Resonator, oscillator, and method for manufacturing resonator

Abstract

To provide a resonator, an oscillator, and a method for manufacturing a resonator that provide a small footprint in a superconducting circuit.SOLUTION: A resonator 1 includes: a junction element 2 made of a Josephson junction; and fishbone waveguides 31 and 32 coupled by the junction element. The resonator 1 is oscillated by passing an AC current through a control line to make it possible to shorten the waveguide length required for the resonator based on the use of the fishbone waveguide, thereby making it possible to reduce the footprint of a superconducting circuit.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a resonator, an oscillator, and a method for manufacturing a resonator.

Background Art

[0002] In a superconducting circuit including qubits and the like, a coplanar waveguide (CPW) is widely used as a high-frequency transmission line. The CPW has a two-dimensional structure in which a linear gap is provided in a superconductor deposited on the surface of a substrate, and a linear superconductor for signal transmission is disposed at the center of the gap. The CPW has an inductance and a capacitance proportional to the length of the waveguide. By appropriately designing the length of the waveguide from the wavelength, it is possible to configure a distributed-constant resonator using the CPW. Alternatively, by adjusting the cavity inductance and / or capacitance, it is possible to configure a lumped-constant resonator using the CPW. A non-linear inductance can be combined with the CPW and applied as a qubit (for example, Patent Document 1). As the non-linear inductance, a single Josephson junction or a SQUID (Super Conducting Quantum Interference Device) in which two or more Josephson junctions form a closed path is used.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] Although the CPW has a wide range of applications as described above, when constructing a resonator, a CPW with a length on the order of the wavelength of the resonance frequency, half of the wavelength, or one-fourth of the wavelength is required. Therefore, a long and narrow chip shape is required. In order to increase the degree of freedom in the chip shape and pattern design of the superconducting circuit including the resonator, it is widely practiced to give a curvature to a part of the CPW and make it a bent shape (meander shape). However, when making a bent shape, if it is bent multiple times, or when adjacent transmission lines are arranged in parallel for a long distance, resonance modes different from the originally designed resonance may occur, making the design difficult. In a superconducting circuit, it is required to reduce the footprint.

[0005] Therefore, an object of the present invention is to provide a resonator that solves the above problems.

Means for Solving the Problems

[0006] According to a first aspect of the present invention, a resonator includes a junction element composed of a Josephson junction and a fishbone-type waveguide coupled by the junction element.

[0007] An oscillator according to a second aspect of the present invention oscillates the resonator by flowing an alternating current through the control line.

[0008] A method for manufacturing a resonator according to a third aspect of the present invention couples a fishbone-type waveguide to a junction element composed of a Josephson junction.

Effects of the Invention

[0009] According to the present invention, by using a fishbone-type waveguide, the waveguide length required for the resonator can be shortened. As a result, the effect of reducing the footprint in the superconducting circuit can be obtained.

Brief Description of the Drawings

[0010]

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Embodiments for Carrying Out the Invention

[0011] (First Embodiment) Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In the following description, a Josephson junction refers to an element having a structure in which a first superconductor and a second superconductor are coupled by a weak coupling region such as a thin insulator. Here, as the weak coupling region, in addition to an insulator, a minute superconductor or a thin normal conductor may be used. Also, a SQUID (Superconducting QUantum Interference Device) is an element in which two Josephson junctions are connected in a loop by a superconducting line. Further, part or all of the circuits described below are configured using, for example, a line (wiring) formed of a superconductor, and are utilized in a temperature environment of about 10 mK (millikelvin) in order to realize a superconducting state.

[0012] Also, in the following description, "vicinity" means a range within 100 micrometers. For example, the vicinity of a node of an electric field is a range within 100 micrometers from the node of the electric field. Also, "equal", "equidistant", etc. are assumed to allow for manufacturing errors.

[0013] FIG. 1 is a diagram showing an example of a chip layout of the resonator 1 according to the present embodiment. The resonator 1 includes a junction element 2, a Fishbone type waveguide 31, and a Fishbone type waveguide 32. The junction element 2, the Fishbone type waveguide 31, and the Fishbone type waveguide 32 are formed on a chip 4. The resonator 1 is a quantum bit that resonates by a standing wave corresponding to a half wavelength.

[0014] The junction element 2 is composed of a Josephson junction. The Fishbone type waveguide 31 and the Fishbone type waveguide 32 are coupled by the junction element 2. The length of the Fishbone type waveguide 31 and the length of the Fishbone type waveguide 32 are equal to each other.

[0015] Referring now to FIG. 11, the fishbone-type waveguide will be described. The resonance element 100 shown in FIG. 11 is a half-wavelength resonance element composed of a fishbone-type waveguide 101. The fishbone-type waveguide is composed of a central waveguide and a plurality of waveguides protruding from both sides thereof at equal intervals. Note that the plurality of protruding waveguides are each called a stub. The stub is preferably shorter than the total length of the central waveguide. In the fishbone-type waveguide, the characteristic impedance and the phase velocity can be arbitrarily adjusted by changing parameters such as the interval between adjacent stubs. The resonance element composed of the fishbone-type waveguide has an increased capacitance and inductance per unit length due to the contribution of the stub. Therefore, the length of the waveguide of the resonance element composed of the fishbone-type waveguide is shorter than that in the case where a waveguide having the same electrical characteristics is composed of a normal waveguide. Even for a standing wave of the same frequency, the wavelength of the standing wave on the fishbone-type waveguide is shorter than the wavelength of the standing wave on the normal waveguide. In the present embodiment, this is referred to as the effective wavelength. The effective wavelength can be obtained by electromagnetic field simulation.

[0016] Returning to FIG. 1, the description of the configuration of the resonator 1 will be continued. The fishbone-type waveguide 31 and the fishbone-type waveguide 32 are each a distributed constant line. When the qubit operates, a standing wave is generated in the qubit. The fishbone-type waveguide 31 and the fishbone-type waveguide 32 each have a length corresponding to one-fourth of the wavelength corresponding to the operating frequency of the resonator 1. In other words, it has a length corresponding to one-fourth of the effective wavelength in the fishbone-type waveguide corresponding to the operating frequency. Therefore, the resonator 1 is a qubit that resonates by a standing wave corresponding to a half wavelength as a whole. Note that the length of each of the fishbone-type waveguide 31 and the fishbone-type waveguide 32 is about 300 μm as an example.

[0017] Fig. 2 shows an enlarged view of the vicinity of the bonding element 2 of the resonator 1. In Fig. 2, the fishbone waveguide 31 is composed of a central waveguide 311 and a plurality of stubs 312. A ground conductor 313 is formed between the plurality of stubs 312. The stubs 312 and the ground conductor 313 are alternately arranged by bending the substrate portion 314. Similarly, the fishbone waveguide 32 is composed of a central waveguide 321 and a plurality of stubs 322. A ground conductor 323 is formed between the plurality of stubs 322. The stubs 322 and the ground conductor 323 are alternately arranged by bending the substrate portion 324. Note that the ground conductor 332 is formed in the region where the fishbone waveguide 31 and the fishbone waveguide 32 are coupled.

[0018] The central waveguide 311, the plurality of stubs 312, the plurality of ground conductors 313, the central waveguide 321, the plurality of stubs 322, and the plurality of ground conductors 323 are each a thin film of a superconducting material formed on a silicon substrate. On the other hand, the substrate portions 314 and 324 are each a portion where the silicon substrate from which the thin film has been peeled off is exposed.

[0019] The bonding element 2 couples the bonding portion 3111 of the central waveguide 311 and the bonding portion 3211 of the central waveguide 321. Fig. 3 shows an example when the bonding element 2 is a SQUID. In Fig. 3, the bonding element 2 is composed of a Josephson junction 21a and a Josephson junction 22a. The Josephson junction 21a and the Josephson junction 22a each couple the bonding portion 3111 and the bonding portion 3211. Fig. 4 shows an example when the bonding element 2 consists of one Josephson junction 21b. The Josephson junction 21b couples the bonding portion 3111 and the bonding portion 3211.

[0020] Note that the resonator 1 is not limited to a qubit forming a half-wavelength resonator. The resonator 1 may be used for a qubit forming a resonator with a wavelength other than a half-wavelength, such as a length of one-fourth of the effective wavelength, by changing the lengths of the fishbone waveguides 31 and 32 respectively. For example, in the present embodiment, an example in which the lengths and shapes of the fishbone waveguide 31 and the lengths and shapes of the fishbone waveguide 32 are equal to each other has been described. That is, an example in which the junction element 2 is arranged at a position one-fourth of the effective wavelength corresponding to the operating frequency of the resonator 1 has been described, but it is not limited to this. The lengths and shapes of the two fishbone waveguides coupled to both ends of the junction element 2 may be different from each other. That is, the junction element 2 may be arranged at a position other than the position one-fourth of the effective wavelength corresponding to the operating frequency of the resonator 1.

[0021] Note that one of the fishbone waveguide 31 and the fishbone waveguide 32 may be a coplanar waveguide (CPW). In that case, the fishbone waveguide and the CPW are coupled by the junction element 2.

[0022] As described above, the resonator 1 according to the embodiment includes a junction element 2 made of a Josephson junction, and fishbone waveguides (in this embodiment, the fishbone waveguide 31 and the fishbone waveguide 32) coupled by the junction element 2.

[0023] With this configuration, in the resonator 1 according to the present embodiment, by using the fishbone waveguide, the waveguide length required for the resonator can be shortened, so that the footprint can be reduced. Here, being able to reduce the footprint means that the footprint can be reduced compared to a superconducting circuit when only CPW is used as the waveguide.

[0024] (Second Embodiment) Hereinafter, a second embodiment of the present invention will be described in detail with reference to the drawings. In this embodiment, a case where the resonator further includes a control line to which a bonding element is magnetically coupled and to which a control signal is input will be described. Note that the same components as those in the above-described first embodiment may be denoted by the same reference numerals, and the description of the same components and operations may be omitted.

[0025] Before describing the resonator 1A according to this embodiment, a qubit including a control line according to related art will be described with reference to FIG. 12. FIG. 12 is a diagram showing an example of a chip layout of a qubit 200 according to related art. The qubit 200 includes a bonding element 201, an input / output port 202, an input / output line 203, a partial waveguide 204, a partial waveguide 205, a control line 206, and a control port 207.

[0026] The input / output line 203 is a CPW. Note that the CPW is impedance-matched to 50Ω, for example. The partial waveguide 204 and the partial waveguide 205 are coupled by the bonding element 201 at a position that is one-fourth of the effective wavelength corresponding to the operating frequency of the qubit 200. The partial waveguide 204, the bonding element 201, and the partial waveguide 205 constitute a resonator. The control line 206 is arranged such that the tip of the control line 206 is near the bonding element 201. The control line 206 is magnetically coupled to the bonding element 201.

[0027] The control line 206 adjusts the resonance frequency (operating frequency) of the qubit 200. By inputting a control signal of direct current (DC) from the control port 207, the resonance frequency of the qubit 200 can be set. More specifically, the resonance frequency of the qubit 200 can be controlled by applying a magnetic field generated from the current flowing through the control line 206 to the junction element 201. In addition to frequency adjustment, the control line 206 is also used to apply an alternating magnetic field to the junction element by flowing an alternating current at the resonance frequency or its harmonic to oscillate the resonator (partial waveguide 204, junction element 201, and partial waveguide 205). The current flowing through the control line 206 may be a current obtained by superimposing a direct current and an alternating current. At this time, since the control line 206 becomes a path through which the energy stored in the resonator flows out to the outside, it causes a decrease in the internal Q value of the resonator. In a half-wavelength resonator, the center of the resonator becomes a node of the electric field. Therefore, by arranging the tip of the control line 206 near the center of the resonator, which is a node of the electric field, the outflow of energy can be reduced.

[0028] FIG. 5 is a diagram showing an example of the chip layout of the resonator 1A according to the present embodiment. The resonator 1A includes a junction element 2, a waveguide 31A, a waveguide 32A, a control line 5, and a control port 6. The junction element 2, the waveguide 31A, the waveguide 32A, the control line 5, and the control port 6 are formed on the chip 4. The function of the resonator 1A as a resonator is borne by the junction element 2, the waveguide 31A, and the waveguide 32A. The resonator 1A is a qubit forming a half-wavelength resonator.

[0029] The waveguide 31A includes a fishbone-type waveguide 310 and a CPW 311A. The waveguide 32A includes a fishbone-type waveguide 320 and a CPW 321A. The fishbone-type waveguide 310 is coupled to the junction element 2 via the CPW 311A. The fishbone-type waveguide 320 is coupled to the junction element 2 via the CPW 321A. That is, each of the two fishbone-type waveguides is coupled to the junction element 2 via a CPW.

[0030] The fishbone-type waveguides 310 and 320 are each a distributed constant line. The fishbone-type waveguides 310 and 320 each have a length corresponding to one-fourth of the effective wavelength corresponding to the operating frequency of the resonator 1A. Therefore, the resonator 1 is a qubit forming a distributed constant type resonator with a half-wavelength as a whole. Note that the length of each of the fishbone-type waveguides 310 and 320 is about 300 μm as an example.

[0031] The control line 5 is magnetically coupled to the junction element 2 and receives an input of a control signal. The control line 5 can set the resonance frequency of the resonator 1A by inputting a control signal of a direct current (DC). More specifically, the resonance frequency can be controlled by applying a magnetic field generated from the current flowing through the control line 5 to the junction element 201. The junction element 201 is a loop structure composed of a plurality of Josephson junctions, that is, a SQUID, and the resonance frequency can be controlled by applying a magnetic field to this SQUID to change the equivalent inductance of the SQUID. The control line 5 is also used to oscillate the resonator (waveguides 31A and 32A) by applying an alternating magnetic field to the junction element 2 by flowing an alternating current having the resonance frequency or its harmonic. Note that the current flowing through the control line may be a current obtained by superimposing a direct current and an alternating current.

[0032] FIG. 6 shows an enlarged view of the vicinity of the bonding element 2 of the resonator 1A. The tip 51 of the control line 5 branches into a first branch line 511 and a second branch line 512. The first branch line 511 and the second branch line 512 are arranged in the vicinity of the bonding element 2 so as to be magnetically coupled to the bonding element 2. That is, the tip 51 of the control line 5 is arranged in the vicinity of the bonding element 2. Here, the position where the bonding element 2 is arranged is the position of one-fourth of the effective wavelength corresponding to the operating frequency of the resonator 1A (the position of the node of the electric field). That is, the tip 51 of the control line 5, the first branch line 511, and the second branch line 512 are arranged near the node of the electric field, which is a standing wave generated in the resonator 1A during the operation of the resonator 1A. In the resonator 1A, by arranging the tip 51 of the control line 5, the first branch line 511, and the second branch line 512 near the node of the electric field, the outflow of energy can be minimized and the decrease in the internal Q value of the resonator can be prevented.

[0033] Furthermore, as described above, the two fishbone-shaped waveguides (the fishbone-shaped waveguide 310 and the fishbone-shaped waveguide 320) are each coupled to the bonding element 2 via a CPW (CPW311A and CPW321A). CPW311A and CPW321A are each linear in shape. The length of each of CPW311A and CPW321A is such that the tip 51 of the control line 5, the first branch line 511, and the second branch line 512 can be arranged in the vicinity of the bonding element 2. The length is preferably 3 μm or more, more preferably 5 μm or more. Also, the length is preferably 1 / 50 or less, more preferably 1 / 100 or less, and even more preferably 1 / 500 or less of the wavelength corresponding to the resonance frequency of the resonator 1A in order to minimize the influence on the resonance frequency of the resonator 1A. By arranging the linear CPW311A and CPW321A in the vicinity of the bonding element 2, the tip 51 of the control line 5, the first branch line 511, and the second branch line 512 can be arranged in the vicinity of the bonding element 2.

[0034] Referring to FIG. 7 here, the details of the arrangement of the first branch line 511 and the second branch line 512 will be described. The first branch line 511 and the second branch line 512 are arranged such that the current flowing through the first branch line 511 and the current flowing through the second branch line 512 are equal in amount and opposite in direction. Specifically, as shown in FIG. 7, the first branch line 511 and the second branch line 512 are arranged to be symmetric about the control line 5. The first branch line 511 is wired along the bonding element 2, and the second branch line 512 is wired in the direction opposite to that of the first branch line 511. For this reason, the second branch line 512 is magnetically coupled to the bonding element 2 while the first branch line 511 is configured not to be magnetically coupled to the bonding element 2. More specifically, for example, as shown in FIG. 7, the control line 5 is a T-shaped line, and the first branch line 511 and the second branch line 512 branched at the tip 51 are arranged linearly side by side. That is, the angle formed by the first branch line 511 and the non-branched portion of the control line 5 is 90 degrees, the angle formed by the second branch line 512 and the non-branched portion of the control line 5 is 90 degrees, and the angle formed by the first branch line 511 and the second branch line 512 is 180 degrees. These angles are the values in an ideal case, and in practice, a manufacturing error of ±10% or less of these angles is allowed. Note that the CPW311A and the CPW321A are arranged to be symmetric about the bonding element 2.

[0035] Note that the arrangements of the first branch line 511 and the second branch line 512 are not limited to the arrangements shown in FIG. 7. As another example, as shown in FIG. 8, the first branch line 511 and the second branch line 512 may be arranged such that the length of the first branch line 511 is shorter than the length of the second branch line 512. By making the length of the first branch line 511 shorter than the length of the second branch line 512, while keeping the CPW311A and CPW321A arranged symmetrically about the bonding element 2, the areas of the first ground region 513 and the second ground region 514 can be made smaller than the arrangement shown in FIG. 7. Accordingly, the CPW311A and CPW321A can be shortened, and the size of the entire resonator can be reduced. Note that in FIG. 8, the CPW311A and CPW321A are arranged symmetrically about the bonding element 2.

[0036] Also, the arrangements of the CPW311A and CPW321A are not limited to the arrangements shown in FIG. 7. As another example, as shown in FIG. 9, the CPW311A and CPW321A may be arranged such that the length of the CPW321A is shorter than the length of the CPW311A. By making the length of the CPW321A shorter than the length of the CPW311A, the areas of the first ground region 513 and the second ground region 514 can be made smaller than the arrangement shown in FIG. 7. Accordingly, the size of the entire resonator can be reduced. Note that in FIG. 9, the first branch line 511 and the second branch line 512 are arranged symmetrically about the control line 5.

[0037] Note that the CPW311A and CPW321A may be omitted from the configuration of the resonator 1A. In that case, the fishbone waveguide 310 and the fishbone waveguide 320 are each directly coupled to the bonding element 2. Even in that case, it is preferable that the tip 51 of the control line 5 be arranged as close as possible to the bonding element 2. In order to arrange the tip 51 of the control line 5 as close as possible to the bonding element 2, the tip 51 is preferably arranged near the outside of each stub of the fishbone waveguide 310 and the fishbone waveguide 320.

[0038] As described above, the control line 5 is also used to apply an alternating magnetic field to the junction element 2 by passing an alternating current having a resonance frequency or its harmonic, thereby oscillating the resonator (waveguide 31A and waveguide 32A). That is, the resonator (in this embodiment, resonator 1A) may be used as an oscillator that oscillates the resonator (in this embodiment, resonator 1A) by passing an alternating current through the control line 5. In the transmitter, the two fishbone-type waveguides may be coupled to the junction element via coplanar waveguides, or the two fishbone-type waveguides may be directly coupled by the junction element.

[0039] (Third Embodiment) Hereinafter, a third embodiment of the present invention will be described in detail with reference to the drawings. In this embodiment, similar to the first embodiment, a qubit is configured by coupling two waveguide structures by a Josephson junction. Here, a case where the waveguide structure is a combination of a fishbone-type waveguide and a straight or meandering CPW will be described. Note that the same components as those in the first embodiment described above may be denoted by the same reference numerals, and the description of the same components and operations may be omitted.

[0040] FIG. 10 is a diagram showing an example of a chip layout of the resonator 1B according to this embodiment. The resonator 1B includes a junction element 2, a waveguide 31B, and a waveguide 32B. The junction element 2, the waveguide 31B, and the waveguide 32B are formed on the chip 4.

[0041] The waveguide 31B includes a fishbone-type waveguide 610, a meander-shaped CPW 611, a fishbone-type waveguide 612, and a straight-shaped CPW 613. The waveguide 32B includes a fishbone-type waveguide 620, a meander-shaped CPW 621, a fishbone-type waveguide 622, and a straight-shaped CPW 623. The fishbone-type waveguide 610 and the fishbone-type waveguide 620 are coupled by a bonding element 2. The fishbone-type waveguide 610, the meander-shaped CPW 611, the fishbone-type waveguide 612, and the straight-shaped CPW 613 are coupled in series from the bonding element 2 in this order. The fishbone-type waveguide 620, the meander-shaped CPW 621, the fishbone-type waveguide 622, and the straight-shaped CPW 623 are coupled in series from the bonding element 2 in this order.

[0042] Note that the length of each of the fishbone-type waveguide 610 and the fishbone-type waveguide 620 is about 300 μm as an example. The length of each of the fishbone-type waveguide 612 and the fishbone-type waveguide 622 is about 600 μm as an example. The radius length of each of the meander-shaped CPW 611 and the meander-shaped CPW 621 is about 250 μm as an example. The length of each of the straight-shaped CPW 613 and the straight-shaped CPW 623 is about 200 μm as an example.

[0043] Therefore, in the resonator 1B, two waveguides are coupled by a bonding element 2. Each of the two waveguides is a combination of a fishbone-type waveguide and a straight or curved CPW. Note that the curved CPW may have a curved shape other than the meander shape.

[0044] Like the resonator 1 according to the first embodiment, the design of the qubit is limited to a linear structure only with a Fishbone-type waveguide. On the other hand, like the resonator 1B according to the present embodiment, by combining CPWs, the design of the qubit can be made to correspond to more diverse chip designs.

[0045] In the resonator 1B, part of the qubits is composed of narrow CPWs (meander-shaped CPW611, straight-shaped CPW613, meander-shaped CPW621, and straight-shaped CPW623). As a result, an air bridge can be installed in the CPW part of the portions constituting the waveguide 31B and the waveguide 32B. The air bridge can suppress the appearance of resonance modes different from the resonator design that may occur when the waveguides are arranged in parallel.

[0046] Note that the air bridge is a structure made of a conductive material, such as metal, and is a structure that electrically connects the GND planes on both sides of the core wire of the CPW. The air bridge does not contact the core wire and has a structure that intersects the core wire three-dimensionally. Therefore, the air bridge and the core wire are not electrically connected. The space between the air bridge and the core wire is generally air or vacuum. When the resonator is a superconducting quantum circuit (qubit) as in this embodiment, the space between the air bridge and the core wire is vacuum. However, although the air bridge is generally fabricated using semiconductor process technology, there is a possibility that a dielectric such as a resist remains around the air bridge during the process of fabricating the air bridge.

[0047] Also, in the resonator 1B according to this embodiment, depending on the vicinity of the center of the resonator or the design with respect to the wavelength, nodes of the electric field can be formed at other locations. Similar to the second embodiment, in the resonator 1B, the tip of the control line can be installed at the position of the node of the electric field in the direction in which the phase of the electric field changes. When the tip of the control line is installed at the position of the node of the electric field, similar to the second embodiment, the control line can be extended to the vicinity of the bonding element 2 by coupling the two fishbone-shaped waveguides to the bonding element 2 via the CPW, respectively.

[0048] Note that the layout of the resonator 1B shown in FIG. 10 is an example, and the waveguide may have a layout other than that shown in FIG. 10 as long as it is a combination of a fishbone-type waveguide and a straight or curved CPW. For example, the layouts of the waveguide 31B and the waveguide 32B may be different from each other. Also, the lengths of the waveguide 31B and the waveguide 32B may be different from each other.

[0049] In addition, in each of the above-described embodiments, an example in the case where the waveguide is a distributed-constant type resonator in a qubit has been described, but it is not limited thereto. In a qubit, in addition to a distributed-constant type resonator, a lumped-constant type resonator is also used. In a lumped-constant type resonator, the resonance frequency is not simply determined from the relationship between the length of the resonator and the wavelength. In other words, in a lumped-constant type resonator, the inductance and the capacitance are determined according to the resonance frequency condition represented by the inductance and the capacitance. However, since the resonator is not limited to a linear structure, a high degree of freedom can be provided in the design of the qubit. Also, generally, the footprint of a lumped-constant type qubit is smaller than that of a distributed-constant type. Even in a fishbone-type waveguide, a lumped-constant type resonator can be configured and used for a qubit.

[0050] Therefore, in a resonator including a junction element composed of a Josephson junction and a fishbone-type waveguide coupled by the junction element, the fishbone-type waveguide may be a lumped-constant type resonator.

[0051] Also, in each of the above-described embodiments, an example in the case where the resonators 1, 1A, and 1B are qubits forming half-wavelength resonators has been described, but it is not limited thereto. The resonators 1, 1A, and 1B may be used for superconducting circuits other than qubits.

[0052] The resonator 1, resonator 1A, and resonator 1B of this disclosure have been described above, but this disclosure is not limited to the above-described embodiments. Various changes that can be understood by those skilled in the art can be made to the configuration and details of this disclosure within the scope of this disclosure.

[0053] Note that some or all of the above embodiments may be described as follows in the appended claims, but are not limited thereto. (Appended Claim 1) A junction element composed of a Josephson junction, A fishbone waveguide coupled by the junction element, A resonator comprising the above. (Appended Claim 2) The resonator according to Appended Claim 1, wherein two of the fishbone waveguides are coupled by the junction element. The resonator according to Appended Claim 1. (Appended Claim 3) The resonator according to Appended Claim 1 or 2, further comprising a control line that is magnetically coupled to the junction element and to which a control signal is input, wherein a tip of the control line is disposed near a node of an electric field that is a standing wave generated in the resonator during operation of the resonator. The resonator according to Appended Claim 1 or 2. (Appended Claim 4) The resonator according to Appended Claim 3, wherein a tip of the control line is disposed near the junction element, the control line branches into a first branch line and a second branch line at the tip, and a length of the first branch line is shorter than a length of the second branch line. The resonator according to Appended Claim 3. (Appended Claim 5) The resonator according to Appended Claim 3 or 4, wherein the two fishbone waveguides are each coupled to the junction element via a coplanar waveguide, and a tip of the control line is disposed near the junction element. The resonator according to Appended Claim 3 or 4. (Appended Claim 6) The coplanar waveguide comprises a first coplanar waveguide and a second coplanar waveguide, and a length of the second coplanar waveguide is shorter than a length of the first coplanar waveguide. The resonator described in Supplementary Note 5. (Supplementary Note 7) Two waveguides are coupled by the said coupling element, each of the said two waveguides is a combination of the said fishbone-shaped waveguide and a coplanar waveguide in a straight or curved shape The resonator described in any one of Supplementary Notes 1 to 6. (Supplementary Note 8) The said fishbone-shaped waveguide is a lumped-constant type resonance element The resonator described in Claim 1. (Supplementary Note 9) An oscillator that oscillates the resonator described in any one of Supplementary Notes 3 to 6 by passing an alternating current through the said control line. (Supplementary Note 10) Couple a fishbone-shaped waveguide to a coupling element composed of a Josephson junction A method for manufacturing a resonator.

Explanation of Reference Numerals

[0054] 1, 1A, 1B... resonators, 2... coupling element, 31, 32, 310, 320, 610, 620, 612, 622... fishbone-shaped waveguides

Claims

1. A resonator comprising a Josephson junction element and a fishbone waveguide coupled by the junction element.

2. The resonator according to claim 1, wherein two of the fishbone waveguides are coupled by the junction element.

3. The resonator according to claim 2, further comprising a control line magnetically coupled to the junction element and to which a control signal is input, wherein a tip of the control line is disposed near a node of an electric field which is a standing wave generated in the resonator during operation of the resonator.

4. The resonator according to claim 3, wherein a tip of the control line is disposed near the junction element, the control line branches into a first branch line and a second branch line at the tip, and a length of the first branch line is shorter than a length of the second branch line.

5. The resonator according to claim 3, wherein the two fishbone waveguides are each coupled to the junction element via a coplanar waveguide, and a tip of the control line is disposed near the junction element.

6. The resonator according to claim 5, wherein the coplanar waveguide comprises a first coplanar waveguide and a second coplanar waveguide, and a length of the second coplanar waveguide is shorter than a length of the first coplanar waveguide.

7. The resonator according to claim 2, wherein two waveguides are coupled by the junction element, and the two waveguides are each a combination of the fishbone waveguide and a coplanar waveguide having a linear or curved shape. ​

8. The fishbone-shaped waveguide is a lumped constant type resonance element The resonator according to claim 1.

9. An oscillator that oscillates the resonator according to any one of claims 3 to 6 by flowing an alternating current through the control line.

10. A method of manufacturing a resonator, comprising coupling a fishbone-shaped waveguide to a junction element composed of a Josephson junction ​

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