Resonators using van der Waals materials

Abstract

The resonator is constructed using one or more van der Waals materials. In some embodiments, a system includes such a resonator. The resonator includes a capacitor (305) and an inductor, the capacitor includes a first conductive layer (205), an insulating layer (215) on the first conductive layer, and a second conductive layer (220) on the insulating layer, the first conductive layer being composed of one or more layers of a first van der Waals material, the insulating layer being composed of one or more layers of a second van der Waals material, and the second conductive layer being composed of one or more layers of a third van der Waals material.

Description

[Technical field]

[0001] One or more aspects of embodiments according to the present disclosure relate to van der Waals materials, and more particularly, to resonators constructed with one or more van der Waals materials. [Background technology]

[0002] Resonators with high quality factors may be used in a variety of applications, including quantum computing. For example, a system containing one or more quantum bits, or "qubits," may be constructed using one or more such resonators.

[0003] It is to this general technology environment that aspects of the present disclosure pertain. Summary of the Invention

[0004] According to an embodiment of the present disclosure, a system is provided that includes a resonator, the resonator including a capacitor and an inductor, the capacitor including a first conductive layer, an insulating layer on the first conductive layer, and a second conductive layer on the insulating layer, the first conductive layer being composed of one or more layers of a first van der Waals material, the insulating layer being composed of one or more layers of a second van der Waals material, and the second conductive layer being composed of one or more layers of a third van der Waals material.

[0005] In some embodiments, the capacitor further includes an insulating underlayer below the first conductive layer and an insulating upper layer above the second conductive layer, the insulating underlayer being composed of one or more layers of the first van der Waals material and the insulating upper layer being composed of one or more layers of the first van der Waals material.

[0006] In some embodiments, the capacitor further includes a first graphene layer between the first conductive layer and the insulating layer, and a second graphene layer between the insulating layer and the second conductive layer.

[0007] In some embodiments, the first conductive layer is a superconducting layer and the second conductive layer is a superconducting layer.

[0008] In some embodiments, the first van der Waals material is a material selected from the group consisting of NbSe2, MoTe2, WTe2, TaS2, BSCCO, graphene, and combinations thereof.

[0009] In some embodiments, the third van der Waals material is the same material as the first van der Waals material.

[0010] In some embodiments, the second van der Waals material is a material selected from the group consisting of BN, WSe2, MoS2, MoSe2, WS2, MoTe2, PtS2, PtSe2, PtTe2, HfS2, HfSe2, ReS2, ReSe2, SnS3, SnSe2, ZrS2, ZrSe2, silicene, germanene, black phosphorus, and combinations thereof.

[0011] In some embodiments, the inductor has an inductance that is primarily due to geometric inductance.

[0012] In some embodiments, the inductor has an inductance that is primarily due to motional inductance.

[0013] In some embodiments, the inductor has an inductance that is primarily due to Josephson inductance.

[0014] In some embodiments, the Josephson inductance is the inductance of a Josephson junction, the Josephson junction including a first conductive layer contiguous with a first conductive layer of the capacitor, an insulating layer contiguous with an insulating layer of the capacitor, and a second conductive layer contiguous with a second conductive layer of the capacitor.

[0015] In some embodiments, the insulating layer of the Josephson junction is thinner than the insulating layer of the capacitor.

[0016] In some embodiments, the Josephson inductance is a Josephson junction inductance, the Josephson junction being formed between a first conductive layer and a second conductive layer.

[0017] In some embodiments, the overlap of the wavefunction of the electrons of the first conductive layer and the wavefunction of the electrons of the second conductive layer results in the formation of a Josephson junction.

[0018] In some embodiments, the system further includes a first electrode in contact with the first conductive layer and a second electrode in contact with the second conductive layer.

[0019] In some embodiments, the first electrode is composed of a superconducting material.

[0020] In some embodiments, the first electrode is composed of a material selected from the group consisting of aluminum, niobium, niobium nitride, niobium titanium nitride, titanium nitride, and molybdenum rhenium.

[0021] In some embodiments, the system further includes a qubit, the capacitor is a first capacitor, and the qubit is capacitively coupled to the first capacitor.

[0022] In some embodiments, the qubit includes a second capacitor, the second capacitor including a first conductive layer, an insulating layer on the first conductive layer, and a second conductive layer on the insulating layer.

[0023] In some embodiments, the qubit is capacitively coupled to the first capacitor as a result of an overlap between the first conductive layer of the second capacitor and the second conductive layer of the first capacitor. [Brief description of the drawings]

[0024] The features, aspects, and embodiments are described in conjunction with the accompanying drawings.

[0025] [Figure 1]FIG. 2 is a schematic diagram of a qubit, according to an embodiment of the present disclosure. [Diagram 2] FIG. 2 is a schematic diagram of a capacitor according to an embodiment of the present disclosure. [Figure 3A] FIG. 2 is a schematic diagram of a resonator according to an embodiment of the present disclosure. [Figure 3B] 1 is an equation describing a resonator according to an embodiment of the present disclosure. [Figure 3C] 1 is a schematic perspective view of a resonator according to an embodiment of the present disclosure. [Figure 3D] FIG. 2 is a schematic diagram of a resonator according to an embodiment of the present disclosure. [Figure 3E] FIG. 2 is a schematic diagram of a resonator according to an embodiment of the present disclosure. [Figure 3F] FIG. 2 is a schematic diagram of a resonator according to an embodiment of the present disclosure. [Figure 3G] FIG. 2 is a schematic diagram of an equivalent circuit of a resonator according to an embodiment of the present disclosure. [Figure 4A] 1 is a schematic diagram of a system including a resonator according to an embodiment of the present disclosure. [Figure 4B] 1 is a schematic diagram of a system including a resonator according to an embodiment of the present disclosure. [Diagram 5] FIG. 2 is a schematic diagram of a qubit, according to an embodiment of the present disclosure. [Figure 6] FIG. 2 is a schematic diagram of a capacitor according to an embodiment of the present disclosure. [Figure 7A] 1 is a photograph of a qubit circuit according to an embodiment of the present disclosure. [Figure 7B] FIG. 7B is an enlarged view of a portion of FIG. 7A. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] The detailed description set forth below in conjunction with the accompanying drawings is intended to describe exemplary embodiments of resonators constructed with one or more van der Waals materials provided in accordance with the present disclosure, and is not intended to represent the only manner in which some embodiments may be constructed or utilized. In this description, features of the present disclosure are described in conjunction with the illustrated embodiments. However, it should be understood that the same or equivalent functions and structures may be accomplished by various embodiments that are also intended to be encompassed within the scope of the present disclosure. As shown elsewhere herein, like element numbers are intended to indicate like elements or features.

[0027] FIG. 1 illustrates a quantum bit or "qubit" in some embodiments. A quantum bit may be characterized by two quantum mechanical states separated by an energy difference. A Josephson junction 105 is connected between a first metal (e.g., superconducting metal) pad 110 and a second metal (e.g., superconducting metal) pad 115. In operation, the first metal pad 110 and the second metal pad 115 form a capacitor connected in parallel with the Josephson junction 105. The structure may be fabricated on a substrate 120. Exemplary electric field lines 125 between a first charge on the first metal pad 110 and a second charge on the second metal pad 115 are shown. These field lines may cross (i) a substrate-air interface, (ii) a metal-air interface, and (iii) a substrate-metal interface at one or more points. At these interfaces, impurities and other defects may result in a two-level system with an energy difference similar to that of a quantum bit. These two-level systems can interact with the qubits, resulting in losses and degradation of performance.

[0028] In some embodiments, the capacitor is instead formed as a stack of van der Waals materials, as shown in FIG. 2. The capacitor includes a first conductive layer 205 on a substrate 210, an insulating layer 215 on the first conductive layer 205, and a second conductive layer 220 on the insulating layer 215. The first conductive layer 205 may be composed of one or more layers of a first van der Waals material, the insulating layer 215 may be composed of one or more layers of a second van der Waals material, and the second conductive layer 220 may be composed of one or more layers of a third van der Waals material. The third van der Waals material may be the same material as the first van der Waals material. Exemplary electric field lines 225 are shown. Except for fringe fields (not shown), each line of the electric field extends directly from the second conductive layer 220 to the first conductive layer 205, passing through (i) a first interface between the second conductive layer 220 and the insulating layer 215, and (ii) a second interface between the first conductive layer 205 and the insulating layer 215. These interfaces may be significantly cleaner than the substrate-air, metal-air, and substrate-metal interfaces of the embodiment of FIG. 1. Although other interfaces (e.g., air-substrate interfaces) exist in the embodiment of FIG. 2, the coupling of the capacitor to these interfaces may be relatively weak, since only the fringe fields may interact with these interfaces. Furthermore, the capacitor of the embodiment of FIG. 2 may be significantly smaller (e.g., up to 1000 times smaller) than the structure of FIG. 1. In some embodiments, the capacitor further includes an insulating underlayer (which may be comprised of one or more layers of van der Waals material) below the first conductive layer, and an insulating overlayer (which may be comprised of one or more layers of van der Waals material) above the second conductive layer. In some embodiments, the capacitor further includes a first graphene layer between the first conductive layer and the insulating layer, and a second graphene layer between the insulating layer and the second conductive layer.

[0029] The first conductive layer 205 and the second conductive layer 220 may be superconducting layers, e.g., at sufficiently low temperatures, current densities, and magnetic fields, each of the first conductive layer 205 and the second conductive layer 220 may be in a superconducting state. As used herein, a material or structure is said to be "superconducting" if it becomes or transitions to a superconducting state at sufficiently low temperatures, current densities, and magnetic fields. As used herein, the term ("superconducting") also applies to structures or materials when they are not in a superconducting state. Thus, aluminum or aluminum electrodes may be referred to as "superconducting" even when at room temperature (even when not in a superconducting state). Each of (i) the first conductive layer 205, (ii) the insulating layer 215, and (iii) the second conductive layer 220 may be composed of a van der Waals material. For example, each of the first conductive layer 205 and the second conductive layer 220 may be composed of niobium selenide (NbSe2), molybdenum telluride (MoTe2), tungsten telluride (WTe2), tantalum sulfide (TaS2), bismuth strontium calcium copper oxide (BSCCO), combinations (e.g., alloys) of these materials, or one of various thicknesses and twist angles of graphene. The insulating layer 215 may be composed of boron nitride (BN), tungsten selenide (WSe2), molybdenum sulfide (MoS2), MoSe2, WS2, MoTe2, PtS2, PtSe2, PtTe2, HfS2, HfSe2, ReS2, ReSe2, SnS3, SnSe2, ZrS2, ZrSe2, silicene, germanene, or black phosphorus. In other embodiments, other suitable conductive (e.g., superconducting) or insulating materials, respectively, may be used. In some embodiments, insulating layer 215 comprises less than 100 monolayers, where a thinner layer may result in a capacitor with a higher capacitance per unit area. In some embodiments, insulating layer 215 comprises less than 10 monolayers (e.g., on the order of 1 or 2), and the thickness may be selected to be the minimum thickness at which tunneling effects are negligible or acceptably small.

[0030] 3A is a schematic diagram of an inductor-capacitor (LC) resonator including a parallel connected capacitor 305 and an inductor 310. FIG. 3B shows the relationship between the Q of the resonator and the resonant frequency ω 量子ビット The relationship between the relaxation time T1 of the resonator and the Q is shown below. It can be seen that the higher the Q, the longer the relaxation time T1. The Q of a capacitor or inductor can be defined as the reciprocal of the loss tangent.

[0031] The inductor may be implemented in a variety of ways. For example, Figures 3C, 3F, and 3G (discussed in more detail below) show embodiments in which the inductance is implemented as a Josephson inductance, while Figures 3D and 3E (discussed in more detail below) show embodiments in which the inductance is primarily due to motional and geometric inductance, respectively. Figure 3C is a schematic perspective view of a resonator structure in some embodiments. The resonator includes a capacitor 305 and a Josephson junction 315 connected in parallel with the capacitor 305. The Josephson junction 315 may act as an inductor 310 with an inductance equal to the Josephson inductance of the Josephson junction 315. The structure may be constructed from three layers, a first conductive layer 205, an insulating layer 215, and a second conductive layer 220, as shown. Each of the first conductive layer 205, the insulating layer 215, and the second conductive layer 220 may be a van der Waals material, and each of the first conductive layer 205 and the second conductive layer 220 may be superconducting. The insulating layer 215 may be thinner in the portion of the structure that forms the Josephson junction 315. Thus, (i) in the portion of the structure that is the capacitor 305, the wave function of the electrons in the first conductive layer 205 may not overlap significantly with the wave function of the electrons in the second conductive layer 220, and (ii) in the portion of the structure that is the Josephson junction 315, the wave function of the electrons in the first conductive layer 205 may overlap significantly with the wave function of the electrons in the second conductive layer 220. The combination of materials used for the first conductive layer 205, the insulating layer 215, and the second conductive layer 220 may be any of the combinations described above in the context of FIG. 2.

[0032] In some embodiments, the inductor may be constructed to exhibit an inductance that is primarily due to motional inductance, or an inductance that is primarily due to geometrical inductance. For example, FIG. 3D shows a resonator including a capacitor 305 and an inductor 310, the inductor constructed as a serpentine conductive trace (constructed from a superconducting material) that has an inductance that is primarily due to motional inductance. In another example, FIG. 3E shows a resonator including a capacitor 305 and an inductor 310, the inductor constructed as a spiral conductive trace (constructed from a superconducting material) that has an inductance that is primarily due to geometrical inductance. In the embodiment of FIG. 3E, the inductor may be fabricated, for example, by fabricating the spiral (except for the conductive trace extending from the inside of the spiral to the outside of the spiral) in one layer (e.g., using photolithography methods), covering the spiral with an insulating layer, fabricating (e.g., using photolithography methods) the conductive trace extending from the inside of the spiral to the outside of the spiral, and connecting the two ends of the conductive trace extending from the inside of the spiral to the outside of the spiral using a conductive via (which may be fabricated prior to fabrication of the conductive trace extending from the inside of the spiral to the outside of the spiral) that bridges from the inside of the spiral to the outside of the spiral and extends through the insulating layer.

[0033] FIG. 3F is a schematic diagram of a merged element resonator in which a single conductor-insulator-conductor sandwich (including a first conductive layer 205, an insulating layer 215, and a second conductive layer 220) operates as both a capacitor and an inductor (parallel plates). In the embodiment of FIG. 3F, the insulating layer 215 is selected to be thin enough that there is a significant Josephson effect (e.g., thin enough that an inductor exists as a result of the wave function of the electrons in the first conductive layer 205 overlapping with the wave function of the electrons in the second conductive layer 220). Due to this overlap, the structure of FIG. 3F includes both a capacitor and a Josephson junction 315 that operates as an inductor. Electrical conductors 320 (sometimes referred to as "electrodes") are shown in FIG. 3F, which may be used to connect the merged element resonator to other circuit elements. FIG. 3G is an equivalent circuit diagram of the structure of FIG. 3F.

[0034] FIG. 4A is a schematic diagram of an LC resonator capacitively coupled to a qubit 405 by a coupling capacitor 410. The LC resonator shown is of the embodiment of FIG. 3E, and in other embodiments, any one of the LC resonators of FIG. 3C, FIG. 3D, or FIG. 3F may be coupled to the qubit 405 in the same manner (using a coupling capacitor 410). The dashed arrows in FIG. 4A indicate that connections to other qubits and resonators may be made in the same manner using additional coupling capacitors. FIG. 4B is a schematic diagram of a system including five elements: two qubits 405, two readout resonators, and a coupler. Each of the five elements includes a parallel plate capacitor, and coupling between adjacent elements of the five elements is provided by constructing each upper conductive plate (e.g., each second conductive layer 220) to overlap the lower plate (e.g., first conductive layer 205) of the adjacent capacitor.

[0035] 5 shows a frequency-tunable Transmon qubit that includes (i) a superconducting quantum interferometer (SQUID) 505 that includes two Josephson junctions 510 connected in a loop, and (ii) a capacitor 515 (e.g., the capacitor of FIG. 3 or the capacitor of FIG. 6 (described in more detail below)) connected in parallel with the SQUID 505. In some embodiments, a fixed-frequency Transmon qubit (having a single Josephson junction 510 connected in parallel with the capacitor 515 instead of the SQUID 505) may be constructed in a similar manner.

[0036] 6 is a schematic diagram of a capacitor 515 in some embodiments. The capacitor 515 includes (similar to the capacitor in the embodiment of FIG. 3) a first conductive layer 205, an insulating layer 215 on the first conductive layer 205, and a second conductive layer 220 on the insulating layer 215. The capacitor further includes two electrodes 320 in contact with the first conductive layer 205 and the second conductive layer 220, respectively.

[0037] FIG. 7A is a photograph of an embodiment of a qubit including a capacitor according to embodiments described herein. FIG. 7B is an expanded view of a portion (labeled "7B") of FIG. 7A. The circuit may be fabricated on a silicon (e.g., float-zone silicon) substrate or wafer. FIG. 7A shows three external connections to the qubit, shown in FIG. 7B. A first wire bond pad 705 is grounded at a point adjacent to the qubit. A bias current provided through the first wire bond pad 705 may be used to generate a magnetic field on the qubit, control the critical current of the qubit's SQUID loop, and control the qubit's frequency. A second wire bond pad 710 may be capacitively coupled to the SQUID. A control pulse may be sent to the qubit via the second wire bond pad 710 to control the qubit's state (e.g., to rotate the qubit's state in the Bloch sphere). The third connection shown in FIG. 7A is a microwave resonator 715, which may be used to read out the qubit. The microwave resonator 715 and the connections to the first and second wire bond pads 705 and 710 may each be constructed as a coplanar microwave waveguide.

[0038] 7B shows an expanded view of the qubit of FIG. 7A, as described above. The capacitor 730 includes a first conductive layer 205 (e.g., a layer of niobium diselenide), an insulating layer 215 (e.g., a layer of boron nitride (e.g., hexagonal boron nitride)), and a second conductive layer 220 (e.g., a layer of niobium diselenide). The capacitance of the capacitor is determined primarily by the area of ​​overlap 735 where the first conductive layer 205, the insulating layer 215, and the second conductive layer 220 each reside. The capacitor is connected to the SQUID 505, and its magnetic field can be controlled by adjusting the current through the conductive segment 740 (which can be connected to the first wirebond pad 705 via a coplanar microwave waveguide).

[0039] The capacitor 730 of Figures 7A and 7B may be fabricated as follows. The first conductive layer 205 may be peeled off from the niobium diselenide bulk crystal using a suitable adhesive peeling tool and transferred to a bare silicon substrate. The insulating layer 215 may then be peeled off from the boron nitride bulk crystal and placed in a position that overlaps the first conductive layer 205 (and leaves a portion of the first conductive layer 205 exposed), and then the second conductive layer 220 may be peeled off from the niobium diselenide bulk crystal and placed on the substrate such that a portion of the second conductive layer 220 overlaps the area where the insulating layer 215 overlaps the first conductive layer 205. An electrode (e.g., an aluminum electrode) may then be fabricated to contact the first conductive layer 205 (e.g., the exposed portion of the first conductive layer 205) and the second conductive layer 220.

[0040] Fabrication of the electrodes may include (i) forming a layer of resist (photoresist or e-beam resist) on the wafer, (ii) patterning the photoresist (e.g., using e-beam lithography) and removing the photoresist in areas where metal (e.g., aluminum) is to be deposited, (iii) depositing a layer of metal (e.g., aluminum) on the wafer, and (iv) using a lift-off process to remove the photoresist and a portion of the metal layer above the photoresist. The conductors forming the external connections (e.g., first wire bond pad 705, second wire bond pad 710, their connected coplanar waveguides, and microwave resonator 715) may be formed simultaneously. Because the shape of the peeled layers may be unpredictable (e.g., may vary from peeling operation to peeling operation), the shape of the metal (e.g., aluminum) layer to be formed may be designed after the first conductive layer 205, insulating layer 215, and second conductive layer 220 are placed on the substrate. The SQUID 505 may be fabricated before or after the capacitor.

[0041] As used herein, a "part" of something means "at least a part" of that thing, and thus can mean all or less than all of that thing. Thus, a "part" of that thing includes the whole thing as a special case, i.e., the whole thing is an example of a part of that thing. The term "or" as used herein is inclusive, so that, for example, "A or B" means any one of (i) A, (ii) B, and (iii) A and B.

[0042] When a layer is referred to as being "between" two layers, it is understood that it may be the only layer between the two layers, or that one or more intervening layers may also be present. The terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the inventive concept. As used herein, the terms "substantially," "about," and similar terms are used as terms of approximation, not as terms of degree, and are intended to account for inherent variations in measurements or calculations that are recognized by those of ordinary skill in the art.

[0043] As used herein, the term "major element" refers to an element present in a composition, polymer, or product in an amount greater than the amount of any other single element in the composition or product. In contrast, the term "major component" refers to an element that constitutes at least 50% by weight or more of a composition, polymer, or product. As used herein, the term "major component" when applied to multiple items means at least half of the multiple items. As used herein, any structure or layer described as being "made of" or "consisting of" a material is understood to (i) in some embodiments, comprise that material as a major component, or (ii) in some embodiments, comprise that material as a major component.

[0044] When an element or layer is described as being "on," "connected," "coupled," or "adjacent to" another element or layer, it is understood that it may be directly abutting, connected, coupled, or adjacent to the other element or layer, or that there may be one or more intervening elements or layers. In contrast, when an element or layer is described as being "directly on," "directly connected," "directly coupled," or "immediately adjacent to" another element or layer, there are no intervening elements or layers present.

[0045] When an element is described as being "directly connected" or "directly coupled" to another element, it is understood that there are no intervening elements present. As used herein, "generally connected" means connected by an electrical path that may include any intervening elements, including intervening elements whose presence qualitatively changes the operation of the circuit. As used herein, "connected" means (i) "directly connected" or (ii) an element connected to an intervening element that does not qualitatively affect the operation of the circuit (e.g., a low value resistor or inductor, or a short transmission line).

[0046] Although limited embodiments of resonators constructed with one or more van der Waals materials have been specifically described and illustrated herein, many modifications and variations will be apparent to those skilled in the art. Thus, it should be understood that resonators constructed with one or more van der Waals materials used in accordance with the principles of the present disclosure may be embodied other than as specifically described herein. Features of certain embodiments are also defined in the following claims and their equivalents.

Claims

1. 1. A system including a resonator, The resonator comprises: A capacitor; an inductor; The capacitor is A first conductive layer; and an insulating layer on the first conductive layer; a second conductive layer on the insulating layer; the first conductive layer being comprised of one or more layers of a first van der Waals material; the insulating layer is composed of one or more layers of a second van der Waals material; the second conductive layer being composed of one or more layers of a third van der Waals material.

2. The capacitor is an insulating underlayer beneath the first conductive layer; an insulating overlayer on the second conductive layer; the insulating underlayer is comprised of one or more layers of a first van der Waals material; The system of claim 1 , wherein the insulating top layer is comprised of one or more layers of a first van der Waals material.

3. The capacitor is a first graphene layer between the first conductive layer and the insulating layer; 10. The system of claim 1, further comprising: a second graphene layer between the insulating layer and the second conductive layer.

4. The system of claim 1 , wherein the first conductive layer is a superconducting layer and the second conductive layer is a superconducting layer.

5. The first van der Waals material is NbSe ２ , MoTe ２ , W.T.e ２ , TaS ２ , BSCCO, graphene, and combinations thereof.

6. The system of claim 1 , wherein the third van der Waals material is the same material as the first van der Waals material.

7. The second van der Waals material is BN, WSe ２ , MoS ２ , MoSe ２ , W.S. ２ , MoTe ２ , PtS ２ , PtSe ２ , PtTe ２ , HfS ２ , HfSe ２ , ReS ２ ,ReSe ２ , SnS ３ , SnSe ２ , ZrS ２ , ZrSe ２ , silicene, germanene, black phosphorus, and combinations thereof.

8. The system of claim 1 , wherein the inductor has an inductance primarily due to geometric inductance.

9. The system of claim 1 , wherein the inductor has an inductance primarily due to motional inductance.

10. The system of claim 1 , wherein the inductor has an inductance primarily due to Josephson inductance.

11. the Josephson inductance is the inductance of a Josephson junction; The Josephson junction is a first conductive layer contiguous with the first conductive layer of the capacitor; an insulating layer contiguous with the insulating layer of the capacitor; a second conductive layer contiguous with the second conductive layer of the capacitor.

12. The system of claim 11 , wherein the insulating layer of the Josephson junction is thinner than the insulating layer of the capacitor.

13. 11. The system of claim 10, wherein the Josephson inductance is an inductance of a Josephson junction, the Josephson junction being formed between the first conductive layer and the second conductive layer.

14. 14. The system of claim 13, wherein an overlap of a wave function of electrons in the first conductive layer and a wave function of electrons in the second conductive layer results in the formation of the Josephson junction.

15. a first electrode in contact with the first conductive layer; The system of claim 1 , further comprising a second electrode in contact with the second conductive layer.

16. The system of claim 15 , wherein the first electrode is comprised of a superconducting material.

17. 17. The system of claim 16, wherein the first electrode is comprised of a material selected from the group consisting of aluminum, niobium, niobium nitride, niobium titanium nitride, titanium nitride, and molybdenum rhenium.

18. further comprising a qubit; the capacitor is a first capacitor, The system of claim 1 , wherein the qubit is capacitively coupled to the first capacitor.

19. the quantum bit includes a second capacitor; The second capacitor comprises: A first conductive layer; and an insulating layer on the first conductive layer; a second conductive layer on the insulating layer.

20. 20. The system of claim 19, wherein the qubit is capacitively coupled to the first capacitor as a result of an overlap between the first conductive layer of the second capacitor and the second conductive layer of the first capacitor.

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