Superconducting quantum circuit

Abstract

To provide a superconducting quantum circuit equipped with quantum bits and / or couplers that enables a reduction in the wiring number of control lines.SOLUTION: A superconducting quantum circuit device is configured using single first wiring that combines wiring transmitting signals that generate the magnetic flux applied to quantum bits with wiring transmitting signals that are input by capacitive coupling to and / or output from the quantum bits.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present disclosure relates to superconducting quantum circuits. [Background technology]

[0002] In recent years, research and development of quantum computers has been progressing worldwide. There are various quantum computer technologies, one of which is a superconducting quantum computer using superconducting elements. As a quantum bit using a superconducting element, for example, one using a Josephson parametric oscillator including a SQUID (Superconducting Quantum Interference Device) is known (for example, Patent Document 1). In a superconducting quantum computer that performs quantum calculations by combining multiple quantum bits, input / output lines for reading out the quantum bit states and control lines for adjusting the quantum bit resonance frequencies are provided. Furthermore, as a coupler that couples multiple quantum bits, a frequency-tunable type including, for example, a SQUID is also known. In the case of a frequency-tunable coupler, input / output lines for reading out the state and control lines (also called "flux bias lines") for adjusting the coupler's resonance frequency are also provided. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 2018-11022 Summary of the Invention [Problem to be solved by the invention]

[0004] In superconducting quantum computers that integrate superconducting quantum circuits containing arrays of quantum bits and couplers, as the number of quantum bits and couplers increases, the total number of wiring required, such as signal lines and control lines, increases significantly, making implementation difficult.

[0005] An object of the present disclosure is to provide a superconducting quantum circuit that enables a reduction in the number of wirings for quantum bits and / or couplers. [Means for solving the problem]

[0006] According to one aspect of the present disclosure, a superconducting quantum circuit is configured by combining wiring for transmitting a signal that generates a magnetic flux to be applied to a quantum bit and wiring for transmitting a signal that is input and / or output to the quantum bit by capacitive coupling, into a single first wiring.

[0007] According to a further aspect of the present disclosure, a coupler that mutually couples a plurality of quantum bits, including at least one of the quantum bits of the superconducting quantum circuit, may be configured as a single second wiring that combines a wiring that transmits a signal that generates a magnetic flux to be applied to the coupler and a wiring that transmits a signal that is input and / or output to the coupler by capacitive coupling. [Effects of the Invention]

[0008] According to the present disclosure, it is possible to provide a quantum bit and / or a coupler that allows the number of wiring lines to be reduced. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 10 is a diagram illustrating a circuit configuration of a quantum bit according to a comparative example. [Figure 2] FIG. 10 is a diagram illustrating a quantum bit of a comparative example. [Figure 3] 1A and 1B are schematic plan views showing an example of a quantum bit layout of a comparative example and an enlarged view of the vicinity of a SQUID. [Figure 4] FIG. 1 is a diagram illustrating an example circuit configuration of a quantum bit according to some embodiments of the present disclosure. [Figure 5] 1A and 1B are diagrams illustrating an example of a bias T circuit and an example of a diplexer. [Figure 6]1A and 1B are schematic plan views showing an example of a quantum bit layout according to some embodiments of the present disclosure and an enlarged view of the vicinity of a SQUID. [Figure 7] FIG. 7 is a diagram illustrating a circuit configuration corresponding to the layout of FIG. 6(B). [Figure 8] FIG. 10 is a diagram illustrating a circuit configuration of a coupler of a comparative example. [Figure 9] 1A and 1B are schematic plan views showing an example of a layout of a coupler of a comparative example and an enlarged view of the vicinity of a SQUID. [Figure 10] FIG. 1 is a diagram illustrating a circuit configuration of an example of a coupler according to the present disclosure. [Figure 11] 1A and 1B are schematic plan views showing an example of a layout of a coupler according to the present disclosure and an enlarged view of the vicinity of a SQUID. [Figure 12] FIG. 1 is a diagram illustrating an air bridge. [Figure 13] FIG. 10 is a diagram showing the circuit configuration of one of several variations of the quantum bit of the present disclosure. [Figure 14] FIG. 14 is an enlarged schematic plan view showing the vicinity of the SQUID in FIG. 13. [Figure 15] FIG. 10 is a diagram showing the circuit configuration of another quantum bit according to some modified examples of the quantum bit of the present disclosure. [Figure 16] FIG. 10 is a diagram showing the circuit configuration of yet another quantum bit according to some modified examples of the quantum bit of the present disclosure. [Figure 17] FIG. 10 is a diagram showing the circuit configuration of yet another quantum bit according to some modified examples of the quantum bit of the present disclosure. [Figure 18] FIG. 10 is a diagram showing the circuit configuration of another coupler in some modified examples of the quantum bit of the present disclosure. [Figure 19] FIG. 10 is a diagram showing the circuit configuration of yet another coupler in some variations of the quantum bit of the present disclosure. [Figure 20] FIG. 10 is a diagram showing the circuit configuration of yet another coupler in some variations of the quantum bit of the present disclosure. [Figure 21]FIG. 10 is a diagram showing the circuit configuration of yet another coupler in some variations of the quantum bit of the present disclosure. [Figure 22] FIG. 1 is a diagram schematically illustrating an example of a quantum computer (annealing machine). [Figure 23] 1A and 1B are diagrams illustrating examples of connections between couplers and quantum bits according to the present disclosure. [Figure 24] FIG. 10 is a diagram schematically illustrating another example of a connection configuration according to the present disclosure. [Figure 25] FIG. 10 is a diagram schematically illustrating another example of a connection configuration according to the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0010] Several examples of the present disclosure will be described. First, a quantum bit that is the premise of the present disclosure will be described using a comparative example. This comparative example is intended to specifically explain one example of the above-mentioned problems. FIG. 1 is a diagram illustrating a comparative example of a quantum bit using a Josephson parametric oscillator. Referring to FIG. 1, quantum bit 101 includes a SQUID 104 in which a first Josephson junction 102a and a second Josephson junction 102b are connected in a circular (loop) shape by a first superconducting member 103a and a second superconducting member 103b. The portion (indicated by an x) where one end of first superconducting member 103a and one end of second superconducting member 103b are coupled via an insulating layer (tunnel insulating layer) not shown corresponds to first Josephson junction 102a, and the portion (indicated by an x) where the other end of first superconducting member 103a and the other end of second superconducting member 103b are coupled via an insulating layer (tunnel insulating layer) not shown corresponds to second Josephson junction 102b. The first Josephson junction 102a and the second Josephson junction 102b are connected in parallel to two paths, one on the left and the other on the right, between one end (node ​​n1) and the other end (node ​​n2) of the SQUID 104. One end (node ​​n1) of the SQUID 104 is connected to an electrode 107, and the other end (node ​​n2) of the SQUID 104 is connected to ground. A capacitance 105 (capacitance) is connected between one end (node ​​n1) of the SQUID 104 and ground. The capacitance 105 is the capacitance of a shunt capacitor connected in parallel to the SQUID 104 between the electrode 107 and ground. A SQUID is generally a closed circuit in which N (N is a predetermined integer greater than or equal to 1) Josephson junctions are connected in a ring shape using a superconducting material. A SQUID that includes a Josephson junction on each of the two paths between nodes n1 and n2 is sometimes called a dc-SQUID, and one with one Josephson junction is sometimes called an rf-SQUID. Although FIG. 1 shows a configuration in which two Josephson junctions are connected in parallel as the configuration of the SQUID 104, the number of Josephson junctions included in the SQUID loop may be any number.

[0011] Quantum bit 101 is provided with two wires: input / output line 108 and control line 109. That is, input / output line 108 is a single wire (made of, for example, a superconducting material) that functions as an input line for, for example, initializing the state of quantum bit 101 and an output line (readout line) for reading out the state of quantum bit 101, and one end of input / output line 108 is connected to electrode 107 of quantum bit 101 via coupling capacitance 110. Coupling capacitance 110 does not involve providing a specific capacitor element between one end of input / output line 108 and electrode 107 of quantum bit 101, but corresponds to the capacitance between one end of input / output line 108 on the substrate and the opposing electrode 107 of quantum bit 101.

[0012] Input / output line 108 is used for inputting a signal to quantum bit 101 and / or outputting a signal from quantum bit 101. The signal from quantum bit 101 may be a signal output from quantum bit 101, or a signal input to quantum bit 101 that is reflected by quantum bit 101 and returns to input / output line 108. Note that input / output via input / output line 108 may be used not only during the calculation operation of quantum bit 101, but also for calibration of quantum bit 101, etc.

[0013] Control line 109 is used to transmit a signal that generates a magnetic flux to be applied to quantum bit 101. More specifically, one end of control line 109 is connected to ground via inductor 111, and is used to adjust the resonant frequency of resonator 106 of quantum bit 101. When quantum bit 101 is operating, inductor 111 is electromagnetically inductively coupled (also referred to as "inductively coupled") to SQUID 104. The electromagnetic inductive coupling between inductor 111 and SQUID 104 is represented by mutual inductance 112. Current supplied from the outside to control line 109 flows to the ground side via inductor 111. A magnetic flux is generated by the current flowing through inductor 111, and a magnetic flux that penetrates SQUID 104 is generated. The resonant frequency of resonator 106 can be adjusted by applying a direct current to control line 109. Furthermore, by applying an AC current (also called a "pump wave") to control line 109, quantum bit 101 undergoes parametric oscillation, and an oscillation output signal (with half the frequency of the pump wave) is output to input / output line 108. The phase of the output signal depends on the oscillation state of quantum bit 101. The oscillation state is also controlled by the input signal from input / output line 108.

[0014] The other end of input / output line 108 is connected to signal source 113 and measuring instrument 114 via circulator 115. The other end of control line 109 is connected to DC power supply 116 and AC power supply 117 via bias T circuit 118. Quantum bit 101 is placed in a refrigerator (not shown) and operates while cooled to an extremely low temperature. Signal source 113, measuring instrument 114, DC power supply 116, and AC power supply 117 are placed in a room-temperature environment outside the refrigerator. When quantum bit 101 is operating, a signal from signal source 113 outside the refrigerator is transmitted via a coaxial cable (not shown) or the like wired inside the refrigerator, is attenuated in stages by attenuators (not shown) installed at each temperature stage, transmitted to input / output line 108 via circulator 115, and input to quantum bit 101. The signal output from quantum bit 101 and the reflected signal are transmitted from input / output line 108 through circulator 115 and via a low-pass filter, a band-pass filter, an isolator, an amplifier (e.g., a HEMT (High Electron Mobility Transistor) amplifier), etc. (all not shown), to measuring instrument 114 outside the refrigerator. An AC signal (microwave) from AC power supply 117 is transmitted through a coaxial cable (not shown) or the like wired inside the refrigerator, is attenuated in stages by attenuators (not shown) installed at each temperature stage, and is input to an RF (Radio Frequency) port of bias T circuit 118. A DC signal from DC power supply 116 is transmitted through a transmission line (not shown) or the like wired inside the refrigerator, and is input to a DC port of bias T circuit 118 via a low-pass filter (not shown).

[0015] The configuration may include a chip (not shown) having quantum bit 101 and coupler 201 (described later) on a wiring layer, a wiring chip (interposer) (not shown) that mounts the chip by bonding it face-down, and a printed wiring board (not shown) that mounts the wiring chip (interposer), and is connected to port 2 (p2) of circulator 115 via a cable member (e.g., a coaxial cable) that is connected to the connector on the printed wiring board.

[0016] 1, bias T circuit 118 is configured as shown in FIG. 3A, for example, and superimposes a modulation current (AC current) on a DC current. During operation of quantum bit 101, a DC current from DC power supply 116 is input to a DC (Direct Current) port of bias T circuit 118, an AC current from AC power supply 117 is input to an RF port of bias T circuit 118, and a current obtained by superimposing an AC current on a DC current is output from the RF+DC port of bias T circuit 118 to control line 109. The current (DC current + AC current) output to control line 109 flows through inductor 111, generating a magnetic field that penetrates the loop of SQUID 104. This magnetic field is the vector addition (superposition) of a DC bias magnetic field (DC bias magnetic flux) corresponding to the DC current flowing through inductor 111 and an AC magnetic field (AC magnetic flux) corresponding to the AC current superimposed on the DC current.

[0017] In quantum bit 101, the resonant frequency of resonator 106 varies depending on the value of the magnetic flux passing through SQUID 104. Changing the value of the DC current output from DC power supply 116 changes the value of magnetic flux Φ passing through SQUID 104. Here, the magnetic flux Φ passing through the loop of SQUID 104 is an integer multiple of the magnetic flux quantum Φ0. When modulated at a frequency approximately twice the resonant angular frequency ω0 of resonator 106 of quantum bit 101 when a DC magnetic field is applied, the vibration amplitude of resonator 106 of quantum bit 101 increases, and oscillation occurs when the signal intensity of control line 109 exceeds a threshold. Even if there is no signal on control line 109, resonator 106 oscillates and outputs a signal with resonant angular frequency ω0.

[0018] Resonator 106 of quantum bit 101 can be considered a nonlinear resonant circuit consisting of capacitance 105 and SQUID 104, which is a nonlinear inductor. The equivalent inductance of the loop of SQUID 104 depends on the magnitude of magnetic flux Φ passing through the loop of SQUID 104. The magnitude of magnetic flux Φ passing through the loop of SQUID 104 depends on the magnitude of the current flowing through inductor 111. Therefore, the resonant frequency of resonator 106 of quantum bit 101 changes depending on the magnitude of the current flowing through inductor 111.

[0019] The two Josephson junctions 102a and 102b of the SQUID 104 have the same critical current value I c , the total current I flowing through the SQUID 104 is expressed by the following equation: I=I c sin(γa)+I c sin(γb) …(1) γa and γb are the phase jumps (phase differences) in the two Josephson junctions 102a and 102b, respectively. γb-γa=2π(Φ / Φ0) …(2) (Φ0 is the magnetic flux quantum, Φ0=h / (2e), h is Planck's constant, and e is the elementary charge.) Therefore, the magnetic flux Φ (external magnetic field) penetrating the loop of the SQUID 104 can only exist as a magnetic field that is an integer multiple of the magnetic flux quantum Φ0. Φ / Φ0=n (n is a positive integer) …(3)

[0020] The maximum value Imax of the current I flowing through the SQUID 104 is given by the following equation. Imax=2I c |cos(πΦ / Φ0)| …(4)

[0021] When the magnetic flux Φ (external magnetic field) applied to the loop of the SQUID 104 is increased, the maximum current becomes 0 when Φ is (integer value + 1 / 2)Φ0, and changes with a period of the magnetic flux quantum Φ0.

[0022] For example, if a magnetic field Φ smaller than half the magnetic flux quantum Φ0 is applied from bottom to top through the loop of SQUID 104, a current flows through the loop of SQUID 104, generating a magnetic field (from top to bottom) in a direction that cancels out the magnetic field, and the magnetic field passing through the loop of SQUID 104 is set to 0 (n = 0 in equation (3)). Alternatively, a current flows through the loop of SQUID 104 in a direction that generates a magnetic field in the same direction as the magnetic field Φ, and the magnetic field passing through the loop of SQUID 104 is set to Φ0 (n = 1 in equation (3)). In this case, generating a downward magnetic field in the loop of SQUID 104 and setting the magnetic flux Φ to 0 (n = 0 in equation (3)) is smaller in value in the loop of SQUID 104 and is more stable in terms of energy than generating an upward magnetic field and setting the magnetic flux Φ to Φ0. Of the two energy levels, the lower energy one is called the ground state, and the higher energy one is called the excited state. For example, a two-level system consisting of the ground state and the first excited state can be treated as a quantum bit.

[0023] Figure 2 is a graph showing the magnetic field dependence of the resonant angular frequency of the resonator 106 of the quantum bit 101 (Reference 1). In the graph shown in Figure 2, the horizontal axis represents the magnitude of the magnetic field bias applied to the loop of the SQUID 104 (the value obtained by dividing the external magnetic flux Φ by the magnetic flux quantum Φ: Φ / Φ0), and the vertical axis represents the magnitude of the resonant angular frequency. Note that the vertical axis is normalized by the maximum value of the resonant angular frequency. When two Josephson junctions with the same critical current value are used, when the applied magnetic field Φ is Φ / Φ0 = (2k + 1) / 2 (k is 0 or a positive integer), Equation (4) shows that the critical current value of the entire loop of the SQUID 104 is 0. When the critical current value of the entire loop of the SQUID 104 is 0, the equivalent inductance of the loop of the SQUID 104 becomes infinite, and the resonant angular frequency becomes 0. In the graph of FIG. 2, the operating point indicated by a circle indicates the resonant angular frequency set by the DC magnetic field (DC bias magnetic flux) generated by the DC current flowing through inductor 111. As described above, to parametrically oscillate resonator 106 of quantum bit 101, an AC current is passed through inductor 111 in addition to the DC magnetic field (DC bias magnetic flux), and an AC magnetic field (AC magnetic flux) is applied to the loop of SQUID 104. In this case, the magnitude of the magnetic field applied to the loop of SQUID 104 fluctuates periodically around the magnitude (operating point) of the magnetic field generated by the DC current, and the resonant angular frequency of resonator 106 also fluctuates. It is known that the oscillation threshold (pump power threshold) of parametric oscillation is minimum when the frequency of the magnetic field coincides with twice the resonant angular frequency (2ω0), and increases as the angular frequency of the AC magnetic field deviates from twice the resonant angular frequency.

[0024] When setting quantum bit 101 to its initial state (a superposition of the ground state and the excited state), a signal output from signal source 113 (e.g., a microwave at the resonant frequency of resonator 106) is input to port 1 (p1) of circulator 115, output from port 2 (p2), propagates through input / output line 108, and is applied to quantum bit 101 via coupling capacitance 110.

[0025] A signal (microwave) may be input to quantum bit 101 to read out the state of quantum bit 101. For example, the state of quantum bit 101 may be read out using a signal reflected at quantum bit 101 of a signal input from input / output line 108 via coupling capacitance 110. In this case, a reflected signal (reflected wave) of a signal (signal wave) propagated from signal source 113 through circulator 115 and input / output line 108 and input to quantum bit 101 via coupling capacitance 110 propagates back to input / output line 108 via coupling capacitance 110, travels in the opposite direction to the original direction, is input to port 2 (p2) of circulator 115, is output from port 3 (p3), and is received by measuring instrument 114 via a coaxial line (cable), an amplifier, etc. (not shown). Regarding reflection at the quantum bit, it has been shown that quantum bit 101 coupled to input / output line 108, which is a one-dimensional coplanar waveguide, completely reflects the microwave signal on the waveguide at a resonant frequency (e.g., a frequency corresponding to the energy difference between the ground state and the first excited state) (Reference 2). Measuring instrument 114 may be, for example, a commercially available network analyzer or spectrum analyzer. By measuring the reflected signal from quantum bit 101 with measuring instrument 114, the state of quantum bit 101 can be observed (read out).

[0026] FIG. 3A is a schematic plan view showing a non-limiting example of the layout of the quantum bit 101 (part of the wiring layer of the quantum chip) of FIG. 1 . The electrode 107 of the quantum bit 101 is cross-shaped with four arms. Each of the four electrodes 107 is surrounded by a ground 120 (ground plane) via a gap 121. The gap 121 shown in white in the figure corresponds to an area that is not covered by wiring and may potentially expose the surface of the quantum chip substrate (e.g., silicon). The capacitance 105 in FIG. 1, which is arranged in parallel with the SQUID 104 between the electrode 107 and the ground 120, corresponds to the capacitance of the gap 121 between the electrode 107 and the ground 120. The gap between the end of the input / output line 108 and the end of the first arm (the upward arm in FIG. 3A ) of the electrode 107 facing that end, forms the coupling capacitance 110 (capacitive component) in FIG. 1 . A SQUID 104 is provided between the end of the second arm of electrode 107 (the arm pointing to the right in Figure 3(A)) and the opposing ground 120, and is inductively coupled to an inductor at one end of control line 109 (the size of SQUID 104 is smaller than the others and is not shown in Figure 3(A)).

[0027] FIG. 3(B) is a schematic plan view of an enlarged area (region 11 enclosed by a square) around the SQUID 104 of the quantum bit 101 in FIG. 3(A). In the layout of FIG. 3(B), Josephson junctions 102a and 102b are also represented by cross marks. Referring to FIG. 3(B), the control line 109 is configured as a coplanar waveguide sandwiched between ground 120 (ground plane) on both sides in the longitudinal direction via gaps 121a and 121b. Note that in FIG. 3(B), the central conductor (signal line) of the coplanar waveguide is indicated by reference numeral 109, which represents the control line. One end of the control line 109 abuts against the ground 120 (ground plane), and gap 121a of the coplanar waveguide is bent at a substantially right angle at the abutment point, extending as linear gap 121c. The wiring pattern of the linear ground 120 (ground surface) surrounded by gap 121 and gap 121c on the SQUID 104 side is indicated by reference symbol 111, which represents an inductor, and when a current flows through this wiring pattern from control line 109, a right-handed (clockwise) magnetic field is generated in accordance with Ampere's right hand screw rule, and it acts as inductor 111 that generates a magnetic flux that penetrates the loop of SQUID 104. When the magnetic field (magnetic field lines) generated by inductor 111 in accordance with the right hand screw rule reaches ground 120 (ground surface) made of a superconducting material (type 1 superconducting material), a superconducting current (eddy current) flows spontaneously inside the superconducting material in ground 120 (ground surface), and the penetration of the magnetic field (magnetic field lines) into ground 120 (ground surface) is prevented (Meissner effect). In the example shown schematically in Fig. 3(B), the magnetic flux passing through the loop of SQUID 104 is generated in inductor 111 by a current that flows from one end of control line 109 through bent inductor 111 to ground 120, and passes through linear gap 121c from the top to the bottom of the paper, circulates through the substrate below gap 121c, and passes through the loop of SQUID 104 from the bottom to the top of the paper. As shown in Fig. 3(B), SQUID 104 is disposed between the end of the arm of electrode 107 and ground 120 (ground surface) facing it.The superconducting member 103a connected to one end of the Josephson junction 102a is connected to one end of the Josephson junction 102b via an electrode 107 made of a superconducting material, and the superconducting member 103b connected to the other end of each of the Josephson junctions 102a and 102b is connected to the ground 120 (ground plane), thereby forming a loop of the SQUID 104 in FIG. 1.

[0028] 3(A) and 3(B) show an example of the layout of a planar circuit and Josephson junctions formed by depositing a superconducting material on the surface of a quantum chip substrate, for example, by molecular beam epitaxy (MBE). The substrate is made of silicon, for example. However, other electronic materials, such as sapphire or compound semiconductor materials (Group IV, Group III-V, Group II-VI), may also be used. Furthermore, while a single crystal substrate is preferable, polycrystalline or amorphous materials may also be used. Examples of superconducting materials include, but are not limited to, niobium (Nb) or aluminum (Al). Any metal that becomes superconducting when cooled to a cryogenic temperature may also be used, such as niobium nitride, indium (In), lead (Pb), tin (Sn), rhenium (Re), palladium (Pd), titanium (Ti), molybdenum (Mo), tantalum (Ta), tantalum nitride, and alloys containing at least one of these. The Josephson junction is an element with a tunnel junction structure in which a superconducting member such as Al is sandwiched between two superconducting members with a thin insulating film (such as AlOx) between them, and is formed by, for example, oblique deposition.

[0029] As described above, input / output lines 108 and control lines 109 are provided for each quantum bit 101. In this case, as the number of quantum bits 101 increases, the amount of wiring required increases, and as a result, wiring issues become a major problem. The above problem is one example, but the present disclosure is not limited to the above and makes it possible to reduce the number of quantum bit wirings in various situations.

[0030] FIG. 4 is a diagram illustrating an example of the configuration of a quantum bit according to the present disclosure. In FIG. 4, elements identical or equivalent to those in FIG. 1 are generally assigned the same reference numerals, and their descriptions are omitted as appropriate to avoid redundancy, with differences being mainly described. In FIG. 4, the circuit configuration of quantum bit 101 itself is the same as that in FIG. 1, except that electrode 107 of quantum bit 101 is connected to control line 109 via coupling capacitance 110. In FIG. 4, control line 109 is given the same reference numeral as in FIG. 1. That is, in the example of FIG. 4, input / output line 108 in FIG. 1 has been eliminated, and control line 109 is configured to not only perform its original function of supplying a signal (current) to inductor 111 for generating a magnetic flux to be applied to quantum bit 101, but also function as an input / output line (108 in FIG. 1) for transmitting signals input and / or output to quantum bit 101 via capacitive coupling.

[0031] One end (node ​​n3) of control line 109 is connected to electrode 107 of resonator 106 via coupling capacitance 110 and to one end of inductor 111, and the other end of control line 109 is connected to DC power supply 116 and AC power supply 117 via bias T circuit 118, as well as to signal source 113 and measuring instrument 114 via circulator 115. Note that in FIG. 4 , part of the wiring (e.g., a coplanar line) of control line 109 may be used as is as inductor 111. Of the control lines 109 connected to ground 120, the part of control line 109 closest to SQUID 104 acts as inductor 111. The wiring between node n3 and inductor 111 may be referred to as control line 109.

[0032] An AC signal (microwave) from signal source 113 is transmitted, for example, through a coaxial cable or the like (not shown) in a refrigerator (not shown), is attenuated stepwise by attenuators (not shown) installed at each temperature stage, and is input to port 1 (p1) of circulator 115. The signal input to port 1 (p1) of circulator 115 is transmitted in one direction, output from port 2 (p2), and input to port 2 (p2) of diplexer 119. When an AC signal from AC power supply 117 is input to port 3 (p3) of diplexer 119, a signal combined with this AC signal is input from port (p1) of diplexer 119 to the RF port of bias T circuit 118. At the RF+DC port of bias T circuit 118, when a DC signal from DC power supply 116 is input to the DC port, a signal in which an AC signal from the RF port is superimposed on the DC signal is applied to control line 109 and input to quantum bit 101 via coupling capacitance 110.

[0033] The output signal / reflected signal from quantum bit 101 is output to control line 109 via coupling capacitance 110, and is input to port 2 (p2) of circulator 115 via bias T circuit 118 and diplexer 119. The signal input to port 2 (p2) of circulator 115 is transmitted in one direction and output from port 3 (p3), and both signals are transmitted to measuring instrument 114 outside the refrigerator via a low-pass filter, band-pass filter, isolator, HEMT amplifier, etc. (not shown).

[0034] The AC signal (microwave) from the AC power supply 117 is transmitted through a coaxial cable (not shown) wired inside a refrigerator (not shown) or the like, and is attenuated in stages by attenuators (not shown) installed at each temperature stage, and is input to port 3 (p3) of the diplexer 119. The DC signal from the DC power supply 116 is transmitted through a transmission line (not shown) wired inside the refrigerator or the like, and is input to the DC port of the bias T circuit 118 via a low-pass filter (not shown).

[0035] That is, in controlling the quantum bit 101, an AC signal (having a frequency approximately twice the resonant frequency of the quantum bit 101 (resonator 106)) from the AC power supply 117 is input to port 3 (p3) of the diplexer 119, and a signal obtained by mixing two signals input from port 2 (p1) and port 3 (p3) is output from port 1 (p1) of the diplexer 119. As shown schematically in FIG. 5B, the diplexer 119 includes, for example, a low-pass filter (LPF) between port 1 (p1) and port 2 (p2) and a high-pass filter (HPF) between port 1 (p1) and port 3 (p3). The diplexer 119 may be configured using a directional coupler and a filter, or a circulator and a filter. At this point, it is assumed that no signal is being output from the signal source 113 (readout is not being performed). An AC signal from AC power supply device 117 is output from port 1 (p1) of diplexer 119 and input to the RF port of bias T circuit 118. A signal in which the AC signal from AC power supply device 117 is superimposed on the DC current from DC power supply device 116 input to the DC port of bias T circuit 118 is output from the RF+DC port of bias T circuit 118 to control line 109. One end of inductor 111, the other end of which is connected to ground 120, is connected to node n3 of control line 109, and magnetic flux (DC magnetic flux+AC magnetic flux) is supplied to the loop of SQUID 104 of quantum bit 101 by the current flowing through inductor 111.

[0036] Of the currents flowing through the control line 109, the DC current I from the DC power supply device 116 DC is blocked (cut) by coupling capacitance 110, and an AC signal (having a frequency approximately twice the resonant frequency of resonator 106) is input to quantum bit 101 from AC power supply device 117. Here, The AC current component of the current flowing through node n3 of the control line 109 is I(ω), The AC current component flowing from the node n3 of the control line 109 to the inductor 111 is I1(ω), The AC current component I2(ω) flowing from node n3 of control line 109 to quantum bit 101 via coupling capacitance 110 is assumed to be I2(ω)=I(ω)-I1(ω), and a rough estimate will be made for the circuit in Figure 4 using a simple model. · Let the inductance of inductor 111 be L, The value of the coupling capacitance 110 is C c , Let the impedance of qubit 101 be Z. q (ω) (Angular frequency ω is approximately twice the resonant angular frequency of quantum bit 101 (resonator 106), ω≈2ω0).

[0037] Z q (ω) and coupling capacitance C c The impedance of the series circuit is TIFF2025131195000002.tif10150…(5) At node n3, TIFF2025131195000003.tif10150…(6) Therefore, I1(ω) and I2(ω) are given as follows: TIFF2025131195000004.tif11150…(7) TIFF2025131195000005.tif11150…(8)

[0038] In equations (7) and (8), The inductance of the electrode 107 of the qubit 101 is Le, The value of the capacitance (shunt capacitance) 105 of the qubit 101 is C, The inductances of the Josephson junctions 102a and 102b of the SQUID 104 are respectively L s1 (Φ), L s2 (Φ) (where Φ is the magnetic flux passing through the loop of SQUID104), The critical current of Josephson junctions 102a and 102b is I c1 , I c2 Then, Impedance Z of quantum bit 101 (series circuit of SQUID 104, resonator 106 of capacitance 105, and electrode 107) q (ω) is given by: TIFF2025131195000006.tif15150…(9) however, TIFF2025131195000007.tif14150…(10)

[0039] The current flowing from node n3 of control line 109 to inductor 111 is a DC current I DC and I1(ω).

[0040] Of the current flowing through node n3 of control line 109, the signal input to quantum bit 101 via coupling capacitance 110 has an angular frequency approximately twice the resonant angular frequency ω0 of quantum bit 101, and a portion of this signal is reflected by resonator 106 of quantum bit 101 (the remainder is transmitted through resonator 106). The AC signal reflected by quantum bit 101 (an AC signal with an angular frequency approximately twice the resonant angular frequency ω0 of quantum bit 101) returns to control line 109 via coupling capacitance 110 and is input to the RF+DC port of bias T circuit 118. In bias T circuit 118, the reflected signal (AC signal) input to the RF+DC port is output from the RF port via a capacitor (C4 in FIG. 5(A)) between the RF+DC port and the RF port. In the bias T circuit 118, the reflected signal (AC signal) input from the RF+DC port is prevented (suppressed) from being output to the DC power supply 116 by the inductor (L4 in FIG. 5(A)) between the RF+DC port and the DC port.

[0041] The reflected signal output from the RF port of bias T circuit 118 (an AC signal with an angular frequency approximately twice the resonant angular frequency ω of the quantum bit) is input to port 1 (p1) of diplexer 119 and output from port 3 (p3) of diplexer 119. The reflected signal input to port 1 (p1) of diplexer 119 (an AC signal with an angular frequency approximately twice the resonant angular frequency ω of the quantum bit) is not output from port 2 (p2) of diplexer 119, and therefore does not propagate to port 2 (p2) of circulator 115. The reflected signal output from port 3 (p3) of diplexer 119 returns to the output end of AC power supply device 117, but may be terminated (e.g., resistive series termination) on the output side of AC power supply 117.

[0042] In this state, when reading out quantum bit 101, signal source 113 outputs an AC signal (microwave signal: resonant angular frequency ω of quantum bit 101). The AC signal from signal source 113 is input to port 1 (p1) of circulator 115, output from port 2 (p2), and input to port 2 (p2) of diplexer 119. An AC signal (with an angular frequency approximately twice the resonant angular frequency ω of quantum bit 101) from AC power supply 117 is input to port 3 (p3) of diplexer 119, and a signal obtained by mixing (combining) the two signals from port 2 (p2) and port 3 (p3) is output from port 1 (p1) of diplexer 119 and input to the RF port of bias T circuit 118. A DC current from DC power supply 116 is input to the DC port of bias T circuit 118. A signal obtained by superimposing a DC current from the DC power supply 116 on a signal obtained by mixing an AC signal (microwave) from the signal source 113 and an AC signal from the AC power supply 117 is output from the RF+DC port of the bias T circuit 118 to the control line 109.

[0043] A signal combining an AC signal (microwave) from signal source 113 and an AC signal (microwave) from AC power supply device 117 is input to quantum bit 101 from node n3 of control line 109 via coupling capacitance 110. In this case, the sum current I'2(ω0)+I''2(2×ω0) of a portion I'2(ω0) of the AC signal I'(ω0) from signal source 113 and a portion I''2(2×ω0) of the AC signal I''(2×ω0) from AC power supply device 117 flowing through control line 109 is input to quantum bit 101 via coupling capacitance 110. Here, I'2(ω0) and I''2(2×ω0) are each calculated from equation (8).

[0044] Quantum bit 101 oscillates at an angular frequency ω0, and among the signals input to quantum bit 101, the AC signal with angular frequency ω0 is partially or almost entirely reflected. Furthermore, an AC signal with angular frequency of approximately 2×ω0 is input to quantum bit 101, and a portion of this signal is reflected. The signal reflected by quantum bit 101 (a superimposed signal of the AC signal with angular frequency ω0 and the AC signal with angular frequency approximately 2×ω0) returns to control line 109 via coupling capacitance 110 and is input to the RF+DC port of bias T circuit 118. In bias T circuit 118, the reflected signal input to the RF+DC port (a combined signal of the AC signal with angular frequency ω0 and the AC signal with frequency approximately 2×ω0) is output from the RF port of bias T circuit 118 via a capacitor (C4 in FIG. 5A) between the RF+DC port and the RF port. The reflected signal output from the RF port of bias T circuit 118 is input to port 1 (p1) of diplexer 119. Of the reflected signals input to port 1 (p1) of diplexer 119, the reflected signal (with an angular frequency of ω0) corresponding to the signal output from signal source 113 passes through the low-pass filter (LPF) of diplexer 119 and is output to port 2 (p2) of diplexer 119. The reflected signal output from port 2 (p2) of diplexer 119 is input to port 2 (p2) of circulator 115, propagates unidirectionally to port 3 (p3), is output from port 3 (p3), and is transmitted to measuring instrument 114. By measuring the reflected signal from quantum bit 101 (an AC signal with an angular frequency of ω0) with measuring instrument 114, the state of quantum bit 101 can be read out. Note that, for example, by terminating the input connector of measuring instrument 114 with 50 ohms, further reflection of the reflected signal that has reached measuring instrument 114 on the measuring instrument 114 side may be suppressed. The AC signal (microwave) output from signal source 113 may be a standing wave (contiguous wave: CW) or a pulse wave. If the AC signal (microwave) output from signal source 113 is a pulse wave, its output period may be set so that the input signal (pulse wave) heading toward control line 109 and the reflected signal (pulse wave) from control line 109 heading toward measuring instrument 114 do not collide in terms of timing at port 2 of circulator 115.

[0045] Of the signals input to port 1 (p1) of diplexer 119, the reflected signal at quantum bit 101 in response to the signal output from AC power supply 117 (a reflected AC signal with an angular frequency of approximately 2×ω0) passes through the high-pass filter (HPF) of diplexer 119, is output from port 3 (p3), and returns to the output end of AC power supply 117. In this case, the output side of AC power supply 117 may be terminated with, for example, a resistor in series.

[0046] DC current I from DC power supply 116 DC and a signal (sum current) I obtained by mixing an AC signal I″1(2×ω0) from AC power supply device 117 (angular frequency=approximately twice the resonant angular frequency ω0 of quantum bit 101: I″(2×ω0) given by equation (7)) and a signal I′1(ω0) from signal source 113 (angular frequency=resonant angular frequency ω0 of quantum bit 101: I′(ω0) given by equation (7)). DC +I'1(ω0)+I''1(2×ω0) flows from node n3 of control line 109 to inductor 111. The signal (microwave) from signal source 113 has a frequency that is about half that of the AC signal from AC power supply 117, and its power is also weak, so the influence of the signal from signal source 113 on the magnetic flux (magnetic flux Φ passing through SQUID 104) generated by inductor 111 can be ignored. That is, in inductor 111, the magnetic field H generated according to the right-hand rule is proportional to the current value I1(ω) flowing through inductor 111, and the magnetic flux Φ is expressed as Φ=BS=μHS (B is the magnetic flux density, μ is the magnetic permeability, and S is the loop area of ​​SQUID 104), and the AC signal from signal source 113 flows in the DC current I from DC power supply 116. DC The power is weaker than that from the AC power supply 117, and its frequency is about half that from the AC power supply 117, which is significantly different, so the effect on the magnetic flux passing through the loop of the SQUID 104, and therefore the effect on the parametric oscillation of the quantum bit 101, can be ignored.

[0047] Note that the readout of quantum bit 101 may be performed within the decoherence time (the time during which the quantum mechanical superposition state is maintained stable) of quantum bit 101 after the supply of a signal to control line 109 (inductor 111) is stopped. In this case, an AC signal (microwave) from signal source 113 propagates through circulator 115, diplexer 119, bias T circuit 118, and control line 109, with a portion branching off to inductor 111 and the other portion being input to quantum bit 101 via coupling capacitance 110. The signal (microwave) reflected by quantum bit 101 returns to control line 109 via coupling capacitance 110 and travels in the reverse direction, reaching measuring instrument 114 via bias T circuit 118, diplexer 119, and circulator 115.

[0048] Fig. 6(A) is a diagram showing an example of the layout of quantum bit 101 of Fig. 4. Referring to Fig. 6(A), quantum bit 101 has control line 109 inductively coupled and capacitively coupled at a different location, and does not have input / output line 108 shown in Fig. 3(A). Gap 121, shown in white, between electrode 107 of quantum bit 101 and ground 120 (ground surface) facing the side of electrode 107 forms capacitance 105 of Fig. 4.

[0049] FIG. 6(B) is an enlarged schematic diagram of the region 11 near the SQUID 104 in the quantum bit 101 of FIG. 6(A). FIG. 6(B) also shows an example of a layout pattern in which the coupling capacitance 110 is set to an appropriate value so that the external Q value of the resonator 106 is a desired value. The Q value (Q-factor) of the resonator represents the sharpness of the resonance, and is given by Q=ω0 / BW, where ω0 is the frequency (resonance angular frequency) at which the power stored in the resonator peaks, and BW is the frequency width at which the power consumed within the resonator 106 is half the peak power value. The external Q value is given by the ratio of the energy stored in the resonator to the energy flowing out from the resonator to the external circuit (load resistance or internal resistance of the power supply) in one cycle, and is larger the weaker the coupling with the external circuit, and smaller the stronger the coupling. The Q value (load Q value) of the resonator is calculated using the internal Q value Qi and the external Q value Qe as follows: 1 / Q = 1 / Qi + 1 / Qe …(11) It can also be expressed as follows.

[0050] In FIG. 6(B), in order to make the value of the coupling capacitance 110 large enough, the electrode 107 of the qubit 101 has a wide tip and is close to the opposing control line 109. For example, in FIG. 3(B), the electrode 107 of the qubit 101 has a constant width S up to the tip, but the electrode 107 of the qubit 101 in FIG. 6(B) has a wide tip (the part of the electrode 107 facing the inductor). Also, one end of the control line 109 is bifurcated at a right angle and separated from the tip of the electrode 107 by a predetermined distance, and the wiring extending in opposite directions acts as inductors 111a and 111b. Further, it is bent by 90 degrees, and the wiring (109a, 109b in FIG. 6(B)) extending along the side of the electrode 107 is connected to the ground 120. It can be said that the gap 121 between the control lines 109a, 109b and the electrode 107 forms the coupling capacitance

[0051] More specifically, referring to FIG. 6(B) in the cross-shaped electrode 107 with arms extending in four directions from the center, one arm of the electrode 107 (the arm extending to the right in the figure in FIG. 6(A)) extends while maintaining the center conductor width S and the slot widths W on both sides. At the tip side of the arm, the center conductor width is widened to S', and the slot widths on both sides are reduced to W'. S’ + 2W’ = S + 2W …(12) S’ > S, W’ < W …(13)

[0052] Furthermore, at the tip side of the arm of the electrode 107, the electrode tip portions 107a and 107b with a center conductor width of S" (S" < S' / 2) are bifurcated and protrude. The Josephson junctions 102a and 102b of the SQUID 104 bridge the concave portion (width is S’ - 2S") between the electrode tip portions 107a and 107b protruding in a bifurcated manner and the wiring (which is also the ground 120, inductors 111a and 111b) facing it.

[0053] The width W' of the gap between the side (upper side) of electrode tip 107a and the opposing control line 109a and the width W' of the gap between the side (lower side) of electrode tip 107b and the opposing control line 109b are narrower than the width W of the gap between electrode 107 other than electrode tips 107a and 107b and ground 120. In addition, the width W" of the gap between the ends of electrode tips 107a and 107b and the opposing inductors 111a and 111b is smaller than the gap between electrode 107 and inductor 111 in Figure 3(B). W" may be set to be equal to the value of the gap W' between electrode tips 107a and 107b and the opposing control lines 109a and 109b. The capacitance between the electrode tips 107a, 107b and the opposing control lines 109a, 109b (coupling capacitance 110 in Figure 4) increases as the length of the opposing sides of the electrode tips 107a, 107b and the control lines 109a, 109b increases, and also increases as the width of the gap between the opposing sides decreases. If the spacing (distance) between the opposing sides of the parallel conductors is d and the length between the opposing sides is l, the electrostatic capacitance C is given by ε(l / d), where ε is the dielectric constant.

[0054] 6(B), one end of control line 109 is branched into two and extended, facing SQUID 104 between electrode tips 107a and 107b, forming inductors 111a and 111b, respectively. These inductors then bend at right angles and extend along the sides of electrode tips 107a and 107b, forming control lines 109a and 109b. This creates a long, narrow gap between electrode 107 (electrode tips 107a and 107b) of quantum bit 101 and control line 109, forming coupling capacitance 110 (not shown) with a sufficiently large value (capacitance value) between electrode 107 and control line 109. However, if coupling capacitance 110 becomes too large, the external Q value of quantum bit 101 will become too low. Therefore, coupling capacitance 110 is preferably set to an appropriate value using electromagnetic field simulation or the like.

[0055] The external Q factor Qe of the resonator increases as the coupling to the load, internal resistance of the power supply, etc. decreases, and decreases as the coupling increases. If the coupling between the control line 109 and the resonator 106 of the quantum bit 101 is too weak, it becomes difficult to read out the state of the quantum bit 101. If the coupling between the control line 109 and the resonator 106 of the quantum bit 101 is too strong, the Q factor of the resonator 106 decreases. For example, if the resonant frequency of the resonator 106 is set near its maximum value, the external Q factor when a signal is input from the control line 109 to the quantum bit 101 is preferably between 10,000 and 100,000. More preferably, the external Q factor is between 10,000 and 50,000. Even more preferably, the external Q factor is between 10,000 and 30,000.

[0056] For the example shown in Figure 6(B), electromagnetic field simulations reveal that the external Q value is approximately 23,000, which is within the desired range. The internal and external Q values ​​of a quantum bit can be experimentally measured, for example, as follows. First, the reflection coefficient (the ratio of the reflected wave to the incident wave) when a signal is input from signal source 113 to quantum bit 101 is measured using measuring instrument 114. The reflection coefficient Γ is also called the S-parameter S11. This reflection coefficient Γ is measured using measuring instrument 114 by sweeping the frequency of the signal input from signal source 113 to quantum bit 101. The frequency range of this measurement is set to include the resonant angular frequency ω0 of resonator 106 of quantum bit 101. This reflection coefficient (S11) can be measured using, for example, a vector network analyzer. A vector network analyzer is a device in which signal source 113 and measuring instrument 114 are mounted in a single housing. The internal and external Q values ​​of quantum bit 101 may be calculated by fitting a theoretical formula to the frequency dependence of the reflection coefficient obtained from this measurement.

[0057] 6(B), when a signal obtained by superimposing an AC signal (having a frequency approximately twice the resonant angular frequency of resonator 106) from AC power supply 117 on a DC current from DC power supply 116 is passed through control line 109, the superimposed signal (current) I branches into two branches (inductors 111a and 111b) from control line 109, resulting in a current value of I / 2. These branches are applied to electrode 107 of quantum bit 101 via control lines 109a and 109b via capacitive coupling. Electrode tips 107a and 107b, inductors 111a and 111b, and control lines 109a and 109b are configured symmetrically with respect to the central axes of control line 109 and SQUID 104.

[0058] When reading out the quantum bit 101, if a signal obtained by superimposing an AC signal (having a frequency approximately twice the resonant frequency of the resonator 106) from the AC power supply 117 and an AC signal (corresponding to the resonant frequency of the resonator 106) from the signal source 103 on a DC current from the DC power supply 116 is passed through the control line 109, the superimposed signal (current) I' branches into a current value I' / 2 through the wiring (inductors 111a and 111b) where the control line 109 branches into two, and the AC current is input to the electrode 107 via a coupling capacitor (composed of the electrode tips 107a and 107b, the opposing sides of the inductors 111a and 111b, and the gap 121 between them).

[0059] As described above, the number of wires connected to the quantum bit has been reduced by half from two (input / output line and control line) to one control line, which makes it possible to suppress the increase in the number of wires that accompanies an increase in the number of quantum bits.

[0060] In FIG. 6(B), inductors 111a and 111b can be considered as part of the wiring constituting control line 109. Control lines 109a and 109b facing the sides of electrode tips 107a and 107b are opposite electrodes of the coupling capacitor on the control line 109 side. They can also be considered as wiring between inductors 111a and 111b that supply magnetic flux to SQUID 104 and ground, or as part of inductors 111a and 111b. In this case, FIG. 6(B) may be represented as a circuit, for example, as shown in FIG. 7. FIG. 7 illustrates the layout of FIG. 6(B) as a circuit configuration. Electrode 107 of quantum bit 101 and node n1 of SQUID 104 are capacitively coupled to control line 109 (109a and 109b in FIG. 6(B)) via coupling capacitances 110a and 110b. 7 is connected to control lines 109a and 109b. One end of each of the control lines 109a and 109b is connected to ground (120 in FIG. 6B), and when a current flows through them, they generate a magnetic flux and also function as inductors L1 and L2.

[0061] FIG. 8 is a diagram illustrating a frequency-tunable coupler of a comparative example. The frequency-tunable coupler 201 includes a SQUID 204 in which two Josephson junctions 202a and 202b are connected in a circular (loop) configuration by superconducting members 203a and 203b. The two Josephson junctions 202a and 202b are connected in parallel to two paths between one end (node ​​n1) and the other end (node ​​n2) of the SQUID 204. One end (node ​​n1) of the SQUID 204 is connected to a first electrode 207-1, and the other end (node ​​n2) is connected to a second electrode 207-2. A capacitance 205 is connected between the first electrode 207-1 and the second electrode 207-2. Note that while FIG. 8 shows a configuration in which the SQUID 204 includes two Josephson junctions, the number of Josephson junctions included in the SQUID loop may be arbitrary.

[0062] Coupler 201 is coupled to input / output line 208 and control line 209. Control line 209 corresponds to control line 109 in FIG. 1 and is a wiring that supplies current to inductor 211. However, since control line 209 is a control line for generating a DC bias magnetic flux, it will be referred to as flux bias line 209 below to clarify its function. Input / output line 208 is used for initializing coupler 201 and reading out the state of coupler 201. Note that reading through input / output line 208 may be used not only during calculation operations by quantum bit 101 and coupler 201, but also for calibrating coupler 201. One end of input / output line 208 is coupled to coupler 201 via coupling capacitance 210 when coupler 201 is operating. The other end of input / output line 208 is connected to signal source 213 and measuring instrument 214 via circulator 215. The other end of flux bias line 209 is connected to DC power supply 216. When coupler 201 is in operation, inductor 211 connected to one end of magnetic flux bias line 209 is electromagnetically coupled to coupler 201 via mutual inductance 212. Magnetic flux bias line 209 is connected to ground via inductor 211, and a DC magnetic field is generated by the DC current flowing through magnetic flux bias line 209. By varying the value of the DC current, the magnetic flux passing through SQUID 204 of coupler 201 is varied, and the resonant frequency ω r The magnetic flux bias line 209 is connected to a DC power supply 216.

[0063] Coupler 201 is placed in the refrigerator and operates in a cryogenically cooled state. Signal source 213, measuring instrument 214, and DC power supply 216 are placed in a room-temperature environment outside the refrigerator. When coupler 201 is operating, a signal from signal source 213 outside the refrigerator is transmitted through a coaxial cable or the like wired inside the refrigerator, is gradually attenuated by attenuators (not shown) installed at each temperature stage, is transmitted to input / output line 208 via circulator 215, and is input to coupler 201. Reflected signals of the output signal / input signal from coupler 201 are transmitted from input / output line 208 via circulator 215 to measuring instrument 214 outside the refrigerator, passing through a low-pass filter (not shown), a band-pass filter, an isolator, a HEMT amplifier, or the like (all not shown). A DC current from a DC power supply 216 is transmitted through a transmission line or the like wired inside the refrigerator, and is supplied to a magnetic flux bias line 209 via a low-pass filter (not shown), and flows to the ground via an inductor 211 .

[0064] When coupler 201 is in operation, a signal from signal source 213 is input to port 1 of circulator 215, output from port 2, passes through input / output line 208, and is applied to first electrode 207-1 of coupler 201 via coupling capacitance 210. A reflected signal from coupler 201 propagates through input / output line 208 via coupling capacitance 210, is input to port 2 of circulator 215, and is input from port 3 to a receiving circuit (not shown) of measuring instrument 214.

[0065] The resonant frequency of coupler 201 can be measured by measuring the reflected signal in response to the output signal / input signal from coupler 201 with measuring instrument 214. A DC current from DC power supply 216 passes through magnetic flux bias line 209 and inductor 211 to ground 120, and a DC magnetic field penetrating the loop of SQUID 204 is applied via mutual inductance 212. The resonant frequency of resonator 206 of coupler 201 changes depending on the value of the magnetic flux penetrating SQUID 204. As shown in FIG. 2, by changing the value of the DC current output from DC power supply 216, the value of the magnetic flux penetrating SQUID 204 can be changed, and the resonant frequency of resonator 206, i.e., the resonant frequency (operating point) of coupler 201 can be changed.

[0066] 9A is a schematic diagram illustrating a non-limiting example of the layout of coupler 201. Coupler 201 includes first electrode 207-1 having a substantially inverted L-shape with horizontal and vertical sides, and second electrode 207-2 having a substantially L-shape with horizontal and vertical sides that is arranged opposite the horizontal and vertical sides of first electrode 207-1. First electrode 207-1 and second electrode 207-2 each have staggered interdigital projections (fingers) extending from one horizontal side to the other, forming a comb-like nested structure (an interdigital capacitor structure). In the non-limiting example of FIG. 9A, each of the opposing finger pairs in the nested electrodes forms a parallel plate capacitor, and 13 pairs of parallel plate capacitors are connected in parallel. Josephson junctions 202a and 202b of SQUID 204 are connected between one end of the horizontal side of first electrode 207-1 (the left end of the figure) and one end of the vertical side of second electrode 207-2 (the top end of the figure). Protrusions 207a and 207b are provided at the center of the horizontal side and the center of the vertical side of first electrode 207-1, respectively, whose tips are capacitively coupled to the tips of the arms of cross-shaped electrodes 107-1 and 107-2 of the first and second quantum bits. Protrusions 207c and 207d are provided at the center of the vertical side and the center of the horizontal side of second electrode 207-2, respectively, whose tips are capacitively coupled to the tips of the arms of cross-shaped electrodes 107-3 and 107-4 of the third and fourth quantum bits. In this example, coupler 204 couples the first through fourth quantum bits through four-body interactions. The magnetic flux bias line 209 and the input / output line 208 are configured as coplanar waveguides with grounds 220 disposed on both sides via gaps 221 .

[0067] 9(B) is an enlarged schematic diagram of region 12 including SQUID 204 in FIG. 9(A). Flux bias line 209 is configured as a coplanar waveguide surrounded on both longitudinal sides by ground 220 with gap 221 between them. The ends of flux bias line 209 are bent at right angles, and the bent central conductor of flux bias line 209 forms inductor 211, one end of which is connected to ground 220. When a direct current flows through flux bias line 209, a magnetic flux flows from inductor 211 to ground 220 and passes through the loop of SQUID 204, generating a magnetic flux.

[0068] As described above, input / output lines 208 for reading out the state of coupler 201 and magnetic flux bias lines 209 for adjusting the resonant frequency of coupler 201 are provided for each coupler 201, and as the number of couplers 201 increases, wiring becomes an issue when the couplers are integrated. In particular, in a four-body interaction coupler 201, since it is surrounded by the four nearest quantum bits 101, it becomes difficult to route the wiring of input / output lines 208 and magnetic flux bias lines 209 on a planar circuit, and this issue must be addressed with three-dimensional wiring. The above issue is one example, but the present disclosure is not limited to the above and makes it possible to reduce the number of wires for coupler 201 in various situations.

[0069] FIG. 10 is a diagram illustrating an example of a coupler 201 according to the present disclosure. In the configuration of FIG. 10, elements that are the same as or equivalent to those in FIG. 8 are assigned the same or equivalent reference numerals, and their descriptions will be omitted as appropriate to avoid duplication. Note that the SQUID 204 is the same as that in FIG. 8, except that the first electrode 207-1 is connected to a magnetic flux bias line 209 via a coupling capacitance 210. That is, the input / output line 208 in FIG. 10 has been eliminated, and a single magnetic flux bias line 209 is configured to function as both the input / output line 208 in FIG. 8 and the magnetic flux bias line 209 that passes a DC current through an inductor 211. The magnetic flux bias line 209 is connected not only to a DC power supply 216 but also to a signal source 213 and a measuring instrument 214 via a circulator 215.

[0070] When coupler 201 is set to the initial state (superposition of the ground state and the excited state), an AC signal (for example, a small microwave signal having a frequency equal to the resonant frequency of resonator 206) output from signal source 213 is input to port 1 (p1) of circulator 215, output from port 2 (p2), propagates through bias T circuit 218 to magnetic flux bias line 209, and is applied to coupler 201 via coupling capacitance 210.

[0071] The control operation of coupler 201 will now be described. At this point, it is assumed that no signal is output from signal source 213 (no readout is being performed). A DC current from DC power supply 216 is input to the DC port of bias T circuit 218, and the DC current from DC power supply 216 is output from the RF+DC port to magnetic flux bias line 209. A magnetic flux flows from magnetic flux bias line 209 to inductor 211 and penetrates SQUID 204 of coupler 201, setting coupler 201 to an operating point of the resonant frequency. Node n3 of magnetic flux bias line 209 is connected to first electrode 207-1 of resonator 206 of coupler 201 via coupling capacitance 210, and the DC current from DC power supply 216 does not flow to the coupler 201 side.

[0072] The operation of reading the state of the coupler 201 will now be described. The state of the quantum bit may be read by inputting a signal (microwave) to the coupler 201 to change the state of the quantum bit and then reading that state. In this case, the quantum state may be read using a reflected signal of the signal input to the coupler 201. The superposition state of the ground state and the excited state in the coupler 201 changes due to reflection at the resonator 206 of the coupler 201. An AC signal (microwave signal: angular frequency is the resonant frequency of the resonator 206 of the coupler 201) output from the signal source 213 is input to port 1 (p1) of the circulator 215, output from port 2 (p2), and input to the RF port of the bias T circuit 218. A DC current from the DC power supply 216 is input to the DC port of the bias T circuit 218, and a signal in which the signal from the signal source 213 is superimposed on the DC current from the DC power supply 216 is output from the RF+DC port to the magnetic flux bias line 209. A node n3 of the magnetic flux bias line 209 is connected to one end of a coupling capacitance 210, the other end of which is connected to the first electrode 207-1, and the other end of an inductor 211, the other end of which is connected to ground.

[0073] An AC signal from a signal source 213 is applied to an electrode 207-1 of the coupler 201 from a node n3 of the magnetic flux bias line 209 via a coupling capacitance 210. A current obtained by superimposing a DC current from a DC power supply 216 and a current (microwave signal) output from the signal source 213 flows to the ground via an inductor 211, generating a magnetic field that penetrates the loop of the SQUID 204. The DC current from the DC power supply 216 adjusts the operating point (resonant frequency ω r ) is determined. The AC current output from signal source 213 has a weaker power than the DC current from DC power supply device 216, and the operating point (resonance frequency) of resonator 206 in coupler 201 is determined by the DC current from DC power supply device 216. For this reason, the influence (fluctuation) of the AC current output from signal source 213 on the operating point (resonance point) of resonator 206 in coupler 201 can be ignored.

[0074] A reflected signal of a signal input to coupler 201 propagates back to magnetic flux bias line 209 via coupling capacitance 210 and is input to the RF+DC port of bias T circuit 218. In bias T circuit 218, the reflected signal (AC signal) input to the RF+DC port is output to the RF port via a capacitor between the RF+DC port and the RF port. The reflected signal output from bias T circuit 218 is input to port 2 (p2) of circulator 215 and propagates from port 3 (p3) to measuring instrument 214. The state of coupler 201 can be read out by measuring the reflected signal from resonator 206 of coupler 201 with measuring instrument 214.

[0075] 11(A) and 11(B) are diagrams showing a non-limiting example of the layout of the coupler 201 of FIG. 10. FIG. 11(B) is a partially enlarged view showing a schematic enlargement of the region 12 of FIG. 11(A). As shown in FIG. 11(B), by widening the width of the magnetic flux bias line 209, a sufficiently large coupling capacitance 210 (FIG. 10) is formed between the end face of the tip of the magnetic flux bias line 209 and the first electrode 207-1 of the coupler 201. Furthermore, by bringing the inductor 211 connected to the tip of the magnetic flux bias line 209 closer to the SQUID 204, a sufficient magnitude of the mutual inductance 212 (FIG. 10) is ensured.

[0076] As shown in FIG. 11(B), the tip of the magnetic flux bias line 209 is formed in a substantially U-shape and is located close to the SQUID 204 bridging the electrodes 207-1 and 207-2. In order to increase the coupling capacitance 210 to a desired level, the tip of the magnetic flux bias line 209 is formed in an inverted U-shape and the length of the side facing the electrode 207 is increased. The wider the magnetic flux bias line 209 is, the larger the coupling capacitance 210 between the first electrode 207-1 can be. However, if the coupling capacitance 210 becomes too large, the external Q value of the coupler 201 will decrease. Therefore, the coupling capacitance 210 is set to an appropriate value.

[0077] More specifically, the magnetic flux bias line 209 includes a linear conductor pattern 209a (superconducting conductor pattern) that is bent at a right angle and extended parallel to the second electrode 207-2 at one end of the magnetic flux bias line 209 (center conductor), a linear conductor pattern 209b (superconducting conductor pattern) that has one end in contact with the end of the conductor pattern 209a and protrudes toward the SQUID 204 in a substantially U-shape so as to approach the SQUID 204, and a linear conductor pattern 209c (superconducting conductor pattern) that extends from the other end of the substantially U-shaped conductor pattern 209b in parallel to the opposing side of the electrode 207-1 and abuts against the ground 220. The conductor pattern 209b (linear conductor closest to the SQUID 204) essentially constitutes an inductor 211 that generates a magnetic flux that passes through the loop of the SQUID 204. The gap 221 between the conductor pattern 209c and the first electrode 207-1 essentially constitutes the coupling capacitance 210.

[0078] In the examples of FIGS. 11(A) and 11(B), an air bridge 224 is provided so that the return current of the current flowing through the magnetic flux bias line 209 flows through the grounds 220 on both sides of the magnetic flux bias line 209. FIG. 12 is a schematic diagram showing a cross section of the air bridge 224 in FIGS. 11(A) and 11(B). The air bridge 224 electrically connects the grounds 220 on both sides of the magnetic flux bias line 209 (center conductor) via gaps 221 on both sides of the magnetic flux bias line 209. The surface of the substrate 230 is exposed in the gaps 221. By allowing the return current of the current flowing through the magnetic flux bias line 209 to flow through the grounds 220 on both sides of the magnetic flux bias line 209, it is expected that the occurrence of unintended resonance modes such as slot line modes can be suppressed, and crosstalk can be suppressed.

[0079] 11(A) and 11(B), the coupling strength between the magnetic flux bias line 209 and the coupler 201 is set to an appropriate value. If the coupling strength between the magnetic flux bias line 209 and the coupler 201 is too weak, it becomes difficult to measure the resonance of the coupler 201. Conversely, if the coupling strength is too strong, the Q value of the coupler 201 decreases. Specifically, when the resonant frequency of the resonator 206 is set near its maximum value, the external Q value when a signal is input from the magnetic flux bias line 209 to the coupler 201 is preferably 10,000 or more and 100,000 or less. The external Q value is more preferably 10,000 or more and 50,000 or less. The external Q value is even more preferably 10,000 or more and 30,000 or less.

[0080] In the example of Figure 11(B), electromagnetic field simulation reveals that the external Q value is approximately 18,000, which is within the preferred range. The internal and external Q values ​​of the coupler can be experimentally measured as follows: First, the reflection coefficient (also called S11) is measured using measuring instrument 214 when a signal is input from signal source 213 to coupler 201. The reflection coefficient is measured while changing the signal frequency. The frequency range of this measurement is set to include the resonant frequency of coupler 201. The reflection coefficient can be measured using, for example, a vector network analyzer. The internal and external Q values ​​of coupler 201 can be calculated by fitting a theoretical formula to the frequency dependence of the reflection coefficient obtained from this measurement. With this coupler 201, the number of control lines can be reduced to half that of the comparative example in Figure 8.

[0081] FIG. 13 is a diagram illustrating a quantum bit 101A, which is a modification of the quantum bit 101 of FIG. 4. In FIG. 13, the same elements as those in FIG. 4 are assigned the same reference numerals, and explanations of the same elements will be omitted, and differences will be described. Referring to FIG. 13, quantum bit 101A includes a plurality of Josephson junctions 122-1 to 122-M (M is a positive integer equal to or greater than 1) connected in series (vertical product) between node n1 of SQUID 104 and electrode 107. A shunt capacitor is connected between electrode 107 and ground in parallel with the series circuit of SQUID 104 and Josephson junctions 122-1 to 122-M. The critical current values ​​of Josephson junctions 102a and 102b may be equal to or different from each other. By changing the critical current values ​​of Josephson junctions 102a and 102b, or the number and critical current values ​​of Josephson junctions 122-1 to 122-M, the nonlinearity of quantum bit 101A can be set to a desired value. Increasing the number of series-connected Josephson junctions 122-1 to 122-M reduces the nonlinearity. The resonance characteristics of resonator 106A of quantum bit 101A can be adjusted. In the example of FIG. 13, the number of wires coupled to quantum bit 101A can also be reduced to half that of the comparative example. The control and readout operations of quantum bit 101A are the same as those in the example of FIG. 4.

[0082] Figure 14 shows an example of the layout of quantum bit 101A in Figure 13, and corresponds to an enlarged view of Figure 6(B). As shown in Figure 14, a plurality of Josephson junctions 122 are connected in series to SQUID 104 between inductor 111 connected to ground 120 and the recess between electrode tips 107a and 107b.

[0083] FIG. 15 is a diagram illustrating another example of a quantum bit according to the present disclosure. In FIG. 15, the same elements as those in FIG. 4 are assigned the same reference numerals, and a description of the same elements will be omitted, with differences being described below. Referring to FIG. 15, resonator 106B of quantum bit 101B includes N (N≧2) SQUIDs 104-1 to 104-N connected in series between electrode 107 and ground, and capacitance 105 connected between electrode 107 and ground. The critical current values ​​of Josephson junctions 102-1a to 102-Na and Josephson junctions 102-1b to 102-Nb may be the same. Alternatively, at least one of them may be different, or all of them may be different. N inductors 111-1 to 111-N corresponding to SQUIDs 104-1 to 104-N, respectively, are connected in series between connection node n3 between control line 109 and coupling capacitance 110 and ground. Inductors 111-1 to 111-N and SQUIDs 104-1 to 104-N are magnetically coupled (induced) via mutual inductances 112-1 to 112-N, respectively. By changing the number of SQUIDs 104-1 to 104-N and the critical current values ​​of Josephson junctions 102-1a to 102-Na and Josephson junctions 102-1b to 102-Nb that make up the SQUIDs, the nonlinearity of quantum bit 101B can be designed to any (desired) value. In the configuration of FIG. 15, the number of control lines coupled to quantum bit 101B can also be reduced to half that of the comparative example of FIG. 1. The control and readout operations of quantum bit 101B are the same as those in the example of FIG. 4.

[0084] FIG. 16 is a diagram illustrating yet another example of a quantum bit according to the present disclosure. In FIG. 16, the same elements as those in FIG. 15 are assigned the same reference numerals, and explanation of the same elements will be omitted, with only differences being explained. Referring to FIG. 16, quantum bit 101C includes the configuration of FIG. 15, with a plurality of Josephson junctions 122-1 to 122-M (M is a positive integer of 1 or greater) connected in series between superconducting member 103-Na of SQUID 104-N and electrode 107. Capacitance 105 is connected between electrode 107 and ground in parallel with the series circuit of N SQUIDs 104-1 to 104-N and M Josephson junctions 122-1 to 122-M. By changing the number of SQUIDs 104-1 to 104-N, the critical current values ​​of Josephson junctions 102-1a to 102-Na and Josephson junctions 102-1b to 102-Nb, and the number and critical current values ​​of Josephson junctions 122-1 to 122-M, the nonlinearity of quantum bit 101C can be designed to any value. The number of control lines coupled to the quantum bit can be reduced to half that of the comparative example in Figure 1. The control and readout operations of quantum bit 101C are the same as those in the example in Figure 4.

[0085] FIG. 17 is a diagram illustrating yet another example of a quantum bit according to the present disclosure. In FIG. 17, the same elements as those in FIG. 4 are assigned the same reference numerals, and a description of the same elements will be omitted, with only differences being described. Referring to FIG. 17, quantum bit 101D differs from the configuration of FIG. 4 in the configuration of SQUID 104A included in resonator 106D. SQUID 104A has a configuration in which one Josephson junction 102 and M (M≧2) Josephson junctions 123-1 to 123-M connected in series are connected in parallel between node n1 connected to electrode 107 and node n2 connected to ground. In an array in which Josephson junctions 123-1 to 123-M are connected in series, let γ1 be the phase difference between both ends of the array (between nodes n1 and n2), γ2 be the phase difference at Josephson junction 102, Φ be the magnetic flux passing through the loop of SQUID 104A, and Φ0 be the magnetic flux quantum. TIFF2025131195000008.tif10150…(14) When the array of Josephson junctions 123-1 to 123-M is made up of identical Josephson junctions, the phase difference γ1 / M obtained by equally dividing the phase difference γ1 at both ends of the array is set as the phase difference between the input and output of each Josephson junction of the Josephson junctions 123-1 to 123-M. The potential energy of the first Josephson junctions 123-1 to 123-M connected in series is the individual potential energy -E J cos(γ1 / M) …(15) It is given by adding M of these. -M×E J cos(γ1 / M) …(16) However, E J is Josephson Energy. TIFF2025131195000009.tif9150…(17) (h is Planck's constant, e is the elementary charge, I C is the critical current)

[0086] The critical current values ​​of Josephson junction 102 and Josephson junctions 123-1 to 123-M may be equal to or different from each other. By changing the number and critical current values ​​of Josephson junctions 123-1 to 123-M and the critical current value of Josephson junction 102, the nonlinearity of quantum bit 101D can be designed to any value. The number of control lines coupled to the quantum bit can be reduced to half that of the comparative example in FIG. 8. The control and readout operations of quantum bit 101D are the same as those in the example in FIG. 4.

[0087] FIG. 18 is a diagram illustrating another example of a coupler according to the present disclosure. In FIG. 18, the same elements as those in FIG. 10 are denoted by the same reference numerals, and explanations of the same elements will be omitted, with differences being described below. A coupler 201A includes a plurality of Josephson junctions 222-1 to 222-M (M is a positive integer equal to or greater than 1) connected in series (vertically stacked) between a node n1 of a SQUID 204 and an electrode 207. A capacitance 205 is connected between the electrode 207 and ground in parallel with the series circuit of the SQUID 204 and the Josephson junctions 222-1 to 222-M. The critical current values ​​of the Josephson junctions 202a and 202b may be equal to or different from each other. The nonlinearity of the coupler 201A can be set to a desired value by changing the critical current values ​​of the Josephson junctions 202a and 202b, the number of Josephson junctions 222-1 to 222-M, and their critical current values. This allows adjustment of the resonance characteristics of resonator 206A. In the example of Fig. 18, the number of wires coupled to coupler 201A can also be reduced to half of that in the comparative example shown in Fig. 8. The control and readout operations of coupler 201A are the same as those in the example of Fig. 10.

[0088] FIG. 19 is a diagram illustrating another example of a coupler according to the present disclosure. In FIG. 19, the same elements as those in FIG. 10 are assigned the same reference numerals, and explanations of the same elements will be omitted, focusing instead on differences. Resonator 206B of coupler 201B includes N (N≧2) SQUIDs 204-1 to 204-N connected in series between electrode 207 and ground, and capacitance 205 connected between electrode 207 and ground. The critical current values ​​of Josephson junctions 202-1a to 202-Na and Josephson junctions 202-1b to 202-Nb may be equal. Alternatively, at least one of them may be different, or all of them may be different. N inductors 211-1 to 211-N corresponding to SQUIDs 204-1 to 204-N, respectively, are connected in series between connection node n3 between control line 209 and coupling capacitance 210 and ground. Inductors 211-1 to 211-N and SQUIDs 204-1 to 204-N are magnetically coupled (induced) via mutual inductances 212-1 to 212-N, respectively. By changing the number of SQUIDs 204-1 to 204-N and the critical current values ​​of Josephson junctions 202-1a to 202-Na and Josephson junctions 202-1b to 202-Nb that make up the SQUIDs, the nonlinearity of coupler 201B can be designed to any (desired) value. In the configuration of FIG. 19, the number of control lines coupled to coupler 201B can also be reduced to half that of the comparative example of FIG. 8. The control and readout operations of coupler 201B are the same as those in the example of FIG. 10.

[0089] Fig. 20 is a diagram illustrating yet another example of a coupler according to the present disclosure. In Fig. 20, the same elements as those in Fig. 19 are assigned the same reference numerals, and explanation of the same elements will be omitted, with differences being explained. Referring to Fig. 20, the configuration of Fig. 19 includes a plurality of Josephson junctions 222-1 to 222-M (M is a positive integer of 1 or more) connected in series (vertically stacked) between the superconducting member 203-Na of the SQUID 204-N and the electrode 207. The capacitance 205 is connected between the electrode 207 and ground in parallel with the series circuit of the N SQUIDs 204-1 to 204-1 to N and the M Josephson junctions 222-1 to 222-M. The nonlinearity of the coupler 201C can be designed to any value by changing the number of SQUIDs 204-1 to 204-N, the critical current values ​​of the Josephson junctions 202-1a to 202-Na and Josephson junctions 202-1b to 202-Nb that make up the SQUIDs, and the number and critical current values ​​of the Josephson junctions 222-1 to 222-M. The number of control lines coupled to the coupler 201C can be reduced to half that of the comparative example in FIG. 8. The control and readout operations of the coupler 201C are the same as those in the example in FIG. 10.

[0090] FIG. 21 is a diagram illustrating yet another example of a coupler according to the present disclosure. In FIG. 21, the same elements as those in FIG. 10 are denoted by the same reference numerals, and explanations of the same elements will be omitted, with only differences being described. Referring to FIG. 21, coupler 201D differs from the configuration of FIG. 10 in the configuration of SQUID 204A. SQUID 204A has a configuration in which one Josephson junction 202a and M (M≧2) series-connected Josephson junctions 223-1 to 223-M are connected in parallel between node n1 connected to electrode 207 and node n2 connected to ground. SQUID 204A corresponds to SQUID 104A of quantum bit 101D in FIG. 17. The critical current values ​​of Josephson junction 202a and Josephson junctions 223-1 to 223-M may be equal to or different from each other. By changing the number M of Josephson junctions 223-1 to 223-M, the critical current value, and the critical current value of Josephson junction 202a, the nonlinearity of coupler 201D can be designed to any value. The number of control lines coupled to coupler D can be reduced to half of that in the comparative example of FIG. 8. The control and readout operations of coupler 201D are the same as those in the example of FIG. 10.

[0091] FIG. 22 is a schematic diagram illustrating an example of the configuration of a superconducting quantum computer 300 (quantum annealing machine). In the example of FIG. 22, each coupler 201 couples four adjacent quantum bits 101 through four-body interactions. A coupler 201 and its four adjacent quantum bits 101 form a unit structure (also called a plaquette) (Reference 3). In the superconducting quantum computer 300, at least one quantum bit 101 is connected to multiple couplers 201. In the example shown in FIG. 22, the superconducting quantum computer 300 has multiple unit structures, and the quantum bit 101 is shared by the multiple unit structures. In the example shown in FIG. 22, 13 quantum bits 101 are integrated, but any number of quantum bits may be integrated in a similar manner. Note that signal sources and readout units are omitted in FIG. 22. The configuration of FIG. 22 is considered suitable for a network using the LHZ (Lechner, Hauke, Zoller) method, which is one of the quantum annealing methods.

[0092] 23 is a diagram illustrating a schematic example of the connection between coupler 201 of FIG. 22 and four quantum bits 101-1 to 101-4 adjacent (closest) to coupler 201. For convenience of illustration, FIG. 23 shows only the configuration of quantum bit 101-1, out of the four quantum bits 101-1 to 101-4, and its connections to control line 109-1 (inductor 111), signal source 113-1, measuring instrument 114-1, DC power supply 116-1, and AC power supply 117-1. The remaining quantum bits 101-2 to 101-4 have the same connection configuration as quantum bit 101-1. Electrode 107 of quantum bit 101-1 is capacitively coupled to electrode 207-2 of coupler 201 via capacitor 131-1. The electrode of quantum bit 101-2 is also capacitively coupled to electrode 207-2 of coupler 201 via capacitor 131-2. The electrodes of quantum bits 101-3 and 101-4 are also capacitively coupled to electrode 207-1 of coupler 201 via capacitors 131-3 and 131-4. In this configuration, the conditions for four quantum bits 101-1 to 101-4 to perform four-body interaction via coupler 201 are as follows: the resonant frequencies of quantum bits 101-1 to 101-4 are ω1 to ω4, respectively, and the resonant frequency of coupler 201 is ω r Assume that quantum bits 101-1 to 101-4 and coupler 201 are detuned from each other, and ω1+ω2=ω3+ω4…(18) Set to.

[0093] Fig. 24 is a diagram schematically showing a modification of Fig. 4. Referring to Fig. 24, in this modification, port 1 (p1) of the circulator 115 is connected to the RF+DC port of the bias T circuit 118, port 2 (p2) of the circulator 115 is connected to the control line 109, and port 3 (p3) of the circulator 115 is connected to the measuring instrument 114. An AC signal from the signal source 113 is input to port 1 (p1) of the circulator 115 via a diplexer 119 (port 3 (p3) is connected to the output of an AC power supply 117) and the bias T circuit 118 (DC port is connected to the output of a DC power supply 116), and then travels in one direction from port 1 (p1) to be output to port 2 (p2) of the circulator 115. The signal output from port 2 (p2) of circulator 115 to control line 109 (the AC signal from AC power supply 117 and / or signal source 113) is input to quantum bit 101 from control line 109 via coupling capacitance 110. The signal (AC signal + DC signal) output from port 2 (p2) of circulator 115 to control line 109 flows through inductor 111, generating a magnetic flux that penetrates SQUID 104 of quantum bit 101. The signal (output signal / reflected signal) from quantum bit 101 propagates to control line 109 via coupling capacitance 110, is input to port 2 (p2) of circulator 115, travels in one direction from port 2 (p2), is output from port 3 (p3) of circulator 115, and is transmitted to measuring instrument 114 via filter 141. As described above, the output from port 3 (p3) of circulator 115 is transmitted to measuring instrument 114 outside the refrigerator via a low-pass filter, band-pass filter, isolator, HEMT amplifier, etc. (not shown). Here, filter 141 (low-pass filter or band-pass filter) passes the reflected signal (angular frequency: ω0) at quantum bit 101 in response to the AC signal from signal source 113, among the reflected signals from quantum bit 101 traveling from port 2 (p2) to port 3 (p3) of circulator 115, and blocks the reflected signal (angular frequency: approximately 2×ω0) at quantum bit 101 in response to the AC signal from AC power supply 117, and supplies the reflected signal (angular frequency: ω0, for example) at quantum bit 101 to measuring instrument 114.

[0094] 25 is a diagram schematically illustrating a modification of FIG. 10. Referring to FIG. 25, in this modification, port 1 (p1) of circulator 215 is connected to the RF+DC port of bias T circuit 218, port 2 (p2) of circulator 215 is connected to magnetic flux bias line 209, and port 3 (p3) of circulator 215 is connected to measuring instrument 214. An AC signal from signal source 213 is input to port 1 (p1) of circulator 215 via bias T circuit 218 (the DC port is connected to the output of DC power supply 216), and travels in one direction from port 1 (p1) to be output to port 2 (p2) of circulator 215. The signal (AC signal) output from port 2 (p2) of circulator 215 to magnetic flux bias line 209 is input to coupler 201 from magnetic flux bias line 209 via coupling capacitance 210. The signal (AC signal + DC signal) output from port 2 (p2) of circulator 215 to magnetic flux bias line 209 flows through inductor 211, generating a magnetic flux that penetrates SQUID 204 in coupler 201. The signal (output signal / reflected signal) from coupler 201 propagates to magnetic flux bias line 209 via coupling capacitance 210, is input to port 2 (p2) of circulator 215, travels in one direction from port 2 (p2), is output from port 3 (p3) of circulator 215, and is transmitted to measuring instrument 214.

[0095] The above-described embodiment may be supplemented as follows (but is not limited to):

[0096] (Supplementary Note 1) In a superconducting quantum circuit, a wiring for transmitting a signal that generates a magnetic flux to be applied to a quantum bit and a wiring for transmitting a signal that is input and / or output to the quantum bit by capacitive coupling are collectively configured as a single first wiring.

[0097] (Supplementary Note 2) In the superconducting quantum circuit of Supplementary Note 1, the quantum bit comprises a first SQUID (Superconducting Quantum Interference Device) including at least one Josephson junction between a first node and a second node, a first electrode connected to the first node, and a first capacitor connected between the first electrode and ground, the second node is connected to the ground, and the first wiring is connected to the ground via a first inductor and to the first electrode via a coupling capacitor.

[0098] (Appendix 3) In the quantum bit of the superconducting quantum circuit of Appendix 2, during operation, a magnetic field is generated that penetrates the first SQUID due to a current flowing from the first wiring to the first inductor, a signal is input from the first wiring to the quantum bit via the coupling capacitor, and a signal from the quantum bit is propagated to the first wiring via the coupling capacitor and read out.

[0099] (Supplementary Note 4) The quantum bit of the superconducting quantum circuit of Supplementary Note 2 or 3 further includes one Josephson junction or multiple Josephson junctions connected in series between the first node and the first electrode of the first SQUID.

[0100] (Supplementary Note 5) The quantum bit of the superconducting quantum circuit of Supplementary Note 2 further comprises at least one second SQUID connected in series to the first SQUID between the first electrode and the ground, the at least one second SQUID including at least one Josephson junction between a first node and a second node of the at least one second SQUID, the second node of the at least one second SQUID being connected to the first node of an adjacent first SQUID or the adjacent second SQUID, the first node of the at least one second SQUID being connected to the second node or the first electrode of the adjacent second SQUID, and at least one second inductor being connected to the at least one second SQUID via mutual inductance between one end of the first wiring and the first inductor.

[0101] (Supplementary Note 6) In the quantum bit of the superconducting quantum circuit of Supplementary Note 5, the first node of the second SQUID is connected to the first electrode via at least one second SQUID, or one Josephson junction, or multiple Josephson junctions connected in series.

[0102] (Supplementary Note 7) In the quantum bit of the superconducting quantum circuit of Supplementary Note 2, the first SQUID includes at least one first Josephson junction connected in parallel between the first node and the second node of the first SQUID, and a plurality of second Josephson junctions connected in series.

[0103] (Supplementary Note 8) In the superconducting quantum circuit of Supplementary Note 2, the first wiring is connected to a wiring that extends from the abutting portion with the ground opposite to the end of the first electrode, the end of the first electrode of the quantum bit is widened, at least a part of the extended wiring that faces the widened end of the first electrode and an opposing side of the first electrode that faces at least a part of the wiring across a gap form the coupling capacitor, the first SQUID of the quantum bit bridges the end of the first electrode and an end of the ground, and at least a part of the wiring that extends opposite to the end of the first electrode acts as the first inductor.

[0104] (Supplementary Note 9) A superconducting quantum circuit device comprises the superconducting quantum circuit of any one of Supplements 1 to 8, and further comprises: a first signal source that generates an AC signal that is applied to the quantum bit of the superconducting circuit by capacitive coupling; a second signal source that generates an AC signal that is applied to the quantum bit by inductive coupling; a third signal source that generates a DC signal that is applied to the quantum bit by inductive coupling; a diplexer that combines signals from the first signal source and the second signal source and outputs the combined signal; and a bias circuit that outputs a signal that is obtained by biasing the output of the diplexer with the DC signal from the third signal source, and the signal from the bias circuit is supplied to the first wiring, propagates from the quantum bit to the first wiring, and further comprises a first measuring instrument that inputs a signal that is branched by a circulator from a path from the first signal source to the first wiring.

[0105] (Supplementary Note 10) In the superconducting quantum circuit of any one of Supplements 1 to 8, a coupler that mutually couples a plurality of quantum bits, including at least one of the quantum bits, is configured as a single second wiring that combines a wiring that transmits a signal that generates a magnetic flux to be applied to the coupler and a wiring that transmits a signal that is input and / or output to the coupler by capacitive coupling.

[0106] (Supplementary Note 11) In the superconducting quantum circuit of Supplementary Note 10, the coupler comprises a first SQUID including at least a first Josephson junction and a second Josephson junction connected in parallel between a first electrode and a second electrode of the coupler, and a first capacitor connected between the first electrode and the second electrode, and the second wiring is connected to ground via a first inductor for the coupler and is connected to the first electrode or the second electrode of the coupler via a coupling capacitor for the coupler.

[0107] (Supplementary Note 12) In the superconducting quantum circuit of Supplementary Note 10 or 11, in the coupler, during operation, a magnetic field penetrating the first SQUID of the coupler is generated by a current flowing from the second wiring to the first inductor for the coupler, a signal is input to the coupler from the second wiring via the coupling capacitor for the coupler, and the signal from the coupler is propagated to the second wiring via the coupling capacitor for the coupler and is read out.

[0108] (Supplementary Note 13) The coupler of the superconducting quantum circuit of Supplementary Note 11 further comprises one Josephson junction or a plurality of Josephson junctions connected in series between the first node of the first SQUID of the coupler and the first electrode of the coupler.

[0109] (Supplementary Note 14) The coupler of the superconducting quantum circuit of Supplementary Note 11 further comprises at least one second SQUID connected in series to the first SQUID between the first electrode and the second electrode of the coupler, the second SQUID including at least a first Josephson junction and a second Josephson junction connected in parallel to each other between a first node and a second node of the second SQUID, the second node of the second SQUID being connected to the first node of an adjacent first SQUID or the adjacent second SQUID, the first node of the second SQUID being connected to the second node or the first electrode of the adjacent second SQUID, and at least one second inductor for the coupler being connected to the at least one second SQUID via mutual inductance between the second wiring and the first inductor for the coupler.

[0110] (Supplementary Note 15) In the coupler of the superconducting quantum circuit of Supplementary Note 11, the first node of the second SQUID is connected to the first electrode via the second node of the adjacent second SQUID, or via one Josephson junction or multiple Josephson junctions connected in series.

[0111] (Supplementary Note 16) In the coupler of the superconducting quantum circuit of Supplementary Note 11, the first SQUID of the coupler includes at least one first Josephson junction and a plurality of second Josephson junctions connected in series between the first node and the second node of the first SQUID.

[0112] (Appendix 17) A superconducting quantum circuit device comprises the superconducting quantum circuit according to appendix 10, a fourth signal source that generates an AC signal that is applied to the coupler of the superconducting circuit by capacitive coupling, a fifth signal source that generates a DC signal that is applied to the coupler by inductive coupling, and a bias circuit that biases an output of the fourth signal source with the DC signal from the fifth signal source, wherein the bias circuit is connected to the second wiring and the device comprises a second measuring instrument that inputs a signal that is propagated from the coupler to the second wiring and branched by a circulator from a path from the fourth signal source to the second wiring.

[0113] [Reference 1] JP 2021-108308 A [Reference 2] Advances in Superconducting Qubit Research and Applications, Yasunobu Nakamura, Applied Physics, Vol. 90, No. 4, 2021, pp. 209-220 [Retrieved January 16, 2024] (Internet <url>https: / / www.jstage.jst.go.jp / article / oubutsu / 90 / 4 / 90_209 / _pdf / -char / ja) [Reference 3] S. Puri, et al., "Quantum annealing with all-to-all connected nonlinear oscillators," Nature Communications, June 2017.

[0114] The disclosures of Patent Document 1 and References 1-3 are incorporated herein by reference. Modifications and adjustments of the embodiments and examples are possible within the scope of the entire disclosure of the present invention (including the scope of the claims), and further based on the basic technical concept thereof. Furthermore, various combinations and selections of the various disclosed elements (including each element of each appendix, each element of each example, each element of each drawing, etc.) are possible within the scope of the claims of the present invention. In other words, the present invention naturally includes various modifications and alterations that would be possible for a person skilled in the art based on the entire disclosure, including the scope of the claims, and the technical concept thereof. [Explanation of symbols]

[0115] 11, 12 areas 101, 101A~101D, 101-1~101-4 qubits 102, 102a, 102b, 102-1a~102-Na, 102-1b~102-Nb, 122-1~122-M, 123-1~123-M, 202, 202a, 202b, 202-1a~202-Na, 202-1b~202-Nb, 222-1~222-M, 223-1~223-M, josephson junction 103a, 103b, 103-1a to 103-Na, 103-1b to 103-Nb, 203a, 203b, 203-1a to 203-Na, 203-1b to 203-Nb Superconducting materials 104, 104A, 104-1~104-N, 204, 204-1~204-N SQUID 105, 205 capacitance 106, 106A, 106B, 106C, 106D, 206, 206A, 206B, 206C, 206D resonator 107, 107-1~107-4 electrode 107a, 107b Electrode tip 108, 208 input / output lines 109, 109a, 109b, 109-1 control lines 110, 110a, 110b, 210 Coupling capacitance 111, 111-1 to 211-N, 111a, 111b, 211, 211-1 to 211-N inductors 112, 112-1 to 112-N, 212, 212-1 to 212-N Mutual inductance 113, 113-1, 213 signal source 114, 114-1, 214 Measuring instruments 115, 115-1, 215 Circulator 116, 116-1, 216 DC power supply 117, 117-1 AC power supply equipment 118, 218 Bias Tee circuit 119 Diplexer 120, 220 grand 121, 121a, 121b, 121c, 121d, 221 gap 123-1~123-N Josephson junctions 131-1~131-4 Capacitors 141 filters 201, 201A, 201B, 201C, 201D Combiner 207-1 First electrode 207-2 Second electrode 207a~207d Protrusions (connection to quantum bits) 209 Control line (magnetic flux bias line) 209a, 209b, 209c Conductor pattern (superconducting conductor pattern) 224 Air Bridge 230 PCB 300 Superconducting Quantum Computer< / url>

Claims

1. Wiring that transmits a signal that generates a magnetic flux to be applied to the quantum bit; A superconducting quantum circuit, wherein wiring for transmitting signals input and / or output to the quantum bit by capacitive coupling is also configured as a single first wiring.

2. The quantum bit is a first SQUID (Superconducting Quantum Interference Device) including at least one Josephson junction between a first node and a second node; a first electrode connected to the first node; a first capacitor connected between the first electrode and ground; the second node is connected to the ground; 2. The superconducting quantum circuit according to claim 1, wherein the first wiring is connected to the ground via a first inductor and to the first electrode via a coupling capacitor.

3. In the quantum bit, during operation, a magnetic field penetrating the first SQUID is generated by a current flowing from the first wiring to the first inductor; a signal is input from the first wiring to the quantum bit via the coupling capacitor; 3. The superconducting quantum circuit according to claim 2, wherein a signal from said quantum bit is propagated to said first wiring via said coupling capacitor and read out.

4. 3. The superconducting quantum circuit of claim 2, further comprising a Josephson junction or a plurality of Josephson junctions connected in series between the first node and the first electrode of the first SQUID in the quantum bit.

5. the first wiring is connected to a wiring that extends from the contact portion with the ground to face an end portion of the first electrode, an end of the first electrode of the quantum bit is widened; at least a part of the widened wiring that faces the widened end of the first electrode and an opposing side of the first electrode that faces at least a part of the wiring across a gap form the coupling capacitor; the first SQUID of the quantum bit bridges an end of the first electrode and an end of the ground; 3. The superconducting quantum circuit according to claim 2, wherein at least a portion of the wiring extending opposite to the end of the first electrode acts as the first inductor.

6. The superconducting quantum circuit according to claim 1; a first signal source that generates an AC signal that is capacitively coupled to the quantum bit of the superconducting quantum circuit; a second signal source that generates an AC signal that is inductively coupled to the quantum bit; a third signal source that generates a DC signal that is applied to the quantum bit by inductive coupling; a diplexer that combines and outputs signals from the first signal source and the second signal source; a bias circuit that biases the output of the diplexer with the DC signal from the third signal source and outputs the biased signal; Equipped with a signal from the bias circuit is supplied to the first wiring; a first measuring instrument that inputs a signal that propagates from the quantum bit to the first wiring and is branched by a circulator from a path from the first signal source to the first wiring.

7. A coupler that mutually couples a plurality of quantum bits including at least one of the quantum bits, Wiring for transmitting a signal for generating a magnetic flux to be applied to the coupler; 2. The superconducting quantum circuit according to claim 1, wherein wiring for transmitting signals input and / or output to said coupler by capacitive coupling is combined into a single second wiring.

8. The coupler a first SQUID including at least a first Josephson junction and a second Josephson junction connected in parallel to each other between a first electrode and a second electrode of the coupler; a first capacitor connected between the first electrode and the second electrode; Equipped with 8. The superconducting quantum circuit according to claim 7, wherein the second wiring is connected to ground via a first inductor for a coupler and is connected to the first electrode or the second electrode of the coupler via a coupling capacitor for the coupler.

9. In the coupler, during operation, a current flowing from the second wiring to the first inductor for the coupler generates a magnetic field that penetrates the first SQUID of the coupler; a signal is input from the second wiring to the coupler via the coupling capacitor for the coupler; 9. The superconducting quantum circuit of claim 8, wherein a signal from the coupler is propagated to the second wiring via the coupling capacitor for the coupler and read out.

10. The superconducting quantum circuit according to claim 7; a fourth signal source that generates an AC signal that is capacitively coupled to the coupler of the superconducting quantum circuit; a fifth signal source that generates a DC signal that is inductively coupled to the coupler; a bias circuit that biases the output of the fourth signal source with the DC signal from the fifth signal source; Equipped with the bias circuit is connected to the second wiring; a second measuring instrument that inputs a signal that propagates from the coupler to the second wiring and is branched from a path from the fourth signal source to the second wiring.

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