BACKGROUND

[0001] In quantum circuits, a Josephson ring modulator (JRM) 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 JRM. Due to coupling the JRM 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 JRM 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 JRM. 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 JRM 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 described herein are devices and methods that mix surface acoustic waves.

[0004] According to an embodiment of the invention, a superconducting device can comprise a first surface acoustic wave (SAW) resonator comprising a first low-loss piezo-electric dielectric substrate. The superconducting device can also comprise a second SAW resonator comprising a second low-loss piezo-electric dielectric substrate. Further, the superconducting device can comprise a JRM coupled to the first and second SAW resonators. 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 microwave frequencies of the first and second SAW resonators.

[0005] In some examples, the first SAW resonator can comprise a first superconducting Bragg mirror and a second superconducting Bragg mirror separated from the first superconducting Bragg mirror by a first distance.

The second SAW resonator can comprise a third superconducting Bragg mirror and a fourth superconducting Bragg mirror separated from the third superconducting Bragg mirror by a second distance. The first distance and the second distance can be odd integer multiples of a half-wavelength supported by the first SAW resonator and the second 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 surface acoustic wave resonators.

[0006] According to some implementations, the superconducting device can also advantageously comprise a first external feedline coupled to the first SAW resonator through a first interdigitated capacitance (IDC) device. The first external feedline carries first input signals and first output signals of the first SAW resonator. Further, the superconducting device can comprise a second external feedline coupled to the second SAW resonator through a second IDC device. The second external feedline carries second input signals and second output signals of the second SAW resonator. An advantage of such a superconducting device is that frequencies of the first and second superconducting SAW resonators can be received, mixed, and amplified.

[0007] According to an embodiment of the invention, provided is a superconducting circuit that can comprise a JRM, a first SAW resonator and a second SAW resonator. The first SAW resonator can be coupled via a first superconducting wire to a first node of the JRM and via a second superconducting wire to a second node of the JRM. The first and second superconducting wires can comprise a same length. The second SAW resonator can be coupled via a third superconducting wire to a third node of the JRM and via a fourth superconducting wire to a fourth node of the JRM. The third and fourth superconducting wires can comprise a same length. The first SAW resonator is spatially and spectrally separated from the second SAW resonator. An advantage of such a superconducting circuit is that dissipationless, three-wave mixing and amplification can be facilitated between low microwave frequencies of the first and second superconducting SAW resonators.

[0008] In accordance with some implementations, the superconducting circuit can comprise a first external feedline coupled to the first SAW resonator through a first IDC device. The first external feedline can carry first input signals and first output signals of the first SAW resonator. The superconducting circuit can also comprise a second external feedline coupled to the second SAW resonator through a second IDC device. The second external feedline can carry second input signals and second output signals of the second SAW resonator. An advantage of such a superconducting circuit is that a first set of frequencies of the first superconducting SAW resonator and a second set of frequencies of the second superconducting SAW resonator can be received, mixed, and amplified.

[0009] Another embodiment of the invention relates to a method that can comprise coupling a first superconducting SAW resonator to a JRM. The method can also comprise coupling a second superconducting SAW resonator to the JRM. The JRM can comprise Josephson junctions arranged in a Wheatstone-bridge configuration. Further, 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 first microwave frequencies of the first superconducting SAW resonator and second microwave frequencies of the second superconducting SAW resonator.

[0010] A further embodiment of the invention relates to a superconducting device that can comprise a first superconducting SAW resonator comprising a first IDC device positioned at a first center of the first

superconducting SAW resonator. The first SAW resonator can also comprise a first superconducting Bragg mirror and a second superconducting Bragg mirror separated from the first superconducting Bragg mirror by a first distance. The superconducting device can also comprise a second superconducting SAW resonator comprising a second IDC device positioned at a second center of the second superconducting SAW resonator. The second superconducting SAW resonator can also comprise a third superconducting Bragg mirror and a fourth superconducting Bragg mirror separated from the third superconducting Bragg mirror by a second distance. The first and second distances are odd integer multiples of a half-wavelength supported by the first SAW resonator and the second SAW resonator. Further, the superconducting device can comprise a JRM coupled to the first and second superconducting SAW resonators. A first set of opposite nodes of the JRM can be connected to opposite nodes of the first IDC device. A second set of opposite nodes of the JRM can be connected to opposite nodes of the second IDC device. An advantage of such a superconducting device is that dissipationless, three-wave mixing and amplification can be performed between microwave frequencies of the first superconducting SAW resonator and microwave frequencies of the second superconducting SAW resonator while occupying a small space and through the use of low-loss resonators.

[0011] Another embodiment of the invention relates to a superconducting device comprising a first

superconducting SAW resonator comprising a first superconducting Bragg mirror and a second superconducting Bragg mirror separated from the first superconducting Bragg mirror by a first distance. The superconducting device can also comprise a second superconducting SAW comprising a third superconducting Bragg mirror and a fourth superconducting Bragg mirror separated from the third superconducting Bragg mirror by a second distance. The first distance and the second distance are odd integer multiples of a half-wavelength supported by the first surface acoustic wave resonator and the second surface acoustic wave resonator. In addition, the second superconducting surface acoustic wave resonator can be spatially and spectrally separated from the first superconducting SAW resonator. Further, the superconducting device can comprise a JRM comprising first and second sets of opposite nodes. The JRM can be connected to the first superconducting SAW resonator via the first set of opposite nodes and to the second superconducting SAW resonator via the second set of opposite nodes. An advantage of such a superconducting device is that dissipationless, three-wave mixing and amplification can be performed between microwave frequencies of the first superconducting SAW resonator and microwave frequencies of the second superconducting SAW resonator while occupying a small space through the use of low-loss resonators.

DESCRIPTION OF THE DRAWINGS

[0012] FIG. 1 is a block diagram of a circuit in accordance with an embodiment of the invention.

[0013] FIG. 2 is a block diagram of a circuit comprising two superconducting SAW resonators in accordance with an embodiment of the invention.

[0014] FIG. 3 is a schematic of a circuit for a superconducting device that comprises SAW resonators coupled to a JRM in accordance with an embodiment of the invention.

[0015] FIG. 4 is a flow diagram of a method for fabrication of a device in accordance with an embodiment of the invention.

[0016] FIG. 5 is a flow diagram of a method for fabrication of a device comprising two superconducting SAW resonators in accordance with an embodiment of the invention.

[0017] FIG. 6 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. 7 is a flow diagram of a method for fabrication of a device comprising external feedlines in accordance with an embodiment of the invention.

[0019] FIG. 8 is a flow diagram of a method for fabrication of a superconducting quantum device in accordance with an embodiment of the invention.

[0020] 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

[0021] 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. [0022] 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 embodiments of the invention. It is evident, however, in various cases, that the embodiments can be practiced without these specific details.

[0023] As it relates to circuits, and more specifically quantum circuits, if a JRM is coupled to two superconducting microwave 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 two superconducting SAW resonators are utilized. The superconducting SAW resonators are compact as compared to superconducting wave resonators and, therefore, a size of the superconducting device is reduced.

[0024] 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 superconducting SAW resonators that enable dissipationless, three-wave mixing and amplification between low microwave frequencies (e.g., about 0.1 GHz to about 4 GHz). Operation at these low microwave frequencies is not available using transmission line resonators or using lumped-elements as provided with prior art superconducting devices.

[0025] 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 can have an advantage of reduced size and low-loss resonators, as compared to conventional techniques.

[0026] According to some implementations, the device can function as a Josephson mixer for surface acoustic waves (phonons), as a lossless frequency converter between two surface acoustic waves, as a nondegenerate parametric Josephson amplifier for surface acoustic waves, and/or as an entangler of two phononic modes (e.g., generating entanglement between two phononic modes).

[0027] FIG. 1 is a block diagram of a circuit 100 comprising a first superconducting SAW resonator 102, a second superconducting SAW resonator 104, and a JRM 106.

[0028] 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 microwave signals or receive microwave signals by the first superconducting SAW resonator 102 and/or the second superconducting SAW resonator 104. As discussed herein, according to some implementations, the circuit 100 can operate as a Josephson mixer between surface acoustic waves (phonons), as a lossless frequency converter between two surface acoustic waves, as a nondegenerate parametric Josephson amplifier for surface acoustic waves, and/or as an entangler of two phononic modes.

[0029] 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, surface acoustic wave 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).

[0030] The first superconducting SAW resonator 102 can comprise a first resonance frequency and the second superconducting SAW resonator 104 can comprise a second resonance frequency. Further, the first

superconducting SAW resonator 102 and the second superconducting SAW resonator 104 can be implemented on respective low-loss piezo-electric dielectric substrates. The low-loss piezo-dielectric substrates can comprise a material selected from a group of materials comprising quartz, gallium arsenide, lithium niobite, and/or zinc oxide, or the like.

[0031] The JRM 106 is a device that can be based on Josephson tunnel junctions. For example, the JRM 106 can comprise Josephson junctions arranged in a Wheatstone-bridge configuration. The 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.

[0032] 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.

[0033] 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 can be formed in a loop. Further, the Josephson junctions can be utilized to perform the mixing as discussed herein. [0034] 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. 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.

[0035] 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.

[0036] 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.

[0037] The nodes can be utilized to couple the JRM 106 to the first superconducting SAW resonator 102 and to the second superconducting SAW 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 first superconducting SAW resonator 102. The first node 124 can be coupled to the first superconducting SAW resonator 102 via a first superconducting wire 132 (or first lead) and the third node 128 can be coupled to the first superconducting SAW resonator 102 via a second superconducting wire 134 (or second lead).

[0038] 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 second superconducting SAW resonator 104. For example, the second node 126 can be coupled to the second superconducting SAW resonator 104 via a third superconducting wire 136 (or third lead) and the fourth node 130 can be coupled to the second superconducting SAW resonator 104 via a fourth superconducting wire 138 (or fourth lead).

[0039] As illustrated, the first superconducting wire 132 and the second superconducting wire 134 can be coupled to the first superconducting SAW resonator 102 at different locations of the first superconducting SAW resonator 102. Further, the third superconducting wire 136 and the fourth superconducting wire 138 can be coupled to the second superconducting SAW resonator 104 at different locations of the second superconducting SAW resonator 104. Further details related to the coupling locations will be provided below with respect to FIG. 3.

[0040] The first superconducting SAW resonator 102, the second superconducting SAW 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 at microwave frequencies from other quantum devices connected to the SAW port (e.g., an idler port) and/or the SAW port (e.g., a signal port) of the device.

[0041] 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.

[0042] In various embodiments, 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.

[0043] 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.

[0044] 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, quantum circuit, quantum processor, artificial intelligence 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.

[0045] FIG. 2 is a block diagram of a circuit 200 comprising two superconducting SAW resonators.

[0046] The first 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 first superconducting SAW resonator 102. The Bragg mirrors comprise respective periodic structures of metallic fingers and dielectric gaps positioned at a defined distance from one another.

[0047] According to some implementations, the first 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.

[0048] Further, a first IDC device 206 and a second IDC device 208 can be included in the first superconducting SAW resonator 102. The first IDC device 206 can couple between the first superconducting SAW resonator 102 and the JRM 106. The second IDC device 208 can couple between the first superconducting SAW resonator 102 and an external port (e.g., a signal port 210).

[0049] For example, the first IDC device 206 can be positioned at a center of the first 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 superconducting 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 superconducting wire 134).

[0050] The second superconducting SAW resonator 104 can comprise a first superconducting metallic/dielectric mirror (e.g., illustrated as a third Bragg mirror 212) and a second superconducting metallic/dielectric mirror (e.g., illustrated as a fourth Bragg mirror 214). The third Bragg mirror 212 can be separated from the fourth Bragg mirror 214 by a distance that is an odd integer multiple of a half-wavelength supported by the second superconducting SAW resonator 104. The Bragg mirrors comprise respective periodic structures of metallic fingers and dielectric gaps positioned at a defined distance from one another.

[0051] According to some implementations, the second superconducting SAW resonator 104 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.

[0052] Further, the second superconducting SAW resonator 104 can comprise a third IDC device 216 and a fourth IDC device 218. The third IDC device 216 can couple between the second superconducting SAW resonator 104 and the JRM 106. The fourth IDC device 218 can couple between the second superconducting SAW resonator 104 and an external port (e.g., an idler port 220).

[0053] For example, the third IDC device 216 can be positioned at a center of the second superconducting SAW resonator 104. A second set of opposite nodes of the JRM 106 can be connected to opposite nodes of the third IDC device 216. For example, the second node 126 of the JRM 106 can be connected to a first side of the third IDC device 216 (e.g., via the third superconducting wire 136). Further, the fourth node 130 of the JRM 106 can be connected to a second side of the third IDC device 216 (e.g., via the fourth superconducting wire 138).

[0054] The circuit 100 can also comprise a first external feedline 222 coupled to the first superconducting SAW resonator 102 through the second IDC device 208. The first external feedline 222 can be connected to the signal port 210 (e.g., a radio frequency (rf) source). The first external feedline 222 can carry one or more input signals and one or more output signals of the first superconducting SAW resonator 102.

[0055] A second external feedline 224 can be coupled to the second superconducting SAW resonator 104 through the fourth IDC device 218. The second external feedline 224 can be connected to the idler port 220. The second external feedline 224 can carry one or more input signals and one or more output signals of the second superconducting SAW resonator 104.

[0056] Further, the JRM 106 can be operatively connected to a pump port 226 (e.g., via coupling to the first superconducting wire 132 and the second superconducting wire 134 or other wires). The pump port 226 can be connected to a microwave source. The pump port 226 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 226 to the JRM 106, the first superconducting SAW resonator 102 and the second superconducting SAW resonator 104 can be electrically connected through the JRM 106. Flowever, when power is not supplied through the pump port 226 (e.g., the power supply is off), the first superconducting SAW resonator 102 and the second superconducting SAW resonator 104 can be electrically isolated from one another.

[0057] For amplification, ideally there would be a microwave signal that is propagating on the idler transmission line (e.g., the second external feedline 224) that is connected to the idler port 220. 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 226) that can generate a parametric amplification between the idler mode and the signal mode supported by the first superconducting SAW resonator 102. In this example, an input signal is not needed at both the signal port 210 and the idler port 220. 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 210, or the idler port 220, 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 226) 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 210 and the idler port 220 can be an amplified superposition of the input signals entering both ports.

[0058] 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.

[0059] In further detail, FIG. 3 is a schematic of a circuit 300 for a superconducting device that comprises SAW resonators coupled to a JRM.

[0060] 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.

[0061] 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 first superconducting SAW resonator 102 (e.g., via the first superconducting wire 132 and the second superconducting 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 second superconducting SAW resonator 104 (e.g., via the third superconducting wire 136 and the fourth superconducting wire 138). 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. [0062] The first set of opposite nodes (e.g., the first node 124 and the third node 128) can be coupled to opposite electrodes of the first IDC device 206 of the first 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 device 206, indicated at 302 (e.g., via the first superconducting wire 132). Further, the third node 128 of the JRM 106 can be coupled to a second electrode of the first IDC device 206, indicated at 304 (e.g., via the second superconducting wire 134). The first IDC device 206 can be positioned at a center of the first superconducting SAW resonator 102.

[0063] The second set of opposite nodes (e.g., the second node 126 and the fourth node 130) can be can be coupled to opposite electrodes of the third IDC device 216 of the second superconducting SAW resonator 104, creating a second orthogonal mode. For example, the second node 126 of the JRM 106 can be coupled to a first electrode of the third IDC device 216, indicated at 306 (e.g., via the third superconducting wire 136). Further, the fourth node 130 of the JRM 106 can be coupled to a second electrode of the third IDC device 216, indicated at 308 (e.g., via the fourth superconducting wire 138). The third IDC device 216 can be positioned at a center of the second superconducting SAW resonator 104.

[0064] As illustrated, the first superconducting SAW resonator 102 can comprise the first IDC device 206, 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 first superconducting SAW resonator 102 can be 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.

[0065] In a similar manner, the second superconducting SAW resonator 104 can comprise the third IDC device 216, the fourth IDC device 218, and a set of metallic/dielectric mirrors (e.g., the third Bragg mirror 212 and the fourth Bragg mirror 214). The components of the second superconducting SAW resonator 104 can also be implemented on a piezo-electric substrate.

[0066] Different ports can be utilized to access the first superconducting SAW resonator 102 and the second superconducting SAW resonator 104. For example, the signal port 210 can be utilized to access the first superconducting SAW resonator 102 and the idler port 220 can be utilized to access the second superconducting SAW resonator 104.

[0067] The signal port 210 can be utilized to carry input signals and output signals. Therefore, in order to measure output signals from the first superconducting SAW resonator 102, an IDC (e.g., the second IDC device 208) 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 first superconducting SAW resonator 102. [0068] A distance between the centers of two consecutive fingers of the IDCs can be generally expressed as X _a l2. 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 312, by a distance that is an odd integer multiple of half-wavelength supported by the first superconducting SAW resonator 102. The defined distance can be expressed as L _a , wherein L _a is an odd-integer multiple of _a /2.

[0069] The idler port 220 can be utilized to carry input signals and output signals. Therefore, in order to measure output signals from the second superconducting SAW resonator 104, an IDC (e.g., the fourth IDC device 218) can be placed between the third Bragg mirror 212 and the fourth Bragg mirror 214. 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 second superconducting SAW resonator 104.

[0070] A distance between the centers of two consecutive fingers of the IDCs can be generally expressed as X _b l2. The respective two sets of fingers of the IDCs can have opposite polarity according to an implementation. Further, the third Bragg mirror 212 and the fourth Bragg mirror 214 can be separated from one other, as indicated by line 314, by a distance that is an odd integer multiple of half-wavelength supported by the second

superconducting SAW resonator 104. The defined distance can be expressed as U, wherein U is an odd-integer multiple of _b /2. Where _b < _a .

[0071] 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 first IDC device 206 (e.g., indicated at 302 or 304) and the maximum amplitude should couple to the other finger, (e.g., indicated at 304 or 302) 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 X _a l2 can be selected to facilitate the maximum on the first finger and the minimum on the other finger.

[0072] In a similar manner, the minimum amplitude should couple to one finger of the third IDC device 216 (e.g., indicated at 306 or 308) and the maximum amplitude should couple to the other finger (e.g., indicated at 308 or 306) where the two fingers are connected to opposite nodes of the JRM 106 (e.g., the second node 126 and the fourth node 130). Therefore, the distance \ _b /2 can be selected to facilitate the maximum on the first finger and the minimum on the other finger.

[0073] 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. However, 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). Accordingly, a first differential mode of the JRM 106 is supported by the first superconducting SAW resonator 102 and a second differential mode of the JRM 106 is supported by the second superconducting SAW resonator 104.

[0074] 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 226. The pump port 226 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 226 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.

[0075] In an example of amplification performed by the device, a first signal f _a which lies within the bandwidth of the first superconducting SAW resonator 102 and a second signal fi _> which lies within the bandwidth of the second superconducting SAW resonator 104. Further, the frequency of the second signal can be larger than the frequency of the first signal (¾ > f _a ). To amplify both signals, the frequency of the pump tone fed through the pump port 226 should be the sum of the first signal and the second signal (e.g., f _a + ¾). The energy of the electromagnetic signal is proportional to its frequency. By taking the pump (e.g., the pump port 226) 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 phonons at f _a and a second set of phonons at ¾. 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 phonons) at the lower frequency f _a and a second half (e.g., the second set of phonons) at the higher frequency ¾. Therefore, amplification can occur because the pump exchanges energy with the signal mode and idler mode and through this exchange entangled phonons are generated in both modes. In this case, the pump frequency should be equal to the difference between f _a and ¾. Here ¾ is larger, so the equation can be ¾ minus fa-

10076] As illustrated the gaps of the first IDC device 206 and the second IDC device 208 are larger (e.g., there is more distance between the fingers) than the gaps (or distance) of the third IDC device 216 and the fourth IDC device 218. The frequency f _a of the first superconducting SAW resonator 102 is lower than the frequency fi _> of the second superconducting SAW resonator 104. There is a one to one mapping between the frequency and the wavelength. The frequencies are linked through the speed of light or the speed of sound through the surface. If the wavelength (l) times the frequency is a constant, it is equal to either the speed of light or the speed of sound in the medium. Since the product is fixed, if one is increased, the other one will decrease and vice versa. Thus, if the frequency is lowered, the corresponding wavelength will increase, and vice versa.

[0077] According to an implementation, in the mixing process a phonon in the first SAW resonator at the signal frequency can be upconverted into a phonon in the second SAW resonator at the idler frequency. According to another implementation, the phonon in the second SAW resonator at the idler frequency can be downconverted to a phonon in the first SAW resonator at the signal frequency. The energy exchange is enabled by the pump drive (e.g., fed through the pump port 226). Accordingly, either a pump photon is absorbed or a pump phonon is emitted to facilitate the process.

[0078] If there is no pump signal applied to the pump port 226, the first superconducting SAW resonator 102 and the second superconducting SAW resonator 104 are separated (e.g., isolated from one another) and information exchange or information communications between the first superconducting SAW resonator 102 and the second superconducting SAW resonator 104 does not occur. Upon or after a pump signal is applied to the pump port 226, it excites the common mode of the JRM 106, as illustrated in FIG. 3, the first superconducting SAW resonator 102 and the second superconducting SAW resonator 104 interact and information is exchanged.

[0079] According to some implementations, the pump drive is fed through the sigma port 318 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.

[0080] 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 (e.g., the sigma port 318). If a signal is input to the sigma 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 sigma port 318 because the phases of the split signals are equal. The pump drive (e.g., the pump port 226) can be fed through the sigma port 318 of the 180-degree hybrid 316.

[0081] 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., the second port 320), the second signal at the other port (e.g., the third port 322) has a minimum value.

[0082] 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.

[0083] The first coupling capacitor 330 can be coupled to the first node 124 of the JRM 106 (through the first IDC device 206) 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 device 206 (illustrated at the first contact point at the second electrode 304 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.

[0084] 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 and the third port 322) of the 180 degree hybrid and the coupling capacitors (e.g., the first coupling capacitor 330 and the second coupling capacitor 332, respectively). Similarly, the first superconducting wire 132 and the second superconducting wire 134 pair, and the third superconducting wire 136 and the fourth superconducting wire 138 pair, 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 IDCs (e.g., the first IDC device 206, the third IDC device 216). Further, the connecting superconducting wires should be as short as possible and wide (e.g., have small series inductance).

[0085] 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 ).

[0086] The effective length of the first superconducting SAW resonator 102 can be slightly larger than L _a .

Further, the effective length of the second superconducting SAW resonator 104 can be slightly larger than U. The lengths are slightly larger than L _a and L _b because the reflection off the Bragg mirrors does not happen on the mirror edges but within a certain penetration depth inside the Bragg mirrors.

[0087] The effective length (L _eff ) of the first superconducting SAW resonator 102 and/or the second

superconducting SAW resonator 104 and the speed of sound in the piezoelectric substrate (v _s ) can determine the cavity free spectral range (FSR): V _FSR = ^Vs . The SAW resonators can be similar to photonic cavities that

^2L eff

support multimodes (resonances). The cavity free spectral range parameter can determine the frequency spacing between the multimodes supported by the first superconducting SAW resonator 102 and/or the second superconducting SAW resonator 104.

[0088] The larger the spacing between the Bragg mirrors, the larger L _eff 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.

[0089] 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.

[0090] FIG. 4 is a flow diagram of a method 400 for fabrication of a device.

[0091] At 402 a first SAW resonator 102 can be coupled to a JRM 106. For example, the first SAW resonator can be coupled to a first set of opposite nodes (e.g., the first node 124 and the third node 128) of the JRM.

[0092] The method 400 can also include, at 404, coupling a second superconducting SAW resonator 104 to the JRM. The second superconducting wave resonator can be coupled to a first set of opposite nodes (e.g., the second node 126 and the fourth node 130) of the JRM.

[0093] The JRM can comprise Josephson junctions arranged in a Wheatstone-bridge configuration. The Josephson junctions can comprise a first material selected from a first group of materials comprising aluminum and niobium. Further, the JRM can be a dispersive nonlinear three-wave mixing element.

[0094] FIG. 5 is a flow diagram of a method 500 for fabrication of a device comprising two superconducting SAW resonators.

[0095] At 502 can comprise forming a first superconducting SAW resonator 102 comprising positioning a first IDC device 206 at a first center of the first superconducting SAW resonator.

[0096] Further, at 504 the method can comprise forming a second superconducting SAW resonator 104 comprising positioning a second IDC device 216 at a second center of the second superconducting SAW resonator. [0097] At 506 the method 500 can comprise connecting a first set of opposite nodes (e.g., the first node 124 and the third node 128) of a JRM 106 to opposite nodes (e.g., the first electrode 302 and the second electrode 304) of the first IDC device.

[0098] In addition, at 508 the method 500 can comprise connecting a second set of opposite nodes (e.g., the second node 126 and the fourth node 130) of the JRM to opposite nodes (e.g., the third electrode 306 and the fourth electrode 308) of the second IDC device.

[0099] FIG. 6 is a flow diagram of a method 600 for fabrication of a device comprising a pump drive port .

[00100] The method 600 starts at 602, when a first superconducting SAW resonator 102 can be coupled to a JRM 106. Further, at 604, a second superconducting SAW resonator 104 can be coupled to the JRM.

[00101] Further, at 606, a first coupling capacitor 330 can be coupled to a first port (e.g., the second port 320) of a pump (e.g., the pump port 226) via a first superconducting wire (e.g., the first lead 326). In addition, at 608 the method can comprise connecting a second coupling capacitor 332 to a second port (e.g., the third port 322) of the pump via a second superconducting wire. According to some implementations, the first and second

superconducting wires can be phase matched.

[00102] FIG. 7 is a flow diagram of a method 700 for fabrication of a device comprising external feedlines.

[00103] The method 700 starts, at 702, and a first superconducting SAW resonator 102 can be coupled to a JRM 106. The first superconducting SAW resonator can be realized on a low-loss piezo-electric dielectric substrate.

[00104] Further, at 704, a second superconducting SAW resonator 104 can be coupled to the JRM. The second superconducting SAW resonator can also be realized on a low-loss piezo-electric dielectric substrate.

[00105] At 706 of the method 700, a first external feedline 222 can be coupled to the first superconducting SAW resonator through a first IDC device 208. The first external feedline can carry first input signals and first output signals of the first superconducting SAW resonator.

[00106] At 708, a second external feedline 224 can be coupled to the second superconducting SAW resonator through a second IDC device 218. The second external feedline can carry second input signals and second output signals of the second superconducting SAW resonator.

[00107] FIG. 8 is a flow diagram of a method 800 for fabrication of a superconducting quantum device. [00108] A first superconducting SAW resonator 102 can be formed at 802 of the method 800. The first superconducting SAW resonator can comprise a first IDC device 206 positioned at a first center of the first superconducting SAW resonator.

[00109] At 804, a second superconducting SAW resonator 104 can be formed. The second superconducting SAW resonator can comprise a second IDC device 216 positioned at a second center of the second superconducting SAW resonator.

[00110] Further, at 806, a JRM 106 can be coupled to the first superconducting SAW resonator and the second superconducting SAW resonator. A first set of opposite nodes (e.g., the first node 124 and the third node 128) of the JRM can be connected to opposite nodes of the first IDC device. A second set of opposite nodes (e.g., the second node 126 and the fourth node 130) of the JRM can be connected to opposite nodes of the second IDC device.

[00111] FIG. 9 is a flow diagram of a method 900 for fabrication of a superconducting quantum device comprising external feedlines.

[00112] At 902 a first superconducting SAW resonator 102 comprising a first low-loss piezo-electric dielectric substrate can be formed. Forming the first SAW resonator can comprise, at 904, separating a first superconducting Bragg mirror 202 from a second superconducting Bragg mirror 204 by a first distance.

[00113] At 906, a first IDC device 206 can be positioned at a first center of the first SAW resonator. A first set of opposite nodes (e.g., the first node 124 and the third node 128) of the JRM can be connected to opposite nodes (e.g., the first electrode 302 and the second electrode 304) of the first IDC device.

[00114] A second superconducting SAW resonator 104 comprising a second low-loss piezo-electric dielectric substrate can be formed at 908. The first SAW resonator can be spatially and spectrally separated from the second SAW resonator. Forming the second SAW resonator can comprise, at 910, separating a third superconducting Bragg mirror 212 from a fourth superconducting Bragg mirror 214 by a second distance.

[00115] At 912, a second IDC device 216 can be positioned at a second center of the second SAW resonator. A second set of opposite nodes (e.g., the second node 126 and the fourth node 130) of the JRM can be connected to opposite nodes (e.g., the third electrode 306 and the fourth electrode 308) of the second IDC device.

[00116] At 914, a pump port 226 can be coupled to the JRM. A pump drive is injected to the JRM through the pump port. In an example, a first coupling capacitor can be connected via a first superconducting wire to a first port of the pump port (e.g., a first external port). Further, a second coupling capacitor can be connected via a second superconducting wire to a second port of the pump (e.g., a second external port). The first and second superconducting wires can be phase matched. For example, the first coupling capacitor can be connected to a first port of a pump via a first superconducting wire comprising a first wire length and the second coupling capacitor can be connected to a second port of the pump via a second superconducting wire comprising a second wire length.

The first and second wire lengths can be a same wire length.

[00117] What has been described above include mere examples. 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 of this invention 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.