The qubit pair is reset to the ground state, and each qubit in the qubit pair is excited to the first excited state; Obtain the initial operating frequency of the quantum bit pair, and calculate the frequency offset corresponding to the initial operating frequency based on the preset operating frequency point; The operating frequency of the qubit pair is tuned to the operating frequency point according to the frequency offset.

[0029] This can be achieved by applying force to each qubit. The pulse method excites the qubits to the first excited state by applying a fast electrical pulse, i.e., by using a Fast-Z pulse method, to tune the operating frequency of the qubit pair to the operating frequency point according to the frequency offset.

[0030] Specifically, before calculating the frequency offset corresponding to the initial operating frequency based on the preset operating frequency point, the method further includes: The transition frequencies of each qubit pair from the ground state to the first excited state and from the first excited state to the second excited state are measured to obtain a set of transition frequencies, and the Hamiltonian model of the qubit pair is established based on the set of transition frequencies. The operating frequency parameter space of the qubit pair is determined based on the Hamiltonian model and the adjustable frequency range of the adjustable coupler. The working frequency parameter space is scanned to obtain the energy difference between the first excited state and the second excited state of the quantum bit pair as a function of the working frequency parameter. The coherent resonance trajectory corresponding to the energy level degeneracy is identified based on the energy difference-frequency relationship. On the coherent resonance trajectory, coordinate points with effective coupling strength greater than a preset strength threshold and without parasitic energy level crossover are selected as operating frequency points.

[0031] In this context, the ground state refers to the lowest energy state of a qubit, such as state 0. The energy of the first excited state is greater than that of the ground state, such as state 1. The energy of the second excited state is greater than that of the first excited state, such as state 2. The transition frequency records the frequency of each qubit in the qubit pair from state 0 to state 1. The transition frequency set can be measured using a microwave spectrometer, and the free Hamiltonian can be determined through the transition frequency, thereby establishing a Hamiltonian model. The working frequency parameter space is the Hamiltonian model and the cross-frequency parameter space of the adjustable frequency range. Energy level degeneracy means that state 11 corresponds to the same energy value as state 02 or state 20. The coherent resonance trajectory is the frequency change estimate corresponding to energy level degeneracy. The effective coupling strength is a parameter used to describe the actual interaction strength between two qubits. Parasitic energy level crossing refers to the unexpected proximity or crossing of two energy levels that should not intersect when adjusting the qubit frequency, magnetic flux, or coupling strength. In this embodiment of the invention, the frequency detuning of the working frequency is... .

[0032] In detail, the method based on minimum-state leakage optimization extracts the target amplitude parameters of the compensation pulse group according to the qubit pair, including: The initial amplitude parameter is determined based on the frequency-flux mapping relationship between the operating frequency point and the adjustable coupler, and the amplitude parameter range is configured with the initial amplitude parameter as the midpoint. Amplitude parameters within the range of amplitude parameters are selected one by one, and the compensation pulse group is updated using the amplitude parameters to obtain the updated compensation pulse group; The qubit pair is coherently evolved using the update compensation pulse group, and the state of the coherently evolved qubit pair is measured to obtain the occupancy probability of the first excited state; The occupancy probabilities of the first excited state corresponding to all amplitude parameters within the amplitude parameter range are aggregated into an occupancy probability set, and the maximum value in the occupancy probability set is selected as the target occupancy probability. The amplitude parameter corresponding to the target occupancy probability is used as the target amplitude parameter.

[0033] The initial amplitude parameter is determined based on the nominal coupling condition of the qubit pair near the operating frequency point. The frequency-flux mapping relationship refers to the tuning sensitivity of the tunable coupler, i.e., the frequency change caused by a unit change in magnetic flux. A magnetic flux range that can cover the frequency fluctuation of the target frequency point from ±50 MHz to ±100 MHz is selected. The amplitude parameter range is generally ±30% of the initial amplitude parameter. Coherent evolution refers to applying a Hamiltonian to the qubit pair according to the update compensation pulse group, so that the 11 state of the qubit pair coherently exchanges with the 02 state or 20 state, thereby performing coherent evolution. Dispersion readout or other equivalent quantum state projection measurement methods can be used for state measurement. The maximum value corresponds to the point where the probability of the qubit in the qubit pair remaining in the first excited state is the highest, that is, the 11 state completely returns to the computation subspace after the evolution is completed, with the least leakage.

[0034] By introducing a working frequency selection mechanism based on the Hamiltonian model before quantum gate operations, the qubit pairs are in structurally optimal energy level configuration before entering non-adiabatic interactions, thus avoiding unavoidable state leakage and parasitic energy level interference caused by improper frequency selection in the subsequent pulse optimization stage. By introducing an amplitude scanning optimization method targeting the occupancy probability of the first excited state, the state leakage problem is transformed into a directly measurable experimental index, enabling precise calibration of the coupler pulse amplitude parameters. This not only effectively suppresses state leakage caused by non-ideal coupling, but also provides a stable and low-noise pulse foundation for subsequent phase compensation and global fidelity optimization.

[0035] The low-leakage pulse group is used to trigger the non-adiabatic interaction between the qubit pairs, and the phase factor group in the evolution process of the non-adiabatic interaction is extracted. Based on the phase matching condition and the phase factor group, single-bit trivial phase compensation is performed on the low-leakage pulse group to obtain the pre-calibrated pulse group.

[0036] Specifically, triggering the non-adiabatic interaction between the qubit pairs using the low-leakage pulse group means simultaneously applying the low-leakage pulse group to both the corresponding tunable coupler on the chip and the control lines of the qubit pairs. When the coupler frequency is pulled up to 7.3 GHz, the coupling strength between the two qubits becomes very strong, and simultaneously, the frequencies of the two qubits are adjusted to... This aligns the energy levels of state 11 with those of state 02 or 20, resulting in resonance. Within a short time window when both strong coupling and resonance conditions are met, a strong quantum state exchange occurs between state 11 and state 02. Since this process is fast and non-adiabatic, it causes coherent oscillations between these two states.

[0037] Specifically, the phase factor set in the non-adiabatic interaction evolution process is extracted, including: Three initial computational ground states are set for the quantum bit pair respectively, and the reference interference fringe phase groups corresponding to the three initial computational ground states are obtained without applying the low leakage pulse group. The three initial computational ground states include the 01 state, the 10 state and the 11 state. Apply to one of the qubits in the qubit pair / 2 pulses are used to obtain qubits in a coherent superposition state, and the low-leakage pulse group is applied to the qubits in the coherent superposition state to obtain qubits in an evolved quantum state; Applying to the qubits of the evolved quantum state / 2 pulses are used to obtain the qubit of the measurement state, and the occupancy probability of the excited state of the qubit of the measurement state in the computing basis is measured to obtain the oscillating interference fringe phase group corresponding to the occupancy probability of the excited state. The phase factor set in the non-adiabatic interaction evolution process is extracted based on the phase difference between the oscillating interference fringe phase set and the initial interference fringe phase set.

[0038] The Ramsey interferometry method can be used to obtain the reference interference fringe phase set and the oscillating interference fringe phase set. The excited state occupancy probability refers to the probability that the quantum bit is in the 0 state or the 1 state after the interference.

[0039] In detail, based on the phase matching condition and the phase factor set, single-bit trivial phase compensation is performed on the low-leakage pulse group to obtain a pre-calibrated pulse group, including: The phase offset corresponding to the phase factor group is calculated based on the phase matching condition; The phase offset is allocated to each qubit of the qubit pair to obtain a first phase compensation amount and a second phase compensation amount; A virtual Z-gate compensation operator is constructed based on the first phase compensation amount and the second phase compensation amount to obtain a set of compensation parameters. A virtual Z-gate compensation instruction is generated based on the compensation parameter set, and the low-leakage pulse set is bound to the virtual Z-gate compensation instruction to obtain a pre-calibration pulse set.

[0040] The phase matching condition is ϕ3−ϕ2−ϕ1= Where ϕ3, ϕ2, and ϕ1 correspond to each phase factor in the phase factor group, and the formula for calculating the phase offset is: =ϕ3−ϕ2−ϕ1− ,in, The phase offset is the offset amount. Since the global phase of any two-qubit gate can be arbitrarily allocated, the phase offset can be allocated by average distribution or according to weight, thereby obtaining the first phase compensation amount corresponding to the first qubit in the qubit pair and the second phase compensation amount corresponding to the other qubit. Constructing a virtual Z-gate compensation operator refers to constructing a virtual Z-rotation operator for each qubit in the qubit pair in the quantum control software based on the first and second phase compensation amounts. This does not change the physical pulse waveform, but achieves phase compensation by modifying the phase reference frame acting on the qubit pair.

[0041] By utilizing low-leakage pulse groups to trigger non-adiabatic interactions between qubit pairs under strong coupling and energy level resonance conditions, the target two-qubit state undergoes controlled coherent evolution within an extremely short time window, thereby obtaining the required conditional phase while maintaining a low state leakage level. By introducing the Ramsey interferometry method, the phase accumulation implicit in the non-adiabatic evolution process can be accurately mapped into measurable interference fringe phase differences, enabling independent extraction of phase factors for each computed state. By using phase-matching conditions to analytically decompose the phase shift and compensating for the trivial phase of a single qubit using a virtual Z-gate, phase calibration is completed without introducing additional physical pulses or increasing system noise. This not only significantly improves the phase accuracy and consistency of the two-qubit quantum gate but also provides a high-quality initial pulse configuration for subsequent global parameter optimization.

[0042] A global optimization parameter set is constructed based on the pre-calibrated pulse set. The global optimization parameter set is iteratively searched and fine-tuned globally with the fidelity of the random reference sequence as the objective function to obtain a high-fidelity global parameter set.

[0043] The construction of a global optimization parameter set based on the pre-calibration pulse set refers to extracting adjustable control parameters related to the evolution of the two-bit quantum gate of the qubit pair from the pre-calibration pulse set, including the compensation parameter set and the amplitude parameters of the qubit pair and the adjustable coupler.

[0044] In detail, the global optimization parameter set is iteratively searched and fine-tuned using the fidelity of the random benchmark sequence as the objective function to obtain a high-fidelity global parameter set, including: The global optimization parameter set is compiled into a global optimization parameter vector, and a random reference sequence is constructed based on the pre-calibrated pulse set; An objective function is constructed based on the fidelity of the random benchmark sequence, and an initial simplex is constructed with the global optimization parameter vector as the center. The fidelity of each vertex in the initial simplex is calculated based on the objective function, and the fidelities are sorted from high to low according to their numerical values ​​to obtain a fidelity sequence. The last fidelity in the fidelity sequence is taken as the worst fidelity, and the vertex corresponding to the worst fidelity in the initial simplex is taken as the worst vertex; the first fidelity in the fidelity sequence is taken as the best fidelity, and the vertex corresponding to the best fidelity in the initial simplex is taken as the best vertex. Calculate the geometric center of each vertex of the initial simplex except for the worst vertex to obtain the simplex centroid. Perform symmetrical reflection of the worst vertex about the simplex centroid to obtain the reflection vertex. Calculate the fidelity of the reflection vertex using the objective function as the reflection fidelity. The initial simplex is updated based on the reflection fidelity to obtain an updated simplex, and the distance from each vertex in the updated simplex to the optimal vertex is calculated to obtain a set of vertex distances. The vertex distance with the largest value in the vertex distance group is selected as the target vertex distance, and it is determined whether the target vertex distance is greater than a preset distance threshold. If so, the updated simplex is used to replace the initial simplex, and the step of calculating the fidelity of each vertex in the initial simplex according to the objective function is returned; If not, then the updated simplex is optimized by parameter mapping to obtain a high-fidelity global parameter set.

[0045] The construction of the random reference sequence refers to the generation of a series of randomly arranged single-bit gates and the pre-calibrated two-bit gates based on the Clifford group and the pre-calibration pulse group. The construction of the objective function based on the fidelity of the random reference sequence refers to the execution of the random reference sequence using the pre-calibration pulse group corresponding to the global optimization parameter group, obtaining the average occupancy probability of the system's final state returning to the ground state, and mapping the average occupancy probability to fidelity.

[0046] Specifically, updating the initial simplex based on the reflection fidelity to obtain an updated simplex includes: When the reflection fidelity is greater than or equal to the maximum value in the fidelity sequence, an extended vertex is generated based on the reflection vertex and the centroid of the simplex. The extended vertex is then used to replace the worst vertex in the initial simplex to obtain an updated simplex. When the reflection fidelity is greater than the worst fidelity and less than the maximum value in the fidelity sequence, the worst vertex in the initial simplex is replaced by the reflection vertex to obtain the updated simplex; When the reflection fidelity is less than or equal to the worst fidelity, a contracted vertex is generated based on the reflection vertex and the centroid of the simplex. The contracted vertex is then used to replace the worst vertex in the initial simplex to obtain an updated simplex.

[0047] Specifically, generating an extended vertex based on the reflection vertex and the simplex centroid means expanding along the direction from the simplex centroid to the reflection vertex to determine the extended vertex; generating a contracted vertex based on the reflection vertex and the simplex centroid means contracting along the direction from the reflection vertex to the simplex centroid to determine the contracted vertex.

[0048] By introducing a gradient-free optimization mechanism with the fidelity of a random benchmark sequence as the objective function, global joint fine-tuning of key control parameters of a two-qubit quantum gate is achieved. Unlike model-based or gradient-based methods, this method directly uses the experimentally measured fidelity of the random benchmark as optimization feedback, which can effectively avoid the influence of unavoidable modeling errors and measurement noise in quantum hardware. Through geometric search operators such as simplex reflection, expansion, and contraction, stable search and fast convergence in the multi-parameter space are achieved without relying on gradient information, thereby simultaneously optimizing the coupler amplitude, the quantum bit frequency adjustment amplitude, and the single-bit phase compensation parameters, significantly improving the overall fidelity and consistency of the two-qubit quantum gate under actual operating conditions.

[0049] Based on the high-fidelity global parameter set, quantum gate operations are performed on the qubit pair, and the residual single-bit phase is compensated by software to obtain a high-fidelity quantum gate.

[0050] Specifically, performing quantum gate operations on the qubit pair based on the high-fidelity global parameter set and performing software compensation for the residual single-bit phase refers to updating the pre-calibration pulse group based on the amplitude parameters of the qubit pair and the tunable coupler in the high-fidelity global parameter set to obtain a high-fidelity pulse group; performing quantum gate operations on the qubit pair using the high-fidelity pulse group, and combining the compensation parameter group in the high-fidelity global parameter set to perform virtual Z-gate software compensation for the residual single-bit phase, thereby obtaining a high-fidelity quantum gate.

[0051] Example 2: This invention discloses a system for implementing a high-fidelity two-qubit quantum gate. The system includes a pulse construction module, an amplitude correction module, a logic calibration module, a global optimization module, and a gate operation module, wherein: The pulse construction module generates a quantum-gated pulse group based on the pre-modified coupler flux bias pulse and the frequency adjustment pulse of the quantum bit pair, and performs waveform smoothing and buffer compensation on the quantum-gated pulse group to obtain a compensated pulse group. The amplitude correction module configures the excited quantum state and frequency detuning of the qubit pair respectively. Based on the minimum state leakage optimization method, it extracts the target amplitude parameter of the compensation pulse group according to the qubit pair and updates the compensation pulse group according to the target amplitude parameter to obtain a low leakage pulse group. The logic calibration module uses the low-leakage pulse group to trigger the non-adiabatic interaction between the qubit pairs, extracts the phase factor group in the evolution process of the non-adiabatic interaction, and performs single-bit trivial phase compensation on the low-leakage pulse group based on the phase matching condition and the phase factor group to obtain the pre-calibration pulse group. The global optimization module constructs a global optimization parameter set based on the pre-calibrated pulse group, and performs iterative search and global fine-tuning on the global optimization parameter set with the fidelity of the random reference sequence as the objective function to obtain a high-fidelity global parameter set. The gate operation module performs quantum gate operations on the qubit pair based on the high-fidelity global parameter set and performs software compensation on the residual single-bit phase to obtain a high-fidelity quantum gate.

[0052] The processes described above with reference to the flowcharts in the embodiments disclosed in this invention can be implemented as computer software programs. The embodiments disclosed in this invention include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium. When the computer program is executed by a central processing unit (CPU), it performs the functions defined in the methods of this application. It should be noted that the computer-readable medium described above in this application can be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wire segments, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to: wireless segments, wire segments, optical fibers, RF, etc., or any suitable combination thereof.

[0053] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0054] Those skilled in the art should understand that the embodiments of the present invention described above and shown in the accompanying drawings are merely examples and do not limit the present invention. The purpose of the present invention has been fully and effectively achieved. The functions and structural principles of the present invention have been shown and explained in the embodiments. Without departing from the stated principles, the implementation of the present invention may have any variations or modifications.

Claims

1. A method for realizing a high-fidelity two-qubit quantum gate, characterized in that, The method includes: A quantum-gated pulse group is generated based on a pre-modified coupler flux bias pulse and a frequency adjustment pulse for the quantum bit pair. The quantum-gated pulse group is then smoothed and buffer period compensated to obtain a compensated pulse group. The quantum bit pairs are configured with excited quantum states and frequency detuning respectively. The target amplitude parameters of the compensation pulse group are extracted based on the quantum bit pairs using a minimum state leakage optimization method. The compensation pulse group is then updated based on the target amplitude parameters to obtain a low leakage pulse group. The low-leakage pulse group is used to trigger the non-adiabatic interaction between the qubit pairs, and the phase factor group in the evolution process of the non-adiabatic interaction is extracted. Based on the phase matching condition and the phase factor group, single-bit trivial phase compensation is performed on the low-leakage pulse group to obtain the pre-calibrated pulse group. A global optimization parameter set is constructed based on the pre-calibrated pulse set. The global optimization parameter set is iteratively searched and fine-tuned globally with the fidelity of the random reference sequence as the objective function to obtain a high-fidelity global parameter set. Based on the high-fidelity global parameter set, quantum gate operations are performed on the qubit pair, and the residual single-bit phase is compensated by software to obtain a high-fidelity quantum gate.

2. The method for realizing a high-fidelity two-qubit quantum gate according to claim 1, characterized in that, A quantum-gated pulse group is generated based on a pre-modified coupler flux bias pulse and a frequency adjustment pulse for the qubit pair, including: The adjustable coupler is modified by a square wave with sinusoidal modification to obtain the coupler flux bias pulse. The frequency adjustment pulse of the quantum bit pair is defined based on the time reference of the coupler magnetic flux bias pulse; A quantum-gated pulse group is generated based on the coupler flux bias pulse and the frequency adjustment pulse.

3. The method for realizing a high-fidelity two-qubit quantum gate according to claim 1, characterized in that, The quantum-gated pulse group is smoothed and buffer period compensated to obtain a compensated pulse group, including: Based on the bandwidth limitation of the tunable coupler and the anharmonicity of the qubit pair, the standard deviation parameter and effective range of the Gaussian filter are determined, and the Gaussian kernel parameter is obtained. Based on the Gaussian kernel parameters, the quantum-gated pulse group is subjected to Gaussian smoothing filtering to obtain a smooth pulse group; The waveform tail duration introduced by the convolution effect after Gaussian smoothing filtering of the smoothed pulse group is calculated based on the attenuation characteristics of the Gaussian kernel parameter under the preset truncation error. Fill the waiting bits corresponding to the waveform tail duration at both ends of the smooth pulse group to obtain the envelope pulse group; The envelope pulse group is time-series marked and integrated to obtain the compensation pulse group.

4. The method for realizing a high-fidelity two-qubit quantum gate according to claim 1, characterized in that, The excited quantum state configuration and frequency detuning configuration of the qubit pairs are performed respectively, including: The qubit pair is reset to the ground state, and each qubit in the qubit pair is excited to the first excited state; Obtain the initial operating frequency of the quantum bit pair, and calculate the frequency offset corresponding to the initial operating frequency based on the preset operating frequency point; The operating frequency of the qubit pair is tuned to the operating frequency point according to the frequency offset.

5. The method for realizing a high-fidelity two-qubit quantum gate according to claim 4, characterized in that, Before calculating the frequency offset corresponding to the initial operating frequency based on the preset operating frequency point, the method further includes: The transition frequencies of each qubit pair from the ground state to the first excited state and from the first excited state to the second excited state are measured to obtain a set of transition frequencies, and the Hamiltonian model of the qubit pair is established based on the set of transition frequencies. The operating frequency parameter space of the qubit pair is determined based on the Hamiltonian model and the adjustable frequency range of the adjustable coupler. The working frequency parameter space is scanned to obtain the energy difference between the first excited state and the second excited state of the quantum bit pair as a function of the working frequency parameter. The coherent resonance trajectory corresponding to the energy level degeneracy is identified based on the energy difference-frequency relationship. On the coherent resonance trajectory, coordinate points with effective coupling strength greater than a preset strength threshold and without parasitic energy level crossover are selected as operating frequency points.

6. The method for realizing a high-fidelity two-qubit quantum gate according to claim 5, characterized in that, The method based on minimum-state leakage optimization extracts the target amplitude parameters of the compensation pulse group according to the qubit pair, including: The initial amplitude parameter is determined based on the frequency-flux mapping relationship between the operating frequency point and the adjustable coupler, and the amplitude parameter range is configured with the initial amplitude parameter as the midpoint. Amplitude parameters within the range of amplitude parameters are selected one by one, and the compensation pulse group is updated using the amplitude parameters to obtain the updated compensation pulse group; The qubit pair is coherently evolved using the update compensation pulse group, and the state of the coherently evolved qubit pair is measured to obtain the occupancy probability of the first excited state; The occupancy probabilities of the first excited state corresponding to all amplitude parameters within the amplitude parameter range are aggregated into an occupancy probability set, and the maximum value in the occupancy probability set is selected as the target occupancy probability. The amplitude parameter corresponding to the target occupancy probability is used as the target amplitude parameter.

7. The method for realizing a high-fidelity two-qubit quantum gate according to claim 1, characterized in that, The phase factor set in the non-adiabatic interaction evolution process was extracted, including: Three initial computational ground states are set for the qubit pair respectively, and the reference interference fringe phase groups corresponding to the three initial computational ground states are obtained without applying the low leakage pulse group. The three initial computational ground states include the 01 state, the 10 state, and the 11 state. Apply to one of the qubits in the qubit pair / 2 pulses are used to obtain qubits in a coherent superposition state, and the low-leakage pulse group is applied to the qubits in the coherent superposition state to obtain qubits in an evolved quantum state; Apply to the qubits of the evolved quantum state / 2 pulses are used to obtain the qubit of the measurement state, and the occupancy probability of the excited state of the qubit of the measurement state in the computing basis is measured to obtain the oscillating interference fringe phase group corresponding to the occupancy probability of the excited state. The phase factor set in the non-adiabatic interaction evolution process is extracted based on the phase difference between the oscillating interference fringe phase set and the initial interference fringe phase set.

8. The method for realizing a high-fidelity two-qubit quantum gate according to claim 1, characterized in that, Based on the phase matching condition and the phase factor set, single-bit trivial phase compensation is performed on the low-leakage pulse group to obtain a pre-calibrated pulse group, including: The phase offset corresponding to the phase factor group is calculated based on the phase matching condition; The phase offset is allocated to each qubit of the qubit pair to obtain a first phase compensation amount and a second phase compensation amount; A virtual Z-gate compensation operator is constructed based on the first phase compensation amount and the second phase compensation amount to obtain a set of compensation parameters. A virtual Z-gate compensation instruction is generated based on the compensation parameter set, and the low-leakage pulse set is bound to the virtual Z-gate compensation instruction to obtain a pre-calibration pulse set.

9. A method for realizing a high-fidelity two-qubit quantum gate according to claim 8, characterized in that, Using the fidelity of the random benchmark sequence as the objective function, the global optimization parameter set is iteratively searched and fine-tuned globally to obtain a high-fidelity global parameter set, including: The global optimization parameter set is compiled into a global optimization parameter vector, and a random reference sequence is constructed based on the pre-calibrated pulse set; An objective function is constructed based on the fidelity of the random benchmark sequence, and an initial simplex is constructed with the global optimization parameter vector as the center. The fidelity of each vertex in the initial simplex is calculated based on the objective function, and the fidelities are sorted from high to low according to their numerical values ​​to obtain a fidelity sequence. The last fidelity in the fidelity sequence is taken as the worst fidelity, and the vertex corresponding to the worst fidelity in the initial simplex is taken as the worst vertex; the first fidelity in the fidelity sequence is taken as the best fidelity, and the vertex corresponding to the best fidelity in the initial simplex is taken as the best vertex. Calculate the geometric center of each vertex of the initial simplex except for the worst vertex to obtain the simplex centroid. Perform symmetrical reflection of the worst vertex about the simplex centroid to obtain the reflection vertex. Calculate the fidelity of the reflection vertex using the objective function as the reflection fidelity. The initial simplex is updated based on the reflection fidelity to obtain an updated simplex, and the distance from each vertex in the updated simplex to the optimal vertex is calculated to obtain a set of vertex distances. The vertex distance with the largest value in the vertex distance group is selected as the target vertex distance, and it is determined whether the target vertex distance is greater than a preset distance threshold. If so, the updated simplex is used to replace the initial simplex, and the step of calculating the fidelity of each vertex in the initial simplex according to the objective function is returned; If not, then the updated simplex is optimized by parameter mapping to obtain a high-fidelity global parameter set.

10. A system for realizing a high-fidelity two-qubit quantum gate, characterized in that, The system includes a pulse construction module, an amplitude correction module, a logic calibration module, a global optimization module, and a gate operation module, wherein: The pulse construction module generates a quantum-gated pulse group based on the pre-modified coupler flux bias pulse and the frequency adjustment pulse of the quantum bit pair, and performs waveform smoothing and buffer compensation on the quantum-gated pulse group to obtain a compensated pulse group. The amplitude correction module performs excited quantum state configuration and frequency detuning configuration on the qubit pair respectively. Based on the minimum state leakage optimization method, it extracts the target amplitude parameter of the compensation pulse group according to the qubit pair and updates the compensation pulse group according to the target amplitude parameter to obtain a low leakage pulse group. The logic calibration module uses the low-leakage pulse group to trigger the non-adiabatic interaction between the qubit pairs, extracts the phase factor group in the evolution process of the non-adiabatic interaction, and performs single-bit trivial phase compensation on the low-leakage pulse group based on the phase matching condition and the phase factor group to obtain the pre-calibration pulse group. The global optimization module constructs a global optimization parameter set based on the pre-calibrated pulse group, and performs iterative search and global fine-tuning on the global optimization parameter set with the fidelity of the random reference sequence as the objective function to obtain a high-fidelity global parameter set. The gate operation module performs quantum gate operations on the qubit pair based on the high-fidelity global parameter set and performs software compensation on the residual single-bit phase to obtain a high-fidelity quantum gate.

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