Vertical super inductor device

Abstract

A vertical superinductor device and a fluxonium qubit including a superinductor are provided. The superinductor includes a substrate and a first vertical stack extending from a surface of the substrate in a vertical direction. The first vertical stack includes a first Josephson junction and a second Josephson junction connected in series in the vertical direction. The superinductor includes a second vertical stack extending from the surface of the substrate in the vertical direction. The second vertical stack includes a third Josephson junction. The superinductor includes a superconducting connector connecting the first and second vertical stacks in series such that the first, second, and third Josephson junctions are connected in series. The fluxonium qubit further includes a shunted Josephson junction connected to the superinductor by a superconducting wire such that the series connected first, second, and third Josephson junctions of the superinductor are connected in parallel with the shunted Josephson junction.

Description

BACKGROUND

[0001] The present invention relates to an inductor device, and more specifically, to a superinductor device with vertically stacked Josephson junction inductors.

[0002] In several superconducting quantum applications, such as fluxonium type qubits and traveling wave parametric amplifiers, lossless inductors with large inductance are desirable. One way to fabricate such inductors is to use arrays of Josephson junctions. Traditionally, these arrays are fabricated as planar structures. However, as the number of Josephson junctions increases, the surface area required for the planar array becomes too large. SUMMARY

[0003] According to embodiments of the invention, a fluxonium qubit includes a superinductor. The superinductor includes a substrate, a first vertical stack extending from a surface of the substrate in a vertical direction, the first vertical stack including a first Josephson junction and a second Josephson junction connected in series along the vertical direction. The superinductor also includes a second vertical stack extending from the surface of the substrate in the vertical direction and spaced apart from the first vertical stack. The second vertical stack includes a third Josephson junction. The superinductor includes a superconducting connector connecting the first vertical stack and the second vertical stack in series such that the first Josephson junction, the second Josephson junction, and the third Josephson junction are connected in series. The fluxonium qubit further includes a shunted Josephson junction connected to the superinductor by a superconducting wire such that the series of the first, second, and third Josephson junctions of the superinductor are connected in parallel with the shunted Josephson junction.

[0004] According to embodiments of the invention, a method of producing a fluxonium qubit includes forming a first vertical stack on a substrate, the first vertical stack extending from a surface of the substrate in a vertical direction, the first vertical stack including a first Josephson junction and a second Josephson junction connected in series along the vertical direction. The method also includes forming a second vertical stack on the substrate, the second vertical stack extending from the surface of the substrate in the vertical direction and spaced apart from the first vertical stack. The second vertical stack includes a third Josephson junction. The method also includes forming a superconducting connector connecting the first vertical stack and the second vertical stack in series such that the first Josephson junction, the second Josephson junction, and the third Josephson junction are connected in series, and connecting a shunted Josephson junction to the first vertical stack and the second vertical stack such that the series of the first Josephson junction, the second Josephson junction, and the third Josephson junction of the superinductor are connected in parallel with the shunted Josephson junction.

[0005] According to embodiments of the present invention, a superinductor includes a substrate, a first vertical stack extending from a surface of the substrate in a vertical direction, the first vertical stack including a first Josephson junction and a second Josephson junction connected in series along the vertical direction. The superinductor also includes a second vertical stack extending from the surface of the substrate in the vertical direction and spaced apart from the first vertical stack. The second vertical stack includes a third Josephson junction. The superinductor includes a superconducting connector connecting the first and second vertical stacks in series such that the first, second, and third Josephson junctions are connected in series.

[0006] According to embodiments of the present invention, a quantum computer includes a refrigeration system under vacuum, the refrigeration system including a containment vessel and a qubit chip contained in a refrigerated vacuum environment defined by the containment vessel. The qubit chip includes a plurality of fluxonium qubits. The quantum computer also includes a plurality of electromagnetic waveguides arranged in the refrigerated vacuum environment so as to direct electromagnetic energy to and receive electromagnetic energy from at least one selected fluxonium qubit of the plurality of fluxonium qubits. Each of the plurality of fluxonium qubits includes a superinductor. The superinductor includes a substrate and a first vertical stack extending from a surface of the substrate in a vertical direction. The first vertical stack includes a first Josephson junction and a second Josephson junction connected in series along the vertical direction. The superinductor also includes a second vertical stack extending from the surface of the substrate in the vertical direction and spaced apart from the first vertical stack. The second vertical stack includes a third Josephson junction. The superinductor includes a superconducting connector connecting the first and second vertical stacks in series such that the first, second, and third Josephson junctions are connected in series. Each fluxonium qubit further includes a shunted Josephson junction connected to the superinductor by a superconducting lead such that the series connected first, second, and third Josephson junctions of the superinductor are connected in parallel with the shunted Josephson junction.

[0007] The devices and methods disclosed herein enable connecting a large number of Josephson junctions in series in a significantly reduced planar surface area compared to conventional Josephson junction arrays. BRIEF DESCRIPTION OF DRAWINGS

[0008] Figure 1A is a schematic illustration of a superinductor including at least three Josephson junctions according to embodiments of the present invention.

[0009] Figure 1Bis a schematic diagram of a superinductor including two Josephson junctions in a first vertical stack and two Josephson junctions in a second vertical stack.

[0010] Figure 2 is a schematic diagram of a superinductor including a support material.

[0011] Figure 3A is a schematic diagram of a superinductor having a first vertical stack and a second vertical stack, each including at least five Josephson junctions.

[0012] Figure 3B is a schematic diagram of a superinductor including four vertical stacks.

[0013] Figure 4 is a schematic diagram of a fluxonium qubit according to an embodiment of the invention.

[0014] Figure 5 is a flowchart illustrating a method of producing a fluxonium qubit according to an embodiment of the invention.

[0015] Figures 6-20 is a schematic illustration of a method of forming a superinductor.

[0016] Figure 21 is a schematic diagram of a quantum computer according to an embodiment of the invention. DETAILED DESCRIPTION

[0017] Figure 1A is a schematic diagram of a superinductor 100 according to an embodiment of the invention. The superinductor 100 includes a substrate 102 and a first vertical stack 104 extending from a surface 106 of the substrate 102 in a vertical direction D. The first vertical stack 104 includes a first Josephson junction 108 and a second Josephson junction 110 connected in series along the vertical direction D. The superinductor 100 includes a second vertical stack 112 extending from the surface 106 of the substrate 102 along the vertical direction D. The second vertical stack 112 includes a third Josephson junction 114. The second vertical stack 112 is spaced apart from the first vertical stack 104.

[0018] The superinductor 100 includes a superconducting connector 118 connecting the first and second vertical stacks 104, 112 in series such that the first Josephson junction 108, the second Josephson junction 110, and the third Josephson junction 114 are connected in series.

[0019] In some embodiments, the top connection does not necessarily short the two vertical stacks. The two vertical stacks can have tunnel barrier terminations, such as but not limited to tunnel barriers, and they can be shorted from the top. This would add inductance to the two inductors in series. This embodiment can provide more manufacturing flexibility.

[0020] Figure 1B is a schematic diagram of an inductor 132 according to an embodiment of the application. In addition to the features shown in Figure 1A the second vertical stack 112 of the super inductor 132 includes a fourth Josephson junction 116 connected in series with the third Josephson junction 114 along the vertical direction D. A superconducting connector 118 connects the first vertical stack 104 and the second vertical stack 112 in series such that the first Josephson junction 108, the second Josephson junction 110, the third Josephson junction 114, and the fourth Josephson junction 116 are connected in series.

[0021] The vertical direction D can be substantially perpendicular to the surface 106 of the substrate 102. The vertical direction D can be exactly perpendicular to the surface 106 of the substrate 102, or can be approximately perpendicular to the surface 106 of the substrate 102. According to embodiments of the application, the first vertical stack 104 and the second vertical stack 112 have the same number of Josephson junctions, such as shown in Figure 1B According to embodiments of the application, the superconducting connector 118 connecting the first and second vertical stacks 104, 112 extends in a direction that is substantially parallel to the surface 106 of the substrate 102. According to embodiments of the application, each of the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction includes a tunnel barrier layer disposed between two superconducting layers. For example, in Figure 1A the second Josephson junction 110 includes a tunnel barrier layer 120 disposed between two superconducting layers 122, 124. The third Josephson junction 114 includes a tunnel barrier layer 126 disposed between two superconducting layers 128, 130. The height of each tunnel barrier layer can be, for example, approximately 1 nm.

[0022] Figure 2 is a schematic diagram of a super inductor 200 according to an embodiment of the application. The super inductor 200 includes Figure 1A the features of the super inductor 100 shown in and further includes a support material 202 disposed between the first and second vertical stacks 204, 206 and under the superconducting connector 208. The support material 202 can be a dielectric material. For example, the support material 202 can be silicon oxide or spin-on glass. The support material 202 can be a dielectric material that can be easily removed, such as by etching.

[0023] By forming at least two Josephson junctions in a vertical stack, the two Josephson junctions cover a smaller surface area of the substrate surface than forming the Josephson junctions side-by-side. Moreover, there is no surface area loss for further increasing the number of Josephson junctions per stack. For example, Figure 3A is a schematic diagram of a superinductor 300 having a first vertical stack 302 and a second vertical stack 304 each comprising at least five Josephson junctions. The first vertical stack 302 comprises five Josephson junctions 306, 308, 310, 312, 314 connected in series. The second vertical stack 304 comprises five Josephson junctions 316, 318, 320, 322, 324 connected in series. A superconducting connector 326 connects the first and second vertical stacks 302, 304 in series such that the five Josephson junctions 306, 308, 310, 312, 314 in the first vertical stack 302 and the five Josephson junctions 316, 318, 320, 322, 324 in the second vertical stack 304 are connected in series.

[0024] As shown in Figure 3A , increasing each vertical stack by three or four Josephson junctions does not increase the surface area of the first and second vertical stacks 302, 304 on the surface of the substrate 328 compared to Figure 1A and 1B . According to embodiments of the present invention, the surface area of each vertical stack is about 1 pm 2 .

[0025] According to embodiments of the present invention, the first vertical stack and the second vertical stack each comprise at least 20, 50, 100, or 200 Josephson junctions. When the first and second vertical stacks are connected, the superinductor comprises 40, 100, 200, or 400 Josephson junctions connected in series. The number of Josephson junctions listed here is provided as a non-limiting example. The first and second vertical stacks can comprise an optional number of Josephson junctions. The number of Josephson junctions per stack can depend on the desired inductance of the superinductor and on the material used to form the individual Josephson junctions. As the inductance of each individual Josephson junction increases, the number of Josephson junctions needed to meet a predetermined total inductance decreases.

[0026] According to embodiments of the present invention, the superinductor comprises three or more vertical stacks. Figure 3Bis a schematic diagram of a superinductor 330 including four vertical stacks. In addition to the first and second vertical stacks 332, 334 including three Josephson junctions 336, 338, 340, the superinductor 330 includes a third vertical stack 342 extending in the vertical direction D. The third vertical stack includes a fourth Josephson junction 344 and a fifth Josephson junction 346 connected in series along the vertical direction D. The superinductor 330 includes a fourth vertical stack 348 extending in the vertical direction D from a surface of the substrate. The fourth vertical stack 348 includes a sixth Josephson junction 350. The superinductor 330 includes superconducting connectors 352, 354 connecting the third and fourth vertical stacks 342, 348 in series with the first and second vertical stacks 332, 334 such that the first Josephson junction 336, the second Josephson junction 338, the third Josephson junction 340, the fourth Josephson junction 344, the fifth Josephson junction 346, and the sixth Josephson junction 350 are connected in series.

[0027] According to embodiments of the present application, a superinductor is connected in parallel with Josephson junctions to form a fluxonium qubit. Figure 4 is a schematic diagram of a fluxonium qubit 400 according to embodiments of the present application. The fluxonium qubit 400 includes a superinductor 402. The superinductor 402 includes a substrate 404 and a first vertical stack 406 extending in a vertical direction D from a surface 408 of the substrate 404. The first vertical stack 406 includes a first Josephson junction 410 and a second Josephson junction 412 connected in series along the vertical direction. The superinductor 402 includes a second vertical stack 414 extending in the vertical direction D from the surface 408 of the substrate 404. The second vertical stack 414 includes a third Josephson junction 416. The second vertical stack 414 is spaced apart from the first vertical stack 406. The superinductor 402 also includes a superconducting connector 420 connecting the first and second vertical stacks 406, 414 in series such that the first Josephson junction 410, the second Josephson junction 412, and the third Josephson junction 416 are connected in series. Although Figure 4 is an example with six Josephson junctions, the general concept of the present application is not limited to this particular number. In other embodiments, there can be more than a total of six Josephson junctions, or less than a total of six Josephson junctions.

[0028] In addition to the superinductor 402, the fluxonium qubit 400 includes a Josephson junction 422 connected to the superinductor 402 via superconducting wires 424 and 426, such that the first Josephson junction 410, the second Josephson junction 412, and the third Josephson junction 416 of the series-connected superinductors 402 are connected in parallel with the shunt Josephson junction 422. The fluxonium qubit 400 may include superinductors having more than two vertically stacked bodies, such as... Figure 3B The super inductor 330 is shown schematically in the image.

[0029] Figure 5 This is a flowchart illustrating a method 500 for generating fluxonium qubits according to an embodiment of the present invention. Note that... Figure 5 The order of the steps is not limiting. For example, in some embodiments, in Figure 5 The last step can also be the first. Method 500 includes forming a first vertical stack 502 extending vertically from the surface of the substrate on a substrate. The first vertical stack includes a first Josephson junction and a second Josephson junction connected in series in the vertical direction. Method 500 also includes forming a second vertical stack 504 extending vertically from the surface of the substrate on the substrate. The second vertical stack includes a third Josephson junction. The second vertical stack is spaced apart from the first vertical stack. Method 500 also includes forming a superconducting connector 506 that connects the first and second vertical stacks in series, such that the first, second, and third Josephson junctions are connected in series. Method 500 also includes connecting a shunt Josephson junction to the first and second vertical stacks 508, such that the series-connected first, second, and third Josephson junctions of the superinductor are connected in parallel with the shunt Josephson junction.

[0030] According to an embodiment of the present invention, the formation process is an addition process that always includes a subtraction step. Figures 6-20 This is a schematic diagram of an additional process that can be used to form a superinductor according to an embodiment of the present invention. Figures 6-20 In the figures, the same reference numerals denote the same features, for example, Figure 6 The attached figures 600 and Figure 7 In the attached figures, reference numeral 700 indicates a substrate.

[0031] To fabricate super inductors, superconducting materials are formed on substrate 600, such as... Figure 6As shown. A superconducting material can be applied using masking and shadow evaporation techniques, resulting in a first portion 602 and a second portion 604 spaced apart from the first portion 602. According to an embodiment of the invention, the first portion 602 and the second portion 604 are spaced approximately 1 μm apart. For example, the substrate 600 can be a silicon substrate, but embodiments of the invention are not limited to silicon substrates. The superconducting material can be, for example, niobium, or any superconducting material suitable for quantum computing applications.

[0032] like Figure 7 As shown, once the first portion 702 and the second portion 704 of the superconducting material are formed, a photoresist 706 can be spin-coated and baked onto the first portion 702, the second portion 704, and the substrate 700. The photoresist can be, for example, an ultraviolet photoresist or an electron beam photoresist. The photoresist can then be patterned to form two holes 808 and 809, as shown. Figure 8 As shown.

[0033] Apart from Figure 8 In addition to the patterning shown, or as an alternative, ion polishing with an etchant can be used to create the opposite contour. Figure 9 Holes 908 and 909 formed by ion milling are shown. Holes 908 and 909 are wider at the upper surfaces of the first portion 902 and the second portion 904 of the superconducting material than at the upper surface of the resist 906. The opposite profile facilitates the removal of the resist during the manufacturing process.

[0034] Figure 10 The deposition of a tunnel barrier layer 1010 is shown. The tunnel barrier layer 1010 is formed on a first portion 1002 and a second portion 1004 of a superconducting material. The tunnel barrier layer 1010 can be a dielectric material. For example, the tunnel barrier layer 1010 can be an oxide, such as alumina. Alternatively, instead of depositing a material to form the tunnel barrier layer 1010, the tunnel barrier layer 1010 can be formed by exposing the upper surfaces of the first portion 902 and the second portion 904 of the superconducting material to oxygen to form an oxide. According to an embodiment of the invention, the tunnel barrier layer 1010 has a thickness between about 0.5 nm and 1.5 nm. According to an embodiment of the invention, the tunnel barrier layer 1010 has a thickness of about 1 nm.

[0035] like Figure 11As shown, once the tunnel barrier layer 1110 is formed, a superconducting material layer 1112 is formed on the tunnel barrier layer. The combination of the first portion 1102, the tunnel barrier layer 1110, and the superconducting material 1112 forms a first Josephson junction. Similarly, the combination of the second portion 1104, the tunnel barrier layer 1110, and the superconducting material 1112 forms a second Josephson junction. The superconducting material 1112 according to an embodiment of the invention may have a thickness of about 30-35 nm. According to an embodiment of the invention, the photoresist 1006 has a thickness of about 1 μm, allowing a plurality of alternating layers of tunnel barrier and superconducting material to be formed within the holes 1108, 1109. According to an embodiment of the invention, the photoresist 1006 has a thickness greater than 1 μm.

[0036] Figure 12 The results are shown by forming an additional tunnel barrier layer 1214 and an additional superconducting material layer 1216, for example, through deposition or exposure to oxygen. The combination of superconducting material 1212, tunnel barrier layer 1214, and superconducting material 1216 forms an additional Josephson junction on each vertical stack. Additional Josephson junctions can be added by alternately forming layers of tunnel barrier and superconducting material.

[0037] The process continues until the resist is stripped off, resulting in... Figure 13 The structure shown includes two vertical stacks 1318 and 1320. At least one of the vertical stacks includes two or more Josephson junctions. According to some embodiments, each vertical stack includes at least five, twenty, fifty, or one hundred Josephson junctions. The first and second vertical stacks may include the same number of Josephson junctions. Alternatively, the first and second vertical stacks may include different numbers of Josephson junctions.

[0038] Once the resist is removed, such as Figure 14 As shown, a new resist layer 1422 is deposited and baked, and then as follows: Figure 15 As shown, patterning is used to expose the substrate 1500 between the two vertically stacked bodies 1518 and 1520. Then, as... Figure 16 As shown, the process involves depositing an oxide or sacrificial material 1624 between two vertical stacks 1618 and 1620. The oxide or sacrificial material 1624 is wide enough to prevent tunneling between the two vertical stacks 1618 and 1620. The oxide or sacrificial material 1624 serves as a support material for the subsequently formed superconducting connector. Once the oxide or sacrificial material 1624 has been deposited, the photoresist 1622 can be removed. Figure 17 The resulting structure is shown in the figure.

[0039] The process then includes forming a superconducting connector to connect the vertical stacks 1818, 1820 in series. Prior to depositing the superconducting connector, the resist 1826 is deposited, baked, and then etched to form a hole 1828 that exposes the oxide or sacrificial material 1824 and the uppermost superconducting layers of both vertical stacks 1820, 1822, as shown in Figure 18

[0040] As shown in Figure 19 a layer of superconducting material 1930 is deposited in the hole 1928 in the resist 1926. The superconducting material 1930 can be deposited by dual angle evaporation, although embodiments of the application are not limited to dual angle evaporation of the superconducting material 1930. The superconducting material 1930 contacts the uppermost superconducting layers of both vertical stacks 1918, 1920. In addition, the superconducting material 1930 connects the Josephson junction of the first vertical stack 1918 in series with the Josephson junction of the second vertical stack 1920. According to embodiments of the application, the superconducting material 1930 extends in a direction that is substantially parallel to the surface of the substrate 1900.

[0041] The process further includes removing the resist 1926, resulting in the superinductor 2032 shown in Figure 20 Although Figure 20 the superinductor 2032 in includes an oxide or sacrificial material 2024, the process can also include etching away the oxide or sacrificial material 2024, resulting in a superinductor similar to the superinductor 100 shown in Figure 1A where the layer of superconducting material 2030 is supported only by the two vertical stacks 2018, 2020.

[0042] Figure 21 is a schematic diagram of a quantum computer 2100 according to embodiments of the application. The quantum computer 2100 includes a refrigeration system under vacuum that includes a containment vessel 2102. The quantum computer 2100 also includes a qubit chip 2104 contained in a refrigerated vacuum environment defined by the containment vessel 2102. The qubit chip 2104 includes a plurality of fluxonium qubits 2106, 2108, 2110. The fluxonium qubits 2106, 2108, 2110 can each include a separate substrate, or can be formed on the qubit chip 2104, with the qubit chip 2104 acting as a shared substrate. The quantum computer 2100 also includes a plurality of electromagnetic waveguides 2112, 2114 arranged in the refrigerated vacuum environment so as to direct electromagnetic energy to and receive electromagnetic energy from at least a selected one of the plurality of fluxonium qubits 2106, 2108, 2110. As shown in Figure 21 ​As shown in FIG. 21, the electromagnetic waveguides 2112, 2114 can be formed on the qubit chip 2104.

[0043] Each fluxonium qubit 2106, 2108, 2110 can have a vertical structure described herein. The vertical structure of the fluxonium qubits 2106, 2108, 2110 significantly reduces their footprint on a conventional array. This fabrication is compatible with conventional superconducting circuit technology. The vertical stacks for arrays fabricated based on epitaxial stacks can have better quality and lower loss than conventional angled-evaporated junctions.

[0044] The description of various embodiments of the application has been presented for purposes of illustration, but is not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope of the application as defined by the appended claims. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application, or technical improvement over technologies found in the marketplace, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A fluxonium qubit, comprising: Super inductors, including: substrate; A first vertical stack extends from the surface of the substrate in a vertical direction, the first vertical stack including a first Josephson junction and a second Josephson junction connected in series along the vertical direction; A second vertical stack extends from the surface of the substrate in the vertical direction and is spaced from the first vertical stack, the second vertical stack including a third Josephson junction; and a superconducting connector connects the first vertical stack and the second vertical stack in series, such that the first Josephson junction, the second Josephson junction, and the third Josephson junction are connected in series; and The shunt Josephson junction is connected to the super inductor via a superconducting wire, such that the first, second, and third Josephson junctions of the super inductor, which are connected in series, are connected in parallel with the shunt Josephson junction.

2. The fluxonium qubit according to claim 1, wherein, The first vertical stack and the second vertical stack each include at least five Josephson junctions.

3. The fluxonium qubit according to claim 1, wherein, The first vertical stack and the second vertical stack each include at least 20 Josephson junctions.

4. The fluxonium qubit according to claim 1, wherein, The first vertical stack and the second vertical stack each include at least 50 Josephson junctions.

5. The fluxonium qubit according to claim 1, wherein, The first vertical stack and the second vertical stack have the same number of Josephson junctions.

6. The fluxonium qubit according to claim 1, wherein, The superconducting connector connecting the first vertical stack and the second vertical stack extends in a direction substantially parallel to the surface of the substrate.

7. The fluxonium qubit according to claim 1, further comprising a support material disposed between the first vertical stack and the second vertical stack and below the superconducting connector.

8. The fluxonium qubit according to claim 1, wherein, Each of the first Josephson junction, the second Josephson junction, and the third Josephson junction includes a tunnel barrier layer disposed between two superconducting layers, and the height of each tunnel barrier layer is approximately 1 nm.

9. The fluxonium qubit according to claim 1, wherein, The first vertical stack is spaced approximately 1 μm apart from the second vertical stack.

10. The fluxonium qubit according to claim 1, wherein, The super inductor also includes: A third vertical stack extends in the vertical direction, the third vertical stack comprising a fourth Josephson junction and a fifth Josephson junction connected in series along the vertical direction; A fourth vertical stack extends from the surface of the substrate in the vertical direction, the fourth vertical stack including a sixth Josephson junction; A superconducting connector connects the third and fourth vertical stacks in series with the first and second vertical stacks, such that the first, second, third, fourth, fifth, and sixth Josephson junctions are connected in series. The shunt Josephson junction is connected to the super inductor, such that the series-connected first Josephson junction, second Josephson junction, third Josephson junction, fourth Josephson junction, fifth Josephson junction and sixth Josephson junction of the super inductor are connected in parallel with the shunt Josephson junction.

11. A method for generating fluxonium qubits, comprising: A first vertical stack extending in a vertical direction from the surface of the substrate is formed on the substrate, the first vertical stack comprising a first Josephson junction and a second Josephson junction connected in series along the vertical direction; A second vertical stack is formed on the substrate, the second vertical stack extending from the surface of the substrate in the vertical direction and spaced apart from the first vertical stack, the second vertical stack including a third Josephson junction; A superconducting connector is formed, which connects the first vertical stack and the second vertical stack in series, such that the first Josephson junction, the second Josephson junction, and the third Josephson junction are connected in series; and A shunt Josephson junction is connected to the first vertical stack and the second vertical stack. The shunt Josephson junction is connected to a super inductor via a superconducting wire, such that the first Josephson junction, the second Josephson junction, and the third Josephson junction of the super inductor are connected in parallel with the shunt Josephson junction.

12. The method according to claim 11, wherein, The formation process is an addition process.

13. The method according to claim 11, wherein, The formation process is a subtractive process.

14. The method according to claim 11, wherein, The first vertical stack and the second vertical stack each include at least five Josephson junctions.

15. The method according to claim 11, wherein, The first vertical stack and the second vertical stack each include at least 20 Josephson junctions.

16. The method according to claim 11, wherein, The first vertical stack and the second vertical stack each include at least 50 Josephson junctions.

17. The method according to claim 11, wherein, The first vertical stack and the second vertical stack have the same number of Josephson junctions.

18. The method according to claim 11, wherein, The superconducting connector that connects the first vertical stack and the second vertical stack extends in a direction substantially parallel to the surface of the substrate.

19. The method according to claim 11, wherein, Each of the first Josephson junction, the second Josephson junction, and the third Josephson junction includes a tunnel barrier layer disposed between two superconducting layers, wherein the height of each tunnel barrier layer is approximately 1 nm.

20. The method according to claim 11, wherein, The first vertical stack and the second vertical stack are spaced about 1 μm apart.

21. The method of claim 11, further comprising forming a support material between the first vertical stack and the second vertical stack and below the superconducting connector.

22. A quantum computer, comprising: A refrigeration system under vacuum, including a container; A qubit chip, contained in a cooled vacuum environment defined by the containment container, wherein the qubit chip comprises a plurality of fluxonium qubits; as well as Multiple electromagnetic waveguides are arranged in the cooled vacuum environment to guide electromagnetic energy to at least one selected fluxonium qubit among the multiple fluxonium qubits and to receive electromagnetic energy from at least one selected fluxonium qubit among the multiple fluxonium qubits. Each of the plurality of fluxonium qubits includes: Super inductors, including: substrate; A first vertical stack extends from the surface of the substrate in a vertical direction, the first vertical stack including a first Josephson junction and a second Josephson junction connected in series along the vertical direction; A second vertical stack extends from the surface of the substrate in the vertical direction and is spaced from the first vertical stack, the second vertical stack including a third Josephson junction; and a superconducting connector connects the first vertical stack and the second vertical stack in series, such that the first Josephson junction, the second Josephson junction, and the third Josephson junction are connected in series; and The shunt Josephson junction is connected to the super inductor via a superconducting wire, such that the first, second, and third Josephson junctions of the super inductor, which are connected in series, are connected in parallel with the shunt Josephson junction.

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