Travelling-wave parametric amplifier and quantum information processing system

Abstract

There is provided a travelling-wave parametric amplifier including: a plurality of group cells each including a plurality of unit cells, wherein the plurality of unit cells include: a transmission line that extends along a predetermined direction; and non-linear inductance elements and shunt capacitors arranged along the transmission line, wherein a respective group cell of the plurality of group cells comprises a periodic structure in which the non-linear inductance elements and the shunt capacitors periodically change along the transmission line, and wherein the plurality of group cells comprise a modulation structure in which the non-linear inductance elements and the shunt capacitors modulate along the transmission line.

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] Patent Literature 1 discloses a travelling-wave parametric amplifier including a plurality of Josephson elements. (Citation List) (Patent Literature) PTL 1: Japanese Patent No. 7064057 (Non-Patent Literature) NPL 1: Luca Planat et al., "Photonic-Crystal Josephson Traveling-Wave Parametric Amplifier", PHYSICAL REVIEW X 10, 021021 (2020). NPL 2: C. Macklin et al., "A near-quantum-limited Josephson traveling-wave parametric amplifier", Science, 350, 6258 (2015). NPL 3: Arpit Ranadive et al., "Kerr reversal in Josephson meta-material and traveling wave parametric amplification", NATURE COMMUNICATIONS 13, 1737 (2022). NPL 4: S. Shu et al., "Nonlinearity and wide-band parametric amplification in a (Nb,Ti)N microstrip transmission line", PHYSICAL REVIEW RESEARCH 3, 023184 (2021). NPL 5: S. O' Peata'in et al., "The Effect of Parameter Variations on the Performance of the Josephson Travelling Wave Parametric Amplifiers", arXiv:2112.07766 (2021).General Disclosure

[0003] According to a first aspect of the present invention, there is provided a travelling-wave parametric amplifier including a plurality of group cells each including a plurality of unit cells. The plurality of unit cells may include: a transmission line that extends along a predetermined direction; and non-linear inductance elements and shunt capacitors arranged along the transmission line. A respective group cell of the plurality of group cells may include a periodic structure in which the non-linear inductance elements and the shunt capacitors periodically change along the transmission line. The plurality of group cells may include a modulation structure in which the non-linear inductance elements and the shunt capacitors modulate along the transmission line.

[0004] In any of the travelling-wave parametric amplifiers, each shunt capacitor of the shunt capacitors may include an open stub branched from the transmission line. Stub length of the open stubs may modulate along the transmission line between the plurality of group cells.

[0005] In any of the travelling-wave parametric amplifiers, periodic maximum stub lengths of the open stubs in the periodic structures may gradually increase along the transmission line from an end of the transmission line in the modulation structure. Periodic minimum stub lengths of the open stubs in the periodic structures may gradually decrease along the transmission line from an end of the transmission line in the modulation structure.

[0006] In any of the travelling-wave parametric amplifiers, a modulation amplitude proportion of a modulation maximum stub length of the open stub in the modulation structure of the plurality of group cells may be 5% or more and 13% or less.

[0007] In any of the travelling-wave parametric amplifiers, each non-linear inductance element of the non-linear inductance elements may include a Josephson junction, Junction areas of the Josephson junctions may modulate along the transmission line between the plurality of group cells.

[0008] In any of the travelling-wave parametric amplifiers, the non-linear inductance element may include: a first junction finger provided on the transmission line; and a second junction finger provided so as to be at least partially overlapped with the first junction finger. An overlapped section of the first junction finger and the second junction finger may form the Josephson junction.

[0009] In any of the travelling-wave parametric amplifiers, periodic maximum junction areas of the Josephson junctions in the periodic structures may gradually increase along the transmission line from an end of the transmission line in the modulation structure. Periodic minimum junction areas of the Josephson junctions in the periodic structures may gradually decrease along the transmission line from an end of the transmission line in the modulation structure.

[0010] In any of the travelling-wave parametric amplifiers, a modulation amplitude proportion of a modulation maximum junction area of the Josephson junction in the modulation structure of the plurality of group cells may be 5% or more and 13% or less.

[0011] In any of the travelling-wave parametric amplifiers, the plurality of group cells may comprise an envelope on the periodic structure in which the non-linear inductance elements and the shunt capacitors modulate along the transmission line.

[0012] In any of the travelling-wave parametric amplifiers, the plurality of group cells may have the modulation structure having a window function, where the modulation strength gradually changes along the transmission line.

[0013] In any of the travelling-wave parametric amplifiers, the plurality of group cells may have the modulation structure having a window function, where the modulation strength gradually changes, is repeated multiple times along the transmission line.

[0014] Any of the travelling-wave parametric amplifiers may include 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.

[0015] Any of the travelling-wave parametric amplifiers may include a plurality of the first ground coupling sections provided along the transmission line at predetermined intervals.

[0016] In any of the travelling-wave parametric amplifiers, the first ground coupling section may cross over the non-linear inductance element.

[0017] In any of the travelling-wave parametric amplifiers, a width of the first ground coupling section may gradually change along a length direction of the first ground coupling section.

[0018] Any of the travelling-wave parametric amplifiers may include ground electrodes provided sandwiching the open stub therebetween; and a second ground coupling section provided over the open stub from one of the ground electrodes sandwiching the open stub therebetween to another of the ground electrodes.

[0019] In any of the travelling-wave parametric amplifiers, a length of a first ground coupling section provided over the transmission line is larger than a length of a second ground coupling section provided over the open stub.

[0020] Any of the travelling-wave parametric amplifiers may include a helical structure in which the transmission line is helically arranged.

[0021] Any of the travelling-wave parametric amplifiers 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. Any of the travelling-wave parametric amplifiers may include a plurality of group cells each including a plurality of unit cells. The plurality of unit cells may include: a transmission line that extends along a predetermined direction; and non-linear inductance elements and shunt capacitors arranged along the transmission line. A respective group cell of the plurality of group cells may include a periodic structure in which the non-linear inductance elements and the shunt capacitors periodically change along the transmission line. The plurality of group cells may include a modulation structure in which the non-linear inductance elements and the shunt capacitors modulate along the transmission line.

[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 example of an enlarged view of a plurality of unit cells 110.Figure 3A shows an example of a periodic structure of shunt capacitors 30.Figure 3B shows an enlarged view of two adjacent group cells 120.Figure 4A shows an example of a configuration of a non-linear inductance element 20.Figure 4B shows an example of a periodic structure of a non-linear inductance element 20.Figure 4C shows an enlarged view of two adjacent group cells 120.Figure 5 shows an enlarged view near a first ground coupling section 51 and a second ground coupling section 52.Figure 6A shows an example of an enlarged view of the travelling-wave parametric amplifier 100.Figure 6B shows a graph illustrating a modulation structure of the travelling-wave parametric amplifier 100.Figure 7A shows a travelling-wave parametric amplifier 500 according to a comparative example.Figure 7B shows an example of a periodic structure of the travelling-wave parametric amplifier 500.Figure 8A shows a simulation result of transmission characteristics of the travelling-wave parametric amplifier 500 according to the comparative example.Figure 8B shows a simulation result of a transmission characteristic of the travelling-wave parametric amplifier 100.Figure 9A shows an experimental result of a transmission characteristic of the travelling-wave parametric amplifier 500 that has not mixed a pump signal.Figure 9B shows an experimental result of transmission characteristics of the travelling-wave parametric amplifier 100 that has not mixed a pump signal.Figure 10A shows transmission characteristics of the travelling-wave parametric amplifier 500 that has mixed a pump signal.Figure 10B shows transmission characteristics of the travelling-wave parametric amplifier 100 that has mixed a pump signal.

[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 a transmission line 10, non-linear inductance elements 20, shunt capacitors 30, 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, let an x-y plane be a plane parallel to an upper surface of the substrate, and the z-axis be a depth direction of the substrate. 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 during 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 helically.

[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 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. Any number of the unit cells 110 may be provided between the input port 102 and the output port 104. A 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 includes at least one of: aluminum, tantalum, niobium, niobium nitride, titanium, titanium nitride, copper, gold, silver, tungsten, or palladium.

[0046] The group cell 120 includes a plurality of unit cells 110. The group cell 120 includes a periodic structure in which the plurality of unit cells 110 periodically change along the transmission line 10. Each group cell 120 of the plurality of group cells 120 may include a periodic structure.

[0047] The periodic structure may have an inductance that periodically changes along the transmission line 10, or may have a capacitance that periodically changes along the transmission line 10. The periodic structure may have both the inductance and the capacitance that periodically change along the transmission line 10. The periodic structure may have an inductance that sinusoidally changes along the transmission line 10, or may have a capacitance that sinusoidally changes along the transmission line 10. Details of the periodic structure will be described below.

[0048] 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. By having the periodic structure, the travelling-wave parametric amplifier 100 of the present example can enhance a phase consistency between the pump signal and the input signal. By enhancing the phase consistency, the travelling-wave parametric amplifier 100 can enhance an energy exchange efficiency between the pump signal and the input signal.

[0049] The travelling-wave parametric amplifier 100 of the present example has a helical structure in which the transmission line 10 is helically arranged. The transmission line 10 of the present example has a helical structure in which the transmission line 10 helically extends from the outer side of the helical structure, at which the input port 102 is provided, to the inner side, and further helically extends from the inner side to the outer side to reach the output port 104. That is, an end 12 and an end 14 of the transmission line 10 are arranged at the outer side of the helical structure. Note that the structure of the travelling-wave parametric amplifier 100 is not limited to the helical structure, and may be a straight structure, a curved structure, a zig-zag structure, or a combination thereof.

[0050] The plurality of group cells 120 have a modulation structure in which the plurality of unit cells 110 modulate along the transmission line 10. The plurality of group cells 120 may have a modulation structure in which the periodic structures of the group cells 120 modulate along the transmission line 10. At least one of the non-linear inductance element 20 or the shunt capacitor 30 may modulate along the transmission line 10 between the plurality of group cells 120. The modulation structure may comprise an envelope on the periodic structure in which the non-linear inductance elements 20 and the shunt capacitors 30 modulate along the transmission line 10. Details of the modulation structure will be described below. A number of the plurality of group cells 120 provided in the travelling-wave parametric amplifier 100 may be arbitrary.

[0051] Figure 2B shows an example of an enlarged view of the plurality of unit cells 110. The shunt capacitor 30 of the present example includes an open stub 32 and a connecting part 34. The unit cell 110 of the present example includes a first ground coupling section 51 and a second ground coupling section 52.

[0052] 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 to each other sandwiching the transmission line 10 therebetween. There may be a vacuum between the open stub 32 and the ground electrode 40.

[0053] The plurality of 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.

[0054] 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.

[0055] The capacitance of the shunt capacitor 30 may be adjusted depending on the size of the open stub 32. For example, the capacitance of the shunt capacitor 30 is adjusted by changing a stub length L of the open stub 32. The capacitance of the shunt capacitor 30 may be also adjusted by changing the interval between the open stub 32 and the ground electrode 40.

[0056] The connecting part 34 electrically connects the transmission line 10 and the open stubs 32. The connecting part 34 of the present example electrically connects the transmission line 10 and two open stubs 32 facing to each other. The connecting part 34 may electrically connect the two open stubs 32 facing to each other. The connecting part 34 may be formed from a same material as those of the first ground coupling section 51 and the second ground coupling section 52. 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.

[0057] The ground electrodes 40 are provided sandwiching the transmission line 10 therebetween. The ground electrodes 40 are arranged along the open stubs 32. The ground electrodes 40 may be provided sandwiching the open stub 32 therebetween. The ground electrodes 40 of the present example may be arranged so as 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.

[0058] 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 electrically connects the one of the ground electrodes 40 sandwiching the transmission line 10 therebetween and the another of the ground electrodes 40. 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 five unit cells 110, but 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.

[0059] Here, two ground electrodes 40 that sandwiches the transmission line 10 ideally have a same electrical potential, but as the transmission line 10 lengthens, they may have different electrical potentials depending on the positions of the ground electrodes 40. By providing the first ground coupling section 51, the electrical potentials of the two ground electrodes 40 that sandwich the transmission line 10 can be the same.

[0060] The second ground coupling section 52 is provided over the open stub 32 from one of the ground electrodes 40 sandwiching the open stub 32 therebetween to another of the ground electrodes 40. The second ground coupling section 52 electrically connects the one of the ground electrodes 40 sandwiching the open stub 32 therebetween and the another of the ground electrodes 40. 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. 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.

[0061] 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. Using the non-linear inductance element 20 with the larger inductance may allow the unit cell 110 to have a higher non-linearity, resulting in higher gain performance and the use of shorter total lengths of the transmission line 10. 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.

[0062] 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. In addition, the cross talk between the transmission lines 10 adjacent to each other in the helical structure can be reduced to enhance the noise performance.

[0063] Figure 3A shows an example of a periodic structure of shunt capacitors 30. Although the group cell 120 of the present example includes thirteen unit cells 110a to 110m, a number of unit cells 110 included in the group cell 120 is not limited thereto. In the present drawing, the first ground coupling section 51 and the second ground coupling section 52 are omitted to briefly describe the configuration of the shunt capacitors 30.

[0064] The group cell 120 includes a periodic structure in which the capacitances of the shunt capacitors 30 periodically change along the transmission line 10. The group cell 120 of the present example includes a periodic structure in which the stub lengths L of the shunt capacitors 30 periodically change along the transmission line 10. The group cell 120 of the present example includes a periodic structure in which the stub lengths L change with a predetermined stub length L set as a mean. In the group cell 120 of the present example, the stub lengths L of the open stubs 32 change sinusoidally from the unit cell 110a to the unit cell 110m.

[0065] A periodic average stub length Lp(ave) is an average of the stub lengths L in the periodic structure of the group cell 120. The periodic average stub length Lp(ave) of the present example is an average of the stub lengths L of the unit cell 110a to the unit cell 110m. The group cell 120 of the present example has the shunt capacitors 30 having the periodic average stub length Lp(ave) at the unit cell 110a, the unit cell 110g, and the unit cell 110m. That is, the respective stub lengths L of the open stub 32a, the open stub 32g, and the open stub 32m are the periodic average stub length Lp(ave).

[0066] A periodic maximum stub length Lp(max) is the maximum stub length L in the periodic structure of the group cell 120. The group cell 120 of the present example has the shunt capacitor 30 having the periodic maximum stub length Lp(max) at the unit cell 110d. That is, the stub length L of the open stub 32d is the periodic maximum stub length Lp(max). In the unit cells 110 between the unit cell 110 having the periodic average stub length Lp(ave) and the unit cell 110 having the periodic maximum stub length Lp(max), the stub lengths L may gradually change from the periodic average stub length Lp(ave) to the periodic maximum stub length Lp(max).

[0067] A periodic minimum stub length Lp(min) is the minimum stub length L in the periodic structure of the group cell 120. The group cell 120 of the present example has the shunt capacitor 30 having the periodic minimum stub length Lp(min) at the unit cell 110j. That is, the stub length L of the open stub 32j is the periodic minimum stub length Lp(min). In the unit cells 110 between the unit cell 110 having the periodic average stub length Lp(ave) and the unit cell 110 having the periodic minimum stub length Lp(min), the stub lengths L may gradually change from the periodic average stub length Lp(ave) to the periodic minimum stub length Lp(min).

[0068] The group cell 120 of the present example includes a periodic structure in which the stub lengths change with the periodic average stub length Lp(ave) as a mean. That is, an amplitude represented by a difference between the periodic maximum stub length Lp(max) and the periodic average stub length Lp(ave) is equal to an amplitude represented by a difference between the periodic minimum stub length Lp(min) and the periodic average stub length Lp(ave). However, the amplitude represented by the difference between the periodic maximum stub length Lp(max) and the periodic average stub length Lp(ave) may be different from the amplitude represented by the difference between the periodic minimum stub length Lp(min) and the periodic average stub length Lp(ave).

[0069] Figure 3B shows an enlarged view of two adjacent group cells 120. In the present drawing, as an example of the group cells 120, a group cell 120A and a group cell 120B are shown. The group cell 120A is an example of a first group cell. The group cell 120B is an example of a second group cell.

[0070] The plurality of group cells 120 include a modulation structure in which the periodic structures of the group cells 120 adjacent to each other gradually change. The plurality of group cells 120 may have a modulation structure in which the capacitances of the periodic structures modulate along the transmission line 10. The capacitances of the modulation structure may be modulated by changing the stub lengths L of the open stubs 32. The stub lengths L of the open stubs 32 of the present example modulate along the transmission line 10 between the plurality of group cells 120. By the modulation structure in which the periodic structures gradually change, a gain ripple can be suppressed.

[0071] The periodic structure of the shunt capacitors 30 of the group cell 120A may be different from the periodic structure of the shunt capacitors 30 of the group cell 120B. In this case, the periodic average stub length Lp(ave) of the group cell 120A may be different from the periodic average stub length Lp(ave) of the group cell 120B. The periodic maximum stub length Lp(max) of the group cell 120A may be different from the periodic maximum stub length Lp(max) of the group cell 120B. The periodic minimum stub length Lp(min) of the group cell 120A may be different from the periodic minimum stub length Lp(min) of the group cell 120B.

[0072] In the present example, a number of the unit cells 110 of each group cell 120 is the same, but may be different from each other. The group cell 120 of the present example includes thirteen unit cells 110, but is not limited thereto.

[0073] An amount of change of the group cells 120 adjacent to each other may be 10% or less, may be 5% or less, or may be 3% or less. The amount of change of the group cells 120 adjacent to each other may be an amount of change of the periodic average stub lengths Lp(ave) of the respective adjacent group cells 120, may be an amount of change the periodic maximum stub lengths Lp(max), or may be an amount of change of the periodic minimum stub lengths Lp(min).

[0074] Although the transmission line 10 of the present example extends in a substantially straight line, the transmission line 10 may also have a helical structure shown in Figure 2A and Figure 2B. In the present example, although the shunt capacitors 30 of the adjacent group cells 120 have been described, the non-linear inductance elements 20 may also have a modulation structure.

[0075] Figure 4A shows an example of an configuration of a non-linear inductance element 20. The present drawing shows an enlarged view around a non-linear inductance element 20.

[0076] 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.

[0077] 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.

[0078] 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.

[0079] W21 is a finger width of the first junction finger 21. W22 is a finger width of the second junction finger 22. The first junction finger 21 and the second junction finger 22 may have any finger width. The first junction finger 21 of the present example has a same finger width as that of the second junction finger 22, but may also have a different finger width from that of the second junction finger 22. The finger widths of the first junction finger 21 and the second junction finger 22 may be 0.5 μm or more and 2 μm or less. The finger widths of the first junction finger 21 and the second junction finger 22 may be changed to adjust a magnitude of a junction area S of the Josephson junction 25.

[0080] 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 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.

[0081] 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.

[0082] Figure 4B shows an example of a periodic structure of the non-linear inductance elements 20. Although the group cell 120 of the present example includes thirteen unit cells 110a to 110m, a number of unit cells 110 included in the group cell 120 is not limited thereto. In the present drawing, the first ground coupling section 51 and the second ground coupling section 52 are omitted to briefly describe the configuration of the non-linear inductance elements 20.

[0083] The group cell 120 includes a periodic structure in which the inductances of the non-linear inductance elements 20 periodically change along the transmission line 10. The group cell 120 of the present example includes a periodic structure in which the junction areas S of the Josephson junctions 25 periodically change along the transmission line 10. The group cell 120 of the present example includes a periodic structure in which the junction areas change with a predetermined junction area S set as a mean. In the group cell 120 of the present example, the junction areas S of the Josephson junctions 25 change sinusoidally from the unit cell 110a to the unit cell 110m.

[0084] A periodic average junction area Sp(ave) is an average of the junction areas S of the Josephson junctions 25 in the periodic structure of the group cell 120. The periodic average junction area Sp(ave) of the present example is an average of the junction areas S of the unit cell 110a to the unit cell 110m. The group cell 120 of the present example has the Josephson junctions 25 having the periodic average junction area Sp(ave) at the unit cell 110a, the unit cell 110g, and the unit cell 110m. That is, the respective junction areas S of the non-linear inductance element 20a, the non-linear inductance element 20g, and the non-linear inductance element 20m are the periodic average junction area Sp(ave).

[0085] A periodic maximum junction area Sp(max) is the junction area S of the maximum Josephson junction 25 in the periodic structure of the group cell 120. The group cell 120 of the present example has the Josephson junction 25 having the periodic maximum junction area Sp(max) at the unit cell 110d. That is, the junction area S of the non-linear inductance element 20d is the periodic maximum junction area Sp(max). In the unit cells 110 between the unit cell 110 having the periodic average junction area Sp(ave) and the unit cell 110 having the periodic maximum junction area Sp(max), the junction areas S may gradually change from the periodic average junction area Sp(ave) to the periodic maximum junction area Sp(max).

[0086] A periodic minimum junction area Sp(min) is the junction area S of the minimum Josephson junction 25 in the periodic structure of the group cell 120. The group cell 120 of the present example has the Josephson junction 25 having the periodic minimum junction area Sp(min) at the unit cell 110j. That is, the junction area S of the non-linear inductance element 20j is the periodic minimum junction area Sp(min). In the unit cells 110 between the unit cell 110 having the periodic average junction area Sp(ave) and the unit cell 110 having the periodic minimum junction area Sp(min), the junction areas S may gradually change from the periodic average junction area Sp(ave) to the periodic minimum junction area Sp(min).

[0087] The group cell 120 of the present example includes a periodic structure in which the junction areas change with a periodic average junction area Sp(ave) set as a mean. That is, an amplitude represented by a difference between the periodic maximum junction area Sp(max) and the periodic average junction area Sp(ave) is equal to an amplitude represented by a difference between the periodic minimum junction area Sp(min) and the periodic average junction area Sp(ave). However, the amplitude represented by the difference between the periodic maximum junction area Sp(max) and the periodic average junction area Sp(ave) may be different from the amplitude represented by the difference between the periodic minimum junction area Sp(min) and the periodic average junction area Sp(ave).

[0088] Figure 4C shows an enlarged view of two adjacent group cells 120. In the present drawing, as an example of the group cells 120, a group cell 120A and a group cell 120B are shown.

[0089] The plurality of group cells 120 include a modulation structure in which the periodic structures of the group cells 120 adjacent to each other gradually change. The plurality of group cells 120 may have a modulation structure in which the inductances of the periodic structures modulate along the transmission line 10. The inductances of the modulation structure may be modulated by changing the junction areas S of the Josephson junctions 25. The junction areas S of the Josephson junctions 25 of the present example modulate along the transmission line 10 between the plurality of group cells 120. The junction areas S of the Josephson junctions 25 may be adjusted by changing the finger widths of the non-linear inductance elements 20. By the modulation structure in which the periodic structures gradually change, a gain ripple can be suppressed.

[0090] The periodic structure of the non-linear inductance elements 20 of the group cell 120A may be different from the periodic structure of the non-linear inductance elements 20 of the group cell 120B. The periodic average junction area Sp(ave) of the group cell 120A may be different from the periodic average junction area Sp(ave) of the group cell 120B. The periodic maximum junction area Sp(max) of the group cell 120A may be different from the periodic maximum junction area Sp(max) of the group cell 120B. The periodic minimum junction area Sp(min) of the group cell 120A may be different from the periodic minimum junction area Sp(min) of the group cell 120B.

[0091] An amount of change of the group cells 120 adjacent to each other may be 10% or less, may be 5% or less, or may be 3% or less. The amount of change of the group cells 120 adjacent to each other may be an amount of change of the periodic average junction areas Sp(ave) of the respective adjacent group cells 120, may be an amount of change the periodic maximum junction areas Sp(max), or may be an amount of change of the periodic minimum junction areas Sp(min).

[0092] In addition to the periodic structure of the non-linear inductance elements 20, the travelling-wave parametric amplifier 100 of the present example may also have the periodic structure of the shunt capacitors 30. In addition to the modulation structure of the non-linear inductance elements 20, the travelling-wave parametric amplifier 100 of the present example may also have the modulation structure of the shunt capacitors 30.

[0093] Figure 5 shows an enlarged view near the first ground coupling section 51 and the second ground coupling section 52.

[0094] The first ground coupling section 51 crosses 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.

[0095] The second ground coupling section 52 crosses over the open stub 32. 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.

[0096] The first ground coupling section 51 of the present example contacts the ground electrode 40 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.

[0097] 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 three times the length of the second ground coupling section 52 or less. By shortening the length of the first ground coupling section 51, it becomes easier to bring the position at which the second ground coupling section 52 connects to the ground electrode 40 nearer to the transmission line 10. 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.

[0098] 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 may be 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.

[0099] Figure 6A shows an example of an enlarged view of the travelling-wave parametric amplifier 100. The travelling-wave parametric amplifier 100 has a modulation structure provided in a helical structure.

[0100] For example, the group cell 120A has a different periodic structure from that of the group cell 120B adjacent to the group cell 120A on the transmission line 10. Similarly, the group cell 120A has a different periodic structure from that of the group cell 120C provided on the inner side of the transmission line 10 than the group cell 120A in the helical structure.

[0101] The transmission lines 10 adjacent to each other in a radial direction of the helical structure may be provided to be spaced apart to the extent that they do not affect each other. The distance between the transmission lines 10 adjacent to each other in the radial direction of the helical structure may be determined by considering the noise performance by the cross talk between the adjacent transmission lines 10. The distance between the transmission lines 10 adjacent to each other in the radial direction of the helical structure may be 200 μm or more and 1000 μm or less, or may be 250 μm or more and 500 μm or less.

[0102] Here, as a transmission characteristic of the travelling-wave parametric amplifier 100, a bandgap in which the transmission characteristic is suppressed within a certain frequency range due to the interaction between dispersion and non-linearity may occur. By having a modulation structure of the plurality of group cells 120, the travelling-wave parametric amplifier 100 of the present example can suppress a gain ripple around the bandgap to utilize a pump signal of a frequency around the bandgap. This allows for enhancing the phase consistency between the pump signal and the input signal. By enhancing the phase consistency to operate in a stable manner, the travelling-wave parametric amplifier 100 of the present example can employ the transmission line 10 having a longer length to enhance an amplification factor. The bandgap will be described below.

[0103] The travelling-wave parametric amplifier 100 may include at least one of a modulation structure in which the non-linear inductance elements 20 are modulated or a modulation structure in which the shunt capacitors 30 are modulated. The travelling-wave parametric amplifier 100 of the present example includes a modulation structure in which both of the non-linear inductance elements 20 and the shunt capacitors 30 are modulated, but is not limited thereto.

[0104] Figure 6B shows a graph illustrating the modulation structure of the travelling-wave parametric amplifier 100. The vertical axis represents index values of the modulation structure, and the horizontal axis represents unit cell numbers. The present drawing shows a graph illustrating the modulation structure of the travelling-wave parametric amplifier 100 and an enlarged view thereof.

[0105] The unit cell number represents a number of the unit cells 110 provided along the transmission line 10. A lower unit cell number means that the unit cell 110 is nearer to the end 12 on the side of the input port 102, and a higher unit cell number means the unit cell 110 is nearer to the end 14 on the side of the output port 104. The travelling-wave parametric amplifier 100 of the present example includes 2400 unit cells 110.

[0106] The index value represents a magnitude of a parameter that is modulated by the modulation structure of the travelling-wave parametric amplifier 100. The index value of the present example represents the magnitude of the inductance of the non-linear inductance element 20 or the magnitude of the capacitance of the shunt capacitor 30. The index value represents a magnitude with respect to one. The index value may be set with respect to the magnitude of the capacitance or the inductance at the ends of the transmission line 10. The index value may be set with respect to an average of the capacitances of all unit cells 110 or an average of the inductances of all unit cells 110.

[0107] A modulation maximum inductance Ijm(max) represents the maximum inductance of the non-linear inductance elements 20 in the modulation structure. A modulation minimum inductance Ijm(min) represents the minimum inductance of the non-linear inductance elements 20 in the modulation structure. A modulation average inductance Ijm(ave) is an average of the inductances of the non-linear inductance elements 20 in the modulation structure.

[0108] For example, when the index value represents a magnitude of the inductance of the non-linear inductance element 20, let one be the index value of the modulation average inductance Ijm(ave). The index value higher than one may indicate that the inductance of the non-linear inductance element 20 is higher than the average. The index value lower than one may indicate that the inductance of the non-linear inductance element 20 is lower than the average.

[0109] A modulation maximum capacitance Icm(max) represents the maximum capacitance of the shunt capacitor 30 in the modulation structure. A modulation minimum capacitance Icm(min) represents the minimum capacitance of the shunt capacitor 30 in the modulation structure.

[0110] The modulation maximum capacitance Icm(max) of the present example is higher than the modulation maximum inductance Ijm(max), but is not limited thereto. The modulation maximum capacitance Icm(max) may be the same as the modulation maximum inductance Ijm(max), or may be lower than the modulation maximum inductance Ijm(max).

[0111] The modulation minimum capacitance Icm(min) of the present example is close to the modulation minimum inductance Ijm(min), but is not limited thereto. The modulation minimum capacitance Icm(min) may be higher than the modulation minimum inductance Ijm(min), or may be lower than the modulation minimum inductance Ijm(min).

[0112] Here, the inductance of the non-linear inductance element 20 may be adjusted depending on the junction area S of the Josephson junction 25. As the junction area S of the Josephson junction 25 becomes larger, the inductance of the non-linear inductance element 20 may become lower. That is, the non-linear inductance element 20 having the periodic maximum junction area Sp(max) may have the minimum inductance in the periodic structure. The non-linear inductance element 20 having the periodic minimum junction area Sp(min) may have the maximum inductance in the periodic structure. The non-linear inductance element 20 having the periodic average junction area Sp(ave) may have the average inductance in the periodic structure.

[0113] The unit cell 110 that is nearest to the ends of the transmission line 10 may have the Josephson junction 25 having the modulation average junction area Sm(ave) of the plurality of group cells 120. That is, at least one of the unit cell 110 that is nearest to the end 12 of the transmission line 10 or the unit cell 110 that is nearest to the end 14 of the transmission line 10 may have the Josephson junction 25 having the modulation average junction area Sm(ave) of the plurality of group cells 120. Both of the unit cell 110 that is nearest to the end 12 of the transmission line 10 and the unit cell 110 that is nearest to the end 14 of the transmission line 10 may have the Josephson junction 25 having the modulation average junction area Sm(ave) of the plurality of group cells 120. The periodic average junction area Sp(ave) may be the same as or may be different from the modulation average junction area Sm(ave) in the modulation structure of the plurality of group cells 120.

[0114] The periodic maximum junction areas Sp(max) of the Josephson junctions 25 in the periodic structure of the group cell 120 may gradually increase along the transmission line 10 from the end of the transmission line 10 in the modulation structure. The periodic minimum junction areas Sp(min) of the Josephson junctions 25 in the periodic structure of the group cell 120 may gradually decrease along the transmission line 10 from the end of the transmission line 10 in the modulation structure. The end of the transmission line 10 may be either the end 12 or the end 14.

[0115] A modulation amplitude proportion of the modulation maximum junction area Sm(max) of the Josephson junction 25 in the modulation structure of the plurality of group cells 120 may be 5% or more and 13% or less. The modulation amplitude proportion may be a ratio of a difference of the modulation maximum junction area Sm(max) and the modulation average junction area Sm(ave) with respect to the modulation average junction area Sm(ave). Moreover, the modulation amplitude proportion may be a ratio of a difference of the modulation minimum junction area Sm(min) and the modulation average junction area Sm(ave) with respect to the modulation average junction area Sm(ave).

[0116] Moreover, the capacitance of the shunt capacitor 30 may be adjusted depending on the stub length L of the open stub 32. As the stub length L of the open stub 32 becomes longer, the capacitance of the shunt capacitor 30 may become higher. That is, the shunt capacitor 30 having the periodic maximum stub length Lp(max) may have the maximum capacitance in the periodic structure. The shunt capacitor 30 having the periodic minimum stub length Lp(min) may have the minimum capacitance in the periodic structure. The shunt capacitor 30 having the periodic average stub length Lp(ave) may have the average capacitance in the periodic structure.

[0117] The periodic maximum stub lengths Lp(max) of the open stubs 32 in the periodic structure of the group cell 120 may gradually increase along the transmission line 10 from the end of the transmission line 10 in the modulation structure. The periodic minimum stub lengths Lp(min) of the open stubs 32 in the periodic structure of the group cell 120 may gradually decrease along the transmission line 10 from the end of the transmission line 10 in the modulation structure. The end of the transmission line 10 may be either the end 12 or the end 14.

[0118] A modulation amplitude proportion of the modulation maximum stub length Lm(max) of the open stub 32 in the modulation structure of the plurality of group cells 120 may be 5% or more and 13% or less. The modulation amplitude proportion may be a ratio of a difference of the modulation maximum stub length Lm(max) and the modulation average stub length Lm(ave) with respect to the modulation average stub length Lm(ave). Moreover, the modulation amplitude proportion may be a ratio of a difference of the modulation minimum stub length Lm(min) and the modulation average stub length Lm(ave) with respect to the modulation average stub length Lm(ave).

[0119] The plurality of group cells 120 may have the modulation structure having any window shape along the transmission line 10. The plurality of group cells 120 of the present example have the modulation structure having a window function, where the modulation strength gradually changes, such as a Hann window shape, a Hamming window shape, a Blackman window shape, or a Blackman Harris window shape along the transmission line 10, but is not limited thereto. That is, when the horizontal axis corresponds to unit cell numbers of the unit cells 110 and the vertical axis corresponds to index values of each group cell 120, the index values follows a periodic structure with a Hann window shape.

[0120] The plurality of group cells 120 may have the modulation structure in which any window shape is repeated multiple times along the transmission line 10. The plurality of group cells 120 may have the modulation structure having a window function, where the modulation strength gradually changes, such as the Hann window shape, the Hamming window shape, the Blackman window shape, or the Blackman Harris window shape, is repeated multiple times along the transmission line 10. The plurality of group cells 120 of the present example may have the modulation structure in which the Hann window shape is repeated multiple times along the transmission line 10. That is, when the horizontal axis corresponds to unit cell numbers of the unit cells 110 and the vertical axis corresponds to index values of each group cell 120, the Hann window shape of the index values may be repeated twice or more.

[0121] Figure 7A shows a travelling-wave parametric amplifier 500 according to a comparative example. The travelling-wave parametric amplifier 500 includes a transmission line 510, non-linear inductance elements 520, and shunt capacitors 530. The travelling-wave parametric amplifier 500 includes a plurality of group cells 620. The plurality of group cells 620 each include a plurality of unit cells 610.

[0122] Figure 7B shows an example of an periodic structure of the travelling-wave parametric amplifier 500. The travelling-wave parametric amplifier 500 includes group cells 620 having periodic structures, but not having a modulation structure. In other words, the group cells 620 of the travelling-wave parametric amplifier 500 don't have any envelope on the periodic structure. That is, the periodic structures of the travelling-wave parametric amplifier 500 are constant throughout the transmission line 510. Thus, in the travelling-wave parametric amplifier 500, the maximum values and the minimum values of the capacitances of the shunt capacitors 530 in the periodic structures are constant. Similarly, in the travelling-wave parametric amplifier 500, the maximum values and the minimum values of the inductances of the non-linear inductance elements 520 in the periodic structures are constant.

[0123] The travelling-wave parametric amplifier 500 according to the comparative example has the periodic structure, but does not have the modulation structure, so gain ripple occurs in a transmission characteristic. The gain ripple may occur over a wide frequency range outside of the bandgap. Moreover, when there is a gain ripple specific to the amplification band, the gain profile may oscillate over a narrow frequency range centered on the bandgap.

[0124] Figure 8A shows a simulation result of a transmission characteristic of the travelling-wave parametric amplifier 500 according to the comparative example. The vertical axis represents transmission characteristics (dB), and the horizontal axis represents frequencies (GHz) of a signal to be transmitted. The present drawing shows a graph illustrating the transmission characteristic of the travelling-wave parametric amplifier 500 and an enlarged view around the bandgap. Note that, the pump signal has not been input to the travelling-wave parametric amplifier 500 of the present example.

[0125] S21' represents a transmission coefficient of the travelling-wave parametric amplifier 500. S11' represents an input reflection coefficient of the travelling-wave parametric amplifier 500. In the bandgap, the transmission coefficient S21' decreases and the input reflection coefficient S11' increases. The transmission coefficient S21' preferably represents a flat transmittance until the frequency of the bandgap is reached and the transmission coefficient S21' rapidly drops. The input reflection coefficient S11' preferably represents a low characteristic until the frequency of the bandgap is reached and the input reflection coefficient S11' rapidly achieves a peak. However, a ripple occurs around the bandgap of the travelling-wave parametric amplifier 500. The input reflection coefficient S11' remains at -20 dB or more even if the input reflection coefficient S11' is 1 GHz or more away from the position at -3 dB near the bandgap.

[0126] Figure 8B shows a simulation result of a transmission characteristic of the travelling-wave parametric amplifier 100. The vertical axis represents transmission characteristics (dB), and the horizontal axis represents frequencies (GHz) of a signal to be transmitted. The present drawing shows a graph illustrating the transmission characteristic of the travelling-wave parametric amplifier 100 and an enlarged view around the bandgap. Note that, the pump signal has not been input to the travelling-wave parametric amplifier 100 of the present example.

[0127] S21 represents a transmission coefficient of the travelling-wave parametric amplifier 100. S11 represents an input reflection coefficient of the travelling-wave parametric amplifier 100. In the bandgap, the transmission coefficient S21 decreases and the input reflection coefficient S11 increases. The transmission coefficient S21 of the travelling-wave parametric amplifier 100 represents a more flat transmittance than the transmission coefficient S21' of the travelling-wave parametric amplifier 500 until the frequency of the bandgap is reached and the transmission coefficient S21 rapidly drops. The input reflection coefficient S11 of the travelling-wave parametric amplifier 100 represents a value lower than the input reflection coefficient S11' of the travelling-wave parametric amplifier 500 until the frequency of the bandgap is reached and the input reflection coefficient S11 rapidly achieves a peak. The input reflection coefficient S11 of the travelling-wave parametric amplifier 100 rapidly drops from the peak of the bandgap to around -25 dB between several hundred MHz. In this manner, by having the envelope on the periodic structure, the travelling-wave parametric amplifier 100 can achieve a transmission characteristic of excellent flatness.

[0128] Figure 9A shows an experimental result of a transmission characteristic of the travelling-wave parametric amplifier 500 that has not mixed a pump signal. The vertical axis represents transmission characteristics (dB), and the horizontal axis represents frequencies (GHz) of a signal to be transmitted. The present drawing shows a graph illustrating a transmission characteristic of the travelling-wave parametric amplifier 500. Note that, in the present example, a baseline transmission characteristic measured without inputting the pump signal to the travelling-wave parametric amplifier 500 is shown.

[0129] A graph Gs' represents a fitting value by a simulation of a transmission characteristic. The graph Gs' predicts in the simulation that a ripple occurs around the bandgap. A graph Gm' represents a measured value of the transmission characteristic of the travelling-wave parametric amplifier 500. The graph Gm' of the present example represents a measured value of a baseline transmission of the travelling-wave parametric amplifier 500. The travelling-wave parametric amplifier 500 of the present example, as predicted in the simulation, shows that there is a ripple in the transmission characteristic around the bandgap.

[0130] Figure 9B shows an experimental result of a transmission characteristic of the travelling-wave parametric amplifier 100 that has not mixed a pump signal. The vertical axis represents transmission characteristics (dB), and the horizontal axis represents frequencies (GHz) of a signal to be transmitted. The present drawing shows a graph illustrating a transmission characteristic of the travelling-wave parametric amplifier 100. Note that, in the present example, a baseline transmission characteristic measured without inputting the pump signal to the travelling-wave parametric amplifier 100 is shown.

[0131] A graph Gs represents a fitting value by a simulation of a transmission characteristic. The graph Gs shows in the simulation that a ripple is suppressed around the bandgap. The graph Gm represents a measured value of the transmission characteristics of the travelling-wave parametric amplifier 100. The graph Gm of the present example represents a measured value of a baseline transmission of the travelling-wave parametric amplifier 100. The travelling-wave parametric amplifier 100 of the present example, as predicted in the simulation, shows that a ripple is suppressed in the transmission characteristic around the bandgap.

[0132] Figure 10A shows a transmission characteristic of the travelling-wave parametric amplifier 500 that has mixed a pump signal. The vertical axis represents gains (dB), and the horizontal axis represents frequencies (GHz) of a signal to be transmitted. The present drawing shows a graph illustrating a transmission characteristic of the travelling-wave parametric amplifier 500 and an enlarged view around the bandgap. The present drawing shows a gain profile when the travelling-wave parametric amplifier 500 has turned on and mixed the pump signal. In the gain profile of the travelling-wave parametric amplifier 500, there is a gain ripple from 10 dB to as high as 25 dB around the bandgap.

[0133] Figure 10B shows a transmission characteristic of the travelling-wave parametric amplifier 100 that has mixed a pump signal. The vertical axis represents gains (dB), and the horizontal axis represents frequencies (GHz) of a signal to be transmitted. The present drawing shows a graph illustrating a transmission characteristic of the travelling-wave parametric amplifier 100 and an enlarged view around the bandgap. The present drawing shows a gain profile when the travelling-wave parametric amplifier 100 has turned on and mixed the pump signal. The amplified signal is obtained at around 7.5 GHz within the bandgap by amplifying with the pump signal. In the gain profile of the travelling-wave parametric amplifier 100, an amplitude of the gain ripple is suppressed to around 5 dB or less.

[0134] By having an envelope on the periodic structure, the travelling-wave parametric amplifier 100 of the present example can suppress the occurrence of the gain ripple as in the travelling-wave parametric amplifier 500. This allows travelling-wave parametric amplifier 100 to elongate the transmission line 10 to obtain an even higher amplification factor. Moreover, the travelling-wave parametric amplifier 100 can utilize the pump signal of the frequency around the bandgap to enhance the phase consistency between the pump signal and the input signal.

[0135] 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.

[0136] 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.

[0137] 10: transmission line; 　　12: end; 　　14: end; 　　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; 　　51: first ground coupling section; 　　52: second ground coupling section; 　　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; 　　520: non-linear inductance element; 　　530: shunt capacitor; 　　610: unit cell; 　　620: group cell.

Claims

1. A travelling-wave parametric amplifier comprising: 　　a plurality of group cells each including a plurality of unit cells, 　　wherein the plurality of unit cells comprise: 　　a transmission line that extends along a predetermined direction; and 　　non-linear inductance elements and shunt capacitors arranged along the transmission line, 　　wherein a respective group cell of the plurality of group cells comprises a periodic structure in which the non-linear inductance elements and the shunt capacitors periodically change along the transmission line, and 　　wherein the plurality of group cells comprise a modulation structure in which the non-linear inductance elements and the shunt capacitors modulate along the transmission line.

2. The travelling-wave parametric amplifier according to claim 1, 　　wherein each shunt capacitor of the shunt capacitors comprises an open stub branched from the transmission line, and 　　wherein stub lengths of the open stubs modulate along the transmission line between the plurality of group cells.

3. The travelling-wave parametric amplifier according to claim 2, 　　wherein periodic maximum stub lengths of the open stubs in the periodic structures gradually increase along the transmission line from an end of the transmission line in the modulation structure, and 　　wherein periodic minimum stub lengths of the open stubs in the periodic structures gradually decrease along the transmission line from an end of the transmission line in the modulation structure.

4. The travelling-wave parametric amplifier according to claim 3, 　　wherein a modulation amplitude proportion of a modulation maximum stub length of the open stub in the modulation structure of the plurality of group cells is 5% or more and 13% or less.

5. The travelling-wave parametric amplifier according to claim 1, 　　wherein each non-linear inductance element of the non-linear inductance elements comprises a Josephson junction, and 　　wherein junction areas of the Josephson junctions modulate along the transmission line between the plurality of group cells.

6. The travelling-wave parametric amplifier according to claim 5, 　　wherein the non-linear inductance element comprises: 　　a first junction finger provided on the transmission line; and 　　a second junction finger provided so as to be at least partially overlapped with the first junction finger, and 　　wherein an overlapped section of the first junction finger and the second junction finger forms the Josephson junction.

7. The travelling-wave parametric amplifier according to claim 5, 　　wherein periodic maximum junction areas of the Josephson junctions in the periodic structures gradually increase along the transmission line from an end of the transmission line in the modulation structure, and 　　wherein periodic minimum junction areas of the Josephson junctions in the periodic structures gradually decrease along the transmission line from an end of the transmission line in the modulation structure.

8. The travelling-wave parametric amplifier according to claim 7, 　　wherein a modulation amplitude proportion of a modulation maximum junction area of the Josephson junction in the modulation structure of the plurality of group cells is 5% or more and 13% or less.

9. The travelling-wave parametric amplifier according to any one of claims 1 to 8, 　　wherein the plurality of group cells comprise an envelope on the periodic structure in which the non-linear inductance elements and the shunt capacitors modulate along the transmission line.

10. The travelling-wave parametric amplifier according to any one of claims 1 to 8, 　　wherein the plurality of group cells have the modulation structure having a window function, where the modulation strength gradually changes along the transmission line.

11. The travelling-wave parametric amplifier according to claim 10, 　　wherein the plurality of group cells have the modulation structure having a window function, where the modulation strength gradually changes, is repeated multiple times along the transmission line.

12. The travelling-wave parametric amplifier according to any one of claims 1 to 8, 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.

13. The travelling-wave parametric amplifier according to claim 12, comprising: 　　a plurality of the first ground coupling sections provided along the transmission line at predetermined intervals.

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

15. The travelling-wave parametric amplifier according to claim 12, 　　wherein a width of the first ground coupling section gradually changes along a length direction of the first ground coupling section.

16. The travelling-wave parametric amplifier according to claim 2, comprising: 　　ground electrodes provided sandwiching the open stub therebetween; and 　　a second ground coupling section provided over the open stub from one of the ground electrodes sandwiching the open stub therebetween to another of the ground electrodes.

17. The travelling-wave parametric amplifier according to claim 2, 　　wherein a length of a first ground coupling section provided over the transmission line is larger than a length of a second ground coupling section provided over the open stub.

18. The travelling-wave parametric amplifier according to any one of claims 1 to 8, comprising: 　　a helical structure in which the transmission line is helically arranged.

19. The travelling-wave parametric amplifier according to any one of claims 1 to 8, 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 plurality of group cells each including a plurality of unit cells, 　　wherein the plurality of unit cells comprise: 　　a transmission line that extends along a predetermined direction; and 　　non-linear inductance elements and shunt capacitors arranged along the transmission line, 　　wherein a respective group cell of the plurality of group cells comprises a periodic structure in which the non-linear inductance elements and the shunt capacitors periodically change along the transmission line, and 　　wherein the plurality of group cells comprise a modulation structure in which the non-linear inductance elements and the shunt capacitors modulate along the transmission line.

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