Resonant LC Power Networks for Superconducting Digital Circuits

Abstract

The superconducting circuit comprises a resonator and a Josephson junction. The resonator comprises an inductor and a capacitor. The inductor comprises a first terminal and a second terminal. The second terminal of the inductor is electrically coupled to the first terminal of the capacitor. The second terminal of the capacitor is electrically coupled to the first terminal of the Josephson junction. The terminal shared by the inductor and the capacitor is configured to be electrically coupled to an alternating current (AC) voltage source having a particular frequency and a particular phase. The inductance of the inductor and the capacitance of the capacitor are selected to cause the resonator to resonate at a frequency and phase that substantially corresponds to the particular frequency and particular phase, respectively, of the AC voltage source to facilitate switching of the state of the Josephson junction via a single flux quantum (SFQ) pulse.

Description

[Technical field]

[0001] This application relates to superconducting circuits. In particular, this application discloses a resonant LC power network for superconducting digital circuits. [Background technology]

[0002] Superconducting digital systems are capable of performing computational operations at clock speeds exceeding 100 GHz. In these systems, circuits comprise superconducting wires and Josephson junctions that together form superconducting loops in which information in the form of single flux quantum (SFQ) is encoded and stored.

[0003] Superconducting circuits can be configured to implement conventional logic gates such as AND gates, OR gates, flip-flops, etc. These gates can then be configured to implement more complex logic such as shift registers, counters, processors, etc.

[0004] Manufacturing superconducting digital systems on a large scale is difficult due to manufacturing limitations related to power distribution, logic efficiency, and memory density. Summary of the Invention

[0005] In a first aspect, a superconducting circuit includes a resonator and a Josephson junction. The resonator includes an inductor including a first terminal and a second terminal, and a capacitor including a first terminal electrically coupled to the second terminal of the inductor. The Josephson junction includes a first terminal electrically coupled to the second terminal of the capacitor and a second terminal electrically coupled to a common node. The terminals shared by the inductor and the capacitor are configured to be electrically coupled to an alternating current (AC) voltage source having a specific frequency and a specific phase. The inductance of the inductor and the capacitance of the capacitor are selected to cause the resonator to resonate at a frequency and phase that substantially matches the specific frequency and specific phase, respectively, of the AC voltage source to facilitate switching of the state of the Josephson junction via a single flux quantum (SFQ) pulse.

[0006] In a second aspect, a method of fabricating a superconducting circuit includes forming a resonator in a first layer of a fabrication stack and forming a Josephson junction device in a second layer of the fabrication stack. The resonator comprises an inductor having a first terminal and a second terminal, and a capacitor having a first terminal electrically coupled to the second terminal of the inductor. The Josephson junction comprises a first terminal electrically coupled to the second terminal of the capacitor and a second terminal electrically coupled to a common node. The terminals shared by the inductor and the capacitor are configured to be electrically coupled to an alternating current (AC) voltage source having a particular frequency and a particular phase. The inductance of the inductor and the capacitance of the capacitor are selected to cause the resonator to resonate at a frequency and phase that substantially corresponds to the particular frequency and particular phase, respectively, of the AC voltage source to facilitate switching of the state of the Josephson junction via a single flux quantum (SFQ) pulse.

[0007] In a third aspect, an apparatus includes a superconducting circuit. The superconducting circuit includes a resonator and a Josephson junction. The resonator includes an inductor having a first terminal and a second terminal, and a capacitor having a first terminal electrically coupled to the second terminal of the inductor. The Josephson junction includes a first terminal electrically coupled to the second terminal of the capacitor and a second terminal electrically coupled to a common node. The terminals shared by the inductor and the capacitor are configured to be electrically coupled to an alternating current (AC) voltage source having a specific frequency and a specific phase. The inductance of the inductor and the capacitance of the capacitor are selected to cause the resonator to resonate at a frequency and phase that substantially corresponds to the specific frequency and specific phase, respectively, of the AC voltage source to facilitate switching of the state of the Josephson junction via a single flux quantum (SFQ) pulse. [Brief description of the drawings]

[0008] The above-mentioned as well as additional features will be better understood from the following illustrative and non-limiting detailed description of exemplary embodiments, with reference to the accompanying drawings, in which: [Figure 1] FIG. 2 illustrates a group of LC tiles arranged on a superconducting integrated circuit according to an example embodiment. [Figure 2A] 1 is a schematic diagram of a superconducting circuit in accordance with an illustrative embodiment. [Figure 2B] 1 is a schematic diagram of a superconducting circuit including a resonator configured to bias a group of Josephson junctions in accordance with an example embodiment. [Figure 2C] FIG. 2 is a schematic diagram of two resonators driven by the same AC voltage source in accordance with an exemplary embodiment. [Figure 3A] FIG. 2 is a schematic diagram of interconnected resonators in accordance with an example embodiment; [Figure 3B] FIG. 2 is a schematic diagram of interconnected resonators in accordance with an example embodiment; [Figure 4A]FIG. 1 is a schematic diagram of a two-stage feed network that facilitates driving resonators of multiple LC tiles associated with a particular phase with a single AC voltage source, according to an example embodiment. [Figure 4B] FIG. 1 is a schematic diagram of a two-stage feed network that facilitates driving resonators of multiple LC tiles associated with a particular phase with a single AC voltage source, according to an example embodiment. [Figure 5A] 1 is a partial cross-sectional view of a fabrication stack of a superconducting circuit in which some examples of LC tiles described above are fabricated, according to an exemplary embodiment. [Figure 5B] FIG. 1 illustrates a spiral inductor implemented in a manufacturing stack in accordance with an illustrative embodiment. [Figure 6] 1 illustrates operations that facilitate fabrication of a superconducting circuit in accordance with an illustrative embodiment.

[0009] All figures are schematic, not necessarily to scale, and generally show only those parts necessary to elucidate the exemplary embodiments; other parts may be omitted or merely suggested. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Various examples of systems, devices, and / or methods are described herein with reference to the accompanying drawings. Any embodiment, implementation, and / or feature described herein as an example should not necessarily be construed as preferred or advantageous over any other embodiment, implementation, and / or feature, unless so stated. Thus, other embodiments, implementations, and / or features may be utilized, and other changes may be made without departing from the scope of the subject matter presented herein.

[0011] Thus, the examples set forth herein are not meant to be limiting, as it will be readily understood that the aspects of the present disclosure, as generally described and illustrated in the Figures herein, can be arranged, substituted, combined, separated, and designed in a wide variety of different configurations.

[0012] Moreover, unless the context otherwise suggests, features shown in each figure may be used in combination with one another. Thus, the drawings should be viewed generally as component aspects of one or more overall embodiments, with the understanding that not all illustrated features are required for each embodiment.

[0013] Moreover, recitations of elements, blocks, or steps in the specification or claims are for clarity and therefore should not be construed as requiring or implying that those elements, blocks, or steps follow a particular arrangement or be performed in a particular order.

[0014] Furthermore, terms such as "substantially" or "about" may be used herein to mean that the recited property, parameter, or value need not be achieved exactly, but that deviations or variations including, for example, tolerances, measurement errors, measurement accuracy limits, and other factors known to those of ordinary skill in the art may occur in an amount that does not eliminate the effect that the property is intended to provide.

[0015] Additionally, terms such as "A coupled to B," "A electrically coupled to B," etc. do not necessarily mean that items A and B are directly coupled to one another. For example, a first component electrically coupled to a second component is interpreted to mean that the components are directly coupled (e.g., via conductors) or are coupled to one another via one or more resistors, capacitors, inductors, and / or other active or passive components.

[0016] As mentioned above, a superconducting circuit comprises superconducting wires and Josephson junctions that together form a superconducting loop in which information in the form of single flux quantum (SFQ) is encoded and stored. Examples of AC-powered single flux quantum (AC-SFQ) superconducting circuits correspond to reciprocal quantum logic (RQL) circuits and quantum flux parametron (QFP) circuits, where both power and clock are provided by multiphase AC signals.

[0017] Superconducting wire is made from materials that can carry direct current (DC) in the absence of an electric field. Such materials have little resistance below a critical temperature. Niobium, an example superconductor, has a critical temperature (Tc) of 9.3 Kelvin. At temperatures below the critical temperature, niobium is superconducting. However, above the critical temperature, niobium behaves like a normal metal with electrical resistance.

[0018] A Josephson junction contains two superconductors coupled through a region that prevents electrical current flow. Examples of this region include or correspond to the superconductors themselves, a metallic region, or a physical constriction of a thin insulating barrier. Some examples of Josephson junctions include a niobium superconductor and an Al 2 O 3 A phase-shifted loop (SFQ) circuit is a circuit that consists of a superconducting loop and a barrier. When the potential difference between the two superconductors is integrated with respect to time over one cycle of phase change, the magnetic flux through the loop changes by an integer multiple of a single quantum of magnetic flux. The voltage pulse associated with a single quantum of magnetic flux corresponds to the SFQ pulse mentioned above. As an example, an overdamped Josephson junction can generate individual SFQ pulses. In an AC-SFQ circuit, each Josephson junction can be part of one or more superconducting loops. The phase difference across the junction can be modulated by the magnetic flux applied to the loop.

[0019] As mentioned above, manufacturing these types of circuits on a large scale is difficult due to manufacturing limitations regarding clock and power distribution, logic efficiency, and memory density.

[0020] Some examples disclosed herein improve some of these problems. For example, some examples of superconducting circuits are disclosed herein that improve clock distribution in a superconducting integrated circuit. The superconducting circuit includes a resonator and a Josephson junction. The resonator includes an inductor including a first terminal and a second terminal, and a capacitor including a first terminal electrically coupled to the second terminal of the inductor.

[0021] The Josephson junction comprises a first terminal electrically coupled to the second terminal of the capacitor and a second terminal electrically coupled to the common node. The first terminal of the capacitor is configured to be electrically coupled to an alternating current (AC) voltage source having a particular frequency and a particular phase. The inductance of the inductor and the capacitance of the capacitor are selected to cause the resonator to resonate at a frequency and phase that substantially corresponds to the particular frequency and particular phase, respectively, of the AC voltage source to facilitate switching of the state of the Josephson junction via a single flux quantum (SFQ) pulse.

[0022] In some instances, these superconducting circuits are replicated across an integrated circuit, with different groups of these circuits coupled to different phases of an AC clock and configured to provide power and clocking to the various AC-SFQ circuits located within the integrated circuit.

[0023] In some instances, superconducting resonators associated with the same phase are electrically coupled to each other through a mesh structure formed within the integrated circuit, ensuring that AC-SFQ circuits located in different regions of the integrated circuit remain equalized to each other.

[0024] Minimizing power loss in the resonator is an important consideration. In this regard, in some examples, the interconnects between various components of the resonator and other circuitry include NbTiN, which exhibits low power loss. Some examples of inductors / coils described herein include NbTiN and have an internal quality factor of 1.0. TIFF2025500394000002.tif6150. Some examples of capacitors described herein correspond to metal-insulator-metal (MIM) capacitors having NbTiN electrodes / terminals and a high-K dielectric, facilitating tuning or adjustment of the capacitance of the capacitor by adjusting the DC voltage applied across the terminals of the capacitor. In some examples, the high-K dielectric is HfOx(Si).

[0025] Resonator losses generally decrease with temperature and increase with frequency. Some examples of the resonators described herein are 85% efficient. This corresponds to, for example, a static power dissipation of 0.12 W on a fully populated integrated circuit with 400 million Josephson junctions.

[0026] 1 shows a group of LC tiles 105 arranged on a superconducting integrated circuit 100. In one example, each LC tile 105 includes a stack of superconducting circuits that implement a resonator. The resonator in each LC tile 105 is driven at a particular frequency and a particular phase, and is configured to resonate at substantially the same frequency and phase as it is driven.

[0027] Some examples of the superconducting circuits of each LC tile 105 further comprise one or more AC-SFQ circuits, which are powered and clocked by the corresponding resonators of the LC tile 105. The physical arrangement of the Josephson junctions of these circuits does not necessarily correspond to the physical arrangement of a particular LC tile 105. In some examples, the Josephson junctions and corresponding capacitors are connected to one inductor from different locations to form an LC tile 105 with a predetermined impedance. This aspect makes it easier to connect the Josephson junctions to an inductor that determines its phase. In some examples, the phase allocation for each Josephson junction can be done using an automated algorithm in conjunction with the location and path of the AC-SFQ circuits.

[0028] In one example, the frequency associated with the resonators of each LC tile 105 is the same (e.g., 100 GHz), and the phase of each resonator is different. The number of phases required is generally related to the size of the pipeline of the AC-SFQ circuit driven by the resonators, the frequency at which the AC-SFQ circuit is clocked, the size of the integrated circuit, etc. If eight phases are required, the phases of the resonators are spaced apart by 45°. For example, the phase of the resonator of the first LC tile 105A is 0°, the phase of the resonator of the second LC tile 105B is 45°, the phase of the resonator of the third LC tile 105C is 90°, etc. If four phases are required, the phases of the resonators are spaced apart by 90°. For example, the phase of the resonator of the first LC tile 105A is 0°, the phase of the resonator of the second tile 105B is 90°, the phase of the resonator of the third LC tile 105C is 180°, etc.

[0029] In the illustrated example, eight phases are used, with the phase of the resonator of the ninth LC tile 105I matching the phase of the resonator of the first LC tile 105A. In this regard, some examples of superconducting integrated circuits 100 include multiple LC tile groups. In some examples, the group or array of LC tiles shown in FIG. 1 is repeated throughout the superconducting integrated circuit 100, with the LC tiles of each group being associated with a first phase, a second phase, etc. Some examples of superconducting integrated circuits include thousands or tens of thousands of LC tiles arranged within each group.

[0030] As described in more detail below, some examples of superconducting integrated circuits 100 include one or more conductive interconnects that facilitate driving the resonators of a particular phase of an LC tile 105 with a common AC voltage source of a particular phase. Some examples of superconducting integrated circuits 100 further include one or more conductive interconnects that facilitate phase and amplitude equalization of various groups of resonators associated with the same phase.

[0031] 2A shows a schematic diagram of an example of a superconducting circuit 200. The example of the superconducting circuit 200 corresponds to the superconducting circuit described above. The superconducting circuit 200 includes a resonator 205 and a Josephson junction 210.

[0032] An example of a resonator 205 includes an inductor 215 and a capacitor 220. The inductor 215 includes a first terminal (e.g., terminal 215A) and a second terminal (e.g., terminal 215B). In some examples, the first terminal is electrically coupled to a common node (e.g., common node 218) and the second terminal (e.g., terminal 215B) is electrically coupled to a first terminal (e.g., terminal 220A) of the capacitor 220. The capacitor 220 includes a second terminal (e.g., terminal 220A) configured to be electrically coupled to the first terminal (e.g., terminal 210A) of the Josephson junction 210. The second terminal (e.g., terminal 210B) of the Josephson junction 210 is electrically connected to the common node (e.g., node 218).

[0033] A first terminal of the capacitor 220 is configured to be electrically coupled to an alternating current (AC) voltage source 225 through a coupling resistor R. In some examples, the AC voltage source 225 and the coupling resistor are off-chip. The AC voltage source 225 outputs a signal having a particular magnitude, frequency, and phase. When driven by the AC voltage source 225, the resonator generates an AC signal that applies a bias voltage to the Josephson junction 210.

[0034] In one example, the inductance of inductor 215 and the capacitance of capacitor 220 are selected to cause resonator 205 to resonate at a frequency and phase that substantially matches a particular frequency and a particular phase, respectively, of AC voltage source 225 to facilitate biasing Josephson junction 210 and thus facilitating switching of the state of Josephson junction 210 (e.g., advancing the superconducting phase) via an SFQ pulse. For example, the inductance and capacitance of resonator 205 are selected to satisfy the following equation: TIFF2025500394000003.tif10150Here, f is the resonant frequency, L is the inductance, and C is the capacitance.

[0035] The particular values ​​selected for the output impedance and magnitude of AC voltage source 225, the inductance of inductor 215, etc. may be based on and / or dependent on various parameters. For example, for a frequency of 30 GHz, a Josephson junction bias current of 30 μA, a load quality factor Q of 230, and a capacitance of 4.5 fF, the inductance is determined to be 6.25 nH, the impedance of resonator 205 is determined to be 1.18 kΩ, the coupling resistance R is determined to be 273 kΩ, and the magnitude of the AC signal is determined to be 45.2 mV.

[0036] 2B illustrates a schematic diagram of an example of a superconducting circuit 240 including a resonator 250 configured to bias a group of Josephson junctions 210. In this example, a plurality of capacitors 220 are electrically coupled to a second terminal of an inductor 215, and each Josephson junction 110 is electrically coupled to one of the plurality of capacitors 220. The inductance of the inductor 215 is inversely proportional to the number of capacitors 220. In particular, the inductance of the inductor 215 and the capacitance of the plurality of capacitors 220 are selected to satisfy the following equation: TIFF2025500394000004.tif10150 where f is the resonant frequency, L is the inductance, C is the capacitance of each of the plurality of capacitors 220, and N corresponds to the number of capacitors 220, which in some examples corresponds to the number of Josephson junctions 210.

[0037] According to this formula, the inductance of the 100 combined bias taps is 10,000 times smaller than the inductance of 100 independent bias taps (e.g., bias taps configured according to resonator 205 of FIG. 2A). For example, for the same frequency, bias current, quality factor Q, and capacitance requirements used in the above example, the inductance is determined to be 62.5 pH, the impedance of the resonator is determined to be 11.8 Ω, the coupling resistance is determined to be 2.73 kΩ, and the magnitude of the AC signal is determined to be 45.2 mV. As described below, the fabrication of the inductor 215 of resonator 250 of FIG. 2B occupies a smaller space (e.g., a two-dimensional area and / or a three-dimensional volume) than the inductor 215 of resonator 205 of FIG. 2A due to the 10,000 times smaller inductance.

[0038] FIG. 2C shows a schematic example of two resonators 260A, 260B driven by the same AC voltage source 225. As mentioned above, in some examples, the number of AC voltage sources 225 corresponds to the number of different phases (e.g., one AC voltage source for each 45° interval of a 360° cycle). In the example of FIG. 2C, the resonators 260A, 260B are configured to resonate with AC signals that are 180° out of phase with each other when driven by the same AC voltage source 225. This in turn makes it easy to divide by two the number of AC voltage sources 225 required to provide any particular number of phases. For example, four AC voltage sources 225 can be used to generate eight phases. The resonators 260A, 260B of the figure generally correspond to the resonator 205 of FIG. 2A. However, the aspects described herein apply equally to the resonator 250 of FIG. 2B.

[0039] As shown, the first terminals of the inductors 215 of the resonators 260A, 260B are electrically coupled to each other. The node where the two inductors 215 are coupled corresponds to a virtual ground node in the sense that the AC voltage at this node is small. In this configuration, the first resonator 260A resonates with a phase that is substantially aligned with the phase of the AC voltage source 225. The second resonator 260B resonates at the same frequency but is 180 degrees out of phase with the first resonator 260A.

[0040] 2C, in some examples, a DC voltage source 260 is inserted in series with the AC voltage source 225 to facilitate tuning of the resonators 260A, 260B. In this regard, as described in more detail below, some examples of the capacitor 220 include a HfO x 2C , the same DC voltage generated by DC voltage source 260 is present on each of the capacitors 220 in the first resonator 260A and the second resonator 260B, ensuring that the corresponding capacitances of the capacitors 220 are matched. In one example, the DC voltage across the capacitors 220 may be in the range of 1-5V, facilitating tunability in the range of ±10%.

[0041] 3A shows a schematic diagram 300 of one example of interconnected resonators 250. Shown are several groups of resonators 250 and conductive interconnects 305 that include short / inductive segments that couple the resonators 250 of the groups together.

[0042] The resonators 250 generally correspond to the resonators 250 shown in FIG. 2B. However, the aspects described herein apply equally to the resonators 205 of FIG. 2A. The resonators 250 are arranged in groups, with each group of resonators 250 coupled to an AC voltage source 225 of a particular phase. The number of groups generally corresponds to the number of phases. For example, a first subset of the resonators 250 (e.g., Phase 1 resonators) are coupled to a first phase (e.g., VAC 1 A second subset of the resonators 250 (e.g., Phase 2 resonators) are configured to be electrically coupled to a first AC voltage source 225 having a second phase (e.g., VAC) that is different from the first phase. 2 ) and so on. If there are eight phases, then in one example there are eight groups of resonators 250.

[0043] The conductive interconnects 305 are configured to facilitate equalization of the phase and amplitude of each of the resonators 250 belonging to the same group. The segments of the conductive interconnects 305 between the resonators 250 are shown as inductive elements. The length of the segments between the resonators 250 for a particular phase is electrically short, and as a result, the propagation time of signals between the resonators of a particular group is very short compared to the period of the resonance.

[0044] In some examples, the conductive interconnect 305 includes a number of conductive interconnects corresponding to the number of phases. For example, the first conductive interconnect 305A is configured to couple resonant energy between a first subset of the multiple resonators 250 (e.g., phase 1 resonators) to facilitate equalizing the phase and amplitude of each of the first subset of resonators 250 with respect to one another. The second conductive interconnect 305B is configured to couple resonant energy between a second subset of resonators 250 to facilitate equalizing the phase and amplitude of each of the second subset of resonators 250 with respect to one another, etc.

[0045] FIG. 3B is another example of a schematic diagram 307 of interconnected resonators 250. Shown are several groups of resonators 250, the details of which are omitted for brevity, conductive interconnects 305 including short / inductive segments coupling the resonators 250 of the groups to each other, and transmission lines 310 facilitating equalization of the phase and amplitude of each of the groups of resonators that are electrically distant from each other when compared to the period of the resonance. In this regard, the electrical length of the transmission lines 310 is related to the phase difference between the resonators 250. In some examples, groups of resonators associated with a particular / same phase that are electrically distant from each other are coupled with a full-wave transmission line. In some examples, groups of resonators associated with phases that differ by, for example, 180 degrees (e.g., group 1 has a phase of 0 degrees and group 2 has a phase of 180 degrees) are coupled by half-wave transmission lines 310 or 3 / 2 wave lines.

[0046] It should be noted that some of the examples of conductive interconnects 305 discussed above may include other components such as capacitors, resistors, mutual inductors, etc. Furthermore, any particular implementation of an integrated circuit may include multiple transmission lines and conductive interconnects that facilitate phase and amplitude equalization of various resonators located across the integrated circuit.

[0047] As will be further described below, in some examples, the conductors are implemented on one or more layers of the fabrication stack. In some examples, the conductors are configured to form a two-dimensional mesh or interconnect. Such a configuration provides good frequency separation between the desired lowest resonant frequency mode and the parasitic modes, which is a central aspect of practical designs. For example, a first group of conductors is implemented on a first layer of the fabrication stack, with the conductors on this layer extending in a first direction (e.g., the X-direction). A second group of conductors is implemented on a second layer of the fabrication stack, with the conductors extending in a second direction (e.g., the Y-direction), which may be orthogonal to the first direction. In some examples, the conductors associated with a particular phase include a first portion implemented on the first layer and a second portion implemented on the second layer. In some examples, one or more vias are implemented between the first and second layers to couple the first and second conductor portions to one another. In some examples, the conductors associated with opposite phases are interleaved with one another.

[0048] FIG. 4A illustrates a schematic diagram of one example of a two-stage feed network 405 or splitter that facilitates driving the resonators 205 of multiple LC tiles 105 associated with a particular phase with a single AC voltage source 225.

[0049] As mentioned above, some examples of superconducting integrated circuits include millions of LC tiles 105, each of which includes a resonator 205 associated with one of several phases (e.g., eight phases). On a large scale, for example, a parallel combination of 50M resonators 205 of a given phase has a relatively small impedance of about 50 μΩ. On the other hand, a typical output impedance of an AC voltage source is about 50Ω. Therefore, a power feed network is required to transform the impedance of the AC voltage source 225 to an impedance that matches the impedance of the resonator 205. In one example, a multi-stage quarter wave segment design can be used to generate hundreds of small load quality factors that are small enough to provide high stability to the power in the resonator regardless of Josephson junction switching statistics.

[0050] As shown in FIG. 4B, the first stage 405A of the two-stage feeding network 405 is configured to split the AC voltage source 225 into a first number of filaments, and the second stage 405B of the two-stage feeding network 405 is configured to split these filaments further. Each of these filaments is electrically coupled to a resonator of a particular LC tile of a particular phase. In one example, the first stage 405A of the two-stage feeding network 405 is configured to split the AC voltage source 225 into 256 filaments, each having an impedance of 100 ohms. The second stage 405B of the two-stage network 405 is configured to split the 256 filaments of the first stage into 33000 filaments, each having an impedance of 100 ohms. In this configuration, a loaded Q of 230 is generated. Lower loaded Q values ​​can be obtained with a feeding network of four or more stages.

[0051] In one example, the first feed network 405A and the second feed network 405B correspond to a Wilkinson network constructed from a parallel combination of many quarter wave segments corresponding to 100 Ω filaments. This configuration facilitates driving the resonators 205 of the LC tile from multiple points evenly spaced across the integrated circuit. This multi-stage configuration has minimal area overhead relative to the size of the LC tile 105. In one example, the total overhead of such a feed network 405 is about 1% of the resources compared to a combination of local resonators. In some examples, the quarter wave segments are implemented as transmission lines, lumped LC, or lumped element transmission lines. As described below, in some examples, the coupling network is formed in the same layer stack as the local LC tiles. This aspect improves tolerance to process variations.

[0052] FIG. 5A shows an example of a partial cross-sectional view of a superconducting circuit fabrication stack 500 in which some examples of LC tiles 105 described above are fabricated. The fabrication stack 500 includes a first / resonator layer 505 in which one or more resonators, such as any of the resonators described above, are formed. Some examples of the resonator layer 505 include one or more inductor layers 505A and one or more capacitor layers 505B in which inductors and capacitors as described above are formed. FIG. 5B shows a top view of one example of an inductor 215 formed in a stacked superconducting circuit. Some examples of the fabrication stack 500 include a ground plane 502 below the one or more capacitor layers 505B to provide isolation.

[0053] Some examples of fabrication stack 500 also include a second / Josephson junction layer 510 in which one or more Josephson junctions are formed, such as any of the Josephson junctions described above. Some examples of fabrication stack 500 further include a third / conductive interconnect layer 515 in which one or more interconnects are formed, such as any of the resonator-resonator interconnects described above.

[0054] In some examples, the area of ​​a particular tile 105 is set by either a capacitor or an inductor to match the area of ​​the corresponding Josephson junction. For example, the critical current density TIFF2025500394000005.tif9150 100 Josephson junctions 110 with an average critical current Ic of 50 μA are placed in a 5×5 μm 2 area, but it need only accommodate one inductor.

[0055] Some examples of capacitors are implemented as metal-insulator-metal (MIM) structures that include a high-K dielectric and a high mechanical inductance electrode (e.g., a NbTiN electrode). MIM capacitors are The capacitance is sized to provide a bias current Ib to the junction given by TIFF2025500394000006.tif10150. The target capacitance for the 35μA junction is 2.6fF, scaling linearly with the junction size.

[0056] In some examples of MIM capacitors, the dielectric is HfO x It contains silicon (Si) and has a high dielectric constant k, which facilitates tuning of the capacitance via an applied DC voltage. In one example, the area A of the smallest capacitor is A = 0.1 μm 2 which corresponds to a capacitor with a dielectric constant k of 32 and a thickness of 10 nm. In some examples, the MIM capacitor has NbTiN electrodes.

[0057] As shown in FIG. 5B, some examples of inductors 215 are implemented as spirals, including high mechanical inductance wires such as NbTiN wire. With a typical inductance of 2 pH / μm for 200 nm NbTiN wire, the spiral inductor is 5×5 μm 2 Fits within the area of.

[0058] In some examples, the maximum number of Josephson junctions in a particular LC tile 105 is set by the total bias current through the inductor 215, which must not exceed the critical current of the high mechanical inductance wire. The critical current of the wire is a function of the cross-sectional area of ​​the wire. A wire comprising NbTiN and having a cross-section of 200 nm wide by 200 nm thick can carry a maximum current of 5 mA. This sets the number of Josephson junctions per tile at approximately 100, with an average critical current of 50 μA.

[0059] 6 illustrates example operations 600 that facilitate fabrication of a superconducting circuit. The operations in block 605 include forming a resonator 205 in a first layer 505 of a fabrication stack 500. The resonator 205 comprises an inductor 215 including a first terminal and a second terminal, and a capacitor 220 including a first terminal electrically coupled to the second terminal of the inductor 215.

[0060] The operations at block 610 include forming a Josephson junction 210 in a second layer 510 of the fabrication stack 500. The Josephson junction 210 comprises a first terminal electrically coupled to a second terminal of the capacitor 220 and a second terminal electrically coupled to a common node. The terminal shared by the inductor 215 and the capacitor 220 is configured to be electrically coupled to an alternating current (AC) voltage source 225 having a particular frequency and a particular phase. The inductance of the inductor 215 and the capacitance of the capacitor 220 are selected to cause the resonator 205 to resonate at a frequency and phase that substantially matches the particular frequency and particular phase, respectively, of the AC voltage source 225 to facilitate switching of the state of the Josephson junction 210 via a single flux quantum (SFQ) pulse.

[0061] In some examples of operations, forming the resonator 205 with the capacitor 220 electrically coupled to the second terminal of the inductor 215 includes forming a plurality of capacitors 220 electrically coupled to the second terminal of the inductor 215, and forming the Josephson junctions 210 with a first terminal electrically coupled to the second terminal of the capacitor 220 includes forming a plurality of Josephson junctions 210. In these examples, each Josephson junction 210 is electrically coupled to one of the plurality of capacitors 220. Also, in these examples, the inductor 215 is configured such that an inductance of the inductor is inversely proportional to the number of the plurality of capacitors 220.

[0062] In some examples, forming the resonator 205 in the first layer 505 includes forming a plurality of resonators 205 in the first layer 505. These examples further include forming a conductive interconnect in a third layer 515 of the fabrication stack 500 configured to couple resonant energy between the plurality of resonators 250 to facilitate equalizing the phase and amplitude of each of the plurality of resonators 250 with respect to one another.

[0063] Some examples include electrically coupling a first subset of the plurality of resonators 250 to a first AC voltage source 225 having a first phase and electrically coupling a second subset of the plurality of resonators 250 to a second AC voltage source 225 having a second phase different from the first phase. In these examples, forming the conductive interconnects in the third layer 515 of the fabrication stack 500 includes forming a first conductive interconnect configured to couple resonant energy between the first subset of the plurality of resonators 250 to facilitate equalizing the phase and amplitude of each of the first subset of the plurality of resonators 250 with respect to one another and forming a second conductive interconnect configured to couple resonant energy between the second subset of the plurality of resonators 250 to facilitate equalizing the phase and amplitude of each of the second subset of the plurality of resonators 250 with respect to one another.

[0064] Some examples of operations include forming a splitter (e.g., a two-stage network 405) in a fourth layer of the fabrication stack, the splitter including a first terminal configured to be coupled to the AC voltage source 225 and a plurality of outputs configured to be electrically coupled to the first terminals of each of the capacitors 220 of the plurality of resonators 250.

[0065] In some examples, forming the splitter in the fourth layer includes forming a Wilkinson network in the fourth layer.

[0066] Some examples include electrically coupling a first terminal of the capacitor 220 to a direct current (DC) voltage source 260 to facilitate adjusting the capacitance of the capacitor 220 and the resonant frequency of the resonator 250.

[0067] Some examples include forming a second resonator 260B in a first layer 505 of the fabrication stack. In these examples, the second resonator 260B comprises an inductor 215 including a first terminal electrically coupled to a first terminal of the inductor 215 of the first resonator 260A. Each first terminal of the inductor 215 corresponds to a virtual ground node. The second resonator 260B also comprises a capacitor 220 including a first terminal electrically coupled to the second terminal of the inductor 215 and a second terminal configured to be electrically coupled to the Josephson junction 210. In these examples, the second resonator 260B is electrically coupled to an AC voltage source 225 via the virtual ground node, thereby configuring the second resonator 260B to be 180 degrees out of phase with the first resonator 260A.

[0068] Although some embodiments have been illustrated and described in detail in the accompanying drawings and the foregoing description, such illustration and description should be considered as illustrative and not limiting. Other variations to the disclosed embodiments can be understood and achieved in practicing the claims, from a study of the drawings, the disclosure, and the appended claims. The mere fact that certain measures or features are recited in mutually different dependent claims does not indicate that a combination of these measures or features cannot be used. Any reference signs in the claims should not be interpreted as limiting the scope.

Claims

1. an inductor including a first terminal and a second terminal; and a capacitor including a first terminal electrically coupled to the second terminal of the inductor; a resonator comprising: a Josephson junction having a first terminal electrically coupled to the second terminal of the capacitor and a second terminal electrically coupled to the common node, the terminal shared by the inductor and the capacitor configured to be electrically coupled to an alternating current (AC) voltage source having a particular frequency and a particular phase; a superconducting circuit, wherein the inductance of the inductor and the capacitance of the capacitor are selected to cause the resonator to resonate at a frequency and phase that substantially matches the particular frequency and the particular phase, respectively, of the AC voltage source to facilitate switching of the state of the Josephson junction via a single flux quantum (SFQ) pulse.

2. the capacitor is one of a plurality of capacitors electrically coupled to the second terminal of the inductor, and the Josephson junction is one of a plurality of Josephson junctions; each Josephson junction is electrically coupled to one of the plurality of capacitors; 2. The superconducting circuit of claim 1, wherein the inductor is configured such that the inductance of the inductor is inversely proportional to the number of the plurality of capacitors.

3. the resonator is one of a plurality of resonators; 3. The superconducting circuit of claim 1, further comprising a conductive interconnect configured to couple resonant energy between the plurality of resonators to facilitate equalizing the phase and amplitude of each of the plurality of resonators with respect to one another.

4. a first subset of the plurality of resonators configured to be electrically coupled to a first AC voltage source having a first phase, and a second subset of the plurality of resonators configured to be coupled to a second AC voltage source having a second phase different from the first phase; 4. The superconducting circuit of claim 3, wherein the conductive interconnect comprises: a first conductor configured to couple resonant energy between the first subset of the plurality of resonators to facilitate equalizing the phase and amplitude of each of the first subset of the plurality of resonators with respect to one another; and a second conductor configured to couple resonant energy between the second subset of the plurality of resonators to facilitate equalizing the phase and amplitude of each of the second subset of the plurality of resonators with respect to one another.

5. 4. The superconducting circuit of claim 3, further comprising a splitter comprising a first terminal configured to be coupled to the AC voltage source and a plurality of outputs configured to be electrically coupled to respective terminals shared by the inductor and the capacitor of each of the plurality of resonators.

6. 6. The superconducting circuit of claim 5, wherein the splitter corresponds to a Wilkinson network.

7. the terminal shared by the inductor and the capacitor is further configured to be electrically coupled to a direct current (DC) voltage source; 3. The superconducting circuit of claim 1, wherein the resonant frequency of the resonator depends in part on the voltage of the DC voltage source.

8. The antenna further includes a second resonator, the second resonator comprising: an inductor including a first terminal electrically coupled to the first terminal of the inductor of the first resonator, the first terminal of each inductor corresponding to a virtual ground node; and a capacitor including a first terminal electrically coupled to the second terminal of the inductor and a second terminal configured to be electrically coupled to a Josephson junction; 2. The superconducting circuit of claim 1, wherein the second resonator is electrically coupled to the AC voltage source through the virtual ground node, thereby configuring the second resonator to be 180 degrees out of phase with the first resonator.

9. 3. The superconducting circuit of claim 1, wherein the inductor, the capacitor, and the Josephson junction are vertically integrated in different layers of an integrated circuit.

10. 10. The superconducting circuit of claim 9, wherein the capacitor corresponds to a metal-insulator-metal (MIM) capacitor including high mechanical inductance electrodes, and the inductor is formed from high mechanical inductance wire.

11. 11. The superconducting circuit of claim 10, wherein the high mechanical inductance wire is NbTiN.

12. forming a resonator in a first layer of a fabrication stack, the resonator comprising: an inductor including a first terminal and a second terminal; and a capacitor including a first terminal electrically coupled to the second terminal of the inductor; and forming a Josephson junction in a second layer of the fabrication stack, the Josephson junction having a first terminal electrically coupled to a second terminal of the capacitor and a second terminal electrically coupled to the common node, the terminal shared by the inductor and the capacitor configured to be electrically coupled to an alternating current (AC) voltage source having a particular frequency and a particular phase; Including, a capacitance of the capacitor selected to cause the resonator to resonate at a frequency and phase that substantially corresponds to the particular frequency and the particular phase, respectively, of the AC voltage source to facilitate switching of the state of the Josephson junction via a single flux quantum (SFQ) pulse.

13. forming the resonator with a capacitor electrically coupled to the second terminal of the inductor includes forming a plurality of capacitors electrically coupled to the second terminal of the inductor; 13. The method of claim 12, wherein forming the Josephson junctions comprising a first terminal electrically coupled to a second terminal of the capacitor comprises forming a plurality of Josephson junctions, each Josephson junction electrically coupled to one of the plurality of capacitors, and wherein the inductor is configured such that the inductance of the inductor is inversely proportional to the number of the plurality of capacitors.

14. Forming the resonator in the first layer includes forming a plurality of resonators in the first layer, and the method further includes:

14. The method of claim 12 or 13, comprising forming a conductive interconnect in a third layer of the fabrication stack configured to couple resonant energy between the plurality of resonators to facilitate equalizing the phase and amplitude of each of the plurality of resonators with respect to one another.

15. electrically coupling a first subset of the plurality of resonators to a first AC voltage source having a first phase; and electrically coupling a second subset of the plurality of resonators to a second AC voltage source having a second phase different from the first phase; forming the conductive interconnect in the third layer of the fabrication stack; forming a first conductor configured to couple resonant energy between the first subset of the plurality of resonators to facilitate equalizing the phase and amplitude of each of the first subset of the plurality of resonators with respect to one another; and 15. The method of claim 14, comprising forming a second conductor configured to couple resonant energy between the second subset of the plurality of resonators to facilitate equalizing the phase and amplitude of each of the second subset of the plurality of resonators with respect to one another.

16. 15. The method of claim 14, further comprising forming a splitter in a fourth layer of the fabrication stack, the splitter including a first terminal configured to be coupled to the AC voltage source and a plurality of outputs configured to be electrically coupled to respective first terminals of each capacitor of the plurality of resonators.

17. 17. The method of claim 16, wherein forming the splitter in the fourth layer includes forming a Wilkinson network in the fourth layer.

18. 14. The method of claim 12 or 13, further comprising electrically coupling the terminal shared by the inductor and the capacitor to a direct current (DC) voltage source to facilitate adjusting the capacitance of the capacitor and the resonant frequency of the resonator.

19. forming a second resonator in the first layer of the fabrication stack, the second resonator comprising: an inductor including a first terminal electrically coupled to the first terminal of the inductor of the first resonator, the first terminal of each inductor corresponding to a virtual ground node; and a capacitor including a first terminal electrically coupled to the second terminal of the inductor and a second terminal configured to be electrically coupled to a Josephson junction; 13. The method of claim 12, wherein the second resonator is electrically coupled to the AC voltage source through the virtual ground node, thereby configuring the second resonator to be 180 degrees out of phase with the first resonator.

20. 1. An apparatus comprising a superconducting circuit, the superconducting circuit comprising: A resonator comprising: an inductor including a first terminal and a second terminal; and a capacitor including a first terminal electrically coupled to the second terminal of the inductor; and a Josephson junction having a first terminal electrically coupled to the second terminal of the capacitor and a second terminal electrically coupled to the common node, the terminal shared by the inductor and the capacitor configured to be electrically coupled to an alternating current (AC) voltage source having a particular frequency and a particular phase; wherein the inductance of the inductor and the capacitance of the capacitor are selected to cause the resonator to resonate at a frequency and phase that substantially matches the particular frequency and the particular phase, respectively, of the AC voltage source to facilitate switching of the state of the Josephson junction via a single flux quantum (SFQ) pulse.

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