Harmonic suppression in dispersive resonators for traveling wave parametric amplifiers

Abstract

A traveling wave parametric amplifier (TWPA) transmission line with improved bandwidth includes one or more unit cells. Each unit cell includes a grounded capacitor and a Josephson junction in series, the Josephson junction configured to provide inductance and nonlinearity. One or more dispersive resonators are coupled to the transmission line. The dispersive resonator is configured to (i) use a first harmonic mode of the resonator for resonant phase matching in the transmission line, and (i i) prevent a second mode of the resonator from interacting with intermodulation products of the transmission line.

Description

Background Art Technical Field

[0001] The present disclosure relates generally to superconducting signal amplifiers.

[0002] Description of Related Technology

[0003] The traveling wave parametric amplifier (TWPA) is a commonly used superconducting amplifier. The TWPA includes a nonlinear LC transmission line with a Josephson junction, providing inductance and nonlinearity. The TWPA is the workhorse amplifier for some quantum computing systems because it has high gain, low noise, and sufficient bandwidth and saturation power for readout of multiple qubits.

[0004] When a TWPA with a signal tone is used to amplify a signal tone, the TWPA amplifies the signal tone by extracting power from the excitation tone. This is a four-wave mixing process in which two pump photons are converted into new photons at the signal frequency and a photon at the idle frequency. In this process, both energy (frequency) and momentum (wave vector) are conserved. For small signals, these two criteria can be met simultaneously. However, at large pump tones, power-dependent phase shifts may occur, so the wave vector criterion is no longer met. In order to meet these two criteria simultaneously, resonant phase matching is introduced. Specifically, by periodically adding microwave resonators throughout the transmission line, the dispersion of the transmission line is changed so that for pump tones near the frequency of the microwave resonators, these two criteria are met simultaneously. These microwave resonators are called dispersive resonators or dispersive features, which are components added to the TWPA transmission line to add dispersion when the TWPA transmission line is used to amplify signals.

[0005] Unfortunately, due to the addition of the dispersive resonator, there may be an additional gain drop, which reduces the usable bandwidth of the TWPA. This drop is when the frequency of the second mode of the dispersive resonator phase matches the four-wave mixing process that produces higher-order intermodulation products. Summary of the invention

[0006] Some embodiments of the present disclosure provide a traveling wave parametric amplifier (TWPA) transmission line with improved bandwidth. The transmission line includes one or more unit cells. Each unit cell includes a grounded capacitor and a Josephson junction in series to provide inductance and nonlinearity. One or more dispersive resonators are coupled to the transmission line. Each dispersive resonator is configured to (i) use the first harmonic mode of the resonator for resonant phase matching in the transmission line, and (ii) prevent the second mode of the resonator from interacting with the intermodulation products of the transmission line. The second mode is prevented from interacting with the intermodulation products of the device, and the drop in signal gain is removed, thereby increasing the available bandwidth of the TWPA. In other words, the resonator is configured to remove or suppress coupling to the second mode in the frequency range of the intermodulation products of the TWPA.

[0007] In some embodiments, a node coupling method is used to suppress coupling of the second mode. Specifically, the resonator is a quarter-wavelength resonator, which is coupled to the transmission line at the voltage node of the second mode of the resonator via a coupling capacitor. The resonator includes a first transmission line grounded from the voltage node of the second mode and a second transmission line to an open circuit. The first mode is the fundamental frequency of the resonator, and the second mode is the third harmonic of the fundamental frequency of the resonator.

[0008] In some embodiments, a transformed resonator approach is used such that the resonator is configured to detune or decouple the second mode by several GHz such that the second mode of the resonator is not aligned with the intermodulation products of the transmission line. The resonator is a one-eighth wavelength transmission line resonator that includes a grounded inductor in parallel with an open transmission line. In some embodiments, the open transmission line is a transformed equivalent capacitor that acts as a shunt capacitor to ground. In some embodiments, the transformed equivalent capacitor has an effective capacitance determined based on (i) the characteristic impedance of the open transmission line and (ii) the target dispersion frequency of the resonator, and the ground inductor has an inductance set according to the target dispersion frequency of the resonator and the effective capacitance of the transformed equivalent capacitor.

[0009] TWPAs are useful for scaling up quantum computers. By using node coupling or transformation resonator methods, the drop in gain can be eliminated or pushed out of the range of intermodulation (IM) products, thereby increasing the available readout bandwidth of the TWPA. Increasing the available readout bandwidth of the TWPA can be used to increase the number of multiplexed qubits measured with a single TWPA, or to further space the readout resonators to reduce crosstalk. Removing the gain drop promotes detuning between the readout resonator and the qubit to reduce Purcell loss in the quantum system.

[0010] The foregoing summary is intended to serve as a brief introduction to some embodiments of the present disclosure. It is not meant to be an introduction or overview of all inventive subject matter disclosed herein. The following detailed description and the drawings referenced in the detailed description will further describe the embodiments described in the summary as well as other embodiments. Therefore, an overview, detailed description, and drawings are provided in order to understand all embodiments described by this document. In addition, the claimed subject matter is not limited by the illustrative details in the summary, specific embodiments, and drawings, but is defined by the appended claims, because the claimed subject matter may be embodied in other specific forms without departing from the spirit of the present subject matter. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The accompanying drawings are illustrative embodiments. They do not show all embodiments. Additionally or alternatively, other embodiments may be used. Details that may be obvious or unnecessary may be omitted to save space or for more effective description. Some embodiments may be implemented with additional components or steps and / or without all components or steps shown. When the same number appears in different drawings, it refers to the same or similar components or steps.

[0012] Figure 1 A traveling wave parametric amplifier (TWPA) transmission line interspersed with dispersive resonators for maintaining energy and momentum conservation constraints is shown in accordance with an exemplary embodiment.

[0013] Figure 2A -B shows an example quarter-wavelength resonator used as a dispersion feature in a TWPA transmission line.

[0014] Figure 3 The drop in transmission of the dispersive resonator in the second mode is shown for an unpumped TWPA.

[0015] Figure 4 The gain drop due to pumping the second mode of the dispersive resonator of the TWPA is shown.

[0016] Figure 5A -B conceptually illustrates harmonic suppression through node coupling consistent with an exemplary embodiment.

[0017] Figure 6 Shown is the drop in transmission in TWPA removed by node coupling in accordance with an illustrative embodiment.

[0018] Figure 7 The gain drop of a pumped TWPA is shown by eliminating node coupling according to an exemplary embodiment.

[0019] Fig. 8A -B illustrates an example 1 / 8th wavelength transmission line resonator consistent with an exemplary embodiment.

[0020] Fig. 9 It is shown that the transmission dip in the unpumped TWPA is eliminated by switching the resonator.

[0021] Fig.10 The elimination of the gain drop of a pumped TWPA by switching the resonator is shown. DETAILED DESCRIPTION

[0022] In the following detailed description, numerous specific details are set forth by way of example in order to provide a thorough understanding of the relevant teachings. However, it should be appreciated that the present teachings may be practiced without these details. In other instances, well-known methods, procedures, components, and / or circuits have been described at a relatively high level without detail in order to avoid unnecessarily obscuring aspects of the present teachings.

[0023] The backbone of the Josephson TWPA is a nonlinear transmission line. The unit cell of the transmission line consists of a grounded capacitor and a Josephson junction in series to provide inductance and nonlinearity. s The signal tone propagates through the p When a TWPA is driven by a pump tone, the TWPA amplifies the signal tone by extracting power from the pump tone. This is a four-wave mixing process, in which the two pump photons are converted into new photons at the signal frequency and a photon at the idler frequency. (The idler signal is a microwave tone that is the result of a nonlinear amplification process; for the four-wave mixing process, the idler signal frequency is f i =2f p –f s ).

[0024] In this process, both energy (frequency) and momentum (wave vector) are conserved, i.e., 2ω p =ω s +ω i and 2k p =k s +k i (ω p ,ω s and ω i are the angular frequencies of the pump, signal and idler signals respectively, and k p , k s and k j are the wave vectors of the pump, signal, and idler signals, respectively). However, at large pump tones, power-dependent phase shifts may occur, so that the wave vector criterion (2k p =k s +k i ).

[0025] To satisfy both criteria simultaneously, resonant phase matching was introduced. Specifically, by periodically adding microwave resonators throughout the transmission line, the dispersion of the transmission line K(ω) is changed so that for pump tones near the frequency of the microwave resonators, both criteria (conservation of energy and momentum) are satisfied simultaneously. These microwave resonators are called dispersive resonators or dispersive features, which are components added to a TWPA transmission line to add dispersion when the TWPA transmission line is used to amplify a signal.

[0026] Figure 1 A TWPA 100 is shown interspersed with dispersive resonators consistent with an illustrative embodiment, the dispersive resonators being used to maintain constraints on energy and momentum conservation. As shown, the TWPA transmission line 100 features a chain of Josephson junction inductive elements (labeled "J") in series with a capacitive element (labeled "C") connected to ground. The TWPA transmission line 100 is also interspersed with periodic dispersive resonators, including resonators 111 and 112 coupled to the transmission line 100 through coupling capacitors.

[0027] There are different ways to achieve decentralization in TWPA. Figure 2A -B shows an example quarter-wavelength resonator 210 used as a dispersion feature in a TWPA transmission line 200. As shown, the TWPA transmission line 200 features a chain of Josephson inductive elements (labeled "J") and capacitive elements (labeled "C"). The TWPA transmission line 200 can also be interspersed with periodic dispersion resonators, including quarter-wavelength resonators 210. The advantage of this type of dispersion feature is that it is easy to make all resonators uniform. The challenge of this approach is that the quarter-wavelength resonator has multiple (harmonic) modes.

[0028] Figure 2A The first mode (dashed line) and second mode (dashed line) of the quarter-wavelength resonator 210 are shown. The first or lowest mode (fundamental frequency or first harmonic) of the quarter-wavelength resonator is used for resonant phase matching in the TWPA. The next lowest mode (second mode) of the quarter-wavelength resonator is a harmonic at three times the fundamental frequency, or the third harmonic. (If a half-wave resonator is used, the second mode will be twice the fundamental frequency, or the second harmonic). In this TWPA implementation, there is a gain drop, which reduces the usable bandwidth of the TWPA. This drop occurs where the second mode phase of the dispersive resonator 210 is matched to the generation of higher-order intermodulation products.

[0029] Figure 3 and Figure 4 A graph showing the performance of the TWPA 200 is shown based on Figure 2B Parameter values ​​shown in . Figure 3The drop in transmission in the second mode for the dispersive resonator for an unpumped TWPA is shown. The figure includes a plot of a simulation of the scattering parameters of an unpumped TWPA with a dispersive resonator at 8.75 GHz. The figure also shows the interaction with the second mode at 26 GHz. Figure 4 The gain drop at the second mode of the dispersive resonator is shown for a pumped TWPA. The figure includes a simulation of the scattering parameters of the TWPA when pumped at 8.55 GHz. Figure 3 and 4 As shown, two typical gain dips can be observed around 8.5 GHz due to the stopband created by the dispersive resonator near the pump frequency. However, there is an additional gain dip around 7.9 GHz due to the generation of IM products near the second mode of the dispersive resonator.

[0030] During parametric amplification, undesirable tones are also generated at the intermodulation products of the signal and pump frequencies. Unfortunately, the higher harmonics of the dispersive resonator may have parasitic interactions with the intermodulation (IM) products, thereby increasing the coupling to the IM products, such as ω IM3 =2ω p +ω s and ω IM5 =4ω p –ω s (ω IM3 and ω IM5 are the angular frequencies of the third- and fifth-order intermodulation products. This occurs under phase-matched conditions (i)k IM3 =2k p +k s and (ii) k IM5 =2k p +k i (where k IM3 and k IM5 is the wave vector generated by the third-order and fifth-order intermodulation. This appears in the device as s The decrease in gain (such as Figure 4 This droop reduces the usable signal bandwidth of the device by up to 300 MHz or more, which limits the range of readout frequencies compatible with TWPA. Moreover, since the droop frequency depends on the pump frequency f p , which limits the range of available pump frequencies compatible with the desired bandwidth.

[0031] Some embodiments of the present invention provide methods for eliminating this drop in the signal gain of a TWPA. In some embodiments, the gain drop is eliminated by removing or suppressing coupling with the second (or higher) harmonic. Specifically, by coupling the resonator to the transmission line at the voltage node of the second mode. This prevents the transmission line from interacting with the second mode of the dispersive resonator, thereby avoiding a drop in gain. This method is also referred to as a node coupling method.

[0032] Figure 5A -B conceptually illustrates harmonic suppression through nodal coupling. The figure shows a TWPA transmission line 500 featuring a chain of Josephson inductive elements (labeled "J") and capacitive elements (labeled "C"). The TWPA transmission line 500 is also interspersed with periodic dispersive resonators, such as quarter-wavelength resonators 520. As shown, the quarter-wavelength resonators 520 are coupled to the TWPA transmission line 500 at the voltage node of the second mode 505 via coupling capacitors 510. Due to this nodal coupling, intermodulation products in the transmission line 500 cannot interact with the second mode of the resonator, thereby removing parasitic gain drops. (Alternatively, nodal coupling can be achieved by inductively coupling the resonator to the transmission line at the current node of the second mode)

[0033] Figure 6 and 7 Shows Figure 3 and 4 The corresponding plots of , where the gain drop in the TWPA is eliminated by node coupling. These plots are based on Figure 5B The simulations were performed with the parameter values ​​shown. Figure 6 Elimination of tilt in transmission in a TWPA by node coupling is shown. The figure includes a plot of a simulation of scattering parameters of an unpumped TWPA (TWPA 500) where the dispersive resonator is at 8.75 GHz, but the second mode node (e.g., voltage node 505) is coupled. As shown, the first harmonic of the dispersive resonator is still at 8.75 GHz. However, the dip at 26 GHz due to the second mode is greatly reduced. Figure 7 Elimination of gain droop of a pumped TWPA (TWPA 500) by nodal coupling is shown. The figure includes simulations of the scattering parameters of the TWPA when the TWPA is pumped to obtain gain at 8.55 GHz but with second mode nodal coupling. As shown, the gain droop at 7.9 GHz has disappeared due to the second mode of the dispersive resonator.

[0034] In some embodiments, the gain drop is eliminated by configuring the dispersive resonator to detune or decouple the second or higher harmonics by several GHz while maintaining the ease of manufacture and uniformity of the quarter-wavelength resonator. Specifically, the quarter-wavelength resonator is replaced by an inductor connected in parallel with the Richard transformation equivalent of a capacitor to form a 1 / 8 wavelength transmission line resonator. Therefore, the 1 / 8 wavelength transmission line resonator is also called a Richard transformation resonator.

[0035] Fig. 8A -B shows an example 1 / 8 wavelength transmission line resonator. The figure shows a TWPA transmission line 800, which is characterized by a chain of Josephson inductor elements (marked "J") and capacitive elements (marked "C"). The TWPA transmission line 800 is also interspersed with periodic dispersion resonators, such as transformation resonators 810. As shown, the TWPA 800 is coupled to the transformation resonator 810 through a coupling capacitor 815. The transformation resonator 810 is formed by an inductor 820 (grounded) in parallel with an open circuit 1 / 8 wavelength transmission line 830. The open circuit transmission line 830 effectively acts as a capacitor that bypasses the ground and is therefore also a transformation equivalent capacitor. Therefore, this method is also called Richard's transformation resonator method. The higher modes of this resonator structure are no longer aligned with the IM products of the parametric process in the TWPA transmission line 800, thereby avoiding a decrease in gain. This method has the additional advantage of reducing the length of the transmission line section and thus reducing the overall footprint of the resonator.

[0036] Inductor 820 and transformation equivalent capacitor 830 are parameterized to detune or decouple the second (or higher) harmonics. Specifically, when combined in parallel with inductor 820 to form resonant circuit 810, the first (harmonic) mode of open transmission line 830 is at the desired or target dispersion frequency. The effective capacitance C0 of open transmission line 830 is determined by the characteristic impedance Z0 of the line and the desired dispersion frequency ω of the resonator. res To set. Specifically:

[0037]

[0038] The inductance in the resonator (eg, inductor 820) is set according to the following equation:

[0039]

[0040] These values ​​can be determined by the coupling capacitor C c The value of (e.g., the capacitance of coupling capacitor 815) is modified.

[0041] Fig. 9 and Fig.10 They are shown respectively Figure 3 and Figure 4, where the gain drop in the TWPA 800 is eliminated by Richard's transformation resonator. These figures are based on Figure 8B Fig. 2. Simulations performed with the parameter values ​​shown in Fig. 2. Fig. 9 Richard's transformation resonator is shown to eliminate the transmission dip in an unpumped TWPA. The figure includes a plot of a simulation of the scattering parameters of an unpumped TWPA with a dispersive resonator at 8.75 GHz, but now the dip due to the second mode is moved from 27 GHz, within the IM product range, to greater than 30 GHz, outside the IM product range. Fig.10 It is shown that Richard's transformation resonator eliminates the gain dip of a pumped TWPA. As shown, when the TWPA is pumped to gain (eg, 8.55 GHz), the dip at 7.9 GHz disappears.

[0042] TWPA can be used to expand quantum computers. By using the node coupling method (described in reference to Figures 5-7 above) or the transformation resonator method (described in reference to Figures 8-10), the gain drop can be eliminated or pushed out of the range of the IM product, thereby increasing the available readout bandwidth of the TWPA. Increasing the available readout bandwidth of the TWPA can be used to increase the number of multiplexed qubits measured using a single TWPA, or to further space the readout resonators to reduce crosstalk. Removing the gain drop promotes detuning between the readout resonator and the qubit to reduce Purcell losses in the quantum system. (The Purcell effect is the enhancement or loss of the spontaneous emission rate of a quantum system due to its environment)

[0043] The description of various embodiments of the present teachings has been presented for illustrative purposes, but is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terms used herein are selected to best explain the principles of the embodiments, practical applications, or technical improvements existing in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

[0044] Although the above has described what is considered to be the best state and / or other examples, it should be understood that various modifications may be made therein, and the subject matter disclosed herein may be implemented in various forms and examples, and the teachings may be applied to many applications, only some of which are described herein. The appended claims are intended to claim any and all applications, modifications and variations that fall within the true scope of the present teachings.

[0045] The components, steps, features, objects, benefits, and advantages discussed herein are merely illustrative. None of them, or the discussion related to them, is intended to limit the scope of protection. Although various advantages have been discussed herein, it will be understood that not all embodiments necessarily include all advantages. Unless otherwise indicated, all measurements, values, ratings, positions, sizes, dimensions, and other specifications in this specification, including those set forth in the appended claims, are approximate and not exact. They are intended to have a reasonable range consistent with the functions to which they are related and the customary practices of the field to which they belong.

[0046] Many other embodiments are also contemplated. These include embodiments with fewer, additional and / or different components, steps, features, objects, benefits and advantages. These also include embodiments in which components and / or steps are arranged and / or ordered in different ways.

[0047] Although the foregoing has been described in conjunction with exemplary embodiments, it should be understood that the term "exemplary" is meant only as an example, rather than the best or optimal. Except as immediately stated above, nothing stated or illustrated is intended or should be construed to cause any component, step, feature, object, benefit, advantage, or equivalent to be dedicated to the public, whether or not stated in the claims.

[0048] It should be understood that, unless a specific meaning is elaborated in addition herein, the terms and expressions used herein have the common meaning consistent with these terms and expressions about their corresponding respective investigation and research fields. Relational terms such as the first and second etc. can be used only to distinguish one entity or action from another, without requiring or implying any actual such relationship or order between these entities or actions. The term "comprise", "comprising" or any other variation thereof is intended to cover non-exclusive inclusion, so that the process, method, article or device comprising a series of elements not only include those elements, but also may include other elements that are not clearly listed or are inherent to such process, method, article or device. In the absence of further constraints, the element with "one" or "an" in front does not exclude the existence of additional identical elements in the process, method, article or device comprising the element.

[0049] The abstract of the present disclosure is provided to allow the reader to quickly determine the nature of the technical disclosure. It should be understood that it is not used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing detailed description, it can be seen that in order to make the present disclosure smooth, various features are grouped together in various embodiments. This method of disclosure should not be interpreted as reflecting the intention that the claimed embodiments require more features than the features explicitly recited in each claim. On the contrary, as reflected in the attached claims, the subject matter of the invention lies in less than all the features of a single disclosed embodiment. Therefore, the following claims are hereby incorporated into the specific implementation mode, wherein each claim is independently a subject matter claimed separately.

Claims

1. A device comprising: a transmission line comprising one or more unit cells, each unit cell comprising a Josephson junction connected in series and a capacitor connected to ground, the Josephson junction being configured to provide inductance and nonlinearity; as well as One or more resonators are coupled to the transmission line, each resonator being configured to (i) use a first mode of the resonator for resonant phase matching in the transmission line, and (ii) prevent a second mode of the resonator from interacting with intermodulation products of the transmission line.

2. The apparatus of the preceding claim, wherein the resonator is configured to remove or suppress coupling of the second mode between the transmission line and the resonator in a frequency range of the intermodulation products of the transmission line.

3. The apparatus of any of the preceding claims, wherein the resonator is coupled to the transmission line via a coupling capacitor at a voltage node of the second mode of the resonator.

4. The device according to the preceding claim, wherein the resonator is a quarter wavelength resonator, the first mode is the fundamental frequency of the resonator, and the second mode is the third harmonic of the fundamental frequency of the resonator.

5. The apparatus of any of the preceding claims, wherein the resonator is coupled to the transmission line at a current node of the second mode of the resonator via inductive coupling.

6. The apparatus of any preceding claim, wherein the resonator is configured to detune or decouple the second mode by several GHz such that the second mode of the resonator is not aligned with the intermodulation products of the transmission line.

7. An apparatus according to any one of the preceding claims, wherein the resonator comprises a grounded inductor connected in parallel with an open transmission line.

8. The device according to the preceding claim, wherein the resonator is a one-eighth wavelength transmission line resonator.

9. The device according to any of the two preceding claims, wherein the open circuit transmission line is a transformation equivalent capacitor operating as a shunt grounded capacitor.

10. The apparatus of the preceding claim, wherein the transformation equivalent capacitor has an effective capacitance determined based on (i) a characteristic impedance of the open transmission line and (ii) a target dispersion frequency of the resonator.

11. The device according to the preceding claim, wherein the grounded inductor has an inductance set according to the target dispersion frequency of the resonator and the effective capacitance of the transformation equivalent capacitor.

12. A method comprising: providing a transmission line including one or more unit cells, each unit cell including a Josephson junction connected in series and a capacitor connected to ground, the Josephson junction being configured to provide inductance and nonlinearity; coupling one or more resonators to the transmission line; as well as The resonator is configured to (i) use a first mode of the resonator for resonant phase matching in the transmission line and (ii) prevent a second mode of the resonator from interacting with intermodulation products of the transmission line.

13. The method according to the preceding claim, wherein the resonator is configured to remove or suppress coupling of the second mode between the transmission line and the resonator in a frequency range of the intermodulation products of the transmission line.

14. The method according to any of the two preceding claims, wherein the resonator is a quarter wave resonator coupled to the transmission line via a coupling capacitor at a voltage node of the second mode of the resonator.

15. The method according to any of the three preceding claims, wherein the resonator comprises a first transmission line from a voltage node of the second mode to ground and a second transmission line to an open circuit.

16. The method according to any of the four preceding claims, wherein the resonator is configured to detune or decouple the second mode by several GHz so that the second mode of the resonator is not aligned with the intermodulation products of the transmission line.

17. The method according to any of the five preceding claims, wherein the resonator is an eighth wavelength transmission line resonator comprising a grounded inductor connected in parallel with an open transmission line.

18. The method according to the preceding claim, wherein the open circuit transmission line is a transformation equivalent capacitor operating as a shunt grounded capacitor.

19. The method of the preceding claim, wherein the transformation equivalent capacitor has an effective capacitance determined based on (i) a characteristic impedance of the open transmission line and (ii) a target dispersion frequency of the resonator.

20. The method according to the preceding claim, wherein the grounded inductor has an inductance set according to the target dispersion frequency of the resonator and the effective capacitance of the transformation equivalent capacitor.

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