Radio frequency field inhomogeneity analysis method and related equipment for quantum computing

Abstract

The present application discloses a method for analyzing radio frequency field inhomogeneity for quantum computing and related equipment, and belongs to the field of quantum computing. The present application obtains the Rabi oscillation signal of the sample to be tested in a preset radio frequency field; performs spectrum analysis on the Rabi oscillation signal to obtain the spectrum components of the Rabi oscillation signal; obtains the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal; calculates the robust control pulse based on the intensity distribution of the radio frequency field and the preset GRAPE algorithm, wherein the robust control pulse is a radio frequency field used to control the nuclear spin quantum state in the sample to be tested. The technical solution of the present application enables the nuclear spin quantum state in the sample to be tested to be correctly controlled when the radio frequency field intensity is uneven, thereby improving the robustness of the control pulse in quantum computing to the uneven radio frequency field.

Description

Technical Field

[0001] The present application belongs to the field of quantum computing, and specifically relates to a method, device, computer equipment and computer-readable storage medium for analyzing radio frequency field inhomogeneity for quantum computing. Background Art

[0002] The nuclear magnetic resonance quantum computer controls the operation of nuclear spins by emitting radio frequency pulses that resonate with nuclear spins through a solenoid coil wrapped around the sample tube. Usually, there are Avogadro's constant number of nuclear spins in the liquid nuclear magnetic resonance sample, and the signal read out by the nuclear magnetic resonance quantum computer comes from the sum of the signals of these nuclear spins. Generally speaking, the nuclear spins in the sample need to remain consistent during the control process. However, since the distribution of radio frequency intensity in the solenoid is not absolutely uniform, the nuclear spins at different spatial positions in the sample tube feel different control pulse intensities, which ultimately affects the control accuracy of quantum computing.

[0003] In existing nuclear magnetic resonance quantum computing, when using GRAPE (Gradient Ascent Pulse Engineering, J. Magn. Reason. 2005 172 (2): 296-305.) to optimize the control design of radio frequency pulses, the robustness of the control pulse to the radio frequency field inhomogeneity is usually considered. By setting the radio frequency field inhomogeneity coefficient, the control pulse that is robust to the radio frequency field inhomogeneity can be calculated in the gradient descent algorithm. However, since it is difficult to directly measure the radio frequency field strength in the coil, the radio frequency field inhomogeneity coefficient in the GRAPE algorithm is generally set subjectively and cannot achieve the best robustness to the actual inhomogeneity of the radio frequency field. Summary of the invention

[0004] The purpose of the embodiments of the present application is to propose a method, device, computer equipment and storage medium for analyzing the inhomogeneity of the radio frequency field for quantum computing. It is difficult to directly measure the radio frequency field strength in the coil in existing nuclear magnetic resonance quantum computing, so the inhomogeneity coefficient of the radio frequency field in the GRAPE algorithm is generally set subjectively, and it cannot achieve the best robust effect on the actual inhomogeneity of the radio frequency field.

[0005] In order to solve the above technical problems, the embodiment of the present application provides a method for analyzing radio frequency field inhomogeneity for quantum computing, which adopts the following technical solution:

[0006] A method for analyzing radio frequency field inhomogeneity for quantum computing, comprising:

[0007] Obtaining a Rabi oscillation signal of a sample to be tested in a preset radio frequency field;

[0008] Performing spectrum analysis on the Rabi oscillation signal to obtain spectrum components of the Rabi oscillation signal;

[0009] Acquiring the intensity distribution of the radio frequency field from the frequency spectrum components of the Rabi oscillation signal;

[0010] A robust control pulse is calculated based on the intensity distribution of the radio frequency field and a preset GRAPE algorithm, wherein the robust control pulse is a radio frequency field used to control the quantum state of nuclear spins in the sample to be tested.

[0011] Furthermore, the step of obtaining the Rabi oscillation signal of the sample to be tested in a preset radio frequency field specifically includes:

[0012] Measuring the free induction decay signal of the sample to be tested;

[0013] Determining the projection sizes of all nuclear spin quantum states in the sample to be tested on a preset projection plane based on the free induction decay signal of the sample to be tested;

[0014] A Rabi oscillation signal of the sample to be tested in a preset radio frequency field is determined based on the projection size.

[0015] Furthermore, the step of performing spectrum analysis on the Rabi oscillation signal to obtain spectrum components of the Rabi oscillation signal specifically includes:

[0016] Performing discrete Fourier transform on the Rabi oscillation signal to obtain frequency spectrum components of the Rabi oscillation signal; or

[0017] The Rabi oscillation signal is fitted in the form of a sine function and a sine function, so as to obtain the frequency spectrum component of the Rabi oscillation signal.

[0018] Further, a discrete Fourier transform is performed on the Rabi oscillation signal based on the following formula:

[0019]

[0020] Where N is the number of sampling points, x j is the strength of the Rabi oscillation signal at the jth sampling point, y k is the frequency of the Rabi oscillation signal e 2πijk / The content of the ingredients.

[0021] Furthermore, the horizontal axis of the discrete Fourier transform result is the frequency component of the Rabi oscillation signal, and the vertical axis of the discrete Fourier transform result is the frequency magnitude of each frequency component in the Rabi oscillation signal. The step of obtaining the intensity distribution of the radio frequency field from the spectrum component of the Rabi oscillation signal specifically includes:

[0022] Determine the frequency components in the Rabi oscillation signal and the frequency magnitude of each frequency component from the discrete Fourier transform result;

[0023] The intensity distribution of the radio frequency field is determined based on the frequency components and the frequency magnitudes of the various frequency components.

[0024] Furthermore, the Rabi oscillation signal is fitted based on the following formula:

[0025] f(x)=∑ i a i sin(b i x+c i )

[0026] Where f(x) is the sum of the sine functions of the Rabi oscillation signal, i is the number of sine functions used, and a is i is the proportion of frequency components, b i is the frequency, c i is the phase size.

[0027] Furthermore, the step of obtaining the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal specifically includes:

[0028] Determine the frequency components in the Rabi oscillation signal and the frequency magnitude of each frequency component from the sine function fitting result;

[0029] The intensity distribution of the radio frequency field is determined based on the frequency components and the frequency magnitudes of the various frequency components.

[0030] Furthermore, the step of calculating the robust control pulse based on the intensity distribution of the radio frequency field and a preset GRAPE algorithm specifically includes:

[0031] Acquire a bias value of an uneven distribution of the radio frequency field from the intensity distribution of the radio frequency field;

[0032] adding the bias value to the Hamiltonian of the radio frequency field;

[0033] The GRAPE algorithm is used to find the optimal parameters of the radio frequency field in the non-uniform state in the biased parameter space to obtain the robust control pulse.

[0034] In order to solve the above technical problems, the embodiment of the present application further provides a radio frequency field inhomogeneity analysis device for quantum computing, which adopts the following technical solution:

[0035] A radio frequency field inhomogeneity analysis device for quantum computing, comprising:

[0036] A Rabi oscillation module is used to obtain a Rabi oscillation signal of a sample to be tested in a preset radio frequency field;

[0037] A spectrum analysis module, used for performing spectrum analysis on the Rabi oscillation signal to obtain spectrum components of the Rabi oscillation signal;

[0038] An intensity distribution module, used for obtaining the intensity distribution of the radio frequency field from the frequency spectrum components of the Rabi oscillation signal;

[0039] A robust control module is used to calculate the robust control pulse of the radio frequency field based on the intensity distribution of the radio frequency field and a preset GRAPE algorithm, wherein the robust control pulse is a radio frequency field used to control the nuclear spin quantum state in the sample to be tested.

[0040] In order to solve the above technical problems, the embodiment of the present application further provides a computer device, which adopts the following technical solution:

[0041] A computer device, wherein the computer device is a quantum computer, the quantum computer comprises a memory, a classical processor and a quantum processor, the memory stores computer-readable instructions, and when the quantum computer executes the computer-readable instructions, the steps of the radio frequency field inhomogeneity analysis method for quantum computing as described above are implemented.

[0042] In order to solve the above technical problems, the embodiment of the present application further provides a computer-readable storage medium, which adopts the following technical solution:

[0043] A computer-readable storage medium stores computer-readable instructions, which, when executed by a quantum computer, implement the steps of the radio frequency field inhomogeneity analysis method for quantum computing as described above.

[0044] Compared with the prior art, the embodiments of the present application have the following beneficial effects:

[0045] The present application discloses a method for analyzing radio frequency field inhomogeneity for quantum computing and related equipment, and belongs to the field of quantum computing. The present application obtains the Rabi oscillation signal of the sample to be tested in a preset radio frequency field, performs spectrum analysis on the Rabi oscillation signal, obtains the spectrum components of the Rabi oscillation signal, obtains the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal, and calculates the robust control pulse based on the intensity distribution of the radio frequency field and the preset GRAPE algorithm, wherein the robust control pulse is the radio frequency field used to control the nuclear spin quantum state in the sample to be tested. The present application first analyzes the inhomogeneity of the coil radio frequency field through the Rabi oscillation signal, and then uses the GRAPE algorithm to optimize the parameters of the radio frequency field to find a set of optimal radio frequency field parameters, so that the nuclear spin quantum state in the sample to be tested can still be correctly controlled when the radio frequency field intensity is uneven, thereby improving the robustness of the control pulse to the radio frequency field inhomogeneity in quantum computing. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the scheme in the present application, a brief introduction is given below to the drawings required for use in the description of the embodiments of the present application. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0047] Figure 1 A diagram of the solenoid field strength distribution is shown;

[0048] Figure 2 A flow chart showing an embodiment of a method for analyzing radio frequency field inhomogeneity for quantum computing according to the present application is shown;

[0049] Figure 3 A schematic diagram of the projection of the sample nuclear spin quantum state on the XY plane is shown in this application;

[0050] Figure 4 A schematic diagram showing a sample and a radio frequency coil portion of a nuclear magnetic resonance quantum computer of the present application;

[0051] Figure 5 A schematic diagram showing the attenuation of the Rabi oscillation signal of the present application in a radio frequency field;

[0052] Figure 6 A schematic diagram showing the Fourier analysis result of a Rabi oscillation signal according to the radio frequency field inhomogeneity analysis method for quantum computing according to the present application is shown;

[0053] Figure 7 A schematic diagram showing the result of fitting the Rabi oscillation signal in the form of a sine sum function according to the radio frequency field inhomogeneity analysis method for quantum computing of the present application;

[0054] Figure 8 A schematic structural diagram of an embodiment of a radio frequency field inhomogeneity analysis device for quantum computing according to the present application is shown;

[0055] Fig. 9 A schematic structural diagram of an embodiment of a computer device according to the present application is shown. DETAILED DESCRIPTION

[0056] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by technicians in the technical field of the present application; the terms used in the specification of the application herein are only for the purpose of describing specific embodiments and are not intended to limit the present application; the terms "including" and "having" and any variations thereof in the specification and claims of the present application and the above-mentioned drawings are intended to cover non-exclusive inclusions. The terms "first", "second", etc. in the specification and claims of the present application or the above-mentioned drawings are used to distinguish different objects, not to describe a specific order.

[0057] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0058] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings.

[0059] Please refer to Figure 1 , Figure 1 is the solenoid field strength distribution diagram, from Figure 1 It can be seen that the field strength distribution inside the solenoid is relatively uniform, the field strength is stronger near the end of the solenoid, and the field strength outside the solenoid drops significantly, which causes the radio frequency field strength received by the part of the sample liquid column outside the coil to not reach the expected strength, and the behavior of the nuclear spins (quantum bits) in the sample under the control pulse is inconsistent. Therefore, when reading out the signal, the polarization of the nuclear spin ensemble will decrease, and the readout signal will decrease in intensity to a certain extent and phase distortion will occur. The most intuitive manifestation of the readout signal being affected is that the signal intensity of the Rabi oscillation experiment has significantly decayed in a time much shorter than the decoherence.

[0060] If you want to use the GRAPE algorithm to calculate an RF field that is robust to RF field inhomogeneity, you need to know the intensity distribution of the RF field in space, which is difficult to measure directly. The purpose of this application is to use a simple Rabi oscillation experiment in nuclear magnetic resonance quantum computing to indirectly obtain the distribution of RF field intensity, so as to use the GRAPE algorithm to calculate a more robust RF control pulse.

[0061] To solve the above technical problems, please refer to Figure 2 , the present application discloses a method for analyzing radio frequency field inhomogeneity for quantum computing, comprising the following steps:

[0062] S201, obtaining a Rabi oscillation signal of a sample to be tested in a preset radio frequency field.

[0063] Among them, Rabi oscillation refers to the fact that when a spin is continuously excited by a radio frequency field that matches the frequency of its energy level difference, the spin quantum state will repeatedly transition between the |0> and |1> energy levels at a certain frequency, and the frequency of Rabi oscillation depends on the intensity of the radio frequency field that excites the spin. In nuclear magnetic resonance quantum computing, the Hamiltonian of the radio frequency field emitted from the y-axis can be simply written as: in, is the reduced Planck constant, γ is the gyromagnetic ratio of the nuclear spin, B rf is the RF field strength, is the spin operator. At this time, the Rabi oscillation can be concretely regarded as the nuclear spin quantum state rotating around the y-axis on the Bloch sphere, please refer to Figure 3 , NMR can obtain the average projection size of all nuclear spin quantum states in the sample in the XY plane by measuring the free induction decay signal of the sample ensemble. During the Rabi oscillation process, the X-axis projection size of the quantum state oscillates in the form of a sine function, which means that the quantum state absorbs the radio frequency field and repeatedly transitions between the |0> and |1> energy levels.

[0064] Specifically, the Rabi oscillation signal of the sample to be tested in a preset radio frequency field is measured by a nuclear magnetic resonance quantum computer. For example, please refer to Figure 4 , Figure 4 This is a schematic diagram of the sample and radio frequency coil part of the nuclear magnetic resonance quantum computer, which is used to measure the Rabi oscillation signal of the sample in a preset radio frequency field. The compound sample of the quantum bit is placed in a transparent glass tube, and the glass tube is placed in a coil that emits radio frequency control pulses. The radio frequency field emitted by the coil is used to control all nuclear spins (i.e., quantum bits) in the glass tube. The read signal is also the sum of the signals of all nuclear spins in the glass tube. In order to enhance the intensity of the nuclear magnetic resonance signal, the volume of the sample liquid column in the glass tube is required to be as large as possible. At the same time, due to the limitation of the uniform field conditions, the number of windings of the radio frequency coil cannot be too many, and the length of the sample liquid column is generally greater than the length of the solenoid.

[0065] Furthermore, the step of obtaining the Rabi oscillation signal of the sample to be tested in a preset radio frequency field specifically includes:

[0066] Measuring the free induction decay signal of the sample to be tested;

[0067] Determine the projection size of all nuclear spin quantum states in the sample to be tested on a preset projection plane based on the free induction decay signal of the sample to be tested;

[0068] The Rabi oscillation signal of the sample to be tested in a preset radio frequency field is determined based on the projection size.

[0069] Specifically, a nuclear magnetic resonance quantum computer is used to measure the free induction decay signal of the sample to be tested under the action of a preset radio frequency field of different durations, and the average projection size of all nuclear spin quantum states in the sample to be tested on a preset projection plane is determined based on the free induction decay signal of the sample to be tested. The preset projection plane is an XY plane, and the average projection size of all nuclear spin quantum states on the preset projection plane is the Rabi oscillation signal of the sample to be tested in the preset radio frequency field.

[0070] S202, performing spectrum analysis on the Rabi oscillation signal to obtain spectrum components of the Rabi oscillation signal.

[0071] In NMR quantum computing, the signal of Rabi oscillation is the ensemble average signal. If all nuclear spins in the sample experience the same radio frequency field intensity, then the signal decay of Rabi oscillation depends on the decoherence time of the sample itself. Please refer to Figure 5 ,from Figure 5 It can be seen that a hard pulse lasting hundreds of microseconds will cause the Rabi signal to attenuate significantly, and this time scale is much smaller than the decoherence time of the sample. This shows that the radio frequency field intensity felt by the nuclear spins in the sample is not consistent, which leads to a decrease in the polarization of the sample ensemble. The Rabi signal at this time is actually the superposition of many Rabi signals with different frequencies, and Rabi signals of different frequencies correspond to the different radio frequency field intensities felt by the nuclear spins in the sample.

[0072] Specifically, the spectrum of the Rabi oscillation signal is analyzed to obtain the spectrum components of the Rabi oscillation signal. In a specific embodiment of the present application, the spectrum of the Rabi oscillation signal can be analyzed by Fourier transform or the form of sine function sum to obtain the spectrum components of the Rabi oscillation signal.

[0073] Furthermore, the step of performing spectrum analysis on the Rabi oscillation signal to obtain spectrum components of the Rabi oscillation signal specifically includes:

[0074] Performing discrete Fourier transform on the Rabi oscillation signal to obtain the frequency spectrum components of the Rabi oscillation signal; or

[0075] The Rabi oscillation signal is fitted in the form of a sine function and the frequency spectrum component of the Rabi oscillation signal is obtained.

[0076] Specifically, in the present application, the spectrum analysis of the Rabi oscillation signal can be performed by two methods, namely, by performing discrete Fourier transform on the Rabi oscillation signal to obtain the spectrum components of the Rabi oscillation signal, or by fitting the Rabi oscillation signal in the form of a sum of sine functions to obtain the spectrum components of the Rabi oscillation signal.

[0077] Furthermore, the Rabi oscillation signal is subjected to discrete Fourier transform based on the following formula:

[0078]

[0079] Where N is the number of sampling points, x j is the strength of the Rabi oscillation signal at the jth sampling point, y k is the frequency of the Rabi oscillation signal e 2πijk / N The content of the ingredients.

[0080] In one embodiment of the present application, the Rabi signal strength x j Perform discrete Fourier transform and obtain the frequency domain component of the Rabi oscillation signal containing e 2πijk / N The content of the ingredient is y k , whose frequency is e 2πijk / N Please refer to Figure 6 , Figure 6 This is the Fourier analysis result of the Rabi oscillation signal. The horizontal axis is the frequency of the signal component, and the vertical axis is the content of each frequency component. It can be seen that the signal has a certain broadening in the frequency domain, which means that the nuclear spins in the sample are indeed doing Rabi oscillations of different frequencies under the drive of radio frequency fields of different intensities. The characteristic of the spectrum diagram is that around a central frequency with the largest proportion, the high-frequency part is quickly cut off, and the low-frequency part has more components. This feature is consistent with the field strength distribution of the solenoid, that is, the field strength distribution in most of the space inside the solenoid is relatively uniform, the field strength in a small part of the space close to the solenoid port is stronger, and the field strength outside the solenoid drops significantly.

[0081] Furthermore, the Rabi oscillation signal is fitted based on the following formula:

[0082] f(x)=∑ i a i sin(b i x+c i )

[0083] Where f(x) is the sum of the sine functions of the Rabi oscillation signal, i is the number of sine functions used, and a is i is the proportion of frequency components, b i is the frequency, c i is the phase size.

[0084] In another embodiment of the present application, since Fourier analysis is required for the Rabi signal, sufficient sampling point experiments need to be performed. If the Rabi oscillation experiment is not to be too cumbersome, the present application provides another method for spectrum analysis of the Rabi oscillation signal. In the case of not having so many sampling points, the function form of multiple sine sums f(x)=∑ i a i sin(b i x+c i ) fits the Rabi oscillation signal, and finally obtains the proportion of each frequency component a from the fitting functioni And the frequency b i , phase size c i , the spectrum components of the Rabi oscillation signal can also be obtained. Please refer to Figure 7 , Figure 7 This is the experimental result obtained by fitting the Rabi oscillation signal in a specific embodiment of the present application through the function form of the sine sum. Figure 7 It can be seen that the frequency components obtained by fitting are also less high-frequency and more low-frequency, which is consistent with the results of Fourier analysis.

[0085] S203, obtaining the intensity distribution of the radio frequency field from the frequency spectrum components of the Rabi oscillation signal.

[0086] Furthermore, the horizontal axis of the discrete Fourier transform result is the frequency component of the Rabi oscillation signal, and the vertical axis of the discrete Fourier transform result is the frequency magnitude of each frequency component in the Rabi oscillation signal. The step of obtaining the intensity distribution of the radio frequency field from the spectrum component of the Rabi oscillation signal specifically includes:

[0087] Determine the frequency components in the Rabi oscillation signal and the frequency magnitude of each frequency component from the discrete Fourier transform result;

[0088] The intensity distribution of the radio frequency field is determined based on the frequency components and the frequency magnitude of each frequency component.

[0089] Specifically, the horizontal axis of the discrete Fourier transform result is set to the frequency component of the Rabi oscillation signal, and the vertical axis of the discrete Fourier transform result is set to the frequency magnitude of each frequency component in the Rabi oscillation signal. The frequency components in the Rabi oscillation signal and the frequency magnitude of each frequency component, the frequency components and the frequency of each frequency component, that is, the intensity distribution of the radio frequency field are determined from the discrete Fourier transform result.

[0090] Please continue to refer to Figure 6 The frequency of the highest peak can be directly obtained from the coordinates of the frequency components of the discrete Fourier transform results. This frequency is the precession frequency of the nuclear spin under the original pulse intensity emitted by the coil. The peak value is the proportion of nuclear spins that feel the RF field of this intensity. The ratio of the RF field intensity and number felt by other nuclear spins in the sample can be obtained through the ratio of the horizontal and vertical coordinates.

[0091] Furthermore, the step of obtaining the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal specifically includes:

[0092] Determine the frequency components in the Rabi oscillation signal and the frequency magnitude of each frequency component from the sine function fitting result;

[0093] The intensity distribution of the radio frequency field is determined based on the frequency components and the frequency magnitudes of the individual frequency components.

[0094] Specifically, the frequency components in the Rabi oscillation signal and the frequency magnitudes of the frequency components are determined from the sinusoidal function fitting result. The frequency components and the frequencies of the frequency components are the intensity distribution of the radio frequency field.

[0095] Please continue to refer to Figure 7 , the different intensities of the RF field in the sample and the proportion of the number of nuclear spins affected can be directly obtained from the amplitude and frequency of the fitted sinusoidal components. In comparison, the RF field intensity distribution obtained by the Fourier analysis method is more accurate and complete, while the sine sum function fitting method is relatively simple and only the main components of the RF field intensity are obtained.

[0096] S204, calculating a robust control pulse based on the intensity distribution of the radio frequency field and a preset GRAPE algorithm, wherein the robust control pulse is a radio frequency field used to control the nuclear spin quantum state in the sample to be tested.

[0097] In nuclear magnetic resonance quantum computing, a set of shaped pulses consists of l hard pulses of different intensities with a duration of Δt. The evolution operator of the nuclear spin under the action of each hard pulse can be written as: Among them, H int is the Hamiltonian of the nuclear spin in a static magnetic field, H rf is the Hamiltonian of the nuclear spin in the control radio frequency field, u m It is the strength of each RF field of each channel. Generally speaking, one channel has the strength of two RF fields.

[0098] Furthermore, the step of calculating the robust control pulse based on the intensity distribution of the radio frequency field and the preset GRAPE algorithm specifically includes:

[0099] Obtaining a bias value of an uneven distribution of the radio frequency field from the intensity distribution of the radio frequency field;

[0100] Add a bias value to the Hamiltonian for the RF field;

[0101] The GRAPE algorithm is used to find the optimal parameters of the RF field in the inhomogeneous state in the biased parameter space, and the robust control pulse is obtained.

[0102] Specifically, the GRAPE algorithm uses a computer gradient descent algorithm to find the optimal parameter u in the parameter space. m , so that the fidelity between the unitary operation of the shaped pulse and the unitary operation to be achieved is maximized. In the embodiment of the present application, the uneven distribution of the RF field is obtained by using the above-mentioned Fourier transform or the form of the sum of sine functions, and the bias value of the uneven distribution of the RF field can be obtained from the intensity distribution of the RF field, and then in the RF field Hamiltonian H rfThe corresponding bias value is added to allow the GRAPE algorithm to find the optimal parameter u under the inhomogeneous RF field in the biased parameter space. m , thus a robust control pulse for RF field inhomogeneities can be obtained.

[0103] The present application discloses a method for analyzing radio frequency field inhomogeneity for quantum computing, which belongs to the field of quantum computing. The present application obtains the Rabi oscillation signal of the sample to be tested in a preset radio frequency field, performs spectrum analysis on the Rabi oscillation signal, obtains the spectrum components of the Rabi oscillation signal, obtains the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal, and calculates a robust control pulse based on the intensity distribution of the radio frequency field and a preset GRAPE algorithm, wherein the robust control pulse is a radio frequency field used to control the nuclear spin quantum state in the sample to be tested. The present application first analyzes the inhomogeneity of the coil radio frequency field through the Rabi oscillation signal, and then uses the GRAPE algorithm to optimize the parameters of the radio frequency field to find a set of optimal radio frequency field parameters, so that the nuclear spin quantum state in the sample to be tested can still be correctly controlled when the radio frequency field intensity is uneven, thereby improving the robustness of the control pulse to the radio frequency field inhomogeneity in quantum computing.

[0104] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing related hardware through computer-readable instructions, and the computer-readable instructions can be stored in a computer-readable storage medium. When the computer-readable instructions are executed, they can include the processes of the embodiments of the above-mentioned methods. Among them, the aforementioned storage medium can be a non-volatile storage medium such as a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0105] It should be understood that, although the steps in the flowchart of the accompanying drawings are displayed in sequence as indicated by the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least a part of the steps in the flowchart of the accompanying drawings may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be executed in turn or alternately with other steps or at least a part of the sub-steps or stages of other steps.

[0106] Further references Figure 8 , as a response to the above Figure 2 The present application provides an embodiment of a radio frequency field inhomogeneity analysis device for quantum computing, and the device embodiment is similar to Figure 2Corresponding to the method embodiment shown, the device can be specifically applied to various electronic devices.

[0107] like Figure 8 As shown, the radio frequency field inhomogeneity analysis device 800 for quantum computing described in this embodiment includes:

[0108] A Rabi oscillation module 801 is used to obtain a Rabi oscillation signal of a sample to be tested in a preset radio frequency field;

[0109] The spectrum analysis module 802 is used to perform spectrum analysis on the Rabi oscillation signal to obtain spectrum components of the Rabi oscillation signal;

[0110] The intensity distribution module 803 is used to obtain the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal;

[0111] The robust control module 804 is used to calculate the robust control pulse of the radio frequency field based on the intensity distribution of the radio frequency field and a preset GRAPE algorithm, wherein the robust control pulse is the radio frequency field used to control the nuclear spin quantum state in the sample to be tested.

[0112] Furthermore, the Rabi oscillation module 801 specifically includes:

[0113] A measuring unit, used for measuring a free induction decay signal of a sample to be tested;

[0114] A projection unit, used to determine the projection size of all nuclear spin quantum states in the sample to be tested on a preset projection plane based on the free induction decay signal of the sample to be tested;

[0115] The Rabi oscillation unit is used to determine the Rabi oscillation signal of the sample to be tested in a preset radio frequency field based on the projection size.

[0116] Furthermore, the spectrum analysis module 802 specifically includes:

[0117] A Fourier transform unit, used for performing discrete Fourier transform on the Rabi oscillation signal to obtain the frequency spectrum components of the Rabi oscillation signal; or

[0118] The sine function fitting unit is used to fit the Rabi oscillation signal in the form of a sine function sum to obtain the frequency spectrum component of the Rabi oscillation signal.

[0119] Furthermore, the Rabi oscillation signal is subjected to discrete Fourier transform based on the following formula:

[0120]

[0121] Where N is the number of sampling points, x j is the strength of the Rabi oscillation signal at the jth sampling point, y kis the frequency of the Rabi oscillation signal e 2πijk / N The content of the ingredients.

[0122] Furthermore, the intensity distribution module 803 specifically includes:

[0123] A first result processing unit, used for determining the frequency components in the Rabi oscillation signal and the frequency magnitude of each frequency component from the discrete Fourier transform result;

[0124] The first intensity distribution unit is used to determine the intensity distribution of the radio frequency field based on the frequency components and the frequency magnitudes of the various frequency components.

[0125] Furthermore, the Rabi oscillation signal is fitted based on the following formula:

[0126] f(x)=∑ i a i sin(b i x+c i )

[0127] Where f(x) is the sum of the sine functions of the Rabi oscillation signal, i is the number of sine functions used, and a is i is the proportion of frequency components, b i is the frequency, c i is the phase size.

[0128] Furthermore, the intensity distribution module 803 specifically includes:

[0129] A second result processing unit, used for determining the frequency components in the Rabi oscillation signal and the frequency magnitude of each frequency component from the sine function fitting result;

[0130] The second intensity distribution unit is used to determine the intensity distribution of the radio frequency field based on the frequency components and the frequency magnitudes of the various frequency components.

[0131] Furthermore, the robust control module 804 specifically includes:

[0132] A bias acquisition unit, used to acquire a bias value of the uneven distribution of the radio frequency field from the intensity distribution of the radio frequency field;

[0133] A bias adding unit, used for adding a bias value to the Hamiltonian of the radio frequency field;

[0134] The parameter optimization unit is used to find the optimal parameters of the radio frequency field in the non-uniform state in the biased parameter space by using the GRAPE algorithm to obtain the robust control pulse.

[0135] The present application discloses a radio frequency field inhomogeneity analysis device for quantum computing, which belongs to the field of quantum computing. The present application obtains the Rabi oscillation signal of the sample to be tested in a preset radio frequency field, performs spectrum analysis on the Rabi oscillation signal, obtains the spectrum components of the Rabi oscillation signal, obtains the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal, and calculates the robust control pulse based on the intensity distribution of the radio frequency field and the preset GRAPE algorithm, wherein the robust control pulse is the radio frequency field used to control the nuclear spin quantum state in the sample to be tested. The present application first analyzes the inhomogeneity of the coil radio frequency field through the Rabi oscillation signal, and then uses the GRAPE algorithm to optimize the parameters of the radio frequency field to find a set of optimal radio frequency field parameters, so that the nuclear spin quantum state in the sample to be tested can still be correctly controlled when the radio frequency field intensity is uneven, thereby improving the robustness of the control pulse to the radio frequency field inhomogeneity in quantum computing.

[0136] To solve the above technical problems, the present application also provides a computer device. Fig. 9 , Fig. 9 This is a basic structural block diagram of the computer device in this embodiment.

[0137] The computer device is a quantum computer device, which may include an operating system, a classical processor, a quantum processor, and a memory. The operating system is a manager of hardware resources, and the operating system has a task scheduler that can assign quantum computing tasks to the quantum bits of the quantum processor for execution. The quantum processor has a quantum chip and a measurement and control device, wherein the quantum chip includes multiple physical quantum bits, which are responsible for executing quantum computing tasks; the measurement and control device is used to measure the physical quantum bits to obtain quantum computing results.

[0138] The classical processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip in some embodiments. The classical processor is generally used to control the overall operation of the computer device. In this embodiment, the classical processor is used to run the computer-readable instructions stored in the memory or process data, such as running the computer-readable instructions in the radio frequency field inhomogeneity analysis method for quantum computing.

[0139] Among them, the classical processor can perform the following steps: perform spectrum analysis on the Rabi oscillation signal to obtain the spectrum components of the Rabi oscillation signal; obtain the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal; calculate the robust control pulse based on the intensity distribution of the radio frequency field and the preset GRAPE algorithm; the quantum processor can perform the following steps: obtain the Rabi oscillation signal of the sample to be tested in the preset radio frequency field.

[0140] It should be noted that the figure only shows the basic structure of the quantum computer device, but it should be understood that it is not required to implement all the components shown, and more or fewer components may be implemented instead. For example, the computer device may also include a network interface, which may include a wireless network interface or a wired network interface, and the network interface is generally used to establish a communication connection between the computer device and other electronic devices. Among them, those skilled in the art can understand that the computer device here is a device that can automatically perform numerical calculations and / or information processing according to pre-set or stored instructions, except Figure 6 The structure shown in the figure includes, but is not limited to, a microprocessor, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), an embedded device, etc.

[0141] The memory includes at least one type of readable storage medium, and the readable storage medium includes flash memory, hard disk, multimedia card, card-type memory (for example, SD or DX memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, etc. In some embodiments, the memory can be an internal storage unit of the computer device, such as a hard disk or memory of the computer device. In other embodiments, the memory can also be an external storage device of the computer device, such as a plug-in hard disk equipped on the computer device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. Of course, the memory can also include both the internal storage unit of the computer device and its external storage device. In this embodiment, the memory can be used to store the operating system and various application software installed on the computer device, such as computer-readable instructions for the radio frequency field inhomogeneity analysis method for quantum computing, etc. In addition, the memory can also be used to temporarily store various types of data that have been output or are to be output.

[0142] The computer device provided in this embodiment can execute the above-mentioned radio frequency field inhomogeneity analysis method for quantum computing. The radio frequency field inhomogeneity analysis method for quantum computing here can be the radio frequency field inhomogeneity analysis method for quantum computing of each of the above-mentioned embodiments.

[0143] In this embodiment, the present application discloses a computer device, which belongs to the field of quantum computing. The present application obtains the Rabi oscillation signal of the sample to be tested in a preset radio frequency field, performs spectrum analysis on the Rabi oscillation signal, obtains the spectrum components of the Rabi oscillation signal, obtains the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal, and calculates the robust control pulse based on the intensity distribution of the radio frequency field and the preset GRAPE algorithm, wherein the robust control pulse is the radio frequency field used to control the nuclear spin quantum state in the sample to be tested. The present application first analyzes the inhomogeneity of the coil radio frequency field through the Rabi oscillation signal, and then uses the GRAPE algorithm to optimize the parameters of the radio frequency field to find a set of optimal radio frequency field parameters, so that the nuclear spin quantum state in the sample to be tested can still be correctly controlled when the radio frequency field intensity is uneven, thereby improving the robustness of the control pulse to the inhomogeneity of the radio frequency field in quantum computing.

[0144] The present application also provides another embodiment, namely, providing a computer-readable storage medium, wherein the computer-readable storage medium is a quantum computer-readable storage medium, wherein the computer-readable storage medium stores computer-readable instructions, and the computer-readable instructions can be executed by at least one processor to enable the at least one processor to perform the steps of the above-mentioned radio frequency field inhomogeneity analysis method for quantum computing.

[0145] In this embodiment, the present application discloses a computer-readable storage medium, which belongs to the field of quantum computing. The present application obtains the Rabi oscillation signal of the sample to be tested in a preset radio frequency field, performs spectrum analysis on the Rabi oscillation signal, obtains the spectrum components of the Rabi oscillation signal, obtains the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal, and calculates the robust control pulse based on the intensity distribution of the radio frequency field and the preset GRAPE algorithm, wherein the robust control pulse is the radio frequency field used to control the nuclear spin quantum state in the sample to be tested. The present application first analyzes the inhomogeneity of the coil radio frequency field through the Rabi oscillation signal, and then uses the GRAPE algorithm to optimize the parameters of the radio frequency field to find a set of optimal radio frequency field parameters, so that the nuclear spin quantum state in the sample to be tested can still be correctly controlled when the radio frequency field intensity is uneven, thereby improving the robustness of the control pulse to the inhomogeneity of the radio frequency field in quantum computing.

[0146] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a number of instructions for a terminal device (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in each embodiment of the present application.

[0147] Obviously, the embodiments described above are only some embodiments of the present application, rather than all embodiments. The preferred embodiments of the present application are given in the accompanying drawings, but they do not limit the patent scope of the present application. The present application can be implemented in many different forms. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present application more thorough and comprehensive. Although the present application is described in detail with reference to the aforementioned embodiments, for those skilled in the art, it is still possible to modify the technical solutions recorded in the aforementioned specific implementation methods, or to perform equivalent replacement of some of the technical features therein. Any equivalent structure made using the contents of the specification and drawings of this application, directly or indirectly used in other related technical fields, is similarly within the scope of patent protection of this application.

Claims

1. A method for analyzing radio frequency field inhomogeneity for quantum computing, characterized in that: include: Obtaining a Rabi oscillation signal of a sample to be tested in a preset radio frequency field; Performing spectrum analysis on the Rabi oscillation signal to obtain spectrum components of the Rabi oscillation signal; Acquiring the intensity distribution of the radio frequency field from the frequency spectrum components of the Rabi oscillation signal; A robust control pulse is calculated based on the intensity distribution of the radio frequency field and a preset GRAPE algorithm, wherein the robust control pulse is a radio frequency field used to control the quantum state of nuclear spins in the sample to be tested.

2. The method for analyzing radio frequency field inhomogeneity for quantum computing according to claim 1, characterized in that: The step of obtaining the Rabi oscillation signal of the sample to be tested in a preset radio frequency field specifically includes: Measuring the free induction decay signal of the sample to be tested; Determining the projection sizes of all nuclear spin quantum states in the sample to be tested on a preset projection plane based on the free induction decay signal of the sample to be tested; A Rabi oscillation signal of the sample to be tested in a preset radio frequency field is determined based on the projection size.

3. The method for analyzing radio frequency field inhomogeneity for quantum computing according to claim 1, characterized in that: The step of performing spectrum analysis on the Rabi oscillation signal to obtain spectrum components of the Rabi oscillation signal specifically includes: Performing discrete Fourier transform on the Rabi oscillation signal to obtain frequency spectrum components of the Rabi oscillation signal; or The Rabi oscillation signal is fitted in the form of a sine function and a sine function, so as to obtain the frequency spectrum component of the Rabi oscillation signal.

4. The method for analyzing radio frequency field inhomogeneity for quantum computing according to claim 3, characterized in that: The Rabi oscillation signal is subjected to a discrete Fourier transform based on the following formula: Where N is the number of sampling points, x j is the strength of the Rabi oscillation signal at the jth sampling point, y k is the frequency of the Rabi oscillation signal e 2πijk / The content of the ingredients.

5. The method for analyzing radio frequency field inhomogeneity for quantum computing according to claim 4, characterized in that: The horizontal axis of the discrete Fourier transform result is the frequency component of the Rabi oscillation signal, and the vertical axis of the discrete Fourier transform result is the frequency magnitude of each frequency component in the Rabi oscillation signal. The step of obtaining the intensity distribution of the radio frequency field from the spectrum component of the Rabi oscillation signal specifically includes: Determine the frequency components in the Rabi oscillation signal and the frequency magnitude of each frequency component from the discrete Fourier transform result; The intensity distribution of the radio frequency field is determined based on the frequency components and the frequency magnitudes of the various frequency components.

6. The method for analyzing radio frequency field inhomogeneity for quantum computing according to claim 3, characterized in that: The Rabi oscillation signal is fitted based on the following formula: f(x)=∑ i a i sin(b i x+c i ) Where f(x) is the sum of the sine functions of the Rabi oscillation signal, i is the number of sine functions used, and a is i is the proportion of frequency components, b i is the frequency, c i is the phase size.

7. The method for analyzing radio frequency field inhomogeneity for quantum computing according to claim 6, characterized in that: The step of obtaining the intensity distribution of the radio frequency field from the spectrum components of the Rabi oscillation signal specifically includes: Determine the frequency components in the Rabi oscillation signal and the frequency magnitude of each frequency component from the sine function fitting result; The intensity distribution of the radio frequency field is determined based on the frequency components and the frequency magnitudes of the various frequency components.

8. The method for analyzing radio frequency field inhomogeneity for quantum computing according to any one of claims 1 to 7, characterized in that: The step of calculating the robust control pulse based on the intensity distribution of the radio frequency field and a preset GRAPE algorithm specifically includes: Acquire a bias value of an uneven distribution of the radio frequency field from the intensity distribution of the radio frequency field; adding the bias value to the Hamiltonian of the radio frequency field; The GRAPE algorithm is used to find the optimal parameters of the radio frequency field in the non-uniform state in the biased parameter space to obtain the robust control pulse.

9. A radio frequency field inhomogeneity analysis device for quantum computing, characterized in that: include: A Rabi oscillation module is used to obtain a Rabi oscillation signal of a sample to be tested in a preset radio frequency field; A spectrum analysis module, used for performing spectrum analysis on the Rabi oscillation signal to obtain spectrum components of the Rabi oscillation signal; An intensity distribution module, used for obtaining the intensity distribution of the radio frequency field from the frequency spectrum components of the Rabi oscillation signal; A robust control module is used to calculate the robust control pulse of the radio frequency field based on the intensity distribution of the radio frequency field and a preset GRAPE algorithm, wherein the robust control pulse is a radio frequency field used to control the nuclear spin quantum state in the sample to be tested.

10. A computer device, characterized in that: The computer device is a quantum computer, which includes a memory, a classical processor and a quantum processor. The memory stores computer-readable instructions. When the quantum computer executes the computer-readable instructions, the steps of the radio frequency field inhomogeneity analysis method for quantum computing as described in any one of claims 1 to 8 are implemented.

11. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-readable instructions, which, when executed by a quantum computer, implement the steps of the radio frequency field inhomogeneity analysis method for quantum computing according to any one of claims 1 to 8.

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