FREQUENCY MULTIPLEXED RESONATOR INPUT AND/OR OUTPUT FOR A SUPERCONDUCTING DEVICE

Abstract

A superconducting input and/or output system employs at least one microwave superconducting resonator. The microwave superconducting resonator(s) may be communicatively coupled to a microwave transmission line. Each microwave superconducting resonator may include a first and a second DC SQUID, in series with one another and with an inductance (e.g., inductor), and a capacitance in parallel with the first and second DC SQUIDs and inductance. Respective inductive interfaces are operable to apply flux bias to control the DC SQUIDs. The second DC SQUID may be coupled to a Quantum Flux Parametron (QFP), for example as a final element in a shift register. A superconducting parallel plate capacitor structure and method of fabricating such are also taught.

Claims

1.-46. (canceled)

47. A method of fabricating a superconducting parallel plate capacitor, the method comprising: depositing a first superconductive layer, the first superconductive layer comprising a material that is superconductive in a range of critical temperatures; depositing a first dielectric layer to overlie at least part of the first superconductive layer; depositing a second superconductive layer to overlie at least part of the dielectric layer, the second superconductive layer comprising a material that is superconductive in the range of critical temperatures; removing a portion of the second superconductive layer to form at least one structure from the second superconductive layer and to expose at least part of the first dielectric layer; depositing a second dielectric layer to overlie at least part of the second superconductive layer and at least part of the first dielectric layer; planarizing the second dielectric layer; removing at least part of the second dielectric layer to form a first via exposing at least part of the second superconductive layer; removing at least part of the second dielectric layer and at least part of the first dielectric layer to form a second via exposing at least part of the first superconductive layer; depositing a first region of a third superconductive layer; and depositing a second region of the third superconductive layer, wherein the first region of the third superconductive layer is electrically isolated from the second region of the third superconductive layer, the first region of the third superconductive layer is superconductingly connected to at least part of the second superconductive layer by way of the first via, and the second region of the third superconductive layer is superconductingly connected to at least part of the first superconductive layer by way of the second via.

48. The method of claim 47 wherein the first dielectric layer comprises silicon nitride.

49. The method of claim 48 wherein the second dielectric layer comprises silicon dioxide.

50. The method of claim 47 wherein the second dielectric layer comprises silicon dioxide.

51. The method of claim 47 wherein the third superconductive layer comprises niobium.

52. The method of claim 47 wherein the thickness of the first and the second superconductive layers is in the range of about 100 nm to 400 nm, the thickness of the first dielectric layer is in the range of about 10 nm to 100 nm, and the thickness of the second dielectric layer is in the range of about 100 nm to 300 nm.

53. The method of claim 47 wherein the first and the second superconductive layers comprise niobium.

54. The method of claim 53 wherein the first dielectric layer comprises silicon nitride.

55. The method of claim 53 wherein the second dielectric layer comprises silicon dioxide.

56. The method of claim 53 wherein the third superconductive layer comprises niobium.

57. The method of claim 53 wherein the thickness of the first and the second superconductive layers is in the range of about 100 nm to 400 nm, the thickness of the first dielectric layer is in the range of about 10 nm to 100 nm, and the thickness of the second dielectric layer is in the range of about 100 nm to 300 nm.

58. A method for operating a superconducting input/output device in an input mode to transmit frequency-multiplexed data to a superconducting device, the data comprising a sequence of bits, and the superconducting device communicatively coupled to a superconducting resonator, the method comprising: initializing the superconducting device to a first state; applying a flux bias to the superconducting device via a first flux bias line to generate a preference for a second state; lowering a potential barrier in the superconducting device via a second flux bias line; determining whether a first bit in the sequence of bits is represented by a second state; upon determining the first bit is represented by the second state, sending a tone via a microwave transmission line to the superconducting resonator; and raising the potential barrier in the superconducting device via the second flux bias line.

59. The method of claim 58 wherein initializing the superconducting device includes initializing a Quantum Flux Parametron (QFP).

60. The method of claim 59 wherein initializing the QFP includes initializing a last stage of a shift register communicatively coupled to a Digital-to-Analog Converter (DAC).

61. A method for operating a superconducting input/output device in a readout mode, the method comprising: applying a first flux bias to a first DC superconducting quantum interference device (SQUID) to tune a resonant frequency of a superconducting resonator; and applying a second flux bias to a second DC superconducting quantum interference device (SQUID) to tune a sensitivity of the superconducting resonator.

62. The method of claim 61 further comprising: stimulating an interaction of the superconducting resonator with a Quantum Flux Parametron (QFP) at a nominal resonant frequency; and detecting a shifted resonant frequency of the superconducting resonator resulting from the interaction of the superconducting resonator with the QFP, wherein the shifted resonant frequency is indicative of a state of the QFP.

63. The method of claim 62 wherein applying the first flux bias to the first DC superconducting quantum interference device (SQUID) to tune the resonant frequency of the superconducting resonator, and applying the second flux bias to the second DC superconducting quantum interference device (SQUID) to tune the sensitivity of the superconducting resonator include causing the nominal resonant frequency of the superconducting resonator and the shifted resonant frequency of the superconducting resonator to lie within a first of a plurality of non-overlapping sub-bands, the first of the plurality of non-overlapping sub-bands allocated to the superconducting resonator.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0024] In the drawings, identical reference numbers identify similar elements or acts. The sizes and relative positions of elements in the drawings are not necessarily drawn to scale. For example, the shapes of various elements and angles are not necessarily drawn to scale, and some of these elements are arbitrarily enlarged and positioned to improve drawing legibility. Further, the particular shapes of the elements as drawn, are not necessarily intended to convey any information regarding the actual shape of the particular elements, and have been solely selected for ease of recognition in the drawings.

[0025] FIG. 1A is a schematic diagram illustrating an example embodiment of a superconducting circuit comprising a superconducting resonator able to tune a resonator frequency.

[0026] FIG. 1B is an example graph illustrating the use of SQUID flux bias to tune the resonator frequency.

[0027] FIG. 1C is a plot illustrating schematically part of a Frequency Multiplexed Resonator (FMR) spectrum.

[0028] FIG. 2A is a schematic diagram illustrating a first example embodiment of a superconducting circuit comprising a superconducting resonator with two SQUID loops, able to independently tune the resonator frequency and sensitivity.

[0029] FIG. 2B is a schematic diagram illustrating a second example embodiment of a superconducting circuit comprising a superconducting resonator with two SQUID loops, able to independently tune the resonator frequency and sensitivity.

[0030] FIG. 2C is a schematic diagram illustrating a third example embodiment of a superconducting circuit comprising a superconducting resonator with two SQUID loops, able to independently tune the resonator frequency and sensitivity.

[0031] FIG. 3 is a plot of the modulation curve for a superconducting circuit comprising a superconducting resonator with two SQUID loops such as the superconducting circuit of FIG. 2A.

[0032] FIG. 4 is a schematic diagram illustrating an example embodiment of a superconducting circuit comprising the superconducting resonator of FIG. 1A and able to independently tune the resonator frequency and sensitivity.

[0033] FIG. 5 is a schematic diagram illustrating an example embodiment of a readout system for a superconducting circuit.

[0034] FIG. 6 is a flow chart illustrating a method of operation of the readout system of FIG. 5.

[0035] FIG. 7 is a schematic diagram of an exemplary hybrid computing system, including a digital computer and a quantum computer, that may incorporate FMR technology as described herein.

[0036] FIG. 8 is a schematic diagram illustrating a first arrangement of superconducting resonators in an example embodiment of a superconducting quantum processor.

[0037] FIG. 9 is a schematic diagram illustrating a second arrangement of superconducting resonators in an example embodiment of a superconducting quantum processor.

[0038] FIGS. 10A to 10F are each respective cross-sectional views of a superconducting integrated circuit at sequential phases of a fabrication process, according to one illustrated embodiment.

[0039] FIG. 11A is a flow chart illustrating a method for using frequency multiplexed resonator technology to transmit data to a superconducting device according to at least one implementation.

[0040] FIG. 11B is a flow chart illustrating a method for using frequency multiplexed resonator technology to transmit data to a superconducting device according to at least another implementation.

[0041] FIG. 12 is a schematic diagram illustrating a frequency multiplexed resonator transceiver according to at least one exemplary implementation.

[0042] FIG. 13A is a schematic diagram illustrating a frequency multiplexed resonator transceiver comprising a superconducting resonator with two SQUID loops according to at least one exemplary implementation.

[0043] FIG. 13B is a schematic diagram illustrating a frequency multiplexed resonator transceiver comprising a superconducting resonator with two SQUID loops according to at least another exemplary implementation.

[0044] FIG. 13C is a schematic diagram illustrating a frequency multiplexed resonator transceiver comprising a superconducting resonator with two SQUID loops according to at least another exemplary implementation.

[0045] FIG. 14 is a schematic diagram illustrating a frequency multiplexed resonator transceiver comprising the superconducting resonator of FIG. 12.

DETAILED DESCRIPTION

Preamble

[0046] In the following description, some specific details are included to provide a thorough understanding of various disclosed embodiments. One skilled in the relevant art, however, will recognize that embodiments may be practiced without one or more of these specific details, or with other methods, components, materials, etc. In other instances, well-known structures associated with superconductive circuits or resonators have not been shown or described in detail to avoid unnecessarily obscuring descriptions of the embodiments of the present methods. Throughout this specification and the appended claims, the words “element” and “elements” are used to encompass, but are not limited to, all such structures, systems, and devices associated with superconductive circuits and resonators.

[0047] Unless the context requires otherwise, throughout the specification and claims which follow, the word “comprise” is synonymous with “including,” and is inclusive or open-ended (i.e., does not exclude additional, unrecited elements or acts).

[0048] Reference throughout this specification to “one embodiment” “an embodiment”, “another embodiment”, “one example”, “an example”, “another example”, “one implementation”, “another implementation”, or the like means that a particular referent feature, structure, or characteristic described in connection with the embodiment, example, or implementation is included in at least one embodiment, example, or implementation. Thus, the appearances of the phrases “in one embodiment”, “in an embodiment”, “another embodiment” or the like in various places throughout this specification are not necessarily all referring to the same embodiment, example, or implementation. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments, examples, or implementations.

[0049] It should be noted that, as used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the content clearly dictates otherwise. Thus, for example, reference to a readout system including “a superconducting resonator” includes a single superconducting resonator, or two or more superconducting resonators. It should also be noted that the term “or” is generally employed in its sense including “and/or” unless the content clearly dictates otherwise.

[0050] The headings provided herein are for convenience only and do not interpret the scope or meaning of the embodiments.

Single SQUID Superconducting Resonator

[0051] FIG. 1A shows a superconducting circuit 100 comprising a superconducting resonator 110 according to at least a first exemplary implementation. Superconducting resonator 110 comprises a capacitance 112, and an inductance 114, which may or may not take the form of discrete capacitors and inductors, respectively.

[0052] Superconducting resonator 110 further comprises a single SQUID loop 116. SQUID loop 116 is a DC SQUID and comprises a pair of Josephson junctions in parallel with one another in a superconducting loop. SQUID loop 116 enables tuning of the resonance frequency of superconducting resonator 110 by adjusting the SQUID flux bias as explained below.

[0053] The resonance frequency ω of superconducting resonator 110 can be determined by the following formula for an LC circuit:

[00001]$\omega =\frac{1}{\surd \left(\mathrm{LC}\right)}$

where C is the value of capacitance 112 and L is the sum of the geometric inductance 114 and the parallel sum of the Josephson inductances from the two Josephson junctions in SQUID loop 116.

[0054] Small fluctuations in capacitance C and/or inductance L result in a fractional frequency perturbation of the resonance frequency as follows:

[00002]$\frac{\mathrm{\delta \omega }}{\omega }=\frac{-\delta C}{2C}+\frac{-\delta L}{2L}$

[0055] In one implementation, superconducting resonator 110 is a distributed resonator. A distributed resonator has capacitance and inductance that cannot be isolated into separate lumped element capacitors and inductors. An advantage of a distributed resonator is that it can be designed to be insensitive to layer thickness. A distributed resonator can also be more tolerant to variations in fabrication. A distributed resonator can exhibit harmonics at every octave which can be a disadvantage in an implementation using more than one octave of bandwidth.

[0056] In other implementations, superconducting resonator 110 is a lumped element design. A lumped element design can advantageously provide a bandwidth greater than one octave, and can reduce or minimize the extent of the resonator's electric field. Since the loss tangent of superconducting resonator 110 can depend on the volume of lossy dielectric exposed to the resonator's electric field, it can be beneficial to use a lumped element design.

[0057] In a lumped element design, capacitance 112 can be implemented using one or more capacitors. The capacitors can be interdigitated capacitors and/or parallel plate capacitors. In one implementation, capacitance 112 is implemented using a parallel plate capacitor. In one example, the capacitance of the parallel plate capacitor is approximately 2 pF.

[0058] The capacitance C of a parallel plate capacitor is given by:

[00003]$C=\frac{ϵA}{d}$

where ∈ is the permittivity of the dielectric separating the plates, A is the area of one of the plates and d is the thickness of the dielectric.

[0059] In practice, area A may be defined by lithography, and fractional errors in area A are expected to be small relative to other errors. The thickness of the dielectric can vary and can contribute significantly to variations in capacitance C and in the resonance frequency ω of a resonator comprising capacitance C. The dependence on variations in dielectric thickness is as follows:

[00004]$\frac{\delta \omega }{\omega }=\frac{\delta d}{2d}$

[0060] In a lumped element design, inductance 114 can be implemented using one or more inductors. In one implementation, inductance 114 is implemented using a niobium spiral inductor. In one example, the geometric inductance of the spiral inductor is approximately 1 nH. In another implementation, inductance 114 is implemented using a spiral inductor comprising a high kinetic inductance material such as TiN or WSi.

[0061] Energy stored in the inertia of the superconducting pairs can contribute a kinetic inductance. The total inductance in superconducting resonator 110 is a sum of the geometric inductance, the kinetic inductance, and the inductance of SQUID loop 116.

[0062] Circuit 100 further comprises a transmission line 120, a coupling capacitance 122, and a last or final shift register stage 140. Last shift register stage 140 comprises inductances 142 and 144, SQUID loop 146 and interface 150. Last or final shift register stage 140 may, for example, take the form of a Quantum Flux Parametron (QFP). Last or final shift register stage 140 is the endpoint of a shift register comprising one or more stages. Last or final shift register stage 140 is a stage that can be communicatively coupled to superconducting resonator 110 for the purposes of reading out the state of a superconducting device. In one implementation, superconducting resonator 110 is fed by a flux shift register which, in turn, is fed by a flux qubit.

[0063] The quantum flux parametron (QFP) is a superconducting Josephson junction device similar in structure to a compound rf-SQUID. The name “quantum flux parametron”, however, encompasses both the operation and the structure of the Josephson junction device, not simply structure alone.

[0064] Interface 130 can provide a flux bias to SQUID loop 116 and can be controlled by a flux DAC (not shown in FIG. 1A) or by an analog line. Using a flux DAC reduces the number of low-frequency analog control lines to the superconducting circuit.

[0065] A flux DAC is an example of an on-chip control circuitry. Further examples can be found in U.S. Pat. Nos. 7,876,248; 7,843,209; 8,018,244; 8,098,179; 8,169,231; and 8,786,476.

[0066] Superconducting resonator 110 can be coupled to transmission line 120 via coupling capacitance 122 (e.g., a discrete capacitor). Transmission line 120 can optionally be coupled to one or more other superconducting resonators (not shown in FIG. 1A).

[0067] Superconducting resonator 110 is connected at node 115 to ground.

[0068] Superconducting resonator 110 comprising single SQUID loop 116 does not enable independent tuning of the resonance frequency and the sensitivity of superconducting resonator 110.

[0069] FIG. 1B is an example graph illustrating the variation of resonator frequency with SQUID flux bias. The SQUID flux bias can be used to tune the resonator frequency. In the example shown in FIG. 1B, the resonator frequency is 5 GHz at zero flux bias, corresponding to point 160 on the graph. Increasing the flux bias tunes the resonator down in frequency. In the example shown in FIG. 1B, the resonator can be tuned down by 50 MHz to a frequency of 4.95 GHz by increasing the flux from zero to Φ.sub.1, the result indicated by point 162 on the graph.

[0070] The sensitivity is proportional to the slope of the graph shown in FIG. 1B. Hence, a smaller increase in flux bias will cause the same frequency shift at lower frequencies. This is illustrated by points 164 and 166 on the graph shown in FIG. 1B. An increase in flux bias from Φ.sub.2 to Φ.sub.3 causes the resonator frequency to shift 50 MHz from 4.7 GHz to 4.65 GHz. The difference between Φ.sub.3 and Φ.sub.2 is less than between Φ.sub.1 and Φ=0.

[0071] As mentioned previously, the sensitivity is not independently tunable and can vary significantly with flux bias. This can result in an undesirable tuning-dependent frequency shift for the same flux modulation from the last or final shift register stage coupled to the resonator. It is desirable to have a superconducting resonator in which resonator frequency and sensitivity can be independently adjusted to provide a suitable operating point. For example, independent adjustment of resonant frequency and sensitivity can be used to compensate for frequency shifts arising from variations occurring during fabrication of superconducting circuits such as circuit 100 of FIG. 1A. FIG. 10 is a plot illustrating schematically part of an FMR spectrum. The FMR spectrum is a plot of resonant amplitude versus frequency. The FMR spectrum comprises spectrum from three resonators shown in their various states. Frequency f.sub.nom is the resonator frequency when no flux bias is applied to SQUID loop 116 of FIG. 1A. Frequency f.sub.1 is the resonator frequency when attached QFP 140 is in a positive latched state. Frequency f.sub.2 is the resonator frequency when attached QFP 140 is in a negative latched state. The change in frequency for a given resonance between when attached QFP 140 is in a positive state and a negative state is Δf.sup.QFP. Adjacent resonators are separated by frequency difference B.sub.bin.

[0072] To guard against variations in the performance of the resonators (for example, caused by variations in fabrication), f.sub.nom.sup.(i) can be selected to lie approximately at the center between f.sub.−1.sup.(i) and f.sub.1.sup.(i+1). Adjacent resonances can be separated by a guard band. In one implementation, adjacent resonators are separated by three times the linewidth of an individual resonance, and B.sub.bin is four times Δf.sup.QFP. As explained below, the flux DACs for superconducting circuit 100 (not shown in FIG. 1A) can be used to position the resonances within the bandwidth to sufficient precision.

[0073] It may be desirable to achieve a dense packing of the resonances within the bandwidth. This can be achieved by positioning the resonances at regularly spaced frequencies with a determined frequency shift (i.e. sensitivity). Guard bands between resonances can be used to reduce electronic cross-talk between neighboring resonators.

Superconducting resonator with Two SQUID Loops

[0074] FIG. 2A shows a superconducting circuit 200a according to at least one implementation, comprising a superconducting resonator 210a with two SQUID loops, able to independently tune the resonator frequency and sensitivity. Superconducting resonator 210a comprises two SQUID loops 216a and 216b. Each of SQUID loops 216a and 216b is a DC SQUID and comprises a pair of Josephson junctions in parallel with one another in a superconducting loop. SQUID loops 216a and 216b advantageously enable independent tuning of the resonance frequency and the sensitivity of superconducting resonator 210a by adjusting the flux bias in SQUID loops 216a and 216b as explained below.

[0075] Components of superconducting circuit 200a labeled with the same numbers as in superconducting circuit 100 of FIG. 1A are similar or even identical to those described in reference to FIG. 1A. For example, capacitance 112 of superconducting circuit 200a can be a parallel plate capacitor, and inductance 114 of superconducting circuit 200a can be a niobium spiral inductor. Superconducting resonator 210a is connected at node 215a to ground, for example to the ground 121 of transmission line 120.

[0076] Interfaces 230a and 230b can provide flux bias to SQUID loops 216a and 216b respectively. Once a suitable operating point has been found (see below), the flux biases provided by interfaces 230a and 230b can be static. This advantageously allows the circuit to use an array of flux DACs requiring only a few wires to program. The two tunable SQUID loops 216a and 216b do not need an independent analog control line for each superconducting resonator 210a.

[0077] FIG. 2B shows a superconducting circuit 200b according to at least another implementation, comprising a superconducting resonator 210b with two SQUID loops, advantageously operable to independently tune the resonator frequency and sensitivity. Superconducting resonator 210b comprises two SQUID loops 216a and 216b. Each of SQUID loops 216a and 216b is a DC SQUID and comprises a pair of Josephson junctions in parallel in a superconducting loop. SQUID loop 216b further comprises inductances 218a through 218d. SQUID loops 216a and 216b enable independent tuning of the resonance frequency and the sensitivity of superconducting resonator 210a by adjusting the flux bias in SQUID loops 216a and 216b as explained below.

[0078] SQUID loop 218b is galvanically coupled to a last or final shift register stage comprising DC SQUID 146 and inductance 144. Interfaces 150 and 152 can provide flux bias to DC SQUIDs 146 and 148 respectively. Superconducting resonator 210b is connected at node 215b to ground, for example to the ground 121 of transmission line 120.

[0079] Components of superconducting circuit 200b labeled with the same numbers as in superconducting circuit 100 of FIG. 1A are similar or even identical to those described in reference to FIG. 1A. For example, capacitance 112 of superconducting circuit 200b can be a parallel plate capacitor, and inductance 114 of superconducting circuit 200b can be a niobium spiral inductor.

[0080] Interfaces 230a and 230b can provide flux bias to SQUID loops 216a and 216b respectively.

[0081] FIG. 2C shows a superconducting circuit 200c according to at least another implementation, comprising a superconducting resonator 210c with two SQUID loops, advantageously operable to independently tune the resonator frequency and sensitivity. Superconducting circuit 200c is connected at node 215c to the ground 121 of transmission line 120 via a coupling capacitor 124. In other respects, superconducting circuit 200c is the same as or similar to superconducting circuit 200b.

[0082] Components of superconducting circuit 200c labeled with the same numbers as in superconducting circuit 100 of FIG. 1A can be as described in reference to FIG. 1A. For example, capacitance 112 of superconducting circuit 200a can be a parallel plate capacitor, and inductance 114 of superconducting circuit 200c can be a niobium spiral inductor.

Independent Tuning of Frequency and Sensitivity Using Two SQUID Loops

[0083] As previously discussed, a superconducting resonator comprising a fixed geometric inductance, a capacitance and a single SQUID loop (such as superconducting resonator 110 of FIG. 1A) does not enable independent tuning of resonance frequency and sensitivity. As described above with reference to FIGS. 2A, 2B and 2C, adding a second SQUID loop to the superconducting resonator provides an additional degree of freedom, and enables independent tuning of resonance frequency and sensitivity.

[0084] FIG. 3 is a plot of the modulation curve for a superconducting circuit comprising a superconducting resonator with two SQUID loops such as the superconducting circuit of FIG. 2A. Plot 300 shows contours of constant frequency including example contours 310 and 315. Plot 300 includes a first axis denoting the flux bias in a first SQUID loop, and a second axis denoting the flux bias in a second SQUID loop.

[0085] In FIG. 3, the frequency at the origin of the plot is 4.932 GHz. Contours 310 and 315 are at 4.926 GHz and 4.922 GHz respectively, separated by 4 MHz. Flux sensitivity can be adjusted by changing location of an operating point of superconducting circuit 200a along a given contour of constant frequency. Since only one of the two SQUID loops 216a and 216b of FIG. 2A is coupled to last or final shift register stage 140, a change in the shift register state results in either a vertical shift or a horizontal shift in plot 300 of FIG. 3. The direction of the shift depends on which SQUID loop (216a or 216b) is coupled to last or final shift register stage 140. In FIG. 2A, SQUID loop 216b is coupled to last or final shift register 140, and the shift will be in the horizontal direction i.e. parallel to the x-axis of plot 300 of FIG. 3.

[0086] The change in flux bias required to cause a given frequency shift will depend on the location of the operating point on the contour. For example, a horizontal shift from location A on contour 310 to location B on contour 315 requires a smaller change in flux bias than a shift from location C on contour 310 to location D on contour 315. The frequency shift is the same in both cases. The frequency shift per unit flux bias is known as the sensitivity. The sensitivity is greater when the operating point is at location A on contour 310 than at location Con location 310.

[0087] A suitable operating point can be established by the method described in the following paragraphs. The SQUID bias for loop 216a is denoted by Φ.sub.a and the SQUID bias for loop 216b is denoted by Φ.sub.b.

[0088] Firstly, Φ.sub.a is kept at zero while Φ.sub.b is increased from zero until a desired operating frequency is found. The shift register is then operated and the frequency shift between the two possible states (i.e., the flux sensitivity) is measured. The process is then repeated while Φ.sub.b is kept at zero and Φ.sub.a is increased from zero until the desired operating frequency is achieved. The flux sensitivity is again measured. If a desired flux sensitivity lies between the bounds set by the first two measurements described above, then an iterative approach can be used to find the preferred operating point.

[0089] The calibration process to determine the preferred operating point steps through possible values of Φ.sub.b, adjusting Φ.sub.a to achieve the desired frequency and then measuring sensitivity. In one implementation, a binomial search can be used to determine the preferred values of Φ.sub.a and Φ.sub.b. In other implementations, other suitable search methods can be used.

Single SQUID Loop with Tunable Coupler

[0090] FIG. 4 shows a superconducting circuit 400 according to at least one implementation, comprising superconducting resonator 110 of FIG. 1A and advantageously operable to independently tune the resonator frequency and sensitivity. Superconducting circuit further comprises interface 130 and last or final shift register stage 140, both as described with reference to FIG. 1A.

[0091] Superconducting circuit 400 further comprises a tunable coupler 440 in between superconducting resonator 110 and last or final shift register stage (or QFP) 140. Superconducting circuit 400 enables independent tuning of the resonance frequency and the sensitivity to QFP flux, provided the variable loading of superconducting resonator 110 by tunable coupler 440 is taken into account.

[0092] Tunable coupler 440 comprises inductances 442 and 444, and DC SQUID 446. Superconducting circuit 400 further comprises interface 450.

Readout System

[0093] FIG. 5 shows a readout system 500 for a superconducting circuit 510 according to at least one exemplary implementation. In the illustrated implementation, superconducting circuit 510 comprises one or more superconducting resonators (not shown in FIG. 5) such as superconducting resonator 210a of FIG. 2A. In the illustrated implementation, superconducting circuit 510 comprises a superconducting quantum processor. In other implementations, superconducting circuit 510 comprises a superconducting classical processor.

[0094] Readout system 500 comprises a digital board 520 and a microwave board 530. Digital board 520 comprises a Field Programmable Gate Array (FPGA) 522 (such as a Xilinx Kintex-7 FPGA from Xilinx, Inc. of San Jose, Calif., US), two Digital-to-Analog Converters (DACs) 524a and 524b, and two Analog-to-Digital Converters (ADCs) 526a and 526b. In other embodiments, digital board 520 comprises two FPGAs, one providing output to DACs 524a and 524b, and the other providing output to ADCs 526a and 526b. In one implementation, each of DACs 524a and 524b can be implemented using an Analog Devices 9129 DAC which is a dual-channel 14-bit DAC operating at up to about 5.6 Gsps (Giga samples per second). ADCs 526a and 526b can be implemented using a multi-channel device such as an E2V EV10AQ190 which is a quad-channel 10-bit ADC capable of operating in dual-channel mode at up to about 2.5 Gsps.

[0095] Readout system 500 advantageously enables independent addressing of the two side-bands of the FMR spectrum. The complex received signal is given by:

x(n)=I(n)+jQ(n)

where I(n) is the output of ADC 526a and Q(n) is the output of ADC 526b.

[0096] The FMR spectrum is computed as follows:

[00005]$X_k=\frac{1}{N}\underset{n=0}{\overset{N-1}{.Math.}}x\left(n\right)\left[\cos \left(\frac{2\pi \mathrm{kn}}{N}\right)-j\sin \left(\frac{2\pi \mathrm{kn}+2\pi k\tau }{N}\right)\right]$

for k∈0,1,2,3 . . . N−1. The second term in the argument of the sine function depends on r and can be used to compensate for the phase imbalance between the two mixer channels that results from the analog nature of the mixer.

[0097] Digital board 520 further comprises two loopback lines 529a and 529b, and a sync/clock connection 528. Loopback line 529a connects the output of DAC 524a to the input of ADC 526a. Loopback line 529b connects the output of DAC 524b to the input of ADC 526b.

[0098] Microwave subsystem or microwave board 530 further comprises a loopback line 572. Loopback line 572 connects the input and output to cryogenic subsystem (not shown in FIG. 5) used to cool superconducting device 510 to temperatures as low as a few mK.

[0099] Loopback lines 529a and 529b on digital board 520, and loopback line 572 on microwave board 530 are optional, and used when required to bypass other elements of readout system 500.

[0100] Readout system 500 further comprises two reconstruction filters 525a and 525b, and two anti-aliasing filters 527a and 527b. Reconstruction filters 525a and 525b are low-pass analog filters that can be used to produce a band-limited analog signal from a digital input. Anti-aliasing filters 527a and 527b are low-pass analog filters that can be used to band-limit a received signal in order to satisfy or approximately satisfy the sampling theorem over a band of interest.

[0101] Microwave board 530 comprises a Voltage-Controlled Oscillator (VCO)/Phase Locked Loop (PLL) 540 which provides a reference microwave signal, mixers 550 and 560, and programmable attenuators 570. Microwave board 530 further comprises amplifiers 562, 564, 566 and 575. Amplifiers 562, 564, 566 and 575 can be used to provide level control on the signal received from superconducting circuit 510. In one implementation, amplifier 566 can be a Miteq AFS4-02000800-30-22P-4, and amplifier 575 can be a Miteq AFD3-040080-28-LN low-noise amplifier. These exemplary amplifiers are available from Miteq Inc., of Hauppauge, N.Y., US. Microwave board 530 further comprises a microwave switch 555 controlled by a signal from FPGA 522 on digital board 520.

[0102] In one implementation, mixers 550 and 560 are complex mixers.

[0103] The illustrated readout system 500 further comprises amplifier 580, attenuators 581 and 582, circulators 583 and 584, and DC blocks 585 and 586. DC blocks 585 and 586 are used as a thermal break on each of the input and output lines to superconducting circuit 510.

[0104] In one implementation, amplifier 580 can be a LNF-3611-28-04000800 low-noise cryogenic amplifier. Amplifier 580 and attenuator 581 can operate at 4 K. Attenuator 582 can operate at 0.6 K. Circulators 583 and 584, and DC blocks 585 and 586, can operate at 8 mK. In one implementation, cryogenic circulators 583 and 584 can each be implemented using a Quinstar CTH0408KC, and DC blocks 585 and 586 can each be implemented using an Aeroflex/Inmet 8039.

[0105] Using 60 resonators and a bandwidth of 2.5 GHz, a data rate of approximately 600 Mbps can be achieved for a shift register stage (SRS) operation time of 25 ns.

Method of Operation of Readout System

[0106] FIG. 6 shows a method 600 of operation of readout system 500 of FIG. 5, according to at least one implementation. Method 600 starts at 605, for example in response to a powering up of readout system 500 or invocation of a routine. At 610, readout system 500 provides a flux signal for readout. In one implementation, readout system 500 increments the shift register (not shown in FIG. 5) at 610. At 620, readout system 500 outputs a frequency comb of DACs 524a and 524b. At 630, readout system 500 opens microwave switch 555. At 640, readout system 500 collects data via ADCs 526a and 526b. At 650, readout system 500 closes microwave switch 555. At 660, FPGA 522 performs a DFT on the data output by ADCs 526a and 526b, and returns the values of the FMR spectrum. Method 600 loops through 610 to 660 until the readout is complete, and then ends at 665 until invoked again.

FMR Technology for Superconducting Qubits

[0107] FIG. 7 shows a hybrid computing system 700 according to at least one exemplary implementation, including a digital computer 705 and a quantum computer 750, that may incorporate FMR technology as described above.

[0108] Digital computer 705 comprises CPU 710, user interface elements 711, 712, 713 and 714, disk 715, controller 716, bus 717 and memory 720. Memory 720 comprises modules 721, 723, 727, 731, 737 and 735.

[0109] Quantum computer 750 comprises quantum processor 740, readout control system 760, qubit control system 765 and coupler control system 770. Quantum computer 750 can incorporate FMR technology comprising superconducting resonators (such as superconducting resonator 210a of FIG. 2A). Computing system 700 can comprise a readout system such as readout system 500 of FIG. 5.

[0110] FIG. 8 shows a first arrangement of superconducting resonators in an example implementation of a superconducting quantum processor 800. Processor 800 comprises 64 unit cells (not shown in FIG. 8) with four sets of superconducting resonators 810a through 810d, 820a through 820d, 830a through 830d, and 840a through 840d, coupled to outer shift registers 850a through 850d respectively. Each unit cell comprises N qubits. In one embodiment, N=8. Processor 800 comprises eight vertically oriented inner shift registers 860 and eight horizontally oriented inner shift registers 870.

[0111] All four set of superconducting resonators 810a through 810d, 820a through 820d, 830a through 830d, and 840a through 840d are coupled to a single common transmission line such as line 120 of FIG. 2A (not shown in FIG. 8).

[0112] FIG. 9 shows a second arrangement of superconducting resonators in an example implementation of a superconducting quantum processor 900. Processor 900 comprises 64 qubits (not shown in FIG. 9) with four sets of superconducting resonators 910a through 910h, 920a through 920h, 930a through 930h and 940a through 940h. Processor 900 comprises eight vertically oriented inner shift registers 960 and eight horizontally oriented inner shift registers 970.

[0113] Two sets of superconducting resonators 910a through 910h and 940a through 940h are coupled to a first transmission line such as line 120 of FIG. 2A (not shown in FIG. 9). The other two sets of superconducting resonators 920a through 920h and 930a through 930h (shown shaded in FIG. 9) are coupled to a second transmission line (also not shown in FIG. 9).

[0114] In the arrangement illustrated in FIG. 9, outer shift registers (such as outer shift registers 850a through 850d of FIG. 8) are not needed. With eight resonators on a side, one for each of the inner shift registers (horizontal or vertical), there is sufficient fault tolerance provided by the cross-over stages of the horizontally and vertically oriented inner shift registers.

High Q Superconducting Capacitor

[0115] It can be important for the performance of FMR systems and methods described above for the capacitance in the superconducting resonator (for example, capacitance 112 in resonator 210a of FIG. 2A) to have a high quality factor (Q).

[0116] A lumped element resonator can be implemented using an interdigitated capacitor or a transmission line resonator, fabricated directly on a crystalline dielectric. The resonator can be designed to reduce capacitor dielectric loss, for example by spreading the fingers of the interdigitated capacitor widely, and by causing the electric field to propagate through the crystalline dielectric rather than be exposed to surface oxides that can dominate the loss.

[0117] A disadvantage of existing techniques to fabricate high Q superconducting capacitors is that those techniques cannot readily be integrated in a heterogeneous, multi-layer fabrication stack while maintaining low loss.

[0118] One approach is to use a distributed microstrip resonator fabricated with amorphous silicon as a deposited dielectric. A disadvantage of this approach is that the capacitance is spread out along the length of the resonator and incorporates a larger volume of dielectric than an equivalent parallel plate capacitor, resulting in higher losses than for a lumped element parallel plate capacitor. Another disadvantage is that the microstrip resonator has a large distributed inductance that needs to be accounted for during design.

[0119] The technology described in this disclosure comprises a superconducting parallel plate capacitor with a thin, high-permittivity dielectric. A parallel-plate design with a thin dielectric can reduce the volume of dielectric for a given capacitance value. It can also provide a reduced capacitor footprint which is an advantage because chip space is at a premium.

[0120] A benefit of a parallel-plate capacitor with a thin dielectric layer is that it can decrease the microwave power required to saturate the loss centers in the dielectric, and consequently can allow high resonator quality factors to be achieved at the operating power typically used with FMR technology. The inventors have observed that decreasing the volume of lossy dielectric can lead to a decrease in the required power to saturate a superconducting resonator such as superconducting resonator 110 of FIG. 1A.

[0121] Reducing the thickness of the dielectric can be challenging. Furthermore, the capacitance can be sensitive to variations in the thickness of the dielectric. Variations in thickness can be introduced during fabrication, for example during planarization of the dielectric. A method for producing a superconducting parallel plate thin-layer capacitor that can be integrated in a heterogeneous multi-layer planarized fabrication stack with deposited dielectrics is described in the next section.

Thin-Layer Capacitor Integration Process

[0122] FIGS. 10A to 10F are each respective cross-sectional views of a superconducting integrated circuit 1000 at sequential phases of a fabrication process, according to one illustrated embodiment. The sequence of FIGS. 10A to 10F. defines a method for fabricating a thin-layer capacitor suitable for use in a superconducting resonator such as superconducting resonator 210a of FIG. 2A.

[0123] As illustrated in FIG. 10A, semiconductor fabrication equipment deposits a trilayer 1005. Trilayer 1005 comprises a first layer 1010 of a superconducting metal, a layer 1020 of a dielectric and a second layer 1030 of a superconducting metal. In one implementation, the first and second layers 1010 and 1030, respectively, of superconducting metal comprise niobium. In other implementations, the first and second layers 1010 and 1030, respectively, comprise Al, TiN, or WSi. Layer 1020 can comprise Si, SiN, amorphous SiH or other suitable inter-layer low-loss dielectric.

[0124] As illustrated in FIG. 10B, semiconductor fabrication equipment patterns trilayer 1005 using an etch process. Layer 1030 of superconducting metal can be removed during patterning except where the upper plate of the thin-layer capacitor is needed.

[0125] As illustrated in FIG. 100, semiconductor fabrication equipment deposits a relatively thick layer 1040 of dielectric. In one embodiment, layer 1040 comprises SiO2.

[0126] As illustrated in FIG. 10D, semiconductor fabrication equipment planarizes layer 1040 (e.g., CMP).

[0127] As illustrated in FIG. 10E, semiconductor fabrication equipment is used to etch vias 1015 and 1035. Via 1015 is a via to the first layer 1010 of superconducting metal, and is a via to the lower plate of the thin-layer capacitor. Via 1035 is a via to the second layer 1030 of superconducting metal, and is a via to the upper plate of the thin-layer capacitor.

[0128] As illustrated in FIG. 10F, semiconductor fabrication equipment deposits a third layer 1050 of superconducting metal. The third layer 1050 of superconducting metal may, for example, comprise niobium. Semiconductor fabrication equipment patterns third layer 1050 to form a first region 1050a and a second region 1050b. First region 1050a can be a contact to the upper plate of the thin-layer capacitor, and second region 1050b can be a contact to the lower plate of the thin-layer capacitor. First region 1050a and second region 1050b can be electrically isolated from each other. First region 1050a and second region 1050b are a first portion of third layer 1050 and a second portion of third layer 1050, respectively.

[0129] In one implementation, the thickness of each of the first and second layers of superconducting metal 1010 and 1030, respectively, is about 300 nm, and the thickness of dielectric layer 1020 is about 50 nm.

[0130] An advantage of the method described above is that dielectric layer 1020 can be sufficiently thin that parasitic capacitance in regions of the circuit other than at the capacitors is relatively small.

Frequency Multiplexed Resonator Transceiver

[0131] FIG. 11A is a flow chart illustrating a method 1100a for using frequency multiplexed resonator technology to transmit data to a superconducting device, according to at least one exemplary implementation. The superconducting device can, for example, be an element of a superconducting classical processor. Alternatively, the superconducting device can, for example, be an element of a superconducting quantum processor.

[0132] In one implementation, method 1100 is executed by a computing system, such as a hybrid computing system comprising a digital computer and an analog computer. Method 1100 includes acts 1105-1165, though those skilled in the art will appreciate that in alternative implementations certain acts may be omitted and/or additional acts may be added. Those skilled in the art will appreciate that the order of the acts is shown for exemplary purposes only and may change in alternative implementations.

[0133] At 1110, the computing system initializes the QFP devices to a “0” state. At 1120, the computing system applies a flux bias using a flux bias line such as flux bias line 155 of FIGS. 12 through 14 to create a preference for a “1” state. At 1130, the computing system reduces the barrier of the QFP devices. At 1140, the computing system decides whether to send a tone to a frequency multiplexed resonator, and, if so, sends the tone to the resonator. The presence of a tone allows the QFP to relax into the “1” state. The absence of a tone causes the QFP to stay in the “0” state.

[0134] At 1145, the computing system determines if there is another resonator. If the computing system determines there is another resonator at 1145, then method 1100 returns to 1140. Method 1100 successively loops around 1140 and 1145 until there are no more resonators to consider, and method 1100 proceeds to 1150.

[0135] At 1150, the computing system fully raises the barrier of each of the QFP devices. At 1160, the quantum processor uses the data, for example through classical QFP logic. Using the data can include transferring the data to a superconducting processor via a shift register, for example. Method 1100 ends at 1165, for example until called or invoked again.

[0136] FIG. 11B is a flow chart illustrating a method 1100b for using frequency multiplexed resonator technology to transmit data to a superconducting device according to another exemplary implementation. Acts 1140 and 1145 of FIG. 11A can be combined into a single act 1148 as shown in FIG. 11B. With reference to FIG. 11B, at 1148, the computing system decides whether to send a tone to each of the superconducting resonators, and then transmits a microwave signal via the transmission line to all the superconducting resonators. The frequency multiplexed microwave signal stimulates the superconducting resonators in parallel.

[0137] The present technology can load data into a shift register on a quantum processor chip using a frequency multiplexed resonator. The frequency multiplexed resonator readout described above (with reference to FIGS. 1A, 1B, 10, 2A, 2B, 2C, 3, 4, 5, and 6) can be run in reverse to allow data to be passed to the processor. In some implementations, the first stage QFP can be used to rectify a microwave signal in the resonator if a signal is present.

[0138] The present technology can be used to input data to the processor as well as to readout qubit states from the processor. The same lines can be used for both input and readout.

[0139] In some implementations, the device can reduce, or minimize, the impact of microwave currents in the resonator on the attached QFP. To circumvent this, a large SENSE SQUID flux bias can be used to break the symmetry of the device, to allow a microwave flux signal to bias the body of the QFP. In another approach, a portion of the resonator inductance can be used to bias the QFP directly with the resonator current. A benefit of the latter approach is that it can separate the DC flux coupling between the QFP and the SENSE SQUID from the microwave flux coupling between the resonator and the body of the QFP.

[0140] Once the data is loaded, the QFP can be read out immediately. The data can be loaded with up to 100% fidelity. Errors can be corrected by repeating the loading sequence.

[0141] FIG. 12 is a schematic diagram illustrating a superconducting transceiver circuit 1200 according to at least one exemplary implementation. Superconducting transceiver circuit 1200 comprises a superconducting resonator able to tune a resonator frequency. Superconducting transceiver circuit 1200 is operable as a frequency multiplexed resonator transceiver.

[0142] Superconducting transceiver circuit 1200 comprises the elements described above in reference to FIG. 1A, and further comprises a flux bias line 155 operable to apply a flux bias to the last or final shift register stage 140. Shift register stage 140 can, for example, comprise a QFP, and can be communicatively coupled to superconducting resonator 110 for the purposes of reading out the state of a superconducting device and/or loading data into a superconducting device.

[0143] In one implementation, data can be loaded into a shift register via the last or final shift register stage 140, and the shift register can be communicatively coupled to a Digital to Analog Converter (DAC) (not shown in FIG. 12). In one implementation, the DAC can be used to apply a bias to a superconducting qubit.

[0144] FIG. 13A is a schematic diagram illustrating a superconducting transceiver circuit 1300a comprising a superconducting resonator with two SQUID loops according to at least one exemplary implementation. Superconducting transceiver circuit 1300a is operable as a frequency multiplexed resonant transceiver.

[0145] As described with reference to FIG. 2A, SQUID loops 216a and 216b advantageously enable independent tuning of the resonance frequency and the sensitivity of superconducting resonator 210a by adjusting the flux bias in SQUID loops 216a and 216b.

[0146] Components of superconducting transceiver circuit 1300a labeled with the same numbers as in superconducting circuit 100 of FIG. 1A are similar or even identical to those described in reference to FIG. 1A. For example, capacitance 112 of superconducting circuit 1300a can be a parallel plate capacitor, and inductance 114 of superconducting circuit 1300a can be a niobium spiral inductor.

[0147] As described with reference to FIG. 2A, interfaces 230a and 230b can provide flux bias to SQUID loops 216a and 216b respectively. Once a suitable operating point has been found (see below), the flux biases provided by interfaces 230a and 230b can be static. This advantageously allows the circuit to use an array of flux DACs requiring only a few wires to program. The two tunable SQUID loops 216a and 216b do not need an independent analog control line for each superconducting resonator 210a.

[0148] Superconducting transceiver circuit 1300a comprises the elements of FIG. 2A. Superconducting transceiver circuit 1300a further comprises an interface 155 operable to apply a flux bias to QFP 140, as described with reference to FIG. 11.

[0149] FIG. 13B is a schematic diagram illustrating a superconducting transceiver circuit 1300b comprising a superconducting resonator with two SQUID loops according to at least another exemplary implementation. Superconducting transceiver circuit 1300b is operable as a frequency multiplexed resonator transceiver.

[0150] Superconducting transceiver circuit 1300b comprises the elements of FIG. 2B. Superconducting transceiver circuit 1300b further comprises an interface 155 operable to apply a flux bias to a last stage QFP 140a, as described with reference to FIG. 11.

[0151] In the example embodiment of FIG. 13B, the coupling between SQUID loop 216b (known as the SENSE SQUID) and last stage QFP 140a is galvanic coupling. When there is no flux in the SENSE SQUID, microwave current will be evenly split on both sides of the SQUID. Since the galvanic coupling to the QFP is symmetric, the result is zero flux coupling into last stage QFP 140a. The symmetry can be broken by introducing a large flux bias into the SENSE SQUID. The circulating current will combine with the microwave current in a manner that depends on the non-linearity of the SQUID junctions. The result can be a net flux signal into last stage QFP 140a.

[0152] In another exemplary implementation, the resonator is coupled directly to the QFP. The coupling is sufficient to load the QFP deterministically when in a metastable state while not destroying data when in a fully latched state.

[0153] In at least one exemplary implementation, the superconducting device is stimulated after partial annealing (reduction of the barrier) at the resonant frequency.

[0154] In another exemplary implementation, the resonator is stimulated after partial annealing using a fast sweep by a Vector Network Analyzer (VNA). The sweep of the VNA can be centered, or least approximately centered, on the resonance frequency of the resonator. The bandwidth of the sweep can be set to a value that is less than the resonator linewidth, and the sweep can use a handful of points within the resonance. The bandwidth of the sweep can be selected to avoid, or at least reduce, overlap with the linewidth of an adjacent resonance.

[0155] In an example implementation, the sweep can be achieved with a trigger signal output from a DAC card, and sent to the VNA. The waveform can include a sufficiently long delay to allow the sweep to finish before full annealing and readout. For example, the delay can be a few milliseconds.

[0156] FIG. 13C is a schematic diagram illustrating a superconducting transceiver circuit 1300c comprising a superconducting resonator with two SQUID loops according to at least another exemplary implementation. Superconducting transceiver circuit 1300c is operable as a frequency multiplexed resonator transceiver, and is able to tune the resonator frequency and sensitivity independently of each other.

[0157] Superconducting transceiver circuit 1300c comprises the elements of FIG. 2C. Superconducting transceiver circuit 1300c further comprises an interface 155 operable to apply a flux bias to a last stage QFP 140a, as described with reference to FIG. 11.

[0158] Superconducting transceiver circuit 1300c is connected at node 215c to the ground 121 of transmission line 120 via a coupling capacitor 124. In other respects, superconducting transceiver circuit 1300c is the same as or similar to superconducting transceiver circuit 1300b.

[0159] Components of superconducting transceiver circuits 1300a, 1300b, and 1300c of FIGS. 13A, 13B, and 13C, respectively, labeled with the same numbers as in superconducting circuit 100 of FIG. 1A can be similar or even identical to those as described in reference to FIG. 1A. For example, capacitance 112 of superconducting circuits 1300a, 1300b, and 1300c can be a parallel plate capacitor, and inductance 114 of superconducting transceiver circuits 1300a, 1300b, and 1300c can be a niobium spiral inductor.

[0160] In superconducting transceiver circuits 1300a, 1300b, and 1300c, superconducting resonator 210a is connected at node 215a to ground, for example to the ground 121 of transmission line 120. In superconducting transceiver circuit 1300c, superconducting resonator 210a is connected at node 215a to ground via capacitor 124.

[0161] FIG. 14 is a schematic diagram illustrating an example embodiment of a superconducting transceiver circuit 1400 comprising superconducting resonator 110 of FIG. 12. Superconducting transceiver circuit 1400 is operable as a frequency multiplexed resonator transceiver, and is advantageously operable to independently tune the resonator frequency and sensitivity. Superconducting transceiver circuit further comprises interface 130 and last or final shift register stage 140, both as described with reference to FIG. 1A.

[0162] Superconducting transceiver circuit 1400 comprises the elements of superconducting circuit 400 of FIG. 4. Superconducting transceiver circuit 1400 further comprises a tunable coupler 440 in between superconducting resonator 110 and last or final shift register stage (or QFP) 140. Superconducting transceiver circuit 1400 enables independent tuning of the resonance frequency and the sensitivity to QFP flux, provided the variable loading of superconducting resonator 110 by tunable coupler 440 is taken into account.

[0163] Tunable coupler 440 comprises, for example, inductances 442 and 444, and DC SQUID 446.

[0164] Superconducting transceiver circuit 400 further comprises interface 450 operable to apply a flux bias to tunable coupler 440, and thereby to adjust the strength of coupling between SQUID loop 216b and last stage QFP 140.

[0165] In some embodiments, the frequency multiplexed resonator input system described above, which can be used to input data to superconducting devices, is used in combination with the frequency multiplexed resonator readout system also described in the present disclosure (with reference to FIGS. 1A, 1B, 10, 2A, 2B, 2C, 3, 4, 5, and 6). In other embodiments, the frequency multiplexed resonator input system described above is used in combination with other readout systems or circuits. For example, in one of the other embodiments, the frequency multiplexed resonator input system is used in combination with the superconducting flux qubit readout system described in U.S. Pat. No. 8,854,074.

[0166] An example embodiment of a frequency multiplexed resonator input/output system is illustrated in FIG. 5 (described above with reference to the readout system). The return pathway in FIG. 5 comprises DC block 585, circulators 584 and 583, amplifiers 575, 566, 564, and 562, attenuator 570, mixer 560, filters 527a and 527b, and ADC 526a and 526b. If the system is to be used for inputting data to the superconducting devices only (and no readout), then the return pathway is not required.

[0167] The various embodiments described above can be combined to provide further embodiments. To the extent that they are not inconsistent with the specific teachings and definitions herein, all of the U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications and non-patent publications referred to in this specification and/or listed in the Application Data Sheet, including but not limited to the following U.S. Provisional Patent Application No. 62/161,780, filed May 14, 2015; U.S. Provisional Patent Application No. 62/288,251, filed Jan. 28, 2016; U.S. Pat. Nos. 8,854,074; and 8,169,231, are incorporated herein by reference, in their entireties. Aspects of the embodiments can be modified, if necessary, to employ systems, circuits and concepts of the various patents, applications and publications to provide yet further embodiments.

[0168] These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.