BACKGROUND

[0001] In quantum circuits, a Josephson ring modulator is coupled to two superconducting microwave resonators and three-way mixing is performed between differential modes supported by the two superconducting microwave resonators and a non-resonant, common drive fed to the Josephson ring modulator. Due to coupling the

Josephson ring modulator to the two superconducting microwave resonators, the device is limited in the choice of the frequency of differential modes, which can cause one or more problems. For example, coupling the Josephson ring modulator to low-frequency, transmission-line resonators can have various problems, such as occupying a large area (e.g., a large footprint). Another problem is the relatively large linear inductance associated with the low resonance-frequency transmission-line compared to the inductance of the Josephson ring modulator. This can result in a very reduced participation ratio which in turn requires, for its operation, very high external quality factors (Qs) for the resonators. However, high external Qs for the resonators is undesirable because it can give rise to very narrow dynamical bandwidths, which severely limit the device usability and practicality.

[0002] In addition, coupling the Josephson ring modulator to low-frequency, lumped-element resonators can require the use of large lumped capacitances and large lumped inductances. Large lumped capacitances and inductances are difficult to realize in practice. Large capacitances can have considerable loss (lowering the internal Q of the device) and as a result can cause a considerable portion of the quantum signal to be lost. Large geometric inductances usually suffer from parasitic capacitances which limit their utility. Large kinetic inductances usually rely on unconventional thin superconductors which are difficult to fabricate and integrate.

SUMMARY

[0003] The following presents a summary to provide a basic understanding of one or more embodiments of the invention. This summary is not intended to identify key or critical elements, or delineate any scope of the particular embodiments or any scope of the claims. Its sole purpose is to present concepts in a simplified form as a prelude to the more detailed description that is presented later. In one or more embodiments of the invention described herein are devices, systems and methods, that mix surface acoustic waves and microwave signals.

[0004] According to an embodiment of the invention, a superconducting device can comprise a superconducting surface acoustic wave resonator (SAW) and a superconducting microwave resonator. The superconducting device can also comprise a Josephson ring modulator (JRM) coupled to the superconducting SAW resonator and the superconducting microwave resonator. The JRM can be a dispersive nonlinear three-wave mixing element. An advantage of such a superconducting device is that dissipationless, three-wave mixing and amplification can be performed between low wave microwave frequencies of the superconducting SAW resonator and high microwave frequencies of the superconducting microwave resonator.

[0005] In some examples, the superconducting SAW resonator of the superconducting device can comprise a first superconducting Bragg mirror and a second superconducting Bragg mirror. The second superconducting Bragg mirror can be separated from the first superconducting Bragg mirror by a distance that is an odd integer multiple of a half-wavelength supported by the superconducting SAW resonator. An advantage of such a superconducting device is that the superconducting device can operate over a single, a few, or many modes of the superconducting SAW resonator.

[0006] According to some implementations, the superconducting device can also advantageously comprise a first external feedline coupled to the superconducting SAW resonator through an interdigitated capacitance device. The first external feedline can carry one or more first input signals and one or more first output signals of the superconducting SAW resonator. Further, the superconducting device can comprise a second external feedline coupled to the superconducting microwave resonator. The second external feedline can carry one or more second input signals and one or more second output signals of the superconducting microwave resonator. An advantage of such a superconducting device is that low frequencies of the superconducting SAW resonator and high frequencies of the superconducting microwave resonator can be received, mixed, and amplified.

[0007] According to an embodiment of the invention, provided is a superconducting circuit that can comprise a superconducting SAW resonator and a JRM coupled to the superconducting SAW resonator. Further, the superconducting circuit can comprise a superconducting microwave resonator coupled to the JRM. The JRM is a dispersive nonlinear three-wave mixing element. According to some implementations, the superconducting SAW resonator is realized on a low-loss piezo-electric dielectric substrate. An advantage of such a superconducting circuit is that dissipationless, three-wave mixing and amplification can be facilitated between low wave microwave frequencies of the superconducting SAW resonator and high microwave frequencies of the superconducting microwave resonator.

[0008] The superconducting SAW resonator of the superconducting circuit can comprise, according to some implementations, a first superconducting Bragg mirror and a second superconducting Bragg mirror. The first superconducting Bragg mirror and the second superconducting Bragg mirror can be separated by a distance that is an odd integer multiple of a half-wavelength supported by the superconducting SAW resonator. An advantage of such a superconducting circuit is that low frequencies of the superconducting SAW resonator and high frequencies of the superconducting microwave resonator can be received, mixed, and amplified.

[0009] In accordance with some implementations, the superconducting circuit can comprise a first external feedline coupled to the superconducting SAW resonator through an interdigitated capacitance device. The first external feedline can carry one or more first input signals and one or more first output signals of the

superconducting surface acoustic wave resonator. In addition, the superconducting circuit can comprise a second external feedline coupled to the superconducting microwave resonator. The second external feedline can carry one or more second input signals and one or more second output signals of the superconducting microwave resonator. An advantage of such a superconducting circuit is that low frequencies of the superconducting surface acoustic wave resonator and high frequencies of the superconducting microwave resonator can be received, mixed, and amplified.

[0010] Another embodiment of the invention relates to a method that can comprise forming a JRM that comprises one or more Josephson junctions arranged in a Wheatstone-bridge configuration. The method can also comprise coupling the JRM to a superconducting SAW resonator and a superconducting microwave resonator. The JRM can be a dispersive nonlinear three-wave mixing element. An advantage of such a method is that a superconducting device can be fabricated, which can perform dissipationless, three-wave mixing between low wave microwave frequencies of the superconducting SAW resonator and high microwave frequencies of the superconducting microwave resonator.

[0011] In some implementations, the method can comprise forming the superconducting SAW resonator from a first superconducting Bragg mirror and a second superconducting Bragg mirror. The method can also comprise separating the first superconducting Bragg mirror from the second superconducting Bragg mirror by a distance defined as an odd integer multiple of a half-wavelength supported by the superconducting surface acoustic wave resonator. An advantage of such a method is that the fabricated superconducting device can operate over a single, a few, or many modes of the superconducting surface acoustic wave resonator

[0012] A further embodiment of the invention relates to a superconducting device that can comprise a superconducting SAW resonator. The superconducting SAW resonator can comprise a first periodic structure comprising first metallic fingers and first dielectric gaps. The superconducting SAW resonator can also comprise a second periodic structure comprising second metallic fingers and second dielectric gaps. The first periodic structure and the second periodic structure can be separated by a distance defined as an odd integer multiple of a half-wavelength supported by the superconducting SAW resonator. Further, the superconducting device can comprise a dispersive nonlinear three-wave mixing element coupled to the superconducting SAW resonator. The dispersive nonlinear three-wave mixing element can comprise one or more Josephson junctions arranged in a Wheatstone-bridge configuration. In addition, the superconducting device can comprise a superconducting microwave resonator coupled to the dispersive nonlinear three-wave mixing element. An advantage of such a superconducting device is that dissipationless, three-wave mixing and amplification can be performed between low wave microwave frequencies of the superconducting SAW resonator and high microwave frequencies of the superconducting microwave resonator while occupying a small space and through the use of low-loss resonators.

DESCRIPTION OF THE DRAWINGS

[0013] FIG. 1 is a block diagram of a circuit comprising the JRM in accordance with an of the invention.

[0014] FIG. 2 is a block diagram of a circuit comprising a superconducting SAW resonator in accordance with an embodiment of the invention.

[0015] FIG. 3 is a schematic of a circuit for a superconducting device that comprises a SAW resonator and superconducting microwave resonator coupled to a JRM in accordance with an embodiment of the invention.

[0016] FIG. 4 is a flow diagram of a method for fabrication of a device in accordance with an embodiment of the invention.

[0017] FIG. 5 is a flow diagram of a method for fabrication of a device comprising a pump drive port in accordance with an embodiment of the invention.

[0018] FIG. 6 is a flow diagram of a method for fabrication of a device comprising two metallic/dielectric mirrors in accordance with an embodiment of the invention.

[0019] FIG. 7 is a flow diagram of a method for fabrication of a device comprising a JRM coupled to a superconducting SAW resonator and a superconducting microwave resonator in accordance with an embodiment of the invention.

[0020] FIG. 8 is a flow diagram of a method for fabrication of a superconducting quantum device in accordance with an embodiment of the invention.

[0021] FIG. 9 is a flow diagram of a method for fabrication of a superconducting quantum device comprising external feedlines in accordance with an embodiment of the invention. DETAILED DESCRIPTION

[0022] The following detailed description is merely illustrative and is not intended to limit embodiments of the invention and/or application or uses thereof. Furthermore, there is no intention to be bound by any expressed or implied information presented in the preceding Background or Summary sections, or in the Detailed Description section.

[0023] One or more embodiments of the invention are now described with reference to the drawings, wherein like referenced numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a more thorough understanding of the one or more embodiments of the invention. It is evident, however, in various cases, that the one or more embodiments of the invention can be practiced without these specific details.

[0024] As it relates to circuits, and more specifically quantum circuits, if a JRM is coupled to two superconducting wave resonators, there is a limitation with respect to the choice of the differential modes that couple to the JRM.

For example, a problem associated with coupling the JRM to low-frequency, transmission-line resonators is that a large area is occupied by the device. A solution provided by the superconducting device, the superconducting circuit, and the methods discussed herein is that a superconducting SAW resonator is utilized, which is compact and, therefore, a size of the superconducting device is reduced.

[0025] Another problem associated with prior art superconducting devices (e.g., devices that utilize two superconducting microwave resonators) is that the prior art superconducting devices are limited to mixing frequencies between 5 Gigahertz (GHz) and 15 GHz. The various superconducting devices, circuits, and methods discussed herein provide a solution to this problem through the utilization of a superconducting SAW resonator and superconducting wave resonator that enable dissipationless, three-wave mixing and amplification between low microwave frequencies (e.g., about 0.1 GHz to about 4 GHz) and high microwave frequencies (e.g., around 5 GHz to around 15 GHz).

[0026] Given the above problems with prior art superconducting devices, the various aspects provided herein can be implemented to produce a solution to one or more of these problems in the form of a superconducting device, superconducting circuit, and method of fabricating the same. Such devices, circuits and methods implementing such a superconducting device can have an advantage of reduced size and low-loss resonators, as compared to conventional techniques.

[0027] According to some implementations, the device can function as a Josephson mixer between surface acoustic waves (phonons) and microwave signals (photons), as a lossless frequency converter between a surface acoustic wave and a microwave signal, as a nondegenerate parametric Josephson amplifier for a surface acoustic wave and a microwave signal, and or as an entangler of a phononic mode and photonic mode.

[0028] FIG. 1 is a block diagram of a circuit 100 comprising a superconducting SAW resonator 102, a superconducting microwave resonator 104, and a JRM 106.

[0029] In a piece of quantum hardware, which includes the superconducting qubits space, a mechanism to implement gate operations or measurements on the quantum hardware is to generate or receive microwave signals by the superconducting SAW resonator 102 and/or via the superconducting microwave resonator 104. As discussed herein, according to some implementations, the circuit 100 can operate as a Josephson mixer between surface acoustic waves (phonons) and microwave signals (photons), as a lossless frequency converter between a surface acoustic wave and a microwave signal, as a nondegenerate parametric Josephson amplifier for a surface acoustic wave and a microwave signal, and/or as an entangler of a phononic mode and photonic mode.

[0030] SAW resonators are electro-mechanical resonators for phonons, which can resonate at microwave frequencies of around 0.5 GHz to 5 GHz. SAW resonators (or SAW filters) are used in many telecommunication applications (e.g., mobile phones). SAW resonators can also be useful in quantum computing applications and quantum circuits in the microwave domain, as discussed herein. Further, SAW resonators can have high internal Quality (Q) factors, which can be in excess of 10 ⁵ . Therefore, SAW resonators can have a very low loss. In addition, SAW resonators are very compact. For example, the surface acoustic resonance wavelengths are very short (e.g., less than 1 micro metre or < 1 miti).

[0031] The superconducting SAW resonator 102 can be a low frequency device and the superconducting microwave resonator 104 can be a high frequency device. Further, the superconducting SAW resonator 102 can be implemented on a low-loss piezo-electric dielectric substrate. The low-loss piezo-electric dielectric substrate can comprise a material selected from a group of materials comprising quartz, gallium arsenide, lithium niobite, and/or zinc oxide, or the like. The superconducting microwave resonator 104 can be implemented using lumped-element capacitance and lumped-element inductance. Further details related to the superconducting SAW resonator 102 and the superconducting microwave resonator 104 will be provided below with respect to FIGs. 2 and 3.

[0032] The JRM 106 is a device that can be based on Josephson tunnel junctions. For example, the JRM 106 can comprise one or more Josephson junctions arranged in a Wheatstone-bridge configuration. The one or more Josephson junctions can comprise a material selected from a group of materials comprising aluminum and niobium. Further, the JRM 106 can perform non-degenerate mixing in the microwave regime, without losses. According to some implementations, the JRM 106 can be a dispersive nonlinear three-wave mixing element. [0033] The JRM 106 can support two differential modes and two common modes (one of which is at zero frequency, and, therefore, not applicable to the one or more embodiments described herein). By coupling the JRM 106 to a suitable electromagnetic environment (which supports two differential microwave modes), the circuit 100 can be used to perform various quantum processing operations such as lossless frequency conversion in the microwave domain, parametric amplification at the quantum limit (e.g., amplification of quantum signals in the microwave domain), and/or generation of two-mode squeezing.

[0034] The JRM 106 can comprise one or more Josephson junctions arranged in a Wheatstone-bridge configuration. The Josephson junctions are illustrated as a first Josephson junction 108, a second Josephson junction 110, a third Josephson junction 112, and a fourth Josephson junction 114. The Josephson junctions (e.g., the first Josephson junction 108, the second Josephson junction 110, the third Josephson junction 112, the fourth Josephson junction 114) can be formed in a loop. Further, the Josephson junctions can be utilized to perform the mixing as discussed herein.

[0035] The JRM 106 also can comprise four additional junctions (internal to the loop), which can be shunt junctions according to some implementations. These four additional junctions are labeled as a first internal junction 116, a second internal junction 118, a third internal junction 120, and a fourth internal junction 122. The four internal junctions can facilitate tuning of the frequency of the circuit 100. The tunability can be obtained with the application of external magnetic flux. For example, induced magnetic flux threads the Josephson ring modulator.

In this configuration, the four internal junctions, which are larger than the junctions on the outer loop, can function as linear inductors shunting the outer Josephson junctions. By threading external flux through the inner loops, the total inductance of the JRM 106 can change, which can lead to a change in the resonance frequencies of the resonator coupled to the JRM 106. According to some implementations, threading the external flux can be facilitated with magnetic coils, on-chip flux lines, nearby flux lines, and/or on a different chip/layer.

[0036] In addition, the configuration of the JRM 106 defines points or nodes where the external junctions meet. Accordingly, there can be a first node 124 at the bottom of the JRM 106; a second node 126 at the right side of the JRM 106; a third node 128 at the top of the JRM 106; and a fourth node 130 at the left side of the JRM 106. It is noted that the terms bottom, right side, top, and left side are for purposes of explaining the disclosed aspects with respect to the figures and the disclosed aspects are not limited to any particular plane or orientation of the JRM 106 and/or the circuit 100 and its associated circuitry.

[0037] The four nodes can be utilized to define the differential mode and the common mode hosted by the circuit 100. The modes can be orthogonal and do not overlap one another. Further, the nodes, as illustrated, can be physically orthogonal. For example, the first node 124 and the third node 128 are vertical to one another and the second node 126 and the fourth node 130 are horizontal to one another. [0038] The nodes can be utilized to couple the JRM 106 to the superconducting SAW resonator 102 and to the superconducting microwave resonator 104. For example, a first set of opposite nodes (e.g., the first node 124 and the third node 128) can be chosen to operatively couple the JRM 106 to the superconducting SAW resonator 102. The first node 124 can be coupled to the superconducting SAW resonator 102 via a first wire 132 (or first lead) and the third node 128 can be coupled to the superconducting SAW resonator 102 via a second wire 134 (or second lead).

[0039] The second set of opposite nodes (e.g., the second node 126 and the fourth node 130) can be chosen to operatively couple the JRM 106 to the superconducting microwave resonator 104. For example, the second node 126 can be coupled to the superconducting microwave resonator 104 via a third wire 136 (or third lead) and the fourth node 130 can be coupled to the superconducting microwave resonator 104 via a fourth wire 138 (or fourth lead).

[0040] As illustrated, the first wire 132 and the second wire 134 can be coupled to the superconducting SAW resonator 102 at different locations of the superconducting SAW resonator 102. Further, the third wire 136 and the fourth wire 138 can be coupled to the superconducting microwave resonator 104 at different locations of the superconducting microwave resonator 104. Further details related to the coupling locations will be provided below with respect to FIG. 3.

[0041] The superconducting SAW resonator 102, the superconducting microwave resonator 104, and the JRM 106 are portions of a frequency- converter/mixer/ amplifier/ entangler device. The device can receive external microwave photons or phonons from other quantum devices connected to the microwave port and/or the SAW port of the device.

[0042] The circuit 100, as well as other aspects discussed herein can be utilized in a device that facilitates manipulation of quantum information in accordance with one or more embodiments described herein. Aspects of devices (e.g., the circuit 100 and the like), systems, apparatuses, or processes explained in this disclosure can constitute machine-executable component(s) embodied within machine(s), e.g., embodied in one or more computer readable mediums (or media) associated with one or more machines. Such component(s), when executed by the one or more machines, e.g., computer(s), computing device(s), virtual machine(s), etc. can cause the machine(s) to perform the operations described.

[0043] In various embodiments of the invention, the device can be any type of component, machine, system, device, facility, apparatus, and/or instrument that comprises a processor and/or can be capable of effective and/or operative communication with a wired and/or wireless network. Components, machines, apparatuses, systems, devices, facilities, and/or instrumentalities that can comprise the device can include tablet computing devices, handheld devices, server class computing machines and/or databases, laptop computers, notebook computers, desktop computers, cell phones, smart phones, consumer appliances and/or instrumentation, industrial and/or commercial devices, hand-held devices, digital assistants, multimedia Internet enabled phones, multimedia players, and the like.

[0044] In various embodiments, the device can be a quantum computing device or quantum computing system associated with technologies such as, but not limited to, quantum circuit, quantum processor, quantum computing, artificial intelligence, medicine and materials, supply chain and logistics, financial services, and/or other digital technologies. The circuit 100 can employ hardware and/or software to solve problems that are highly technical in nature, that are not abstract and that cannot be performed as a set of mental acts by a human. Further, in certain embodiments, some of the processes performed can be performed by one or more specialized computers (e.g., one or more specialized processing units, a specialized computer with a quantum computing component, etc.) to carry out defined tasks related to machine learning.

[0045] The device and/or components of the device can be employed to solve new problems that arise through advancements in technologies mentioned above, computer architecture, and/or the like. One or more embodiments of the device can provide technical improvements to quantum computing systems, quantum circuit systems, quantum processor systems, artificial intelligence systems and/or other systems. One or more embodiments of the circuit 100 can also provide technical improvements to a quantum processor (e.g., a superconducting quantum processor) by improving processing performance, processing efficiency, processing characteristics, timing characteristics, and/or power efficiency of the quantum processor.

[0046] FIG. 2 is a block diagram of a circuit 200 comprising a superconducting SAW resonator.

[0047] The superconducting SAW resonator 102 can comprise a first superconducting metallic/dielectric mirror (e.g., a first Bragg mirror 202) and a second superconducting metallic/dielectric mirror (e.g., a second Bragg mirror 204). The first Bragg mirror 202 can be separated from the second Bragg mirror 204 by a distance that is an odd integer multiple of a half-wavelength supported by the superconducting SAW resonator 102. A Bragg mirror comprises a periodic structure of metallic fingers and dielectric gaps positioned at a defined distance from one another.

[0048] According to some implementations, the superconducting SAW resonator 102 can be attached to (e.g., realized on) a low-loss piezo-electric dielectric substrate (not shown). The low-loss piezo-electric dielectric substrate can comprise a material selected from a group of materials comprising one or more of quartz, gallium arsenide, lithium niobite, and zinc oxide, or a similar material. [0049] Further, a first interdigitated capacitance device or first IDC device 206 and a second IDC device 208 can be included. The first IDC device 206 can couple between the superconducting SAW resonator 102 and the JRM 106. The second IDC device 208 can couple between the superconducting SAW resonator 102 and an external port (e.g., a signal port 212).

[0050] For example, the first IDC device 206 can be positioned at a center of the superconducting SAW resonator 102. A first set of opposite nodes of the JRM 106 can be connected to opposite nodes of the first IDC device 206. For example, the first node 124 of the JRM 106 can be connected to a first side of the first IDC device 206 (e.g., via the first wire 132). Further, the third node 128 of the JRM 106 can be connected to a second side of the first IDC device 206 (e.g., via the second wire 134).

[0051] A second set of opposite nodes of the Josephson ring modulator can be connected to the superconducting microwave resonator 104. For example, the second node 126 of the JRM 106 can be connected to a first side of the superconducting microwave resonator 104 (e.g., via the third wire 136). Further, the fourth node 130 of the JRM 106 can be connected to a second side of the superconducting microwave resonator 104 (e.g., via the fourth wire 138).

[0052] The circuit 100 can also comprise a first external feedline 210 coupled to the superconducting SAW resonator 102 through the second IDC device 208. The first external feedline 210 can be connected to a signal port 212 (e.g., a radio frequency (rf) source). The first external feedline 210 can carry one or more input signals and one or more output signals of the superconducting SAW resonator 102.

[0053] A second external feedline 214 can be coupled to the superconducting microwave resonator 104. The second external feedline 214 can be connected to an idler port 216 (e.g., a microwave source). The second external feedline 214 can carry one or more input signals and one or more output signals of the superconducting microwave resonator 104.

[0054] Further, the JRM 106 can be operative connected to a pump port 218 (e.g., via the second wire 134 or another wire). The pump port 218 can be connect to a microwave source. The pump port 218 can supply the required energy for the operation of the circuit 100. For example, upon or after pump power is supplied from the pump port 218 to the JRM 106, the superconducting SAW resonator 102 and the superconducting microwave resonator 104 can be electrically connected through the JRM 106. Flowever, when power is not supplied through the pump port 218 (e.g., the power supply is off), the superconducting SAW resonator 102 and the superconducting microwave resonator 104 can be electrically isolated from one another.

[0055] For amplification, ideally there would be a microwave signal that is propagating on the idler transmission line (e.g., the second external feedline 214) that is connected to the idler port 216. In an example, assume that the microwave signal is weak and it carries some quantum information that is of value. The information goes into the circuit 100 and there is a pump tone that is fed to the device (e.g., via the pump port 218) that can generate a parametric amplification between the idler mode and the signal mode supported by the superconducting SAW resonator 102. In this example, an input signal is not needed at both the signal port 212 and the idler port 216. Instead, a signal is only needed on one port and quantum noise can enter through the other port. The deterministic signal carrying quantum information and the quantum noise can be mixed by the device via the pump drive and amplified upon leaving the device. Thus, the signal that carries information can come either from the signal port 212, or the idler port 216, or can have two signals carrying information entering both ports at substantially the same time. For simplicity, assume the signal is entering the circuit 100 through one port and the other port is only receiving quantum noise. In this case, through the interaction with the pump (e.g., the pump port 218) and the JRM 106 three-wave mixing takes place between the common mode (pump) and two differential modes (the idler and the signal). If the pump frequency is the sum of the signal and idler resonance frequencies, the device functions as a phase-preserving parametric amplifier operating near the quantum limit. The respective output signal exiting the signal port 212 and idler port 216 can be an amplified superposition of the input signals entering both ports (e.g., the signal port 212 and idler port 216).

[0056] According to some implementations, magnetic flux threading the JRM 106 can be induced through the one or more external superconducting magnetic coils. For example, magnetic flux threading the JRM 106 can be induced using external superconducting magnetic coils attached to a device package or using on-chip flux lines.

[0057] FIG. 3 is a schematic of a circuit 300 for a superconducting device that comprises a SAW resonator and superconducting microwave resonator coupled to a JRM.

[0058] It is noted that the Josephson junctions and the four internal junctions of the JRM 106 are not labeled in FIG. 3 for purposes of simplicity. Flowever, the element numbering of the junctions for purposes of explanation are the same as the labeling of FIGs. 1 and 2. In addition, the circuit 300 and its associated components can be implemented on a single chip, according to some implementations.

[0059] As mentioned, the nodes of the JRM 106 can comprise a first set of opposite nodes that can be oriented in a vertical direction to one another. For example, the first set of opposite nodes can comprise the first node 124 and the third node 128, which can operatively couple the JRM 106 to the superconducting SAW resonator 102 (e.g., via the first wire 132 and the second wire 134). Further, the nodes of the JRM 106 can comprise a second set of opposite nodes, which can be oriented in a horizontal manner. For example, the second set of opposite nodes can comprise the second node 126 and the fourth node 130, which can operatively couple the JRM 106 to the superconducting microwave resonator 104. It is noted that although illustrated and described with respect to a horizontal direction and/or a vertical direction, the disclosed aspects are not limited to this orientation and other orientations can be utilized.

[0060] The first set of opposite nodes (e.g., the first node 124 and the third node 128) can be coupled to opposite electrodes of a first interdigitated capacitor or first IDC 302 (e.g., the first IDC device 206) of the superconducting SAW resonator 102, creating a first orthogonal mode. For example, the first node 124 of the JRM 106 can be coupled to a first electrode of the first IDC 302, indicated at 304. Further, the third node 128 of the JRM 106 can be coupled to a second electrode of the first IDC 302, indicated at 306. The first IDC 302 can be positioned at a center of the superconducting SAW resonator 102.

[0061] The second set of opposite nodes (e.g., the second node 126 and the fourth node 130) can be coupled to a second capacitor 310 (e.g., a shunting capacitor) forming a superconducting microwave resonator 104, where the JRM is the inductive element of the resonator. The superconducting microwave resonator can support a second orthogonal differential mode of the JRM 106. The capacitance (e.g., the first capacitor 308) functions as a coupling capacitor between the microwave resonator (formed by the JRM 106 and the second capacitor 310) and the external feedline/port (e.g., the idler port 216) of the device. According to some implementations, the first capacitor 308 and the second capacitor 310 can be respective capacitors chosen from a group of capacitors comprising a gap capacitor, an interdigitated capacitor, and/or a plate capacitor. In the case of plate capacitance, the dielectric material should have very low-loss at the level of single microwave photons.

[0062] As illustrated, the superconducting SAW resonator 102 can comprise the first IDC 302, a second IDC 312 (e.g., the second IDC device 208), and a set of metallic/dielectric mirrors (e.g., the first Bragg mirror 202 and the second Bragg mirror 204). The components of the superconducting SAW resonator 102 (e.g., the first IDC 302, the second IDC 312, the first Bragg mirror 202, the second Bragg mirror 204) is implemented on a piezo-electric substrate. For example, the piezo electric substrate can comprise one or more of quartz, gallium arsenide, lithium niobite, zinc oxide, and/or similar materials.

[0063] Different ports can be utilized to access the superconducting SAW resonator 102 and the superconducting microwave resonator 104. For example, the signal port 212 can be utilized to access the superconducting SAW resonator 102 and the idler port 216 can be utilized to access the superconducting microwave resonator 104.

[0064] The signal port 212 can be utilized to carry input signals and output signals. Therefore, in order to measure output signals from the superconducting SAW resonator 102, an IDC (e.g., the second IDC 312) can be placed between the first Bragg mirror 202 and the second Bragg mirror 204. One set of IDC fingers that are connected together are located at an rf-voltage anti-node (maximum/minimum) of the supported phononic mode. Therefore, the spacing between the fingers can be determined by the wavelength supported by the superconducting SAW resonator 102.

[0065] A distance between the centers of two consecutive fingers of the IDCs (e.g., the first IDC 302 and the second IDC 312) can be generally expressed as \ _a /2. The respective two sets of fingers of the IDCs can have opposite polarity according to an implementation. Further, the first Bragg mirror 202 and the second Bragg mirror 204 can be separated from one other, as indicated by line 314, by a distance that is an odd integer multiple of halfwavelength supported by the superconducting SAW resonator 102. The defined distance can be expressed as L _a , wherein L _a is an odd-integer multiple of X _a l2. Where \ _b < l ₃ .

[0066] A microwave tone is characterized by a wave that has a maximum amplitude and a minimum amplitude. The minimum amplitude should couple to one finger of the IDC (e.g., indicated at 304 or 306) and the maximum value should couple to the other finger, (e.g., indicated at 304 or 306) where the two fingers are connected to opposite nodes of the JRM 106 (e.g., the first node 124 and the third node 128). Therefore, the distance \ _a /2 can be selected to facilitate the maximum on the first finger and the minimum on the other finger.

[0067] Further, for purposes of explanation, the maximum amplitude has a plus sign (or a positive value) and the minimum amplitude has a minus sign (or a negative value). Therefore, the two opposite nodes of the JRM 106 can be excited by the positive (on the first finger) and the negative rf-voltages (on the second finger). These signals can alternate with time. Flowever, they should be opposite to one another at any given time. When the polarity is different, it can be referred to as a differential mode (where differential means opposite sign).

[0068] This can also apply to the case of the superconducting microwave resonator 104. As mentioned, the superconducting microwave resonator can comprise a first capacitor 308 coupling the resonator to the external port (e.g., the idler port 216) and the second capacitor 310 shunting the JRM 106. The two electrodes of the capacitor shunting the JRM 106 (e.g., the second capacitor 310) can have opposite voltages and can excite a second differential mode. Accordingly, a first differential mode of the JRM 106 is supported by the superconducting SAW resonator 102 and a second differential mode of the JRM 106 is supported by the superconducting microwave resonator 104.

[0069] Further, in order to perform the mixing, or the amplification, microwave energy is supplied for device operation. The energy source for the mixing and/or amplification is supplied through the pump port 218. The pump port 218 can provide a microwave signal, which can be a strong, coherent, non-resonant microwave tone that can supply energy for the circuit 100 to operate. According to some implementations, the microwave signal supplied by the pump port 218 can comprise a frequency that satisfies a defined equation determined based on the energy conservation of the three-wave mixing occurring in the circuit 100. [0070] In an example of amplification performed by the device, a first signal fa which lies within the bandwidth of the superconducting SAW resonator 102 and a second signal fa which lies within the bandwidth of the

superconducting microwave resonator 104. Further, the frequency of the second signal can be larger than the frequency of the first signal (fa > f _a ). To amplify both signals, the frequency of the pump tone fed through the pump port 218 should be the sum of the first signal and the second signal (e.g., f _a + fa). The energy of the

electromagnetic signal is proportional to its frequency. By taking the pump (e.g., the pump port 218) frequency to be the sum, if the pump interacts with the dispersive nonlinear medium (e.g., the JRM 106), a downconversion process can occur where the energetic photons of the pump split into a first set of photons at f _a and a second set of photons at fa. If the frequency is the sum, then the photons can split in this manner. For example, the photons can split into two halves: a first half (e.g., the first set of photons) at the lower frequency f _a and a second half (e.g., the second set of photons) at the higher frequency fa. Therefore, amplification can occur because the pump exchanges energy with the signal mode and idler mode and through this exchange entangled photons are generated in both modes. Similarly, a conversion process with non phonon-photon gain can convert one mode to the other (e.g., a photon to a phonon or a phonon to a photon). In this case, the pump frequency should be equal to the difference between fa and fa. Here fa is larger, so the equation can be fa minus fa.

[0071] According to an implementation, in the mixing process (conversion without photon-phonon gain) a phonon in the SAW resonator at the signal frequency can be upconverted into a microwave photon in the microwave resonator at the idler frequency. According to another implementation, the photon in the microwave resonator at the idler frequency can be downconverted to a phonon in the SAW resonator at the signal frequency. The energy exchange is enabled by the pump drive (e.g., fed through the pump port 218). Accordingly, either a pump photon is emitted or a pump photon is absorbed to facilitate the process.

[0072] If there is no pump signal applied to the pump port 218, the superconducting SAW resonator 102 and the superconducting microwave resonator 104 are separated (e.g., isolated from one another) and information exchange or information communications between the superconducting SAW resonator 102 and the

superconducting microwave resonator 104 does not occur. Upon or after a pump signal is applied to the pump port 218, it excites the common mode of the JRM 106, as illustrated in FIG. 2, the superconducting SAW resonator 102 and the superconducting microwave resonator 104 interact and information is exchanged.

[0073] According to some implementations, the pump drive is fed through the sigma port of a 180-degree hybrid 316, which is capacitively coupled to opposite nodes of the JRM 106, which in turn excites a common-mode of the JRM 106. According to some implementations, the 180-degree hybrid 316 operates as a power splitter.

[0074] By way of explanation and not limitation, a 180-degree hybrid is a passive microwave component that comprises four ports. A first port is referred to as a sum port 318 (or sigma port). If a signal is input to the sum port 318, the signal splits equally between two other ports (e.g., a second port 320 and a third port 322). The signals that are output from the second port 320 and the third port 322 can have the same phase. Thus, the first port is referred to as the sum port 318 because the phases of the split signals are equal. The pump drive (e.g., the pump port 218) can be fed through the sum port 318 of the 180-degree hybrid 316.

[0075] A fourth port can be referred to as a delta port 324 (or a difference port). If a signal is injected through the delta port 324 of the 180-degree hybrid (which, in FIG. 3, is terminated with 50 ohms), the hybrid would split the signal into two signals, coming out of the two ports (e.g., the second port 320 and the third port 322), but the split signals have a 180-degree phase difference. For example, if a first signal has a maximum value at one port (e.g., 320), the second signal at the other port (e.g., 322) has a minimum value. The pump port 218 can be fed through the sum port 318.

[0076] Also illustrated are a first lead 326 coming out of the second port 320 and a second lead 328 coming out of the third port 322. The signals that are output at the second port 320 and the third port 322 are half of the pump signal and have the same phase, as discussed above. The signals encounter small coupling capacitors (e.g., a first coupling capacitor 330 and a second coupling capacitor 332) that can be coupled to two opposite nodes of the JRM 106. According to some implementations, the first coupling capacitor 330 and the second coupling capacitor 332 can be respective capacitors chosen from a group of capacitors comprising a gap capacitor, an interdigitated capacitor, and a plate capacitor. As it relates to plate capacitance, the dielectric material should have very low-loss at the level of single microwave photons.

[0077] The first coupling capacitor 330 can be coupled to the first node 124 of the JRM 106 (through the first IDC 302) and the second coupling capacitor 332 can be coupled to the third node 128 of the JRM 106. In further detail, the first lead 326 and the second lead 328 can couple to two different sets of fingers of the first IDC 302 (illustrated at the first contact point 306 and a third contact point 334), that couple to two opposite nodes of the JRM 106. This connection enables exciting the common mode of the JRM 106 where the two opposite nodes of the JRM 106 are excited, not with opposite rf-voltage signs, but with equal signs. For example, the two opposite nodes can be excited with a positive-positive signal or a negative-negative signal.

[0078] The first lead 326 and the second lead 328 can be connecting superconducting wires that should be equal in length (e.g., phase matched) between the ports (e.g., the second port 320, the third port 322) of the 180 degree hybrid and the coupling capacitors (e.g., the first coupling capacitor 330, the second coupling capacitor 332, respectively). Also, the first wire 132 and the second wire 134 can be connecting superconducting wires that should be equal in length (e.g., phase matched) between the opposite nodes of the JRM 106 and the electrodes of the first IDC 302. Also, the third wire 136 and the fourth wire 138 can be connecting superconducting wires that should be equal in length (e.g., phase matched) between the opposite nodes of the JRM 106 and the electrodes of the second capacitor 310. Further, the connecting superconducting wires should be as short as possible and wide (e.g., have small series inductance).

[0079] The following provides further technical comments for an understanding of the various aspects disclosed herein. The speed of sound in the various piezoelectric substrates can be slower than the speed of light by several orders of magnitude (e.g., approximately five orders of magnitude, for example, 10 ⁵ ).

[0080] The effective length of the superconducting SAW resonator 102 can be slightly larger than L _a . This can be because the reflection off the Bragg mirrors does not happen on the mirror edges but within a certain penetration depth inside the Bragg mirrors.

[0081] The effective length (L _eff ) of the superconducting SAW resonator 102 and the speed of sound in the piezoelectric substrate (v _s ) can determine the cavity free spectral range (FSR): V _FSR = ^Vs . The SAW

^{2 L} eff

resonator can be similar to photonic cavities that support multimodes (resonances). The cavity free spectral range parameter can determine the frequency spacing between the multimodes supported by the superconducting SAW resonator 102.

[0082] The larger the spacing between the Bragg mirrors, the larger Leff is, and as a result the smaller the frequency separation between the SAW resonator modes. The Bragg mirrors can operate as reflective mirrors within a certain bandwidth. Modes that fall beyond their bandwidth are not supported by the SAW resonator because their phononic modes are not confined.

[0083] Depending on the VFSR and the bandwidth of the Bragg mirrors, the circuit 100 can operate over a single, a few, or many modes of the SAW resonator. It is noted that not all the modes supported by the SAW resonator would strongly couple to the JRM. Three-wave mixing operations in the circuit 100 can take place with phononic modes that couple strongly to the JRM. Modes couple strongly to the JRM when their anti-nodes align with the IDC fingers coupled to the JRM.

[0084] The circuit 100 can be a three-wave mixer, such as a Josephson mixer that relies on non-linear inductance of the Josephson junctions, which is lossless. The Josephson mixer is used to allow mixing between phonons supported by the superconducting SAW resonator 102 and microwave signals, which are carried by photons. This is different from conventional devices that couple a phonon to a phonon or a photon to a photon. Therefore, the disclosed aspects provide a significant improvement in the coupling. For example, the circuit 100 can allow conversion from a microwave signal to acoustic waves that resonate at low microwave frequencies. Further, the circuit 100 can amplify in a nondegenerate manner. Nondegenerate here means: (1) the circuit 100 is amplifying two different frequencies: one frequency at a high microwave frequency (example 12 GHz) and another relatively low microwave frequency (example 1 GHz), thus, nondegenerate means that the frequencies are different so there is a spectral nondegeneracy; and (2) there is also a spatial nondegeneracy because the microwave signal is supported by the superconducting microwave resonator 104, which is physically different than the superconducting SAW resonator 102 that supports the surface acoustic wave. Therefore, there is a spectral and a physical nondegeneracy. Due to this process of parametric amplification that is nondegenerate, the circuit 100 can entangle a phononic mode with a photonic mode, where entanglement is a quantum property where the two modes are strongly correlated with one another and inseparable from one another. Therefore, if a measurement is taken of one, the state of the other can be determined. Thus, they are entangled and they form one entity, although they can be separated in space by distance.

[0085] FIG. 4 is a flow diagram of a method 400 for fabrication of a device.

[0086] At 402, a JRM 106 can be formed. The JRM can comprise Josephson junctions (e.g., the first Josephson junction 108, the second Josephson junction 110, the third Josephson junction 112, the fourth Josephson junction 114) arranged in a Wheatstone-bridge configuration. The one or more Josephson junctions can comprise a first material selected from a first group of materials comprising aluminum and niobium.

[0087] Further, at 404, the JRM can be coupled to a superconducting SAW resonator 102 and a superconducting microwave resonator 104. The JRM can be a dispersive nonlinear three-wave mixing element.

[0088] FIG. 5 is a flow diagram of a method 500 for fabrication of a device comprising a pump drive port.

[0089] The method 500 starts at 502, when a JRM 106 is formed as described with reference to Fig. 4, the JRM can comprise one or more Josephson junctions arranged in a Wheatstone-bridge configuration. Further, the JRM can comprise a port, through which a pump drive (e.g., the pump port 218) can be fed.

[0090] At 504, a superconducting SAW resonator 102 can be formed. The superconducting SAW resonator can be realized on a piezoelectric substrate. A superconducting microwave resonator 104 can be formed at 506. Further, at 508, the JRM can be coupled to the superconducting SAW resonator and the superconducting microwave resonator.

[0091] A pump drive can be injected to the JRM through the port, at 510. For example, the pump drive can be fed through a sigma port of a 180-degree hybrid (e.g., the 180-degree hybrid 316). The 180-degree hybrid can be capacitively coupled to opposite nodes of the JRM, which in turn excites a common-mode of the JRM. [0092] FIG. 6 is a flow diagram of a method 600 for fabrication of a device comprising two metallic/dielectric mirrors.

[0093] The method 600 starts, at 602, with forming a JRM 106 as described with reference to Fig. 4, the JRM can comprise Josephson junctions arranged in a Wheatstone-bridge configuration.

[0094] A superconducting SAW resonator 102 can be formed, at 604. The SAW resonator can be formed from a first superconducting Bragg mirror (e.g., the first Bragg mirror 202) and a second superconducting Bragg mirror (e.g., the second Bragg mirror 204) realized over a piezoelectric substrate. At 606, the first superconducting Bragg mirror can be separated from the second superconducting Bragg mirror by a distance defined as an odd integer multiple of a half-wavelength of the main mode supported by the SAW resonator.

[0095] The method 600 can continue, at 608 and a superconducting microwave resonator 104 can be formed. Further, at 610 of the method 600, the JRM can be coupled to the superconducting surface acoustic wave resonator and the superconducting microwave resonator.

[0096] FIG. 7 is a flow diagram of a method 700 for fabrication of a device comprising a JRM coupled to a superconducting SAW resonator and a superconducting microwave resonator.

[0097] At 702, a JRM 106 that comprises Josephson junctions can be formed as described with reference to Fig. 4, the Josephson junctions can be arranged in a Wheatstone-bridge configuration.

[0098] A superconducting SAW resonator 102 can be formed at 704. The superconducting SAW resonator is realized on a low-loss piezo-electric dielectric substrate. For example, the low-loss piezo-electric dielectric substrate can comprise one or more materials selected from a group of materials comprising one or more of quartz, gallium arsenide, lithium niobite, and zinc oxide.

[0099] To form the superconducting SAW resonator, at 706, an interdigitated capacitance device (e.g., the first IDC 302) can be positioned at a center of the SAW resonator. The interdigitated capacitance device can be positioned between two metallic/dielectric Bragg mirrors. For example, the interdigitated capacitance device can be positioned between a first Bragg mirror 202 and a second Bragg mirror 204.

[00100] At 708 a superconducting microwave resonator 104 can be formed. The superconducting microwave resonator can be implemented using lumped-element capacitance and/or lumped-element inductance.

[00101] Further, at 710, a first set of opposite nodes (e.g., the first node 124 and the third node 128) of the JRM can be coupled to opposite nodes of the interdigitated capacitance device. For example, one node of the first set of opposite nodes can be coupled to a first electrode of the interdigitated capacitance device (indicated at 304 of FIG. 3). Another node of the first set of opposite nodes can be coupled to a second electrode of the interdigitated capacitance device (indicated at 306 of FIG. 3). It is noted that, according to some implementations, coupling the JRM to opposite nodes of the interdigitated capacitance device (at 710) can occur before forming the

superconducting microwave resonator (at 708).

[00102] In addition, at 712, a second set of opposite nodes (e.g., the second node 126 and the fourth node 130) of the JRM can be coupled to one or more capacitors (e.g., the first capacitor 308, the second capacitor 310) of the superconducting microwave resonator. For example, one node of the second set of opposite nodes can be connected to a first capacitor of the superconducting microwave resonator. Further, the two nodes of the second set of opposite nodes can be connected to two electrodes of the second capacitor of the superconducting microwave resonator.

[00103] FIG. 8 is a flow diagram of a method 800 for fabrication of a superconducting quantum device.

[00104] A superconducting SAW resonator 102 can be formed at 802. To form the surface acoustic wave resonator, at 804 of the method, a first periodic structure (e.g., the first Bragg mirror 202) and a second periodic structure (e.g., the second Bragg mirror 204) can be separated by a distance defined as an odd integer multiple of a half-wavelength supported by the superconducting SAW resonator. The first periodic structure can comprise first metallic fingers and first dielectric gaps in between the metallic fingers. The second periodic structure can comprise second metallic fingers and second dielectric gaps in between the metallic fingers.

[00105] At 806, a superconducting microwave resonator (e.g., the superconducting microwave resonator 104) can be formed. The superconducting microwave resonator can comprise one or more capacitors (e.g., the first capacitor 308 and the second capacitor 310). One capacitor of the one or more capacitors can be a shunting capacitor for the JRM.

[00106] Further, a JRM 106 can be coupled to the surface acoustic wave resonator, at 808 of the method. At 810, the superconducting microwave resonator can be coupled to the JRM as described with reference to Fig. 4, the JRM can comprise Josephson junctions arranged in a Wheatstone-bridge configuration. In some implementations, the JRM can be a dispersive nonlinear three-wave mixing element. It is noted that, according to some implementations, coupling the JRM to the SAW resonator (at 810) can occur before forming the superconducting microwave resonator (at 808).

[00107] According to some implementations, an interdigitated capacitance device can be positioned at a center of the SAW resonator. Further to these implementations, a first set of opposite nodes of the JRM can be connected to opposite nodes of the interdigitated capacitance device. In some implementations, the method can include inducing magnetic flux threading the JRM.

[00108] FIG. 9 is a flow diagram of a method 900 for fabrication of a superconducting quantum device comprising external feedlines.

[00109] At 902, a JRM 106 can be formed. As described with reference to Fig. 4, the JRM can comprise

Josephson junctions arranged in a Wheatstone-bridge configuration. According to some implementations, the JRM can be a dispersive nonlinear three-wave mixing element.

[00110] At 904, the JRM can be coupled to a superconducting SAW resonator 102 and a superconducting microwave resonator (e.g., the superconducting microwave resonator 104).

[00111] A first external feedline 210 can be coupled to the SAW resonator, at 906. For example, the first external feedline can be coupled to the SAW resonator through another interdigitated capacitance device. The first external feedline can carry one or more first input signals and one or more first output signals of the SAW resonator.

[00112] Further, at 908, a second external feedline (e.g., the second external feedline 214) can be coupled to the superconducting microwave resonator. The second external feedline can carry one or more second input signals and one or more second output signals of the superconducting microwave resonator.

[00113] In an example, one superconducting SAW resonator (low-frequency) and one superconducting microwave resonator (high-frequency) can be coupled to the JRM. The superconducting SAW resonator can comprise two superconducting Bragg mirrors separated from one another by a distance that is an odd integer multiple of halfwavelength of the main mode supported by the superconducting SAW resonator. The superconducting SAW resonator can be realized on a low-loss piezo-electric dielectric substrate. Further, the JRM can be realized using Al or Nb Josephson junctions.

[00114] One pair of opposite nodes of the JRM can be connected to opposite nodes of the IDC. The IDC can be positioned off-center of the SAW resonator (e.g., at a location that does not coincide with a voltage node of the desired coupled mode). The other pair of opposite nodes of the JRM can be connected to a shunt capacitor and, optionally, a shunt inductor. The microwave resonator can be coupled to an external feedline through a coupling capacitor. The external feedline can carry the input and output signals of the microwave resonator. The superconducting SAW resonator can have a separate external feedline which can carry the input and output signals of the SAW resonator. The external feedline can be coupled to the SAW resonator using a designated IDC. The IDC fingers can be located close to rf-voltage antinodes. A pump drive can be injected to the JRM using a separate port. The pump port can be connected to the sigma port of a 180-degree hybrid, which in turn could be capacitively coupled to opposite nodes of the JRM (giving rise to a common excitation of the JRM).

[00115] A preferred embodiment of the invention provides a superconducting device, comprising: a

superconducting surface acoustic wave resonator comprising: a first periodic structure comprising first metallic fingers and first dielectric gaps, and a second periodic structure comprising second metallic fingers and second dielectric gaps, wherein the first periodic structure and the second periodic structure are separated by a distance defined as an odd integer multiple of a half-wavelength supported by the superconducting surface acoustic wave resonator; a dispersive nonlinear three-wave mixing element coupled to the superconducting surface acoustic wave resonator, the dispersive nonlinear three-wave mixing element comprising one or more Josephson junctions arranged in a Wheatstone-bridge configuration; and a superconducting microwave resonator coupled to the dispersive nonlinear three-wave mixing element.

[00116] Preferably, the superconducting device further comprises: an interdigitated capacitance device positioned at a center of the superconducting surface acoustic wave resonator, wherein a first set of opposite nodes of the dispersive nonlinear three-wave mixing element are connected to opposite nodes of the interdigitated capacitance device, and wherein a second set of opposite nodes of the dispersive nonlinear three-wave mixing element are connected to a shunt capacitor, wherein the interdigitated capacitance device, the shunt capacitor, and the dispersive nonlinear three-wave mixing element, and the one or more Josephson junctions form the

superconducting microwave resonator.

[00117] Preferably, induced magnetic flux threads the dispersive nonlinear three-wave mixing element.

[00118] A preferred embodiment of the invention provides a superconducting device, comprising: a

superconducting surface acoustic wave resonator comprising: a first periodic structure comprising first metallic fingers and first dielectric gaps, and a second periodic structure comprising second metallic fingers and second dielectric gaps, wherein the first periodic structure and the second periodic structure are separated by a distance defined as an odd integer multiple of a half-wavelength supported by the superconducting surface acoustic wave resonator; a Josephson ring modulator coupled to the superconducting surface acoustic wave resonator, the Josephson ring modulator comprises one or more Josephson junctions arranged in a Wheatstone-bridge configuration; and a superconducting microwave resonator coupled to the Josephson ring modulator, wherein the Josephson ring modulator is a dispersive nonlinear three-wave mixing element.

[00119] Preferably, the superconducting device further comprises: an interdigitated capacitance device positioned at a center of the superconducting surface acoustic wave resonator, wherein a first set of opposite nodes of the Josephson ring modulator are connected to opposite nodes of the interdigitated capacitance device.

[00120] What has been described above include mere examples of systems and methods. It is, of course, not possible to describe every conceivable combination of components or methods for purposes of describing this invention, but one of ordinary skill in the art can recognize that many further combinations and permutations are possible. Furthermore, to the extent that the terms“includes,”“has,”“possesses,” and the like are used in the detailed description, claims, appendices and drawings such terms are intended to be inclusive in a manner similar to the term“comprising” as“comprising” is interpreted when employed as a transitional word in a claim. The descriptions of the various embodiments of the invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments of the invention disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope of the invention. The terminology used herein was chosen to best explain the principles of the embodiments of the invention, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments of the invention disclosed herein.