Travelling-wave parametric amplifier and quantum information processing system

Abstract

There is provided a travelling-wave parametric amplifier comprising: a transmission line; a plurality of unit cells provided along the transmission line; and a resonator coupled to the plurality of unit cells, wherein each unit cell of the plurality of unit cells includes a non-linear inductance element and a shunt capacitor. There is also provided a quantum information processing system comprising: a quantum operation unit that outputs an output signal of qubits; and a travelling-wave parametric amplifier that amplifies the output signal output from the quantum operation unit, wherein the travelling-wave parametric amplifier comprises: a transmission line; a plurality of unit cells provided along the transmission line; and a resonator coupled to the plurality of unit cells, wherein each unit cell of the plurality of unit cells includes a non-linear inductance element and a shunt capacitor.

Description

TRAVELLING-WAVE PARAMETRIC AMPLIFIER AND QUANTUM INFORMATION PROCESSING SYSTEM

[0001] The present invention relates to a travelling-wave parametric amplifier and a quantum information processing system.

[0002] Travelling-wave parametric amplifiers having a Josephson element are disclosed in Non-Patent Literature 1 and others. (Citation List) (Non-Patent Literature) NPL 1: C. Macklin et al., "A near-quantum-limited Josephson traveling-wave parametric amplifier", Science, 350, 6258 (2015). NPL 2: Luca Planat et al., "Photonic-Crystal Josephson Traveling-Wave Parametric Amplifier", PHYSICAL REVIEW X 10, 021021 (2020). NPL 3: Arpit Ranadive et al., "Kerr reversal in Josephson meta-material and traveling wave parametric amplification", NATURE COMMUNICATIONS 13, 1737 (2022). NPL 4: C. Kissling et al., "Vulnerability to Parameter Spread in Josephson Traveling-Wave Parametric Amplifiers", IEEE Transactions on Applied Superconductivity, vol. 33, no. 5, pp. 1-6, Aug. 2023. NPL 5: T. C. White et al., "Traveling wave parametric amplifier with Josephson junctions using minimal resonator phase matching", APPLIED PHYSICS LETTERS 106, 242601 (2015). NPL 6: Kaidong Peng et al., "Floquet-Mode Traveling-Wave Parametric Amplifiers", American Physical Society, PRX Quantum 3, 020306 Published 8 April, 2022. NPL 7: Farzad Faramarzi et al., "A 4-8 GHz Kinetic Inductance Travelling-Wave Parametric Amplifier Using Four-Wave Mixing with Near Quantum-Limit Noise Performance", APL Quantum 1, 036107 (2024). NPL 8: Kevin O'Brien et al., "Resonant Phase Matching of Josephson Junction Traveling Wave Parametric Amplifiers", Phys. Rev. Lett. 113, 157001 (2014). NPL 9: Martina Esposito et al., "Perspective on traveling wave microwave parametric amplifiers", APPLIED PHYSICS LETTERS 119, 120501 (2021).General Disclosure

[0003] According to a first aspect of the present invention, there is provided a travelling-wave parametric amplifier including: a transmission line; a plurality of unit cells provided along the transmission line; and a resonator coupled to the plurality of unit cells. Each unit cell of the plurality of unit cells may include a non-linear inductance element and a shunt capacitor.

[0004] In the travelling-wave parametric amplifiers described above, the resonator may be coupled to the plurality of unit cells adjacent to each other.

[0005] Any of the travelling-wave parametric amplifiers described above may include a group cell including the plurality of unit cells and coupled to the resonator that is common to them.

[0006] Any of the travelling-wave parametric amplifiers described above may include a plurality of the group cells. Any of the travelling-wave parametric amplifiers described above may include a plurality of resonators provided to be individually associated with the plurality of group cells.

[0007] In any of the travelling-wave parametric amplifiers described above, the resonator may be a waveguide resonator.

[0008] In any of travelling-wave parametric amplifiers described above, the resonator may include a shared electrode part provided to face a plurality of the shunt capacitors. The resonator may include an extension part provided to extend in a predetermined length from the shared electrode part.

[0009] In any of the travelling-wave parametric amplifiers described above, the transmission line may include a straight section. The plurality of resonators may be provided along the straight section alternately on one side and another side of the straight section. The plurality of resonators may be provided on both sides of the straight section along the straight section.

[0010] In any of the travelling-wave parametric amplifiers described above, the transmission line may include a curved section. The plurality of resonators may be provided along the curved section on one side of the curved section.

[0011] In any of the travelling-wave parametric amplifiers described above, the non-linear inductance element may include a Josephson junction.

[0012] Any of the travelling-wave parametric amplifiers described above may include ground electrodes provided sandwiching the transmission line therebetween. Any of the travelling-wave parametric amplifiers described above may include a first ground coupling section provided over the transmission line from one of the ground electrodes sandwiching the transmission line therebetween to another of the ground electrodes.

[0013] Any of the travelling-wave parametric amplifiers described above may include a plurality of the first ground coupling sections provided along the transmission line at predetermined intervals.

[0014] In any of the travelling-wave parametric amplifiers described above, the first ground coupling section may cross over the non-linear inductance element.

[0015] In any of the travelling-wave parametric amplifiers described above, a width of the first ground coupling section may gradually change along a length direction of the first ground coupling section.

[0016] In any of the travelling-wave parametric amplifiers described above, the shunt capacitor may include an open stub branched from the transmission line.

[0017] Any of the travelling-wave parametric amplifiers described above may include ground extension parts provided sandwiching the open stub therebetween. Any of the travelling-wave parametric amplifiers described above may include a second ground coupling section provided over the open stub from one of the ground extension parts sandwiching the open stub therebetween to another of the ground extension parts.

[0018] In any of the travelling-wave parametric amplifiers described above, a shortest distance between the resonator and the ground extension parts may be 20 μm or more and 60 μm or less.

[0019] In any of the travelling-wave parametric amplifier described above, a length of the open stub extending from the transmission line may be longer than a length of the ground extension parts extending from the transmission line.

[0020] In any of the travelling-wave parametric amplifiers described above, a length of the first ground coupling section provided over the transmission line may be larger than a length of the second ground coupling section provided over the open stub.

[0021] Any of the travelling-wave parametric amplifiers described above may operate in a cryogenic environment.

[0022] According to a second aspect of the present invention, there is provided a quantum information processing system including: a quantum operation unit that outputs an output signal of qubits; and a travelling-wave parametric amplifier that amplifies the output signal output from the quantum operation unit. The travelling-wave parametric amplifier may include: a transmission line; a plurality of unit cells provided along the transmission line; and a resonator coupled to the plurality of unit cells. Each unit cell of the plurality of unit cells may include a non-linear inductance element and a shunt capacitor.

[0023] The summary clause does not necessarily describe all features of the embodiments of the present invention. The present invention may also be a sub-combination of the features described above.

[0024] Figure 1 shows an example of a configuration of a quantum information processing system 200.Figure 2A shows an example of a configuration of a travelling-wave parametric amplifier 100.Figure 2B shows an enlarged view of a group cell 120.Figure 3A shows an example of a configuration of a non-linear inductance element 20.Figure 3B shows an enlarged view of the vicinity of the unit cells 110.Figure 3C shows an enlarged view around the open stubs 32.Figure 4 shows an enlarged view of a straight section 16 and a curved section 18.Figure 5 shows an example of a circuit diagram of the travelling-wave parametric amplifier 100.Figure 6A shows an example of a circuit diagram of a travelling-wave parametric amplifier 500 of a comparative example.Figure 6B shows another example of a circuit diagram of a travelling-wave parametric amplifier 500 of another comparative example.Figure 7 illustrates a coupled mode of the resonator 60.Figure 8A shows an example of a simulation result of the travelling-wave parametric amplifier 100.Figure 8B shows another example of a simulation result of the travelling-wave parametric amplifier 100.Figure 9A shows an example of a mode profile of the fundamental mode.Figure 9B shows another example of a mode profile of the first harmonic mode.Figure 10A illustrates a simulation result of transmission characteristics of the travelling-wave parametric amplifier 100 with a pump signal mixed.Figure 10B shows quantum efficiency of the travelling-wave parametric amplifier 100.

[0025] Hereinafter, the present invention will be described through embodiments of the present invention, but the following embodiments do not limit the present invention according to the claims. In addition, not all of the combinations of features described in the embodiments are imperative to the solving means of the invention.

[0026] Figure 1 shows an example of a configuration of a quantum information processing system 200. The quantum information processing system 200 may be a quantum computer that performs information processing based on the laws of quantum mechanics. The quantum information processing system 200 of the present example includes a travelling-wave parametric amplifier 100, a quantum operation unit 210, a circulator 220, a qubit resonator 230, a pump signal input unit 240, and an isolator 250.

[0027] The quantum operation unit 210 outputs an output signal of qubits. The quantum operation unit 210 may manipulate a state of qubits using a quantum mechanical phenomenon. The quantum operation unit 210 may be a classical electronic device sending a control signal to the qubit resonator 230. The quantum operation unit 210 may be a superconducting qubit device using a superconducting circuit. The quantum operation unit 210 may input the output signal into the travelling-wave parametric amplifier 100 via the circulator 220 and the pump signal input unit 240.

[0028] The circulator 220 separates the output signal of the quantum operation unit 210 from an input signal into the travelling-wave parametric amplifier 100. By providing the circulator 220, occurrence of noises can be suppressed. In addition, by providing the circulator 220, destruction of qubits due to the back-propagation noise from the travelling-wave parametric amplifier 100 can be suppressed. This allows for enhancing the measurement precision of qubits by the qubit resonator 230.

[0029] The qubit resonator 230 resonates with the qubits manipulated by the quantum operation unit 210 to read the state of the qubits. The qubit resonator 230 may read the state of the qubits by combining a microwave having a predetermined frequency with the qubits. The qubit resonator 230 may include a LC resonator by which a resonant frequency changes depending on the state of qubits.

[0030] The pump signal input unit 240 inputs a pump signal into the travelling-wave parametric amplifier 100. The pump signal is used to amplify the output signal of the quantum operation unit 210 at the travelling-wave parametric amplifier 100. The pump signal input unit 240 inputs the output signal of the quantum operation unit 210 into the travelling-wave parametric amplifier 100 as an input signal into the travelling-wave parametric amplifier 100. The pump signal input unit 240 may input the input signal and the pump signal into the travelling-wave parametric amplifier 100.

[0031] The travelling-wave parametric amplifier 100 outputs an amplified signal obtained by amplifying a weak input signal with a pump signal stronger than the input signal. The travelling-wave parametric amplifier 100 of the present example amplifies the output signal of qubits output from the quantum operation unit 210. The travelling-wave parametric amplifier 100 may include a non-linear element for causing the input signal to interact with the pump signal. A specific configuration of the travelling-wave parametric amplifier 100 will be described below.

[0032] The travelling-wave parametric amplifier 100 may operate in a cryogenic environment. The travelling-wave parametric amplifier 100 operating in the cryogenic environment can reduce thermal noises. Similarly, the quantum information processing system 200 may also operate in the cryogenic environment. That is, the quantum operation unit 210, the circulator 220, the qubit resonator 230, the pump signal input unit 240, and the isolator 250 each may be operated in the cryogenic environment.

[0033] The isolator 250 separates the amplified signal that the travelling-wave parametric amplifier 100 amplified, from a signal internal to the travelling-wave parametric amplifier 100. By providing the isolator 250, reflections of the amplified signal of the travelling-wave parametric amplifier 100 can be suppressed to reduce noises.

[0034] The characteristic impedance of the quantum information processing system 200 of the present example is 50 ohms, but is not limited thereto. By matching characteristic impedances in the quantum information processing system 200, unnecessary reflections of signals can be suppressed to enhance the stability of the system.

[0035] In the present example, although an example where the travelling-wave parametric amplifier 100 is applied to the quantum information processing system 200 has been described, the application form of the travelling-wave parametric amplifier 100 is not limited thereto. The travelling-wave parametric amplifier 100 may be used to amplify a weak signal in other applications such as a Superconducting Quantum Interference Device (SQUID) or encryption communications.

[0036] Figure 2A shows an example of a configuration of the travelling-wave parametric amplifier 100. The travelling-wave parametric amplifier 100 includes a plurality of group cells 120 each including a plurality of unit cells 110. The travelling-wave parametric amplifier 100 of the present example includes M group cells 120. M may be any natural number. The travelling-wave parametric amplifier 100 of the present example includes a transmission line 10, non-linear inductance elements 20, shunt capacitors 30, ground electrodes 40, resonators 60, an input port 102, and an output port 104. The travelling-wave parametric amplifier 100 of the present example is provided on a substrate 150.

[0037] In the description, the travelling-wave parametric amplifier 100 may be described with the Cartesian coordinate axes of an x-axis, a y-axis, and a z-axis. In the description, a plane parallel to an upper surface of the substrate 150 is defined as an x-y plane, and a depth direction of the substrate 150 is defined as the z-axis. Note that, a positive side of a z-axis direction is referred to as "upper", and a negative side of the z-axis direction is referred to as "lower". Herein, "upper", "lower", "front", and "rear" directions are not limited to a direction of gravity, or an installation direction while mounting the travelling-wave parametric amplifier 100.

[0038] The substrate 150 may be a dielectric substrate such as silicon. The substrate 150 may also be another material such as a compound semiconductor.

[0039] The transmission line 10 is an electrically conductive layer provided above the substrate 150. The transmission line 10 connects the input port 102 and the output port 104. The transmission line 10 connects to the input port 102 at an end 12 and connects to the output port 104 at an end 14. The transmission line 10 transmits an input signal input into the input port 102 to the output port 104.

[0040] The transmission line 10 extends along a predetermined direction. The transmission line 10 may extend in a straight line, may extend in a curved line, or may extend to follow a shape in which a straight line and a curved line are combined. The transmission line 10 of the present example extends in a serpentine manner from the end 12 of the input port 102 to the end 14 of the output port 104.

[0041] A material of the transmission line 10 may be a superconducting material. The material of the transmission line 10 may include at least one of: aluminum, tantalum, niobium, niobium nitride, titanium, titanium nitride, copper, gold, silver, tungsten, or palladium. The material of the transmission line 10 may include a material that is the same as that of the non-linear inductance element 20. The material of the transmission line 10 may be the same as a material of a ground electrode 40.

[0042] The unit cell 110 includes a transmission line 10, a non-linear inductance element 20, and a shunt capacitor 30. The plurality of unit cells 110 are coupled to each other via the transmission line 10. Therefore, the plurality of unit cells 110 are provided along the transmission line 10. Any number of unit cells 110 may be provided between the input port 102 and the output port 104. The number of unit cells 110 of the present example is 1000 or more and 5000 or less, but is not limited thereto. By increasing the number of unit cells 110, an amplification factor of the travelling-wave parametric amplifier 100 can be increased.

[0043] A plurality of the non-linear inductance elements 20 are arranged along the transmission line 10. The non-linear inductance element 20 has a non-linear inductance, a magnitude of which changes depending on a magnitude of an electrical current flowing through the transmission line 10. The non-linear inductance element 20 may include a Josephson junction. A specific configuration of the non-linear inductance element 20 will be described below.

[0044] A plurality of the shunt capacitors 30 are arranged along the transmission line 10. The shunt capacitor 30 adds a capacitance to the transmission line 10. The plurality of shunt capacitors 30 may be provided such that each one has any capacitance. Specific structure and arrangement of the shunt capacitors 30 will be described below.

[0045] The ground electrodes 40 are provided above the substrate 150 and set to a ground potential. The ground electrodes 40 may be provided sandwiching the transmission line 10 therebetween. The ground electrodes 40 are provided to be spaced apart from the transmission line 10, the non-linear inductance element 20, and the shunt capacitor 30. A material of the ground electrode 40 may include at least one of: aluminum, tantalum, niobium, niobium nitride, titanium, titanium nitride, copper, gold, silver, tungsten, or palladium.

[0046] The group cells 120 each include a plurality of unit cells 110, and are coupled to a resonator 60 that is common to them. That is, one group cell 120 is coupled to one resonator 60. The group cells 120 of the present example each include the plurality of unit cells 110 arranged successively along the transmission line 10. The plurality of unit cells 110 included in one group cell 120 may be coupled to one resonator 60.

[0047] The plurality of group cells 120 may each have a same structure. The plurality of group cells 120 may each include a same number of unit cells 110. The plurality of group cells 120 may each include a same number of non-linear inductance elements 20 and may each include a same number of shunt capacitors 30. Any number of the plurality of group cells 120 may be provided in the travelling-wave parametric amplifier 100. The travelling-wave parametric amplifier 100 of the present example includes 144 group cells 120, but is not limited thereto.

[0048] Each unit cell of the plurality of unit cells 110 includes a non-linear inductance element 20 and a shunt capacitor 30. The plurality of unit cells 110 may each include a same inductance. The plurality of unit cells 110 may each include a same capacitance.

[0049] The plurality of resonators 60 are provided to be individually associated with the plurality of group cells 120. The resonators 60 are individually coupled to each of the plurality of unit cells 110 included in the associated group cells 120. The plurality of resonators 60 of the present example each have a same structure, but each may have a different structure.

[0050] Here, by having the non-linear element, the travelling-wave parametric amplifier 100 can enable an energy exchange between the pump signal and the input signal to amplify the input signal. In the travelling-wave parametric amplifier 100 of the present example, by having the resonators 60 coupled to the plurality of unit cells 110, a phase matching between the pump signal and the input signal can be enhanced. In the travelling-wave parametric amplifier 100, by enhancing the phase matching, an energy exchange efficiency between the pump signal and the input signal can be enhanced.

[0051] The travelling-wave parametric amplifier 100 of the present example has a structure in which the transmission line 10 is serpentine. The structure of the travelling-wave parametric amplifier 100 may be a straight-line structure, a curved-line structure, a zig-zag structure, or a combined structure thereof. The travelling-wave parametric amplifier 100 of the present example has a structure in which the transmission line 10 is folded twice between the input port 102 and the output port 104 in a serpentine manner. The structure of the travelling-wave parametric amplifier 100 is not limited thereto.

[0052] Figure 2B shows an enlarged view of a group cell 120. The shunt capacitor 30 of the present example includes an open stub 32 and a connecting part 34.

[0053] The group cell 120 includes N unit cells 110. N may be any natural number. The group cell 120 may include 5 or more and 20 or less unit cells 110 or may include 10 or more and 15 or less unit cells 110. The group cell 120 of the present example includes 13 unit cells 110. A number of unit cells 110 included in the group cell 120 is not limited thereto.

[0054] The open stub 32 branches from the transmission line 10. The open stub 32 is provided to be spaced apart from the ground electrode 40, adding a capacitance to the transmission line 10. The unit cells 110 of the present example are arranged on both sides of the transmission line 10, and include two open stubs 32 facing each other sandwiching the transmission line 10 therebetween. However, one of the open stubs 32 of the two open stubs 32 facing each other sandwiching the transmission line 10 may be omitted. The unit cell 110 may have the open stub 32 on only one side of the transmission line 10. There may be a vacuum between the open stub 32 and the ground electrode 40.

[0055] A plurality of the open stubs 32 are provided along the transmission line 10 at predetermined intervals. The plurality of open stubs 32 of the present example are provided equidistantly along the transmission line 10 at the predetermined intervals, but are not limited thereto. An interval of the open stubs 32 adjacent to each other may be larger than a width of the open stub 32. The interval of the open stubs 32 adjacent to each other may be determined by considering an impedance of the transmission line 10 or the like.

[0056] The open stub 32 may be a metal layer provided on the substrate 150. A material of the open stub 32 may include at least one of: aluminum, tantalum, niobium, niobium nitride, titanium, titanium nitride, copper, gold, silver, tungsten, or palladium. The material of the open stub 32 of the present example is aluminum.

[0057] The capacitance of the shunt capacitor 30 may be adjusted depending on a size and position of the open stub 32. For example, the capacitance of the shunt capacitor 30 is adjusted by changing a stub length of the open stub 32. The stub length will be described below. The capacitance of the shunt capacitor 30 may be also adjusted by changing intervals between the open stub 32 and the ground electrode 40.

[0058] The connecting part 34 electrically connects the transmission line 10 and the open stub 32. The connecting part 34 of the present example electrically connects the transmission line 10 to the open stub 32 facing the transmission line 10. The connecting part 34 may cross over the transmission line 10 and electrically connect two open stubs 32 facing each other sandwiching the transmission line 10 therebetween. When the unit cells 110 have the open stub 32 on only one side of the transmission line 10, the connecting part 34 may electrically connect one open stub 32 to the transmission line 10. Note that although the shunt capacitor 30 of the present example includes the connecting part 34, the connecting part 34 may be omitted and the open stub 32 may be directly connected to the transmission line 10. A material of the connecting part 34 may be the same as or different from the material of the ground electrode 40.

[0059] The ground electrodes 40 are provided around the transmission line 10, the shunt capacitors 30, and the resonator 60. The ground electrodes 40 of the present example are arranged along the open stubs 32. The ground electrodes 40 of the present example may be arranged to maintain predetermined intervals from the three sides of the open stub 32. The intervals between the ground electrodes 40 and the open stubs 32 may be constant. The ground electrodes 40 each include a ground electrode part 41 and a ground extension part 42.

[0060] The ground electrode parts 41 are provided around the group cell 120. The ground electrode parts 41 may be arranged adjacent to the open stubs 32. The ground electrode parts 41 may be arranged adjacent to the transmission line 10. The ground electrode parts 41 are provided around the resonator 60. The ground electrode parts 41 are set to a ground potential.

[0061] The ground extension parts 42 extend from the vicinity of the transmission line 10 to be spaced apart from the transmission line 10. The ground extension parts 42 may be provided parallel to the open stubs 32. The ground extension parts 42 may be provided alternately with the open stubs 32. The ground extension parts 42 are provided sandwiching the open stubs 32. The ground extension parts 42 may be sandwiched between the plurality of open stubs 32. The ground extension parts 42 may be set to the ground potential by coupling to the ground electrode parts 41. The ground extension parts 42 may be spaced apart from the ground electrode parts 41. Note that the ground extension parts 42 are electrically connected to the ground electrode parts 41 to be set to the ground potential.

[0062] The resonator 60 is coupled to the plurality of unit cells 110. The resonator 60 of the present example is coupled to the plurality of unit cells 110 adjacent to each other. A material of the resonator 60 may include at least one of: aluminum, tantalum, niobium, niobium nitride, titanium, titanium nitride, copper, gold, silver, tungsten, or palladium. The material of the resonator 60 may be the same as the material of the ground electrode 40. The resonator 60 of the present example includes a shared electrode part 62 and an extension part 64.

[0063] The shared electrode part 62 is provided to face the plurality of shunt capacitors 30. The shared electrode part 62 may have a width large enough to face the plurality of shunt capacitors 30 provided in the group cell 120. The shared electrode part 62 is equivalent to an open-circuit end of the resonator 60. The shared electrode part 62 is provided to be spaced apart from the shunt capacitors 30 and the ground electrodes 40.

[0064] The extension part 64 is provided to extend in a predetermined length from the shared electrode part 62. The shared electrode part 62 and the extension part 64 may be integrally formed. The shared electrode part 62 and the extension part 64 may be integrally formed with the ground electrodes 40. The extension part 64 of the present example has its one end connected to the shared electrode part 62 and another end connected to the ground electrodes 40.

[0065] The resonator 60 may be a waveguide resonator. A resonant frequency of the resonator 60 may be adjusted depending on a size of the shared electrode part 62 and the extension part 64, a distance from the open stubs 32, and the like. The waveguide resonator, due to its manufacturability combined with good control of the resonant frequency, has excellent homogeneity compared to lumped-element LC resonators. This enables a higher yield of the travelling-wave parametric amplifier 100 than the lumped-element LC resonators. In addition, by suppressing variation in characteristics of the resonator 60, the phase matching of the travelling-wave parametric amplifier 100 can be enhanced.

[0066] On the other hand, the waveguide resonator has a larger footprint than the lumped-element LC resonators, so it is not easy to install the waveguide resonators densely enough to enable a continuous phase correction. In addition, as a chip size of the travelling-wave parametric amplifier 100 gets larger, it becomes less easy to obtain homogeneous non-linear inductance elements 20. Furthermore, the waveguide resonator, coupled to the higher harmonic modes, may deteriorate gain profiles.

[0067] In the travelling-wave parametric amplifier 100 of the present example, by coupling each of the resonators 60 to the plurality of unit cells 110, a number of resonators 60 can be reduced. By doing this, it becomes easier to miniaturize the travelling-wave parametric amplifier 100, and the manufacture of the homogeneous non-linear inductance elements 20 can be provided. In addition, the reduction of the number of resonators 60 can cause a reduction in the risk of having a resonator 60 with outstanding resonant frequency, suppressing variation in characteristics. Furthermore, by being coupled to unit cells 110, the resonators 60 can suppress coupling to the higher harmonics modes as described below.

[0068] The resonators 60 may be a waveguide resonator formed with a non-uniform waveguide such that the impedance of the waveguide may vary along the extension part 64. This variation may be introduced to vary the frequency spacing among the modes supported by the waveguide resonator. In an example, the extension part 64 may have a part being 50 ohms impedance and a part being other than 50 ohms impedance. For example, the extension part 64 may have parts being 50 ohms and 40 ohms or may have parts being 50 ohms and 60 ohms. The extension part 64 may have three parts with different impedance. An impedance of a middle part of the extension part 64 may be lower than the impedances of the parts at both ends of the extension part 64. The extension part 64 may have three parts of 50 ohms, 40 ohms, and 50 ohms. The impedance of each part of the extension part 64 may be adjusted by varying the width of the extension part 64. Here, when the impedance of the resonator 60 is uniform, the spacing of the modes is approximately equal, such as 1f, 3f, and 5f, but when the impedance of the resonator 60 is inhomogeneous, it is not equal, such as 1f + delta1, 3f + delta2, 5f + delta3. This principle can be used to suppress the influence on the gain spectrum by dropping unwanted dips caused by higher frequency modes into the band gap.

[0069] Figure 3A shows an example of a configuration of a non-linear inductance element 20. The present drawing shows an enlarged view around the non-linear inductance element 20.

[0070] The non-linear inductance element 20 includes a first junction finger 21 and a second junction finger 22. The non-linear inductance element 20 of the present example includes a Josephson junction 25. The Josephson junction 25 may maintain in a superconducting state during the operation of the travelling-wave parametric amplifier 100.

[0071] The first junction finger 21 is provided on the transmission line 10. The first junction finger 21 may constitute a part of a transmission path of the transmission line 10. The first junction finger 21 may be connected to the transmission line 10 of the adjacent unit cell 110.

[0072] The second junction finger 22 is provided on the transmission line 10. The second junction finger 22 may constitute a part of a transmission path of the transmission line 10. The second junction finger 22 is provided so as to be at least partially overlapped with the first junction finger 21. The second junction finger 22 may be provided above the first junction finger 21 in the overlapped section with the first junction finger 21. That is, the second junction finger 22 may be formed after the first junction finger 21 is formed. The overlapped section of the first junction finger 21 and the second junction finger 22 forms the Josephson junction 25.

[0073] The Josephson junction 25 may include a dielectric film between the first junction finger 21 and the second junction finger 22. The Josephson junction 25 may have a stack structure in which a dielectric film separates two metals. The junction area of the Josephson junction 25 may be adjusted by changing a width of the first junction finger 21 and a width of the second junction finger 22. The inductance of the non-linear inductance element 20 may be adjusted by the junction area of the Josephson junction 25. The dielectric film of the Josephson junction 25 may be an oxide film obtained by oxidizing an upper surface of the first junction finger 21. For example, the Josephson junction 25 has a stack structure of aluminum - aluminum oxide - aluminum.

[0074] The Josephson junction 25 may be formed within an electron beam deposition apparatus. The electron beam deposition apparatus may include an argon ion gun, and may be capable of supplying oxygen gas. This allows the electron beam deposition apparatus to form a stack structure of metal - oxide film - metal. Note that other configurations such as the transmission line 10, the shunt capacitor 30, and the ground electrode 40 may be formed using the electron beam deposition apparatus as well. However, the manufacturing method of the travelling-wave parametric amplifier 100 is not limited thereto.

[0075] Figure 3B shows an enlarged view of the vicinity of the unit cells 110. The unit cell 110 of the present example includes a first ground coupling section 51 and a second ground coupling section 52.

[0076] The first ground coupling section 51 is provided over the transmission line 10 from one of the ground electrodes 40 sandwiching the transmission line 10 therebetween to another of the ground electrodes 40. The first ground coupling section 51 of the present example electrically connects one of the ground extension parts 42 sandwiching the transmission line 10 therebetween and another of the ground extension parts 42. The travelling-wave parametric amplifier 100 of the present example has a plurality of the first ground coupling sections 51 provided along the transmission line 10 at predetermined intervals. For the first ground coupling sections 51 of the present example, one is provided for each four unit cells 110, but this is not limited thereto. The first ground coupling sections 51 may be provided at each distance of any magnitude or may be provided for each any number of unit cells 110. The first ground coupling sections 51 may be repeatedly provided all over the transmission line 10 from the end 12 to the end 14.

[0077] The first ground coupling section 51 may cross over the non-linear inductance element 20. The first ground coupling section 51 is provided to be spaced apart from the non-linear inductance element 20. A space may be provided between the first ground coupling section 51 and the non-linear inductance element 20, and the space between the first ground coupling section 51 and the non-linear inductance element 20 may be a vacuum. The first ground coupling section 51 may cross over the Josephson junction 25. The first ground coupling section 51 of the present example fully covers over the Josephson junction 25, but may also cover only a part of the Josephson junction 25.

[0078] The second ground coupling section 52 crosses over the open stub 32. The second ground coupling section 52 is provided over the open stub 32 from one of the ground extension parts 42 sandwiching the open stub 32 therebetween to another of the ground extension parts 42. The second ground coupling section 52 electrically connects one of the ground extension parts 42 sandwiching the open stub 32 therebetween and another of the ground extension parts 42. The second ground coupling section 52 is provided to be spaced apart from the open stub 32. A space may be provided between the second ground coupling section 52 and the open stub 32, and the space between the second ground coupling section 52 and the open stub 32 may be a vacuum. The second ground coupling section 52 may be provided for each unit cell 110. The adjacent second ground coupling sections 52 may electrically connect to each other.

[0079] By providing the second ground coupling section 52 in the ground extension part 42, the ground extension part 42 spaced apart from the ground electrode part 41 can be set to the ground potential. This allows the resonator 60 to be provided between the ground electrode part 41 and the ground extension part 42, enhancing the flexibility of the arrangement of the resonator 60. By providing the second ground coupling section 52, a ground current can flow along the transmission line 10 over the open stub 32. This allows the ground current to flow through the ground electrode 40 at a position nearer to the transmission line 10.

[0080] The second ground coupling section 52 can reduce unnecessary electrical paths of the ground current to decrease a stray inductance. In this manner, by decreasing the stray inductance, it becomes easier to use the non-linear inductance element 20 with a larger inductance. By using the non-linear inductance element 20 with a larger inductance, the unit cell 110 can have a higher non-linearity. As a result, higher gain characteristics can be achieved. In addition, by providing the second ground coupling section 52, the ground current can flow through the ground electrode 40 at a position nearer to the transmission line 10, so the stray coupling between transmission lines 10 adjacent to each other can be suppressed.

[0081] The first ground coupling section 51 may contact the ground electrode 40 at a same position as that of the second ground coupling section 52. The first ground coupling section 51 of the present example contacts the ground extension part 42 at a same position as that of the second ground coupling section 52. However, the first ground coupling section 51 may contact the ground electrode 40 at a different position from that of the second ground coupling section 52. The first ground coupling section 51 may connect to the ground electrode part 41.

[0082] A length of the first ground coupling section 51 provided over the transmission line 10 may be larger than a length of the second ground coupling section 52 provided over the open stub 32. The length of the first ground coupling section 51 may be 10 μm or more and 100 μm or less. The length of the second ground coupling section 52 may be 10 μm or more and 100 μm or less. The width W51 of the first ground coupling section 51 may gradually change along a length direction of the first ground coupling section 51. The width W51 of the first ground coupling section 51 may be 3 μm or more and 15 μm or less.

[0083] The width W 52 of the second ground coupling section 52 may gradually change along a length direction of the second ground coupling section 52. The width W 52 of the second ground coupling section 52 may be 3 μm or more and 15 μm or less. The width W 52 of the second ground coupling section 52 may be the same as or different from the width W 51 of the first ground coupling section 51. The condition that the width W 52 of the second ground coupling section 52 and the width W 51 of the first ground coupling section 51 are the same may mean that, when the respective widths change along the length direction, the averages of the widths are the same.

[0084] The travelling-wave parametric amplifier 100 of the present example can suppress undesired propagation modes, such as the slot-line mode, to maintain a coplanar waveguide mode (a CPW mode). This allows the travelling-wave parametric amplifier 100 to suppress reflections of signals to enhance the quality of the signal propagation.

[0085] Figure 3C shows an enlarged view around the open stubs 32. The open stubs 32 include an open stub 32a and an open stub 32b.

[0086] The open stub 32a extends from the transmission line 10 toward a direction of the resonator 60 and couples to the resonator 60. The open stub 32a of the present example faces the shared electrode part 62 at its end opposite to an end that faces the transmission line 10. The open stub 32a is sandwiched between two adjacent ground extension parts 42a.

[0087] The open stub 32b extends from the transmission line 10 toward a direction opposite to the resonator 60. The open stub 32b may not face the shared electrode part 62. The open stub 32b faces the ground electrodes 40 at its end opposite to an end that faces the transmission line 10. The open stub 32b is sandwiched between two adjacent ground extension parts 42b. Note that the open stub 32b can be omitted.

[0088] The ground extension part 42a extends from the transmission line 10 toward the direction opposite to the resonator 60. The ground extension part 42a of the present example faces the shared electrode part 62 at its end opposite to an end that faces the transmission line 10.

[0089] The ground extension part 42b extends from the transmission line 10 toward the direction opposite to the resonator 60. The ground extension part 42b may not face the shared electrode part 62. The ground extension part 42b couples to the ground electrode part 41 at its end opposite to an end that faces the transmission line 10.

[0090] A stub length L32a is a length of the open stub 32a. The stub length L32a may be a length of the open stub 32a in a longitudinal direction.

[0091] A stub length L32b is a length of the open stub 32b. The stub length L32b may be a length of the open stub 32b in a longitudinal direction.

[0092] The stub length L32a may be the same as or different from the stub length L32b. The stub length L32a may be 1.5 times or more and 5 times or less the stub length L32b. Note that a relationship between the stub length L32a and the stub length L32b is not limited thereto.

[0093] The open stub 32a may be adjacent to an open stub 32b in an adjacent group cell 120. Similarly, the open stub 32b may be adjacent to an open stub 32a in an adjacent group cell 120. The stub length L32a of the present example is longer than the stub length L32b. By making the stub length L32a longer than the stub length L32b, the open stub 32a can be easily caused to face the resonator 60. Note that the stub length L32a may be the same as the stub length L32b or may be shorter than the stub length L32b.

[0094] A ground length L42a is a length of the ground extension part 42a. The ground length L42a may be a length of the ground extension part 42a in a longitudinal direction. The ground length L42a of the present example is shorter than the stub length L32a. The ground length L42a of the present example is longer than the stub length L32b, but may be the same as the stub length L32b or may be shorter than the stub length L32b.

[0095] The stub length L32a may be longer than the ground length L42a. That is, a length of the open stub 32 extending from the transmission line 10 may be longer than a length of the ground extension part 42 extending from the transmission line 10.

[0096] A distance D32 is a shortest distance between the resonator 60 and the open stub 32a. More specifically, the distance D32 is the shortest distance between the shared electrode part 62 and the open stub 32a. The distance D32 may be larger than an interval between the open stub 32 and the ground electrode 40. A coupling capacitance between the resonator 60 and the shunt capacitor 30 may be adjusted depending on a width of the open stub 32a facing the shared electrode part 62, the distance D32, and the like.

[0097] A distance D42 is a shortest distance between the resonator 60 and the ground extension part 42a. More specifically, the distance D42 is the shortest distance between the shared electrode part 62 and the ground extension part 42a. The distance D42 may be 5 μm or more and 150 μm or less or may be 20 μm or more and 60 μm or less. In an example, the distance D42 is 40 μm. The distance D42 is larger than the distance D32. That is, the ground extension part 42a is spaced further apart from the resonator 60 than the open stub 32a.

[0098] A third ground coupling section 53 connects the ground electrode parts 41 across the extension part 64. The third ground coupling section 53 crosses over the extension part 64. The third ground coupling section 53 is provided to be spaced apart from the extension part 64. A space may be provided between the third ground coupling section 53 and the extension part 64, and the space between the third ground coupling section 53 and the extension part 64 may be a vacuum.

[0099] Here, two ground electrode parts 41 sandwiching the extension part 64 ideally have a same electrical potential, but as the extension part 64 lengthens, they may have different electrical potentials depending on the positions of the ground electrode parts 41. By providing the third ground coupling section 53, the electrical potentials of the two ground electrode parts 41 sandwiching the extension part 64 can be the same. The third ground coupling section 53 may be formed in the same process and at the same time as the first ground coupling section 51 and the second ground coupling section 52.

[0100] Figure 4 shows an enlarged view of a straight section 16 and a curved section 18. The transmission line 10 of the present example includes the straight section 16 and the curved section 18. Note that the transmission line 10 may omit the curved section 18 or may omit the straight section 16.

[0101] The straight section 16 is a region where the transmission line 10 extends in a straight manner. The plurality of resonators 60 are provided along the straight section 16 alternately on one side and another side of the straight section 16. This allows for easily avoiding the interference between adjacent resonators 60. In the present example, a resonator 60a is provided on the one side of the straight section 16, and a resonator 60b is provided on the another side of the straight section 16. Note that the plurality of resonators 60 may be provided only in a region on one of the sides sandwiching the straight section 16, or may be provided in a random manner. The plurality of resonators 60 may be provided on both sides of the straight section 16.

[0102] The curved section 18 is a region where the transmission line 10 extends in a curved manner. The plurality of resonators 60 are provided along the curved section 18 alternately on one side of the curved section 18. In the present example, a plurality of resonators 60c are provided on an outer side of the curved section 18. When the transmission line 10 follows a semi-circular shape or a fan sector shape, the term "outer side of the curved section 18" may refer to an outer side of a circular shape. When the transmission line 10 has an arbitral radius of curvature, the term "outer side of the curved section 18" may refer to a region on a side opposite to a side that follows the radius of curvature. Note that the plurality of resonators 60 may be provided along the curved section 18 alternately on one side and another side of the curved section 18, or may be provided in a random manner. By shortening the length of the transmission line 10, a radius of curvature of the curved section 18 can be larger in the sane chip area.

[0103] In the travelling-wave parametric amplifier 100 of the present example, by changing the arrangement scheme of the resonators 60 tailored to the shape of the transmission line 10, the resonators 60 can be individually coupled to each of the plurality of group cells 120. This allows the resonators 60 to be coupled to all of the unit cells 110 included in the travelling-wave parametric amplifier 100 to achieve a continuous phase matching. Note that although the group cell 120 of the present example is coupled to one resonator 60, the group cell 120 may be coupled to a plurality of resonators 60. The group cell 120 may be coupled to the resonators 60a and 60b. In an example, the open stub 32a may face the resonator 60a and the open stub 32b may face the resonator 60b.

[0104] Figure 5 shows an example of a circuit diagram of the travelling-wave parametric amplifier 100. The travelling-wave parametric amplifier 100 includes M group cells 120. The resonators 60 of the present example are each coupled to the plurality of unit cells 110. The group cells 120 of the present example each include N unit cells 110. The resonators 60 of the present example are individually coupled to each of the N unit cells 110. Each of the group cells 120 may be coupled to a plurality of the resonators 60.

[0105] Lj represents the inductance of the Josephson junction 25. Cj represents the capacitance of the Josephson junction 25. Cg represents the capacitance of the shunt capacitor 30. That is, Cg represents the shunt capacitance with respect to the ground potential of the unit cells 110. Cc is the coupling capacitance which dictates the coupling strength between the resonator 60 and the transmission line 10. The resonators 60 of the present example are each a waveguide resonator.

[0106] In the travelling-wave parametric amplifier 100 of the present example, by using the resonators 60 each coupled to the plurality of unit cells 110, the total number of resonators 60 can be reduced. In the travelling-wave parametric amplifier 100, by changing the number of unit cells 110 to which the resonators 60 couple, the total number of resonators 60 may be adjusted. For example, in the travelling-wave parametric amplifier 100, by increasing the number of unit cells 110 to which the resonators 60 couple, the total number of resonators 60 is reduced. This allows the travelling-wave parametric amplifier 100 to achieve a continuous phase matching without increasing the density of the resonators 60 too much. In the travelling-wave parametric amplifier 100 of the present example, by enhancing the phase matching between the pump signal and the input signal to stabilize its operation, a longer transmission line 10 can be employed to enhance the amplification factor.

[0107] Figure 6A shows an example of a circuit diagram of a travelling-wave parametric amplifier 500 of a comparative example. The travelling-wave parametric amplifier 500 of the present example includes a plurality of unit cells 110 and an LC resonant circuit 560. The LC resonant circuit 560 of the present example is a lumped-element LC resonator. The LC resonant circuit 560 includes an inductance Lr and a capacitance Cr.

[0108] A plurality of the LC resonant circuits 560 are arranged at certain intervals with respect to the transmission line 510. The LC resonant circuit 560 of the present example includes LC resonant circuits 560, one for each four unit cells 110. The LC resonant circuit 560 is coupled to only one node Nc for connecting to the transmission line 510. That is, the LC resonant circuit 560 is not coupled to each of the four unit cells 110.

[0109] In this manner, the travelling-wave parametric amplifier 500 performs a phase correction for each four unit cells 110. Here, the LC resonant circuit 560 may include a parallel plate capacitor and a nanowire inductor connected in parallel. It is not easy to manufacture the LC resonant circuits 560 precisely and homogeneously, and due to variations in parameters such as the capacitance or the inductance, a variation in the resonant frequency of the LC resonant circuits 560 may occur. Thus, although the intervals between the LC resonant circuits 560 can be narrowed to increase the density of the LC resonant circuits 560, a problem concerning the homogeneity of the LC resonant circuits 560 may occur. In addition, it is not easy to form the LC resonant circuits 560 for all of the unit cells 110 without increasing the chip area. So, it is not easy to achieve a fully continuous phase matching.

[0110] Figure 6B shows another example of a circuit diagram of a travelling-wave parametric amplifier 500 of another comparative example. The travelling-wave parametric amplifier 500 of the present example includes a plurality of unit cells 110 and a waveguide resonant circuit 660.

[0111] A plurality of the waveguide resonant circuits 660 are arranged at certain intervals with respect to the transmission line 510. The waveguide resonant circuit 660 is coupled to only one node Nc for connecting to the transmission line 510. Since the area of the waveguide resonant circuit 660 is larger than that of the LC resonant circuit 560, it is not easy to increase the density of the waveguide resonant circuits 660. Thus, the phase correction of the travelling-wave parametric amplifier 500 becomes unintentionally non-continuous, so it is not easy to optimize the characteristics of the travelling-wave parametric amplifier 500.

[0112] Here, unlike the LC resonant circuits 560 which supports only one frequency mode, the waveguide resonant circuit 660 has a plurality of resonant frequencies. That is, the waveguide resonant circuit 660 may couple to unwanted higher harmonics such as a third harmonic mode (3f0), in addition to a fundamental mode (f0). The unnecessary coupling to the harmonic modes may result in dips in the gain spectrum of the waveguide resonant circuit 660.

[0113] In contrast to this, the travelling-wave parametric amplifier 100 can suppress the coupling to the third harmonic mode between the transmission line 10 and the resonator 60 by coupling the resonator 60 to the plurality of unit cells 110. Also, the travelling-wave parametric amplifier 100 may drop dips caused by the third harmonic mode into the band gap depending on the configuration of the resonator 60. Thus, it becomes easier for the travelling-wave parametric amplifier 100 to stably amplify an input signal with a frequency near the fundamental mode.

[0114] Figure 7 illustrates a coupled mode of the resonator 60. The resonator 60 may be a waveguide resonator.

[0115] The solid line represents a waveform of a wave passing through the transmission line 10 at a lower frequency near the fundamental mode (f0) of the resonator 60. The dashed line represents a waveform of a wave passing through the transmission line 10 at a higher frequency near the third harmonic mode (3f0) of the resonator 60. When a pump wave having a lower frequency near the fundamental mode (f0) of the resonator 60 passes through the transmission line 10, a wavelength of the pump wave is longer, so the wavelength appearing along the coupler at any time is approximately half-wavelength. Thus, charges induced in the shared electrode part 62 of the resonator 60 become either positive or negative.

[0116] On the other hand, when a pump wave having a higher frequency near the third harmonic mode (3f0) passes through the transmission line 10, the wavelength of the pump wave is shorter, so there will be a waveform of one or more periods along the coupler. This will cause positive and negative charges to be induced in the shared electrode part 62 of the resonator 60 at the same time. Since a line direction of the resonator 60 is orthogonal to the transmission line 10, the shared electrode part 62 can be considered as one conductor having a single electrical potential at any time. As a result, a high electrical potential is not induced in the shared electrode part 62 even when a pump wave of a high frequency having positive and negative amplitudes in a length direction of the coupler passes through at the same time.

[0117] In this manner, the resonator 60 can provide a low-pass filter effect in coupling to the transmission line 10, suppressing the coupling to a higher frequency near the third harmonic mode (3f0). This allows the resonator 60 to couple to the transmission line 10 in the fundamental mode (f0) to perform the phase matching, achieving an excellent phase-matched gain.

[0118] Figure 8A shows an example of a simulation result of the travelling-wave parametric amplifier 100. In the present example, a wave of a lower frequency near the fundamental mode (f0) propagates through the transmission line 10. The travelling-wave parametric amplifier 100 includes the resonator 60 coupled to the plurality of unit cells 110, and charges of the same sign are induced in each open stub 32. This causes charges of a sign opposite to that in the open stubs 32 to be induced in the shared electrode part 62. In the present example, positive charges are induced at ends of the open stubs 32 facing the shared electrode part 62, and negative charges are induced in the shared electrode part 62.

[0119] Figure 8B shows another example of a simulation result of the travelling-wave parametric amplifier 100. In the present example, a wave of a higher frequency near the third harmonic mode (3f0) propagates through the transmission line 10. The travelling-wave parametric amplifier 100 includes open stubs 32 in which positive charges are induced and open stubs 32 in which negative charges are induced at any time. Accordingly, in the shared electrode part 62, there are regions where positive charges are induced and regions where negative charges are induced. Thus, the electrical potential induced in the shared electrode part 62 becomes substantially weak, and the coupling to the signal near the third harmonic mode (3f0) can be suppressed.

[0120] Figure 9A shows an example of a mode profile of the fundamental mode. In the present example, a calculation was done in the fundamental mode of 8.02 GHz, and the Q-factor was 682.86.

[0121] Figure 9B shows another example of a mode profile of the first harmonic mode. In the present example, a calculation was done in the first harmonic mode of 23.7 GHz in comparison to the fundamental mode, and the Q-factor was 5122.5. In this manner, the coupling strength for the first harmonic mode is almost an order of magnitude weaker than for the fundamental mode.

[0122] Figure 10A illustrates a simulation result of transmission characteristics of the travelling-wave parametric amplifier 100 with a pump signal mixed. The present drawing illustrates a gain simulation result using a harmonic balance method. The vertical axis represents transmission characteristics (dB), and the horizontal axis represents frequencies (GHz) of a signal to be transmitted. The travelling-wave parametric amplifier 100 of the present example includes 142 group cells 120 on a 5 × 15 mm chip. In the present example, each group cell 120 has 14 unit cells 110.

[0123] S21 represents a forward transfer coefficient of the travelling-wave parametric amplifier 100. S12 represents a backward transfer coefficient of the travelling-wave parametric amplifier 100. S11 represents an input reflection coefficient of the travelling-wave parametric amplifier 100. S22 represents an output reflection coefficient of the travelling-wave parametric amplifier 100.

[0124] In a bandgap, the forward transfer coefficient S21 decreases and the input reflection coefficient S11 and the output reflection coefficient S22 increase. The forward transfer coefficient S21 of the travelling-wave parametric amplifier 100 exhibits a wideband transmittance above 20 dB until the frequency of the bandgap is reached and the forward transfer coefficient drops rapidly. The input reflection coefficient S11 and the output reflection coefficient S22 exhibit a low value of around -20 dB until the frequency of the bandgap is reached and they change rapidly.

[0125] The travelling-wave parametric amplifier 100 can provide a precise and narrow bandgap for phase correction to form a band-stop response. This allows for enhancing the gain without forming a large bandgap, making it less susceptible to inhomogeneity in critical current in the Josephson junction 25.

[0126] Figure 10B shows quantum efficiency of the travelling-wave parametric amplifier 100. The vertical axis represents a ratio of the quantum efficiency QE to an ideal quantum efficiency QE_ideal, and the horizontal axis represents frequencies (GHz) of a signal to be transmitted. The travelling-wave parametric amplifier 100 of the present example exhibits a characteristic near the ideal quantum efficiency in regions of both ends of the bandgap.

[0127] While the present invention has been described by way of the embodiments, the technical scope of the present invention is not limited to the above described embodiments. It is apparent to persons skilled in the art that various alterations or improvements can be made to the above described embodiments. It is also apparent from the described scope of the claims that the embodiments added with such alterations or improvements can be included the technical scope of the present invention.

[0128] Each process such as the operations, procedures, steps, and stages performed by a device, system, program, and method shown in the claims, description, or drawings can be performed in any order unless the order is indicated by "prior to," "before," or the like or the output from a previous process is used in a later process. Even if an operation flow is described using phrases such as "first" or "next" in the claims, description, or drawings for convenience purpose, it does not necessarily mean that the operations must be performed in this order.

[0129] 10: transmission line; 　　12: end; 　　14: end; 　　16: straight section; 　　18: curved section; 　　20: non-linear inductance element; 　　21: first junction finger; 　　22: second junction finger; 　　25: Josephson junction; 　　30: shunt capacitor; 　　32: open stub; 　　34: connecting part; 　　40: ground electrode; 　　41: ground electrode part; 　　42: ground extension part; 　　51: first ground coupling section; 　　52: second ground coupling section; 　　53: third ground coupling section; 　　60: resonator; 　　62: shared electrode part; 　　64: extension part; 　　100: travelling-wave parametric amplifier; 　　102: input port; 　　104: output port; 　　110: unit cell; 　　120: group cell; 　　150: substrate; 　　200: quantum information processing system 　　210: quantum operation unit; 　　220: circulator; 　　230: qubit resonator; 　　240: pump signal input unit; 　　250: isolator; 　　500: travelling-wave parametric amplifier; 　　510: transmission line; 　　560: LC resonant circuit; 　　660: waveguide resonant circuit.

Claims

1. A travelling-wave parametric amplifier comprising: 　　a transmission line; 　　a plurality of unit cells provided along the transmission line; and 　　a resonator coupled to the plurality of unit cells, wherein 　　each unit cell of the plurality of unit cells includes a non-linear inductance element and a shunt capacitor.

2. The travelling-wave parametric amplifier according to claim 1, wherein the resonator is coupled to the plurality of unit cells adjacent to each other.

3. The travelling-wave parametric amplifier according to claim 1, comprising: 　　a group cell including the plurality of unit cells and coupled to the resonator that is common to them.

4. The travelling-wave parametric amplifier according to claim 3, comprising: 　　a plurality of the group cells; and 　　a plurality of resonators provided to be individually associated with the plurality of group cells.

5. The travelling-wave parametric amplifier according to claim 1, wherein the resonator is a waveguide resonator.

6. The travelling-wave parametric amplifier according to claim 1, wherein the resonator includes: 　　a shared electrode part provided to face a plurality of the shunt capacitors; and 　　an extension part provided to extend in a predetermined length from the shared electrode part.

7. The travelling-wave parametric amplifier according to claim 4, wherein 　　the transmission line includes a straight section, and 　　the plurality of resonators are provided along the straight section alternately on one side and another side of the straight section, or on both sides of the straight section.

8. The travelling-wave parametric amplifier according to claim 4, wherein 　　the transmission line includes a curved section, and 　　the plurality of resonators are provided along the curved section on one side of the curved section.

9. The travelling-wave parametric amplifier according to claim 1, wherein the non-linear inductance element includes a Josephson junction.

10. The travelling-wave parametric amplifier according to any one of claims 1 to 9, comprising: 　　ground electrodes provided sandwiching the transmission line therebetween; and 　　a first ground coupling section provided over the transmission line from one of the ground electrodes sandwiching the transmission line therebetween to another of the ground electrodes.

11. The travelling-wave parametric amplifier according to claim 10, comprising: 　　a plurality of the first ground coupling sections provided along the transmission line at predetermined intervals.

12. The travelling-wave parametric amplifier according to claim 10, wherein the first ground coupling section crosses over the non-linear inductance element.

13. The travelling-wave parametric amplifier according to claim 10, wherein a width of the first ground coupling section gradually changes along a length direction of the first ground coupling section.

14. The travelling-wave parametric amplifier according to claim 1, wherein the shunt capacitor includes an open stub branched from the transmission line.

15. The travelling-wave parametric amplifier according to claim 14, comprising: 　　ground extension parts provided sandwiching the open stub therebetween; and 　　a second ground coupling section provided over the open stub from one of the ground extension parts sandwiching the open stub therebetween to another of the ground extension parts.

16. The travelling-wave parametric amplifier according to claim 15, wherein a shortest distance between the resonator and the ground extension parts is 20 μm or more and 60 μm or less.

17. The travelling-wave parametric amplifier according to claim 15, wherein a length of the open stub extending from the transmission line is longer than a length of the ground extension parts extending from the transmission line.

18. The travelling-wave parametric amplifier according to claim 15, wherein a length of the first ground coupling section provided over the transmission line is larger than a length of the second ground coupling section provided over the open stub.

19. The travelling-wave parametric amplifier according to any one of claims 1 to 9, which operates in a cryogenic environment.

20. A quantum information processing system comprising: 　　a quantum operation unit that outputs an output signal of qubits; and 　　a travelling-wave parametric amplifier that amplifies the output signal output from the quantum operation unit, wherein 　　the travelling-wave parametric amplifier comprises: 　　a transmission line; 　　a plurality of unit cells provided along the transmission line; and 　　a resonator coupled to the plurality of unit cells, wherein 　　each unit cell of the plurality of unit cells includes a non-linear inductance element and a shunt capacitor.

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