Superconducting quantum circuits

Abstract

To provide a superconducting quantum circuit which enables the resonance operation point thereof to be easily adjusted.SOLUTION: A superconducting quantum circuit includes loop structure in which a first superconducting line, a first Josephson junction, a second superconducting line, and a second Josephson junction are circularly connected, and connects a plurality of SQUIDs (Superconducting Quantum Interference Devices) in parallel having a different in a junction area of the first Josephson junction and a junction area of the second Josephson junction. In the plurality of SQUIDs, any one of or both of a sum of the junction area of the first Josephson junction and the junction area of the second Josephson junction and a ratio of the junction area of the first Josephson junction and the junction area of the second Josephson junction is / are different each other between the plurality of SQUIDs.SELECTED DRAWING: Figure 2A

Description

[Technical Field]

[0001] The present invention relates to a superconducting quantum circuit, a quantum bit circuit, a quantum bit coupler, and a quantum computer. [Background technology]

[0002] Quantum computers using superconducting quantum circuits are being developed widely. These quantum computers generally consist of microwave LC resonant circuits made of superconductors, and include nonlinear elements including Josephson junctions (e.g., superconducting quantum interference devices (SQUIDs)).

[0003] Such a microwave LC resonant circuit is composed of, for example, a planar circuit in which a superconducting material is vapor-deposited on a semiconductor substrate. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Special Publication No. 2021-500737 [Patent Document 2] Patent Publication No. 2021-108308 Summary of the Invention [Problem to be solved by the invention]

[0005] The techniques disclosed in the above prior art documents have the problem that it is difficult to adjust the resonant operating point, as will be explained in detail later.

[0006] Therefore, an object of the present disclosure is to provide a superconducting quantum circuit, a quantum bit circuit, a quantum bit coupler, and a quantum computer that solve the above problems. [Means for solving the problem]

[0007] According to one embodiment of the present disclosure, there is provided a superconducting quantum circuit having a loop structure in which a first superconducting line, a first Josephson junction, a second superconducting line, and a second Josephson junction are connected in a ring shape, and a plurality of SQUIDs (Superconducting Quantum Interference Devices) are connected in parallel, each SQUID having a different junction area between the first Josephson junction and the second Josephson junction, and the plurality of SQUIDs differ from one another in either or both of the sum of the junction areas of the first Josephson junction and the second Josephson junction and the ratio of the junction area between the first Josephson junction and the second Josephson junction. [Effects of the Invention]

[0008] According to the present disclosure, it is possible to easily adjust the resonant operating point. [Brief explanation of the drawings]

[0009] [Figure 1A] FIG. 1 is a diagram illustrating a related art. [Figure 1B] FIG. 1 is a diagram illustrating a related art. [Figure 1C] FIG. 1 is a diagram illustrating a related art. [Figure 2A] FIG. 1 is a diagram illustrating an embodiment. [Figure 2B] FIG. 1 is a diagram illustrating an embodiment. [Figure 3] FIG. 1 is a diagram illustrating a configuration example of an embodiment. [Figure 4] FIG. 1 is a diagram illustrating a configuration example of an embodiment. [Figure 5] FIG. 10 is a diagram illustrating a modified example of an embodiment. [Figure 6A] FIG. 10 is a diagram illustrating a configuration example of another embodiment. [Figure 6B] FIG. 10 is a diagram illustrating a configuration example of another embodiment. [Figure 7] FIG. 10 is a diagram illustrating a modified example of another embodiment. [Figure 8]FIG. 10 is a diagram illustrating a modified example of another embodiment. [Figure 9] FIG. 10 is a diagram illustrating yet another embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0010] The above-mentioned problems will be described below, followed by a description of some embodiments.

[0011] The SQUID behaves as a variable inductance that depends on the magnitude of the magnetic flux Φ that penetrates the loop surface. Therefore, by applying a DC current to the control line that is coupled to the SQUID via mutual inductance, it is possible to adjust the circuit characteristics such as the resonant frequency.

[0012] The effective critical current value I of a SQUID c depends on the magnetic flux Φ, and the inductance (self-inductance) L is the critical current value I c In other words, the self-inductance L of the SQUID is inversely proportional to the critical current value I c Then, it is given by: L=Φ0 / (2I c )∝1 / I c ···(1) Here, Φ0 is the magnetic flux quantum (Φ0=h / 2e: h is the Plank constant, e is the elementary charge). Therefore, L is expressed as follows: c In reality, a shielding current flows through the SQUID to cancel out the external magnetic field, so the parameter β in the following equation (2) is introduced (however, for simplicity, β can be calculated as 1). β=2L*I c / Φ0···(2)

[0013] When the two Josephson junctions of a SQUID have the same critical current value I0, the total current I flowing through the SQUID can be expressed as follows: I=I0sin(γA)+I0sinγB ···(3) Here, γA and γB are the phase jumps (phase differences) in the two Josephson junctions, respectively, and are related by the following equation (4): γB-γA=2πΦ / Φ0 (4) Here, Φ is the magnetic flux (external magnetic flux) that penetrates (interlinks) the loop surface of the SQUID.

[0014] From equations (3) and (4), the maximum value of the current I flowing through the SQUID is I max is given by the following equation: I max =2I0|cos(πΦ / Φ0)| (5)

[0015] I max When the magnetic flux Φ is an integer multiple (including 0) of the magnetic flux quantum Φ0 (Φ / Φ0=n), 2I o , and becomes 0 when it is a half-integer multiple (Φ / Φ0=1 / 2+n).

[0016] When two Josephson junctions have the same critical current value I0, that is, in the case of a symmetrical SQUID, there is only one operating point (resonant operating point) where the gradient (gradient relative to the magnetic flux) becomes 0 and coherence is improved (magnetic flux phase = πΦ / Φ0 = nπ, maximum resonant frequency), as will be described later. The resonant operating point is determined by the DC magnetic field Φ applied to the SQUID. dc In general, a resonator has an inductance component Lc other than the SQUID, and the inductance is the SQUID inductance L + Lc, but for simplicity, if we set Lc = 0, the resonant angular frequency at the resonant operating point can be given by the following equation (6) from the above equation (1) (however, β in the above equation (2) is set to 1). TIFF0007767848000001.tif16150...(6)

[0017] When the resonant frequency (angular frequency) has a gradient with respect to the magnetic flux Φ, the resonant frequency fluctuates due to, for example, environmental magnetic field noise. Therefore, when high coherence is required, it is desirable to have an operating point where the gradient of the resonant frequency with respect to the magnetic flux is small. However, there is a trade-off between sensitivity to magnetic flux and the ability to adjust parameters, and it is known that achieving both is difficult.

[0018] If an LC resonator is constructed using a single Josephson junction, as shown in Figure 1A, instead of a SQUID in which two Josephson junctions are inserted in a superconductor loop, the sensitivity to magnetic flux Φ becomes extremely small, but adjusting the parameters of the resonator becomes almost impossible (extremely difficult).In Figure 1A, due to the nonlinearity of the Josephson junction, the resonant mode of the superconducting LC resonant circuit has nonlinearity, and the energy level spacing becomes non-equidistant, so it operates as a quantum bit, which is a quantum two-level system with two states.

[0019] As a method for giving a resonator using a SQUID an operating point with low sensitivity to magnetic flux Φ, it is generally performed to use an asymmetric SQUID as shown in Fig. 1B (see, for example, Patent Documents 1, 2, etc.). Fig. 1B illustrates a lumped-constant resonator using an asymmetric SQUID. Referring to Fig. 1B, the SQUID 10 has a loop structure in which a first superconducting line 103, a first Josephson junction 101, a second superconducting line 104, and a second Josephson junction 102 are connected in a ring. In the first and second Josephson junctions 101 and 102 where insulators with a thickness on the order of nm (nano-meter) not shown are sandwiched between the first superconducting line 103 and the second superconducting line 104, a superconducting current flows due to the tunnel effect of electron pairs (Cooper pairs) in the superconducting state. 12 is an input / output capacitor, 13 is an input / output line, and the signal (input / output signal) of the input / output line 13 is AC-coupled to the SQUID 10. A DC current is supplied from a signal source (current source) not shown to the flux line 14, which functions as a magnetic field generation part and gives the magnetic flux Φ linked to the SQUID 10. That is, the magnetic flux generated in the flux line 14 penetrates the loop surface of the SQUID 10 from the front to the back of the paper surface or vice versa.

[0020] In the SQUID 10, the critical current value I0(1 + x) of the first Josephson junction 101 is different from the critical current value I0(1 - x) of the second Josephson junction 102 (however, 0 < x < 1). Note that the critical current value of the Josephson junction is proportional to the junction area of the Josephson junction. Therefore, by adjusting the ratio of the junction area of the first Josephson junction 101 to the junction area of the second Josephson junction 102, the ratio of the critical current value of the first Josephson junction 101 to the critical current value of the second Josephson junction 102 can be adjusted.

[0021] The inductance of SQUID 10 forms a parallel resonance circuit with capacitor 11. The first node 105 on the first superconducting line 103 of SQUID 10 and the second node 106 on the second superconducting line 104 are connected to the opposing electrodes of capacitor 11 and are shunted by capacitor 11. As shown in FIG. 1B, one end of SQUID 10 may be configured to be connected to ground.

[0022] In the resonator using the asymmetric SQUID illustrated in FIG. 1B, the resonance frequency f is maximum when the value obtained by dividing the magnetic flux Φ linked to the SQUID by the magnetic flux quantum Φ0 is 0, minimum when it is 1 / 2, and the gradient with respect to the magnetic flux Φ becomes 0.

[0023] In SQUID 10, when the critical currents in the first and second Josephson junctions 101 and 102 are I0(1 + x) and I0(1 - x), the maximum value of the current that can flow through SQUID 10 can be regarded as the following equation (7).

[0024] TIFF0007767848000002.tif14150···(7)

[0025] In equation (7), since 0 < x < 1, the maximum value of the current flowing through SQUID 10 is 2I when the magnetic flux Φ is an integer multiple of the magnetic flux quantum Φ0. o It becomes 2I0x at half-integer multiples, which is the minimum value. The minimum value 2I0x is x times the maximum value and is equal to the difference I0(1 + x) - I0(1 - x) in the critical currents of the first and second Josephson junctions 10l and 102. From equation (7), when x = 0, the maximum value of the current flowing through SQUID 10 becomes 0.

[0026] FIG. 1C is a diagram showing the relationship between the resonance frequency f of the resonator using the asymmetric SQUID 10 of FIG. 1B and the magnetic flux Φ passing through the loop of SQUID 10. The horizontal axis (X) is the value obtained by dividing the magnetic flux Φ passing through the loop of SQUID 10 by the magnetic flux quantum Φ0 (range from 0 to 1), and the vertical axis (Y) is the resonance frequency f (unit: GHz (gigahertz)).

[0027] As shown in equation (2) above, the inductance L of SQUID 10 is inversely proportional to the critical current value. Therefore, from equation (7) above, the resonant frequency of the resonator is maximum / minimum when the magnetic flux phase (the value obtained by dividing the magnetic flux Φ passing through the loop of SQUID 10 by the magnetic flux quantum Φ0) is 0 (an integer) or 1 / 2 (a half integer), as shown in Figure 1C, and the gradient with respect to the magnetic flux is 0. Note that the resonant frequency f in Figure 1C is given by the following equations from equations (6) and (7) above.

[0028] TIFF0007767848000003.tif34150...(8)

[0029] where: TIFF0007767848000004.tif10150 ···(9) Then, the first derivative of g(θ) with respect to θ is TIFF0007767848000005.tif6150...(10)

[0030] The second derivative is TIFF0007767848000006.tif6150 ···(11)

[0031] 0 <x<1より、x 2 -1<0, and in the range 0≦θ≦π, it is maximum (maximum) at θ=0, π (horizontal axis X=0, 1 in Fig. 1C) and minimum (minimum) at θ=π / 2 (horizontal axis X=1 / 2 in Fig. 1C), and the slope (gradient) with respect to the magnetic flux phase θ is 0. Note that the minimum value is √x times the maximum value. Since the inflection point is g''(θ)=0, between 0≦θπ≦π, it is πΦ / Φ0=π / 4, 3π / 4 (X=1 / 4, 3 / 4 in Fig. 1C).

[0032] When an asymmetric SQUID is used, the resonant operating point, which is only one point (flux phase 0, maximum resonant frequency) in a symmetric SQUID resonator, can be increased to two points (flux phase 0 / 0.5, maximum / minimum resonant frequency).

[0033] The resonators according to the following embodiments are realized, for example, by lines (wiring) formed on a substrate using a superconductor. Silicon is used for the substrate, but other electronic materials such as sapphire or compound semiconductor materials (Group IV, Group III-V, Group II-VI) may also be used. Furthermore, the substrate is preferably single-crystal, but may also be polycrystalline or amorphous. The material for the lines may be, for example, niobium (Nb) or aluminum (Al), but is not limited thereto. 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, or an alloy containing at least one of these. Furthermore, to achieve the superconducting state, the resonator circuit is used in a temperature environment of approximately 10 mK (millikelvin), which is achieved by a refrigerator.

[0034] 2A is a diagram illustrating a first embodiment. For simplicity, two SQUIDs 10A and 10B are shown as multiple SQUIDs arranged in parallel in FIG. 2A, but the number of SQUIDs is not limited to two. The two parallel-connected SQUIDs 10A and 10B are configured as an asymmetric SQUID 10. In SQUID 10A, the critical current value of the first Josephson junction 101A is different from the critical current value of the second Josephson junction 102A, and in SQUID 10B, the critical current value of the first Josephson junction 101B is different from the critical current value of the second Josephson junction 102B. Furthermore, in the two SQUIDs 10A and 10B, either or both of the sum (or half thereof) of the critical current value of the first Josephson junction and the critical current value of the second Josephson junction and the ratio of the critical current value of the first Josephson junction to the critical current value of the second Josephson junction are configured to be different between the SQUIDs 10A and 10B.

[0035] In FIG. 2A, the critical current value I0(1 + x) of the first Josephson junction 101A of the SQUID 10A is different from the critical current value I0(1 - x) of the second Josephson junction 102A (0 < x < 1). Here, I0 is 1 / 2 (average value) of the sum I0(1 + x) + I0(1 - x) = 2I0 of the critical current values of the first and second Josephson junctions 101A and 102A of the SQUID 10A. As described above, the critical current value I0(1 + x) of the first Josephson junction 101A of the SQUID 10A corresponds (is proportional) to the junction area of the first Josephson junction 101A, and the critical current value I0(1 - x) of the second Josephson junction 102A corresponds (is proportional) to the junction area of the second Josephson junction 102A. Here, assume that the first Josephson junction 101A and the second Josephson junction 102A are made of insulators of the same material. 1 / 2 of the sum of the critical current value of the first Josephson junction 101A and the critical current value of the second Josephson junction 102A can be made to correspond to 1 / 2 of the sum of the junction area of the first Josephson junction 101A and the junction area of the second Josephson junction 102A, assuming linearity holds. 12 and 13 are input / output (IO) capacitors and input / output (IO) lines. A direct current is supplied to the flux line 14A from a power source (current source) not shown, which functions as a magnetic field generation part and generates a magnetic flux ΦA that intersects the loop surface of the SQUID 10A.

[0036] The critical current value I0'(1 + x') of the first Josephson junction 101B of SQUID10B is different from the critical current value I0'(1 - x') of the second Josephson junction 102B (0 < x' < 1). Here, I0' is 1 / 2 (average value) of the sum I0'(1 + x') + I0'(1 - x') = 2I0' of the critical current values of the first and second Josephson junctions 101B and 102B of SQUID10B. The critical current value I0'(1 + x') of the first Josephson junction 101B of SQUID10B corresponds (is proportional) to the junction area of the first Josephson junction 101B, and the critical current value I0'(1 - x') of the second Josephson junction 102B corresponds (is proportional) to the junction area of the second Josephson junction 102B. Here, assume that the first Josephson junction 101B and the second Josephson junction 102B are made of insulators of the same material. Assuming linearity holds, 1 / 2 of the sum of the critical current value of the first Josephson junction 101B and the critical current value of the second Josephson junction 102B can be made to correspond to 1 / 2 of the sum of the junction area of the first Josephson junction 101B and the junction area of the second Josephson junction 102B. A direct current is supplied from a power source (current source), not shown, to the flux line 14B, which functions as a magnetic field generation part and generates a magnetic flux ΦB that intersects the loop surface of SQUID10B.

[0037] One end of the first node 105A of SQUID10A, the first node 105B of SQUID10B, and the capacitor 11 (Cavity Capacitor: the capacitance of the resonator 20) is commonly connected to the node 107 (common connection point) and is connected to the input / output (IO) line 13 via the input / output (IO) capacitor 12. The other end of the second node 106A of SQUID10A, the second node 106B of SQUID10B, and the capacitor 11 (Cavity Capacitor: the capacitance of the resonator 20) is commonly connected to the node 108 and is connected to the ground.

[0038] The inductances of SQUIDs 10A and 10B form a parallel resonator together with capacitor 11. A first node 105A on first superconducting line 103A of SQUID 10A and a second node 106A on second superconducting line 104A of SQUID 10A are connected to the counter electrode of capacitor 11 and are shunted by capacitor 11. A first node 105B on first superconducting line 103B of SQUID 10B and a second node 106B on second superconducting line 104B of SQUID 10B are connected to the counter electrode of capacitor 11 and are shunted by capacitor 11. As shown in FIG. 2A, one end of SQUIDs 10A and 10B may be connected to ground.

[0039] The resonator 20 is an LC resonator in which the SQUIDs 10A and 10B and the capacitor 11 of the resonator 20 are connected in parallel.

[0040] In this case, the effective inductance of the resonator 20 is inversely proportional to the sum of the effective critical current values ​​of the SQUIDs 10A and 10B. A , L B Then, the parallel inductance L is L=L A ×L B / (L A +L B ) ···(12)

[0041] From the above equation (1) where β in the above equation (2) is set to 1, the current flowing through SQUID 10A and 10B is I A , I B Then, L A =Φ0 / (2I A ) ···(13) L B =Φ0 / (2I B ) ···(14)

[0042] Substituting equations (13) and (14) into equation (12), the following equation (15) is obtained. L=Φ0 / (2I A )*Φ0 / (2I B ) / {Φ0 / (2IA )+Φ0 / (2I B )} =Φ0 / {2(I A +I B )} (15)

[0043] In each of SQUIDs 10A and 10B, the gradient of the critical current with respect to the magnetic flux Φ becomes 0 when the ratio Φ / Φ0 of the magnetic flux Φ to the magnetic flux quantum Φ0 is an integer (n) or a half-integer (1 / 2+n), and therefore, when the magnetic flux phase is an integer or a half-integer, the sensitivity to the magnetic flux Φ is suppressed.

[0044] By setting the maximum and minimum critical current values ​​of N SQUIDs connected in parallel to different values, a maximum of 2 N It is possible to realize resonant operating points with mutually different resonant frequencies.

[0045] Critical current value I of two Josephson junctions 101A and 102A of SQUID 10A A1 , I A2 are different values ​​as follows: I A1 =I0(1+x) (16) I A2 =I0(1-x) (17)

[0046] Here, I0 is half the sum (average critical current value) of the critical current value of Josephson junction 101A and the critical current value of Josephson junction 102A of SQUID 10A. x is a parameter that represents the asymmetry of SQUID 10A (0 <x<1)。

[0047] The critical current I of two Josephson junctions 101B and 102B of SQUID 10B B1 ',I B2 ' are different values ​​as follows: I B1 '=I0'(1+x') (18) I B2 '=I0'(1-x') (19)

[0048] Here, I0' is half the sum (average critical current value) of the critical current value flowing through Josephson junction 101B of SQUID 10B and the critical current value of Josephson junction 102B. x' is a parameter that represents the asymmetry of SQUID 10B. (0 <x’<1)。

[0049] SQUID10A critical current value I A1 and I A2 If the ratio is r, r = (1 - x) / (1 + x) (20)

[0050] Therefore, x=(1-r) / (1+r) (21) where x is the critical current value I of SQUID10A. A1 and I A2 Similarly, the critical current value I of SQUID10B corresponds to the ratio r of B1 ' and I B2 If the ratio of ' is r', then r'=(1-x') / (1+x') (22)

[0051] Therefore, x'=(1-r') / (1+r') (23) and x' is the critical current value I of SQUID10B. B1 ' and I B2 It corresponds one-to-one to the ratio r' of '.

[0052] In SQUID 10A, the currents in the first and second Josephson junctions 101A and 102A are I0(1+x) and I0(1-x), respectively. From equation (7) above, the critical current value of SQUID 10A (the maximum value of the current that can be passed through the SQUID) can be expressed as equation (24).

[0053] TIFF0007767848000007.tif14150...(24) However, Φ A is the magnetic flux linking the loop of SQUID10A.

[0054] In SQUID 10B, the currents in the first and second Josephson junctions 101B and 102B are I0'(1+x') and I0'(1-x'), respectively, and the critical current value of SQUID 10B (the maximum value of the current that can be passed through the SQUID) can be regarded as equation (25).

[0055] TIFF0007767848000008.tif14150...(25) However, Φ B is the magnetic flux linking the loop of SQUID10B.

[0056] From the above equation (24), the critical current value I of SQUID10A is A teeth, Magnetic flux Φ A When is an integer multiple of the magnetic flux quantum Φ0, the maximum value is 2Io. Magnetic flux Φ A When is a half-integer multiple of the magnetic flux quantum Φ0, the minimum value is 2I0x.

[0057] From the above equation (25), the critical current I of SQUID10B is B teeth, Magnetic flux Φ B When is an integer multiple of the magnetic flux quantum Φ0, the maximum value is 2Io'. Magnetic flux Φ B When is a half-integer multiple of the magnetic flux quantum Φ0, the minimum value is 2I0'x'.

[0058] The sum of the critical current values ​​of SQUID10A and 10B, I A +I B is the magnetic flux linkage Φ of SQUID10A and 10B A , Φ B Regarding a) 2I0+2I0' (ΦA / Φ0=n, ΦB / Φ0=n') (26) b) 2xI0+2I0' (ΦA / Φ0=1 / 2+n, ΦB / Φ0=n') ···(27) c) 2I0+2x'I0' (ΦA / Φ0=n, ΦB / Φ0=n'+1 / 2 ) ···(28) d) 2xI0+2x'I0' (ΦA / Φ0=1 / 2+n,ΦB / Φ0=1 / 2+n') ···(29) There are four combinations of Φ, which correspond to the resonant operating points. A / Φ0, Φ B There are four resonant operating points in the range of / Φ0 from 0 to 1 / 2.

[0059] The resonant frequency f of the resonator 20 is given by the following equation (30). TIFF0007767848000009.tif12150...(30)

[0060] Therefore, the resonant frequency f at the four resonant operating points in the above equations (26) to (29) is a , f b , f c , f d is given by equations (31) to (34).

[0061] TIFF0007767848000010.tif12150...(31)

[0062] TIFF0007767848000011.tif12150...(32)

[0063] TIFF0007767848000012.tif12150...(33)

[0064] TIFF0007767848000013.tif26153...(34)

[0065] (A) When the average critical current values ​​of SQUIDs 10A and 10B are equal but the asymmetries are different, i.e., I0 = I0', x ≠ x', f a >f b ,f c >f d ···(35) f b and f c The magnitude relationship between x and x' changes depending on which is larger. When x>x', f a >f b >fc >f d ···(36) x <x'のとき、 f a >f c >f b >f d ···(37) Thus, there are four different resonant operating points.

[0066] (B) When the asymmetry of SQUIDs 10A and 10B is equal but the average critical current values ​​are different, i.e., I0≠I0', x=x', f a >f b ,f c >f d ···(38) f b and f c The magnitude relationship between I0 and I0' changes depending on which is larger. I0 <I0'のとき、 f a >f b >f c >f d ···(39) When I0>I0', f a >f c >f b >f d ···(40)

[0067] (C) When the average critical current values ​​and asymmetries of SQUIDs 10A and 10B are different from each other, i.e., when I0≠I0', x≠x', f a >f b ,f c >f d ···(41) f b and f c The magnitude relationship between I0 and I0' and between x and x' changes depending on the magnitude. When I0' / I0>(1-x) / (1-x'), f a >f b >f c >f d···(42) When I0' / I0<(1-x) / (1-x'), f a >f c >f b >f d ···(43) Thus, there are four different resonant operating points.

[0068] However, if I0' / I0=(1-x) / (1-x'), f a >f b =f c >f d ···(44) In this case, the resonant operating points are degenerated to three. Therefore, in the case of (C), when the average critical current values ​​and asymmetry of SQUIDs 10A and 10B are different from each other, the average critical current values ​​and asymmetry of SQUIDs 10A and 10B may be set so as to result in four different resonant operating points.

[0069] (D) When the average critical current values ​​of SQUIDs 10A and 10B are equal and the asymmetries are equal, i.e., I0=I0', x=x', f a >f b =f c >f d ···(45) This results in three resonant operating points.

[0070] In each of the two asymmetric SQUIDs 10A and 10B connected in parallel, if at least one of the current values ​​I0 and I0', which are half the sum (2I0, 2I0') of the critical current values ​​of the two Josephson junctions of each SQUID, and the parameters x and x' (corresponding to the ratio of the critical current values ​​of the two Josephson junctions) representing the asymmetry, is different from each other, then 2 2Similarly, in the case of N asymmetric SQUIDs connected in parallel, in order to avoid the degeneracy as in (C) above, by changing Io, which is half the sum of the critical current values ​​of the two Josephson junctions of each SQUID (2I0, 2I0'), and the value of the parameter x, different 2 N resonant operating points can be realized.

[0071] In the present embodiment described above, in order to adjust the resonant operating point (an operating point with no magnetic field gradient and resistant to magnetic field noise) of resonator 20 including SQUIDs 10A and 10B, a direct current is applied from flux lines 14A and 14B to apply a static magnetic field to SQUIDs 10A and 10B. In Fig. 2A, if a signal of frequency ω0 is input from input / output line 13 and the resonant frequency when a static magnetic field is applied to SQUIDs 10A and 10B is ω0, then pump light (microwave current + direct current) of sufficiently high intensity and with a frequency ωp nearly twice the resonant frequency ω0 may be applied from flux lines 14A and 14B to cause parametric oscillation under conditions with a magnetic field gradient other than the operating point that is resistant to magnetic field noise.

[0072] 2B is a contour diagram showing the calculation results of the resonance frequency of the resonator 20 of FIG. 2A. The X-axis is Φ A / Φ0, and the Y axis is Φ B / Φ0 (Φ A , Φ B is the magnetic flux passing through the loops of SQUIDs 10A and 10B in Figure 2A. In Figure 2B, the gray scale becomes darker as the resonant frequency increases. It has a valley (slope = 0) at (X, Y) = (0.5, 0.5), peaks (slope = 0) at (X, Y) = (0, 0), (0, 1), (1, 0), and (1, 1), and is at a mid-level at (X, Y) = (0.5, 0), (0.5, 1), (0, 0.5), and (1, 0.5).

[0073] Generally, when a circuit pattern creates a large loop, a magnetic field is generated from the loop, interfering with other circuits. Furthermore, when the loop area becomes large, it is affected by external magnetic fields and unwanted signals are induced within the loop. Therefore, in order to reduce the contribution of the closed-loop current caused by the loop between adjacent SQUIDs 10A and 10B, it is desirable to increase the distance between SQUIDs 10A and 10B. For example, when SQUIDs 10A and 10B are processed to micrometer size, the distance between SQUIDs 10A and 10B is set to, for example, the order of millimeters.

[0074] FIG. 3 is a diagram illustrating a lumped-element resonator 20. FIG. 3 schematically illustrates a portion of the wiring pattern (planar circuit) of the resonator 20, which has SQUIDs 10A and 10B and a single electrode 15, formed on the circuit surface (main surface) of a silicon substrate, for example. The gray areas, including the electrodes 15 and ground pattern 16, represent the areas where a superconductor thin film is deposited on the silicon substrate, and the white areas 18 represent the exposed areas of the silicon substrate (gap in the coplanar waveguide). That is, the resonator 20 is formed as a coplanar planar circuit in which the signal line and the ground pattern 16 surrounding the signal line (signal electrode) are both located on the same plane on the silicon substrate. In FIG. 3, the capacitor 11 of FIG. 2A is formed, for example, in the gap between the electrode 15 and the opposing ground pattern 16. 3, one end of each of the two SQUIDs 10A and 10B is connected to one end of an electrode 15, and the other ends of each of the two SQUIDs 10A and 10B are connected to a ground pattern 16. The electrode 15 has a shape in which a first pattern, the two ends of which in the longitudinal direction are connected to one end of each of the SQUIDs 10A and 10B, intersects with a first pattern, the one end of which in the longitudinal direction is capacitively coupled to the input / output line 13. However, it goes without saying that the planar shape of the electrode 15 is not limited to the example in FIG.

[0075] The electrodes 15 and ground pattern 16 may be made of, for example, superconducting materials such as Nb or Al. The SQUIDs 10A and 10B may also be formed on a silicon substrate using, for example, a wiring pattern of an Nb-Al based superconducting conductor. The Josephson junctions may be formed using a known method (for example, a thin Al film may be formed on the Nb wiring, and the Al surface may be thermally oxidized to form an AlOx film of a predetermined thickness, and then an Nb film may be formed on top).

[0076] A DC signal is supplied to each of the flux lines 14A and 14B from a power supply (current source) (not shown). Ground patterns 16 are disposed on both longitudinal sides of the flux lines 14A and 14B, facing each other with a gap therebetween. The longitudinal ends of the flux lines 14A and 14B abut on one longitudinal side against linear ground patterns (ground lines) 16A and 16B, respectively. The ground lines 16A and 16B face the SQUIDs 10A and 10B, respectively, on the other longitudinal side. Notches 17A and 17B are provided in the ground pattern 16 (the ground pattern arranged opposite to one side of the flux lines 14A and 14B in the longitudinal direction, with a gap therebetween), and extend along the ground lines 16A-1 and 16B-1, which abut the longitudinal ends of the flux lines 14A and 14B, respectively, and extend in a direction perpendicular to the longitudinal direction of the flux lines 14A and 14B.

[0077] The current from the flux line 14A (14B) branches into two at its end, into ground lines 16A-1 and 16A-2 (ground lines 16B-1 and 16B-2). At this time, the current flowing in the ground line 16A-2 (16B-2) side and the current flowing in the opposite direction, into ground line 16A-1 (16B-1) side, do not cancel each other out in the magnetic fields applied to the loop of SQUID 10A (SQUID 10B). That is, the line length of ground line 16A-1 extending along cutout portion 17A is set longer than ground line 16A-2 by approximately the length of cutout portion 17A, and the magnetic field created by the current flowing on the ground line 16A-1 side (first magnetic field penetrating the loop of SQUID 10A) is stronger than the magnetic field created by the current flowing on the ground line 16A-2 side (second magnetic field penetrating the loop of SQUID 10A in the opposite direction to the first magnetic field). Therefore, the configuration of flux line 14A and ground lines 16A-1 and 16A-2 illustrated in FIG. 3 enables efficient generation of the magnetic field applied to the loop of SQUID 10A. Similarly, for flux line 14B, the magnetic field generated by the current flowing on the ground line 16B-1 side (first magnetic field penetrating the loop of SQUID 10B) is larger than the magnetic field generated by the current flowing on the ground line 16B-2 side (second magnetic field penetrating the loop of SQUID 10B in the opposite direction to the first magnetic field), enabling efficient generation of the magnetic field applied to the loop of SQUID 10B. The line widths of ground lines 16A-1 and 16A-2 (16B-1 and 16B-2) do not have to be the same; they may be different from each other, for example, by making ground line 16A-1 (16B-1) larger than ground line 16A-2 (16B-2). Note that the flux lines 14A and 14B illustrated in FIG. 3 are merely examples, and it goes without saying that any configuration other than that shown in FIG. 3 may be used as long as it satisfies the conditions for efficiently generating the magnetic field applied to the SQUID loop.

[0078] In FIG. 3, the resonator 20 is illustrated as having two SQUIDs 10A and 10B connected in parallel, but it goes without saying that the number of SQUIDs is not limited to two.

[0079] In the example of FIG. 4, four SQUIDs 10A, 10B, 10C, and 10D are connected between the electrode 15 and the ground pattern 16 of FIG. 3. Flux lines 14A, 14B, 14C, and 14D are provided to the four SQUIDs 10A, 10B, 10C, and 10D, respectively, and a magnetic flux Φ is applied to the loop of each SQUID. A DC current signal is supplied to each of the flux lines 14A, 14B, 14C, and 14D from a power supply (current source) not shown. For the four SQUIDs connected in parallel, the average critical current value of the two Josephson junctions and the asymmetry (the ratio of the critical current values ​​of the two Josephson junctions of the SQUID) can be set to different values, thereby achieving a 2-phase synchronous rectification. 4 = 16 resonant operating points with different resonant frequencies can be realized.

[0080] 2A, 3, and 4 illustrate lumped-constant resonators, the resonators of the embodiments are not limited to lumped-constant resonators, and it goes without saying that distributed-constant resonators such as λ / 4 resonators may also be used, as illustrated in FIG. 5. In the example of FIG. 5, a waveguide (λ / 4 waveguide) 19 having a length close to a quarter of the resonant wavelength (wavelength of the standing wave) λ is provided between input / output capacitor 12 and node 107, which is the common connection point of first nodes 105A and 105B of SQUIDs 10A and 10B, and the ends of λ / 4 waveguide 19 are connected to ground at SQUIDs 10A and 10B. Note that capacitor 11 connected in parallel to SQUIDs 10A and 10B of lumped-constant resonator 20 of FIG. 2A is not shown in FIG. 5, for example, the capacitance between the SQUIDs 10A, 10B and the ground pattern, the capacitance between the λ / 4 waveguide 19 and the ground pattern, etc. are included in the distributed constant capacitance. Furthermore, because Josephson junctions 101A, 102A, 101B, and 102B of SQUIDs 10A and 10B each have a small capacitance component, the capacitance components of these Josephson junctions may be included as the distributed constant capacitance.

[0081] 6A and 6B are diagrams illustrating a second embodiment of the present invention. Referring to FIG. 6B, a resonator 20 is shown, which is composed of two electrodes 15A and 15B bridged by two SQUIDs 10A and 10B. As shown in FIGS. 6A and 6B, first nodes 105A and 105B of the two SQUIDs 10A and 10B are connected to a first electrode 15A (a common connection node 107 of the first nodes 105A and 105B is the first electrode 15A). The first electrode 15A is connected to a first input / output line 13A via a first input / output capacitor 12A. Second nodes 106A and 106B of the two SQUIDs 10A and 10B are connected to a second electrode 15B (a common connection node 108 of the second nodes 106A and 106B is the second electrode 15B). The second nodes 106A and 106B are connected to a second input / output line 13B via a second input / output capacitor 12B.

[0082] 6B, flux lines 14A and 14B generate magnetic flux that penetrates the loops of SQUIDs 10A and 10B when a current is supplied to each of them. Flux line 14A (14B), ground lines 16A-1 and 16A-2 (16B-1 and 16B-2), and notched portion 17A (17B) have the same pattern and function as those in FIG. 3 described above. Because the example shown in FIG. 6B is a planar circuit, it is not possible to individually manipulate the magnetic flux that penetrates the loops of three or more SQUIDs using flux lines, as shown in FIG. 4.

[0083] In the second embodiment, the resonator 20 may be a distributed constant resonator such as a λ / 2 resonator, as shown in Fig. 7. The first nodes 105A and 105B of the two SQUIDs 10A and 10B are connected to one end of a waveguide (λ / 4 waveguide) 19A having a length close to a quarter of the resonant wavelength (wavelength of the standing wave) λ, and the other end of the waveguide 19A is connected to a first input / output line 13A via a first input / output capacitor 12A. The second nodes 106A and 106B of the two SQUIDs 10A and 10B are connected to one end of a waveguide (λ / 4 waveguide) 19B having a length close to a quarter of the resonant wavelength (wavelength of the standing wave) λ, and the other end of the waveguide 19B is connected to a second input / output line 13B via a second input / output capacitor 12B. 7, like Fig. 5, does not show the capacitor 11 connected in parallel to the SQUIDs 10A and 10B of the lumped constant resonator 20 of Fig. 2. In the distributed constant resonator 20 of Fig. 7, for example, the capacitance (capacitance) component between the SQUIDs 10A and 10B and the ground pattern and the capacitance component between the λ / 4 waveguides 19A and 19B and the ground pattern are included in the distributed constant capacitance. In addition, because the Josephson junctions 101A, 102A, 101B, and 102B of the SQUIDs 10A and 10B each have a small capacitance component, the capacitance components of these Josephson junctions may be included as the distributed constant capacitance.

[0084] 6A illustrates a configuration in which the connection point between the first nodes 105A and 105B of the two SQUIDs 10A and 10B and the connection point between the second nodes 106A and 106B are connected to the first and second input / output lines 13A and 13B via the first and second input / output capacitors 12A and 12B, respectively. However, the second embodiment is not limited to this configuration. For example, as a modification of the second embodiment, the connection point between the first nodes 105A and 105B of the two SQUIDs 10A and 10B and the connection point between the second nodes 106A and 106B may be connected to another quantum bit (not shown) or ground. As an example, when one is connected to ground and the other is connected to an input / output line, the SQUIDs operate as a single quantum bit. Furthermore, as illustrated in FIG. 8, when node 107, which is the common connection point of first nodes 105A and 105B of two SQUIDs 10A and 10B, and node 108, which is the common connection point of second nodes 106A and 106B, are connected to first and second quantum bits 22A and 22B, respectively, resonator 20 operates as a quantum bit coupler.

[0085] As described above, the resonator 20 of the embodiment may be used as a quantum bit or as a coupler between quantum bits. An example in which the resonator of the embodiment is used as a quantum bit circuit for a quantum computer will be described below. The quantum computer is a quantum annealing-type computer that calculates solutions to combinatorial optimization problems that can be mapped to an Ising model. In the quantum computer shown in FIG. 9, four resonators 20A to 20D are connected by one coupling circuit 21. The coupling circuit 21 couples the four resonators 20A to 20D and is composed of one Josephson junction 213 and four capacitors 211A to 211D. The input / output lines 13 of the resonators 20A and 20B are connected to one end of a superconducting conductor 212-1 via capacitors 211A and 211B of the coupling circuit 21, and the other end of the superconducting conductor 212-1 is connected to one end of the Josephson junction 213. The input / output lines 13 of the resonators 20C and 20D are connected to one end of the superconducting conductor 212-2 via the capacitors 211C and 211D of the coupling circuit 21, and the other end of the superconducting conductor 212-2 is connected to the other end of the Josephson junction 213. Although Fig. 9 illustrates a quantum computer having four resonators 20, a quantum computer integrating any number of resonators 20 may be realized by arranging and connecting a plurality of unit structures, each having the configuration shown in Fig. 9 as a unit structure.

[0086] The disclosures of Patent Documents 1 and 2 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 ideas thereof. Furthermore, various combinations and selections of the various disclosed elements (including each element of each claim, 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 ideas thereof.

[0087] <Addendum> The derivation of the above formula (7) will be explained below. The currents I1 and I2 flowing through the two Josephson junctions of the asymmetric SQUID are I1 = I0(1 + x) ···(A.1) I2 = I0(1 - x) ···(A.2) I1 + I2 = 2I0 ···(A.3)

[0088] The current I flowing through this asymmetric SQUID is given as follows. I = I0(1 + x)*sin(γ A ) + I0(1 - x)*sin(γ B ) ···(A.4)

[0089] [[ID=1"7]] Equation (A.4) is γ B -γ A = 2πΦ / Φ0 ···(A.5) and is given as follows using this.

[0090] I = I0(1 + x)*sin(γ A ) + I0(1 - x)*sin(γ A ―2πΦ / Φ0)} = I0{sin(γ A ) + sin(γ A ―2πΦ / Φ0)} + xI0{sin(γ A ) - sin(γA ― 2πΦ / Φ0)} = 2I0[cos(πΦ / Φ0) sin {γ A ―πΦ / Φ0)}] + 2xI0[sin(πΦ / Φ0) cos{γ A ―πΦ / Φ0)}] = 2I0[cos(πΦ / Φ0) {sin(γ A ) cos(πΦ / Φ0) - sin(πΦ / Φ0)cos(γ A )}] +2xI0[sin(πΦ / Φ0){cos(γ A )cos(πΦ / Φ0) + sin(γ A )sin(πΦ / Φ0)}] = 2I0{cos 2 (πΦ / Φ0) + xsin 2 (πΦ / Φ0)}sin(γ A ) +2I0{-sin(πΦ / Φ0)cos(πΦ / Φ0) + x cos(πΦ / Φ0)sin(πΦ / Φ0)}cos(γ A ) =2I0{cos 2 (πΦ / Φ0) +xsin 2 (πΦ / Φ0)}sin(γ A ) - 2I0(1-x) sin(πΦ / Φ0)cos(πΦ / Φ0) cos(γ A ) ···(A.6)

[0091] Here, α = {cos 2 (πΦ / Φ0) +xsin 2 (πΦ / Φ0)} ···(A.7) β = (1-x) sin(πΦ / Φ0)cos(πΦ / Φ0) ···(A.8) If we set them as such, equation (A.6) becomes I = 2I0[αsin(γ A ) + β cos(γ A )] = 2I0√(α 2 + β 2 )sin(γ A + C) ···(A.9) However, cos (C) = α / √(α 2 + β 2 ), sin (C) = β / √(α 2 + β 2 ) ···(A.10)

[0092] When calculating the inside of the SQRT in equation (A.9), it is given by the following equation (A.11). √(α 2 + β 2 ) = ([cos 2 (πΦ / Φ0) +xsin 2 (πΦ / Φ0)] 2 + [(1-x) sin(πΦ / Φ0)cos(πΦ / Φ0)] 2 ) 1 / 2 = ([cos 4 (πΦ / Φ0)+ cos 2(πΦ / Φ0) sin 2 (πΦ / Φ0)] + x 2 [sin 4 (πΦ / Φ0)+ cos 2 (πΦ / Φ0) sin 2 (πΦ / Φ0)]) 1 / 2 =([cos 2 (πΦ / Φ0)(cos 2 (πΦ / Φ0)+ sin 2 (πΦ / Φ0)] + x 2 [sin 2 (πΦ / Φ0)(sin 2 (πΦ / Φ0)+ cos 2 (πΦ / Φ0) )]) 1 / 2 =√{cos 2 (πΦ / Φ0) + x 2 sin 2 (πΦ / Φ0)} (A.11)

[0093] Therefore, equation (A.9) becomes I=2I0{cos 2 (πΦ / Φ0) + x 2 sin 2 (πΦ / Φ0)} 1 / 2 sin(γA+C) =Asin(γA+C) (A.12) however, A=2I0{cos 2 (θ) + x 2 sin 2 (θ)} 1 / 2 (θ=πΦ / Φ0) (A.13)

[0094] |I|≦A (A.14) Therefore, the amplitude A in equation (A.13) can be regarded as the maximum value (critical current value) of the current flowing through the asymmetric SQUID. [Explanation of symbols]

[0095] 10, 10A, 10B, 10C, 10D SQUID 11 Capacitor 12 Input and output capacitors 12A First Input / Output Capacitor 12B Second Input / Output Capacitor 13 Input / Output Lines 13A First input / output line 13B Second input / output line 14, 14A, 14B, 14C, 14D Flux Line 15 Electrode (conductor) 15A First Electrode 15B Second electrode 16 Grand Pattern 16A, 16A-1, 16A-2, 16B, 16B-1, 16B-2, 16C, 16D Grand Line 17A, 17B, 17C, 17D Notch 18 Silicon substrate surface 19, 19A, 19B Quarter Waveguide 20, 20A, 20B, 20C, 20D resonator 21 Combined circuit 22A First qubit 22B Second qubit 101, 101A, 101B, 101C, 101D First Josephson junction 102, 102A, 102B, 102C, 102D Second Josephson junction 103, 103A, 103B First superconducting line 104, 104A, 104B Second superconducting line 105, 105A, 105B First node 106, 106A, 106B Second node 107, 108 nodes (common connection points) 211A, 211B, 211C, 211D capacitors 212-1 First superconductor 212-2 Second superconductor 213 Josephson junction

Claims

1. a plurality of SQUIDs (Superconducting Quantum Interference Devices) are connected in parallel, each having a loop structure in which a first superconducting line, a first Josephson junction, a second superconducting line, and a second Josephson junction are connected in a circular fashion, and the junction areas of the first Josephson junction and the second Josephson junction are different from each other; The plurality of SQUIDs include: the sum of the junction area of ​​the first Josephson junction and the junction area of ​​the second Josephson junction; a ratio of a junction area of ​​the first Josephson junction to a junction area of ​​the second Josephson junction; a superconducting quantum circuit, wherein one or both of the above are different among the plurality of SQUIDs.

2. 2. The superconducting quantum circuit according to claim 1, wherein the plurality of SQUIDs are bridged between one electrode and ground.

3. 2. The superconducting quantum circuit according to claim 1, wherein the plurality of SQUIDs are bridged between two electrodes.

4. 4. The superconducting quantum circuit according to claim 1, further comprising a current supply line for generating a magnetic flux interlinking with the loop of each of the SQUIDs, the current supply line corresponding to each of the SQUIDs being separate from the loop of the SQUID.

5. a substrate surface provided with the plurality of SQUIDs, the current supply lines disposed for each of the plurality of SQUIDs, and ground patterns disposed at least on both sides of the current supply lines in a longitudinal direction thereof so as to face the current supply lines; The ground pattern is a ground line consisting of first and second lines that abut against a longitudinal end of the current supply line at one longitudinal side and face the SQUID at the other longitudinal side, and that extend in opposite directions from the abutting point with the current supply line along a direction perpendicular to the current supply line; a notch portion extending along the one side in the longitudinal direction of one of the first and second lines of the ground line; 5. The superconducting quantum circuit of claim 4, comprising:

6. The plurality of SQUIDs include: the sum of the critical current value of the first Josephson junction and the critical current value of the second Josephson junction; a ratio of a critical current value of the first Josephson junction to a critical current value of the second Josephson junction; 6. The superconducting quantum circuit according to claim 1, wherein one or both of the above are different among the plurality of SQUIDs.

7. 7. The superconducting quantum circuit according to claim 1, comprising N (N is an integer of 2 or more) SQUIDs connected in parallel, and the number of operating points at which the gradient of the resonant frequency with respect to the magnetic flux is 0 is 2 to the power of N.

8. A quantum bit circuit comprising the superconducting quantum circuit according to any one of claims 1 to 7.

9. A quantum bit coupler, which is a circuit for coupling quantum bits, comprising the superconducting quantum circuit according to any one of claims 1 to 7.

10. A quantum computer configured by coupling a plurality of quantum bits and quantum bit couplers, A quantum computer, wherein at least one of the quantum bits and the quantum bit coupler comprises the superconducting quantum circuit according to any one of claims 1 to 7.

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