Microwave filters with superconductor-insulator transition materials

Abstract

A microwave filter includes a superconductor-to-insulator transition (SIT) layer including a material exhibiting a superconductor-to-insulator transition associated with a superconducting gap frequency. For signals transmitting through the layer, the microwave filter is a low-pass filter in which twice the superconducting gap frequency is a cutoff frequency.

Description

MICROWAVE FILTERS WITH SUPERCONDUCTOR-INSULATORTRANSITION MATERIALSCROSS- REFERENCE FIELD OF THE DISCLOSURE

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 533,094 filed August 16, 2023, the disclosure of which is hereby incorporated by reference in its entirety.FIELD OF THE DISCLOSURE

[0002] The present disclosure relates to filters, such as microwave filters.BACKGROUND

[0003] High-energy photons (e.g., > 20 GHz to THz) can deteriorate qubit performance. Accordingly, signals associated with quantum computation (e.g., qubit control or readout signals) can be filtered to remove high-energy signal components.SUMMARY

[0004] Some aspects of this disclosure relate to a microwave filter. The microwave filter includes a superconductor-to-insulator transition (SIT) layer including a material exhibiting a superconductor-to-insulator transition associated with a superconducting gap frequency. For signals transmitting through the layer, the microwave filter is a low-pass filter in which twice the superconducting gap frequency is a cutoff frequency.

[0005] This and other microwave filters described herein can have one or more of at least the following characteristics.

[0006] In some implementations, the SIT layer includes a nitride alloy, niobium silicon, molybdenum germanium, molybdenum carbide, molybdenum rhenium, indium oxide, granular aluminum, or a cuprate superconductor.

[0007] In some implementations, the SIT layer includes NtySi i -xwith x between 0.15 and 0.25.

[0008] In some implementations, the SIT layer exhibits a sheet resistance between 100 Q and 2 kQ at a temperature less than 10 mK and for a frequency above twice the superconducting gap frequency.

[0009] In some implementations, the SIT layer exhibits a resistance per millimeter of at least 660 Q / mm at a temperature less than 10 mK and for a frequency of 10 GHz.

[0010] In some implementations, twice the superconducting gap frequency of the layer is between 8 GHz and 50 GHz.[OH] In some implementations, the microwave filter is a microstrip, a stripline, or a coplanar waveguide.

[0012] In some implementations, the SIT layer is arranged in a shape such that the microwave filter behaves as a notch filter that attenuates signal components having a frequency within a predefined frequency range.

[0013] In some implementations, the shape includes at least one of a spurline geometry or a stub geometry.

[0014] In some implementations, the predefined frequency range overlaps a frequency range of 8 GHz to 10 GHz.

[0015] In some implementations, the microwave filter is a cable.

[0016] In some implementations, the microwave filter includes a dielectric layer in which the SIT layer is embedded.

[0017] In some implementations, the microwave filter includes a first superconductor layer on a first side of the dielectric layer, and a second superconductor layer on a second side of the dielectric layer, the second side opposite the first side.

[0018] In some implementations, the dielectric layer includes a polyimide.

[0019] In some implementations, the microwave filter includes a voltage source coupled to the first superconductor layer, the voltage source configured to apply a voltage to the first superconductor layer to provide an electric field across the SIT layer between the first superconductor layer and the second superconductor layer.

[0020] In some implementations, the microwave filter includes a dielectric layer; and a superconductor layer. The SIT layer is on a first side of the dielectric layer, and the superconductor layer is on a second side of the dielectric layer, the second side opposite the first side.

[0021] In some implementations, the microwave filter includes a substrate on which the SIT layer is disposed; a first superconductor layer disposed on the substrate, the first superconductor layer extending adjacent to a first side of the SIT layer; and a second superconductor layer disposed on the substrate. The second superconductorlayer extends adjacent to a second side of the SIT layer, the second side opposite the first side.

[0022] In some implementations, the SIT layer and the first and second superconductor layers are disposed on a first surface of the substrate, and the microwave filter includes a third superconductor layer disposed on a second surface of the substrate opposite the first surface.

[0023] In some implementations, the microwave filter includes a magnetic field source arranged to apply a magnetic field to the SIT layer; and a controller coupled to the magnetic field source, the controller configured to provide signals to the magnetic field source to adjust a magnitude of the magnetic field.

[0024] In some implementations, the magnetic field source includes a trace arranged adjacent to the SIT layer, and the controller is configured to adjust a current through the trace to adjust the magnitude of the magnetic field.

[0025] In some implementations, the microwave filter includes a controller configured to apply a bias current through the SIT layer to adjust the superconducting gap frequency of the SIT layer to cause the microwave filter to have a target cutoff frequency.

[0026] In some implementations, the microwave filter includes a bias tee through which the bias current is applied to the SIT layer as a direct-current (DC) current.

[0027] In some implementations, the microwave filter includes a controller configured to apply at least one of a magnetic field, an electric field, or a current to the SIT layer, to adjust the superconducting gap frequency of the SIT layer to cause the micro wave filter to have a target cutoff frequency.

[0028] In some implementations, the microwave filter includes a printed circuit board, and the SIT layer is a trace on the printed circuit board.

[0029] In some implementations, the microwave filter includes a nonsuperconductor metal layer stacked on the SIT layer.

[0030] In some implementations, the SIT layer has a first footprint area that is orthogonal to a stack direction, and the non-superconductor metal layer has a second footprint area that is orthogonal to the stack direction. The first footprint area is different from the second footprint area.

[0031] In some implementations, a portion of the second footprint area protrudes beyond the first footprint area.

[0032] In some implementations, the microwave filter is coupled to a quantum computing device. The quantum computing device includes a quantum processor, a qubit readout resonator, or a qubit.

[0033] In some implementations, the microwave filter is configured to filter signal components having a frequency above twice the superconducting gap frequency from a signal that couples to the quantum computing device.

[0034] Some aspects of this disclosure describe a method. The method includes providing a microwave signal into a circuit device; and filtering the microwave signal by transmitting the microwave signal through a layer of a first material, the first material exhibiting a superconductor-to-insulator transition associated with a superconducting gap frequency. The filtering attenuates at least one signal component of the micro wave signal, the at least one signal component having a frequency at least twice the superconducting gap frequency.

[0035] Some aspects of this disclosure describe another method. The method includes obtaining a target cutoff frequency for a low-pass filter including a superconductor-to-insulator (SIT) layer exhibiting a superconductor-to-insulator transition associated with a superconducting gap frequency; and applying at least one of a magnetic field, an electric field, or a current to the SIT layer, to adjust the superconducting gap frequency of the SIT layer to cause the low-pass filter to have the target cutoff frequency.

[0036] In some implementations, applying the at least one of the magnetic field, the electric field, or the current causes the superconducting gap frequency of the SIT layer to be half the target cutoff frequency.

[0037] In some implementations, the SIT layer is coupled to a quantum device, and the adjusted superconducting gap frequency of the SIT layer causes the quantum device to be isolated from an environment of the quantum device.

[0038] Some aspects of this disclosure describe an apparatus. The apparatus includes a source circuit having a first impedance; and a superconductor-to-insulator transition (SIT) layer coupled to the source circuit. The SIT layer includes a material exhibiting a superconductor-to-insulator transition associated with a superconducting gap frequency, the SIT layer having a second impedance different from the first impedance. Based on an impedance mismatch between the first impedance and the second impedance, a signal component having a frequency above twice the superconducting gap frequency is reflected from the SIT layer to the source circuit.

[0039] In some implementations, the source circuit includes a transmission line.

[0040] In some implementations, a ratio of the second impedance to the first impedance is at least 10 at 60 GHz.

[0041] Implementations described herein can be used to realize one or more potential advantages. In some implementations, filters can be provided with high levels of attenuation extending to high frequencies, resulting in effective filter operation. In some implementations, filters can be effectively thermalized and / or exhibit reduced scintillation compared to some alternative filter schemes. In some implementations, filters can be integrated on-chip, in packaging, and / or in cables, allowing for efficient spatial utilization and extensive filtering of on-chip signals. In some implementations, filters can have shapes that provided additional filtering effect(s), such a notch filtering, to remove undesired frequency component(s). In some implementations, operations of quantum computing devices that receive / couple to a signal transmitted through the filter can be improved, because high-frequency photons can be removed from the signal prior to signal reception / coupling. In some implementations, filter cutoff frequency can be adjusted / set to provide flexible and reconfigurable filtering and device-environment coupling / decoupling.

[0042] The details of one or more implementations are set forth in the accompanying drawings and the description below. Other aspects, features and advantages will be apparent from the description and drawings, and from the claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0043] FIG. 1 is a diagram illustrating an example of a circuit system including a microwave filter.

[0044] FIG. 2 is a diagram illustrating filtering.

[0045] FIG. 3 A is a plan-view diagram illustrating an example of a filter.

[0046] FIG. 3B-3C are cross-sectional diagrams illustrating the filter of FIG. 3 A.

[0047] FIG. 4A is a plan-view diagram illustrating an example of a filter.

[0048] FIG. 4B is a cross-sectional diagram illustrating an example of a filter.

[0049] FIG. 5 A is a plan-view diagram illustrating an example of a filter.

[0050] FIG. 5B is a cross-sectional diagram illustrating the filter of FIG. 5 A.

[0051] FIGS. 6-7 are cross-sectional diagrams illustrating examples of filters.

[0052] FIGS. 8A-8E are plan-view diagrams illustrating examples of filters.

[0053] FIGS. 9A-9B are plan-view diagrams illustrating examples of geometries of superconductor-to-insulator transition layers.

[0054] FIG. 10 is a diagram illustrating an example of packaging including a filter.

[0055] FIGS. 11 A- 1 ID are diagrams illustrating an example of a process of making a filter.

[0056] FIG. 12 is a diagram illustrating a system including an adjustable filter.

[0057] FIG. 13 is a diagram illustrating a process for controlling a filter.

[0058] FIG. 14 is a diagram illustrating a filter system.

[0059] FIGS. 15A-15B are diagrams illustrating a system including an adjustable filter.DETAILED DESCRIPTION

[0060] This disclosure relates to microwave filters configured to filter components (e.g., high-frequency components, equivalently referred to as high-energy photons) out of signals, such as control signals for quantum processors. Lumped- el ement / distributive reflective filtering may be insufficient to adequately filter high- frequency signals, e.g., may provide too-low attenuation for out-of-band signal components. For example, low-pass combline cavity filters may permit high transmission at frequencies significantly above the filters’ cutoff frequency, e.g.. at 60 GHz. Some approaches to filtering employ lossy conductive and / or magnetic powders suspended in dielectrics (e.g., epoxy or glycerol) to form an effective dielectric within the cavity of a waveguide or within the annular section of a coaxial cable. The powders are a lossy medium for high-energy photons. As a further example of filtering, cables formed of steel and teflon may behave as a low-pass filter.

[0061] However, powder-based and steel / teflon filters may be poorly thermalized, employing thick dielectrics between housing and active components. These thick dielectrics may generate heat due to interactions with filtered-out high energy’ photons. In addition, some dielectrics, such as epoxy and teflon dielectrics, may exhibit scintillation due to background radiation and / or cosmic rays, further raising the temperature of the filter. High filter temperatures can lead to worse filter performance and / or may negatively affect quantum computing device operation (e.g., qubit operation). Moreover, powder-based and steel / teflon filters may not integratewell with high-density wiring schemes and may be incompatible with in-packaging and / or on-chip filtering.

[0062] Some implementations according to the present disclosure include filters (e.g., microwave filters) including a layer of a superconductor material having (e.g., close to, when at an operating temperature) a disorder-tuned superconductor-to- insulator transition. These so-called superconductor-insulator transition (SIT) materials exhibit a high-resistivity normal state and a temperature-dependent transition from superconductor to this high-resistivity normal state with increasing temperature, the critical transition temperature associated with a corresponding superconducting energy gap A (and, corresponding, a superconducting gap frequency / A). Signal components having a frequency above twice the superconducting gap frequency ( / / A) are reflected by the SIT material, which, to these high-frequency signal components, behaves as an insulator due to the resistivity of the normal state. For signal components having a frequency below twice the superconducting gap frequency, the SIT material behaves as a superconductor that transmits these low-frequency signal components with little or no attenuation or attenuation. Accordingly, the filter including the SIT layer behaves as a low-pass filter with cutoff frequency equal to twice the superconducting gap frequency, where the cutoff frequency is a frequency at which the frequency response of the filter exhibits a change in behavior to result in increased filtering. In some implementations, the cutoff frequency is tunable by using electromagnetic fields to adjust the superconducting gap frequency, allowing filtering to be adjusted and, in some implementations, interdevice coupling to be toggled on / off

[0063] Filtering based on SIT layers can be provided in various forms and contexts, e.g., in cabling, in packaging, and on-chip, offering design flexibility with which alternative filtering schemes (e.g., alternative micro wave filtering schemes) may be incompatible. As a result, filtering can be provided extensively throughout systems of interest (e.g., quantum computing systems) to drastically reduced the prominence of undesired signal components and, as a result, obtain improved system behavior. Moreover, compared to some alternative filtering schemes, the filters described herein can provide improved thermalization and / or exhibit reduced or eliminated scintillation.

[0064] SIT layer-based microwave filters can be understood as impedance- mismatched systems in which out-of-band signal components (signal componentshaving frequency above twice the superconducting gap frequency) are exposed to an impedance mismatch between a source circuit and the filter. For example, as shown in FIG. 1, a circuit system 100 includes a source circuit 102 coupled to a microwave filter 104. The source circuit 102 can include or be, for example, a transmission line (e.g., an on-chip transmission line), a cable, or another signal-carrying component that carries signals to the microwave filter 104. The source circuit 102 is associated with an output impedance Zo. which can be, for example. 50 Q, 25 Q, or another value. In some implementations, the output impedance Zo is less than 100 Q, an impedance range associated with commercially-available circuit components, such as coaxial cables.

[0065] The microwave filter 104 has a frequency-dependent input impedance Z (e.g., a characteristic impedance) based on the frequency -dependent superconductor- to-insulator transition of a layer of SIT material 106 included in the micro wave filter 104. Microwave signals (which can, but need not, include non-microwave components, such as DC components) are provided from the source circuit 102 to the layer of SIT material 106. For signal components with frequency less than twice the superconducting gap frequency of the SIT material, the SIT material behaves as a superconductor, and Z is approximately equal to Zo (e.g., based on geometry of the layer of the SIT material 106, dielectric(s), and / or ground plane(s) as determined bymicrowave engineering-associated constraints). As a result, these signal components are transmitted through the layer of SIT material 106 with little or no attenuation and little or no reflection. For signal components with frequency greater than twice the superconducting gap frequency of the SIT material, the SIT material behaves as an insulator, and Z is higher than Zo. For example, Z for can be at least ten times Zo or at least 100 times Zo, or another value, in various implementations. As a result of this impedance mismatch, these higher-frequency signal components are reflected from the layer of SIT material 106. Accordingly, based on this frequency -dependent behavior of the layer of SIT material 106, the microwave filter 104 is a low-pass filter with a cutoff frequency equal to twice the superconducting gap frequency.

[0066] FIG. 2 illustrates a simplified example of attenuation by a filter including an SIT material. The x-axis represents the frequency of a signal component transmitted to a layer of the SIT material, and the y-axis represents transmission by the layer. Below twice the gap frequency, signals are fully transmitted (experience 0 dB attenuation). Above twice the gap frequency, signals are attenuated, with the levelof attenuation increasing at higher frequencies. Accordingly, the layer behaves as a low-pass filter with a cutoff frequency equal to twice the gap frequency. The low-pass filter can further provide one or more other filtering effects, e.g., as described with respect to FIGS. 9A-9B.

[0067] Some filters described herein can be referred to as “microwave’' filters because they have a low-pass cutoff frequency in the microwave frequency range, so as to transmit some microwave frequencies and filter out other microwave frequencies. For example, in some implementations, the SIT layer is configured to exhibit a value of 2 X superconducting gap frequency between 8 GHz and 50 GHz, such as between 10 GHz and 20 GHz. In some implementations, 2 X superconducting gap frequency is approximately 12 GHz. In some implementations, the SIT layer is configured to exhibit a superconducting critical temperature between 50 mK and 680 mK. In some implementations, to facilitate desired current levels, the SIT layer is configured (e.g., based on the SIT material and / or the cross-sectional area of the SIT layer in the x-z plane as defined below) to exhibit a superconducting critical current between 0. 1 mA and 25 mA, such as between 1 mA and 10 mA.

[0068] Twice the superconducting gap frequency is related to the superconducting critical temperature 7c by the relationship fix = 3.52&B7C / / Z, where / 2A is twice the superconducting gap frequency, k& is Boltzmann’s constant, and h is Planck’s constant. As discussed below, the superconducting gap frequency depends on conditions of the SIT material, such as a current through the SIT layer, a magnetic field magnitude to which the SIT layer is exposed, and / or a temperature of the SIT layer, and one or more of these parameters can be varied to adjust the superconducting gap frequency and. accordingly, the behavior of the filter. However, particular numerical values disclosed herein refer to zero-temperature, zero-applied electric field, and zero-applied magnetic field values, unless indicated otherwise.

[0069] Parameters of the SIT layer can be selected to obtain a target superconducting gap frequency corresponding to a target cutoff frequency. For example, because different materials have different superconducting gap frequencies, an SIT material having a target superconducting gap frequency can be used for the SIT layer. In some implementations, as discussed below in reference to niobiumsilicon, the superconducting gap frequency of a material varies with the stoichiometry of the material, such that the stoichiometry can be selected to obtain a targetsuperconducting gap frequency and target cutoff frequency. In some implementations, the superconducting gap frequency of an SIT layer varies with the thickness of the SIT layer (e.g., thin-film vs. bulk properties), such that the thickness of the SIT layer can be selected to obtain a target superconducting gap frequency and target cutoff frequency. In some implementations, the superconducting gap frequency can be actively tuned / adjusted by use of electrical and / or magnetic control, as discussed below in reference to FIGS. 3 A, 5A-5B. 6, and 12-15.

[0070] The SIT layer can be an extended strip of SIT material having one of various configurations, such as stripline, microstrip, and / or coplanar waveguide. FIGS. 3A-3C illustrate an example of a filter 300 having an SIT layer 302 arranged in a microstrip configuration. FIG. 3 A shows the filter 300 in a plan view, and FIGS. 3B-3C show cross-sectional views of the filter 300.

[0071] The SIT layer 302 extends in a transmission direction y along which signals (e.g., un-reflected signal components having frequencies below the superconducting gap frequency of the SIT layer 302) are transmitted through the SIT layer 302. The SIT layer 302 is stacked on an underlying substrate 308 in a stack direction z (out of the page of the drawing of FIG. 3 A; x, y, and z are mutually orthogonal in all the figures of this disclosure), and the SIT layer 302 has a width in a lateral direction x orthogonal to they and z directions. For example, the transmission direction y and the lateral direction x can together define a generally planar shape of SIT layer 302 (e.g., parallel to a surface of the substrate 308), and the stack direction x can be orthogonal to the surface of the substrate 308.

[0072] In some implementations, the SIT layer 302 has a thickness (in the stack direction z) between 10 nm and 100 nm (e.g., between 20 nm and 60 nm), a range which may be associated with target film impedances and superconducting gap frequencies, such as 2 X superconducting gap frequencies between 8 GHz and 50 GHz. However, other thicknesses are also within the scope of this disclosure. In some implementations, a width of the SIT layer 302 in the lateral direction x is between 0. 1 pm and 64 pm, a range which may be associated with target film impedances and superconducting gap frequencies. s

[0073] The substrate 308, and other substrates described herein, can be any suitable type of substrate, e.g., a semiconductor substrate (e g., a silicon substrate), a dielectric substrate (e.g.. a glass, sapphire, or polymer substrate), or a circuit board(e.g., a printed circuit board (PCB) composed of a laminate such as FR-4). In some implementations, a substrate includes multiple materials / layers. For example, a dielectric layer (e.g., alumina) can be formed on an underlying semiconductor substrate, and the dielectric layer can be used as a dielectric material in a stripline, microstrip, or coplanar waveguide configuration of the SIT layer. The substrate 308 can be a dielectric layer, e.g., a polyimide such as kapton, an oxide such as alumina or silicon oxide, or a nitride such as silicon nitride.

[0074] The SIT layer 302 is provided on a first side of the substrate 308 (on surface 310 shown in FIG. 3B), and a superconducting (SC) layer 314 is provided on a second, opposite side of the substrate 308 (on surface 312 shown in FIG. 3B). The two surfaces 310, 312 are on opposite sides of the substrate 308 in the stack direction z.

[0075] The SIT layer 302 is configured as a conductor layer (signal-carry ing layer) of the microstrip configuration, and the SC layer 314 is configured as a ground plane of the microstrip configuration. In some implementations, a width of the SIT layer 302 in the lateral direction x is less than a width of the SC layer 314 in the lateral direction x, e.g., such that a footprint of the SC layer 314 orthogonal to the stack direction z (in a plane view showing x-y planes, as in FIG. 3A), encompasses and is larger than a footprint of the SIT layer 302. The SC layer 314 can be planar, e.g., effectively infinite compared to the lateral extent of the SIT layer 302.

[0076] The SIT material of the SIT layer 302 can be any suitable material exhibiting a temperature-dependent superconductor-to-insulator transition associated with a superconducting gap frequency that provides a desired cutoff frequency for the filter 300. For example, in some implementations, the SIT material can include any superconducting alloy exhibiting a normal-state resistance of 100 or more, such as nitride alloys (e.g., niobium nitride, titanium nitride, niobium titanium nitride, tantalum nitride), niobium-silicon, moly bdenum germanium, molybdenum carbide, molybdenum rhenium, indium oxide, granular aluminum, or a cuprate superconductor. In some implementations, the SIT material has a stoichiometry’ corresponding to a target zero-field superconducting gap frequency of the SIT layer 302. For example, niobium-silicon NbxSii-x has a superconducting gap frequency (and corresponding superconducting critical temperature To) that varies with x, where 7c is approximately 0.5 K for x = 0. 15 and decreases to near 0 K for x = 0.25. These values correspond to fiN = 36 GHz for x = 0.15, and lower / A for higher x. Accordingly, byvarying the stoichiometric parameter x (e.g., between 0. 15 and 0.25), a filter including a niobium-silicon layer can be provided with a desired target cutoff frequency (equal to f x) of 36 GHz or less. As another example, the ratio of Ti to N in titanium nitride can be varied to vary the superconducting gap frequency of titanium nitride (with the gap frequency decreasing with decreasing N%), and, accordingly, the cutoff frequency of a filter in which signals transmit through a titanium nitride layer.

[0077] In some implementations, the SIT material has a 7c below that of a superconductor material used for one or more other portions of the device, such as for the superconductor layer 314, the metal contacts 304, other wiring / traces, and / or quantum devices such as qubits, readout resonators, qubit couplers, quantum processors, etc. For example, the SIT material can have a 7c below that of aluminum (1.20 K). With this characteristic, the SIT material loses its superconductivity (behaves as an insulator) for some frequencies that are below the superconducting gap frequency of the other superconductor material such as aluminum.

[0078] The selection of the SIT material and the geometry of the SIT layer 302 may represent a tradeoff between the SIT layer’s superconducting critical current (which can be scaled by scaling the SIT layer’s cross-sectional area in the x-z plane as shown in FIG. 3B) and the SIT layer’s resistance for out-of-band signals (e.g., signal components with frequencies above tw ice the superconducting gap frequency of the SIT layer). A high resistance for out-of-band signals may be desired to obtain high levels of attenuation for out-of-band signals, and high resistances may correspond to low7superconducting critical currents, which may limit the utility of the filter 300 for transmission of high-amplitude, low-noise signals. For purposes of this disclosure, it has been recognized that particular values of the resistance and / or superconducting critical current, and / or particular selections of the SIT material, may effectively balance these considerations and provide high-quality filtering without overly impairing transmission of desired (e.g., lower-frequency) signal components.

[0079] For example, in some implementations, the sheet resistance of the SIT layer 302 or another SIT layer described herein (resistance per square) is between 100 Q and 2 kQ, e.g., between 100 Q and 400 Q. In some implementations, the SIT layer has a direct-current (DC) superconducting critical current between 1 and 10 mA. It has been recognized for purposes of this disclosure that niobium-silicon (e.g., NbxSii-xwith x between 0. 15 and 0.25) provides a potentially-desirable combination of a low superconducting gap frequency (associated with a low77c) that provides a useful filtercutoff frequency, and a sheet resistance on the order of 100 Q to several hundredOhms, with a relatively high superconducting critical cunent to support relatively high supercurrents. These values can apply at a temperature less than 10 mK, and for frequencies at which the SIT layer is in its non-superconductor state (such as a frequency between two times the superconducting gap frequency and three times the superconducting gap frequency).

[0080] These sheet resistances can provide an above-gap impedance that results in reflection of above-gap signal components (signal components having a frequency above twice the superconducting critical frequency). The impedance Z of a lossy transmission line (here representing the impedance of the SIT layer 302 and other SIT layers described herein) can be expressed as Z = (where R. / .. and C areresistance, inductance, and capacitance per length, respectively, and a> is signal p angular frequency), and the mismatch loss =receive(for signals transmitted to the SITlayer from a source circuit having impedance Zo such as source circuit 102) is— 20 log(l — T2), where T = — z+z0Based on a target mismatch loss, these equations indicate a target ratio Z / Zo of the SIT layer 302 impedance to the output impedance of the source circuit, and this target ratio, together with assumptions for L and C, knowledge of Zo (e.g., 50 Q) and selection of a particular frequency to of a signal to be filtered-out, can indicate a target resistance per length R of the SIT layer. For example, a target mismatch loss of 20dB (corresponding to 17100thof an undesired signal component being transmitted) can correspond to Z / Zo ~ 38, which can correspond to a target resistance per length R of the SIT layer of at least about 2400 Q / mm at 10 GHz. A target mismatch loss of lOdB (corresponding to 1 / 10thof an undesired signal component being transmitted) can correspond to Z / Zo ~ 10.5, which can correspond to a target resistance per length R of the SIT layer 302 of at least about 660 Q / mm at 10 GHz (e.g., for a temperature less than 10 mK).

[0081] The particular values of layer impedance / resistance can be varied. In some implementations, the ratio of the impedance of an SIT layer to the output impedance of a source circuit providing signals to the SIT layer, is at least 5, at least 10, at least 50, or at least 100 (e.g., and, in some cases, less than 1000 or less than 10,000). at 60 GHz (e.g., for a temperature less than 10 mK). In some implementations, the resistance-per-length of the SIT layer at 10 GHz is at least 500 Q / mm or at least 1000Q / mm (e.g., and, in some cases, less than 5000 Q / mm or less than 10,000 / mm). These values can, in some cases, provide what has been recognized for purposes of this disclosure to be an effective balance between high attenuation of undesired signals and capacity to carry relatively high levels of desired signals without losing superconductivity'.

[0082] The SC layer 314 configured as a ground plane (e.g., coupled to an electrical ground) can be composed of any suitable one or more superconductor materials. “Superconductor” and “superconductor material,” as referred to herein, refer to materials that become superconducting under compatible conditions, e.g., below the superconducting critical temperature, superconducting critical current, and critical magnetic field of the materials. In some implementations, the SC layer 314 is composed of an SIT material, e.g., the same SIT material that composes the SIT layer 302. In some implementations, the SC layer 314 is composed of a different superconductor material, such as aluminum, e.g., a superconductor that exhibits a superconductor-to-metal transition. Non-limiting examples of superconductor materials that can form the SC layer 314 include aluminum, niobium, titanium, niobium nitride (NbN), niobium-titanium (NbTi), tungsten, tantalum, and titaniumtungsten (TiW), and non-limiting examples of classes of superconductor materials that can form the SC layer 314 include elemental superconductors, alloysuperconductors. ceramic superconductors (e.g.. yttrium barium copper oxide (YBCO) and magnesium diboride), and organic superconductors. In some implementations, the SC layer 314 is composed of a superconductor material that has a larger superconducting energy gap than the SIT material of the SIT layer 302; this may facilitate superconducting operation of the filter 300. which can be held at a temperature lower than the superconducting gap temperatures of both the SIT material and the superconductor material with the superconductor material far from its transition temperature. In some implementations, the SC layer 314 is in contact with a metal contact (e.g.. having characteristics as described below for metal contacts 304) to provide conduction to the SC layer 314.

[0083] During operation, the filters described herein can be maintained at a temperature lower than the superconducting critical temperature of the SIT layer. For example, a filter including an SIT layer can be disposed inside a refrigerator (e g., a dilution refrigerator) configured to maintain a cryogenic temperature lower than the superconducting critical temperature of the SIT layer.

[0084] In some implementations, contact to the SIT layer is made by metal contact layers, e.g., contact layers composed of a superconductor metal and / or nonsuperconductor metal, such as aluminum, tin, titanium, gold, silver, and / or platinum. In some implementations, the contact layer includes a bilayer of a superconductor metal and a noble metal, such as titanium-gold, ruthenium-gold, or aluminum-silver. The bilayer may provide the contact layer with improved stability to atmospheric exposure, and may reduce local heating that may occur if a normal metal contact is not proximitized to the SIT material.

[0085] For example, as show n in FIGS. 3A-3C, a pair of metal contacts 304 can be spaced apart from one another in the transmission direction y to provide signals into the SIT layer 302 / receive signals from the SIT layer 302. In this example, the metal contacts 304 are layers that are at least partially below the SIT layer 302, with an area of contact and overlap 316 (in the stack direction z) between the SIT layer 302 and the metal contacts 304 permitting signal conduction between the SIT layer 302 and the metal contacts 304. Further traces and / or wire bonds can transfer signals to / from the metal contacts 304. For example, wire bonds can be made to portions of the metal contacts 304 that are not beneath the SIT layer 302 (outside the area of contact and overlap 316). An example of a fabrication process for forming metal contact layers and an SIT layer is shown in FIGS. 11A-1 ID.

[0086] The filtering SIT layers described herein, such as the SIT layer 302 of the filter 300, can be implemented in various forms and used in various contexts, such as on-chip, packaging-integrated, and cable-integrated. For example, in some implementations the SIT layer is disposed on a substrate, and a quantum computing device is disposed on the substrate or another substrate. The quantum computing device is arranged to couple to a signal that is filtered by the filter including the SIT layer. For example, the quantum computing device can be a qubit, a qubit readout resonator, a qubit control element (e.g., a pad that couples to a qubit), a quantum processor, etc., and the signal can be a qubit control signal, a qubit readout signal, a reset signal, etc. The quantum computing device can couple to the signal as the signal is transmitted through the SIT layer, and / or the SIT layer can transmit the signal to another signal-carrying circuit element such as a coplanar waveguide, stripline, or microstrip (which can be, though need not be, a filtering SIT layer) which couples to the quantum computing device.

[0087] For example, as shown in FIG. 4A, a quantum computing device 402 and an SIT layer 404 of a filter are disposed on and / or in a substrate 400. The SIT layer 404 is shown in a plan view as in FIG. 3 A, in which the stack direction z is in / out of the page and directions x and v define planes of the view. For example, the SIT layer 404 has a generally elongated shape (e.g., as a trace extending on and / or in the substrate 400), and a signal filtered by the SIT layer 404 propagates in the direction of elongation, the transmission direction y. The signal can couple to the quantum computing device 402 arranged adjacent to the SIT layer 404 (e.g., spaced apart from the SIT layer 404 in the lateral direction x). The SIT layer 404 can be configured in a signal-carrying configuration such as a coplanar waveguide, a stripline, or a microstrip, e.g., as described with respect to FIGS. 3A-3C, 5A-5B, and 6-7. For example, the SIT layer 404 can be provided on a surface of the substrate 400 in a microstrip configuration or coplanar w aveguide configuration, and / or embedded in the substrate 400 in a stripline configuration (e.g., where the substrate 400 can be a dielectric layer).

[0088] As another example, as shown in FIG. 4B in a cross-sectional view, a first substrate 410 (e.g., a carrier chip) and a second substrate 412 (e.g., a qubit chip) are arranged in a flip-chip configuration. An SIT layer 414 is arranged in and / or on the first substrate 410 414 (e.g., as described for the SIT layer 404), so as to cany signals that couple to a quantum computing device 416 arranged in and / or on the second substrate 412. For example, the quantum computing device 416 can be arranged directly above (aligned with) a portion of the SIT layer 414. The substrates 410, 412 can be spaced apart from one another in the stack direction z.

[0089] As noted above, for on-chip and other implementations of the filtering SIT layers described herein, the SIT layer need not be arranged for coupling to a quantum computing device. Rather, in some implementations the SIT layer is configured as a signal-carrying element for routing signals on / in a chip / substrate (and filtering the signal), without necessarily coupling to a quantum computing device. For example, the SIT layer can be a trace extending on and / or in a circuit board or a substrate hosting one or more circuit devices.

[0090] In some implementations, the SIT layer itself forms all or a portion of a quantum computing device. For example, a meandering / spiral SIT layer can form a qubit readout resonator that (i) couples to a qubit for readout and (ii) filters signals transmitting in the qubit readout resonator.

[0091] In some implementations, a filter incorporating an SIT layer has a cutoff frequency that is adjustable by application of magnetic and / or electrical fields to the SIT layer. The SIT layer’s superconducting gap energy (and superconducting gap frequency) depend on the magnetic and / or electric field applied to the SIT layer, and on the current flowing through the SIT layer. Accordingly , application of a magnetic and / or electrical field and / or a current can adjust the superconducting gap frequency, thereby adjusting the filter’s cutoff frequency.

[0092] Implementations according to this disclosure can optionally include configurations (such as devices, controllers, and / or suitable circuit interconnections) for applying magnetic and / or electrical fields and / or currents to SIT layers to adjust the SIT layers’ superconducting gap frequencies. As shown in FIG. 3A, the filter 300 includes an input bias tee 320 and an output bias tee 322. In this example, the bias tees 320, 322 are coupled to the metal contacts 304 to as to provide signals in / out of the SIT layer 302 via the metal contacts 304. For example, the bias tees 320, 322 can include circuits on and / or in the substrate 308 (e.g., as integrated circuits on / in the substrate 308). and / or can include circuits separate from the substrate 308, e.g.. as separate discrete circuits.

[0093] Input signals IDC and IAC are provided to the input bias tee 320 and input into the SIT layer 302 as a summed signal I C+IAC. IAC can be, for example, a control signal, a readout signal, or a data signal, and can include microwave frequency components / pulses. ZDC is a bias current. The superconducting gap frequency of the SIT layer 302 depends on the magnitude of IDC. For example, higher values of IDC correspond to low er values of the superconducting gap frequency and, correspondingly, lower cutoff frequencies of the filter 300. In some implementations, I is selected and controlled using a controller, e.g., as described for controllers 1202, 1402, and 1502. In some implementations, ID is between -100 mA and 100 mA, where negative current values can correspond to non-reciprocal behaviors, e.g., associated with microwave rectification.

[0094] The output bias tee 322 receives Znc.out and ZAC, out after transmission through the SIT layer 302. Znc.out can, in some cases, simply be equal to ZDC, because IDC is a signal in the pass-band of the low -pass filter 300. In some cases, ZDC, out is attenuated compared to ZDC. ZAC, out can be a filtered (and, in some cases, attenuated) version of ZAC, e.g., because signal component(s) in ZAC that have a frequency higher than twice the adjusted superconducting gap frequency of the SIT layer 302 arepartially or substantially reflected from the SIT layer 302 without transmitting to the output bias tee 322. In some implementations, as in the example of FIG. 3 A, the output bias tee 322 can be configured to separate Znc.out from ZAC, out. For example, ZAC, out can be provided to a circuit output for measurement, can couple to a quantum computing device to control the quantum computing device, and / or can otherwise be used for circuit operation. In some implementations, Zoc.out can be filtered from the output without being used for further circuit operations.

[0095] In some implementations, a filter includes a magnetic field source arranged to provide an adjustable magnetic field to an SIT layer, in order to adjust the cutoff frequency of the filter. For example, FIGS. 5A-5B illustrate an example of a filter 500. FIG. 5A shows the filter 500 in a plan view as in FIG. 3A (showing an x-y plane), and FIG. 5B shows a cross-section of the filter 500 in the x-z plane. Elements of the filter 500 can have characteristics as described for corresponding elements of the filter 300, except where indicated otherwise. For example, as described for the filter 300, the filter 500 has an SIT layer 302 in a microstrip configuration with a superconductor layer 314 configured as a ground plane.

[0096] The filter 500 includes a magnetic field source 502 arranged to provide a controllable magnetic field 504 to the SIT layer 302. For example, the magnetic field source 502 can be adjacent to the SIT layer 302. e.g., spaced apart from the SIT layer 302 in the lateral x direction. In some implementations, the magnetic field source 502 is spaced apart from the SIT layer 302 in the stack direction z, e.g., above or below the SIT layer 302 and at least partially aligned with the SIT layer 302 in a plan view. The magnetic field source 502 can be in and / or on the substrate 308, e.g., embedded in the substrate 308 and / or provided on a surface 506 (indicated in FIG. 5B) on which the SIT layer 302 is provided. In some implementations, the magnetic field source 502 includes a conducting meander, spiral, coil, or other shape (e.g., composed of a superconductor material or a non-superconductor metal) through which a current is provided to provide the magnetic field 504. In some implementations, the magnetic field source 502 includes a conducting line (e.g., an extended strip of superconductor material or a non-superconductor metal) through which a current is provided to provide the magnetic field 504. For example, in some implementations the conducting line extends parallel to, and spaced apart from in the x and / or z direction, the extended line of the SIT layer in a coplanar waveguide, microstrip, or stripline configuration.

[0097] Higher magnitudes of the magnetic field 504 (e.g., corresponding to higher magnitudes of current provided through the magnetic field source 502) correspond to lower superconducting gap frequencies of the SIT layer 302. In some implementations, a substantially DC current is provided through the magnetic field source 502 to provide a substantially constant magnetic field 504 to the SIT layer 302, to set a target superconducting gap frequency in the SIT layer 302 and, accordingly, a target cutoff frequency in the filter 500 equal to twice the superconducting gap frequency. The current through the magnetic field source 502 can be controlled by a controller, e.g., as described for controller 1202, 1402, and / or 1502. The current provided can depend on the characteristics of the magnetic field source, e.g., to provide a target magnetic field magnitude to the SIT layer 302. The magnetic field magnitude can be a fraction of the critical magnetic field He of the SIT layer 302, e.g., in some implementations less than 0.177c, less than 0.0577c, or less than 0.0177c. In some implementations, the magnetic field magnitude is less than 350 ml In some implementations, the current provided is less than 100 mA.

[0098] Microwave filters as described herein need not include a mechanism for adjusting the cutoff frequency. For example, a filter as shown in FIGS. 3A-3C need not include bias tee(s), and a filter as shown in FIGS. 5A-5B need not include a magnetic field source.

[0099] FIG. 6 illustrates an example of a filter 600 (shown in cross-sectional view) having an SIT layer 602 arranged in a stripline configuration. The SIT layer 602 is embedded in a dielectric layer 608, e.g., a polyimide such as kapton, an oxide such as alumina, or a nitride such as silicon nitride. Superconductor (SC) layers 604, 606 are arranged on first and second sides of the dielectric layer 608, respectively, sandwiching the dielectric layer 608 in which the SIT layer 602 is embedded. The SC layers 604, 606 need not be identical, e.g., can differ from one another in thickness, composition, and / or other parameters.

[0100] Except where indicated otherwise, elements of the filter 600 can have characteristics (e.g., materials, dimensions (e.g.. thicknesses), geometries, and properties such as impedance, resistance, superconducting gap frequencies, etc.) as described for corresponding elements of the filter 300. For example, the SC layers 604, 606 can be composed of an SIT material or another type of superconductor material, such as aluminum.

[0101] In the filter 600 having the stripline configuration, the SIT layer 602 acts as a central conductor, and the SC layers 604, 606 can, in some implementations, act as ground planes, e.g., which may be shorted to one another / held at the same potential. Accordingly, signals can be transmitted with low noise / interference and filtered by the SIT layer 602. Signals are transmitted in the illustrated transmission direction which is orthogonal to the stack direction z along which the layers 604, 602, 606 are arranged in sequence, and orthogonal to the lateral direction x. where the lateral direction x and the transmission direction;’ together define a plane corresponding to the substantially planar shapes of the layers 602, 604, 606. Signal components having a frequency above twice the superconducting gap frequency of the SIT layer 602 are attenuated by the filter 600, e.g., by being reflected from the SIT layer 602 back to a source circuit (not shown).

[0102] In some implementations, a width of the SIT layer 602 in the lateral direction x is less than widths of the SC layers 604, 606 in the lateral direction x, e.g., so that footprints of the SC layers 604. 606 orthogonal to the stack direction z (in a plan view) encompass and are larger than a footprint of the SIT layer 602. The SC layers 604, 606 can be planar, e.g., effectively infinite compared to the lateral extent of the SIT layer 602.

[0103] The filter 600 can be arranged on-chip (e.g. on a surface of an underlying substrate), in packaging, and / or can be embedded in a cable, e.g., a flexible cable. Accordingly, a filtering function can be provided in cabling to / from devices such as quantum computing processors (the cable itself being a filter). A dielectric, such as a flexible polyimide dielectric, such as kapton, can extend along the cable and encapsulate the inner SIT layer 602 as the dielectric layer 608. An insulating material, such as rubber, can coat an exterior of the cable for insulation and physical protection. In some implementations, the SC layers 604, 606 are a single SC layer that circumferentially surrounds the SIT layer 602 in a coaxial arrangement, e.g., as a cable.

[0104] In some implementations, a filter having a stripline configuration, such as the filter 600, has an adjustable cutoff frequency based on an adjustable superconducting gap frequency of the SIT layer. For example, the filter 600 includes a voltage source 610 coupled to SC layer 604, and the other SC layer 606 is grounded. A voltage Tapp can be applied to the SC layer 604 (e.g., by a controller as described in reference to FIG. 1202, 1402, and / or 1502) to apply an electric field to the SIT layer602 (between the SC layer 604 and the SC layer 606), where the superconducting gap frequency depends on the value of the electric field. For example, higher magnitudes of Fapp (corresponding to higher electric field magnitudes) can correspond to lower values of the superconducting gap frequency and, correspondingly, lower cutoff frequencies of the filter 600. In some implementations, FaPPis a substantially DC signal. Examples in which the filter 600 does not have an adjustable cutoff frequency can correspond to FaPP= 0 (the SC layers 604. 606 grounded together).

[0105] Other device configurations to provide a stripline filter or cable filter with an adjustable cutoff frequency are also within the scope of this disclosure. For example, an adjustable DC bias signal can be applied to the SIT layer 602 in the transmission direction y as shown in FIG. 3 A. and / or a magnetic field source can be provided in and / or on the dielectric layer 608 to provide an adjustable magnetic field to the SIT layer 602.

[0106] In some implementations, a filter including an SIT layer is configured with a coplanar waveguide configuration. For example, as shown in FIG. 7 in a cross- sectional view, a filter 700 includes an SIT layer 702 and SC layers 704 disposed on a surface 706 of a substrate 708. The SIT layer 702, SC layers 704, and substrate 708 can have characteristics as described for the SIT layer 302, SC 314, and substrate 308, respectively, except where indicated otherwise.

[0107] In the coplanar waveguide configuration, the SIT layer 702 is a central conducting track, and the SC layers 704 are return tracks. For example, the SC layers 704 can be grounded. In some implementations, the SC layers 704 extend on the substrate 708 far from the SIT layer 702, e.g., as effectively semi-infinite planes. The SC layer 704 can be shorted to one another. Signals (e.g., microwave signals) can be transmitted along the coplanar waveguide in the transmission direction y and can be filtered based on the superconducting gap frequency of the SIT layer 702, e.g., with reflection of signal components having frequencies above twice the superconducting gap frequency.

[0108] In some implementations (not shown in FIG. 7). a filter having a coplanar waveguide configuration can have an adjustable cutoff frequency. For example, a controllable magnetic field source can be provided in and / or on the substrate 708 as described with respect to FIGS. 5A-5B, and / or a controllable bias current (e.g., a DC bias current) can be provided through the SIT layer 702 as described with respect to FIG. 3A, e.g., using one or more bias

[0109] In some implementations, a filter having a coplanar waveguide configuration includes an additional SC layer as a ground plane on a back surface of the substrate, e.g., SC layer 712 back surface 710 in FIG. 7. The back surface SC layer 712 can be shorted to SC layers 704 (the return tracks).

[0110] In some implementations, a non-superconductor metal layer is stacked with the SIT layer for one or both of (i) thermalization (e.g., improving transport of thermal energy compared to a superconductor-only layer / stack) and (ii) signal transport in parallel with signal transport in the SIT layer. The non-superconductor metal layer can be on top of the SIT layer or below the SIT layer, e.g., with respect to an underlying substrate / chip.[OHl] FIGS. 8A-8E illustrate (in a plan view) examples of stacks of a nonsuperconductor metal layer and an SIT layer, in which footprints of the nonsuperconductor metal layer and footprints of the SIT layers are separately indicated. The footprints are areas orthogonal to the stack direction z. In some implementations, the footprints of the non-superconductor metal layer and SIT layer are different. For example, the footprint of the non-superconductor metal layer can protrude beyond the footprint of the SIT layer, and / or the footprint of the SIT layer can protrude beyond the footprint of the non-superconductor metal layer. In some implementations, the footprint of the non-superconductor metal layer is discontinuous.

[0112] As shown in FIG. 8A, in a multilayer stack 800. a footprint 802 of a nonsuperconductor metal layer overlaps a footprint 804 of an SIT layer. Although portions of the footprint 804 are shown, for clarity, as not overlapping with the footprint 802, in some implementations the footprint 802 extends fully along the footprint 804 in the transmission direction y. The presence of the non-superconductor metal layer, having footprint 804, permits dissipative (lossy) transmission of signals through the non-superconductor metal layer in parallel with transmission through the SIT layer. For example, signal components having frequencies above twice the superconducting gap frequency of the SIT layer may be significantly or entirely filtered out by the SIT layer, but may be transmitted (with some attenuation) through the non-superconductor metal layer. For example, if microwave cavity modes exist which may permit transmission from one port to another despite the SIT layer appearing as an open circuit, then the non-superconductor metal layer can advantageously provide a dissipative dominant TEM mode.

[0113] As show n in FIG. 8B, in a multilayer stack 810, a footprint 812 of a nonsuperconductor metal layer is discontinuous, e.g., includes separate, non- overlapping / non-touching portions such as portions 819a, 819b, 819c. The portions 819a, 819b, 819c are laterally separated from one another along the transmission direction y of the multilayer stack 810. A footprint 814 of an SIT layer extends to overlap with the separate portions of the footprint 812 and includes portions that do not overlap the footprint 812. The footprint 812 protrudes beyond the footprint 814, e.g., in the lateral direction x orthogonal to the transmission direction y and orthogonal to the stack direction z. In various implementations, the footprint 812 can protrude beyond the footprint 814 on one or both lateral sides of the footprint 812 (shown as both lateral sides in FIG. 8B). In some implementations, lateral protrusions of the non-superconductor metal (e.g., protrusions 813) are connected to one or more thermalization paths, e.g., metal traces and / or metal vias 815. This can promote thermalization in the multilayer stack 810 and reduce heating of the multilayer stack 810, e.g., due to the multilayer stack’s dissipation function.

[0114] Various shapes of the footprints are within the scope of this disclosure. In FIG. 8B, each portion 819a, 819b, 819c of the footprint 812 has a substantially rectangular shape in the plan view. As shown in FIG. 8C in a plan view, in another example of a multilayer stack 820. each portion 823a, 823b, 823c (discontinuous from one another and laterally separated along the transmission direction y of the multilayer stack 820) of a footprint 822 of a non-superconductor metal layer has a polygonal shape that is widest at a location of overlap with a footprint 824 of an SIT layer and narrows to a point protruding beyond the footprint 824 in the lateral direction x. As shown in FIG. 8D in a plan view, in another example of a multilayer stack 830, portions 833a, 833b, 833c (laterally separated along the transmission direction y of the multilayer stack 830) of a footprint 832 of a non-superconductor metal layer are connected by lengthwise portions 835a, 835b, 835c of the footprint 832 that extend in the transmission direction y. The lengthwise portions 835a, 835b, 835c overlap with a footprint 834 of an SIT layer. The portions 833a, 833b, 833c protrude beyond the footprint 834 in the lateral direction x. Because the footprint 832 extends in the transmission direction v, signals can be carried by the non-superconductor metal layer in a dissipative manner. As shown in FIG. 8E, in another example of a multilayer stack 840, portions 843a. 843b, 843c (laterally separated along the transmission direction y of the multilayer stack 840) of a footprint 842 of a non-superconductormetal layer are connected by a single lengthwise portion 845 of the footprint 842 that extends in the transmission direction y. The lengthwise portion 845 overlaps with a footprint 844 of an SIT layer. The portions 843a, 843b, 843c protrude beyond the footprint 844 in the lateral direction x. Because the footprint 842 extends in the transmission direction)-’, signals can be carried by the non-superconductor metal layer in a dissipative manner. The portions 833a, 833b. 833c and 843a, 843b, 843c of FIGS. 8D-8E have nanowing shapes as described in reference to portions 823a, 823b, 823c.

[0115] As described with respect to FIG. 8B, a thermalization structure such as a metal via and / or metal trace can be thermally coupled to (e.g., in contact with) the non-superconductor metal in these structures to promote thermalization and reduce heating of the multilayer stacks of FIGS. 8 A and 8C-8E. Moreover, the continuous lengthwise extensions of the non-superconductor metal layers shown in FIGS. 8D-8E can provide a parallel, dissipative conduction path for signals transmitted through the corresponding SIT layers, as discussed above.

[0116] The multilayer stacks illustrated in FIGS. 8A-8E can be included in any of the filter configurations described herein, such as coplanar waveguide, microstrip, stripline, and / or cable configurations, e.g., as the center stack / line or conducting stack / line of a stripline, microstrip, coplanar w aveguide, or cable.

[0117] In some implementations, an SIT layer of a microwave filter has a shape, in a plan view, that provides an additional filtering effect besides the low-pass filter behavior provided by the superconducting gap frequency of the SIT layer. For example, as shown in FIG. 9A in a plan view, a filter 900 includes an SIT layer 902. An area 910 surrounding the SIT layer 902 in the plan view can be. for example, a substrate (e.g., a dielectric layer) on which the SIT layer 902 is disposed. Signals are transmitted through the SIT layer 902 generally in the transmission direction y. The SIT layer 902 can be, for example, the center line or conducting line of a stripline, microstrip, or coplanar waveguide, e.g., SIT layer 302, 404. 414, 602, and / or 702.

[0118] The SIT layer 902 has a shape that includes a spurline 904. The spurline 904 causes the filter including the SIT layer 902 to behave as a notch filter (band-stop filter) for signal components in a frequency range defined by the geometry of the SIT layer 902. For example, in some implementations, the spurline length)’' is equal tothe wavelength corresponding to the center rejection frequency of the notch filter in the material of the SIT layer 902. Other geometric parameters of theSIT layer 902 (such as y, x, x', and / or W, as shown in FIG. 9A) can be configured to adjustgand / or the stop band width of the notch filter.

[0119] In various implementations, the center rejection frequency can be above or below twice the superconducting gap frequency of the SIT layer. In some implementations, the stop band of the notch filter (based on the shape of the SIT layer) includes twice the superconducting gap frequency of a material. For example, in some implementations the stop band includes 88 GHz, corresponding to twice the superconducting frequency of aluminum. A stop band at higher frequencies than twice the superconducting gap frequency of the SIT layer can be useful even given the existing filtering of those frequencies based on the attenuation / reflection by the SIT layer, e.g., because certain of the higher frequencies may be particularly sensitive for operation of the device (such as twice the superconducting gap frequency of a material) and / or because certain of the higher frequencies may correspond to high intensities of environmental interference. The shape of the SIT layer can be configured so that the stop band includes these frequencies, to filter out signal components to which device operation is particularly sensitive and / or to filter out undesired signal components that may be high-intensity.

[0120] In some implementations, the stop band of the notch filter corresponds to a cavity mode associated with packaging of the filter, e.g., the stop band may overlap some or all of the range 8 GHz to 10 GHz, which may be below twice the superconducting gap frequency of the SIT layer. As another example, in some implementations the shape of the SIT layer is configured so that the stop band includes a pump frequency of an amplifier that contributes to a signal transmitted in the SIT layer, e.g., 10 GHz.

[0121] The spurline geometry can advantageously be formed within a pitch 906 of the SIT layer 902, e.g., to facilitate more efficient use of space. In some implementations, a portion 912 of the SIT layer 902 that has a reduced width (in a lateral direction x) because of the presence of the spurline 904 (e.g., the portion 912 adjacent to the spurline 904) is thicker than one or more portions of the SIT layer 902 that have a larger width in the lateral direction x, e.g., one or more portions that are not adjacent to the spurline 904. This can reduce the current density' in the portion 912 to maintain current levels above the superconducting critical current of the SIT layer 902.

[0122] An SIT layer can have a shape that includes zero, one, or multiple spurlines to behave as zero, one. or multiple notch filters, which may have the same or different respective stop bands.

[0123] In some implementations, instead of or in addition to a spurline geometry, an SIT layer includes a stub geometry that can cause the SIT layer to behave as a filter in addition to the filtering based on the superconducting gap frequency. For example, as shown in FIG. 9B in a plan view, a filter 920 includes an SIT layer 922 having a transmission direction y. The SIT layer 922 has a shape that includes a stub 924 projecting (e.g., in a lateral direction x) from the adjacent portion of the SIT layer 922. In some implementations, the stub 924 includes a first portion 925 extending from the adjacent portion of the SIT layer 922 in the lateral direction x, and a second portion 927 extending from the first portion in the transmission direction y. The SIT layer 922 can be, for example, the center line or conducting line of a stripline, microstrip, or coplanar waveguide, e.g., SIT layer 302, 404, 414, 602, and / or 702.

[0124] The geometry of the SIT layer 922 (e.g., shape(s), length(s) and / or width(s) of the stub 924 or portion(s) thereof) can be configured to set one or more filter parameters. For example, in some implementations, the stub 924 causes the SIT layer 922 to behave as a notch filter, and a geometry' of the stub 924 can be configured to set the center frequency and / or stop width of the notch filter. For example, the notch filter can have any of the frequency properties described for the notch filter of FIG. 9A. In some implementations, the geometry causes the SIT layer 922 to behave as a bandpass filter or a low-pass filter, e.g., using serially-connected stubs.

[0125] Other SIT layer geometries besides spurline and notch can instead or additionally be used to cause various filter behaviors, e.g., spiral-shaped, hairpinshaped, and / or another suitable shape to form a notch filter, a low-pass filter, a bandpass filter, a high-pass filter, and / or another filter type.

[0126] FIG. 10 illustrates an example of filters including SIT layers integrated into packaging 1000. The packaging 1000 includes a signal input 1002 and a signal output 1004, e.g., ports configured to receive respective coaxial cables. A signal (e.g., microwave signal) received at the signal input 1002 is provided to a first meandering SIT layer 1008a on a first substrate 1006a, e.g., in a microstrip configuration or a coplanar waveguide configuration (although meandering in this example, in other implementations the SIT layer can be non-meandering). For example, the first substrate 1006a can be a PCB wirebonded to the signal input 1002. Some or all tracesin / on the PCB can be SIT layers configured to behave as filters. Optional components of the packaging 1000 include a copper thermalization plate on the PCB and one or more shields to block RF, infrared, and / or magnetic interference. Components of the input signal having a frequency above twice a superconducting gap frequency of the first meandering SIT layer 1008 are attenuated. For example, a coaxial cable configured with a 50 output impedance can be connected to the signal input 1002, and signal components having a frequency above twice the superconducting gap frequency see a significantly higher input impedance presented by the SIT layer 1008a, e.g., between 500 Q and 50 kQ or between 5 k and 50 kQ, and are substantially or entirely reflected. Signal components having a frequency below twice the superconducting gap frequency see an approximately 50 Q input impedance and transmitted through the SIT layer 1008a with little or no attenuation.

[0127] The filtered signal is provided to a circuit device 1010, which can include (but is not limited to), for example, a quantum computing circuit including one or more qubits, one or more qubit readout resonators, and / or one or more qubit control lines. An output microwave signal can be provided out of the circuit device 1010 through a second meandering SIT layer 1008b on a second substrate 1006b, the second meandering SIT layer 1008b filtering the output micro wave signal as described throughout this disclosure. The filtered output signal is provided at the signal output 1004. e.g., to a coaxial cable.

[0128] FIGS. 1 1 A-l ID illustrate an example of a process for making a filter having an SIT layer in a microstrip configuration, e.g., the filter 300. Illustrated in FIGS. 11 A-l ID are cross-sections of a portion of the filter in which an SIT layer overlies a metal contact. For example, the illustrated cross-sections can correspond to the same view as FIG. 3B.

[0129] As shown in FIG. 11 A, a pattern of photoresist 1102 is provided on a substrate 1108 (e.g., the substrate 1108 having characteristics as described for substrate 308, such as a dielectric substrate / layer). The photoresist 1102 can be patterned using suitable photolithography processes. The photoresist 1102 defines a gap 1104 between portions of the photoresist spaced apart from one another in the lateral direction x.

[0130] As shown in FIG. 1 IB, a metal layer 1106 is formed on the photoresist 1102 and in the gap 1104. The metal layer 1106 can be formed using one or more suitable processes, e.g., physical vapor deposition, chemical vapor deposition, and / oratomic layer deposition. The metal layer 1106, as discussed with respect to FIGS. 3A- 3C. can include a non-superconductor metal and / or a superconductor metal.

[0131] As shown in FIG. 1 1C, an SIT layer 1110 is formed on the metal layer 1106. In some implementations, prior to forming the SIT layer 1110, an oxide removal process is performed to remove oxide from the surface of the metal layer 1106. For example, the metal layer 1106 can be an aluminum layer, and an oxide removal process such as a BCh plasma etch can be performed to remove aluminum oxide. In some implementations, oxide removal can be omitted, e.g., in implementations in which the metal layer 1106 is a noble metal such as gold. The SIT layer 1110 can be formed using one or more suitable processes, e g., physical vapor deposition, chemical vapor deposition, and / or atomic layer deposition.

[0132] As shown in FIG. 1 ID, a liftoff process is performed (e.g., using a solvent bath) to remove the photoresist 1102. In addition, a superconductor layer 1112 is formed on an opposing side of the substrate 1108 from the SIT layer 1110. In some implementations, the superconductor layer 1112 is formed prior to forming the SIT layer 1110. For example, the superconductor layer 1112 can be formed on an underlying first substrate (not shown), and the substrate 1108 can be a dielectric layer formed on the superconductor layer 1112. The resulting filter 1114 has a microstrip configuration as described for the filter 300, in which signals can be provided to / from the filtering SIT layer 11 10 through metal layers 1106.

[0133] Analogous processes to that of FIGS. 1 1 A-l ID (including, for example, photolithography, material deposit! on / growth, etching / liftoff, etc.) can be used to form filters having other configurations, e.g., stripline and coplanar waveguide.

[0134] FIG. 12 illustrates an example of a system 1200 including a filter 1208 having an adjustable cutoff frequency. The filter 1208 includes an SIT layer 1206 (e.g., having characteristics as described for SIT layers 106, 302, 404, 414, 602, 702, 902, 922, 1008a, and / or 1008b) and a source 1204 of an electric field, magnetic field, and / or current to be provided to the SIT layer 1206. For example, the source 1204 can include a current source to provide a bias current to the SIT layer 1206. such as the input bias tee 320; a voltage source such as voltage source 610, to apply an electric field to the SIT layer 1206; and / or a magnetic field source such as magnetic field source 502, to provide a magnetic field to the SIT layer 1206. For example, the source 1204 can include one or more conducting wires / traces through which a current can be provided to generate the magnetic field. As described above, the superconducting gapfrequency of the SIT layer 1206, and correspondingly the low-pass cutoff frequency of the filter 1208, varies with the electric field, magnetic field, and / or current applied to the SIT layer 1206.

[0135] A controller 1202 (which is shown as separate from the filter 1208 but which can equivalently be understood as wholly or partially included in the filter 1208) is configured to provide signal(s) to the source 1204 to set a target electric field, magnetic field, and / or current corresponding to a target superconducting gap frequency and target cutoff frequency. For example, the controller 1202 can provide one or more currents and / or voltages (e.g., DC currents and / or DC voltages) to drive the source 1204 to generate the electric field, magnetic field, and / or current. The controller 1202 can include circuitry such as a computing system, e.g., a microprocessor or field-programmable gate array. The controller 1202 can be a roomtemperature system, a cold system (e.g., co-located in a fridge with the filter 1208), or a combination of room-temperature and cold components.

[0136] For example, in some implementations, the controller 1202 is configured to perform the process 1300 shown in FIG. 13. The process 1300 includes obtaining a target cutoff frequency for a low-pass filter including an SIT layer (1302). The low- pass filter can be any of the SIT layer-based low-pass filters described herein, e.g., filters 300, 500, 600, 700, or 1208. Obtaining the target cutoff frequency can include, for example, receiving a user input of the target cutoff frequency, obtaining the target cutoff frequency as an output of an operation or from a computing device, and / or determining the target cutoff frequency automatically based on an operation (e.g., computation) being performed using signal(s) passed through the low-pass filter.

[0137] The process 1300 includes applying at least one of a magnetic field, an electric field, or a current to the SIT layer, to adjust the superconducting gap frequency of the SIT layer to cause the low-pass filter to have the target cutoff frequency (1304). For example, the process 1300 can include applying a bias current through the SIT layer as described in reference to FIG. 3A, applying a magnetic field to the SIT layer as described in reference to FIGS. 5A-5B, and / or applying an electric field to the SIT layer as described in reference to FIG. 6 (e.g., by applying a voltage), where the superconducting gap frequency of the SIT layer varies with a magnitude of the bias current, magnetic field, and / or electric field. For example, the superconducting gap frequency can be adjusted to be equal to half the target cutoff frequency.

[0138] In some implementations, the controller 1202 is configured to apply the magnetic field, electric field, and / or current based on a lookup table (e.g.. a lookup table stored on the controller 1202), the lookup table storing correspondences between target cutoff frequencies and corresponding signal(s) to be provided by the controller 1202 to the source 1204 to obtain the target cutoff frequencies. In some implementations, the controller 1202 is configured to execute one or more algorithms to determine, based on the target cutoff frequency, the signal(s) to be provided to the source 1204 to obtain the target cutoff frequency.

[0139] Referring again to FIG. 12, a source circuit 1212 provides one or more signals to the SIT layer 1206 as described in reference to FIG. 1. The signals are filtered based on the adjustable superconducting gap frequency of the SIT layer 1206, and filtered signals are provided to an output 1214. For example, the output 1214 can be, or can be coupled to, a quantum computing device.

[0140] The use of filters with adjustable cutoff frequencies can facilitate a wide range of useful system configurations and operations, e.g., by providing multiple SIT layers having different superconducting gap frequencies in various series and / or parallel combinations with one another. For example, as shown in FIG. 14, a system 1400 includes a controller 1402 and source circuit 1412 having characteristics as described for the controller 1202 and source circuit 1212. The controller 1402 is coupled to two electric field, magnetic field, and / or cunent sources 1404. 1408, each of which can have characteristics as described for the source 1204. The sources 1404, 1408 are respectively configured to generate electrical and / or magnetic fields, and / or currents, that adjust the superconducting gap frequencies of two corresponding SIT layers 1406, 1410. For example, SIT layer 1406 has a first cutoff frequency / 2A.1 (twice its superconducting gap frequency), and SIT layer 1410 has a second cutoff frequency / 2A.2. / 3 A.1 and / 3 , 2 are independently adjustable by the controller 1402 using the sources 1404, 1408. SIT layer 1406 shunts the source circuit 1412 to ground, and SIT layer 1410 is connected in series between the source circuit 1412 and an output port 1414. The source circuit 1412 provides signals (e.g.. quantum computing control, readout, and / or other signals) to the layers 1406, 1410.

[0141] The system 1400 can be configured as a band-pass filter by appropriate adjustment of / 3 ,I and / 2A,2. For example, the controller 1402 can set / 3A, 1 < / , 2, such that SIT layer 1406 forms a first low-pass filter with cutoff frequency / 3 A.1, and SIT layer 1410 forms a second low -pass filter with cutoff frequency / 3A, 2. In this case, theSIT layers 1406, 1410 function as an adjustable band-pass filter, because signals (from the source circuit 1412) with frequency less than / 2A,I are shunted to ground; signals with frequency greater than / 2A.2 see high resistance from both layers 1406, 1410; and signals with frequency / 2A.1 < are 2A,2 are provided through SIT layer 1410 to the output port 1414. It will be understood that, although FIG. 14 illustrates an adjustable band-pass filter system, in a corresponding non-adjustable band-pass filter system. / 2A.1 < A.2 and the controller 1402 and sources 1404, 1408 need not be included.

[0142] As another example, SIT layers with adjustable superconducting gap frequency can be controlled to controllably isolate devices from the devices’ environment and couple the devices to the devices’ environment. For example, as shown in FIGS. 15A-15B, a system 1500 includes a controller 1502, a source 1504, and an SIT layer 1506 having characteristics as described in reference to the corresponding elements of FIG. 12. The SIT layer 1506 is coupled between a quantum device 1510 and an environment 1512. The quantum device 1510 can include, for example, a qubit, a qubit readout resonator, a qubit control pad, etc. The environment 1512 can include one or more circuits, such as a source circuit for providing signals to the quantum device 1510 and / or a readout circuit for receiving signals from the quantum device 1510.

[0143] The controller 1502 can control the source 1504 to controllably couple / decouple the quantum device 1510 from the environment 1512, by adjusting the superconducting gap frequency of the SIT layer 1506 to permit more or less interaction between the quantum device 1510 and the environment 1512. In a nonlimiting example of a process shown in FIGS. 15A-15B, the controller 1502 first controls the source 1504 to provide a smaller magnitude of electric and / or magnetic fields and / or current (e.g., zero bias field / current) to the SIT layer 1506, which in some implementations can correspond to a higher superconducting gap frequency and, correspondingly, a higher cutoff frequency / 2A,I. The relatively high cutoff frequency _ 2A,i permits a wider range of signals to be provided between the quantum device 1510 and the environment 1512, to drive the quantum device 1510 and / or read out the quantum device 1510. For example, the quantum device 1510 can include a qubit, and / yi can be set to be greater than a qubit frequency of the qubit (e.g., 6 GHz), so that a driving signal can be provided from the environment 1512 to the quantum device 1510 to excite the qubit.

[0144] Subsequently, as shown in FIG. 15B, the controller 1502 can control the source 1504 to provide a larger magnitude of electric and / or magnetic fields and / or current to the SIT layer 1506, to cause the cutoff frequency of the SIT layer 50 be / A,2 < / 2 1. This adjustment cuts off at least some previously-permitted interactions between the quantum device 1510 and the environment 1512. Continuing with the prior example in which the quantum device 1510 includes a qubit, / / A, 2 can be set to be lower than the qubit frequency (e.g., 4 GHz < 6 GHz), isolating the qubit from the environment 1512 and permitting isolated time-evolution of the qubit’s state. The cutoff frequency can then be adjusted again (e.g., by lowering the magnitude of the electric and / or magnetic fields and / or current applied by the source 1504) to re-couple the qubit to the environment 1512. e.g., to permit readout of the time-evolved state of the qubit.

[0145] The filters described herein can advantageously be integrated into various contexts such as packaging, cabling, and on-chip. On-chip integration can offer advantages such as improved spatial utilization and more extensive filtering, e.g., because filtering can be performed in interconnects between components in / on a chip as opposed to, for example, being limited to an input to the chip. Some other filter designs, such as powder-based microw ave filters, may not be able to be integrated on- chip with other components such as integrated amplifiers, qubits, qubit readout resonators, qubit control pads, and / or digital logic elements.

[0146] Unless indicated otherwise, values provided herein (e.g., for superconducting critical temperature and superconducting gap frequency) refer to ambient-pressure values. In addition, unless indicated otherwise, values provided herein for superconducting critical temperature, superconducting gap frequency, and superconducting critical current are zero-temperature, zero-applied electric field, and zero-applied magnetic field values.

[0147] A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made. Elements of one or more implementations may be combined, deleted, modified, or supplemented to form further implementations. In yet another example, the logic flow s depicted in the figures do not require the particular order shown, or sequential order, to achieve desirable results. In addition, other steps may be provided, or steps may be eliminated, from the described flows, and other components may be added to, or removed from,the described systems. Accordingly, other implementations are within the scope of the following claims.

Claims

What is claimed is:

1. A microwave filter comprising: a superconductor-to-insulator transition (SIT) layer comprising a material exhibiting a superconductor-to-insulator transition associated with a superconducting gap frequency, wherein, for signals transmitting through the layer, the microwave filter is a low-pass filter in which twice the superconducting gap frequency is a cutoff frequency.

2. The micro wave filter of claim 1, wherein the SIT layer comprises a nitride alloy, niobium silicon, molybdenum germanium, molybdenum carbide, molybdenum rhenium, indium oxide, granular aluminum, or a cuprate superconductor.

3. The microwave filter of claim 2, wherein the SIT layer comprises Nb- Si i-v with x between 0. 15 and 0.25.

4. The microwave filter of any one of the preceding claims, wherein the SIT layer exhibits a sheet resistance between 100 and 2 k at a temperature less than 10 mK and for a frequency above twice the superconducting gap frequency.

5. The micro wave filter of any one of the preceding claims, wherein the SIT layer exhibits a resistance per millimeter of at least 660 Q / mm at a temperature less than 10 mK and for a frequency of 10 GHz.

6. The microwave filter of any one of the preceding claims, wherein twice the superconducting gap frequency of the layer is between 8 GHz and 50 GHz.

7. The microwave filter of any one of the preceding claims, wherein the microwave filter is a microstrip, a stnpline, or a coplanar waveguide.

8. The microwave filter of any one of the preceding claims, wherein the SIT layer is arranged in a shape such that the microwave filter behaves as a notch filterthat attenuates signal components having a frequency within a predefined frequency range.

9. The microwave filter of claim 8, wherein the shape comprises at least one of a spurline geometry or a stub geometry.

10. The microwave filter of claim 8 or claim 9, wherein the predefined frequency range overlaps a frequency range of 8 GHz to 10 GHz.

11. The microwave filter of any one of the preceding claims, wherein the microwave filter is a cable.

12. The microwave filter of any one of the preceding claims, comprising a dielectric layer in which the SIT layer is embedded.

13. The microwave filter of claim 12, comprising: a first superconductor layer on a first side of the dielectric layer, and a second superconductor layer on a second side of the dielectric layer, the second side opposite the first side.

14. The microwave filter of claim 12 or claim 13, wherein the dielectric layer comprises a polyimide.

15. The microwave filter of claim 14, comprising a voltage source coupled to the first superconductor layer, the voltage source configured to apply a voltage to the first superconductor layer to provide an electric field across the SIT layer between the first superconductor layer and the second superconductor layer.

16. The microwave filter of any one of the preceding claims, comprising: a dielectric layer; and a superconductor layer, wherein the SIT layer is on a first side of the dielectric layer, and wherein the superconductor layer is on a second side of the dielectric layer, the second side opposite the first side.

17. The microwave filter of any one of the preceding claims, comprising: a substrate on which the SIT layer is disposed; a first superconductor layer disposed on the substrate, the first superconductor layer extending adjacent to a first side of the SIT layer; and a second superconductor layer disposed on the substrate, the second superconductor layer extending adjacent to a second side of the SIT layer, the second side opposite the first side.

18. The microwave filter of claim 17, wherein the SIT layer and the first and second superconductor layers are disposed on a first surface of the substrate, and wherein the microwave filter comprises: a third superconductor layer disposed on a second surface of the substrate opposite the first surface.

19. The microwave filter of any one of the preceding claims, comprising: a magnetic field source arranged to apply a magnetic field to the SIT layer; and a controller coupled to the magnetic field source, the controller configured to provide signals to the magnetic field source to adjust a magnitude of the magnetic field.

20. The microwave filter of claim 19, wherein the magnetic field source comprises a trace arranged adjacent to the SIT layer, and wherein the controller is configured to adjust a current through the trace to adjust the magnitude of the magnetic field.

21. The microwave filter of any one of the preceding claims, comprising a controller configured to: apply a bias current through the SIT layer to adjust the superconducting gap frequency of the SIT layer to cause the microwave filter to have a target cutoff frequency.

22. The microwave filter of claim 21, comprising a bias tee through which the bias current is applied to the SIT layer as a direct-current (DC) current.

23. The microwave filter of any one of the preceding claims, comprising a controller configured to: apply at least one of a magnetic field, an electric field, or a current to the SIT layer, to adjust the superconducting gap frequency of the SIT layer to cause the microwave filter to have a target cutoff frequency.

24. The microwave filter of any one of the preceding claims, comprising a printed circuit board. wherein the SIT layer is a trace on the printed circuit board.

25. The microwave filter of any one of the preceding claims, comprising a nonsuperconductor metal layer stacked on the SIT layer.

26. The microwave filter of claim 25, wherein the SIT layer has a first footprint area that is orthogonal to a stack direction, and wherein the non-superconductor metal layer has a second footprint area that is orthogonal to the stack direction, wherein the first footprint area is different from the second footprint area.

27. The microwave filter of claim 26, wherein a portion of the second footprint area protrudes beyond the first footprint area.

28. The microwave filter of any one of the preceding claims, wherein the microwave filter is coupled to a quantum computing device, wherein the quantum computing device comprises a quantum processor, a qubit readout resonator, or a qubit.

29. The microwave filter of claim 28, wherein the microwave filter is configured to filter signal components having a frequency above twice the superconducting gap frequency from a signal that couples to the quantum computing device.

30. A method, comprising:providing a microwave signal into a circuit device; and filtering the microwave signal by transmitting the microwave signal through a layer of a first material, the first material exhibiting a superconductor-to-insulator transition associated with a superconducting gap frequency, wherein the filtering attenuates at least one signal component of the microwave signal, the at least one signal component having a frequency at least twice the superconducting gap frequency.

31. A method, comprising: obtaining a target cutoff frequency for a low-pass filter including a superconductor-to-insulator (SIT) layer exhibiting a superconductor-to-insulator transition associated with a superconducting gap frequency; and applying at least one of a magnetic field, an electric field, or a current to the SIT layer, to adjust the superconducting gap frequency of the SIT layer to cause the low-pass filter to have the target cutoff frequency.

32. The method of claim 31, wherein applying the at least one of the magnetic field, the electric field, or the current causes the superconducting gap frequency of the SIT layer to be half the target cutoff frequency.

33. The method of claim 31 or claim 32, wherein the SIT layer is coupled to a quantum device, and wherein the adjusted superconducting gap frequency of the SIT layer causes the quantum device to be isolated from an environment of the quantum device.

34. An apparatus comprising: a source circuit having a first impedance; and a superconductor-to-insulator transition (SIT) layer coupled to the source circuit, the SIT layer comprising a material exhibiting a superconductor-to-insulator transition associated with a superconducting gap frequency, the SIT layer having a second impedance different from the first impedance, wherein, based on an impedance mismatch between the first impedance and the second impedance, a signal component having a frequency above twice the superconducting gap frequency is reflected from the SIT layer to the source circuit.

35. The apparatus of claim 34, wherein the source circuit comprises a transmission line.

36. The apparatus of claim 34 or claim 35, wherein a ratio of the second impedance to the first impedance is at least 10 at 60 GHz.

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