Oscillator

Abstract

To provide an oscillator capable of reducing crosstalk.SOLUTION: An oscillator includes a superconductor ground plane 2006, a spaced-apart surrounded conductive member 2005 in the ground plane, a SQUID 2001 having one end connected to the conductive member and the other end connected to the ground plane, a superconductor first connection circuit 2007a that connects the ground planes existing on both sides near the connection portion between the conductive member and the SQUID, and a superconducting loop circuit 2009 surrounding the SQUID and using the ground plane and the first connection circuit.SELECTED DRAWING: Figure 29

Description

Technical Field

[0001] The present invention relates to an oscillator, and more particularly to a technique for reducing crosstalk in a superconducting quantum circuit.

Background Art

[0002] In a chip of a quantum circuit in which a plurality of qubits are integrated, reducing crosstalk is an important issue. Here, crosstalk means that, for example, when a control signal is input to a certain qubit, for some reason, the control signal couples with another qubit and controls the other qubit unintentionally. Specifically, for example, it changes the resonance frequency of another qubit. In experiments, crosstalk has been observed both when a DC (Direct Current) control signal is input to a qubit and when a high-frequency control signal such as 20 GHz is input to a qubit.

[0003] A chip of a superconducting quantum circuit is manufactured using, for example, a coplanar waveguide structure. Patent Document 1 discloses a technique capable of reducing crosstalk in such a chip of a quantum circuit. In the configuration described in this document, by using an air bridge to electrically connect the GND (ground) on both sides of the core wire of the coplanar waveguide, the GND on both sides of the core wire is kept at the same electric potential. As a result, the slot line mode is suppressed, and thus crosstalk can be reduced.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, superconducting quantum circuits are technologies in the process of development in research and development, and there is a need for the provision of new technologies for reducing crosstalk.

[0006] This disclosure has been made to solve such problems, and an object thereof is to provide an oscillator capable of reducing crosstalk.

Means for Solving the Problems

[0007] The oscillator according to the first aspect of the present disclosure is a ground plane of a superconductor, a conductive member surrounded by the ground plane with a space therebetween, a SQUID having one end connected to the conductive member and the other end connected to the ground plane, a first connection circuit of a superconductor that connects the ground planes existing on both sides in the vicinity of the connection portion between the conductive member and the SQUID, a superconducting loop circuit that surrounds the SQUID and uses the ground plane and the first connection circuit and has.

Effect of the Invention

[0008] According to the above configuration, it is possible to provide an oscillator capable of reducing crosstalk.

Brief Description of the Drawings

[0009]

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Embodiments for Carrying Out the Invention

[0010] In the following description, a Josephson junction refers to an element having a structure in which a thin insulating film is sandwiched between a first superconductor and a second superconductor. Also, a SQUID (Superconducting QUantum Interference Device) is an element in which two Josephson junctions are connected in a loop by a superconducting circuit. Further, part or all of the circuits described below are configured using, for example, a circuit (wiring) formed of a superconductor, and in order to realize a superconducting state, it is used in a temperature environment of about 10 mK (millikelvin), for example.

[0011] [Prior Consideration] First, the problem of crosstalk in a chip of a superconducting quantum circuit in which a plurality of quantum bits are integrated will be described.

[0012] As an example of a chip of a quantum circuit in which a plurality of qubits are integrated, FIG. 1 shows a chip layout of a 2-bit lumped-element superconducting quantum circuit. FIG. 2 shows an equivalent circuit diagram of the 2-bit lumped-element superconducting quantum circuit of FIG. 1. This 2-bit lumped-element superconducting quantum circuit has a configuration in which a first qubit 1001 and a second qubit 1002 are coupled via a capacitor 1303. Both the first qubit 1001 and the second qubit 1002 have the same configuration. The first qubit 1001 has a configuration in which two lumped-element lines are connected to both ends of a SQUID 1102. Since these lumped-element lines have a length corresponding to 1 / 4 of the wavelength corresponding to the operating frequency of the first qubit 1001, they are hereinafter referred to as a λ / 4 line 1103a and a λ / 4 line 1103b. When the operating frequency of the first qubit 1001 is about 10 GHz, the lengths of the λ / 4 line 1103a and the λ / 4 line 1103b are about 2 to 3 mm. A control line 1104 is magnetically coupled to the SQUID 1102. In other words, the control line 1104 and the SQUID 1102 are magnetically coupled non-contactingly by mutual inductance. By inputting a DC control signal from the control line 1104, the resonance frequency of the first qubit 1001 can be set. With a DC control signal for setting a certain resonance frequency input to the control line 1104, the first qubit 1001 can be oscillated by further inputting a control signal having a frequency twice the set resonance frequency to the control line 1104. The operating frequency (set resonance frequency) of the first qubit 1001 is, for example, about 10 GHz. Therefore, when operating the first qubit 1001, a signal obtained by superimposing a DC control signal and a high-frequency control signal of about 20 GHz is input from the control line 1104. Since the configuration and the method of operating the second qubit 1002 are the same as those of the first qubit 1001, detailed description thereof is omitted.

[0013] In the configuration shown in the figure, the first qubit 1001 and the second qubit 1002 exist on a chip 1004 that is electrically connected to the wiring of a printed circuit board (PCB) 1005 using bonding wires 1006. The second qubit 1002 has a SQUID 1202, a λ / 4 line 1203a, and a λ / 4 line 1203b. A control line 1204 is magnetically coupled to the SQUID 1202. One end of the λ / 4 line 1103a of the first qubit 1001 is connected to the SQUID 1102, and the other end of the λ / 4 line 1103a is connected to a capacitor 1301. Also, one end of the λ / 4 line 1103b of the first qubit 1001 is connected to the SQUID 1102, and the other end of the λ / 4 line 1103b is connected to a capacitor 1303. Similarly, one end of the λ / 4 line 1203a of the second qubit 1002 is connected to the SQUID 1202, and the other end of the λ / 4 line 1203a is connected to a capacitor 1302. Also, one end of the λ / 4 line 1203b of the second qubit 1002 is connected to the SQUID 1202, and the other end of the λ / 4 line 1203b is connected to a capacitor 1303. As shown in FIG. 2, the SQUID 1102 is an element in which a Josephson junction 1105a and a Josephson junction 1105b are connected in a loop, and both ends thereof are connected to the λ / 4 lines 1103a and 1103b. Similarly, the SQUID 1202 is an element in which a Josephson junction 1205a and a Josephson junction 1205b are connected in a loop, and both ends thereof are connected to the λ / 4 lines 1203a and 1203b.

[0014] FIG. 3A shows an enlarged view of the vicinity of the SQUID 1102 of the first qubit 1001 in FIG. 1. Also, FIG. 3B shows an enlarged view of the vicinity of the SQUID 1202 of the second qubit 1002 in FIG. 1. Here, the first qubit 1001 in FIG. 3A will be described, and the description of the qubit 1002 for which a similar description is possible will be omitted.

[0015] The tip of the control line 1104 branches into a first branch line 11041 and a second branch line 11042. Among these, the first branch line 11041 is laid out near the SQUID 1102 so as to be magnetically coupled with the SQUID 1102. On the other hand, the second branch line 11042 is laid out away from the SQUID 1102 so as not to be magnetically coupled with the SQUID 1102.

[0016] The control line 1104 and the λ / 4 lines 1103a, 1103b are configured as coplanar waveguides. There is a GND (ground) plane 1106 around the lines configured as coplanar waveguides. Both the first branch line 11041 and the second branch line 11042 are connected to this GND plane 1106. Note that such branching suppresses the bias of the current from the control line 1104 flowing through the GND plane 1106 on both sides of the control line 1104, respectively.

[0017] In FIG. 3A, the reference numeral 11031a represents the core wire of the λ / 4 line 1103a, and the reference numeral 11031b represents the core wire of the λ / 4 line 1103b. Similarly, in FIG. 3B, the reference numeral 12031a represents the core wire of the λ / 4 line 1203a, and the reference numeral 12031b represents the core wire of the λ / 4 line 1203b. Further, in FIG. 3B, the reference numerals 12041 and 12042 represent the first branch line and the second branch line of the control line 1204, and the reference numeral 1206 represents the GND plane.

[0018] Crosstalk means that, for example, when a DC or high-frequency control signal is input from the control line 1104 to the first qubit 1001, the control signal is coupled to the SQUID 1202 of the second qubit 1002 for some reason, and the second qubit 1002 is affected. Specifically, for example, the resonance frequency of the second qubit 1002 changes.

[0019] In order to understand the cause of this crosstalk, simulations were performed using electromagnetic field analysis software. Here, the simulations were carried out using ANSYS HFSS manufactured by ANSYS Japan Co., Ltd. As a result of the simulation, when a 20 GHz control signal was input from the control line 1104 of the first qubit 1001 to the first qubit 1001, strong currents flowed along the λ / 4 lines 1103a, 1103b, 1203b, and 1203a. And the following results were obtained. Fig. 4 is a graph showing the current flowing through the SQUID 1102 of the first qubit 1001 and the current flowing through the SQUID 1202 of the second qubit 1002 when a 20 GHz control signal is input from the control line 1104 of the first qubit 1001 to the first qubit 1001. In the graph of Fig. 4, the horizontal axis indicates the phase of the control signal, and the vertical axis indicates the magnitude of the current. As shown in Fig. 4, a current that varies sinusoidally according to the phase flows through the SQUID 1102 of the first qubit 1001. Note that the vertical axis of Fig. 4 is normalized so that the maximum value is 1. Since the SQUID 1102 of the first qubit 1001 is designed to be magnetically coupled to the control line 1104, the flow of current through the SQUID 1102 of the first qubit 1001 is the intended operation. However, as shown in Fig. 4, a current also flows through the SQUID 1202 of the second qubit 1002 where no current should originally flow. The maximum value of the current flowing through the SQUID 1202 of the second qubit 1002 is 0.32, that is, a large current of 32% of the current flowing through the SQUID 1102 of the first qubit 1001 also flows. That is, it can be seen that the SQUID 1202 of the second qubit 1002 is affected by high-frequency crosstalk.

[0020] The results of FIG. 4 show that when a high-frequency control signal of 20 GHz is input from the control line 1104, a high-frequency electromagnetic field propagates along the λ / 4 lines 1103a, 1103b, 1203b, 1203a. This is presumably because a potential difference occurs between the GND planes 1106 and 1206 on both sides of the core wires 11031a, 11031b, 12031b, 12031a of the λ / 4 lines 1103a, 1103b, 1203b, 1203a, which are supposed to be at the same potential. Therefore, to solve this problem, the GND planes 1106 and 1206 on both sides of the core wires 11031a, 11031b, 12031b, 12031a of the λ / 4 lines 1103a, 1103b, 1203b, 1203a may be electrically short-circuited. Specifically, this can be achieved, for example, by installing air bridges at various locations on the λ / 4 lines 1103a, 1103b, 1203b, 1203a, as described in Patent Document 1. At that time, there is a method of making the interval at which the air bridges are installed sufficiently shorter than the wavelength of the propagating electromagnetic field. Here, since the frequency of the control signal being considered as an example is 20 GHz, the wavelength on the silicon substrate is approximately 5.9 mm. Consider installing air bridges at an interval sufficiently shorter than that, for example, an interval of 600 μm (about 1 / 10 of the wavelength) or less. Here, an air bridge is a structure made of a conductive material, for example, metal, and is a structure that electrically connects the GND planes on both sides of the core wire. The air bridge does not contact the core wire and has a structure that intersects the core wire three-dimensionally. Therefore, the air bridge and the core wire are not electrically connected. Generally, the space between the air bridge and the core wire is air or vacuum. In the case of a superconducting quantum circuit, the space between the air bridge and the core wire is vacuum. However, although air bridges are generally fabricated using semiconductor process technology, there is a possibility that a dielectric such as resist remains around the air bridge during the process of fabricating the air bridge.

[0021] FIG. 5 shows a chip layout when air bridges 1107a to 1107m and 1207a to 1207m are installed at intervals sufficiently shorter than the wavelength corresponding to 20 GHz for the λ / 4 lines 1103a, 1103b, 1203b, 1203a according to such a concept. Further, FIG. 6 shows a simulation result when a control signal of 20 GHz is input from the control line 1104 of the first qubit 1001 to the first qubit 1001 in the configuration shown in FIG. 5. By installing the air bridges 1107a to 1107m and 1207a to 1207m, the current flowing along the λ / 4 lines 1103a, 1103b, 1203b, 1203a is suppressed. As a result, as shown in FIG. 6, the current flowing through the SQUID 1202 of the second qubit 1002 is reduced to about 1% of the current flowing through the SQUID 1102 of the first qubit 1001. Therefore, it can be seen that by installing a plurality of air bridges 1107a to 1107m and 1207a to 1207m at intervals sufficiently shorter than the wavelength of the control signal over the entire λ / 4 lines 1103a, 1103b, 1203b, 1203a, high-frequency crosstalk can be significantly suppressed.

[0022] However, forming air bridges over the entire λ / 4 lines 1103a, 1103b, 1203b, 1203a may reduce the Q value (Quality factor) of the qubits. The possible cause is dielectric loss due to dielectrics such as resist that remain when the air bridges are fabricated. When the qubits operate, standing waves are generated in the qubits. Since this standing wave is generated over the entire qubit, an electric field is also generated on the λ / 4 line during the operation of the qubit. Therefore, when air bridges are formed over the entire λ / 4 lines 1103a, 1103b, 1203b, 1203a, the electric field generated on the λ / 4 line spreads into the dielectrics remaining near the air bridges, which can cause dielectric loss in the dielectrics to reduce the Q value. Therefore, an embodiment capable of reducing crosstalk while suppressing the reduction of the Q value of the qubits will be described.

[0023] [First Embodiment] FIG. 7 is a chip layout of a 2-bit distributed-constant type superconducting quantum circuit in which two superconducting circuits (oscillators) according to the first embodiment are integrated. The superconducting circuit described here is also referred to as an oscillator because it oscillates. FIG. 8 shows an equivalent circuit diagram of the 2-bit distributed-constant type superconducting quantum circuit of FIG. 7. The superconducting circuit of the first embodiment is a superconducting qubit, specifically, the first qubit 1 or the second qubit 2 in the equivalent circuit diagram shown in FIG. 8. The 2-bit distributed-constant type superconducting quantum circuits of FIGS. 7 and 8 have a configuration in which the first qubit 1 and the second qubit 2 are coupled via a capacitor 303. Both the first qubit 1 and the second qubit 2 have the same configuration.

[0024] The first qubit 1 has a configuration in which two distributed constant lines (transmission lines) are connected to both ends of the SQUID 102. Since these distributed constant lines have a length corresponding to 1 / 4 of the wavelength corresponding to the operating frequency (resonance frequency) of the first qubit 1, they are hereinafter referred to as the λ / 4 line 103a and the λ / 4 line 103b. When the operating frequency of the first qubit 1 is about 10 GHz, the lengths of the λ / 4 line 103a and the λ / 4 line 103b are about 2 to 3 mm. A control line 104 is magnetically coupled to the SQUID 102. In other words, the control line 104 and the SQUID 102 are magnetically coupled non-contact by mutual inductance. By inputting a DC control signal from the control line 104, the resonance frequency of the first qubit 1 can be set. With a DC control signal for setting a certain resonance frequency input to the control line 104, the first qubit 1 can be oscillated by further inputting a control signal with a frequency twice the set resonance frequency to the control line 104. The operating frequency (set resonance frequency) of the first qubit 1 is, for example, about 10 GHz. Therefore, when operating the first qubit 1, a signal obtained by superimposing a DC control signal and a high-frequency control signal of about 20 GHz is input from the control line 104. Since the configuration and the method of operating the second qubit 2 are the same as those of the first qubit 1, detailed description thereof is omitted.

[0025] In the configuration shown in FIG. 7, the first qubit 1 and the second qubit 2 exist on a chip 4 that is electrically connected to the wiring of the printed circuit board 5 using bonding wires 6. The second qubit 2 includes a SQUID 202, a λ / 4 line 203a, and a λ / 4 line 203b. A control line 204 is magnetically coupled to the SQUID 202. One end of the λ / 4 line 103a of the first qubit 1 is connected to one end of the SQUID 102, and the other end of the λ / 4 line 103a is connected to a capacitor 301. Also, one end of the λ / 4 line 103b of the first qubit 1 is connected to the other end of the SQUID 102, and the other end of the λ / 4 line 103b is connected to a capacitor 303. Similarly, one end of the λ / 4 line 203a of the second qubit 2 is connected to one end of the SQUID 202, and the other end of the λ / 4 line 203a is connected to a capacitor 302. Also, one end of the λ / 4 line 203b of the second qubit 2 is connected to the other end of the SQUID 202, and the other end of the λ / 4 line 203b is connected to a capacitor 303.

[0026] As shown in FIG. 8, the SQUID 102 is an element in which a Josephson junction 105a and a Josephson junction 105b are connected in a loop, and both ends thereof are connected to the λ / 4 lines 103a and 103b. Similarly, the SQUID 202 is an element in which a Josephson junction 205a and a Josephson junction 205b are connected in a loop, and both ends thereof are connected to the λ / 4 lines 203a and 203b. Also, as will be described later, in this embodiment, an air bridge 107 (see FIG. 7) is provided at a predetermined position for the first qubit 1, and an air bridge 207 (see FIG. 7) is provided at a predetermined position for the second qubit 2.

[0027] FIG. 9 shows an enlarged view of the vicinity of the first qubit 1 in the chip layout of FIG. 7. FIG. 10A shows an enlarged view of the vicinity of the SQUID 102 of the first qubit 1 in the chip layout of FIG. 7. FIG. 10B shows an enlarged view of the vicinity of the SQUID 202 of the second qubit 2 in the chip layout of FIG. 7.

[0028] Here, the first qubit 1 will be described, and the description of qubit 2 for which a similar description is possible will be omitted. The tip of the control line 104 branches at the branch point 108 into a first branch line 1041 and a second branch line 1042. Among these, the first branch line 1041 is laid out near the SQUID 102 so as to be magnetically coupled to the SQUID 102. On the other hand, the second branch line 1042 is laid out away from the SQUID 102 so as not to be magnetically coupled to the SQUID 102. Specifically, while the first branch line 1041 is magnetically coupled to the SQUID 102, the second branch line 1042 is not magnetically coupled to the SQUID 102. The first branch line 1041 is wired along the SQUID 102, and the second branch line 1042 is wired in the direction opposite to that of the first branch line 1041.

[0029] The control line 104 and the λ / 4 lines 103a, 103b are configured as coplanar waveguides. A GND plane 106 exists around the lines configured as coplanar waveguides. Both the first branch line 1041 and the second branch line 1042 are connected to this GND plane 106.

[0030] In the figure, the reference numeral 1031a represents the core wire of the λ / 4 line 103a, the reference numeral 1031b represents the core wire of the λ / 4 line 103b, the reference numeral 2031a represents the core wire of the λ / 4 line 203a, and the reference numeral 2031b represents the core wire of the λ / 4 line 203b. Further, the reference numerals 2041 and 2042 represent the first branch line and the second branch line of the control line 204, the reference numeral 208 represents the branch point, and the reference numeral 206 represents the GND plane.

[0031] The difference between the superconducting qubit according to the first embodiment and the superconducting qubit described with reference to FIGS. 3A and 3B lies in its layout. Specifically, in the superconducting qubit according to the first embodiment, the way the air bridges are arranged is different from that of the superconducting qubit described with reference to FIGS. 3A and 3B. As shown in FIGS. 9 and 10A, in the first qubit 1 according to the first embodiment, on the λ / 4 lines 103a and 103b, the air bridges 107a and 107b are installed only near the nodes of the standing wave electric field generated in the qubit during the operation of the qubit. That is, for the λ / 4 lines 103a and 103b, the air bridges 107a and 107b are installed only near the nodes of the standing wave electric field generated when the superconducting qubit (oscillator) oscillates. In other words, on the λ / 4 lines 103a and 103b, the air bridges 107a and 107b are installed only near the positions farthest from the connection points with the capacitors 301 and 303. Specifically, it is preferable to install the air bridges 107a and 107b on the λ / 4 lines 103a and 103b only at positions as close as possible to the connection points with the SQUID 102. For example, on the λ / 4 lines 103a and 103b, it is preferable to install the air bridges 107a and 107b only at positions within 1 / 20 of the length of the λ / 4 lines 103a and 103b from the connection points between the λ / 4 lines 103a and 103b and the SQUID 102. More preferably, on the λ / 4 lines 103a and 103b, the air bridges 107a and 107b are installed only at positions within 1 / 30 of the length of the λ / 4 lines 103a and 103b from the connection points with the SQUID 102. In the example shown in FIGS. 9 and 10A, on the λ / 4 lines 103a and 103b, the air bridges 107a and 107b are installed only at a position about 60 μm from the connection points with the SQUID 102 (in other words, at a position on the λ / 4 lines 103a and 103b and at a distance of approximately 1 / 30 of the length of the λ / 4 lines 103a and 103b from the connection points with the SQUID 102). In this embodiment, the length of the air bridge, in other words, the length from the location where one end of the air bridge is connected to the GND plane to the location where the other end of the air bridge is connected to the GND plane, is preferably shorter. Specifically, the length of the air bridge is preferably 1 / 10 or less of the wavelength of the high-frequency control signal input from the control line on the chip, more preferably 1 / 30 or less, and even more preferably 1 / 50 or less. For example, when the frequency of the control signal is 20 GHz, the wavelength of the control signal on the chip is about 5.9 mm. In that case, the length of the air bridge is preferably 590 μm or less, more preferably 196 μm or less, and even more preferably 118 μm or less. Note that in all embodiments and modifications other than the first embodiment described in this specification, the preferred length of the air bridge is as described above. Note that in this embodiment, the length of the air bridge is set to 62 μm. This length is about 1 / 95 of the wavelength of the 20 GHz control signal on the chip. In all embodiments and modifications other than the first embodiment described in this specification, the length of the air bridge is also set to 62 μm.

[0032] When the standing wave generated in the first qubit 1 during the operation of the first qubit 1 forms an antinode of the electric field near the connection points with the capacitors 301 and 303 on the λ / 4 lines 103a and 103b, and forms a node of the electric field near the connection points with the SQUID 102 on the λ / 4 lines 103a and 103b. In other words, on the λ / 4 lines 103a and 103b, the amplitude of the electric field is the largest near the connection points with the capacitors 301 and 303, decreases as it moves away from the capacitors 301 and 303, and is the smallest near the connection points with the SQUID 102. In the first embodiment, on the λ / 4 line, the air bridges 107a and 107b are installed only near the node of the electric field of this standing wave, that is, near the place where the electric field is the weakest. By doing so, most of the components of the electric field of the standing wave generated in the first qubit 1 during the operation of the first qubit 1 will be far away from the air bridges 107a and 107b. Therefore, even if a dielectric such as a resist remains in the air bridges 107a and 107b, the electric field spreading into the residue can be minimized. As a result, it is possible to reduce dielectric loss, and as a result, there is an effect that a decrease in the Q value of the first qubit 1 can be suppressed. Although the description is omitted, air bridges 207a and 207b are also arranged for the second qubit 2 in the same manner as the first qubit 1.

[0033] As shown in Fig. 9, in the superconducting circuit of the first embodiment, in addition to the air bridges 107a and 107b installed on the λ / 4 lines, air bridges 107c to 107h are also installed at arbitrary positions on the control line 104. Since the control line 104 extending in a direction different from that of the λ / 4 lines 103a and 103b is far from the λ / 4 lines 103a and 103b, even if the air bridges 107c to 107h are installed on the control line 104, it does not directly affect the Q value of the first qubit 1. In other words, arranging the air bridges 107c to 107h on the control line 104 does not cause a decrease in the Q value of the first qubit 1. More specifically, the air bridges 107c to 107h are provided in the non-branching portion of the control line 104, which is the portion other than the first branch line 1041 and the second branch line 1042. Similarly, in this embodiment, an air bridge 207c or the like is also installed on the control line 204 of the second qubit 2.

[0034] As described above, in this embodiment, the air bridges 107a, 107b, 207a, and 207b are installed only near the nodes of the electric field on the λ / 4 lines 103a, 103b, 203a, and 203b. Thereby, while suppressing a decrease in the Q values of the first qubit 1 and the second qubit 2, high-frequency crosstalk can be suppressed. Here, the simulation results will be shown. Fig. 11 shows the results of simulation when a 20 GHz control signal is input from the control line 104 of the first qubit 1 to the first qubit 1 in the configuration of the first embodiment. As shown in Fig. 11, the current flowing through the SQUID 202 of the second qubit 2 became 1% or less of the current flowing through the SQUID 102 of the first qubit 1. From this, it has the effect that by using the superconducting circuit of the first embodiment, high-frequency crosstalk can be significantly reduced while suppressing a decrease in the Q value of the qubit.

[0035] Incidentally, the superconducting circuit described above, i.e., the oscillator, can also be described as follows. The oscillator includes a SQUID, a transmission line (distributed constant line) connected to the SQUID, a GND plane, and a connection circuit. Here, the connection circuit is a circuit that connects the GND planes existing on both sides of the transmission line, and the above-described air bridge that connects the GND planes across the transmission line corresponds to this. And this connection circuit is provided at a position corresponding to the vicinity of the node of the standing wave electric field generated during the oscillation of the oscillator. According to such a configuration, it is possible to reduce crosstalk while suppressing a decrease in the Q value of the qubit. Incidentally, for the control line magnetically coupled to the SQUID and to which a control signal is input, a connection circuit (air bridge) may also be provided for reducing crosstalk. That is, the oscillator may further include a connection circuit (a circuit such as the air bridge 107c that connects the GND planes across the control line) that connects the GND planes existing on both sides of the control line.

[0036] [Second Embodiment] Next, the second embodiment will be described. Regarding the components similar to those in the first embodiment, the description will be omitted as appropriate. FIG. 12 is a chip layout of a 2-bit distributed constant type superconducting quantum circuit in which two superconducting circuits (oscillators) according to the second embodiment are integrated. The chip layout shown in FIG. 12 is different from that in the first embodiment in the configuration near the SQUID 102 and the SQUID 202. This difference will be described later using an enlarged view. The superconducting circuit of the second embodiment is a superconducting qubit, and its equivalent circuit diagram is the same as that in FIG. 8, so the description of the equivalent circuit diagram will be omitted here. The chip layout shown in FIG. 12 is a layout of a 2-bit distributed constant type superconducting quantum circuit configured by coupling two qubits according to this second embodiment via a capacitor 303.

[0037] The difference between the superconducting qubit according to the second embodiment and the superconducting qubit of the first embodiment lies in the way the air bridges are arranged. Fig. 13 shows an enlarged view of the vicinity of the first quantum bit 1 in the chip layout of Fig. 12. As shown in Fig. 13, similar to the first embodiment, in the superconducting circuit of the second embodiment, on the λ / 4 lines 103a and 103b, the air bridges 107a and 107b are installed only at locations as close as possible to the connection points with the SQUID 102, and further, air bridges 107c to 107h are also installed on the control line 104. However, in the second embodiment, it is different from the first embodiment in that there is a certain constraint on the positions of the air bridges 107a and 107b installed on the λ / 4 lines 103a and 103b. This will be explained. Fig. 14 shows an enlarged view of the vicinity of the SQUID 202 of the second quantum bit 2 in the chip layout of Fig. 12. Note that the positions of the air bridges 107a and 107b with respect to the first quantum bit 1 are the same as the positions of the air bridges 207a and 207b with respect to the second quantum bit 2.

[0038] The air bridges 207a and 207b installed in the first embodiment did not necessarily have to be installed at positions equidistant from the branch point 208 of the control line 204 as shown in FIG. 10B. However, in the second embodiment, as shown in FIG. 14, the air bridges 207a and 207b are installed at positions equidistant from the branch point 208 of the control line 204. In other words, they are installed at the end points of the first branch line 2041 and the second branch line 2042, which have the same length as each other, that is, at the grounding points of the first branch line 2041 with the GND plane 206 and the second branch line 2042 with the GND plane 206. Specifically, as shown in FIG. 14, in the second embodiment, the air bridges 207a and 207b are installed at two locations on the λ / 4 lines 203a and 203b that are equidistant from the branch point 208 of the control line 204. Although the distance is described as equal here, this is an ideal case, and in practice, a manufacturing error of ±10% or less is allowed. That is, the difference between the two may be 10% or less of the length of either one. Thus, in this embodiment, the installation positions of the air bridges 207a and 207b only need to be at substantially the same distance from the branch point 208. In the first embodiment, regarding the placement of the air bridges 207a and 207b near the connection points with the SQUID 202 on the λ / 4 lines 203a and 203b, only the requirement was to arrange them as close as possible to the SQUID 202. Therefore, as shown in FIG. 10B, the positions of the two air bridges 207a and 207b near the connection points with the SQUID 202 on the λ / 4 lines 203a and 203b did not necessarily have to be equidistant from the branch point 208 of the control line 204. This is the difference between the first embodiment and the second embodiment.

[0039] Here, the first branch line 2041 and the second branch line 2042 are arranged such that the current flowing through the first branch line 2041 and the current flowing through the second branch line 2042 are equal in amount and opposite in direction. Specifically, as shown in the figure, the first branch line 2041 and the second branch line 2042 have a bilaterally symmetric configuration. The first branch line 2041 is wired along the SQUID 202, and the second branch line 2042 is wired in the opposite direction to the first branch line 2041. For this reason, while the first branch line 2041 is magnetically coupled to the SQUID 202, the second branch line 2042 is configured not to be magnetically coupled to the SQUID 202. More specifically, for example, as shown in FIG. 14, the control line 204 is a T-shaped line, and the first branch line 2041 and the second branch line 2042 branched at the branch point 208 are arranged linearly side by side. That is, the angle formed by the first branch line 2041 and the non-branched portion of the control line 204 is 90 degrees, the angle formed by the second branch line 2042 and the non-branched portion of the control line 204 is 90 degrees, and the angle formed by the first branch line 2041 and the second branch line 2042 is 180 degrees. These angles are values in an ideal case, and actually, manufacturing errors of ±10% or less of these angles are allowed.

[0040] Incidentally, as shown in FIG. 14, the positional relationship among the SQUID 202, the λ / 4 lines 203a and 203b, and the control line 204 is as follows, for example. The λ / 4 lines 203a and 203b and the SQUID 202 are arranged side by side in a first direction (the vertical direction in the drawing) near the SQUID 202. Also, the first branch line 2041 and the second branch line 2042 are wired in this first direction (the vertical direction in the drawing). Note that the non-branched portion of the control line 204 extends in a second direction (the left-right direction in the drawing) near the SQUID 202 and extends from the branch point 208 so as to move away from the SQUID 202. That is, the non-branched portion of the control line 204 is wired on the side opposite to the SQUID 202 with respect to the branch point 208. The first branch line 2041 exists at a position facing the SQUID 202, while the second branch line 2042 exists at a position not facing the SQUID 202.

[0041] The aim of adopting the above-described configuration in the second embodiment will be described later. First, in the second embodiment, FIG. 15 shows the simulation results when a control signal of 20 GHz is input from the control line 104 of the first qubit 1 to the first qubit 1. As shown in FIG. 15, when a high-frequency control signal of 20 GHz is input from the control line 104 of the first qubit 1, the current flowing through the SQUID 202 of the second qubit 2 becomes 1% or less of the current flowing through the SQUID 102 of the first qubit 1. That is, it can be seen that, as in the first embodiment, the second embodiment can also significantly suppress high-frequency crosstalk. From this, the second embodiment has the effect of suppressing a decrease in the Q value of the qubit while suppressing high-frequency crosstalk, as in the first embodiment.

[0042] [Regarding Further Effects of the Second Embodiment] Next, the aim of the second embodiment will be described. So far, means for suppressing crosstalk when a high-frequency control signal such as 20 GHz is input from the control line have been described. However, in experiments, crosstalk has also been observed when a DC control signal is input from the control line. The cause is thought to be, for example, that the SQUID 202 of the second qubit 2 senses the magnetic field generated when the DC control signal flows through the control line 104 of the first qubit 1 and then flows through the GND plane. That is, it is considered that the mechanism of generation (in other words, the path and manner of propagation of the current causing crosstalk) is different from that of the high-frequency crosstalk propagating along the λ / 4 line described so far. The second embodiment aims to suppress not only the high-frequency crosstalk described so far but also DC crosstalk (specifically, crosstalk generated by the flow of current through the GND plane). Details thereof will be described below.

[0043] FIG. 16A is a diagram showing the layout of the second qubit 1002 in the quantum circuit shown in FIG. 1, that is, the layout of the second qubit 1002 when no air bridge is installed, and FIG. 16B is its equivalent circuit diagram. Further, FIG. 16C is a diagram showing the layout of the second qubit 2 of the second embodiment, and FIG. 16D is its equivalent circuit diagram. As shown in FIGS. 16C and 16D, in the second embodiment, air bridges 207a and 207b are arranged in the vicinity of the connection points with the SQUID 202 on the λ / 4 lines 203a and 203b so as to be equidistant from the branch point 208 of the control line 204. As a result, a superconducting loop 209 (a loop circuit indicated by a dotted line in FIGS. 16C and 16D) of GND plane 206 - air bridge 207a - GND plane 206 - second branch line 2042 - first branch line 2041 - GND plane 206 - air bridge 207b - GND plane 206 is formed so as to surround the outside of the SQUID 202. That is, the superconducting loop 209 is a circuit of a superconductor using the GND plane 206, the air bridges 207a and 207b, the first branch line 2041, and the second branch line 2042. Note that the superconducting loop is also referred to as a superconducting loop circuit. In this way, the first branch line 2041 and the second branch line 2042 of the control line 204 are arranged on the superconducting loop 209. As a property peculiar to superconductivity, there is a property that the magnetic flux penetrating the inside of the superconducting loop must be conserved. In the second embodiment, this property peculiar to superconductivity is utilized. Note that, although not particularly limited in the first embodiment as described above, in this embodiment, with respect to the second qubit 2, the air bridges 207a and 207b, the GND plane 206, and the control line 204 are made of a superconductor. The same applies to the first qubit 1.

[0044] FIGS. 17A and 17B are diagrams for explaining the operation of the second qubit 1002 without an air bridge installed. FIG. 17A is a diagram for explaining the operation when setting the resonance frequency of the qubit 1002, and FIG. 17B is a diagram for explaining the operation of the qubit 1002 when a DC current causing crosstalk flows through the GND plane 1206.

[0045] First, referring to FIG. 17A, in the case of the qubit 1002 without an air bridge installed, the control of the resonance frequency of the qubit 1002 is performed as follows. That is, when a DC control current (control signal) I0 is input from the control line 1204, I0 is split into I1 and I2 by the first branch line 12041 and the second branch line 12042. As a result, a part of the magnetic flux G1 generated by I1 penetrates the loop of the SQUID 1202. As a property peculiar to the SQUID, the magnetic flux penetrating the loop of the SQUID must be an integer multiple of the magnetic flux quantum. Therefore, when the magnetic flux penetrating the loop of the SQUID 1202 among the magnetic flux G1 generated by I1 is not exactly an integer multiple of the magnetic flux quantum, a circulating current flows through the SQUID 1202 so that the total magnetic flux penetrating the loop of the SQUID 1202 becomes an integer multiple of the magnetic flux quantum. The magnetic flux generated by this circulating current is indicated by the symbol G3 in the figure. Note that the symbol G2 represents the magnetic flux generated by I2. On the other hand, when the magnetic flux penetrating the loop of the SQUID 1202 among the magnetic flux G1 generated by I1 is exactly an integer multiple of the magnetic flux quantum, no circulating current flows through the SQUID 1202. By changing the magnitude and direction of the control current I0, the magnitude and direction of I1 also change, and the magnitude and direction of the magnetic flux penetrating the loop of the SQUID 1202 among the magnetic flux G1 generated by I1 can be changed. Therefore, the magnitude and direction of the circulating current flowing through the SQUID 1202, that is, the magnitude and direction of the current flowing through the Josephson junctions 1205a and 1205b, can be controlled by the magnitude and direction of the control current I0. Since the equivalent inductance of the Josephson junction can be controlled by the magnitude of the current flowing through the Josephson junction, the equivalent inductances of the Josephson junctions 1205a and 1205b can be controlled by changing the magnitude and direction of the control current I0. Therefore, the effective inductance of the SQUID 1202 can be controlled, and thereby the resonance frequency of the second qubit 1002 can be controlled.That is, by changing the effective inductance of the SQUID 1202, the total inductance of the second qubit 1002 composed of the SQUID 1202 and the λ / 4 lines 1203a and 1203b can be changed, so that the resonance frequency of the second qubit 1002 can be changed. On the other hand, since I2 is far from the SQUID 1202, the magnetic flux G2 generated by I2 hardly penetrates the loop of the SQUID 1202. Here, since the superconductor has the property of perfect diamagnetism, the magnetic field cannot penetrate the superconductor. Therefore, the magnetic field can only penetrate where there is no superconductor. For this reason, the magnetic flux G2 generated by I2 mainly penetrates the gap between the core wires 12031a and 12031b of the λ / 4 lines 1203a and 1203b and the GND plane 1206, and the magnetic flux G2 generated by I2 has no effect on the SQUID 1202. The operations described so far are the operations as intended.

[0046] On the other hand, referring to FIG. 17B, consider the case where a DC current that causes crosstalk flows in the GND plane 1206 in the qubit 1002 where no air bridge is installed. For example, in the 2-bit distributed-constant quantum circuit of FIG. 1, it is assumed that the DC control current input to the first qubit 1001 flows from the control line 1104 to the GND plane 1106 and then flows into the GND plane 1206. When a DC current IR1 that causes crosstalk flows in the GND plane 1206 as shown in FIG. 17B, a part of the magnetic flux G4 generated by IR1 penetrates the loop of the SQUID 1202. According to the magnitude and direction of the magnetic flux penetrating the loop of the SQUID 1202, a circulating current flows in the SQUID 1202 as described above, and thus a current flows through the Josephson junctions 1205a and 1205b. Therefore, the effective inductance of the SQUID 1202 fluctuates due to the current IR1, and thereby the resonance frequency of the second qubit 1002 fluctuates. This is the mechanism of DC crosstalk, and such DC crosstalk can be observed in the second qubit 1002 when a DC control current is input to the first qubit 1001, and has also been observed in experiments. In FIG. 17B, the magnetic flux generated by the circulating current is indicated by the symbol G5.

[0047] On the other hand, the operation of the second qubit 2 of the second embodiment will be described. FIGS. 18A and 18B are diagrams for explaining the operation of the second qubit 2 of the second embodiment. FIG. 18A is a diagram for explaining the operation when setting the resonance frequency of the second qubit 2, and FIG. 18B is a diagram for explaining the operation of the qubit 2 when a DC current that causes crosstalk flows in the GND plane 206.

[0048] First, referring to FIG. 18A, the control of the resonance frequency of the second qubit 2 of the second embodiment is performed as follows. That is, when a DC control current I0 is supplied from the control line 204, I0 is divided into I1 and I2 by the first branch line 2041 and the second branch line 2042. As a result, a part of the magnetic flux G1 generated by I1 penetrates the loop of the SQUID 202. According to the magnitude and direction of the magnetic flux penetrating the loop of this SQUID 202, a circulating current flows through the SQUID 202 as described above, so that currents flow through the Josephson junctions 205a and 205b. Therefore, by changing the magnitude and direction of the control current I0, the effective inductance of the SQUID 202 can be controlled, and thereby the resonance frequency of the second qubit 2 can be controlled. The magnetic flux generated by this circulating current is indicated by the symbol G3 in the figure. On the other hand, since I2 is separated from the SQUID 202, the magnetic flux G2 generated by I2 hardly penetrates the loop of the SQUID 202. Since the magnetic flux G2 generated by I2 mainly penetrates the gap between the core wires 2031a and 2031b of the λ / 4 lines 203a and 203b and the GND plane 206, it has no effect on the SQUID 202. In the second embodiment, since the air bridges 207a and 207b in the vicinity of the connection points with the SQUID 202 on the λ / 4 lines 203a and 203b are installed at an equal distance from the branch point 208 of the control line 204, the first branch line 2041 and the second branch line 2042 have the same shape and the same inductance. As described above, there is a property peculiar to superconductivity that the magnetic flux penetrating the inside of the superconducting loop 209 must be conserved. However, since I1 and I2 are equal in magnitude and opposite in direction, the magnetic flux G1 (magnetic flux = current × inductance) generated by I1 and the magnetic flux G2 generated by I2 in the area inside the superconducting loop 209 are equal in amount and opposite in direction, so they cancel each other out. For this reason, the magnetic flux in the area inside the superconducting loop 209 is conserved as zero. Therefore, even when a control current is input, no screening current is generated in the superconducting loop 209. Thus, the resonance frequency is not set to an unintended frequency.

[0049] On the other hand, referring to FIG. 18B, consider the case where a DC current that causes crosstalk flows in the GND plane 206 in the second qubit 2 of the second embodiment. When a DC current IR1 that causes crosstalk flows in the GND plane 206 as shown in FIG. 18B, a part of the magnetic flux G4 generated by IR1 penetrates the loop of the SQUID 202. However, as described above, due to the superconducting property that the magnetic flux inside the superconducting loop 209 must be conserved, a shielding current IS1 flows as shown in FIG. 18B. That is, the shielding current IS1 flows along the path of the GND plane 206, the air bridge 207b, the GND plane 206, the first branch line 2041, the second branch line 2042, the GND plane 206, the air bridge 207a, and the GND plane 206. The magnetic flux G6 generated by the shielding current IS1 inside the superconducting loop 209 is completely canceled by the magnetic flux generated by the current IR1 inside the superconducting loop 209. This is because, as described above, there is a superconducting property that the magnetic flux in the superconducting loop must be conserved. A part of the magnetic flux G6 generated by the shielding current IS1 penetrates the loop of the SQUID 202. The magnetic flux G4 generated by the current IR1 that causes crosstalk inside the loop of the SQUID 202 and the magnetic flux G6 generated by the shielding current IS1 inside the loop of the SQUID 202 are in opposite directions. Therefore, inside the loop of the SQUID 202, the magnetic flux G4 generated by the current IR1 that causes crosstalk and the magnetic flux G6 generated by the shielding current IS1 cancel each other out, so that the magnetic flux penetrating the loop of the SQUID 202 becomes zero or very small. At least, due to the effect of the shielding current IS1, the magnetic flux penetrating the loop of the SQUID 202 becomes smaller than the magnetic flux penetrating the loop of the SQUID 202 among the magnetic fluxes generated by IR1 that causes crosstalk. As a result, the variation in the effective inductance of the SQUID 202 due to the current IR1 that causes crosstalk, that is, the variation in the resonance frequency of the second qubit 2, can be suppressed by the effect of the shielding current IS1. That is, DC crosstalk can be suppressed.

[0050] As described above, the second embodiment can suppress not only the cross-talk of high-frequency propagating along the λ / 4 line while suppressing the decrease in the Q value of the qubit, but also the DC cross-talk generated by the DC current propagating through the GND plane.

[0051] Note that it is preferable that the control line 204 is arranged so that no shielding current flows through the superconducting loop 209 due to the control current (control signal) of the control line. That is, as in this embodiment, it is preferable that the control line 204 is arranged so that two types of magnetic fluxes having the same magnitude and opposite directions penetrate the superconducting loop 209 by the control current (control signal) flowing through the control line 204. Note that the magnitudes of these two types of magnetic fluxes do not necessarily have to be exactly the same, and an error is allowed. That is, these two types of magnetic fluxes may be magnetic fluxes having substantially the same magnitude. For example, the difference between the two may be 10% or less of the magnitude of either one. However, although the configuration in which two types of magnetic fluxes having substantially the same magnitude and opposite directions penetrate the superconducting loop 209 is a preferable configuration as a configuration for suppressing the influence of the current IR1 that causes cross-talk, it is not necessarily an essential configuration. Therefore, the superconducting circuit that can achieve the above-described effects, that is, the oscillator, can also be described as follows. The oscillator includes a SQUID, a transmission line (distributed constant line) connected to the SQUID, a GND plane, and a connection circuit. Here, two transmission lines are connected to the SQUID, one transmission line is connected to one end of the SQUID, and the other transmission line is connected to the other end of the SQUID. The connection circuit is a circuit that connects the GND planes existing on both sides of the transmission line, and is provided for each of the two transmission lines. This connection circuit is provided near the node of the standing wave electric field generated during the oscillation of the oscillator. And a superconducting loop circuit using the GND plane and the connection circuit is provided around the SQUID in the oscillator. According to such a configuration, it is possible to suppress the decrease in the Q value of the qubit, suppress the cross-talk of high-frequency propagating along the λ / 4 line, and also suppress the DC cross-talk generated by the DC current propagating through the GND plane.

[0052] Incidentally, the inventor performed a simulation on the position of the air bridge provided for the control line 104 in this embodiment. The simulation results regarding the position of the air bridge provided for the control line 104 will be described below. In this simulation, in the second embodiment, a simulation was performed for the case where one air bridge is installed on the control line. In particular, the simulation examined how the crosstalk suppression effect changes when the position of the air bridge installed on the control line is changed. In the following description, the simulation for the first qubit will be described, and the description of the simulation for the second qubit that obtains the same result will be omitted.

[0053] FIG. 19 is a diagram showing six types of configurations for which simulations were performed. FIG. 19 shows six configuration examples as configuration examples when the number of air bridges installed on the control line in the second embodiment is one. The distances of these six configuration examples from the branch point 108 of the control line 104 to the air bridge 107c on the control line 104 are different. Specifically, simulations were performed for six cases where the distance on the control line 104 from the branch point 108 to the air bridge 107c is approximately λ / 4 (case 1), approximately λ / 6 (case 2), approximately λ / 10 (case 3), approximately λ / 20 (case 4), approximately λ / 50 (case 5), and approximately λ / 100 (case 6). Here, λ is the on-chip wavelength of the 20 GHz signal input from the control line 104, and in this embodiment, λ is approximately 5.9 mm. In this simulation, when a 20 GHz control signal was input to the control line 104 of the first qubit 1, it was examined what percentage of the current flowing through the SQUID 102 of the first qubit 1 was the current flowing through the SQUID 202 of the second qubit 2. The larger this percentage value, the greater the influence of crosstalk, and the smaller this percentage, the smaller the influence of crosstalk (that is, the higher the crosstalk suppression effect).

[0054] The results of the simulation are shown in FIG. 20. FIG. 20 graphically shows the results for the six cases described above. In the graph of FIG. 20, the horizontal axis represents the distance (in mm) from the branch point 108 of the control line 104 to the air bridge 107c installed on the control line 104, divided by the wavelength (5.9 mm) of the 20 GHz signal on the chip. Also, in FIG. 20, the vertical axis represents the percentage of the current flowing through the SQUID 202 of the second qubit 2 with respect to the current flowing through the SQUID 102 of the first qubit 1. Each point plotted in FIG. 20 corresponds to the above-described case 1, case 2, case 3, case 4, case 5, and case 6, in order from the right.

[0055] As shown by the results in Fig. 20, in the second embodiment, when only one air bridge is installed on the control line, it can be seen that the air bridge installed on the control line has a higher crosstalk suppression effect when it is farther from the branch point of the control line than when it is closer to the branch point of the control line. From Fig. 20, it can be seen that in order to suppress crosstalk to less than 10%, the distance from the air bridge installed on the control line to the branch point of the control line is preferably 1 / 20 or more of the wavelength of the control signal (the value on the horizontal axis of Fig. 20 is 0.05 or more). Based on the above, the following can be said. When only one air bridge is installed on the control line, in order to enhance the crosstalk suppression effect, the longer the distance from the air bridge installed on the control line to the branch point of the control line, the better. For example, the distance from the air bridge installed on the control line to the branch point of the control line is preferably 1 / 20 or more of the wavelength of the high-frequency control signal input from the control line (the control signal with a frequency twice the operating frequency of the qubit) on the chip. In other words, the distance on the control line from this air bridge to the branch point is preferably 1 / 20 or more of the wavelength of the control signal. More preferably, the distance from the air bridge installed on the control line to the branch point of the control line is preferably 1 / 10 or more of this wavelength. In the second embodiment, the number of air bridges installed on the control line may be two or more. The above-described position of the air bridge installed on the control line may also be adopted in the first embodiment.

[0056] [First Modification Example of the Second Embodiment] In the second embodiment, the first branch line 2041 and the second branch line 2042 had the same shape and the same inductance. However, even if the first branch line 2041 and the second branch line 2042 do not have the same shape, the same effect as that of the second embodiment can be obtained. In other words, even if the first branch line 2041 and the second branch line 2042 do not have the same inductance, two types of magnetic fluxes having the same magnitude and opposite directions can be made to penetrate the superconducting loop 209 by the control current (control signal) flowing through the control line 204. That is, it is possible to obtain the same effect as that of the second embodiment by other configurations. As an example of a modification of such a second embodiment, for example, the air bridges 207a and 207b are installed at an equal distance from the branch point 208 of the control line 204. Consider the case where the line width of the second branch line 2042 is wider than that of the first branch line 2041. That is, consider the case where the inductance L2 of the second branch line 2042 is smaller than the inductance L1 of the first branch line 2041. In this case, the control current I0 input from the control line 204 is divided into the current I1 flowing through the first branch line 2041 and the current I2 flowing through the second branch line 2042. However, the current is divided in the ratio of the reciprocals of the inductances. That is, I1 : I2 = L2 : L1. Therefore, I1L1 = I2L2. Thus, the magnetic flux I1L1 (the product of I1 and L1) generated by the current I1 flowing through the first branch line 2041 (inductance L1) and the magnetic flux I2L2 (the product of I2 and L2) generated by the current I2 flowing through the second branch line 2042 (inductance L2) are equal regardless of the values of L1 and L2. Here, since the air bridges 207a and 207b are arranged at the positions where the first branch line 2041 is grounded to GND and the second branch line 2042 is grounded, that is, at the ends of the respective branch lines, the magnetic fluxes penetrating the inside of the superconducting loop 209 generated by the control current are the magnetic fluxes I1L1 and I2L2. For this reason, the magnetic fluxes generated by I1 and I2 in the area inside the superconducting loop 209 are equal in amount and opposite in direction, so they cancel each other out.Therefore, there is a property specific to superconductivity that the magnetic flux passing through the inside of the superconducting loop 209 must be conserved as described above. However, the magnetic flux in the area inside the superconducting loop 209 remains zero and is conserved. For this reason, when a control current is input, no screening current is generated in the superconducting loop 209 due to the control current, and thus it does not affect the setting of the resonance frequency.

[0057] [Second Modification of the Second Embodiment] FIG. 21 is a layout of a superconducting circuit according to the second modification. FIG. 22 is an equivalent circuit diagram of the superconducting circuit according to the second modification. The superconducting circuit according to this modification can also be used as a superconducting qubit, similar to the above-described embodiments. Here, similar to the description of the above-described embodiments, the configuration of one qubit will be specifically described with reference to the drawings, and the description of other qubits having the same configuration will be omitted. Also, the description of the same configuration as that of the second embodiment will be appropriately omitted, and the different points will be specifically described. In the above-described embodiment, the terminal side of the control line 204 branched, and the two terminals of the control line 204 were each connected to the GND planes 206 existing on both sides of the control line 204. In contrast, in this modification, the terminal side of the control line 204 is not branched, and the terminal of the control line 204 is connected only to one of the GND planes 206 existing on both sides of the control line 204. That is, in this modification, the control line 204 is a single unbranched line. Note that the terminal side of the control line 204 is wired along the SQUID 202 so that the control line 204 is magnetically coupled to the SQUID 202. In the example shown in the figure, the control line 204 is an L-shaped line, and more specifically, it has the following configuration. That is, the control line 204 in FIG. 21 is an L-shaped line including a portion extending in the first direction (the vertical direction in the drawing) along the SQUID 202 and a portion extending in the second direction (the left-right direction in the drawing). That is, the control line 204 in FIG. 21 is bent at 90 degrees near the SQUID 202, and the portion of the control line 204 extending in the second direction extends away from the SQUID 202.

[0058] In the superconducting qubit according to this modification example, a superconducting loop 209 is formed by air bridges 207a, 207b, and 207c so as to surround the outside of the SQUID 202. That is, in this modification example, the superconducting loop 209 is a superconducting circuit using the GND plane 206 and the air bridges 207a, 207b, and 207c. In the configuration shown in FIG. 21, similar to the first or second embodiment, the air bridges 207a and 207b are provided at positions close to the SQUID 202. The air bridge 207a is a superconducting connection circuit that connects the GND planes 206 existing on both sides of the λ / 4 line 203a, and the air bridge 207b is a superconducting connection circuit that connects the GND planes 206 existing on both sides of the λ / 4 line 203b. Also, the air bridge 207c is a superconducting connection circuit that connects the GND planes 206 existing on both sides of the control line 204.

[0059] Also in this modification example, similar to the first and second embodiments, the air bridges 207a and 207b are installed only at positions as close as possible to the connection points with the SQUID 202 on the λ / 4 lines 203a and 203b. Therefore, also in this modification example, the effects as described in the first and second embodiments, that is, the effect of reducing the high-frequency crosstalk while suppressing the decrease in the Q value of the qubit can be obtained.

[0060] Further, also in this modification example, since the outside of the SQUID 202 is structured such that it is surrounded by the superconducting loop 209, the effect as described in the second embodiment, that is, the effect of suppressing the crosstalk caused by the current flowing through the GND plane by the action of the shielding current can be obtained.

[0061] Here, in the second embodiment, a superconducting loop circuit using the first branch line 2041 and the second branch line 2042 was formed. However, in this modification, such a superconducting loop circuit is not formed. Even when a superconducting loop circuit is formed using the first branch line 2041 and the second branch line 2042, theoretically, as described above, the screening current caused by the control current flowing through the control line 204 is not generated. However, if, for some reason, a screening current caused by the control current occurs, the magnetic flux caused by the screening current may act strongly on the SQUID 202. This is because a large mutual inductance exists between the linearly configured first branch line 2041 and the SQUID 202. When the magnetic flux caused by this screening current acts on the SQUID 202, setting the resonance frequency to the intended value is inhibited. Also, if, for some reason, the magnetic flux generated by the control current flowing through the second branch line 2042 penetrates the loop of the SQUID 202, setting the resonance frequency to the intended value is also inhibited. In contrast, in this modification, the superconducting loop 209 surrounding the SQUID 202 does not use the first branch line 2041 and the second branch line 2042. That is, as described above, the superconducting loop 209 composed of the GND plane 206 and the air bridges 207a, 207b, 207c surrounds the SQUID 202. Therefore, compared with the configuration shown in the second embodiment, it is possible to suppress the inhibition of setting the resonance frequency to the intended value. Also, by not branching the control line 204, the control current contributing to the application of magnetic flux to the SQUID 202 can be increased compared to the case where the control line 204 is branched.

[0062] [Third Embodiment] FIG. 23 shows the layout of the superconducting circuit of the third embodiment. FIG. 24 shows the equivalent circuit diagram of the superconducting circuit of the third embodiment. The superconducting circuit of the third embodiment is a superconducting qubit, similar to the above-described embodiments. Also in the description of this embodiment, as in the description of the above-described embodiments, the configuration of one qubit will be specifically described with reference to the drawings, and the description of other qubits having the same configuration will be omitted. This also applies to the description of other embodiments to be described later, unless otherwise specified. The equivalent circuit diagram of FIG. 24 is the same as the equivalent circuit diagram of the first qubit 1 or the second qubit 2 in FIG. 8, except that the configuration of the control line is different. Specifically, in the superconducting qubit according to the third embodiment, unlike the superconducting qubits of the first and second embodiments, the control line 104 does not branch. And in the superconducting qubit according to the third embodiment, a superconducting loop 109 is formed by air bridges 107a, 107b, 107c so as to surround the outside of the SQUID 102. That is, in this embodiment, the superconducting loop 109 is a superconducting circuit using the GND plane 106 and the air bridges 107a, 107b, 107c. And the control line 104 has a shape that enters from the outside of the superconducting loop 109 into the inside of the superconducting loop 109, turns back inside the superconducting loop 109, and then goes out to the outside of the superconducting loop 109. That is, in this embodiment, the control line 104 is wired in a U shape so as to turn back near the SQUID 102. In this embodiment, the air bridges 107a, 107b are provided at positions close to the SQUID 102, similar to the first or second embodiment. In this embodiment, the air bridge 107c connects the GND plane 106 across the control line 104, similar to the first and second embodiments. However, in this embodiment, the air bridge 107c is a superconducting connection circuit that connects the GND planes 106 existing on both sides of the forward and return paths of the U-shaped control line 104.

[0063] Incidentally, as shown in FIG. 23, the positional relationship among the SQUID 102, the λ / 4 lines 103a and 103b, and the control line 104 is as follows, for example. The λ / 4 lines 103a and 103b and the SQUID 102 are arranged side by side in the first direction (the vertical direction in the drawing) in the vicinity of the SQUID 102. Further, the control line 104 extends in the second direction (the left - right direction in the drawing) in the vicinity of the SQUID 102 and turns back near the SQUID 102. That is, the control line 104 is wired on the side opposite to the SQUID 102 with respect to the turning portion as a reference.

[0064] Also in the third embodiment, as in the first and second embodiments, the air bridges 107a and 107b are installed only at positions as close as possible to the connection points with the SQUID 102 on the λ / 4 lines 103a and 103b. Therefore, also in the third embodiment, the effects as described in the first and second embodiments, that is, the effect of suppressing the decrease in the Q value of the qubit while reducing the high - frequency crosstalk can be obtained.

[0065] In addition, in the third embodiment, since the superconducting loop 109 surrounds the outside of the SQUID 102, the effect as described in the second embodiment, that is, the effect of suppressing the crosstalk caused by the current flowing through the GND plane by the action of the shielding current can be obtained. Also, as shown in FIG. 23, when the control current I0 is supplied from the control line 104 when controlling the qubit, the magnetic fluxes generated by I0 are equal in amount and opposite in direction on the right side and the left side of the control line 104. Therefore, the magnetic fluxes G0a and G0b generated by I0 inside the superconducting loop 109 can be made zero or very small in total. Therefore, the shielding current generated in the superconducting loop when the control current I0 is input from the control line 104 can be made zero or very small. Thus, it does not affect the setting of the resonance frequency.

[0066] [Fourth Embodiment] FIG. 25 shows the layout of the superconducting circuit of the fourth embodiment. FIG. 26 is an equivalent circuit diagram of the superconducting circuit of the fourth embodiment. The superconducting circuit of the fourth embodiment is a superconducting qubit, similar to the above-described embodiments. Also in the description of this embodiment, as in the description of the above-described embodiments, the configuration of one qubit will be specifically described with reference to the drawings, and the description of other qubits having the same configuration will be omitted. The equivalent circuit diagram of FIG. 26 is the same as the equivalent circuit diagram of the first qubit 1 or the second qubit 2 in FIG. 8, except that the configuration of the control line is different. Specifically, in the superconducting qubit according to the fourth embodiment, unlike the superconducting qubits of the first and second embodiments, the control line 104 does not branch. And in the superconducting qubit according to the fourth embodiment, a superconducting loop 109 is formed by air bridges 107a, 107b, 107c, 107d so as to surround the outside of the SQUID 102. That is, in this embodiment, the superconducting loop 109 is a superconducting circuit using the GND plane 106 and the air bridges 107a, 107b, 107c, 107d. And the control line 104 has a shape that enters from the outside of the superconducting loop 109 into the inside of the superconducting loop 109 and then exits to the outside of the superconducting loop 109. That is, in this embodiment, the control line 104 is wired linearly while intersecting three-dimensionally with one of the two transmission lines (λ / 4 lines 103a, 103b) connected to the SQUID 102. More specifically, as shown in FIG. 25, an air bridge 107e is provided in the middle of the control line 104 to straddle the λ / 4 line 103b. That is, the control line 104 and the λ / 4 line 103b intersect three-dimensionally due to the air bridge 107e. In this embodiment, the air bridges 107a, 107b are provided at positions close to the SQUID 102, similar to the first and second embodiments. In this embodiment, the air bridges 107c, 107d connect the GND planes 106 existing on both sides of the control line 104 across the control line 104, similar to the first and second embodiments. The air bridges 107c, 107d are provided on both sides of the position where the control line 104 and the λ / 4 line 103b intersect three-dimensionally.

[0067] Incidentally, as shown in FIG. 25, the positional relationship among the SQUID 102, the λ / 4 lines 103a and 103b, and the control line 104 is, for example, as follows. The λ / 4 lines 103a and 103b and the SQUID 102 are arranged side by side in a first direction (the vertical direction in the drawing) near the SQUID 102. Also, the control line 104 extends while three-dimensionally intersecting the λ / 4 line 103b in a second direction (the left-right direction in the drawing) near the SQUID 102. In other words, the control line 104 is wired across the transmission line in a direction intersecting the direction in which the transmission line and the SQUID are arranged.

[0068] Also in the fourth embodiment, as in the first, second, and third embodiments, the air bridges 107a and 107b are installed only at positions as close as possible to the connection points with the SQUID 102 on the λ / 4 lines 103a and 103b. Therefore, also in the fourth embodiment, the effects as described in the first, second, and third embodiments, that is, the effect of suppressing the decrease in the Q value of the qubit and reducing the high-frequency crosstalk can be obtained.

[0069] Further, in the fourth embodiment, since the superconducting loop 109 surrounds the outside of the SQUID 102, the effects as described in the second and third embodiments, that is, the effect of suppressing the crosstalk caused by the current flowing through the GND plane by the action of the shielding current can be obtained. Also, as shown in FIG. 25, when the control current I0 is supplied from the control line 104 when controlling the qubit, the magnetic fluxes generated by I0 are equal in amount and opposite in direction on the right side and the left side of the control line 104. For this reason, the magnetic fluxes G0a and G0b generated by I0 inside the superconducting loop 109 can be made zero or very small in total. Therefore, when the control current I0 is input from the control line 104, the shielding current generated in the superconducting loop can be made zero or very small. Thus, it does not affect the setting of the resonance frequency.

[0070] [Other configurations] In the first, second, third, and fourth embodiments, an air bridge is used as a connection circuit for electrically short-circuiting the GND planes on both sides of the core wire of the λ / 4 line. Any conductor can be used as the material of the air bridge. However, in order to make the potentials of the GND planes on both sides of the core wire as equipotential as possible, a conductor with lower electrical resistance is more preferable, and a material that becomes a superconductor at the temperature (about 10 mK) at which the quantum circuit operates is most preferable. In order to obtain the effect of suppressing DC crosstalk using the shielding current, a superconducting loop circuit made of a superconductor is required. Therefore, the air bridge and the GND plane constituting the superconducting loop circuit need to be superconductors. Examples of materials that become superconductors at the temperature at which the quantum circuit operates include aluminum (Al), tantalum (Ta), niobium (Nb), and alloys containing these. Instead of the air bridge, bonding wires may be used to electrically short-circuit the GNDs on both sides of the λ / 4 line or the control line. Any conductor can be used as the material of the bonding wire, but a conductor with lower electrical resistance is more preferable, and a material that becomes a superconductor at the temperature at which the quantum circuit operates is most preferable. Also in the case of using bonding wires, the bonding wires must be superconductors in order to obtain the effect of suppressing DC crosstalk using the shielding current. Examples of materials that become superconductors at the temperature at which the quantum circuit operates include aluminum (Al). Instead of the air bridge, the following connection circuit may be used. That is, TSVs (Through Silicon Vias) are formed on the GND planes on both sides of the core wire of the λ / 4 line, and a structure in which wirings for electrically connecting these TSVs are formed on the back surface of the chip may be used as the connection circuit. Even with such a structure, a connection circuit that intersects the core wire of the λ / 4 line three-dimensionally without contacting the core wire of the λ / 4 line can be realized. Any conductor can be used as the material of the TSV and the wiring on the back surface of the chip. However, in order to make the potentials of the GND planes on both sides of the core wire as equipotential as possible, a conductor with lower electrical resistance is more preferable, and a material that becomes a superconductor at the temperature (about 10 mK) at which the quantum circuit operates is most preferable.In order to obtain the suppression effect of DC crosstalk using the shielding current, a superconducting loop circuit made of a superconductor is required. Therefore, the TSVs, the wiring on the back surface of the chip, and the GND plane that constitute the superconducting loop circuit need to be superconductors. Examples of materials that become superconductors at the temperature at which the quantum circuit operates include aluminum (Al), tantalum (Ta), niobium (Nb), and alloys containing these. Further, in a configuration in which a chip on which a quantum circuit is formed is flip-chip connected to a substrate such as an interposer, instead of using an air bridge, bumps for connecting the chip and the substrate and wiring on the substrate may be used. That is, the bumps and the wiring on the substrate may electrically short-circuit the λ / 4 line on the chip or the GND planes on both sides of the control line. Also in this case, the material of the bumps and the wiring on the substrate may be any conductor, but a conductor with a smaller electrical resistance is more preferable, and a material that is a superconductor at the temperature at which the quantum circuit operates is most preferable. Examples of materials that become superconductors at the temperature at which the quantum circuit operates include indium (In) for the bumps, and niobium (Nb), aluminum (Al), etc. for the wiring of the interposer. Also in this case, in order to obtain the suppression effect of DC crosstalk using the shielding current, the bumps and the wiring on the substrate must be superconductors.

[0071] Also, in the first, second, third, and fourth embodiments, as an example of a quantum circuit in which a plurality of quantum bits are integrated, the embodiments have been described using a 2-bit distributed constant type quantum circuit. However, the number of integrated quantum bits does not have to be 2, and these embodiments can also be applied to a quantum circuit in which any number of 3 or more distributed constant type quantum bits are integrated, and the same effects can be obtained.

[0072] Also, although the distributed constant type quantum bits have been described so far, the idea of reducing crosstalk caused by current flowing through the GND plane by the shielding effect of the superconducting loop is also applicable to the lumped constant type quantum bits. Hereinafter, the lumped constant type quantum bits will be described.

[0073] FIG. 27 is an example of an equivalent circuit diagram of a lumped-constant type qubit 2000. The lumped-constant type qubit 2000 is a loop-shaped circuit in which each terminal of a SQUID 2001 is connected to each terminal of a capacitor 2003 by superconducting wiring. In other words, the input / output terminals of the SQUID 2001 are shunted by the capacitor 2003. That is, it can also be said that a loop circuit is configured by connecting the capacitor 2003 and the SQUID 2001 in a ring shape, and the SQUID 2001 is incorporated in the loop line. The SQUID 2001 is a loop-shaped circuit including two Josephson junctions 2002a and 2002b. That is, the SQUID 2001 is configured by connecting the two Josephson junctions 2002a and 2002b in a ring shape. One terminal of the SQUID 2001 may be grounded. A control line 2004 is magnetically coupled to the SQUID 2001. In other words, the control line 2004 and the SQUID 2001 are magnetically coupled non-contactingly by mutual inductance.

[0074] In the distributed-constant type qubit shown in FIG. 2, a resonator was configured using a SQUID and a λ / 4 line. However, as shown in FIG. 27, the lumped-constant type qubit 2000 is different from the distributed-constant type qubit in that an LC resonance circuit is configured by the effective inductance of the SQUID 2001 and the capacitor 2003. The distributed-constant type qubit as shown in FIG. 2 has a size comparable to the length of the wavelength corresponding to the operating frequency of the qubit, so the size of the qubit is very large. On the other hand, in the lumped-constant type qubit 2000 as shown in FIG. 27, since a distributed-constant line is not used, a qubit can be realized with a circuit that is very small compared to the wavelength corresponding to the operating frequency of the qubit 2000. For this reason, when integrating a large number of qubits 2000, there is an advantage that a large number of qubits 2000 can be integrated in a small area.

[0075] The method of operating the lumped-constant type qubit 2000 is the same as that of the distributed-constant type qubit in FIG. 2. That is, by inputting a DC control signal from the control line 2004, the resonance frequency of the qubit 2000 can be set. With a DC control signal for setting a certain resonance frequency input to the control line 2004, the qubit 2000 can be oscillated by further inputting a control signal having a frequency twice the set resonance frequency to the control line 2004. The operating frequency (set resonance frequency) of the qubit 2000 is, for example, about 10 GHz. Therefore, when operating the qubit 2000, a signal obtained by superimposing a DC control signal and a high-frequency control signal of about 20 GHz is input from the control line 2004. Note that, as described above, the lumped-constant type qubit oscillates by a control signal from the control line. For this reason, a configuration including the lumped-constant type qubit may be referred to as an oscillator.

[0076] FIG. 28 shows an example of the layout of the lumped-element type qubit 2000 of FIG. 27. In this example, a thin film of a superconducting material (such as niobium or aluminum) is formed on a silicon substrate to realize the qubit 2000 having a coplanar waveguide structure. As shown in FIG. 28, in the qubit 2000, a cross-shaped electrode (also referred to as a conductive member) 2005 is formed inside a cross-shaped region formed in the GND plane 2006. That is, the GND plane 2006 is arranged around the electrode 2005 so as to surround the electrode 2005. Note that the GND plane 2006 and the electrode 2005 are separated from each other, and there is a gap between them. One end of the electrode 2005 is connected to the GND plane 2006 using two thin electrodes. A Josephson junction 2002a is provided in the middle of one of the two thin electrodes, and a Josephson junction 2002b is provided in the middle of the other. With such a configuration, the SQUID 2001 is constituted by the electrode 2005, the GND plane 2006, and the two Josephson junctions 2002a and 2002b. That is, the SQUID 2001 uses the electrode 2005 and the GND plane 2006 to connect the two Josephson junctions 2002a and 2002b constituting the SQUID 2001 in a loop shape. In this way, one end of the SQUID 2001 is connected to the electrode 2005, and the other end is connected to the GND plane 2006. It can also be said that the SQUID 2001 is arranged between the electrode 2005 and the GND plane 2006. In this way, in the qubit 2000, as shown in FIG. 28, the SQUID 2001 is connected to one of the four end portions (that is, the tips of the four arms of the cross-shaped electrode 2005) that are the portions protruding outside the cross-shaped electrode 2005 so as to bridge the GND plane 2006. Since there is a gap between the cross-shaped electrode 2005 and the GND plane, a capacitor 2003 is formed between the electrode 2005 and the GND plane 2006. Also, a control line 2004 is arranged linearly near the SQUID 2001. That is, in FIG. 28, the horizontally long electrode arranged below the cross-shaped electrode 2005 is the control line 2004.When a current flows through the control line 2004, since a part of the magnetic flux generated by the current flowing through the control line 2004 penetrates the loop of the SQUID 2001, it is possible to control the effective inductance of the SQUID 2001 or oscillate the quantum bit 2000.

[0077] In the layout of FIG. 28, it is susceptible to the influence of crosstalk described so far, particularly the crosstalk caused by current flowing through the GND plane. This can occur when, for example, a DC control current is input to a certain quantum bit 2000 in a chip integrating a plurality of quantum bits 2000, and the magnetic field generated when the control current flows through the control line and then through the GND plane is sensed by the SQUID 2001 of another quantum bit 2000. A method similar to the method described above can be applied to reduce the influence of such crosstalk. Hereinafter, embodiments for reducing the influence of crosstalk in a lumped-constant type quantum bit will be described.

[0078] [Fifth Embodiment] FIG. 29 is a diagram showing the layout of qubits according to the fifth embodiment. Hereinafter, differences from the configuration shown in FIG. 28 will be described, and descriptions of the same configurations will be omitted as appropriate. Since the equivalent circuit diagram of the lumped-constant type qubit 2000 according to this embodiment is the same as that in FIG. 27, the layout shown in FIG. 28 will be described. Also in this embodiment, a qubit 2000 having a coplanar waveguide structure is shown. For this reason, as shown in FIG. 29, the electrode 2005 and the control line 2004 are configured as coplanar waveguides, and a superconducting GND plane 2006 exists around the line configured as a coplanar waveguide. Also in this embodiment, as shown in FIG. 29, in the qubit 2000, a cross-shaped electrode (also referred to as a conductive member) 2005 is formed inside a cross-shaped region formed in the GND plane 2006. That is, the GND plane 2006 is arranged around the electrode 2005 so as to surround the electrode 2005. Also, a gap exists between the GND plane 2006 and the electrode 2005, and a capacitor 2003 is formed between the electrode 2005 and the GND plane 2006 due to this gap. Also in this embodiment, in the qubit 2000, a SQUID 2001 is connected to one of the four end portions (that is, the tips of the four arms of the cross-shaped electrode 2005) that are portions protruding outward from the cross-shaped electrode 2005 so as to bridge the GND plane 2006. However, although one end of the SQUID 2001 is directly connected to the electrode 2005, the other end is connected to the GND plane 2006 via a thin electrode 2008. Note that the electrode 2008 may be referred to as a connection conductive member or a conductive line. In the example shown in FIG. 29, the electrode 2005, the SQUID 2001, and the electrode 2008 are arranged in the first direction (the vertical direction in the drawing). In other words, the SQUID 2001 and the electrode 2008 are arranged in the direction in which the arm to which the SQUID 2001 is connected extends among the four arms of the cross-shaped electrode 2005. Also in this embodiment, the SQUID 2001 is composed of a Josephson junction 2002a provided in the middle of one of the two thin electrodes and a Josephson junction 2002b provided in the middle of the other.That is, in the present embodiment, in order to connect the two Josephson junctions 2002a and 2002b that constitute the SQUID 2001 in a loop shape, the electrodes 2005 and 2008 are used. Therefore, as described above, one end of the SQUID 2001 is connected to the electrode 2005, and the other end is connected to the GND plane 2006 via the electrode 2008. It can also be said that the SQUID 2001 is disposed between the electrode 2005 and the GND plane 2006.

[0079] As shown in FIG. 29, in the present embodiment, the control line 2004 is disposed beside the SQUID 2001, and the tip of the control line 2004 branches into a first branch line 20041 and a second branch line 20042 at the branch point 2108. Then, in order to make the first branch line 20041 magnetically coupled to the SQUID 2001, the first branch line 20041 is disposed near the SQUID 2001. On the other hand, in order to prevent the second branch line 20042 from being magnetically coupled to the SQUID 2001, the second branch line 20042 is disposed away from the SQUID 2001. Specifically, in order to make the first branch line 20041 magnetically coupled to the SQUID 2001 while preventing the second branch line 20042 from being magnetically coupled to the SQUID 2001, these branch lines are wired as follows. That is, the first branch line 20041 is wired along the SQUID 2001, and the second branch line 20042 is wired along the electrode 2008 in the direction opposite to that of the first branch line 20041. Both the first branch line 20041 and the second branch line 20042 are connected to the GND plane 2006.

[0080] The control line 2004 is a T-shaped line, and the first branch line 20041 and the second branch line 20042 branched at the branch point 2108 are arranged linearly side by side. Here, the positional relationship among the SQUID 2001, the electrode 2005, and the control line 2004 is, for example, as follows as shown in FIG. 29. The electrode 2005 and the SQUID 2001 are arranged side by side in the first direction (the vertical direction in the drawing) in the vicinity of the SQUID 2001 as described above. Also, the first branch line 20041 and the second branch line 20042 are also wired in this first direction (the vertical direction in the drawing). Note that the non-branched portion of the control line 204 (that is, the portion of the control line 2004 other than the first branch line 20041 and the second branch line 20042) extends in the second direction (the left-right direction in the drawing) in the vicinity of the SQUID 2001 and extends from the branch point 2108 so as to move away from the SQUID 2001. That is, the non-branched portion of the control line 2004 is wired on the side opposite to the SQUID 2001 with the branch point 2108 as a reference. The first branch line 20041 exists at a position facing the SQUID 2001, while the second branch line 20042 exists at a position not facing the SQUID 2001.

[0081] In this embodiment, the air bridge 2007a is provided near the terminal on the electrode 2005 side of the SQUID 2001. The air bridge 2007a is a superconducting connection circuit that connects the GND planes 2006 existing on both sides of the connection point between the SQUID 2001 and the electrode 2005. In the configuration shown in FIG. 29, the air bridge 2007a straddles the vicinity of the connection portion between the electrode 2005 and the SQUID 2001 and connects the GND planes 2006 existing on both sides of this connection portion. More specifically, the air bridge 2007a connects the GND planes 2006 existing on both sides of the end portion of the electrode 2005 that is connected to the SQUID 2001, straddling the end portion. Thereby, in this embodiment, a superconducting loop 2009 is formed so as to surround the SQUID 2001 by the air bridge 2007a, the GND plane 2006, the first branch line 20041, and the second branch line 20042. Specifically, this superconducting loop 2009 surrounds the SQUID 2001 and the thin electrode 2008. The air bridge 2007a, the GND plane 2006, the first branch line 20041, and the second branch line 20042 that constitute the superconducting loop 2009 are all superconductors. The first branch line 20041 and the second branch line 20042 that constitute the superconducting loop 2009 have the same shape. Thus, in this embodiment, since there is a superconducting loop 2009 that surrounds the SQUID 2001, an effect can be obtained in which the influence of crosstalk can be reduced. Further, in the superconducting loop 2009, since the first branch line 20041 and the second branch line 20042 have the same shape, the current input from the control line 2004 is shunted equally and in opposite directions to the first branch line 20041 and the second branch line 20042. Therefore, the generation of the shielding current in the superconducting loop 2009 due to inputting a control current to the control line 2004 is suppressed, and the resonance frequency is suppressed from being set to an unintended frequency.

[0082] Note that, as shown in FIG. 30, an air bridge 2007b that connects the GND planes 2006 on both sides of the core wire of the non-branched portion of the control line 2004 may be further added.

[0083] [Modification of the Fifth Embodiment] FIG. 31 shows the layout of a lumped-constant type qubit according to a modification of the fifth embodiment. Hereinafter, differences from the fifth embodiment will be specifically described. In the fifth embodiment, the terminal side of the control line 2004 branches, and the two terminals of the control line 2004 are respectively connected to the GND planes 2006 existing on both sides of the control line 2004. In contrast, in this modification, the terminal side of the control line 2004 does not branch, and the terminal of the control line 2004 is connected only to one of the GND planes 2006 existing on both sides of the control line 2004. That is, in this modification, the control line 2004 is a single line without branching. Note that the terminal side of the control line 2004 is wired along the SQUID 2001 so that the control line 2004 is magnetically coupled to the SQUID 2001. In the example shown in the figure, the control line 2004 is an L-shaped line, and more specifically, it has the following configuration. That is, the control line 2004 in FIG. 31 is an L-shaped line including a portion extending in the first direction (the vertical direction in the drawing) along the SQUID 2001 and a portion extending in the second direction (the horizontal direction in the drawing). That is, the control line 2004 in FIG. 31 is bent by 90 degrees near the SQUID 2001, and the portion of the control line 2004 extending in the second direction extends away from the SQUID 2001. Note that in the example shown in FIG. 31, the control line 2004 is L-shaped, but the control line 2004 may be a straight line extending in the first direction (the vertical direction in the drawing).

[0084] In the superconducting qubit according to this modification example, a superconducting loop 2009 is formed by air bridges 2007a and 2007b so as to surround the outside of the SQUID 2001. That is, in this modification example, the superconducting loop 2009 is a superconducting circuit using the GND plane 2006 and the air bridges 2007a and 2007b. In the configuration shown in FIG. 31, the air bridge 2007a is provided in the vicinity of the terminal on the electrode 2005 side of the SQUID 2001, similar to the fifth embodiment. The air bridge 2007a is a superconducting connection circuit that connects the GND planes 2006 existing on both sides of the connection portion between the SQUID 2001 and the electrode 2005. Further, the air bridge 2007b is a superconducting connection circuit that connects the GND planes 2006 existing on both sides of the control line 2004.

[0085] Also in this modification example, since there is a superconducting loop 2009 surrounding the SQUID 2001, an effect can be obtained that the influence of crosstalk caused by current flowing through the GND plane can be reduced.

[0086] Here, in the fifth embodiment, a superconducting loop circuit using the first branch line 20041 and the second branch line 20042 was formed, but in this modification example, such a superconducting loop circuit is not formed. Therefore, as described in the description of the second modification example of the second embodiment, it is possible to suppress the inhibition of setting the resonance frequency to an intended value. Further, by not branching the control line 2004, the control current contributing to the application of magnetic flux to the SQUID 2001 can be increased compared to the case where the control line 2004 is branched.

[0087] [Sixth Embodiment] Next, another embodiment for reducing the influence of crosstalk in a lumped-constant type qubit will be described. FIG. 32 shows the layout of a lumped-constant type qubit according to the sixth embodiment. Hereinafter, the differences from the fifth embodiment will be specifically described. As shown in FIG. 32, in this embodiment, unlike the fifth embodiment, the control line 2004 is not branched. Also, in this embodiment, a superconducting loop 2009 is formed by air bridges 2007a and 2007b so as to surround the outside of the SQUID 2001. That is, in this embodiment, the superconducting loop 2009 is a superconducting circuit using the GND plane 2006 and the air bridges 2007a and 2007b. And the control line 2004 has a shape such that it enters from the outside of the superconducting loop 2009 into the inside of the superconducting loop 2009, turns back inside the superconducting loop 2009, and then goes out to the outside of the superconducting loop 2009. That is, in this embodiment, the control line 2004 is wired in a U shape so as to turn back near the SQUID 2001. In this embodiment, the air bridge 2007a is provided in the vicinity of the terminal on the electrode 2005 side of the SQUID 2001, similar to the fifth embodiment. The air bridge 2007b connects the GND plane 106 across the control line 2004. Specifically, the air bridge 2007b is a superconducting connection circuit that connects the GND planes 2006 existing on both sides of the forward and return paths of the U-shaped control line 104.

[0088] Incidentally, the positional relationship among the SQUID 2001, the electrode 2005, and the control line 2004 is as follows, for example, as shown in FIG. 32. The electrode 2005 and the SQUID 2001 are arranged side by side in the first direction (the vertical direction of the drawing) near the SQUID 2001. Also, the control line 2004 extends in the second direction (the left - right direction of the drawing) near the SQUID 2001 and turns back near the SQUID 2001. That is, the control line 2004 is wired on the side opposite to the SQUID 2001 with respect to the turning - back portion. Thus, the structures of the control line 2004 and the superconducting loop 2009 of the present embodiment are the same as those in the third embodiment (the embodiment of the distributed - constant - type quantum bit).

[0089] Also in this embodiment, since there is a superconducting loop 2009 surrounding the SQUID 2001, an effect can be obtained that the influence of crosstalk caused by current flowing through the GND plane can be reduced. Also, for the same reason as in the third embodiment, the generation of the screening current in the superconducting loop 2009 due to inputting a control current to the control line 2004 is suppressed, and the resonance frequency is suppressed from being set to an unintended frequency.

[0090] [Seventh Embodiment] Next, another embodiment for reducing the influence of crosstalk in a lumped-constant type qubit will be described. FIG. 33 shows the layout of a lumped-constant type qubit according to the seventh embodiment. Hereinafter, differences from the fifth embodiment will be specifically described. As shown in FIG. 33, in this embodiment, unlike the fifth embodiment, the control line 2004 does not branch. Also, in this embodiment, superconducting loops 2009 are formed by air bridges 2007a, 2007b, 2007c so as to surround the outside of the SQUID 2001. That is, in this embodiment, the superconducting loop 2009 is a superconducting circuit using the GND plane 2006 and the air bridges 2007a, 2007b, 2007c. And the control line 2004 has a shape that enters from the outside of the superconducting loop 2009 into the inside of the superconducting loop 2009 and then exits to the outside of the superconducting loop 2009. That is, the control line 2004 is wired linearly with a three-dimensional intersection with the electrode 2008 connected to the SQUID 2001. Note that the control line 2004 may be wired linearly with a three-dimensional intersection with the SQUID 2001. More specifically, as shown in FIG. 33, an air bridge 2007d is provided in the middle of the control line 2004 to straddle the electrode 2008 or the SQUID 2001. That is, the control line 2004 and the electrode 2008 or the SQUID 2001 intersect three-dimensionally due to the air bridge 2007d. In this embodiment, the air bridge 2007a is provided in the vicinity of the terminal on the electrode 2005 side of the SQUID 2001, similar to the fifth embodiment. The air bridges 2007b, 2007c connect the GND planes 106 existing on both sides of the control line 2004. The air bridges 2007b, 2007c are provided on both sides of the position where the control line 2004 and the electrode 2008 or the SQUID 2001 intersect three-dimensionally.

[0091] Note that the positional relationship among the SQUID 2001, the electrode 2005, and the control line 2004 is as follows, for example, as shown in FIG. 33. The electrode 2005, the SQUID 2001, and the electrode 2008 are arranged in the first direction (the vertical direction of the drawing) in the vicinity of the SQUID 2001. Further, the control line 2004 extends while three-dimensionally intersecting with the electrode 2008 or the SQUID 2001 in the second direction (the left-right direction of the drawing) in the vicinity of the SQUID 2001. In other words, the control line 2004 is wired across the electrode 2008 or the SQUID 2001 in a direction intersecting with the direction in which the electrode 2005 and the SQUID 2001 are arranged. Thus, the structure of the control line 2004 and the structure of the superconducting loop 2009 in the present embodiment have the same structure as those in the fourth embodiment (the embodiment of the distributed-constant type quantum bit).

[0092] Also in the present embodiment, since there is a superconducting loop 2009 surrounding the SQUID 2001, an effect can be obtained that the influence of crosstalk caused by current flowing through the GND plane can be reduced. Further, for the same reason as in the fourth embodiment, the generation of the shielding current in the superconducting loop 2009 due to inputting a control current to the control line 2004 is suppressed, and the resonance frequency is suppressed from being set to an unintended frequency.

[0093] The above has described the fifth to seventh embodiments. The lumped-constant type circuits shown in these embodiments, that is, the oscillators including qubits having the above-described configurations, can also be described as follows. The oscillator has a GND plane (GND plane 2006), a conductive member (electrode 2005), a SQUID (SQUID 2001), a first connection circuit (air bridge 2007a), and a superconducting loop circuit (superconducting loop 2009). Here, the GND plane is made of a superconductor. The conductive member is surrounded by the GND plane with a gap therebetween. In this oscillator, a capacitor (capacitor 2003) is formed by the gap between the GND plane and the conductive member. One end of the SQUID is connected to the conductive member, and the other end is connected to the GND plane. The first connection circuit is a superconducting circuit that connects the GND planes existing on both sides in the vicinity of the connection portion between the conductive member and the SQUID. The superconducting loop circuit is a circuit using the GND plane and the first connection circuit and surrounds the SQUID. According to such an oscillator, the influence of crosstalk caused by current flowing through the GND plane can be reduced by the superconducting loop surrounding the SQUID. Also, in this oscillator, a control line (control line 2004) may be arranged so that two types of magnetic fluxes having the same magnitude and opposite directions penetrate the superconducting loop circuit by a control signal flowing through the control line. This control line is magnetically coupled to the SQUID and a control signal is input thereto. Note that the magnitudes of the above-described two types of magnetic fluxes do not have to be exactly the same, and an error is allowed. That is, these two types of magnetic fluxes may be magnetic fluxes having substantially the same magnitude. For example, the difference between the two may be 10% or less of the magnitude of either one. By doing so, the generation of screening current in the superconducting loop circuit due to inputting a control signal to the control line is suppressed, and the resonance frequency is suppressed from being set to an unintended frequency.

[0094] In particular, the oscillator shown in the fifth embodiment can also be described as an oscillator having the following characteristics. That is, in the oscillator shown in the fifth embodiment, in the above-described oscillator, the control line branches from a branch point on the control line into a first branch line and a second branch line. Here, the first branch line is wired along the SQUID, and the second branch line is wired in the direction opposite to that of the first branch line. The superconducting loop circuit is a circuit using a GND plane, a first connection circuit, a first branch line, and a second branch line. Further, the length of the first branch line used in the superconducting loop circuit is the same as the length of the second branch line used in the superconducting loop circuit. Note that the lengths of the first branch line and the second branch line do not have to be exactly the same, and an error is allowed. That is, the lengths of these two lines may be substantially the same. For example, the difference between the two may be 10% or less of the length of either one. According to such a configuration, an example of the arrangement of the control line can be provided in which two types of magnetic fluxes having substantially the same magnitude and opposite directions penetrate the superconducting loop circuit by the control signal flowing through the control line. Note that this oscillator may have a connection circuit (air bridge 2007b that connects the GND planes across the control line) that connects the GND planes existing on both sides of the control line.

[0095] In particular, the oscillator shown in the sixth embodiment can also be described as an oscillator having the following characteristics. That is, in the oscillator shown in the sixth embodiment, in the above-described oscillator, the control line is wired in a U shape so as to fold back near the SQUID. Further, this oscillator has a second connection circuit of a superconductor (air bridge 2007b that connects the GND planes across the control line) that connects the GND planes existing on both sides of the two forward and return paths of the U-shaped control line. The superconducting loop circuit is a circuit using a GND plane, a first connection circuit, and a second connection circuit. According to such a configuration, an example of the arrangement of the control line can be provided in which two types of magnetic fluxes having the same magnitude and opposite directions penetrate the superconducting loop circuit by the control signal flowing through the control line.

[0096] Also, in particular, the oscillator shown in the seventh embodiment can also be described as an oscillator having the following characteristics. That is, in the oscillator shown in the seventh embodiment, in the above-described oscillator, the control line is a connection conductive member (electrode 2008) for connecting the other end of the SQUID and the GND plane or is wired linearly in a three-dimensional intersection with the SQUID. Further, this oscillator has a second connection circuit of a superconductor (air bridges 2007b and 2007c that connect the GND planes across the control line) that connects the GND planes existing on both sides of the control line. The second connection circuit is provided on both sides of the position where the control line and the connection conductive member or the SQUID intersect three-dimensionally. And the superconducting loop circuit is a circuit using the GND plane, the first connection circuit, and the second connection circuit. According to such a configuration, an arrangement example of the control line can be provided in which two types of magnetic fluxes having the same magnitude and opposite directions penetrate the superconducting loop circuit by the control signal flowing through the control line.

[0097] [First Modification Example of the Fifth to Seventh Embodiments] Regarding the above-described fifth to seventh embodiments, the following modification examples can also be provided. Here, a modification example for the fifth embodiment will be described, but the same modification examples are possible for the sixth and seventh embodiments.

[0098] FIG. 34 shows an equivalent circuit diagram of a lumped-constant type qubit 2000 according to a first modification of the fifth embodiment. This qubit 2000 is different from the lumped-constant type qubit 2000 shown in FIG. 27 in that a linear inductor 2010 is inserted into a loop composed of a SQUID 2001 and a capacitor 2003. The lumped-constant type qubit 2000 in FIG. 27 has a problem that its non-linearity is too high for application to a quantum computer. Here, the non-linearity of the circuit constituting the qubit is quantified by a coefficient (non-linear coefficient) defined by the coefficient of the non-linear term of the Hamiltonian of the circuit constituting the qubit. In the qubit 2000 shown in FIG. 34, the non-linear coefficient can be adjusted by the inductance of the linear inductor 2010. Also, for this reason, without increasing the capacitance of the capacitor 2003, the non-linearity can be reduced, so that an increase in loss in the circuit constituting the qubit can also be suppressed. The layout of the qubit 2000 in FIG. 34 is shown in FIG. 35. The layout in FIG. 35 is different from the layout in FIG. 29 in that the shape of the electrode 2005 is adjusted so that the linear inductance of the electrode 2005 becomes a predetermined value. Thus, in this modification, the electrode 2005 is used as a linear inductor having a predetermined inductance. In the example shown in FIG. 35, specifically, by narrowing the width of the cross-shaped arm portion of the electrode 2005 compared to FIG. 29, the linear inductance of the electrode 2005 is made larger than that of the layout in FIG. 29. The layout shown in FIG. 35 is the same as the layout shown in FIG. 29 except for the above points. For this reason, also in this modification, the influence of crosstalk caused by current flowing through the GND plane can be reduced, and it is possible to suppress the resonance frequency from being set to an unintended frequency by the screening current generated in the superconducting loop due to the control current.

[0099] Note that, as shown in FIG. 36, an air bridge 2007b connecting the GND planes 2006 on both sides of the core wire of the non-branching portion of the control line 2004 may be further added.

[0100] [Second Variant of the Fifth to Seventh Embodiments] For the fifth to seventh embodiments described above, it is also possible to provide the following variant. Here, a variant for the fifth embodiment will be described, but the same variants are possible for the sixth and seventh embodiments as well.

[0101] FIG. 37 shows an equivalent circuit diagram of the lumped-constant type qubit 2000 according to the second variant of the fifth embodiment. This qubit 2000 is different from the lumped-constant type qubit 2000 shown in FIG. 27 in that a Josephson junction 2011 is inserted into the loop composed of the SQUID 2001 and the capacitor 2003. As described above, the lumped-constant type qubit 2000 in FIG. 27 has a problem that its non-linearity is too high for application to a quantum computer. In the qubit 2000 shown in FIG. 37, the non-linear coefficient can be adjusted by adding the Josephson junction 2011 to the loop composed of the SQUID 2001 and the capacitor 2003. Also, in order to reduce non-linearity, it is not necessary to increase the capacitance of the capacitor 2003, so an increase in loss in the circuit constituting the qubit can also be suppressed. The layout of the qubit 2000 in FIG. 37 is shown in FIG. 38. The layout in FIG. 38 is different from the layout in FIG. 29 in that a Josephson junction 2011 is added in the middle of the thin electrode 2008. That is, in this variant, the SQUID 2001 is connected to the GND plane 2006 via the Josephson junction 2011. The layout shown in FIG. 37 is the same as the layout shown in FIG. 29 except for the above points. Therefore, also in this variant, the influence of crosstalk caused by current flowing through the GND plane can be reduced, and it is possible to suppress the resonance frequency from being set to an unintended frequency due to the screening current generated in the superconducting loop by the control current.

[0102] Note that, as shown in FIG. 39, an air bridge 2007b that connects the GND planes 2006 on both sides of the core wire of the control line 2004 may be further added.

[0103] [Third Variation of the Fifth to Seventh Embodiments] Regarding the fifth to seventh embodiments described above, it is also possible to provide the following variations. This variation is different from the fifth to seventh embodiments described above in that the critical current values of the two Josephson junctions 2002a and 2002b constituting the SQUID 2001 are set to different values. By adopting such a configuration, an inflection point can be provided in the function showing the relationship between the resonance frequency of the loop circuit composed of the SQUID 2001 and the capacitor 2003 and the magnetic field applied to the SQUID 2001 (the function showing the magnetic field dependence of the resonance frequency). Therefore, by setting this inflection point as the operating point and operating the quantum bit 2000, it is possible to suppress the deviation of the resonance frequency variation accompanying the periodic magnetic field variation by the alternating control signal. For this reason, it is possible to suppress the adverse effects when a deviation occurs in the resonance frequency variation. In order to change the critical current value of the Josephson junction, for example, the area of the Josephson junction may be changed. That is, by using two Josephson junctions having different areas, Josephson junctions 2002a and 2002b having different critical current values can be realized.

[0104] Also in this variation, it is possible to reduce the influence of crosstalk caused by current flowing through the GND plane, and it is possible to suppress the resonance frequency from being set to an unintended frequency due to the screening current generated in the superconducting loop caused by the control current.

[0105] Note that also in this variation, an air bridge 2007b connecting the GND planes 2006 on both sides of the core wire of the control line 2004 may be added.

[0106] [Eighth Embodiment] So far, the distributed-constant or lumped-constant qubits formed on the chip have been described. However, in a configuration where a chip on which a quantum circuit is formed is flip-chip connected to a substrate such as an interposer, a configuration for suppressing crosstalk may be realized. That is, as described above, instead of using an air bridge, bumps for connecting the chip and the substrate and wirings on the substrate may be used. As an eighth embodiment, an example of such a configuration will be described. Note that flip-chip connection may also be referred to as flip-chip mounting.

[0107] In this embodiment, the circuit described in the fifth embodiment is realized in a configuration where the chip 2018 is flip-chip connected to the substrate 2019. FIG. 40 is a diagram showing the chip 2018 forming a part of the qubit 2000. On this chip 2018, a GND plane 2006, electrodes 2005, SQUIDs 2001, etc. are formed using a superconducting material. Since these arrangements are the same as those in the fifth embodiment, the description thereof is omitted. The equivalent circuit diagram of the circuit of this embodiment is the same as FIG. 27, and a part of the equivalent circuit diagram is formed on the chip 2018. Specifically, on the chip 2018, a GND plane 2006, electrodes 2005, SQUIDs 2001, and electrodes 2008 are formed. Also, on the chip 2018, a capacitor 2003 is formed by the gap between the GND plane 2006 and the electrode 2005. The chip 2018 is flip-chip connected to a substrate such as an interposer using bumps, and in FIG. 40, reference numerals 2012a and 2012b indicate the positions where the bumps are connected. As shown in FIG. 40, these bumps (bumps 2022a and 2022b described later) are provided on both sides near the connection portion of the electrode 2005 with the SQUID 2001. That is, the positions of these bumps correspond to the portions where the air bridge 2007a is connected to the GND plane 2006 in the fifth embodiment.

[0108] FIG. 41 is a diagram showing a substrate 2019 such as an interposer to which the chip 2018 is flip-chip connected. In flip-chip connection, the plane of the chip 2018 shown in FIG. 40 and the plane of the substrate 2019 shown in FIG. 41 face each other and are connected via bumps (bumps 2022a and 2022b described later). On the substrate 2019, a GND plane 2015 of the substrate and a control line 2016 are formed using a superconducting material. The tip of the control line 2016 branches into a first branch line 2017a and a second branch line 2017b at a branch point 20170. And in order for the first branch line 2017a to be magnetically coupled to the SQUID 2001, the first branch line 2017a is arranged near the SQUID 2001. On the other hand, in order for the second branch line 2017b not to be magnetically coupled to the SQUID 2001, the second branch line 2017b is arranged at a position away from the SQUID 2001. Specifically, in order for the first branch line 2017a to be magnetically coupled to the SQUID 2001 while the second branch line 2017b is not magnetically coupled to the SQUID 2001, these branch lines are wired as follows. That is, the first branch line 2017a of the substrate 2019 is wired along the SQUID 2001 of the chip 2018, and the second branch line 2017b of the substrate 2019 is wired along the electrode 2008 of the chip 2018 in a direction opposite to the first branch line 2017a. Both the first branch line 2017a and the second branch line 2017b are connected to the GND plane 2015. The first branch line 2017a and the second branch line 2017b are symmetric lines, and in the example shown in FIG. 41, they are shaped like winding in opposite directions to each other. Specifically, the first branch line 2017a and the second branch line 2017b extend a predetermined length in a first direction (the vertical direction of the drawing) from the branch point 20170, and the tips of each extend a predetermined length in the direction (the left direction of the drawing) in which the unbranched portion of the control line 2016 extends from the branch point 20170. That is, in the example shown in FIG. 41, the first branch line 2017a and the second branch line 2017b are folded back in the direction in which the unbranched portion extends.However, this is only an example, and the first branch line 2017a and the second branch line 2017b do not have to be folded back. That is, the control line 2016 may be a T-shaped line that branches into the first branch line 2017a and the second branch line 2017b at the branch point 20170. Note that the non-branching portion of the control line 2016 refers to the portion of the control line 2016 other than the first branch line 2017a and the second branch line 2017b. The non-branching portion of the control line 2016 extends in the second direction (the left-right direction in the drawing) in the vicinity of the SQUID 2001. In the example shown here, specifically, as can be seen from FIGS. 40 and 41, the non-branching portion of the control line 2016 extends across the connection point between the SQUID 2001 and the electrode 2008.

[0109] In FIG. 41, reference numerals 2013a and 2013b indicate the positions where the above-described bumps are connected. In the example shown in FIG. 41, the connection positions of the bumps indicated by reference numerals 2013a and 2013b are located within the bridge electrode (conductive member) 2014 provided with a gap around it, but the gap does not have to be provided around the bridge electrode 2014. That is, the bumps may be connected to the GND plane 2015. Note that the bridge electrode 2014 is a superconductor.

[0110] FIG. 42 is a cross-sectional view of a structure in which chip 2018 and substrate 2019 are flip-chip connected using bumps 2022a and 2022b, specifically showing a cross-sectional view taken along the cutting line A-A' in FIGS. 40 and 41. In FIG. 42, reference numeral 2020 indicates the silicon substrate of chip 2018, and reference numeral 2021 indicates the silicon substrate of substrate 2019. Also, as shown in FIG. 42, let the distance between chip 2018 and substrate 2019 be d. Although not shown explicitly in FIG. 42, substrate 2019 may further have TSVs (Through Silicon Vias). The TSVs can, for example, serve to electrically connect the GND plane on the back surface of the substrate (the lower surface of substrate 2019 in FIG. 42) formed on the back surface of substrate 2019 and the GND plane 2015 on the surface of substrate 2019 (the upper surface of substrate 2019 in FIG. 42). Alternatively, the TSVs can, for example, serve to electrically connect the control line on the back surface of the substrate formed on the back surface of substrate 2019 and the control line 2016 on the surface of substrate 2019 formed on the surface of substrate 2019. As shown in FIG. 42, an electrically connected circuit of GND plane 2006 of chip 2018 - bump 2022a - bridge electrode 2014 of substrate 2019 - bump 2022b - GND plane 2006 of chip 2018 is formed, and this circuit serves the same function as an air bridge. Therefore, using GND plane 2006 of chip 2018, bumps 2022a and 2022b, and bridge electrode 2014 of substrate 2019, a superconducting loop 2009 surrounding the outside of SQUID 2001 is formed. Thus, also in this embodiment, the influence of crosstalk caused by current flowing through the GND plane can be reduced.

[0111] When a control signal is input from the control line 2016 in FIG. 41, the control signal branches and flows into the first branch line 2017a and the second branch line 2017b. Since the first branch line 2017a is positioned directly below the SQUID 2001 in FIG. 40, the SQUID 2001 senses the magnetic flux generated by the current flowing through the first branch line 2017a. On the other hand, since the second branch line 2017b is not positioned directly below the SQUID 2001, the current flowing through the second branch line 2017b hardly acts on the SQUID 2001. And since the first branch line 2017a and the second branch line are shaped to wind in opposite directions, the magnetic flux generated by the current flowing through the first branch line 2017a and the magnetic flux generated by the current flowing through the second branch line 2017b are equal in amount and opposite in direction inside the two branch lines. For this reason, also in this embodiment, it is possible to suppress the resonance frequency from being set to an unintended frequency by the screening current generated in the superconducting loop due to the control current.

[0112] In FIGS. 40 to 42, a lumped-constant type qubit having a configuration in which a control line branches as in the fifth embodiment has been taken as an example. Similarly, for various qubits already described, a configuration using flip-chip connection can be provided. For example, a configuration using flip-chip connection can be provided for a lumped-constant type qubit using a control line of another shape or a distributed-constant type qubit. Some examples of such other configurations of qubits using flip-chip connection will be illustrated below.

[0113] The configuration of the chip and the substrate when connecting the GND planes on both sides of the control line as shown in FIG. 30 will be described. The layout of the chip when connecting the GND planes on both sides of the control line is shown in FIG. 43. Also, the layout of the substrate when connecting the GND planes on both sides of the control line is shown in FIG. 44. Hereinafter, the differences from FIGS. 40 and 41 described above will be explained. In order to realize the connection of the GND planes 2015 on both sides of the control line 2016, bumps for connecting the GND planes 2015 on both sides of the control line 2016 of the substrate 2019 to the bridge electrodes (conductive members) 2014a of the chip 2018 are provided between the chip 2018 and the substrate 2019. In FIG. 43, reference numerals 2012c and 2012d indicate the connection positions of these bumps on the chip 2018. Also, in FIG. 44, reference numerals 2013c and 2013d indicate the connection positions of these bumps on the substrate 2019. In the example shown in FIG. 43, the connection positions of the bumps are located within the bridge electrode 2014a provided with voids around it, but voids do not have to be provided around the bridge electrode 2014a. That is, the bumps may be connected to the GND plane 2006. Note that the bridge electrode 2014a is a superconductor. Therefore, the above-described bumps and the bridge electrode 2014a of the chip 2018 serve as the air bridge 2007b in FIG. 30. In this way, by flip-chip connecting the chip of FIG. 43 and the substrate of FIG. 44, a configuration similar to the embodiment shown in FIG. 30 can be realized with a three-dimensional circuit, and the same effects as the embodiment of FIG. 30 can be obtained.

[0114] Next, the configuration of the chip and the substrate when a U-shaped control line is used as shown in FIG. 32 will be described. The layout of the chip when a U-shaped control line is used is shown in FIG. 45. Also, the layout of the substrate when a U-shaped control line is used is shown in FIG. 46. Hereinafter, the differences from FIGS. 40 and 41 described above will be explained.

[0115] FIG. 45 is a diagram showing a chip 2018 forming part of a qubit 2000. On this chip 2018, a GND plane 2006, an electrode 2005, and a SQUID 2001 are formed using a superconducting material. Since these arrangements are the same as those in the sixth embodiment, the description thereof is omitted. In FIG. 45, reference numerals 2012a and 2012b indicate positions where bumps are connected, and those positions are the same as the positions shown in FIG. 40.

[0116] FIG. 46 is a diagram showing a substrate 2019 such as an interposer to which the chip 2018 is flip-chip connected. On the substrate 2019, a GND plane 2015 of the substrate and a control line 2016 are formed using a superconducting material. Considering the superconducting loop 2009 projected onto the substrate 2019, which will be described later, the control line 2016 has a shape such that it enters from the outside of the projected superconducting loop 2009 into the inside of the superconducting loop 2009, folds back inside the superconducting loop 2009, and then exits to the outside of the superconducting loop 2009. That is, the control line 2016 is wired in a U shape so as to fold back near the SQUID 2001. The control line 2016 extends in a second direction (the left-right direction in the drawing) near the SQUID 2001 and folds back near the SQUID 2001.

[0117] In FIG. 46, reference numerals 2013a and 2013b indicate the positions where the above-described bumps are connected. In the example shown in FIG. 46, the connection positions of the bumps indicated by reference numerals 2013a and 2013b are located within a bridge electrode (conductive member) 2014 provided with a gap around it, but a gap may not be provided around the bridge electrode 2014. That is, a bump may be connected to the GND plane 2015. Note that the bridge electrode 2014 is a superconductor.

[0118] As can be seen from FIGS. 45 and 46, an electrically connected circuit is formed, namely, the GND plane 2006 of chip 2018 - bump - bridge electrode 2014 of substrate 2019 - bump - GND plane 2006 of chip 2018. Therefore, using the GND plane 2006 of chip 2018, the bump, and the bridge electrode 2014 of substrate 2019, a superconducting loop 2009 surrounding the outside of SQUID 2001 is formed. It should be noted that, as is clear from this, in the case of a configuration by flip - chip connection, a structure that serves the role of the air - bridge 2007b in FIG. 32 is unnecessary.

[0119] In this way, by flip - chip connecting the chip in FIG. 45 and the substrate in FIG. 46, a configuration similar to that of the sixth embodiment can be realized with a three - dimensional circuit, and the same effects as those of the sixth embodiment can be obtained.

[0120] Next, the configurations of the chip and the substrate when a linear control line is used as shown in FIG. 33 will be described. The layout of the chip when a linear control line is used is shown in FIG. 47. Also, the layout of the substrate when a linear control line is used is shown in FIG. 48. Hereinafter, the differences from FIGS. 40 and 41 described above will be explained.

[0121] FIG. 47 is a diagram showing chip 2018 forming part of quantum bit 2000. On this chip 2018, using a superconducting material, a GND plane 2006, an electrode 2005, a SQUID 2001, and an electrode 2008 are formed. Since these arrangements are the same as those in the seventh embodiment, the description thereof is omitted. In FIG. 47, reference numerals 2012a and 2012b indicate the positions where the bumps are connected, and those positions are the same as the positions shown in FIG. 40.

[0122] FIG. 48 is a diagram showing a substrate 2019 such as an interposer to which the chip 2018 is flip-chip connected. On the substrate 2019, a GND plane 2015 of the substrate and a control line 2016 are formed using a superconducting material. Considering the projection of the superconducting loop 2009 described later onto the substrate 2019, the control line 2016 has a shape that enters from the outside of the projected superconducting loop 2009 into the inside of the superconducting loop 2009 and then exits to the outside of the superconducting loop 2009. That is, the control line 2016 is wired linearly over the electrode 2008 connected to the SQUID 2001 or over the SQUID 2001. The control line 2016 extends while intersecting the electrode 2008 or the SQUID 2001 three-dimensionally in the second direction (the left-right direction in the drawing) in the vicinity of the SQUID 2001. In other words, the control line 2016 is wired to go over the electrode 2008 or the SQUID 2001 in a direction intersecting the direction in which the electrode 2005 and the SQUID 2001 are arranged.

[0123] In FIG. 48, reference numerals 2013a and 2013b indicate the positions where the above-described bumps are connected. In the example shown in FIG. 48, the connection positions of the bumps indicated by reference numerals 2013a and 2013b are located within a bridge electrode (conductive member) 2014 provided with a gap around it, but a gap may not be provided around the bridge electrode 2014. That is, a bump may be connected to the GND plane 2015. Note that the bridge electrode 2014 is a superconductor.

[0124] As can be seen from FIGS. 47 and 48, an electrically connected circuit of the GND plane 2006 of the chip 2018 - bump - the bridge electrode 2014 of the substrate 2019 - bump - the GND plane 2006 of the chip 2018 is formed. Therefore, using the GND plane 2006 of the chip 2018, the bump, and the bridge electrode 2014 of the substrate 2019, a superconducting loop 2009 surrounding the outside of the SQUID 2001 is formed. Note that, as is clear from this, in the case of a configuration by flip - chip connection, a structure that serves the role of the air bridges 2007b and 2007c in FIG. 33 is unnecessary.

[0125] Thus, by flip - chip connecting the chip in FIG. 47 and the substrate in FIG. 48, a configuration similar to that of the seventh embodiment can be realized with a three - dimensional circuit, and the same effects as those of the seventh embodiment can be obtained.

[0126] [Ninth Embodiment] Hereinafter, another embodiment in a configuration where the chip 2018 is flip - chip connected to the substrate 2019 will be described as the ninth embodiment. Before explaining the details of the ninth embodiment, first, considerations regarding the eighth embodiment will be described.

[0127] FIG. 49 is a diagram in which drawings for explanation are added to the layout shown in FIG. 41. Specifically, it is a diagram in which a drawing of projecting the SQUID 2001 of the chip 2018 onto the substrate 2019 is added. Note that, similarly, in some of the figures described later, a drawing of projecting the SQUID 2001 of the chip 2018 onto the substrate 2019 is added.

[0128] As shown in FIG. 49, a superconducting loop 2500 that is closed on the substrate 2019 is formed on the substrate 2019 according to the eighth embodiment. This superconducting loop 2500 is a superconducting loop different from the superconducting loop 2009 described above. In the configuration where the chip 2018 is flip-chip connected to the substrate 2019, when the quantum circuit is operated, current may flow through the GND plane 2015 of the substrate 2019. This may occur, for example, when a control current is input to the control line 2016 on the substrate 2019, and after the control current flows through the control line 2016, it flows to the GND plane 2015 of the substrate 2019. So far, a configuration for suppressing crosstalk caused by current flowing through the GND plane 2006 of the chip 2018 has been described. In contrast, the ninth embodiment shows a configuration for suppressing crosstalk caused by current flowing through the GND plane 2015 of the substrate 2019.

[0129] FIG. 50 is a diagram for explaining the problem when a current IR1 that causes crosstalk flows through the GND plane 2015 of the substrate 2019 shown in FIG. 49. In this case, a part of the magnetic flux G10 generated by IR1 penetrates the superconducting loop 2500 of the substrate 2019. Since the magnetic flux penetrating the inside of the superconducting loop 2500 of the substrate 2019 must be conserved, a shielding current IS1 as shown in FIG. 50 flows. As a result, IS1 generates a magnetic flux G11, and the magnetic flux G11 generated inside the superconducting loop 2500 of the substrate 2019 cancels the magnetic flux G10 generated by IR1 inside the superconducting loop 2500 of the substrate 2019. However, as shown in FIG. 50, since the path of the shielding current IS1 passes very close to the SQUID 2001, there is a possibility that the SQUID 2001 on the chip 2018 may sense a part of the magnetic flux G11 generated by the shielding current IS1. Then the SQUID 2001 will be controlled (for example, the resonance frequency of the quantum bit will fluctuate). It is preferable to layout the substrate so as to eliminate such possibilities as much as possible.

[0130] FIG. 51 is an example of the layout of such a substrate and is the layout of the substrate 2019 according to the ninth embodiment. In the configuration shown in FIG. 51, a superconducting loop 2600 is formed by using bumps that connect the GND plane 2015 of the substrate 2019 and the GND plane 2006 of the chip 2018. In FIG. 51, reference numerals 2012e and 2012f indicate the positions where these bumps are connected. As shown in FIG. 51, in the present embodiment, the GND plane 2015 has a region of the SQUID 2001 projected onto the substrate 2019 and its peripheral region cut out. That is, the GND plane 2015 has a shape that is cut out in a predetermined shape (a rectangle in the example shown in FIG. 51) so as to be spaced apart from the SQUID 2001 projected onto the substrate 2019 by a predetermined interval. Note that, in the present embodiment, in order to secure a path for the control line 2016, the GND plane 2015 has a shape such that the outside of the rectangle is cut out along the control line 2016.

[0131] The superconducting loop 2600 is a loop circuit having a shape corresponding to the outer periphery of the above-described rectangle, and is a three-dimensional superconducting loop using the substrate 2019, the above-described bumps, and the chip 2018. As shown by reference numerals 2012e and 2012f in FIG. 51, the bumps are provided on both sides of the control line 2016 in order to form the superconducting loop 2600 across the control line 2016. In the example shown in FIG. 51, specifically, it is provided in the vicinity of the above-described rectangle. With such a configuration, a three-dimensional superconducting loop 2600 using the GND plane 2015 of the substrate 2019, the bumps, and the GND plane 2006 of the chip 2018 is configured. Note that, among the superconducting loop 2600, the line crossing the control line 2016 is realized using the GND plane 2006 of the bumps and the chip 2018, and the remaining lines are realized by the GND plane 2015 of the substrate 2019. That is, the superconducting loop 2600 is a circuit using the GND plane 2015 of the substrate 2019 and a connection circuit (the GND plane 2006 of the bumps and the chip 2018) that connects the GND planes 2015 of the substrate 2019 existing on both sides of the control line 2016. Note that the superconducting loop 2600 is a circuit that surrounds a region (a region where the projected SQUID 2001 exists) on the substrate 2019 corresponding to the region where the SQUID 2001 exists as shown in FIG. 51, with a predetermined interval (see g1, g2, g3, g4 in FIG. 51). The control line 2016 is not branched and is linear. The control line 2016 enters the superconducting loop 2600 from the outside of the superconducting loop 2600 of the substrate 2019 and is connected to the superconducting loop 2600 (the GND plane 2015 of the substrate 2019). That is, the linear control line 2016 is provided so as to cross the superconducting loop 2600 (the above-described rectangle). More specifically, the control line 2016 is wired linearly over or through the electrode 2008 connected to the SQUID 2001. The control line 2016 extends while being three-dimensionally crossed with the electrode 2008 or the SQUID 2001 in the second direction (the left-right direction in the drawing) in the vicinity of the SQUID 2001.In other words, the control line 2016 is wired so as to cross the direction in which the electrodes 2005 and the SQUID 2001 are arranged and to go over the electrode 2008 or the SQUID 2001.

[0132] According to the configuration according to the ninth embodiment, the superconducting loop 2600 of the substrate 2019 can be arranged at a position far from the position of the projected SQUID 2001. For this reason, as shown in FIG. 52, even when a current IR1 that causes crosstalk flows through the GND plane 2015 of the substrate 2019, the magnetic flux G11 generated by the shielding current IS1 flowing through the superconducting loop 2600 of the substrate 2019 does not affect the SQUID 2001. Or, even if it does have an effect, there is an effect that the influence can be reduced compared to the layout configuration shown in FIG. 50.

[0133] Here, when the distance between the chip and the substrate is d (see FIG. 42), the distances between the sides of the superconducting loop 2600 (the rectangle described above) and the sides of the projected SQUID 2001, that is, g1, g2, g3, and g4 in FIG. 51 are preferably as large as possible. That is, the separation distance between the SQUID 2001 and the superconducting loop 2600 is preferably as large as possible. For example, g1, g2, g3, and g4 are preferably at least d or more, more preferably 2d or more, and even more preferably 3d or more.

[0134] [First Modification of the Ninth Embodiment] A first modification of the ninth embodiment will be described. Note that descriptions of configurations similar to those of the ninth embodiment will be omitted as appropriate. FIG. 53 is a layout of the substrate 2019 according to the first modification of the ninth embodiment. FIG. 54 is a cross-sectional view of a structure in which the chip 2018 and the substrate 2019 are flip-chip connected using bumps 2022a and 2022b, specifically showing a cross-sectional view taken along the cutting line B-B' in FIG. 53. As shown in FIG. 53, the control line 2016 may be disposed only inside the superconducting loop 2600 of the substrate 2019. In this case, as shown in FIG. 54, the control line 2016 reaches the surface of the substrate 2019 from the back surface of the substrate 2019 through the TSV 2016a that penetrates the substrate 2019, passes through the wiring for the control line on the surface of the substrate 2019, and returns to the back surface of the substrate 2019 through the TSV 2016b. Note that the back surface of the substrate 2019 refers to the lower surface of the substrate 2019 in FIG. 54, and the surface of the substrate 2019 refers to the upper surface of the substrate 2019 in FIG. 54. Also, in FIG. 54, the reference numeral 2016c indicates the wiring for the control line on the back surface of the substrate 2019. Also, in the configuration shown in FIG. 54, the GND plane 2015 on the surface of the substrate 2019 is connected to the GND plane 2015b on the back surface of the substrate 2019 via the TSV 2015a.

[0135] In the ninth embodiment, a part of the superconducting loop 2600 used the GND plane 2006 of the chip 2018, but in this modification, as shown in FIG. 53, the superconducting loop 2600 is closed on the substrate 2019. That is, in this modification, as shown in FIG. 53, the superconducting loop 2600 is the GND plane 2015 of the substrate 2019 that completely surrounds the region of the substrate 2019 corresponding to the region where the SQUID 2001 exists with a predetermined interval. Even with such a configuration, the same effect as that of the ninth embodiment can be obtained.

[0136] [Second Modification of the Ninth Embodiment] A second modification of the ninth embodiment will be described. Regarding the configurations similar to those of the first modification of the ninth embodiment, the description will be omitted as appropriate. FIG. 55 is a layout of the substrate 2019 according to the second modification of the ninth embodiment.

[0137] Since the current flowing through the control line 2016 is a current obtained by superimposing a DC current and a high-frequency current such as 20 GHz, a high-frequency signal flows through the control line 2016. Therefore, it is preferable to improve the transmission characteristics of the control line 2016 at high frequencies. Usually, since the impedance of the signal source device that supplies a signal to the control line 2016 is 50 Ω, it is necessary to make the characteristic impedance of the control line 2016 as close as possible to 50 Ω in order to improve the transmission characteristics of the control line 2016 at high frequencies. In the first modification of the ninth embodiment, since the distance from the control line 2016 to the GND plane 2015 is relatively far, the characteristic impedance of the control line 2016 may become higher than 50 Ω. In particular, as shown in FIG. 53, on both sides of the control line 2016 (the upper side and the lower side of the control line 2016 in FIG. 53), the distance from the control line 2016 to the GND plane 2015 is far. In the case where the characteristic impedance of the control line 2016 becomes higher than 50 Ω in the structure shown in FIG. 53, it is preferable to lower the characteristic impedance of the control line 2016 and make it closer to 50 Ω. For this purpose, it is necessary to arrange the GNDs on both sides of the control line 2016 closer to the control line 2016 than the configuration shown in FIG. 53. In the second modification of the ninth embodiment, as shown in FIG. 55, GND (GND line 2015c) is arranged closer to the control line 2016 than the GND plane 2015 on both sides of the control line 2016. That is, GND lines 2015c are provided along the control line 2016 on both sides of the control line 2016. Thereby, the characteristic impedance of the control line 2016 is made close to a predetermined value (for example, 50 Ω). Therefore, it can be expected that the transmission characteristics of the control line 2016 at high frequencies are improved compared to the configuration of the first modification. Note that the above-described GND line 2015c is connected to the GND plane on the back surface of the substrate 2019 via the TSV 2015d. Also, the control line 2016 is connected to the wiring for the control line on the back surface of the substrate 2019 via the TSV 2016a (TSV 2016b).The control line 2016 and the GND line 2015c are wired inside the superconducting loop 2600 on the surface of the substrate 2019 facing the chip 2018. The control line 2016 is connected to the TSV 2016a (TSV 2016b) penetrating the inside of the substrate 2019, and the GND line 2015c is connected to the TSV 2015d penetrating the inside of the substrate 2019. The TSV 2015d is provided along the TSV 2016a (TSV 2016b).

[0138] [Third Modification of the Ninth Embodiment] The third modification of the ninth embodiment will be described. Note that the description of the configuration similar to the second modification of the ninth embodiment will be omitted as appropriate. FIG. 56 is a layout of the substrate 2019 according to the third modification of the ninth embodiment. The configuration shown in FIG. 56 is also a structure for making the characteristic impedance of the control line 2016 close to a predetermined value (for example, 50 Ω), similar to the second modification described above. In the configuration shown in FIG. 55, two GND TSVs 2015d were arranged on both sides of each of the TSVs 2016a and 2016b for the control line 2016. On the other hand, in the configuration shown in FIG. 56, four GND TSVs 2015d are arranged around each of the TSVs 2016a and 2016b for the control line 2016. On the surface of the substrate 2019, the GND line 2015c is wired so as to surround the control line 2016.

[0139] Incidentally, it is most preferable to arrange TSVs for GND so as to completely surround the periphery of the TSV for the control line, creating a TSV structure similar to a coaxial cable, in order to improve the high-frequency characteristics of the control line 2016. That is, it is most preferable to use a double-structure TSV having a GND TSV in the shape of a hollow cylinder and a control-line TSV that passes through the hollow part and is electrically insulated from the GND TSV via silicon to improve the high-frequency characteristics of the control line. However, if it is difficult to form such a coaxial TSV, for example, by arranging four GND TSVs 2015d around the TSV 2016a (TSV 2016b) for the control line 2016 as shown in FIG. 56, and making the structure approximately close to a coaxial structure, the high-frequency characteristics will be improved. Arranging four GND TSVs 2015d as shown in FIG. 56 rather than arranging two GND TSVs 2015d as shown in FIG. 55 results in a shape of the TSV closer to a coaxial structure, so it can be expected that the high-frequency characteristics of the control line 2016 will be even better in the configuration of FIG. 56 than in the configuration of FIG. 55. Thus, a plurality of TSVs 2015d may be provided for one TSV 2016a (TSV 2016b) so as to surround the TSV 2016a (TSV 2016b). Note that the number of TSVs 2015d surrounding the periphery of the TSV 2016a (TSV 2016b) is not limited to two or four, and may be three or five or more.

[0140] [Other Modifications of the Ninth Embodiment] As another modification of the ninth embodiment, configurations as shown in FIGS. 57 and 58 are also conceivable. These examples are the same as the ninth embodiment except that the shape of the control line 2016 is U-shaped. That is, as shown in FIG. 57 or FIG. 58, the control line 2016 may enter from the outside of the superconducting loop 2600 of the substrate 2019 into the inside of the superconducting loop 2600 of the substrate 2019, fold back inside the superconducting loop 2600 of the substrate 2019, and then go out to the outside of the superconducting loop 2600. Also, in the configurations shown in FIGS. 57 and 58, similar to the configurations shown in FIGS. 53, 55, and 56, the control line 2016 may be arranged only inside the superconducting loop 2600 of the substrate 2019 by using TSVs.

[0141] Note that the present invention is not limited to the above-described embodiments, and can be appropriately modified without departing from the gist. For example, the oscillator described above can be used for any application. For example, the oscillator described above may be used as a phase detector or as a quantum computer.

[0142] Also, part or all of the above embodiments can be described as follows in the appended claims, but are not limited thereto. (Appended Claim 1) A ground plane of a superconductor, A conductive member surrounded with a gap on the ground plane, A SQUID having one end connected to the conductive member and the other end connected to the ground plane, A first connection circuit of a superconductor that connects the ground planes existing on both sides in the vicinity of the connection portion between the conductive member and the SQUID, A superconducting loop circuit that surrounds the SQUID and uses the ground plane and the first connection circuit And an oscillator having the same. (Appended Claim 2) It has a control line that is magnetically coupled to the SQUID and to which a control signal is input, The control line is arranged such that two types of magnetic fluxes having substantially the same magnitude and opposite directions penetrate the superconducting loop circuit by the control signal flowing through the control line. The oscillator according to Supplementary Note 1. (Supplementary Note 3) The control line branches into a first branch line and a second branch line from a branch point on the control line. The first branch line is wired along the SQUID. The second branch line is wired in a direction opposite to that of the first branch line. The superconducting loop circuit is a circuit using the ground plane, the first connection circuit, the first branch line, and the second branch line. The length of the first branch line used in the superconducting loop circuit is substantially the same as the length of the second branch line used in the superconducting loop circuit. The oscillator according to Supplementary Note 2. (Supplementary Note 4) A control line that is magnetically coupled to the SQUID and to which a control signal is input, and a second connection circuit that connects the ground planes existing on both sides of the control line. The oscillator according to any one of Supplementary Notes 1 to 3, having the above. (Supplementary Note 5) The control line is wired in a U shape so as to fold back near the SQUID. The oscillator has a second connection circuit of a superconductor that connects the ground planes existing on both sides of the forward and return paths of the U-shaped control line. The superconducting loop circuit is a circuit using the ground plane, the first connection circuit, and the second connection circuit. The oscillator according to Supplementary Note 2. (Supplementary Note 6) The control line is a connection conductive member for connecting the other end of the SQUID and the ground plane or is wired linearly in a three-dimensional intersection with the SQUID. The oscillator has a second connection circuit of a superconductor that connects the ground planes existing on both sides of the control line. The second connection circuit is provided on both sides of the position where the control line and the connection conductive member or the SQUID intersect three-dimensionally. The superconducting loop circuit is a circuit using the ground plane, the first connection circuit, and the second connection circuit. The oscillator according to appended note 2. (Appended note 7) A control line that is magnetically coupled to the SQUID and to which a control signal is input, and a second connection circuit of a superconductor that connects the ground planes existing on both sides of the control line are provided. The terminal side of the control line is wired along the SQUID, and the terminal of the control line is connected to one of the ground planes existing on both sides of the control line. The superconducting loop circuit is a circuit using the ground plane, the first connection circuit, and the second connection circuit. The oscillator according to appended note 1. (Appended note 8) The conductive member is used as a linear inductor. The oscillator according to any one of appended notes 1 to 7. (Appended note 9) The other end of the SQUID is connected to the ground plane via a Josephson junction. The oscillator according to any one of appended notes 1 to 8. (Appended note 10) The two Josephson junctions included in the SQUID have different critical current values. The oscillator according to any one of appended notes 1 to 9. (Appended note 11) A control line that is magnetically coupled to the SQUID and to which a control signal is input is provided on a substrate, and the ground plane, the conductive member, and the SQUID are provided on a chip that is flip-chip connected to the substrate. The first connection circuit is composed of a bump that connects the ground plane of the chip and a conductive member included in the substrate, and the conductive member included in the substrate. The oscillator according to Appendix 1 or 2. (Appendix 12) The superconducting loop circuit is a first superconducting loop circuit. The oscillator further includes a second superconducting loop circuit. The second superconducting loop circuit is a circuit that surrounds, with a predetermined interval, a region on the substrate corresponding to the region where the SQUID exists, and uses a ground plane of the substrate and a second connection circuit that connects the ground planes of the substrate existing on both sides of the control line. The oscillator according to Appendix 11. (Appendix 13) The superconducting loop circuit is a first superconducting loop circuit. The oscillator further includes a second superconducting loop circuit. The second superconducting loop circuit is the ground plane of the substrate that completely surrounds, with a predetermined interval, a region on the substrate corresponding to the region where the SQUID exists. The oscillator according to Appendix 11. (Appendix 14) Ground lines are provided along the control line on both sides of the control line. The oscillator according to Appendix 13. (Appendix 15) The control line is connected to a first through electrode that penetrates the inside of the substrate. The ground line is connected to a second through electrode that penetrates the inside of the substrate. The second through electrode is provided along the first through electrode. The oscillator according to Appendix 14. (Appendix 16) A plurality of the second through electrodes are provided for one of the first through electrodes so as to surround the first through electrode. The oscillator according to Appendix 15.

Description of Reference Numerals

[0143] 1, 2 qubit 102 SQUID 103a, 103b λ / 4 line 104 control line 106 GND plane 107 air bridge 108 branching point 109 superconducting loop 202 SQUID 203a, 203b λ / 4 line 204 control line 206 GND plane 207 air bridge 208 branching point 209 superconducting loop 301, 302, 303 capacitor 1001, 1002 qubit 1041, 1042 branching line 1102 SQUID 1103a, 1103b λ / 4 line 1104 control line 1106 GND plane 1107 air bridge 1202 SQUID 1203a, 1203b λ / 4 line 1204 control line 1206 GND plane 2000 qubit 2001 SQUID 2002a, 2002b Josephson junction 2003 capacitor 2004 control line 2005 electrode 2006 GND plane 2007 air bridge 2008 electrode 2009 superconducting loop 2010 inductor 2011 Josephson junction 2014, 2014a bridge electrode 2015 GND Plane 2015a TSV 2015b GND Plane 2015c GND Line 2015d TSV 2016 Control Line 2016a, 2016b TSV 2017a, 2017b Branch Line 2018 Chip 2019 Substrate 2020, 2021 Silicon Substrate 2022a, 2022b Bump 2041, 2042 Branch Line 2108 Branch Point 2500, 2600 Superconducting Loop 11041, 11042 Branch Line 20041, 20042 Branch Line 20170 Branch Point

Claims

1. A ground plane of a superconductor, a conductive member surrounded by the ground plane with a gap therebetween, a SQUID having one end connected to the conductive member and the other end connected to the ground plane, a first connection circuit of a superconductor connecting the ground planes existing on both sides in the vicinity of the connection portion between the conductive member and the SQUID, a superconducting loop circuit surrounding the SQUID and using the ground plane and the first connection circuit, a control line magnetically coupled to the SQUID and to which a control signal is input and the control line is arranged such that two types of magnetic fluxes having substantially the same magnitude and opposite directions penetrate the superconducting loop circuit by the control signal flowing through the control line. An oscillator.

2. The control line is branched into a first branch line and a second branch line from a branch point on the control line, the first branch line is wired along the SQUID, the second branch line is wired in a direction opposite to that of the first branch line, the superconducting loop circuit is a circuit using the ground plane, the first connection circuit, the first branch line, and the second branch line, and the length of the first branch line used in the superconducting loop circuit is substantially the same as the length of the second branch line used in the superconducting loop circuit. The oscillator according to claim 1.

3. A ground plane of a superconductor, a conductive member surrounded by the ground plane with a gap therebetween, a SQUID having one end connected to the conductive member and the other end connected to the ground plane, a first connection circuit of a superconductor connecting the ground planes existing on both sides in the vicinity of the connection portion between the conductive member and the SQUID, a superconducting loop circuit surrounding the SQUID and using the ground plane and the first connection circuit, a control line magnetically coupled to the SQUID and to which a control signal is input, and a second connection circuit connecting the ground planes existing on both sides of the control line. An oscillator having the same.

4. The control line is wired in a U shape so as to fold back near the SQUID, and the oscillator has a second connection circuit of a superconductor connecting the ground planes existing on both sides of the forward path and the return path of the U-shaped control line. The superconducting loop circuit is a circuit using the ground plane, the first connection circuit, and the second connection circuit. The oscillator according to claim 1.

5. The control line is a connection conductive member for connecting the other end of the SQUID and the ground plane or is wired linearly in a three-dimensional intersection with the SQUID. The oscillator has a second connection circuit of a superconductor that connects the ground planes existing on both sides of the control line. The second connection circuit is provided on both sides of the position where the control line and the connection conductive member or the SQUID intersect three-dimensionally. The superconducting loop circuit is a circuit using the ground plane, the first connection circuit, and the second connection circuit. The oscillator according to claim 1.

6. A ground plane of a superconductor, a conductive member surrounded by the ground plane with a space therebetween, a SQUID having one end connected to the conductive member and the other end connected to the ground plane, a first connection circuit of a superconductor that connects the ground planes existing on both sides in the vicinity of the connection portion between the conductive member and the SQUID, a superconducting loop circuit that surrounds the SQUID and uses the ground plane and the first connection circuit, a control line that is magnetically coupled to the SQUID and to which a control signal is input, and a second connection circuit of a superconductor that connects the ground planes existing on both sides of the control line. It has, The terminal side of the control line is wired along the SQUID, and the terminal of the control line is connected to one of the ground planes existing on both sides of the control line. The superconducting loop circuit is a circuit using the ground plane, the first connection circuit, and the second connection circuit. Oscillator.

7. A ground plane of a superconductor, a conductive member surrounded by the ground plane with a space therebetween, a SQUID having one end connected to the conductive member and the other end connected to the ground plane, a first connection circuit of a superconductor that connects the ground planes existing on both sides in the vicinity of the connection portion between the conductive member and the SQUID, and a superconducting loop circuit that surrounds the SQUID and uses the ground plane and the first connection circuit. It has, The SQUID has its other end connected to the ground plane via a Josephson junction different from the Josephson junctions included in the SQUID. Oscillator.

8. A ground plane of a superconductor, a conductive member surrounded with a space from the ground plane, an SQUID having one end connected to the conductive member and the other end connected to the ground plane, a first connection circuit of a superconductor that connects the ground planes present on both sides in the vicinity of the connection portion between the conductive member and the SQUID, a superconducting loop circuit that surrounds the SQUID and uses the ground plane and the first connection circuit, and has a Josephson junction different from the Josephson junctions included in the SQUID is inserted into a loop formed by the SQUID and the conductive member. Oscillator.

9. The two Josephson junctions included in the SQUID have different critical current values. The oscillator according to any one of Claims 1 to 8.

10. A ground plane of a superconductor, a conductive member surrounded with a space from the ground plane, an SQUID having one end connected to the conductive member and the other end connected to the ground plane, a first connection circuit of a superconductor that connects the ground planes present on both sides in the vicinity of the connection portion between the conductive member and the SQUID, a superconducting loop circuit that surrounds the SQUID and uses the ground plane and the first connection circuit, and has a control line that is magnetically coupled to the SQUID and to which a control signal is input is provided on a substrate, the ground plane, the conductive member, and the SQUID are provided on a chip that is flip-chip connected to the substrate, the first connection circuit is composed of bumps that connect the ground plane of the chip and a conductive member included in the substrate, and the conductive member included in the substrate. Oscillator.

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