Electrode potential calibration method for chip ion trap

Abstract

The invention discloses an electrode potential calibration method for a chip ion trap, and belongs to the technical field of ion trap quantum computation.The method comprises the steps that an electrode voltage value needed by an ion chain moving in the axial direction of the ion trap is calculated based on a simulation model; applying an electrode voltage value to the ion trap, and measuring the ion chain trapping frequency and the balance position of each ion; substituting the electrode voltage value into an external electric field analysis model, and calculating the ion chain trapping frequency and the external electric field intensity of each ion balance position; and constructing a total loss function, and optimizing the external electric field analytical model. According to the technical scheme provided by the invention, the external electric field analytical model containing the stray field is constructed, the preliminary experimental measurement is performed in combination with the simulation data, and the multiple loss functions are constructed on the basis of the experimental data to optimize the electric field analytical model, so that the electrode potential calibration efficiency is improved, and the measurement accuracy is improved. And the calibration precision of the ion trap electrode potential is enhanced.

Description

Technical Field

[0001] The invention relates to the technical field of ion trap quantum computing, and in particular to a method for calibrating electrode potential for a chip ion trap. Background Art

[0002] The chip ion trap is one of the important platforms for quantum information processing and quantum precision measurement. To ensure that the electric field distribution in the chip ion trap meets the requirements of trapping and operation, accurately calibrating the potential distribution of the electrode and its effect on the ion chain is the core link in the design and optimization of the chip ion trap.

[0003] In the prior art, the voltage of the electrodes in the chip ion trap is changed pair by pair, so that the ion chain moves in the ion trap, and the image of the ion chain is collected. The spatial electric field distribution generated by the pair of electrodes under unit voltage is calculated by the interpolation method using the ion force balance condition. The spatial electric field distribution of the entire chip ion trap is calculated by applying voltage to all electrodes pair by pair. However, this method still has shortcomings. First, the electrode voltage is changed pair by pair, and the coupling effect when multiple pairs of electrodes are simultaneously applied with voltage and the change in the ion chain trapping height are not fully considered, which makes it difficult for the calculated electric field distribution to accurately reflect the electric field distribution under actual operation. Secondly, when calculating the spatial electric field by the interpolation method, the spatial resolution and accuracy are limited by the number of ions and the distance between ions, making it difficult to accurately calculate the spatial electric field distribution. Summary of the invention

[0004] Based on this, the technical solution provided by the present invention constructs an external electric field analysis model including stray fields, conducts preliminary experimental measurements in combination with simulation data, and constructs multiple loss functions based on the experimental data to optimize the electric field analysis model. This not only improves the calibration efficiency of the chip ion trap electrode potential, but also enhances the calibration accuracy of the chip ion trap electrode potential.

[0005] In order to achieve the above-mentioned purpose, the present invention provides an electrode potential calibration method for a chip ion trap, comprising the following steps: S1: based on a simulation model, calculating a plurality of groups of electrode voltage values ​​required for the center of the ion chain to move a preset distance along the axial direction of the ion trap; S2: applying the plurality of groups of electrode voltage values ​​to the ion trap, and measuring the ion chain trapping frequency and the equilibrium position of each ion corresponding to each group of electrode voltage values; S3: substituting the plurality of groups of electrode voltage values ​​into an external electric field analytical model, calculating the ion chain trapping frequency and the strength of the external electric field at the equilibrium position of each ion; S4: constructing a total loss function and optimizing the external electric field analytical model.

[0006] Wherein, the external electric field includes an electrode electric field and a stray electric field.

[0007] Furthermore, step S1 specifically includes:

[0008] S11: constructing the simulation model of the chip ion trap;

[0009] S12: applying a unit voltage to each electrode of the simulation model respectively, and solving the spatial distribution of the electric field intensity of each electrode under the unit voltage condition by simulation;

[0010] S13: setting a height variation range of the ion chain center relative to the ion trap surface during movement, and the preset distance;

[0011] S14: According to the height variation range and the preset distance, the plurality of groups of electrode voltage values ​​are set so that the plurality of groups of electrode voltage values ​​satisfy the following relationship:

[0012] ,

[0013] Where N is the total number of electrodes, is the kth electrode voltage value, is the axial direction of the ion trap, is the electric field of the kth electrode Quantity, is the electric field of the kth electrode Quantity, is the electric field of the kth electrode Quantity, are the coordinates of the center of the ion chain, is the vertical distance between the center of the ion chain and the surface of the ion trap, Determined by the altitude variation range.

[0014] Specifically, step S2 includes:

[0015] Measuring the trapped frequency of the ion chain by radio frequency resonance or sideband excitation;

[0016] The ion trap is photographed, and the equilibrium position of each ion in the ion chain and the coordinates of the center of the ion chain are measured by proportionally magnifying the picture.

[0017] Furthermore, step S3 specifically includes:

[0018] S31: Construct the external electric field analytical model to satisfy the relationship:

[0019] ,

[0020] in, is the analytical value of the electric field of the kth electrode, is the analytical value of the stray electric field, is the center coordinate of the kth electrode, , , , , , , are model parameters of the external electric field analytical model.

[0021] S32: Initializing the external electric field analytical model, substituting the plurality of groups of electrode voltage values ​​into the external electric field analytical model respectively, and calculating the ion chain trapping frequency.

[0022] Wherein, the calculation formula of the ion chain trapping frequency is:

[0023] ,

[0024] M is the mass of the ion, e is the charge number of the ion, is the analytical value of the electric field of the kth electrode at coordinates The first derivative of The analytical value of the stray electric field is The first derivative at .

[0025] S33: Substituting the equilibrium position of each ion measured in step S2 into the external electric field analysis model, and calculating the intensity of the external electric field at the equilibrium position of each ion.

[0026] Furthermore, step S4 specifically includes:

[0027] S41: constructing a first loss function as the sum of squares of the errors between the ion chain trapping frequency obtained in step S2 and the ion chain trapping frequency obtained in step S3;

[0028] Constructing a second loss function as the sum of squares of errors between the strength of the external electric field obtained in step S3 and the strength of the external electric field calculated theoretically;

[0029] Constructing a total loss function as a linear superposition of the first loss function and the second loss function;

[0030] S42: minimizing the total loss function using a global optimal method, optimizing the external electric field analytical model, and obtaining optimized values ​​of model parameters of the external electric field analytical model;

[0031] The theoretical calculation formula of the strength of the external electric field is as follows:

[0032] ,

[0033] is the dielectric constant of vacuum, is the equilibrium position of the i-th ion, is the equilibrium position of the jth ion.

[0034] Preferably, the number of ions in the ion chain is greater than 10 and less than or equal to 30.

[0035] The beneficial effects achieved by the present invention through the above technical solution are:

[0036] 1) Based on the simulation model, an analytical model is constructed to calibrate the electrode potential. This not only introduces the influence of stray electric fields, breaks through the calculation limitations of the simulation model, and improves the accuracy of the ion trap electrode potential calibration, but also replaces the simulation model calculation with a simple analytical model, which greatly improves the efficiency of the electrode potential calibration.

[0037] 2) Using simulation model data as a guide, the loss function is constructed through experimental data, which simplifies the analytical model structure and enables the analytical model to converge and optimize quickly.

[0038] 3) The external electric field is calculated through the experimentally measured ion equilibrium position, and the loss function is constructed using the characteristics of force balance at the equilibrium position, which avoids the complexity of theoretical calculation of the ion equilibrium position and improves modeling efficiency.

[0039] 4) The total loss function is constructed by linearly superimposing the loss function related to the trapping frequency and the loss function related to the ion equilibrium position, which weakens the influence of the experimental error of a single physical quantity on the analytical model and further improves the calculation accuracy of the analytical model. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the flow chart of the electrode potential calibration method according to an embodiment of the present invention.

[0041] Figure 2 It is a schematic diagram of the chip ion trap structure of an embodiment of the present invention. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solution and advantages of the present invention more clear, the specific implementation method of the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the embodiments described herein are only used to explain the present invention, but are not used to limit the scope of the present invention.

[0043] Please refer to the attached Figure 1 , Figure 1 : is a schematic flow chart of the electrode potential calibration method according to an embodiment of the present invention. As can be seen from the figure, the steps of the electrode potential calibration method provided by the embodiment of the present invention include:

[0044] S1. Based on the simulation model, calculate several sets of electrode voltage values ​​required for the ion chain center to move a preset distance along the axial direction of the ion trap.

[0045] S2. Apply several groups of electrode voltage values ​​to the ion trap, and measure the ion chain trapping frequency and the equilibrium position of each ion corresponding to each group of electrode voltage values.

[0046] S3. Substituting several groups of electrode voltage values ​​into the external electric field analytical model, calculating the ion chain trapping frequency and the strength of the external electric field at the equilibrium position of each ion, wherein the external electric field includes the electrode electric field and the stray electric field.

[0047] S4. Construct a total loss function and optimize the external electric field analytical model.

[0048] Exemplarily, step S1 specifically includes:

[0049] S11. Construct a simulation model of the chip ion trap. Figure 2 , Figure 2 Schematic diagram of the chip ion trap structure of an embodiment of the present invention. As can be seen from the figure, in the embodiment of the present invention, the axial direction of the ion trap is set to Direction, height is set to Direction, horizontal radial is set to direction. From the simulation, the kth electrode is along , , The electric field distribution functions obtained by interpolating the electric field components in the direction are recorded as , as well as .

[0050] S12, applying a unit voltage to each electrode of the simulation model, respectively, and using the boundary element simulation method to solve the spatial distribution of the electric field intensity of each electrode near the confinement area under the unit voltage condition. After applying a unit voltage to each electrode to be calibrated, the spatial distribution of the electric field component along the height direction and the axial direction of the ion trap is mainly extracted. In the embodiment of the present invention, the simulation model is calculated using the boundary element method.

[0051] S13, setting a height variation range of the ion chain center relative to the ion trap surface during movement, and a preset distance.

[0052] S14. Obtain several groups of electrode voltage values ​​according to the height variation range and the preset distance. In the embodiment of the present invention, the simulation model does not consider the influence of stray fields and is an approximate electric field model. The ion chain includes 10-30 ions, which are arranged in a chain and are approximately located at a height h relative to the ion trap. In order to make the ion chain move a preset distance along the axis of the ion trap in the calibration interval in the ion trap, a boundary condition needs to be given, that is, when the height of the ion trap is h, the change in the z component of the electric field strength is less than a given value. , the x-component and y-component of the electric field intensity are zero. Specifically, the voltage values ​​of several groups of electrodes satisfy the following relationship:

[0053] ,

[0054] Where N is the total number of electrodes, is the kth electrode voltage value, is the axial direction of the ion trap, is the electric field of the kth electrode Quantity, is the electric field of the kth electrode Quantity, is the electric field of the kth electrode Quantity, are the coordinates of the center of the ion chain, is the vertical distance of the ion chain center on the ion trap surface, The height variation range of the ion chain in the ion trap determines the ion chain. In this way, the ion chain can be evenly distributed in the calibration interval when it moves within a predetermined distance, and the voltage variation range of each electrode to be calibrated covers a certain reasonable range, thereby obtaining several groups of electrode voltage values ​​that meet the conditions.

[0055] Illustratively, the electric field distribution of each electrode obtained by simulation in the embodiment of the present invention is used as a preliminary approximation, and the voltage setting for moving ions under the condition of approximately constant ion trapping height is obtained based on this, which can effectively suppress the measurement error caused by the height change during ion movement.

[0056] In particular, step S2 specifically includes: measuring the trapped frequency of the ion chain by radio frequency resonance or sideband excitation. Taking a picture of the ion trap, and measuring the coordinates of the equilibrium position of each ion and the center of the ion chain by proportionally magnifying the picture. In an embodiment of the present invention, the proportional magnification of the picture can use the size of the electrode in the ion trap as a reference for the magnification of the picture.

[0057] Exemplarily, step S3 specifically includes:

[0058] S31, constructing the external electric field analytical model to satisfy the relationship:

[0059] ,

[0060] in, is the analytical value of the electric field of the kth electrode, is the analytical value of the stray electric field, is the center coordinate of the kth electrode.

[0061] The external electric field analytical model has a reasonable number of model parameters, so that the values ​​calculated by the external electric field analytical model can be adjusted to approximate the actual electric field intensity distribution. In the embodiment of the present invention, the model parameters include , , , , , , In the embodiment of the present invention, the electric field distribution and stray field distribution of the electrode are described in a parameter-containing expression manner, and a sparsely arranged ion chain can be used to improve the sensitivity of measuring the electric field without worrying about the influence of interpolation errors.

[0062] S32, initialize the external electric field analytical model, substitute several groups of electrode voltage values ​​into the external electric field analytical model, and calculate the ion chain trapping frequency. In the embodiment of the present invention, the analytical model is initialized by fitting the electric field distribution data obtained by the ion trap boundary element simulation. Specifically, the calculation formula of the ion chain trapping frequency is:

[0063] ,

[0064] Where M is the mass of the ion, is the ionic charge number, is the analytical value of the electric field of the kth electrode at coordinates The first derivative of The analytical value of the stray electric field is The first derivative at .

[0065] S33. Substitute the equilibrium position of each ion measured in step S2 into the external electric field analysis model to calculate the strength of the external electric field at the equilibrium position of each ion.

[0066] Specifically, step S4 is as follows:

[0067] S41, constructing a first loss function as the sum of squares of the errors between the ion chain trapping frequency obtained in step S2 and the ion chain trapping frequency obtained in step S3. Constructing a second loss function as the sum of squares of the errors between the strength of the external electric field obtained in step S3 and the strength of the external electric field calculated theoretically. Constructing a total loss function as the linear superposition of the first loss function and the second loss function.

[0068] Exemplarily, in one or other embodiments of the present invention, the external electric field at each ion equilibrium position is calculated using an external electric field analytical model with applied voltage, and the sum of squares of errors between the external electric field and the Coulomb electric field generated by other ions in the ion chain at the ion equilibrium position is defined as the first loss function. The ion chain trapping frequency is calculated using an external electric field analytical model with applied voltage. The sum of squares of errors between the external electric field and the measured ion chain trapping frequency is defined as the second loss function. Using the superposition principle, the first loss function and the second loss function are added with a certain weight as the total loss function.

[0069] Specifically, under the above-mentioned conditions of several groups of electrode voltage values, the images of ions arranged in a chain are collected to obtain the relationship data between the ion equilibrium position and the ion trap voltage setting. According to Coulomb's law, the Coulomb electric field force of other ions in the ion chain on each ion at the equilibrium position is calculated, and the external electric field strength on each ion at the equilibrium position can be obtained by using the force balance condition of the ions in the ion chain. The specific calculation formula is as follows:

[0070] ,

[0071] in, is the dielectric constant of vacuum, is the equilibrium position of the i-th ion, is the equilibrium position of the jth ion.

[0072] S42. The global optimal method minimizes the total loss function, optimizes the external electric field analytical model, obtains the optimized values ​​of the model parameters of the external electric field analytical model, and thus calibrates the electrode electric field distribution and the stray electric field distribution of each electrode in the measurement interval.

[0073] In an embodiment of the present invention, the electric field distribution is calibrated by using ion image and ion chain trapping frequency, two measurement quantities respectively related to field strength and the first-order derivative of field strength, which can effectively suppress the system impact caused by imaging magnification error caused by using ion image measurement alone.

[0074] In an embodiment of the present invention, the parameters of the external electric field analytical model include the width and length of the electrode and the spatial relative position of the ion and the electrode. The multi-objective optimization method can be compatible with a variety of different types of data. In one or other embodiments of the present invention, the trapped position of a single ion under different electrode voltages can also be used as a data input. The parameterized expression of the electrode potential can be further simplified, or an asymmetric factor can be introduced to meet the needs of asymmetric electrodes. The parameterized expression of the stray field can also have a more sophisticated expression. Due to the limited range of ion movement and the excessive number of electrodes, the parameter space is too large, resulting in an increase in the complexity of the optimization. The area and number of electrodes that can be calibrated using this method at a single time are limited, and the usable range of the method can be expanded by segmented calibration.

[0075] Finally, it should be noted that the above specific implementation method is only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A method for calibrating electrode potential of a chip ion trap, characterized in that: The method comprises: S1: Based on the simulation model, calculate the electrode voltage values ​​required for the ion chain center to move a preset distance along the axial direction of the ion trap; S2: applying the plurality of sets of electrode voltage values ​​to the ion trap, and measuring the ion chain trapping frequency and the equilibrium position of each ion corresponding to each set of electrode voltage values; S3: Substituting the plurality of sets of electrode voltage values ​​into an external electric field analytical model to calculate the ion chain trapping frequency and the strength of the external electric field at the equilibrium position of each ion; S4: constructing a total loss function to optimize the external electric field analytical model; Wherein, the external electric field includes an electrode electric field and a stray electric field.

2. The electrode potential calibration method according to claim 1, characterized in that: Step S1 specifically includes: S11: constructing the simulation model of the chip ion trap; S12: applying a unit voltage to each electrode of the simulation model respectively, and solving the spatial distribution of the electric field intensity of each electrode under the unit voltage condition by simulation; S13: Setting the height variation range of the ion chain center relative to the ion trap surface during the movement, and the preset distance; S14: According to the height variation range and the preset distance, the plurality of groups of electrode voltage values ​​are set so that the plurality of groups of electrode voltage values ​​satisfy the following relationship: ， Where N is the total number of electrodes, is the kth electrode voltage value, is the axial direction of the ion trap, is the electric field of the kth electrode Quantity, is the electric field of the kth electrode Quantity, is the electric field of the kth electrode Quantity, are the coordinates of the center of the ion chain, is the vertical distance between the center of the ion chain and the surface of the ion trap, Determined by the altitude variation range.

3. The electrode potential calibration method according to claim 1, characterized in that: Step S2 includes: Measuring the trapped frequency of the ion chain by radio frequency resonance or sideband excitation; The ion trap is photographed, and the equilibrium position of each ion in the ion chain and the coordinates of the center of the ion chain are measured by proportionally magnifying the picture.

4. The electrode potential calibration method according to claim 1, characterized in that: Step S3 specifically includes: S31: Construct the external electric field analytical model to satisfy the relationship: ， in, is the analytical value of the electric field of the kth electrode, is the analytical value of the stray electric field, is the center coordinate of the kth electrode, , , , , , , are model parameters of the external electric field analytical model; S32: Initializing the external electric field analytical model, substituting the plurality of groups of electrode voltage values ​​into the external electric field analytical model respectively, and calculating the ion chain trapping frequency; Wherein, the calculation formula of the ion chain trapping frequency is: ， M is the mass of the ion, e is the charge number of the ion, is the analytical value of the electric field of the kth electrode at coordinates The first derivative at The analytical value of the stray electric field is The first derivative at ; S33: Substituting the equilibrium position of each ion measured in step S2 into the external electric field analysis model, and calculating the intensity of the external electric field at the equilibrium position of each ion.

5. The electrode potential calibration method according to claim 1, characterized in that: Step S4 specifically includes: S41: constructing a first loss function as the sum of squares of the errors between the ion chain trapping frequency obtained in step S2 and the ion chain trapping frequency obtained in step S3; Constructing a second loss function as the sum of squares of errors between the strength of the external electric field obtained in step S3 and the strength of the external electric field calculated theoretically; Constructing a total loss function as a linear superposition of the first loss function and the second loss function; S42: minimizing the total loss function using a global optimal method, optimizing the external electric field analytical model, and obtaining optimized values ​​of model parameters of the external electric field analytical model; The theoretical calculation formula of the strength of the external electric field is as follows: ， is the dielectric constant of vacuum, is the equilibrium position of the i-th ion, is the equilibrium position of the jth ion.

6. The electrode potential calibration method according to claim 1, characterized in that: in, The number of ions in the ion chain is greater than 10 and less than or equal to 30.

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