Superconducting quantum circuit device

Abstract

To provide a superconducting quantum circuit device appropriate for increasing a strength of four-body interaction by suppressing influences of floating capacitance exerted upon the strength of the four-body interaction.SOLUTION: First-fourth quantum bits 20A-20C and a coupler 21, which is disposed in a region enclosed by a ground surface 40 separately from the ground surface and couples the first-fourth quantum bits, are provided on a substrate. The coupler comprises: a first electrode 16 and a second electrode 18; and a nonlinear element 10 bridging these electrodes. The first electrode includes first and second opposite parts which respectively extend from a location different from a side opposed to the second electrode to the sides of the first and second quantum bits and which have the ends capacitively coupled oppositely with the first and second quantum bits. The second electrode includes third and fourth opposite parts which respectively extend from a location different from a side opposed to the first electrode to the sides of the third and fourth quantum bits and which have the ends capacitively coupled oppositely with ends of the third and fourth quantum bits.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] This invention relates to a superconducting quantum circuit device. [Background technology]

[0002] A qubit, which consists of a superconducting quantum circuit, is generally constructed as a planar circuit on a semiconductor substrate on which a superconductor has been deposited, and has inter-bit coupling for quantum computation. This inter-bit coupling needs to be switched on or off and on in strength to perform quantum computation under various conditions. For this reason, a coupler consisting of a superconducting quantum circuit with a superconducting quantum interference device (SQUID), similar to the qubit itself, is often used for inter-bit coupling. In such a coupler, the magnitude of the coupling can be variably controlled by applying magnetic flux to the SQUID loop (which contains two Josephson junctions).

[0003] An example of this type of coupler is shown in Figure 1. Figure 1 corresponds to Figure 4 in Patent Document 1 (however, the reference numerals have been changed from those in Patent Document 1). Figure 1 includes four fixed-frequency quantum circuits (qubits) 111 to 114, each capacitively coupled to an adjustable coupler 120. The adjustable coupler 120 has a SQUID in which the ends of two superconducting lines forming a loop are connected via two Josephson junctions. The adjustable coupler 120 functions as a frequency-variable coupler by changing the current passing through a magnetic flux bias line (control line) 130 inductively coupled to the SQUID, thereby changing the magnetic flux passing through the SQUID loop. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Special Publication No. 2021-516389 [Non-patent literature]

[0005] [Non-Patent Document 1] Uri Vool et al., "Introduction to Quantum Electromagnetic Circuits", International Journal of Circuit Theory and Applications 45, 897-934 (2017) [Summary of the Invention] [Problem to be Solved by the Invention]

[0006] In FIG. 1, before the X-shaped tunable coupler 120 is coupled to qubits, ground planes (GND) are disposed on both sides of the waveguide (coplanar waveguide), and the stray capacitance Cs, which is the capacitance between the electrode of the qubit and the ground plane of the tunable coupler 120 that is capacitively coupled to the qubit, becomes large. For this reason, the coupling strength (magnitude of the coupling constant) of the four-body interaction coupler for four qubits cannot be increased (this problem will be described in detail below).

[0007] The present disclosure has been devised in view of the above problem, and an object thereof is to provide a superconducting quantum circuit device including a coupler having a configuration suitable for suppressing the influence of stray capacitance on the strength of four-body interaction and increasing the strength of four-body interaction. [Means for Solving the Problem]

[0008] According to the present disclosure, the superconducting quantum circuit device includes, on a substrate: first to fourth qubits; and a coupler disposed spaced apart from the ground plane in a region surrounded by the ground plane, the coupler coupling the first to fourth qubits through four-body interaction. The coupler includes a first electrode and a second electrode disposed opposite to each other, and a non-linear element including at least one Josephson junction that bridges the first electrode and the second electrode. The first electrode extends from a point separate from the side of the first electrode facing the second electrode towards the first and second qubits, and its ends are provided with first and second opposing portions that capacitively couple with the ends of the coupler connection portions of the first and second qubits, respectively. The second electrode extends from a point on the second electrode that is not facing the first electrode towards the third and fourth qubits, and its ends are provided with third and fourth opposing portions that capacitively couple with the ends of the coupler connection portions of the third and fourth qubits, respectively. The ends of the first and second opposing portions and the ends of the third and fourth opposing portions are arranged within the region enclosed by the ground plane. [Effects of the Invention]

[0009] According to this disclosure, it is possible to realize a superconducting quantum circuit device with a configuration suitable for suppressing the influence of stray capacitance on the strength of the four-body interaction in the coupler and maximizing the strength of the four-body interaction. [Brief explanation of the drawing]

[0010] [Figure 1] This diagram illustrates the configuration of related technologies. [Figure 2] This is a diagram illustrating the circuit of the embodiment. [Figure 3] This is a diagram illustrating a schematic embodiment. [Figure 4] This figure schematically illustrates a modified example of the embodiment. [Figure 5] This is a diagram illustrating an example of the analysis of an embodiment. [Figure 6] This figure illustrates the characteristics of the strength of the tetrabody interaction in the embodiment. [Figure 7] This figure illustrates the characteristics of the strength of the tetrabody interaction in the embodiment. [Figure 8] This figure illustrates an example of an embodiment. [Figure 9] This figure schematically illustrates the cross-section of line AA in Figure 8. [Figure 10](A) and (B) are diagrams illustrating modified examples of the embodiments. [Figure 11] (A) and (B) are diagrams illustrating modified examples of the embodiments. [Figure 12] This figure schematically illustrates another embodiment. [Modes for carrying out the invention]

[0011] An embodiment will now be described. Figure 2 illustrates a system in which Josephson parametric oscillators (JPOs) are used as qubits, with four JPO1 (20A) to JPO4 (20D) interacting via a coupler 21. Note that in Figure 2, the connections to the readout circuits for each JPO are omitted.

[0012] Referring to Figure 2, the system comprises four JPO1(20A) to JPO4(20D) and a coupler 21. JPO1(20A) to JPO4(20D) are connected to the coupler 21 via capacitive coupling through coupling capacitors 31A to 31D, respectively. In the following embodiment, each JPO is of the lumped parameter type, but it goes without saying that they may also be of the distributed parameter type.

[0013] The coupler 21 has a nonlinear element 10 which includes at least one Josephson junction (JJ), and a capacitor 15 is connected in parallel to the nonlinear element 10. The nonlinear element 10 may be configured to include a SQUID in which a first superconducting line and a first Josephson junction and a second superconducting line and a second Josephson junction are connected in a ring.

[0014] JPO1(20A) to JPO4(20D) each comprises a SQUID (loop) 210A to 210D in which the first superconducting sections 203A to 203D, the first Josephson junctions 201A to 201D, the second superconducting sections 204A to 204D, and the second Josephson junctions 202A to 202D are each connected in a ring shape; a magnetic field generating section 207A to 207D generates a magnetic flux that penetrates the SQUID loops 210A to 210D by passing a DC current or pump signal supplied from a signal generating section (current control section) (not shown) to control lines 23A to 23D; and capacitors 206A to 206D connected between the first superconducting sections 203A to 203D and the second superconducting sections 204A to 204D, with the second superconducting sections 204A to 204D being connected to ground. The first superconducting sections 203A and 203B of JPO1(20A) and JPO2(20B) are connected to one end of the first and second coupler connection sections 24A and 24B, respectively, and the other ends of the first and second coupler connection sections 24A and 24B are connected to one end of the coupler 21 via coupling capacitors 31A and 31B (capacitive connection). Similarly, the first superconducting sections 203C and 203D of JPO3(20C) and JPO4(20D) are connected to one end of the third and fourth coupler connection sections 24C and 24D, respectively, and the other ends of the third and fourth coupler connection sections 24C and 24D are connected to the other end of the coupler 21 via coupling capacitors 31C and 31D (capacitive connection). The frequency of the pump signals supplied to control lines 23A to 23D of JPO1(20A) to JPO4(20D) is set to a frequency close to twice the resonant angular frequency. In JPO1(20A) to JPO4(20D), there is a threshold for the pump strength; exceeding this threshold causes oscillation, and even without an input signal, it outputs a signal at the resonant frequency. This is called parametric oscillation.

[0015] The capacitance values ​​of capacitors 206A to 206D in JPO1 (20A) to JPO4 (20D) are C J Let Cg be the capacitance value of capacitor 15 of coupler 21, and C be the capacitance value of coupling capacitors 31A to 31D.

[0016] The capacitances 33 and 34 connected between coupling capacitors 31A and 31B and one end of the coupler 21, and between coupling capacitors 31C and 31C and the other end of the coupler 21, and between coupling capacitors 31C and 31C, and between coupling capacitors 31C and the other end of the coupler 21, and between coupling capacitors 33 and 34, respectively, represent stray capacitances (capacitance value: Cs).

[0017] Figure 3 is a schematic example illustrating the configuration of the coupler 21 (wiring pattern formed on the substrate) when JPO1(20A) to JPO4(20D) are configured as lumped-parameter types, as an example of Figure 2. In Figure 3, each JPO from JPO1(20A) to JPO4(20D) has the configuration shown in Figure 2. In Figure 3, for the sake of drawing convenience, only the configuration of JPO2(20B) is shown in the callout. Also, in Figure 3, the connection parts (waveguides) between JPO1(20A) to JPO4(20D) and the readout circuits are omitted.

[0018] The coupler 21 is positioned within a region 41 surrounded by the ground plane (ground pattern: GND) 40 on the substrate, spaced apart from the edges (43a, 43b, 43c1, 43c2, 43d1, 43d2) of the ground plane 40. In Figure 3, there is no ground wiring pattern in region 41, and the gap region between the ground plane 40 and the coupler 21 is the exposed substrate surface.

[0019] The coupler 21 comprises a nonlinear element 10 including at least one Josephson junction (JJ), first and second electrodes 16 and 18 (made of superconducting material) connected to one end and the other end of the nonlinear element 10, and a capacitor (Cg) 15 shunt-connected (in parallel) to the nonlinear element 10. The first electrode 16 has first and second opposing portions 17A and 17B (made of superconducting material) extending toward JPO1 (20A) and JPO2 (20B), respectively. The second electrode 18 has third and fourth opposing portions 19A and 19B (made of superconducting material) extending toward JPO3 (20C) and JPO4 (20D), respectively. In the coupler 21 of Figure 3, the capacitor (Cg) 15 shunt-connected to the nonlinear element 10 corresponds to the capacitance between the opposing first and second electrodes 16 and 18. Note that in Figure 3, for the sake of drawing convenience, two JPOs (JPO1, JPO2) are shown placed to the left of the coupler 21, and two other JPOs (JPO3, JPO4) are shown to the right of the coupler 21. However, for example, JPO1 could be placed to the left of the coupler 21, JPO2 to the top of the coupler 21, JPO3 to the right of the coupler 21, and JPO4 to the bottom of the coupler 21. Alternatively, the four JPOs could be placed in the first to fourth quadrants with the center of the coupler 21 as the origin.

[0020] JPO1(20A) to JPO4(20D) are configured as waveguide resonators terminated to ground by SQUID210A to 210D, respectively. These waveguide resonators generate parametric oscillation by modulating the magnetic flux passing through the SQUID loops 210A to 210D at a frequency approximately twice the resonant frequency using a pump signal (microwave) from a control line (23A to 23D in Figure 8) not shown in Figure 3.

[0021] In JPO2(20B), the second coupler connection portion 24B, which is a conductive portion (waveguide made of a superconducting material) 205B connected to the first superconducting portion 203B of the SQUID loop 210B, is capacitively coupled to the end of the second opposing portion 17B extending from the first electrode 16 of the coupler 21. The capacitance value C of the coupling capacitor 31B is the capacitance component (capacitive component) between the end of the second coupler connection portion 24B and the end of the second opposing portion 17B which is positioned opposite to that end.

[0022] In JPO1(20A), as in JPO2(20B), the first coupler connection portion 24A, which is a conductive portion (waveguide made of a superconducting material) connected to the first superconducting portion 203A of the SQUID loop 210A, is capacitively coupled to the end of the first opposing portion 17A that extends from the first electrode 16 of the coupler 21. The capacitance value C of the coupling capacitor 31A is the capacitance component (capacitive component) between the end of the first coupler connection portion 24A and the end of the first opposing portion 17A. Similarly, in JPO3(20C) and JPO4(20D), the third and fourth coupler connections 24C and 24D, which are conductive parts (waveguides made of superconducting material) connected to the first superconducting parts 203C and 203D of the SQUID loops 210C and 210D, are capacitively coupled to the ends of the third and fourth opposing parts 19A and 19B, which extend from the second electrode 18 of the coupler 21. The capacitance value C of the coupling capacitors 31C and 31D is the capacitance component (capacitive component) between the ends of the third and fourth coupler connections 24C and 24D and the ends of the third and fourth opposing parts 19A and 19B. The first to fourth coupler connections 24A to 24D consist of coplanar waveguides (CPW) sandwiched between ground planes with gaps on both sides.

[0023] In Figure 3, reference numerals 33-1 and 33-2 represent the stray capacitances between the first and second opposing portions 17A and 17B of the first electrode 16 and ground, and reference numerals 34-1 and 34-2 represent the stray capacitances between the third and fourth opposing portions 19A and 19B of the second electrode 18 and ground. The parallel combined capacitance of stray capacitances 33-1 and 33-2 is equal to the value Cs of the stray capacitance 33 at node n1 (one end of the coupler 21) in Figure 2, and each capacitance value is set to half of Cs (Cs / 2). The parallel combined capacitance of stray capacitances 34-1 and 34-2 is equal to the value Cs of the stray capacitance 34 at node n2 (the other end of the coupler 21) in Figure 2, and each capacitance value is set to half of Cs (Cs / 2).

[0024] The ends (open-end ends) of the first and second opposing portions 17A and 17B of the coupler 21, and the ends (open-end ends) of the third and fourth opposing portions 19A and 19B are located within a region 41 defined by the mutually spaced and opposing edges 43a and 43b, 43c1 and 43d1, 43c2 and 43d2 of the ground surface 40. Although the edges 43a, 43b, 43c1, 43d1, 43c2, and 43d2 of the ground surface 40 form a quadrilateral with straight sides as the edge of region 41, it goes without saying that the edge of region 41 is not limited to a quadrilateral. Furthermore, the edges 43a, 43b, 43c1, 43d1, 43c2, and 43d2 of the ground surface 40 are not limited to straight lines, but may include irregularities or curves.

[0025] In Figure 3, the gap (capacitive coupling portion) between the ends of the first and second opposing portions 17A and 17B of the first electrode 16 of the coupler 21 and the ends of the first and second coupler connection portions 24A and 24B of JPO1 (20A) and JPO2 (20B), and the gap (capacitive coupling portion) between the ends of the third and fourth opposing portions 19A and 19B of the second electrode 18 of the coupler 21 and the ends of the third and fourth coupler connection portions 24C and 24D of JPO3 (20C) and JPO4 (20D) are located within a region 41 defined by the mutually spaced and opposing edges 43a and 43b, 43c1 and 43d1, 43c2 and 43d2 of the ground surface 40.

[0026] The gap between the first and second electrodes 16 and 18 of the coupler 21 and the edges 43a and 43b of the ground surface 40 may be approximately on the order of the size of the electrodes 16 and 18 (including a fraction of the size to several times the size). In Figure 3, the ratio of the size of the gap (gap width) between the first and second electrodes 16 and 18 of the coupler 21 and the ground surface 40 to the size of the first and second electrodes 16 and 18 is a schematic example, and various variations are possible.

[0027] By reducing the stray capacitance Cs / 2 between the first and second electrodes 16 and 18 of the coupler 21 (the ends of the first and second opposing parts 17A and 17B, and the ends of the third and fourth opposing parts 19A and 19B) and ground, and by lowering the contribution rate of the stray capacitance Cs / 2, which contributes to the coupling of the tetrabody interaction, to the total capacitance which is the sum of the self-capacitance Cg of the coupler 21, the coupling capacitance C, and the stray capacitance Cs / 2, it is possible to increase the strength of the coupling of the tetrabody interaction.

[0028] In Figure 3, the ends of the first and second coupler connection portions 24A and 24B of JPO1 (20A) and JPO2 (20B), and the ends of the third and fourth coupler connection portions 24C and 24D of JPO3 (20C) and JPO4 (20D) do not protrude into the region 41 enclosed by the mutually spaced and opposing edges 43a and 43b, 43c1 and 43d1, and 43c2 and 43d2 of the ground surface 40. However, as shown in Figure 4, the ends of the first and second coupler connection portions 24A and 24B, and the ends of the third and fourth coupler connection portions 24C and 24D may be configured to protrude into the region 41. This makes it possible to further reduce the stray capacitance Cs between each electrode 16, 18 of the first and second electrodes 16, 18 of the coupler 21 and the ground plane 40 by increasing the size of the gap (gap width) between the coupling capacitors 31A, 31D between JPO1(20A), 18, and the coupler 21, while maintaining the capacitance value C of the coupling capacitors 31A, 18, and the coupler 21.

[0029] Figure 5 is a diagram illustrating the four-body interaction of the four JPO1(20A) to JPO4(20D) described with reference to Figures 2 to 4, and corresponds to Figure 2. Note that the magnetic field generating sections 207A to 207D are not shown. In Figure 5, Josephson junctions are indicated by a symbol of an "x" enclosed in a square, and Φ1 to Φ4 within the SQUID loops 210A to 210D of JPO1(20A) to JPO4(20D) represent the magnetic flux passing through each SQUID loop. E is attached to the two Josephson junctions in the SQUID loops 210A to 210D of JPO1 to JPO4. J This represents Josephson energy. E J =(hbar / 2e)Ic (1) (where hbar = h / (2π), h is Planck's constant, e is the elementary charge, and Ic is the critical current)

[0030] E Jg This represents the Josephson energy of the Josephson junction of coupler 21.

[0031] Magnetic fluxes φ1-φ4, φg1, and φg2 are placed at each node 1-4, g1, and g2 (for details on the fluxes placed at each node, see, for example, Non-Patent Document 1). For the circuit shown in Figure 5, the classical Hamiltonian is quantized according to standard methods such as Non-Patent Document 1, and the Hamiltonian H'total is obtained by further performing unitary transformations and the rotating wave approximation. This Hamiltonian H'total can be expressed as equation (2) below, focusing on the four-body interaction term.

[0032] TIFF0007913258000001.tif37108(2)

[0033] In equation (2), H' JPO,i (i = 1, 2, 3, 4) is the Hamiltonian of JPO1(20A) to JPO4(20D). H' coupler This is the Hamiltonian of coupler 21. a + k ak (k = 1, 2, 3, 4) are the boson creation operators and annihilation operators corresponding to JPO1(20A) to JPO4(20D). a + g_ , a g_ are the boson creation operator and annihilation operator corresponding to the coupler 21.

[0034] In formula (2), g (4) is a coefficient (coupling constant) of the four-body interaction, and is expressed by the following formula (3) based on circuit parameters (for example, capacitance Cg of the coupler 21, coupling capacitance C, stray capacitance Cs) and the resonant angular frequencies of each JPO and the coupler 21.

[0035] TIFF0007913258000002.tif14150(3)

[0036] In formula (3), ω is the resonant angular frequency of each JPO, and is given by the following formula (4). TIFF0007913258000003.tif6150(4)

[0037] ω - is the resonant angular frequency of the coupler 21, and is given by the following formula (5). TIFF0007913258000004.tif10150(5)

[0038] e is the elementary electric charge (elementary charge).

[0039] In formula (4), Ec is the capacitance C of each JPO J is the charging energy of, and is given by the following formula (6). TIFF0007913258000005.tif11150(6)

[0040] E J is the Josephson energy of each JPO.

[0041] In formula (5), E'cg is the combined capacitance: Cg This is the charge energy of +C+Cs / 2, and is given by equation (7) below. TIFF0007913258000006.tif14150 (7)

[0042] E Jg This is the Josephson energy of the Josephson junction of coupler 21.

[0043] From equation (3), the coefficient of the tetrabody interaction (coupling constant) g (4) The denominator of this expression includes the stray capacitance Cs as the term Cg+C+Cs / 2. The smaller the value of the stray capacitance Cs, the smaller the coefficient of the four-body interaction (coupling constant) g. (4) The contribution rate of Cg+C to increases. Also, the larger the value of the stray capacitance Cs, the greater the contribution of g (4) It becomes smaller.

[0044] Also, from equations (5) and (7), a g- The resonant angular frequency ω_ of coupler 21, which corresponds to the (boson annihilation operator of coupler 21), also depends on the stray capacitance Cs.

[0045] Now, let's look at the effect of stray capacitance Cs on the circuit. Figure 6 shows the coefficients (coupling constants) of the four-body interaction with and without stray capacitance Cs. (4) ratio (g (4) (Cs) / g (4) (0) (vertical axis) represents the stray capacitance C s This is a graph plotted against the value (horizontal axis).

[0046] As an example of setting specific circuit parameters in Figure 5, The resonant angular frequency ω of each JPO is Let ω / 2π = 10 GHz (gigahertz), Capacitance C of each JPO J =1000fF(femtofarad), Capacitance C of coupler 21 g =200fF, Each coupling capacitance C = 1fF, When set to this value, the difference between having and not having stray capacitance Cs is g. (4) Ratio: g (4) (Cs) / g (4) The graph for (0) is shown.

[0047] g (4) (Cs), g (4) (0) is given by equations (8) and (9) below, respectively.

[0048] TIFF0007913258000007.tif20116 (8)

[0049] TIFF0007913258000008.tif21103(9)

[0050] Therefore, g (4) (Cs) / g (4) (0) is given by the following equation (10).

[0051] TIFF0007913258000009.tif20108(10)

[0052] In equations (8) to (10), TIFF0007913258000010.tif19150 (11) TIFF0007913258000011.tif14150 (12)

[0053] The resonant frequency ω_ / 2π of the coupler 21 is ω_ / 2π = 9.98 GHz when there is no stray capacitance Cs, but it changes depending on the stray capacitance Cs.

[0054] With this setting, if there is no stray capacitance Cs (when Cs=0), TIFF0007913258000012.tif14108(13) This is the result.

[0055] As shown in Figure 6, the value of the stray capacitance Cs determines g (4) It can be seen that it decreases sharply. One of the reasons for this decrease is that the resonant angular frequency ω_ of the coupler 21 changes due to the influence of the stray capacitance Cs, and g (4) This is because the denominator of [Equation (3)] becomes large.

[0056] However, even if we could somehow fix ω_ to 9.98GHz in the above settings, g (4) The coefficient of the four-body interaction (coupling constant) g decreases with the value of the stray capacitance Cs (see Figure 7). Therefore, when there is stray capacitance Cs at both ends of the coupler 21, the larger the stray capacitance Cs, the greater the coefficient of the four-body interaction (coupling constant) g. (4) It becomes smaller.

[0057] Figure 7 shows that in Figure 5, ω = 10 GHz, ω_ = 9.98 GHz, C J When = 1000fF, Cg = 200fF, and C = 1fF, the difference in g with and without stray capacitance Cs. (4) ratio (g (4) (Cs) / g (4) This is the graph of (0).

[0058] The difference between Figure 7 and Figure 6 is that in Figure 7, the resonant angular frequency ω of the coupler 21 is fixed at 9.98 GHz. As shown in Figure 7, g (4) (Cs) / g (4) The graph in (0) does not show the same rapid decrease as in Figure 6.

[0059] Next, an example configuration of the embodiment will be described. Figure 8 is a diagram showing a non-limiting example of the embodiment described above, and schematically shows a non-limiting example of a wiring pattern (planar circuit) of a superconducting quantum circuit fabricated on a substrate such as silicon.

[0060] Figure 8 shows a planar configuration of a coupler in which four qubits are composed of four lumped-parameter JPO1(20A) to JPO4(20D), and these four qubits are coupled together by a four-body interaction.

[0061] The lumped-parameter JPO1(20A) to JPO4(20D) are composed of resonators made up of linear (non-linear) inductance and capacitance components and nonlinear elements including Josephson junctions.

[0062] In this embodiment, the coupler 21 and JPO1(20A) to JPO4(20D) are realized, for example, by a transmission line (wiring) formed on a substrate using a superconductor. Although silicon (Si) is used as the substrate, 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 substrates may also be used. As the transmission line material (wiring material), for example, Nb (niobium) or Al (aluminum) are used, but the invention is not limited to these, and any metal that becomes superconducting when cooled to extremely low temperatures may be used, such as niobium nitride, indium (In), lead (Pb), tin (Sn), rhenium (Re), palladium (Pd), titanium (Ti), titanium nitride, Mo (molybdenum), Ta (tantalum), tantalum nitride, and alloys containing at least one of these. Furthermore, in order to achieve a superconducting state, the coupler circuit is used in a temperature environment of approximately 10 mK (millikelvin) achieved by a refrigerator.

[0063] Referring to Figure 8, the planar shape of the first electrode 16 is roughly trapezoidal, and its shape is that of a trapezoid rotated approximately 45 degrees counterclockwise. The first and second opposing parts 17A and 17B of the first electrode 16 extend from near the intersection of the top base and the hypotenuse (leg) of the trapezoid towards the placement of JPO1 (20A) and JPO2 (20B), respectively, to the left and upward in the figure. The planar shape of the second electrode 18 is an inverted trapezoidal shape obtained by rotating a trapezoid approximately 135 degrees clockwise. The third and fourth opposing parts 19A and 19B of the second electrode 18 extend from near the intersection of the top base and the hypotenuse (leg) of the trapezoid towards the placement of JPO3 (20C) and JPO4 (20D), respectively, to the right and downward in the figure. The first electrode 16 and the second electrode 18 are positioned with their respective trapezoidal bases facing each other, and the combined planar shape of the main body excluding the opposing parts is close to a hexagon. Note that in Figure 8, the stray capacitance at one end of the opposing parts (17A, 17B, 19A, 19B) is not shown.

[0064] The first electrode 16 has a projection 16C that protrudes downward in the figure near the intersection of one end of its lower base and its hypotenuse. The second electrode 18 has a cut portion 18C that is cut off parallel to the projection 16C of the first electrode 16 near the intersection of one end of its lower base and its hypotenuse. A nonlinear element 10 such as a SQUID is placed in the gap between the projection 16C near the intersection of one end of the lower base and the hypotenuse of the first electrode 16 and the cut portion 18C near the intersection of one end of the lower base and the hypotenuse of the first electrode 16. The obliquely arranged electrode configuration makes the arrangement area more compact.

[0065] JPO1(20A) to JPO4(20D) each consist of coplanar waveguides 25A, 25B, 25C, and 25D and SQUIDs 26A, 26B, 26C, and 26D, respectively. They are microwave-range LC resonant circuits composed of the linear inductance and capacitance components of the coplanar waveguides 25A, 25B, 25C, and 25D, and the nonlinear inductance and capacitance components of the SQUIDs 26A, 26B, 26C, and 26D. The resonant frequency can be adjusted by applying DC (direct current) current to control lines 23A, 23B, 23C, and 23D, which are inductively coupled to SQUIDs 26A, 26B, 26C, and 26D, and parametric oscillation can be induced by applying AC (alternating current) current.

[0066] JPO1(20A) to JPO4(20D) are capacitively coupled to the readout circuit via capacitors 32A to 32D, with connection points (I / O waveguides) 22A to 22D (capacitor 15 in Figure 2 is omitted). Figure 8 shows parts of each of the connection points (I / O coplanar waveguides) 22A, 22B, 22C, and 22D. The wiring patterns of the connection points (I / O coplanar waveguides) 22A to 22D may be extended to, for example, the area around the chip and connected to, for example, a wiring board (not shown) via bump electrodes. Furthermore, they may be connected to a measuring device outside the refrigerator via readout wiring.

[0067] For control lines 23A, 23B, 23C, and 23D, which are composed of coplanar waveguides, there are air bridge wirings (also simply called "air bridges") 27A, 27B, 27C, and 27D that are overhead wirings on the wiring layer to stabilize the ground potential surrounding JPO1 (20A) to JPO4 (20D). The control lines 23A, 23B, 23C, and 23D may also be connected to a wiring board (not shown) via bump electrodes (not shown) (not shown) in areas such as around the chip, and then connected to a signal generation device (current control unit) outside the refrigerator.

[0068] Figure 9 schematically shows a cross-section of line AA perpendicular to control line 23D in Figure 8. The cross-sections for control lines 23A to 23D have the same configuration. For example, a wiring layer is formed on the surface of a silicon substrate 42, and the JPO 20 (20A to 20D) and the central coupler (21) and ground plane 40 shown in Figure 8 are formed on this wiring layer. Control line 23D is constructed as a coplanar waveguide on the same wiring layer as this wiring layer.

[0069] Ground planes (ground patterns) 40-1 and 40-2 are provided on both sides of the longitudinal direction of the control line 23D (wiring) with a gap in between. An air bridge wiring 27D made of a superconducting material (e.g., A1) is provided in an arch shape, straddling the control line 23D from above, and connecting the ground planes 40-1 and 40-2 on both sides.

[0070] The air bridge wiring structure for the ground plane 40 eliminates the division of the ground plane 40 on both sides by the control lines 23 (23A~23D) consisting of coplanar waveguides, and equalizes the charge distribution of the ground plane 40 surrounding JPO1 (20A)~JPO4 (20D), thereby stabilizing the ground potential. In Figure 8, as a non-limiting embodiment, the connection section with the readout circuit (coplanar waveguide for I / O) 22A~22D also has an air bridge wiring configuration 28A, 28B, 28C, and 28D that are overhead wired on the wiring layer, similar to the control lines 23A~23D. The air bridge wiring 28A~28D of the connection section (coplanar waveguide for I / O) 22A~22D also has a similar cross-sectional configuration.

[0071] Furthermore, referring to Figure 8, air bridge wiring 29A to 29D made of superconducting material (e.g., Al) is provided to connect the GND patterns on both sides of the coupler connection portions 24A to 24D of JPO1 (20A) to JPO4 (20D) from above.

[0072] When the coupler 21 and multiple qubits are configured on a planar circuit, the ground is divided at the qubits and coupling points, which can lead to AC (alternate current) / DC (direct current) crosstalk via slot line modes, etc. However, by connecting the ground planes using an air bridge wiring structure as shown in Figure 8, the charge distribution on the ground planes on both sides of the signal conductor is made uniform, thereby avoiding the occurrence of the aforementioned crosstalk.

[0073] Capacitance C between waveguides 25A-25D of JPO1(20A)-JPO4(20D) and ground (201A-201D in Figure 2) J , Capacitance C of the capacitor (15 in Figure 2) between the first and second electrodes 16 and 18 of the coupler 21. g , Regarding the capacitance C of the coupling capacitors (31A, 31B in Figure 2) between the first and second opposing parts 17A, 17B of the coupler 21 and the coupler connection parts 24A, 24B of the waveguides 25A, 25B of JPO1 (20A) and JPO2 (20B), and the capacitance C of the coupling capacitors (31C, 31D in Figure 2) between the third and fourth opposing parts 19A, 19B of the coupler 21 and the coupler connection parts 24C, 24D of the waveguides 25C, 25D of JPO3 (20C) and JPO4 (20D), for example, C J >C g >C That is also acceptable.

[0074] Furthermore, by bringing the resonant angular frequency ω of each JPO1(20A) to JPO4(20D) closer to the resonant angular frequency of the coupler 21, the strength of the four-body interaction coupling can be set to be larger.

[0075] The first and second electrodes 16 and 18 of the coupler 21 are coupled by a capacitor 15, and are also coupled to JPO1 (20A), JPO2 (20B), JPO3 (20C), and JPO4 (20D) via coupling capacitors 31A, 31B, 31C, and 31D, respectively, and the entire structure is surrounded by a ground plane (ground pattern) 40. The first and second opposing portions 17A and 17B, and the third and fourth opposing portions 19A and 19B, which capacitively couple with JPO1(20A), JPO2(20B), and JPO3(20C) and JPO3(20D), respectively protrude toward the ground surface 40 from the first electrode 16 and the second electrode 18, and can couple with JPO1(20A), JPO2(20B), and JPO3(20C) and JPO3(20D) at a location away from the first electrode 16 and the second electrode 18.

[0076] Capacitor (C) between the first and second electrodes 16 and 18 g )15 strengthens the coupler 21 against disturbances such as charge noise. In addition, reducing the stray capacitance (capacitor 15) between the first and second electrodes 16 and 18 has the effect of strengthening the tetrabody interaction.

[0077] The coupling strength (coupling constant) of the tetrabody interaction by the coupler 21 decreases if there is a stray capacitance between the ends of the coupler 21 and the ground.

[0078] With respect to the first and second electrodes 16 and 18 of the coupler 21, the stray capacitance of the first and second electrodes 16 and 18 of the coupler 21 is reduced by separating the parts of the first and second opposing portions 17A and 17B, and the third and fourth opposing portions 19A and 19B (excluding the ends) from the ground plane 40 with a large gap (for example, about the same size as the coupler 21), for example, about 100 μm (micrometers), where the superconductor is not deposited. By placing the first and second electrodes 16 and 18, up to the open ends of the first and second opposing portions 17A and 17B, and the third and fourth opposing portions 19A and 19B, within the region (gap region) 41 surrounded by the ground plane 40, the stray capacitance Cs of the first and second opposing portions 17A and 17B, and the third and fourth opposing portions 19A and 19B of the coupler 21 is reduced. By reducing the stray capacitance Cs at the ends of the coupler 21, the coefficient of the tetrabody interaction (coupling constant) g (4) It is possible to set the value of to a large value.

[0079] Figures 10(A) and (B) schematically show examples of air bridge wiring 29A to 29D made of superconducting material (e.g., Al) that connects the GND patterns on both sides of the first to fourth coupler connection portions 24A to 24D of JPO1(20A) to JPO4(20D) from above. Note that in Figures 10(A) and (B), only an example of the arrangement of air bridge wiring 29A is shown, and air bridge wirings 29B to 29D are omitted simply for the sake of drawing convenience.

[0080] The example in Figure 10(A) shows a configuration in which the coupler connection portion 24A of JPO1(20A) (qubit) does not protrude into the region 41 defined by the ground plane 40 (the end of the coupler connection portion 24A is located to the left of the boundary (dashed line) defined by edges 43c1 and 43c2). The same configuration is used for JPO2(20B) to JPO4(20D).

[0081] For each of the air bridges 29A to 29D, the distance separating the air bridge 29A to 29D from the coupling capacitors 31A to 31D (the distance from the ends of the coupling connectors 24A to 24D to the air bridge wiring 29A to 29D) should be greater than the length of each gap in the coupling capacitors 31A to 31D (the gap between the ends of the coupling connectors 24A and 24B, the ends of the coupling connectors 24C and 24D, the first and second opposing parts 17A and 17B of the first electrode 16 facing these, and the third and fourth opposing parts 19A and 19B of the second electrode 18).

[0082] By adopting this structure, the stray capacitance Cs between the coupler 21 and ground is reduced, thereby reducing the capacitance C of the coupler 21. g Of the capacitances obtained by adding the coupling capacitance C and Cs / 2, the capacitance C that contributes to the tetrabody interaction coupling is C. g By increasing the contribution rate of +C, the coupling of quantum states between JPOs (qubits) can be made larger. Furthermore, by connecting the ground plane 40 surrounding the coupler 21 with air bridge wiring 29A~29D, it is possible to enhance noise immunity.

[0083] In the example shown in Figure 10(B), the coupler connection portion 24A of JPO1(20A) is configured to protrude into region 41. That is, the end of the coupler connection portion 24A is located within region 41, beyond the boundary (dashed line) defined by edges 43c1 and 43c2. JPO2(20B) to JPO4(20D) are configured similarly. With this configuration, it is possible to increase the gap between the first and second electrodes 16 and 18 of the coupler 21 and ground while maintaining the capacitance of the coupling capacitors 31-A to 31-D between JPO1(20A) to JPO4(20D) and each opposing portion (17A, 17B, 19A, 19B) of the coupler 21, thereby further reducing the stray capacitance between the coupler 21 and ground.

[0084] Figures 11(A) and (B) show modified versions of Figures 10(A) and (B), respectively, corresponding to a configuration in which the coupler connection portion 24A of JPO1(20A) does not extend into region 41 and a configuration in which the coupler connection portion 24A of JPO1(20A) protrudes into region 41. Generally, as the length of an air bridge wiring structure increases, the air bridge may collapse due to the influence of its own weight, etc., increasing the possibility of the air bridge wiring coming into contact with the signal conductor or the air bridge itself being damaged. According to the configuration in Figure 11(A), the coupler connection portion 24A of JPO1(20A) has a narrower wire width from the open end to the installation site of the air bridge wiring 29A. After passing the installation site of the air bridge wiring 29A, the wire width becomes wider via a tapered section and connects to the first superconducting portion 203A of the SQUID loop 210A of JPO1.

[0085] Figure 12 is a schematic diagram showing the configuration of a quantum computer 300 integrating the JPO20s of the above-described embodiment, as an example of the configuration of another embodiment. In the configuration shown in Figure 12, each four-body interaction coupler 21 is connected to four JPO20s, as illustrated in Figures 2 to 4. Each JPO20 is connected to one to four four-body interaction couplers 21, and the JPO20s are shared and arranged in multiple unit structures, resulting in the arrangement of unit structures shown in Figures 2 to 4. In the quantum computer 300, at least one JPO20 is connected to multiple couplers 21. In particular, in the example shown in Figure 12, at least one JPO20 is connected to four four-body interaction couplers 21. The quantum computer 300 can also be described as follows: The quantum computer 300 has multiple JPO20s, and each JPO20 is connected to one to four four-body interaction couplers 21. The number of four-body interaction couplers 21 connected to each JPO20 corresponds to the number of unit structures to which the JPO20 is shared. Thus, in the example shown in Figure 12, the quantum computer 300 has multiple unit structures, and the JPO20 is shared by multiple unit structures. In the example shown in Figure 12, 13 superconducting nonlinear JPO20s are integrated, but any number of JPO20s can be integrated in the same way. Note that the current control unit and readout unit are omitted in Figure 12. The configuration in Figure 12 is considered suitable for the LHZ (Lechner, Hauke, Zoller) network, which is one of the quantum annealing methods.

[0086] Furthermore, the disclosures in Patent Document 1 and Non-Patent Document 1 mentioned above are incorporated herein by reference. Within the framework of the full disclosure of the present invention (including the claims), further modifications and adjustments to the embodiments or examples are possible based on the fundamental technical concept. Also, within the framework of the claims of the present invention, various combinations or selections of various disclosed elements (including each element of each claim, each element of each embodiment, each element of each drawing, etc.) are possible. In other words, the present invention naturally includes the full disclosure, including the claims, and various modifications and alterations that a person skilled in the art could make in accordance with the technical concept. [Explanation of Symbols]

[0087] 10 Nonlinear elements 15 Capacitors 16 Electrodes (First Electrode) 16C protrusion 17A Opposing part (first opposing part) 17B Opposing section (second opposing section) 18 Electrode (Second Electrode) 18C cut section 19A Opposing part (third opposing part) 19B Opposing section (4th opposing section) 20, 20A~20D JPO1~JPO4 (qubits) 21 Combiner 22A~22D Readout circuit connection section 23A~23D Control lines (flux lines) 24A~24D Coupler connection section 25A~25D coplanar waveguide 26A~26D Nonlinear elements (SQUIDs) 27A~27D Air Bridge Wiring 28A~28D Air Bridge Wiring 29A~29D Air Bridge Wiring 30 locations (GND pattern protrusions) 31A~31D Coupling Capacitors 32A~32D Capacitors (Input / Output Capacitors) 33, 33-1, 33-2, 34, 34-1, 34-2 Stray capacitance 40, 40-1, 40-2 Ground surface (ground pattern) 41 area 41 42 Substrates (Silicon Substrates) 43a, 43b, 43c1, 43c2, 43d1, 43d2 51 Control Line 111-114 Fixed-Frequency Quantum Circuits 120 Adjustable Coupler 130 control line 201A, 201B, 201C, 201D Josephson junctions (first Josephson junctions) 202A, 202B, 202C, 202D Josephson junctions (second Josephson junctions) 203A, 203B, 203C, 203D: First superconducting section 204A, 204B, 204C, 204D: Second superconducting section 205A, 205B, 205C, 205D Conductive part 206A, 206B, 206C, 206D Capacitors 207A, 207B, 207C, 207D Magnetic field generation section 210A, 210B, 210C, 210D SQUID loop 300 Quantum Computer

Claims

1. On the circuit board, The first to fourth qubits, A coupler is positioned within a region enclosed by a ground plane, spaced apart from the ground plane, and connects the first to fourth qubits via a four-body interaction. Equipped with, The aforementioned coupler is, A first electrode and a second electrode are positioned opposite each other, A nonlinear element comprising at least one Josephson junction bridging the first electrode and the second electrode, Equipped with, The first electrode is, The first electrode extends from a location separate from the side facing the second electrode towards the first and second qubits, and each electrode has first and second opposing portions whose ends face and capacitively couple with the ends of the coupler connection portion of the first and second qubits, respectively. The second electrode is, The second electrode extends from a location separate from the side facing the first electrode towards the third and fourth qubits, and each end has a third and fourth opposing portion that capacitively couples with the ends of the coupler connection portion of the third and fourth qubits, respectively. The ends of the first and second opposing parts and the ends of the third and fourth opposing parts are arranged within the region enclosed by the ground surface. The strength of the tetra-body interaction bond g (4) is, The capacitance value of the capacitive coupling between each of the first to fourth qubits and the coupler is C, The capacitance value between the first electrode and the second electrode of the coupler is C g. Let C s be the value of the stray capacitance between each of the first and second electrodes of the coupler and ground. Then, the formula (C g + C + C s / 2) is included in the denominator. A superconducting quantum circuit device that increases the strength of the four-body interaction g(4) by reducing the stray capacitance Cs and increasing the contribution rate of (Cg + C) to the strength of the four-body interaction g(4).

2. The superconducting quantum circuit device according to claim 1, wherein the coupler connection portions of the first and second qubits and the coupler connection portions of the third and fourth qubits are provided with a portion of each, including the end portion, protruding within the region surrounded by the ground plane along their respective longitudinal directions.

3. The ground planes are positioned on both sides of the longitudinal direction of the coupler connection portion of the first to fourth qubits, with gaps in between. The superconducting quantum circuit device according to claim 1 or 2, wherein at least one of the coupling connections of the first to fourth qubits is provided with an air bridge that spans the coupling connection and connects the ground planes on both sides of the coupling connection to each other.

4. On the substrate, The first to fourth qubits, A coupler is positioned within a region enclosed by a ground plane, spaced apart from the ground plane, and connects the first to fourth qubits via a four-body interaction. Equipped with, The aforementioned coupler is, A first electrode and a second electrode are positioned opposite each other, A nonlinear element comprising at least one Josephson junction bridging the first electrode and the second electrode, Equipped with, The first electrode is, The first electrode extends from a location separate from the side facing the second electrode towards the first and second qubits, and each electrode has first and second opposing portions whose ends face and capacitively couple with the ends of the coupler connection portion of the first and second qubits, respectively. The second electrode is, The second electrode extends from a location separate from the side facing the first electrode towards the third and fourth qubits, and each end has a third and fourth opposing portion that capacitively couples with the ends of the coupler connection portion of the third and fourth qubits, respectively. The ends of the first and second opposing parts and the ends of the third and fourth opposing parts are arranged within the area enclosed by the ground plane. At least one of the coupler connection portions of the first to fourth qubits is: A first section having a first width along the longitudinal direction, starting from the end, is followed by a second section having a second width that expands from the first width and is larger than the first width. In the first section of the coupling connection, the ground surfaces are arranged on both sides of the coupling connection in the longitudinal direction with gaps between them. A superconducting quantum circuit device comprising air bridge wiring that spans the coupling connection portion of the first section and connects the ground planes on both sides of the coupling connection portion to each other.

5. Each of the first to fourth qubits is, A superconducting quantum circuit device according to any one of claims 1 to 4, comprising a resonator including a loop circuit in which a first superconducting line and a first Josephson junction and a second superconducting line and a second Josephson junction are connected in a ring, and a capacitor connected in parallel with the loop circuit.

6. In each of the first to fourth qubits, The second superconducting line of the loop circuit is connected to ground. The first superconducting line of the loop circuit is connected to the coupler connection section. The ends of the coupler connection portion of the first and second qubits are capacitively coupled to the first and second opposing portions of the coupler. The superconducting quantum circuit device according to claim 5, wherein the ends of the coupling connection portions of the third and fourth qubits are capacitively coupled to the third and fourth opposing portions of the coupling.

7. The superconducting quantum circuit device according to any one of claims 1 to 5, wherein the coupler includes a loop circuit in which both ends of two superconducting lines constituting a loop are connected via two Josephson junctions.

8. Half of the stray capacitance Cs is the value of the stray capacitance between the first and second opposing portions of the first electrode of the coupler and the ground, and the value of the stray capacitance between the third and fourth opposing portions of the second electrode and the ground. The superconducting quantum circuit device according to any one of claims 1 to 7, wherein the strength of the bond g (4) of the four-body interaction includes the cube of the formula (C g + C + C s / 2) in the denominator.

9. The superconducting quantum circuit device according to any one of claims 1 to 8 is A superconducting quantum circuit device comprising a quantum computer having the first to fourth qubits that perform Josephson parametric oscillation and the coupler as a unit structure.

10. Having multiple of the aforementioned unit structures, The superconducting quantum circuit device according to claim 9, wherein the unit structure constitutes a quantum computer in which at least one of the first to fourth qubits constituting the unit structure is shared with one or more other unit structures.

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