A superconducting quantum chip and its parameter determination method

By using a coplanar waveguide-step impedance resonator unit in superconducting quantum chips, the physical size of the resonator is optimized, and the problem of large space occupancy in traditional superconducting quantum chips is solved, and higher integration and freedom are achieved.

CN115241366BActive Publication Date: 2025-08-15YANGTZE DELTA IND INNOVATION CENT OF QUANTUM SCI & TECH
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Patent Information

Application Number
CN202210928530.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-08-03
Publication Date
2025-08-15
Estimated Expiration
2042-08-03

AI Technical Summary

Technical Problem

The layout form of resonators in traditional superconducting quantum chips takes up a lot of space and is difficult to meet the needs of high integration.

Method used

The coplanar waveguide-step impedance resonator unit is used to replace the traditional uniform impedance resonator. By adjusting the relationship between characteristic impedance ratio and electrical length, the physical size of the resonator is optimized and the layout size of the qubit is reduced.

Benefits of technology

Under the same parallel resonance condition, the electrical length of the coplanar waveguide-step impedance resonator is smaller, significantly reducing the size of the quantum chip and improving the integration and freedom of the quantum chip.

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Abstract

This application discloses a superconducting quantum chip and a method for determining its parameters, relating to the field of quantum chips. The superconducting quantum chip comprises a chip substrate and a quantum module formed on the chip substrate. The quantum module comprises a bit capacitor unit, a readout line unit, and a Josephson junction unit. The quantum module also comprises a coplanar waveguide-step impedance resonator unit. In the superconducting quantum chip of this application, the coplanar waveguide-step impedance resonator unit functions as a resonator. Due to the physical properties of the coplanar waveguide-step impedance resonator unit, under the same parallel resonance conditions, the electrical length of the step impedance resonator is significantly smaller than that of a uniform impedance resonator. This reduces the layout size of a single quantum bit, resulting in a smaller quantum chip with a specific number of bits, a higher degree of freedom for the quantum chip, and improved quantum chip integration.
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Description

Technical Field

[0001] The present invention relates to the field of quantum chips, and in particular to a superconducting quantum chip and a method for determining its parameters. Background Art

[0002] Quantum chips are the core components of quantum computers and primarily include superconducting quantum chips, semiconductor quantum chips, quantum dot chips, ion traps, and NV (diamond) color centers. Currently, superconducting quantum chips typically employ structures such as quantum bits, readout cavities, resonators, Josephson junctions, microwave circuits, and ports formed on a substrate.

[0003] The resonators in traditional superconducting quantum chips all use coplanar waveguides with uniform impedance, that is, the resonators are coplanar waveguide-uniformity impedance resonators (CPW-UIR), and the resonator length is λ g / 4, where λ g is the waveguide wavelength corresponding to the resonant frequency.

[0004] As the demand for quantum computer computing power increases, the requirements for the integration of quantum chips are also getting higher and higher. In order to reduce the size of traditional superconducting quantum chips, the resonators are arranged in the form of winding lines, but this layout still takes up a large amount of space.

[0005] Therefore, how to provide a solution to the above technical problems is a problem that those skilled in the art need to solve. Summary of the Invention

[0006] In view of this, the present invention aims to provide a superconducting quantum chip and a method for determining its parameters to reduce the size of the superconducting quantum chip. The specific solution is as follows:

[0007] A superconducting quantum chip includes a chip substrate and a quantum module formed on the chip substrate, wherein the quantum module includes a bit capacitor unit, a read line unit, a Josephson junction unit, and a coplanar waveguide-step impedance resonator unit.

[0008] Preferably, the coplanar waveguide-step impedance resonator unit is specifically a coplanar waveguide-2nd-order stepped impedance resonator unit.

[0009] Preferably, the coplanar waveguide-step impedance resonator unit is specifically a coplanar waveguide-3rd-order stepped impedance resonator unit.

[0010] Preferably, the bit capacitor unit is a cross-structured bit capacitor unit.

[0011] Preferably, the read line unit is specifically a transmission line of a coplanar waveguide structure.

[0012] Preferably, the coplanar waveguide-step impedance resonator unit is specifically λ g / 4 type coplanar waveguide-step impedance resonator unit, where λ g is the waveguide wavelength corresponding to the resonant frequency of the coplanar waveguide-step impedance resonator unit.

[0013] Accordingly, the present application also discloses a method for determining parameters of a superconducting quantum chip, which is applied to the superconducting quantum chip as described in any one of the above items, comprising:

[0014] Determine the characteristic impedance of each order transmission line of the coplanar waveguide-step impedance resonator unit according to a preset accuracy and use it as a characteristic impedance parameter;

[0015] calculating a characteristic impedance ratio between the characteristic impedances of all the characteristic lines;

[0016] Determine a curve relationship between the electrical length of the characteristic line and the total electrical length under the characteristic impedance ratio; the total electrical length is specifically the sum of the electrical lengths of all the characteristic lines;

[0017] Determining, based on the curve relationship, a minimum total electrical length interval of the total electrical length and a corresponding electrical length interval of the characteristic line;

[0018] Within the electrical length interval of the characteristic line of each order, the electrical length corresponding to the preset accuracy is determined respectively, so as to use the electrical length as the electrical length parameter of each order transmission line of the coplanar waveguide-step impedance resonator unit.

[0019] Preferably, the coplanar waveguide-step impedance resonator unit is a coplanar waveguide-2nd-order step impedance resonator unit;

[0020] The process of calculating the characteristic impedance ratio between the characteristic impedances of all the characteristic lines includes:

[0021] A characteristic impedance ratio of the characteristic impedance of the second-order characteristic line to the characteristic impedance of the first-order characteristic line is calculated.

[0022] Preferably, the process of determining the curve relationship between the electrical length of the characteristic line and the total electrical length under the characteristic impedance ratio includes:

[0023] Determine the curve relationship between the characteristic line and the total electrical length at the first order under the characteristic impedance ratio.

[0024] Preferably, the process of determining the electrical length corresponding to the preset accuracy within the electrical length interval of each order of the characteristic line includes:

[0025] Determining, within the electrical length interval of the first-order characteristic line, the electrical length corresponding to the preset accuracy as the first-order electrical length parameter of the first-order characteristic line;

[0026] Determining the total electrical length corresponding to the electrical length parameter of the first order according to the curve relationship;

[0027] The second-order electrical length parameter of the second-order characteristic line is determined according to the total electrical length and the first-order electrical length parameter.

[0028] This application discloses a superconducting quantum chip, comprising a chip substrate and a quantum module formed on the chip substrate. The quantum module comprises a bit capacitor unit, a readout line unit, and a Josephson junction unit. The quantum module also comprises a coplanar waveguide-step impedance resonator unit. In the superconducting quantum chip of this application, the coplanar waveguide-step impedance resonator unit is used to implement the function of a resonator. Due to the physical properties of the coplanar waveguide-step impedance resonator unit, under the same parallel resonance conditions, the electrical length of the step impedance resonator is significantly smaller than that of the uniform impedance resonator, thereby reducing the layout size of a single quantum bit, making the quantum chip with a specific number of bits smaller, the quantum chip with a higher degree of freedom, and the quantum chip with improved integration. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0030] Figure 1 This is a structural distribution diagram of a superconducting quantum chip in an embodiment of the present invention;

[0031] Figure 2 This is a structural distribution diagram of a coplanar waveguide-uniform impedance resonator unit in an embodiment of the present invention;

[0032] Figure 3 This is a flowchart of a method for determining parameters of a superconducting quantum chip according to an embodiment of the present invention;

[0033] Figure 4 This is a structural distribution diagram of a coplanar waveguide-2nd-order stepped impedance resonator unit in an embodiment of the present invention;

[0034] Figure 5 is a graph showing the relationship between the electrical length θ1 and the normalized electrical length Ln in an embodiment of the present invention;

[0035] Figure 6aand Figure 6b These are the structural distribution diagrams of the superconducting quantum chip in this embodiment and the traditional superconducting quantum chip respectively;

[0036] Figure 7a and Figure 7b Graph showing simulation results of a single-bit superconducting quantum chip in this embodiment;

[0037] Figure 8a and Figure 8b This is the simulation result of the traditional single-bit superconducting quantum chip. DETAILED DESCRIPTION

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0039] As the demand for quantum computer computing power increases, the requirements for the integration of quantum chips are also getting higher and higher. In order to reduce the size of traditional superconducting quantum chips, the resonators are arranged in the form of winding lines, but this layout still takes up a large amount of space.

[0040] In the superconducting quantum chip of the present application, a coplanar waveguide-step impedance resonator unit is used to realize the function of the resonator. Due to the physical characteristics of the coplanar waveguide-step impedance resonator unit, under the same parallel resonance conditions, the electrical length of the step impedance resonator is significantly smaller than that of the uniform impedance resonator, thereby reducing the layout size of a single quantum bit, making the quantum chip with a specific number of bits smaller, the quantum chip has a higher degree of freedom, and the quantum chip has improved integration.

[0041] The embodiment of the present invention discloses a superconducting quantum chip, see Figure 1 As shown, Figure 1 This is a structural diagram of the superconducting quantum chip applied to a single-bit superconducting quantum chip. The superconducting quantum chip includes a chip substrate 10 and a quantum module formed on the chip substrate 10. The quantum module includes a bit capacitor unit 20, a read line unit 30, and a Josephson junction unit. The quantum module also includes a coplanar waveguide-step impedance resonator unit 40.

[0042] In some specific embodiments, the bit capacitor unit 20 formed on the chip substrate 10 is specifically a cross-structured bit capacitor unit; further, the read line unit 30 formed on the chip substrate 10 is specifically a transmission line of a coplanar waveguide structure CPW.

[0043] It can be understood that the coplanar waveguide-step impedance resonator unit 40 mainly includes a coplanar waveguide-step impedance resonator (CPW-SIR), which is a transverse electromagnetic field or quasi-transverse electromagnetic field mode resonator composed of two or more CPW transmission lines with different characteristic impedances, see Figure 2 As shown in Figure 1, θ1, θ2, ..., θn are the electrical lengths of different CPW transmission line segments, and Z1, Z2, ..., Zn are the characteristic impedances of each CPW (coplanar waveguide) transmission line segment. As the number of CPW transmission lines increases, the physical dimensions of the resonator can be adjusted within a certain range to reflect the relationship between the electrical lengths and characteristic impedances of the multiple CPW transmission lines. This serves as a basis for the miniaturized design of the superconducting quantum chip in this embodiment.

[0044] In some specific embodiments, the coplanar waveguide-step impedance resonator unit is specifically λ g / 4 type coplanar waveguide-step impedance resonator unit, where λ g is the waveguide wavelength corresponding to the resonant frequency of the coplanar waveguide-step impedance resonator unit.

[0045] Furthermore, considering the influence of both the processing accuracy and the miniaturization effect of the resonant cavity unit, the coplanar waveguide-step impedance resonator unit can usually be selected as a coplanar waveguide-2nd order step impedance resonator unit or a coplanar waveguide-3rd order step impedance resonator unit.

[0046] According to the description of this embodiment, the parameters of a specific superconducting quantum chip may include: the chip substrate 10 is a Si silicon wafer, and its dielectric constant ε r =11.9, thickness is 500um; the line width of the reading line unit 30 is 10um, and the slot width is 5um; the coplanar waveguide-step impedance resonator unit is specifically a coplanar waveguide-2nd order step impedance resonator unit, wherein the first-order characteristic line, that is, the characteristic impedance of the Z1 section CPW transmission line is approximately 74Ω, corresponding to the center line width w=2um, the slot line width s=5um, and the second-order characteristic line, that is, the characteristic impedance of the Z2 section CPW transmission line is approximately 38Ω, corresponding to the center line width w=8um, and the slot line width s=2um.

[0047] This application discloses a superconducting quantum chip, comprising a chip substrate and a quantum module formed on the chip substrate. The quantum module comprises a bit capacitor unit, a readout line unit, and a Josephson junction unit. The quantum module also comprises a coplanar waveguide-step impedance resonator unit. In the superconducting quantum chip of this application, the coplanar waveguide-step impedance resonator unit is used to implement the function of a resonator. Due to the physical properties of the coplanar waveguide-step impedance resonator unit, under the same parallel resonance conditions, the electrical length of the step impedance resonator is significantly smaller than that of the uniform impedance resonator, thereby reducing the layout size of a single quantum bit, making the quantum chip with a specific number of bits smaller, the quantum chip with a higher degree of freedom, and the quantum chip with improved integration.

[0048] Accordingly, the present application also discloses a method for determining parameters of a superconducting quantum chip, which is applied to any of the superconducting quantum chips mentioned above, see Figure 3 Shown, including:

[0049] S1: According to a preset accuracy, determine the characteristic impedance of each order transmission line of the coplanar waveguide-step impedance resonator unit and use it as a characteristic impedance parameter;

[0050] The preset accuracy is set according to actual processing capabilities or design requirements. It is known that the coplanar waveguide-step impedance resonator unit includes multiple-order transmission lines, and the characteristic impedance of each order transmission line is determined separately.

[0051] S2: Calculate the characteristic impedance ratio between the characteristic impedances of all characteristic lines;

[0052] S3: Determine the curve relationship between the electrical length of the characteristic line and the total electrical length under the characteristic impedance ratio; the total electrical length is specifically the sum of the electrical lengths of all characteristic lines;

[0053] S4: Determine the minimum total electrical length interval and the electrical length intervals of the corresponding characteristic lines according to the curve relationship;

[0054] S5: Determine the electrical length corresponding to the preset accuracy within the electrical length interval of each order characteristic line, so as to use the electrical length as the electrical length parameter of each order transmission line of the coplanar waveguide-step impedance resonator unit.

[0055] It can be understood that the coplanar waveguide-step impedance resonator unit 40 mainly includes a coplanar waveguide-step impedance resonator (CPW-SIR), which is a transverse electromagnetic field or quasi-transverse electromagnetic field mode resonator composed of two or more CPW transmission lines with different characteristic impedances, wherein θ1, θ2...θn are the electrical lengths of different sections of CPW transmission lines, and Z1, Z2...Zn are the characteristic impedances of each section of CPW (Coplanar Waveguide) transmission line. As the number of CPW transmission lines increases, the physical size of the resonator can be adjusted within a certain range as the electrical length relationship and characteristic impedance relationship of multiple CPW transmission lines change, thereby serving as the basis for the miniaturized design of the superconducting quantum chip in this embodiment.

[0056] In some specific embodiments, the coplanar waveguide-step impedance resonator unit is a coplanar waveguide-2-step step impedance resonator unit; taking the coplanar waveguide-2-step step impedance resonator unit as an example, its structure diagram is as follows: Figure 4 As shown, ignoring the step discontinuity and the edge capacitance of the open section, the input impedance Zin can be approximately expressed as follows according to transmission line theory:

[0057]

[0058] Its parallel resonance condition is:

[0059] Z2-Z1×tanθ1×tanθ2=0;

[0060] Then we have:

[0061]

[0062] It can be seen that the resonance condition of the coplanar waveguide-2nd order stepped impedance resonator unit is not only related to the electrical lengths θ1 and θ2, but also to the characteristic impedance ratio Rz. Compared with the coplanar waveguide-uniform impedance resonator CPW-UIR, whose structure only depends on the electrical length of the CPW transmission line, the coplanar waveguide-2nd order stepped impedance resonator unit has an additional parameter characteristic impedance ratio Rz to adjust the total electrical length of the resonator unit.

[0063] Furthermore, the total electrical length θtotal of the coplanar waveguide-2nd-order stepped impedance resonator unit is specifically:

[0064] θtotal=θ1+θ2=θ1+arctan(Rz / tanθ1);

[0065] At this time, the electrical length of the CPW-UIR in the traditional superconducting quantum chip is π / 2. After normalizing θtotal, the normalized electrical length Ln of the coplanar waveguide-2nd order step impedance resonator unit can be obtained as follows:

[0066]

[0067] Furthermore, for different characteristic impedance ratios Rz, the relationship curve between the electrical length θ1 and the normalized electrical length Ln is as follows: Figure 5 As shown, it can be seen that when Rz>1, the normalized electrical length Ln reaches a maximum value. At this time, the electrical length of the CPW-UIR is less than the total electrical length θtotal of the coplanar waveguide-2nd order step impedance resonator unit in this embodiment. On the contrary, when Rz<1, the normalized electrical length reaches a minimum value. The electrical length of the CPW-UIR is greater than the total electrical length θtotal of the coplanar waveguide-2nd order step impedance resonator unit in this embodiment. Therefore, selecting a coplanar waveguide-2nd order step impedance resonator unit with Rz<1 can reduce the total electrical length θtotal. Other multi-order coplanar waveguide-step impedance resonator units also have this characteristic, and this theory can be applied to the miniaturization design of superconducting quantum chips. Considering product accuracy and efficiency, a coplanar waveguide-2nd order step impedance resonator unit or a coplanar waveguide-3rd order step impedance resonator unit is generally selected as the coplanar waveguide-step impedance resonator unit.

[0068] In some specific embodiments, when the coplanar waveguide-step impedance resonator unit is a coplanar waveguide-2nd-order step impedance resonator unit, the process of calculating the characteristic impedance ratio between the characteristic impedances of all characteristic lines in step S2 includes:

[0069] Calculate the characteristic impedance ratio of the characteristic impedance of the second-order characteristic line to the characteristic impedance of the first-order characteristic line.

[0070] Furthermore, the process of determining the curve relationship between each characteristic line and the total electrical length of all characteristic lines under the characteristic impedance ratio in step S3 includes:

[0071] Determine the curve relationship between the first-order characteristic line and the total electrical length of all characteristic lines under the characteristic impedance ratio.

[0072] Furthermore, step S5 is a process of determining the electrical length corresponding to the preset accuracy within the electrical length interval of each order characteristic line, including:

[0073] Determining, within the electrical length interval of the first-order characteristic line, an electrical length corresponding to a preset accuracy as a first-order electrical length parameter of the first-order characteristic line;

[0074] According to the curve relationship, determine the total electrical length corresponding to the first-order electrical length parameter;

[0075] The second-order electrical length parameter of the second-order characteristic line is determined according to the total electrical length and the first-order electrical length parameter.

[0076] Taking a specific superconducting quantum resonator as an example, its chip substrate 10 is a Si silicon wafer, and its dielectric constant ε r =11.9, thickness is 500um; the line width of the read line unit 30 is 10um, and the slot width is 5um; the coplanar waveguide-step impedance resonator unit is specifically a coplanar waveguide-2nd order step impedance resonator unit, and the process of calculating the coplanar waveguide-2nd order step impedance resonator unit is as follows:

[0077] According to the preset accuracy, the characteristic impedance parameters are determined to include: the characteristic impedance Z1 of the first-order characteristic line is approximately 74Ω, and the characteristic impedance ZW of the second-order characteristic line is approximately 38Ω;

[0078] The characteristic impedance ratio between the characteristic impedances of all characteristic lines is calculated as

[0079] Determine the curve relationship between the first-order characteristic line and the total electrical length of all characteristic lines under the characteristic impedance ratio. Figure 5 The curve with Rz=0.5 is approximate and can be used as a reference;

[0080] According to the curve relationship of Rz=0.514, the minimum total electrical length interval and the electrical length intervals of each corresponding characteristic line are determined, where the elements in the minimum total length interval include the minimum value of the curve relationship Ln. However, considering the design requirements, it is not necessary to directly select the minimum value. Only one data that is easy to process can be selected from the results close to the minimum value. Therefore, the minimum total electrical length interval can be selected as the first 1 / n interval between the minimum and maximum values on the curve relationship Ln. n can be adjusted according to actual design requirements. For example, when n=3, the first 1 / 3 interval where Ln is the smallest in the curve relationship is taken as the minimum total electrical length interval, and then the electrical length interval of the corresponding first-order characteristic line is determined.

[0081] Furthermore, an electrical length that is convenient for design or processing and meets the preset accuracy requirements is determined within the electrical length range of the first-order characteristic line as the first-order electrical length parameter of the first-order characteristic line. For example, the first-order electrical length parameter can be taken as θ1=45°. According to the curve relationship, the total electrical length corresponding to the first-order electrical length parameter θ1=45° can be determined, and then the second-order electrical length parameter of the second-order characteristic line can be determined based on the total electrical length and the first-order electrical length parameter θ1.

[0082] like Figure 6a and Figure 6bAs shown, at this time, the total electrical length of all characteristic lines in the coplanar waveguide-step impedance resonator unit is about 3437.053um, and the layout area of the meandering line part is 914um×123.7um; under the same parallel resonance conditions, the resonator length in the traditional single-bit superconducting quantum chip is about 4277.244um, and the layout area of the meandering line part is 1152um×123.7um.

[0083] Specifically, such as Figure 7a and Figure 7b The simulation results of a single-bit superconducting quantum chip under this condition are shown, and the resonator operating frequency is 6.1956 GHz;

[0084] Specifically, such as Figure 8a and Figure 8b The simulation results of a traditional single-bit superconducting quantum chip are shown, with the resonator operating frequency at 6.1978 GHz.

[0085] It can be seen that when the superconducting quantum chip in this embodiment and the traditional superconducting quantum chip operate at similar frequencies, the resonator size of the coplanar waveguide-2nd order stepped impedance resonator unit is reduced by about 19.6% compared with the resonator size of the traditional UIR.

[0086] It can be understood that the above is a detailed description of the coplanar waveguide-2nd order stepped impedance resonator unit, and the parameter determination method of the coplanar waveguide-3rd order stepped impedance resonator unit is similar to it, except that with the increase of transmission lines, the characteristic impedance ratio is no longer a single quantity. When calculating the characteristic impedance ratio in step S2, the characteristic impedance of a certain characteristic line is generally used as the denominator, and the characteristic impedances of other characteristic lines are used as numerators, and the corresponding multiple characteristic impedance ratios are calculated respectively; in step S3, under this group of specific multiple characteristic impedance ratios, the curve relationship in which the electrical length of the characteristic line with the characteristic line as the denominator is the independent variable and the total electrical length of all characteristic lines is the dependent variable is determined; subsequently, under this curve relationship, the determination of the minimum total electrical length interval, the electrical length interval of the independent variable, and the specific electrical length parameter are similar to the above, and will not be repeated here.

[0087] In the superconducting quantum chip of the present application, a coplanar waveguide-step impedance resonator unit is used to realize the function of the resonator. Due to the physical characteristics of the coplanar waveguide-step impedance resonator unit, under the same parallel resonance conditions, the electrical length of the step impedance resonator is significantly smaller than that of the uniform impedance resonator, thereby reducing the layout size of a single quantum bit, making the quantum chip with a specific number of bits smaller, the quantum chip has a higher degree of freedom, and the quantum chip has improved integration.

[0088] Finally, it should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or device comprising the element.

[0089] The above is a detailed introduction to a superconducting quantum chip and a method for determining its parameters provided by the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only intended to help understand the method and core concept of the present invention. At the same time, for those skilled in the art, according to the concept of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

Claims

1. A method for determining parameters of a superconducting quantum chip, characterized in that: Applications in superconducting quantum chips include: Determine the characteristic impedance of each order transmission line of the coplanar waveguide-step impedance resonator unit according to a preset accuracy and use it as a characteristic impedance parameter; calculating a characteristic impedance ratio between the characteristic impedances of all characteristic lines; Determine a curve relationship between the electrical length of the characteristic line and the total electrical length under the characteristic impedance ratio; the total electrical length is specifically the sum of the electrical lengths of all the characteristic lines; Determine the minimum total electrical length interval of the total electrical length and the corresponding electrical length interval of the characteristic line according to the curve relationship; the minimum total length interval is selected as the first 1 / n interval between the minimum value and the maximum value on the curve relationship; Determining the electrical length corresponding to the preset accuracy within the electrical length interval of the characteristic line of each order, so as to use the electrical length as the electrical length parameter of each order transmission line of the coplanar waveguide-step impedance resonator unit; The coplanar waveguide-step impedance resonator unit is a coplanar waveguide-2nd-order step impedance resonator unit; The process of calculating the characteristic impedance ratio between the characteristic impedances of all the characteristic lines includes: Calculating a characteristic impedance ratio of the characteristic impedance of the second-order characteristic line to the characteristic impedance of the first-order characteristic line; The process of determining the curve relationship between the electrical length of the characteristic line and the total electrical length under the characteristic impedance ratio includes: Determine a curve relationship between the characteristic line and the total electrical length at the first order under the characteristic impedance ratio; The process of determining the electrical length corresponding to the preset accuracy within the electrical length interval of each order of the characteristic line includes: Determining, within the electrical length interval of the first-order characteristic line, the electrical length corresponding to the preset accuracy as the first-order electrical length parameter of the first-order characteristic line; Determining the total electrical length corresponding to the electrical length parameter of the first order according to the curve relationship; The second-order electrical length parameter of the second-order characteristic line is determined according to the total electrical length and the first-order electrical length parameter.

Citation Information

Patent Citations

  • Superconducting quantum circuit and preparation method thereof

    CN110378482A