Method and apparatus for determining parameters in a discrete multi-frequency parametric amplifier

Abstract

The application relates to a method and device for determining parameters in a discrete multi-frequency parametric amplifier, which comprises the following steps: determining a load impedance value according to a capacitance value and an inductance value of a resonant cavity; determining a plurality of frequency ratios which are the same as the number of matching frequencies to be amplified, wherein the frequency ratios correspond to the matching frequencies to be amplified one by one; determining the electrical length of an impedance transmission line in a multi-frequency impedance matcher on the respective matching frequency according to the frequency ratios; determining the reflection coefficient corresponding to the impedance transmission line in the multi-frequency impedance matcher according to the electrical length of the impedance transmission line in the multi-frequency impedance matcher on the respective matching frequency and the load impedance value; and determining the characteristic impedance of the corresponding impedance transmission line according to the reflection coefficient. According to the scheme, the working frequency of the discrete parametric amplifier is accurately set to be consistent with the frequency of the bit signal to be amplified, so that the working bandwidth of the quantum amplifier is greatly widened, and the quantum bit signal can be amplified in a larger frequency range.

Description

Technical Field

[0001] This application relates to the field of quantum information technology, and in particular to a method and apparatus for determining parameters in a discrete multi-frequency parametric amplifier. Background Technology

[0002] Quantum parametric amplifiers (MPA) are key components in quantum information technology. Utilizing nonlinear effects, they can generate and annihilate photons of different frequencies. Josephson MPA can be applied in quantum computing to amplify weak qubit signals while maintaining noise levels close to the quantum limit, resulting in an excellent signal-to-noise ratio. It is a crucial component in high-fidelity readout circuits for quantum computing. Josephson MPA can also be applied in quantum radar, generating two entangled quantum signals to achieve target imaging and detection at extremely low power. Therefore, research on this device is of great significance.

[0003] Currently, Josephson parametric amplifiers (JPAs) are mainly implemented in two ways: resonant and traveling-wave. A resonant JPA utilizes the Josephson junction inductance and lumped capacitance to form a resonant cavity. The signal enters the cavity and travels back and forth multiple times, absorbing pump energy before being output, thus amplifying the signal. A traveling-wave JPA uses a long transmission line; the signal absorbs pump energy as it travels along the line before being output, also amplifying the signal. The advantage of the resonant type is its extremely low noise; even with amplification in both orthogonal directions, noise as low as half a photon can be achieved, a level unattainable by other methods. The disadvantages of the resonant JPA are also significant: small bandwidth and low saturation power. Early JPAs had bandwidths less than 50MHz, severely limiting their application in multi-bit quantum signal amplification. Increasing bandwidth has become a crucial research direction to simultaneously read out more bits of signal, and significant progress has been made. The main way to increase bandwidth is by adding impedance matching devices. The reason why impedance matching devices increase bandwidth is easy to understand. If the impedance of the JPA resonator is less than 10 ohms, while the ambient impedance is approximately 50 ohms, impedance mismatch is the main reason for the JPA resonator's low coupling to the outside world and high quality factor, resulting in a small bandwidth. Therefore, impedance matching devices can significantly improve the bandwidth of the JPA. Researchers have designed different types of impedance matching devices, such as quarter-wavelength impedance matching devices. All of these impedance matching devices can achieve bandwidth increase within a continuous frequency band, amplifying signals at all frequencies within that band.

[0004] Figure 1 The traditional broadband impedance matching design is presented. A resonator composed of capacitor C and inductor L is coupled to the external environment through a broadband impedance transformer. The resulting JPA frequency-gain diagram is shown below. Figure 2As shown, the qubit signal is amplified within a continuous frequency range. It is evident that the range of amplifiable qubit frequencies is limited by the bandwidth of the broadband impedance converter, resulting in a relatively small frequency range for amplifiable qubit signals.

[0005] Current research indicates that the bandwidth and gain of broadband impedance matching JPAs are gradually reaching their limits, making further bandwidth increases difficult. Therefore, new impedance matching design methods are needed to achieve breakthroughs in JPA performance. Summary of the Invention

[0006] In reality, the frequency of the quantum bit signal to be amplified is not continuous; the bit signal is discretely arranged within a frequency range. Therefore, the amplifier does not need to have a continuous bandwidth; it only needs to have high gain and a certain bandwidth at the frequency corresponding to the bit. Thus, addressing the limitations of broadband impedance converters in amplifying quantum bit signals, this application proposes a frequency-discrete, multi-frequency parametric amplifier. By precisely setting the operating frequency of the discrete parametric amplifier to match the frequency of the bit signal to be amplified, the operating bandwidth of the quantum amplifier is greatly broadened, amplifying the quantum bit signal over a larger frequency range.

[0007] According to a first aspect of this application, a method for determining parameters in a discrete multi-frequency parametric amplifier is provided, the discrete multi-frequency parametric amplifier including a resonant cavity and a multi-frequency impedance matching circuit, characterized in that it includes:

[0008] The load impedance value is determined based on the capacitance and inductance values ​​of the resonant cavity.

[0009] Determine a frequency ratio that is the same as the number of matching frequencies to be amplified, wherein the frequency ratio corresponds one-to-one with the matching frequencies to be amplified;

[0010] Based on the frequency ratio, determine the electrical length of the impedance transmission line in the multi-frequency impedance matching device at its respective matching frequency;

[0011] Based on the electrical lengths of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies and the load impedance value, determine the reflection coefficient corresponding to the impedance transmission lines in the multi-frequency impedance matching device; and

[0012] Based on the reflection coefficient, the characteristic impedance of the corresponding impedance transmission line is determined.

[0013] According to a second aspect of this application, a device for determining parameters in a discrete multi-frequency parametric amplifier is provided, the discrete multi-frequency parametric amplifier including a resonant cavity and a multi-frequency impedance matching circuit, characterized in that it includes:

[0014] The first determining module is used to determine the load impedance value based on the capacitance and inductance values ​​of the resonant cavity;

[0015] The second determining module is used to determine a frequency ratio that is the same as the number of matching frequencies to be amplified, wherein the frequency ratio corresponds one-to-one with the matching frequencies to be amplified.

[0016] The third determining module is used to determine the electrical length of the impedance transmission line in the multi-frequency impedance matching device at its respective matching frequency based on the frequency ratio.

[0017] The fourth determining module is used to determine the reflection coefficient corresponding to the impedance transmission line in the multi-frequency impedance matching device based on the electrical length of the impedance transmission line in the multi-frequency impedance matching device at its respective matching frequency and the load impedance value; and

[0018] The fifth determining module is used to determine the characteristic impedance of the corresponding impedance transmission line based on the reflection coefficient.

[0019] According to a third aspect of this application, an electronic device is provided, comprising:

[0020] Processor; and

[0021] A memory storing computer instructions that, when executed by the processor, cause the processor to perform the method described in the first aspect.

[0022] According to a fourth aspect of this application, a non-transitory computer storage medium is provided, which stores a computer program that, when executed by a plurality of processors, causes the processors to perform the method described in the first aspect.

[0023] Based on the method and apparatus for determining parameters in a discrete multi-frequency parametric amplifier provided in this application, a multi-frequency impedance transformation method is proposed by performing variable substitution and considering the transmission between two adjacent stepped transmission lines, while maintaining the linear characteristics of the reflection coefficient. This simplifies the transcendental constraint equations in the transmission line theory solution into a single matrix equation, simplifying the design process and facilitating the design of multi-frequency impedance transformers with high accuracy. According to the scheme of this application, firstly, multi-frequency impedance matching only needs to consider the gain at the quantum bit signal frequency, without needing to amplify the entire frequency band. Therefore, it can amplify quantum bit signals with a wider range of distributions, resulting in a discrete multi-frequency parametric amplifier with a wide frequency coverage. Secondly, the length of the multi-frequency impedance matching transmission line is significantly smaller than that of the broadband impedance matching transmission line, thus achieving the same effect in a smaller size, improving integration density, and making it more suitable for chip integration design and micro / nano fabrication. Furthermore, the design of the multi-frequency impedance matching transmission line proposed in this application is relatively simple and computationally inefficient.

[0024] Furthermore, the discrete multi-frequency parametric amplifier designed in this application can be used not only for amplifying quantum bit signals but also for amplifying other signals. For example, an amplifier designed with a broadband impedance converter can amplify signals in one frequency band, while the discrete multi-frequency parametric amplifier designed in this application can amplify signals in multiple frequency bands. Therefore, if multiple frequency band signals need to be amplified, multiple amplifiers designed with broadband impedance converters may be required. However, with the solution in this application, only one discrete multi-frequency parametric amplifier is needed, thus greatly improving the integration. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings, without exceeding the scope of protection claimed by this application.

[0026] Figure 1 This is a schematic diagram of a traditional broadband impedance matching design scheme.

[0027] Figure 2 Is adopted Figure 1 The design scheme shown presents a JPA frequency-gain diagram.

[0028] Figure 3 This is a schematic diagram of the resonant cavity of a discrete multi-frequency parametric amplifier.

[0029] Figure 4 This is a flowchart of a method for determining parameters in a discrete multi-frequency parametric amplifier according to an embodiment of this application.

[0030] Figure 5 This is a flowchart of a method for determining parameters in a discrete multi-frequency parametric amplifier according to another embodiment of this application.

[0031] Figure 6 The diagrams show a traditional broadband impedance matching circuit and a multi-frequency impedance matching circuit in the discrete multi-frequency parametric amplifier of this application.

[0032] Figure 7 This is a schematic diagram of signal amplification by a discrete multi-frequency parametric amplifier according to an embodiment of this application.

[0033] Figure 8 This is a simulation result of a parametric amplifier based on a 3-frequency, 6-section stepped impedance converter.

[0034] Figure 9 This is a simulation result of a parametric amplifier based on a 4-frequency, 8-section stepped impedance converter.

[0035] Figure 10 The figures show the simulation results of traditional binomial broadband impedance matching and the multi-frequency impedance matching of this application.

[0036] Figure 11 This is a schematic diagram of a parameter determination device in a discrete multi-frequency parametric amplifier according to an embodiment of this application.

[0037] Figure 12 This is a schematic diagram of a parameter determination device in a discrete multi-frequency parametric amplifier according to another embodiment of this application.

[0038] Figure 13 This is a structural diagram of an electronic device provided in this application. Detailed Implementation

[0039] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0040] Research on impedance transformation initially focused on achieving wider impedance matching bandwidth. Common broadband structures include stepped-down, multi-section stepped-impedance, and multi-section fractal stepped-impedance transmission lines. With the advent of multi-frequency communication systems, researchers began to systematically study multi-frequency impedance transformation. Commonly used structures for multi-frequency / broadband impedance transformation include multi-section stepped-impedance transmission line structures, Π-type and T-type structures, and combinations thereof. Among these, the multi-section stepped-impedance transmission line structure is the most widely used. This application employs a multi-section stepped-impedance transmission line approach.

[0041] Regarding impedance matching device design methods, transmission line theory, ABCD matrix, or exact solution methods for impedance / admittance matrices are effective means for analyzing and designing microwave impedance matching devices. However, with the increase in frequency bands and bandwidth, the complexity of the constraint equations obtained by these methods increases exponentially. Even if broadband impedance transformation results are obtained using the above methods, it is difficult to implement multi-frequency impedance transformation in practice. This application proposes a multi-frequency impedance transformation method by performing variable substitution and considering the transmission between two adjacent stepped transmission lines, while maintaining the linear characteristics of the reflection coefficient. This method simplifies the transcendental constraint equations obtained from transmission line theory into a single matrix equation, simplifying the design process and facilitating the design of multi-frequency impedance matching devices with high accuracy.

[0042] In this application, the discrete multi-frequency parametric amplifier includes a resonant cavity and a multi-frequency impedance matching device, wherein the resonant cavity includes an inductor and a capacitor, and the multi-frequency impedance matching device includes a transmission line.

[0043] According to some embodiments, in the resonant cavity, the capacitor can be an on-chip lumped parallel-plate capacitor. Generally, a parallel-plate capacitor is used, that is, the upper and lower electrode plates are spaced a certain distance apart to form a capacitor. The electrode material can be a superconducting material such as aluminum, niobium, or tantalum. The space between the plates can be filled with a dielectric material such as air, silicon nitride, amorphous silicon, or silicon oxide. The capacitance can be any suitable value, for example, between 1 and 10 picofarads (pF).

[0044] In some embodiments, the inductor can be a loop device consisting of two Josephson junctions (i.e., a superconducting quantum interference ring, SQUID), which can be excited by current or magnetic flux to produce a nonlinear mixing effect. The two Josephson junctions in the SQUID have equal resistances. Generally, the inductor can consist of a single superconducting quantum interference ring, and the inductance value can be any suitable value, for example, between 20 and 300 pichenries (pH). To improve the dynamic range of the parametric amplifier, multiple superconducting quantum interference rings can be connected in series, such as... Figure 3 As shown, L1, L2, ... L n These represent the 1st, 2nd...nth SQUIDs, respectively, and the symbol × represents a Josephson knot.

[0045] The resonant cavity is coupled to the external environment (e.g., a 50-ohm external impedance) via an impedance-matched transmission line. The signal to be amplified enters from the input terminal, passes through the matching transmission line into the LC resonant cavity, receives pump energy through a nonlinear mixing process, increases in amplitude, and the amplified signal is output from the input terminal again through the matching transmission line. Since the signal passes through the input port twice, it can be considered a type of reflective amplifier. If coupled to a multi-frequency impedance-matched system, multi-frequency parametric amplification can be achieved.

[0046] In this application, a multi-frequency impedance matching device is designed based on a multi-section stepped impedance transmission line according to reflection theory. This application differs from the binomial multi-section transmission lines and Chebyshev transmission lines in the prior art. Essentially, these methods in the prior art achieve good matching by utilizing constructed small reflections to cancel each other out at multiple specified matching frequencies or over a wide bandwidth. These small reflections include those caused by impedance discontinuities between the external impedance, the stepped impedance transmission line, and the load impedance. From the perspective of constructing the multi-frequency impedance transformation constraint equations, if the constraint equations are constructed based on transmission line theory, the ABCD matrix, the impedance matrix, or the admittance matrix, the computational complexity of the constraint equations is 2. N The complexity increases dramatically as the number of impedance transformation bands increases, reaching a point where analytical solutions become impossible. Even when using numerical methods to solve the constraint equations, initial values ​​still need to be designed.

[0047] This application is based on a general-purpose multi-section impedance transmission line. Utilizing the one-to-one correspondence between the characteristic impedance and reflection coefficient of the transmission line, and through variable substitution and considering the transmission between two adjacent stepped transmission lines, the nonlinear input impedance is transformed into a linear reflection coefficient characterized by a small reflection coefficient. By rationally designing the electrical length of the transmission line, it is made suitable for on-chip transmission lines such as coplanar waveguides and microstrip lines that can be fabricated in micro- and nano-scale processes, while controlling the approximate accuracy of the reflection coefficient between adjacent transmission lines. By rationally designing multiple frequency intervals, a one-to-one correspondence with the frequency distribution of discontinuous bits is achieved, resulting in a larger bandwidth at the frequency of the bit to be amplified.

[0048] Next, we will introduce the design steps for the relevant parameters of the multi-frequency impedance matching circuit of the discrete multi-frequency parametric amplifier in this application. Figure 4 This is a flowchart of a method for determining parameters in a discrete multi-frequency parametric amplifier according to an embodiment of this application. Figure 4 As shown, the method includes the following steps.

[0049] Step S401: Determine the load impedance value based on the capacitance and inductance values ​​of the resonant cavity.

[0050] According to some embodiments, the load impedance value Zr of the resonant cavity is determined based on the capacitance value C and the inductance value L of the resonant cavity, as shown in equation (1):

[0051]

[0052] Step S402: Determine a frequency ratio that is the same as the number of matching frequencies to be amplified, wherein the frequency ratio corresponds one-to-one with the matching frequencies to be amplified.

[0053] According to some embodiments, the electrical length of the transmission line of the multi-frequency impedance matching circuit at each matching frequency is θ. i The characteristic impedance is Zn. According to some embodiments, the number of matching frequencies to be amplified is determined to be N. For N matching frequencies to be amplified, the first matching frequency, or the lowest matching frequency, is set to f0. These N matching frequencies can be proportionally converted to f0:n1f. 0: :n2f 0: :…n N-1 f 0: where n1, n2, ..., n N-1 It is the frequency ratio.

[0054] For example, if the number of matching frequencies to be amplified is determined to be four, namely 1GHz, 2GHz, 4GHz and 8GHz, then n1, n2 and n3 are 2, 4 and 8 respectively.

[0055] Step S403: Determine the electrical length of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies based on the frequency ratio.

[0056] According to some embodiments, the relationship between electric length and frequency can be derived from equation (2):

[0057]

[0058] Where r is a positive real number and rf0 is the reference frequency.

[0059] The electrical length of each transmission line section at each matching frequency is obtained as shown in equation (3):

[0060]

[0061]

[0062] Step S404: Determine the reflection coefficient corresponding to the impedance transmission line in the multi-frequency impedance matching device based on the electrical length of the impedance transmission line in the multi-frequency impedance matching device at its respective matching frequency and the load impedance value.

[0063] Step S405: Determine the characteristic impedance of the corresponding impedance transmission line based on the reflection coefficient.

[0064] According to some embodiments, an N-frequency impedance transformer is designed, consisting of 2N sections of stepped impedance transmission lines. Let the electrical length of each transmission line section at each matching frequency be θ. i The characteristic impedance is Zn(i, n∈[1,2N]).

[0065] According to some embodiments, N-frequency impedance transformation constraint equations can be constructed. These constraint equations include a zero-frequency condition and a reflection coefficient matching condition at a specified matching frequency. The impedance transformation constraint equation A·Γ=B is established, where A represents the coefficient matrix formed by the reflection coefficient constraint conditions at each matching frequency, as shown in equation (5):

[0066]

[0067] Wherein, represents the electrical length of the impedance transmission line in the multi-frequency impedance matching circuit at its respective matching frequency.

[0068] B represents the reflection coefficient for each matched frequency, which can be represented by equation (6):

[0069]

[0070] Where Z0 represents the external impedance, for example, 50 ohms, Z L This represents the load impedance.

[0071] Γ is the transpose matrix, denoted by equation (7), which includes the reflection coefficients of each transmission line:

[0072]

[0073] The reflection coefficient can be obtained using the impedance transformation constraint equation. Among them, N+1 reflection coefficients are obtained, and the other N coefficients are mirror images of these N+1 reflection coefficients. The relationship between the reflection coefficients at the matching frequency and the mirror frequency is shown in equation (8). The input impedances at the matching frequency and the mirror frequency are conjugates:

[0074]

[0075] The relationship between the reflection coefficient and the characteristic impedance is shown in equation (9):

[0076]

[0077] Finally, based on the relationship between the reflection coefficient and the characteristic impedance, the characteristic impedance Z of each transmission line can be calculated. n As shown in equation (10):

[0078]

[0079] Thus, step S404 can specifically include:

[0080] Based on the electrical lengths of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies and the load impedance value, an impedance transformation constraint equation is constructed; and

[0081] Based on the impedance transformation constraint equation, the reflection coefficients corresponding to each impedance transmission line in the multi-frequency impedance matching device are determined.

[0082] Step 406: Determine the size of the impedance transmission line based on the electrical length and characteristic impedance of any impedance transmission line in the multi-frequency impedance matching device.

[0083] According to some embodiments, the specific dimensions of each transmission line section, including the transmission line length and width, are determined based on the electrical length θ and impedance value Z. The transmission line can be a coplanar waveguide or a microstrip line. The physical length and dimensions of each stepped transmission line section are determined sequentially and then connected in series. A capacitor and an inductor resonant cavity are connected to the ends of the transmission lines.

[0084] Figure 5 This is a flowchart of a method for determining parameters in a discrete multi-frequency parametric amplifier according to another embodiment of this application. Figure 4 compared to, Figure 5 Steps S501 to S506 shown are Figure 4 Steps S401 to S406 are the same, except that... Figure 5 The method shown also includes step S507.

[0085] In step S507, the frequency corresponding to the electrical length of each transmission line in the multi-frequency impedance matching device being 90° is determined as the reference frequency.

[0086] In the process of determining the electrical length of each transmission line section in the multi-frequency impedance matching circuit described above, a positive real number r and a reference frequency rf0 were used. The selection of r determines the electrical length of the transmission line.

[0087] According to some embodiments, the frequency at which the electrical length of each transmission line segment in the impedance transformation is 90° is defined as the reference frequency. The method for determining r is as follows: for a given frequency ratio of f0:n1f... 0: :n2f 0: :…n N-1 f 0: For N-frequency impedance transformation, it is required that the image frequency of the specified matching frequency does not appear in f0~n N-1 f 0: Within the frequency range.

[0088] For example, assuming the total electrical length of a dual-frequency impedance transformer at the lower frequency is θ, then the reference frequency range of a multi-frequency impedance transformer is n. N-1 <r<Nπ / θ.

[0089] So, for Figure 5 Step S503 shown may specifically include: determining the electrical length of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies based on the frequency ratio that is the same as the number of matching frequencies to be amplified and the reference frequency.

[0090] Figure 6 These are schematic diagrams of a traditional broadband impedance matching circuit and a schematic diagram of the multi-frequency impedance matching circuit in the discrete multi-frequency parametric amplifier of this application. Figure 6 As shown, a broadband impedance matching transmission line consists of multiple stepped transmission lines with an electrical length of θ = λ / 4; a multi-frequency impedance matching transmission line consists of multiple stepped transmission lines with an electrical length of θ < λ / 4. For the same number of transmission line sections, the total length of a multi-frequency impedance matching circuit is much shorter than that of a broadband impedance matching circuit. Figure 6 In the diagram, Z0 represents the external impedance, Z... L This represents the load impedance. It is evident that the electrical length of the transmission line in the multi-frequency impedance matching device of this application is shorter than the electrical length of the transmission line obtained through conventional methods.

[0091] Figure 7 This is a schematic diagram of signal amplification using a discrete multi-frequency parametric amplifier according to an embodiment of this application. Figure 7 As shown, based on the above-mentioned multi-frequency impedance matching device design, the discrete multi-frequency parametric amplifier of this application can amplify signals with discrete discontinuous bandwidths (such as quantum bit signals) and amplify more bits and a wider range of frequencies.

[0092] Example 1

[0093] The multi-bit frequencies are located at 4.3GHz, 5.8GHz, and 7.3GHz, respectively. A parametric amplifier needs to be designed to amplify the bit frequency signals at the corresponding frequency positions. According to the scheme of this application, the design steps are as follows:

[0094] 1. This parametric amplifier is designed as a 3-frequency impedance transformer, with center frequencies at 4.3 GHz, 5.8 GHz, and 7.3 GHz. According to the design method described above, 6 stepped impedance transformer sections are required. The electrical length and characteristic impedance values ​​of the stepped impedance transformer obtained according to the method are shown in the table. This multi-frequency impedance transformer can match a 50-ohm impedance to 20 ohms.

[0095] 2. Based on the values ​​of the 3-frequency, 6-section stepped impedance transformer shown in Table 1, on a sapphire substrate (dielectric constant ε...), r =10.4) was prepared using niobium as the superconducting material (thickness T = 100 nm, conductivity set to 6.7 e) as the substrate. 15 S / m, loss tangent 5e -4 A coplanar waveguide transmission line is constructed. The center conductor width W, spacing G, and length L corresponding to the characteristic impedance value of each section are determined. The substrate parameters are: dielectric constant ε... r =10.4, height H=500 mm, superconducting layer thickness 100 nm, loss tangent 10 -4 .

[0096] 3. Prepare a resonant cavity consisting of lumped capacitance and Josephson junction inductance at the end of the transmission line in section 6.

[0097] 4. Simulate the parametric amplifier using software (e.g., Advance Design software), and the results are as follows. Figure 8 As shown, the insertion loss S11 at the corresponding positions of 4.3GHz, 5.8GHz, and 7.3GHz is less than 50dB.

[0098] Table 1. Parameter Design of Three-Frequency Impedance Converter

[0099]

[0100] Example 2

[0101] The multiple bit frequencies are located at 1GHz, 2.9GHz, 3.5GHz, and 4.9GHz, respectively. A parametric amplifier needs to be designed to amplify the bit frequency signals at the corresponding frequency positions. According to the scheme of this application, the design steps are as follows:

[0102] The parametric amplifier was designed as a 4-frequency impedance transformer, with center frequencies at 1 GHz, 2.9 GHz, 3.5 GHz, and 4.9 GHz. Following the design method described above, eight stepped impedance transformer sections are required. The electrical length and characteristic impedance values ​​of the stepped impedance transformer obtained using the method are shown in Table 2. A microstrip transmission line was used, and the specific dimensions of each matching section were calculated and connected in series to form the transmission line. A resonant cavity consisting of a lumped capacitance and a Josephson junction inductance was fabricated at the end of the 8th transmission line section. Figure 9 The results of the ADS simulation show that the S11 is less than 20dB at frequencies of 1, 2.6, 3.5, and 4.9 GHz. Since the 2.9 GHz frequency is close to the 3.5 GHz frequency, the insertion loss is relatively small in the 2.9–3.5 GHz range.

[0103] Table 2. Parameter Design of Quad-Frequency Impedance Converter

[0104]

[0105] Example 3

[0106] The multi-bit frequencies are located at 4GHz, 6GHz, and 8GHz, respectively. A parametric amplifier needs to be designed to amplify the bit frequency signals at these corresponding frequency positions. This embodiment compares the amplification effects of using binomial broadband impedance matching and multi-frequency impedance matching. Figure 10 As can be seen, the transmission line length L using the multi-frequency matching method described in this application is approximately 1.52 mm, with insertion loss S11 <-40 dB in the 4 GHz, 6 GHz, and 8 GHz bands, and insertion loss S11 <-30 dB in the 3.5 GHz to 8.5 GHz range. In contrast, using traditional binomial broadband matching requires five stepped impedance matching sections to achieve the same bandwidth, with a length L ≈ 2.62 mm, significantly longer than the multi-frequency matching scheme of this application. Furthermore, with the same transmission line length, the bandwidth using binomial broadband matching is 4.5 GHz to 7.5 GHz, a much smaller amplification bandwidth than the multi-frequency matching scheme of this application. In summary, the multi-frequency impedance matching parametric amplifier has the advantages of high integration, a wide frequency range, and simple design.

[0107] Based on the above-described method, according to another aspect of this application, a device for determining parameters in a discrete multi-frequency parametric amplifier is provided. For example... Figure 11As shown, the device includes a first determining module 1101, used to determine the load impedance value based on the capacitance and inductance values ​​of the resonant cavity; a second determining module 1102, used to determine a frequency ratio equal to the number of matching frequencies to be amplified, wherein the frequency ratio corresponds one-to-one with the matching frequencies to be amplified; a third determining module 1103, used to determine the electrical length of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies based on the frequency ratio; a fourth determining module 1104, used to determine the reflection coefficient corresponding to the impedance transmission lines in the multi-frequency impedance matching device based on the electrical length of the impedance transmission lines at their respective matching frequencies and the load impedance value; a fifth determining module 1105, used to determine the characteristic impedance of the corresponding impedance transmission line based on the reflection coefficient; and a sixth determining module 1106, used to determine the size of the impedance transmission line based on the electrical length and characteristic impedance of any impedance transmission line in the multi-frequency impedance matching device.

[0108] The third determining module 1105 is used for:

[0109] Based on the electrical lengths of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies and the load impedance value, an impedance transformation constraint equation is constructed; and

[0110] Based on the impedance transformation constraint equation, the reflection coefficients corresponding to each impedance transmission line in the multi-frequency impedance matching device are determined.

[0111] Figure 12 This is a schematic diagram of a parameter determination device in a discrete multi-frequency parametric amplifier according to another embodiment of this application. Figure 11 compared to, Figure 12 Modules 1201 to 1206 shown are Figure 11 Modules 1101 to 1106 are the same, except that, Figure 12 The device shown also includes a seventh determining module 1207, used to determine the frequency corresponding to the electrical length of each transmission line in the multi-frequency impedance matching device when it is 90° as the reference frequency.

[0112] The third determining module 1203 can also be used to: determine the electrical length of the impedance transmission line in the multi-frequency impedance matching device at its respective matching frequency based on the frequency ratio that is the same as the number of matching frequencies to be amplified and the reference frequency.

[0113] Based on the method and apparatus for determining parameters in a discrete multi-frequency parametric amplifier provided in this application, a multi-frequency impedance transformation method is proposed by performing variable substitution and considering the transmission between two adjacent stepped transmission lines, while maintaining the linear characteristics of the reflection coefficient. This simplifies the transcendental constraint equations in the transmission line theory solution into a single matrix equation, simplifying the design process and facilitating the design of multi-frequency impedance transformers with high accuracy. According to the scheme of this application, firstly, multi-frequency impedance matching only needs to consider the gain at the quantum bit signal frequency, without needing to amplify the entire frequency band. Therefore, it can amplify quantum bit signals with a wider range of distributions, resulting in a discrete multi-frequency parametric amplifier with a wide frequency coverage. Secondly, the length of the multi-frequency impedance matching transmission line is significantly smaller than that of the broadband impedance matching transmission line, thus achieving the same effect in a smaller size, improving integration density, and making it more suitable for chip integration design and micro / nano fabrication. Furthermore, the design of the multi-frequency impedance matching transmission line proposed in this application is relatively simple and computationally inefficient.

[0114] Furthermore, the discrete multi-frequency parametric amplifier designed in this application can be used not only for amplifying quantum bit signals but also for amplifying other signals. For example, an amplifier designed with a broadband impedance converter can amplify signals in one frequency band, while the discrete multi-frequency parametric amplifier designed in this application can amplify signals in multiple frequency bands. Therefore, if multiple frequency band signals need to be amplified, multiple amplifiers designed with broadband impedance converters may be required. However, with the solution in this application, only one discrete multi-frequency parametric amplifier is needed, thus greatly improving the integration.

[0115] See Figure 13 , Figure 13 An electronic device is provided, including a processor and a memory. The memory stores computer instructions, which, when executed by the processor, cause the processor to perform the computer instructions to achieve the following: Figure 4 and Figure 5 The method and its detailed scheme are shown.

[0116] It should be understood that the above-described device embodiments are merely illustrative, and the device disclosed in this invention can be implemented in other ways. For example, the division of units / modules described in the above embodiments is only a logical functional division, and there may be other division methods in actual implementation. For example, multiple units, modules, or components may be combined, integrated into another system, or some features may be ignored or not executed.

[0117] Furthermore, unless otherwise specified, the functional units / modules in the various embodiments of the present invention can be integrated into one unit / module, or each unit / module can exist physically separately, or two or more units / modules can be integrated together. The integrated units / modules described above can be implemented in hardware or as software program modules.

[0118] If the integrated unit / module is implemented in hardware, the hardware can be digital circuits, analog circuits, etc. The physical implementation of the hardware structure includes, but is not limited to, transistors, memristors, etc. Unless otherwise specified, the processor or chip can be any suitable hardware processor, such as a CPU, GPU, FPGA, DSP, and ASIC, etc. Unless otherwise specified, the on-chip cache, off-chip memory, and storage can be any suitable magnetic or magneto-optical storage medium, such as resistive random access memory (RRAM), dynamic random access memory (DRAM), static random access memory (SRAM), enhanced dynamic random access memory (EDRAM), high-bandwidth memory (HBM), hybrid memory cube (HMC), etc.

[0119] If the integrated unit / module is implemented as a software program module and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer electronic device (which may be a personal computer, server, or network electronic device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0120] This application embodiment also provides a non-transitory computer storage medium storing a computer program, which, when executed by multiple processors, causes the processors to perform actions such as... Figure 4 and Figure 5The method and its detailed scheme are shown.

[0121] The embodiments of this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this application. Furthermore, any changes or modifications made by those skilled in the art based on the ideas of this application, and on the specific implementation methods and application scope of this application, are all within the scope of protection of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for determining parameters in a discrete multi-frequency parametric amplifier, the discrete multi-frequency parametric amplifier comprising a resonant cavity and a multi-frequency impedance matching circuit, characterized in that, include: The load impedance value is determined based on the capacitance and inductance values ​​of the resonant cavity. The lowest matching frequency among the matching frequencies to be amplified is used as the reference frequency, and a frequency ratio is determined that is the same as the number of matching frequencies to be amplified, wherein the frequency ratio corresponds one-to-one with the matching frequencies to be amplified. According to the frequency ratio, according to Determine the electrical length of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies, wherein, Indicates frequency ratio, Indicates the electrical length, This represents the reference frequency, where r is a positive real number. For reference frequency, , This indicates the number of matching frequencies to be amplified; Based on the electrical lengths of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies and the load impedance value, determine the reflection coefficient corresponding to the impedance transmission lines in the multi-frequency impedance matching device; and Based on the reflection coefficient, determine the characteristic impedance of the corresponding impedance transmission line; The step of determining the reflection coefficient corresponding to the impedance transmission line in the multi-frequency impedance matching device based on the electrical length of the impedance transmission line in the multi-frequency impedance matching device at its respective matching frequency and the load impedance value includes: Based on the electrical lengths of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies and the load impedance value, an impedance transformation constraint equation is constructed; and Based on the impedance transformation constraint equation, determine the reflection coefficient corresponding to each impedance transmission line in the multi-frequency impedance matching device; The impedance transformation constraint equation is A. Γ=B, where A represents the coefficient matrix formed by the reflection coefficient constraints at each matching frequency, B represents the reflection coefficient at each matching frequency, and Γ represents the reflection coefficient corresponding to each impedance transmission line. .

2. The method as described in claim 1, characterized in that, Also includes: The dimensions of the impedance transmission line are determined based on the electrical length and characteristic impedance of any impedance transmission line in the multi-frequency impedance matching device.

3. The method as described in claim 1, characterized in that, Also includes: The frequency corresponding to the electrical length of each transmission line in the multi-frequency impedance matching device being 90° is determined as the reference frequency.

4. The method as described in claim 3, characterized in that, Determining the electrical length of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies based on the frequency ratio includes: The electrical length of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies is determined based on the frequency ratio, which is the same as the number of matching frequencies to be amplified, and the reference frequency.

5. A device for determining parameters in a discrete multi-frequency parametric amplifier, the discrete multi-frequency parametric amplifier comprising a resonant cavity and a multi-frequency impedance matching circuit, characterized in that, include: The first determining module is used to determine the load impedance value based on the capacitance and inductance values ​​of the resonant cavity; The second determining module is used to take the lowest matching frequency among the matching frequencies to be amplified as the reference frequency and determine the frequency ratio that is the same as the number of matching frequencies to be amplified, wherein the frequency ratio corresponds one-to-one with the matching frequencies to be amplified. The third determining module is used to determine the frequency ratio based on... Determine the electrical length of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies, wherein, Indicates frequency ratio, Indicates the electrical length, This represents the reference frequency, where r is a positive real number. For reference frequency, , This indicates the number of matching frequencies to be amplified; The fourth determining module is used to determine the reflection coefficient corresponding to the impedance transmission line in the multi-frequency impedance matching device based on the electrical length of the impedance transmission line in the multi-frequency impedance matching device at its respective matching frequency and the load impedance value; and The fifth determining module is used to determine the characteristic impedance of the corresponding impedance transmission line based on the reflection coefficient. The fourth determining module is used for: Based on the electrical lengths of the impedance transmission lines in the multi-frequency impedance matching device at their respective matching frequencies and the load impedance value, an impedance transformation constraint equation is constructed; and Based on the impedance transformation constraint equation, determine the reflection coefficient corresponding to each impedance transmission line in the multi-frequency impedance matching device; The impedance transformation constraint equation is A. Γ=B, where A represents the coefficient matrix formed by the reflection coefficient constraints at each matching frequency, B represents the reflection coefficient at each matching frequency, and Γ represents the reflection coefficient corresponding to each impedance transmission line. .

6. The apparatus as claimed in claim 5, characterized in that, Also includes: The sixth determining module is used to determine the size of the impedance transmission line based on the electrical length and characteristic impedance of any impedance transmission line in the multi-frequency impedance matching device.

7. The apparatus as described in claim 5 or 6, characterized in that, Also includes: The seventh determining module is used to determine the frequency corresponding to the electrical length of each transmission line in the multi-frequency impedance matching device being 90° as the reference frequency.

8. An electronic device, characterized in that, The device includes a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program in the memory, implements the method of any one of claims 1 to 4.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 4.

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