Superconducting quantum circuits

Abstract

Provided is a superconducting quantum circuit comprising a coupler which is configured to be able to enhance a four-body interaction by means of a circuit parameter. The superconducting quantum circuit comprises first to a fourth quantum bits, and a coupler that couples the first to fourth quantum bits by a four-body interaction. The coupler comprises a loop circuit which is connected between one end and the other end of the coupler, and a capacitor which is connected in parallel to the loop circuit. The loop circuit includes n (n being a positive integer of 2 or more) first Josephson junctions that are spaced apart from each other and are arranged in serial form, and second Josephson junctions that are arranged in parallel to the n first Josephson junctions and have a junction size smaller than the junction size of the first Josephson junctions. The first and second quantum bits are each capacitively coupled with the one end of the coupler, and the third and fourth quantum bits are each capacitively coupled with the other end of the coupler.

Description

[Technical Field]

[0001] This invention relates to superconducting quantum circuits. [Background technology]

[0002] One method for solving combinatorial optimization problems is quantum annealing, and one type of quantum annealing is called the LHZ (Lechner, Hauke, Zoller) method (see, for example, patent documents). (See reference 1). In order to physically implement the LHZ method of quantum annealing, the fundamental element is quantum It is necessary to realize bits and their networks, particularly networks in which four qubits interact simultaneously (four-body interaction). One proposed implementation method uses Josephson parametric oscillators (JPOs) as qubits (see, for example, Non-Patent Document 1).

[0003] (a) One such method, as shown in Figure 1, can achieve tetrabody interaction with a simple structure. Figure 1 is based on Figure 4a of Non-Patent Literature 1. Figure 1 shows a common Angular frequency ω r,i A system in which JPO1 to JPO4 (i=1,2,3,4) interact via a single Josephson junction (JJ) is illustrated (JPO1 to JPO4 with different resonant angular frequencies are shown in different patterns according to Figure 4 of Non-Patent Literature 1).

[0004] Each JPO's SQUID (Superconducting Quantum Interference Device) loop is: It is driven by a flux pump whose amplitude and frequency can be adjusted. The angular frequency of the pump signal is ω p,k (t)(k=1,2,3,4) is the angular frequency twice the angular frequency of the resonator: 2ω r,i It is said to be nearby. Joseph In a Josephson Parametric Amplifier (JPA), the pump There is a threshold for the strength of this, and if it exceeds this threshold, oscillation occurs, and even without an input signal, the resonant angular frequency ω r,i This will output a signal. This will result in a parametric oscillator. This specification deals with resonators that produce parametric oscillations, so here, JPA in Figure 4 of Non-Patent Document 1 is denoted as JPO.

[0005] The local tetra-body coupling is achieved by the nonlinear inductance of the central Josephson junction (JJ) (coupler).

[0006] As the angular frequency of the pump signals for JPO1 to JPO4, TIFF0007899883000001.tif6150(1.1) Select this option to detune the resonator.

[0007] Assuming they are detuned from each other, the central Josephson junction JJ (coupler) in the two-photon drive rotating coordinate system is, TIFF0007899883000002.tif6150(1.2) This causes a combination of the form shown.

[0008] This four-body interaction is always at work, and its strength G depends on the nonlinearity of the central Josephson junction JJ and the detuning of the resonator consisting of the JPO and the Josephson junction JJ. i (i = 1~4) are the annihilation operators for the resonant modes (bosons) of JPO1~4, a i + (i=1~4) is a generative operation. He is a child.

[0009] G in equation (1.2) is given by the following: TIFF0007899883000003.tif11150(1.3)

[0010] In Equation (1.3), Δ k (k = 1, 2, 3, 4) is the difference (detuning) between the k-th mode angular frequency ω r,k of the JPO and the mode angular frequency (resonance angular frequency) ω c defined by the capacitance and inductance of the central Josephson junction JJ (coupler). TIFF0007899883000004.tif6150(1.4)

[0011] φ0 is the magnetic flux quantum (reduced magnetic quantum flux): TIFF0007899883000005.tif9150(1.5) However, TIFF0007899883000006.tif6150 is the Dirac constant, TIFF0007899883000007.tif9150(1.6) (where h is Planck's constant and e is the elementary charge)

[0012] In Equation (1.3), φ c is the standard deviation of the zero-point magnetic flux fluctuation of the JJ mode.

[0013] E J is the Josephson energy of the central Josephson junction JJ and is proportional to the critical current I c of the Josephson junction. TIFF0007899883000008.tif9150(1.7)

[0014] g k (k = 1, 2, 3, 4) represents the magnitude of the coupling between the k-th JPO and the mode of the central Josephson junction JJ. TIFF0007899883000009.tif11150(1.8) ​

[0015] In equation (1.8), φ k (k=1,2,3,4) is the zero-point magnetic flux variation of the JPO mode. C is the capacitance value of the coupling capacitor between the coupler and the qubit.

[0016] Note that in Non-Patent Document 1, C is used as the four-body coupling strength in equations (1.2) and (1.3), but in order to distinguish it from coupling capacitor C, etc., here , is designated as G. Furthermore, Non-Patent Document 1 does not clearly explain the method for strengthening the tetrabody interaction with respect to the configuration shown in Figure 1.

[0017] (b) The other method uses a Josephson Ring Modulator (JRM), as shown in Figure 2. Figure 2 is a supplement to Non-Patent Literature 1. This figure is based on Figure 8. Note that Figure 2 refers to Supplementary Note 8 of Non-Patent Document 1. In Supplementary Figure 8, JPA is represented as JPO. Microwave drive signals with equal signal strength and opposite phase (capacitor C) x and C y The solid and dashed arrows indicate the activation of the tetra-phase bond between JPOs.

[0018] In the example shown in Figure 2, a tunable four-body interaction is achieved by using an unequilibrium shunt-type JRM. The JRM consists of two sets of two Josephson junctions (JJs) connected in series, which are connected in parallel between the first node, which is the connection point between JPO1 and JPO2, and the second node, which is the connection point between JPO3 and JPO4. Capacitors C are connected to the first and second nodes, respectively. x A microwave drive signal is applied via this, and at each connection point of the two parallel-connected Josephson junctions (JJ), a capacitor C is applied. y Capacitor C via xA microwave drive signal in the opposite phase to the microwave drive signal applied to the device is applied.

[0019] In this case, to realize the four-body interaction, the oscillation angular frequencies satisfied by JPO1~JPO4 and the angular frequencies ω of the drive signals input from capacitors Cx and Cy are required. d For example, combinations like TIFF0007899883000010.tif6150 (1.9) In this case, drive signal TIFF0007899883000011.tif6150(1.10) (where n is the number of photons in mode z) For this, the following Hamiltonian can be derived using the rotational wave approximation.

[0020] TIFF0007899883000012.tif13150(1.11)

[0021] however, TIFF0007899883000013.tif11150(1.12)

[0022] The second term on the right-hand side of equation (1.11) is the term for the tetrabody interaction. Equation (1.12) is the term for the tetrabody interaction. The coupling coefficient represents the strength of the connection, and √n is proportional to the strength of the microwave drive.

[0023] As an example of a related technology configuration similar to that shown in Figure 1, Patent Document 2 discloses a circuit using a lumped-parameter JPO, as shown in Figure 3.

[0024] Referring to Figure 3, the system comprises four JPO1(120A) to JPO4(120D) and a coupler 121. The coupler connection points 124A to 124D of JPO1(120A) to JPO4(120D) and the coupler 121, which consists of a Josephson junction (JJ), are capacitively coupled via capacitors (coupling capacitors) 131A to 131D. The readout circuit connection points 122A to 122D of JPO1(120A) to JPO4(120D) are capacitively coupled to the readout circuits 140A to 140D via capacitors 132A to 132D. JPO1(120A) to JPO4(120D) are connected via control lines 123A-123D to signal generation units 150A-150D, which generate pump signals to create magnetic flux through the SQUID loop of JPO1(120A) to JPO4(120D). The nonlinear element 110 of the coupler 121 is an element that can be considered as an LC resonator with a Josephson junction (JJ) as the nonlinear inductance, and the nonlinear element 110 may be a SQUID containing two Josephson junctions (JJ).

[0025] Furthermore, a coupler having a circuit similar to the loop circuit shown in Figure 5(B), which will be described later, is disclosed in Non-Patent Document 2. However, the disclosure in Non-Patent Document 2 is not a coupler for a four-body interaction of four qubits. The differences between the disclosure of this application and the disclosure in Non-Patent Document 2 will be described in detail in the embodiments. [Prior art documents] [Patent Documents]

[0026] [Patent Document 1] International Publication No. 2017 / 001404 [Patent Document 2] International Publication No. 2021 / 014885 [Non-patent literature]

[0027] [Non-Patent Document 1] Shruti Puri, et. al., "Quantum annealing with all-to-all connected nonlinear oscillators", Nature Communications 8, 15785 (2017) [Non-Patent Document 2] Yufeng Ye, et. al., "Engineering Purely Nonlinear Coupling between Superconducting Qubits Using a Quarton", PHYSICAL REVIEW LETTERS 127, 050502 (2021) [Non-Patent Document 3] Uri Vool, et. al., "Introduction to Quantum Electromagnetic Circuits", International Journal of Circuit Theory and Applications 45, 897 (2016) [Non-Patent Document 4] T Yamashita, et.al., "Superconducting π qubit with three Josephson junctions", Appl. Phys. Lett. 88, 132501 (2006) [Non-Patent Document 5] VV Ryazanov, et.al., "Coupling of Two Superconductors through a Ferromagnet: Evidence for a π Junction", Phys. Rev. Lett. 86, 2427 - Published 12 March 2001 [Overview of the project] [Problems that the invention aims to solve]

[0028] Non-patent documents 1 and 2, shown in Figures 1 to 3, do not mention any methods for strengthening the tetrabody interaction. Furthermore, while the strength of the tetrabody interaction can be adjusted in the configuration shown in Figure 2, it requires an external input (a microwave drive signal input to capacitors Cx and Cy in opposite phase).

[0029] This disclosure was conceived in view of the above-mentioned problems, and its purpose is to provide a superconducting quantum circuit equipped with a coupler configured to enhance the four-body interaction through circuit parameters. [Means for solving the problem]

[0030] According to one aspect of the present disclosure, a superconducting quantum circuit comprises first to fourth qubits and a coupler that couples the first to fourth qubits by a four-body interaction. The coupler comprises a loop circuit connected between one end and the other end of the coupler and a capacitor connected in parallel to the loop circuit, the loop circuit having n (n is a positive integer of 2 or more) first Josephson junctions arranged in series and spaced apart from each other, and a second Josephson junction arranged in parallel to the n first Josephson junctions, the junction size of which is smaller than the junction size of the first Josephson junctions. The first and second qubits are capacitively coupled to one end of the coupler, and the third and fourth qubits are capacitively coupled to the other end of the coupler, and the magnitude of the coupling coefficient of the four-body interaction by the coupler can be set based on circuit parameters including at least n and the ratio α (0 < α < 1) of the Josephson energies of the second Josephson junction and the first Josephson junction. [Effects of the Invention]

[0031] According to this disclosure, it is possible to realize a superconducting quantum circuit equipped with a coupler whose configuration allows for strengthening of the four-body interaction through circuit parameters. [Brief explanation of the drawing]

[0032] [Figure 1]This is a schematic diagram illustrating related technologies. [Figure 2] This is a schematic diagram illustrating related technologies. [Figure 3] This is a diagram illustrating related technologies. [Figure 4A] This is a schematic diagram illustrating an example of an embodiment. [Figure 4B] This is a schematic diagram illustrating another example of the embodiment. [Figure 5] (A), (B), and (C) are diagrams illustrating embodiments. [Figure 6] This is a diagram illustrating an embodiment. [Figure 7] This is a diagram illustrating the strength of the tetrabody interaction in the embodiment. [Figure 8] This is a diagram illustrating an embodiment. [Figure 9A] This figure schematically shows an example of a coupler in one embodiment. [Figure 9B] This figure schematically shows another example of the coupler in one embodiment. [Figure 10] This is a diagram illustrating an embodiment. [Modes for carrying out the invention]

[0033] Several embodiments are described below. Figure 4A is a diagram illustrating one embodiment. Referring to Figure 4A, the superconducting quantum circuit 1 comprises four JPO1(20A) to JPO4(20D) and a coupler 21. JPO1(20A) to JPO4(20D) are connected to the coupler 21 by capacitive coupling via coupling capacitors 31A to 31D, respectively. In the following embodiments, examples of lumped-parameter types are described for each JPO, but of course, each JPO may also be a distributed-parameter type.

[0034] JPO1(20A) to JPO4(20D) are, respectively, The first superconducting sections 203A-203D, the first Josephson junctions 201A-201D, the second superconducting sections 204A-204D, and the second Josephson junctions 202A-202D are connected in a ring shape as a SQUID (SQUID loop) 210A-210D, The magnetic field generating section 207A-207D consists of a line (inductor) that inductively couples with the SQUID loops 210A-210D and supplies pump signals to control lines 23A-23D from a signal generating section (not shown), thereby generating a magnetic flux that penetrates the SQUID loops 210A-210D. Capacitors 206A to 206D are connected between the first superconducting section 203A to 203D and the second superconducting section 204A to 204D, It is equipped with.

[0035] The second superconducting sections 204A to 204D of JPO1(20A) to JPO4(20D) are connected to ground.

[0036] The coupler connection sections 24A and 24B, which are connected to the first superconducting sections 203A and 203B of JPO1(20A) and JPO2(20B), are respectively connected to the first and second opposing sections 17A and 17B of the coupler 21 via coupling capacitors 31A and 31B.

[0037] The coupler connection sections 24C and 24D, which are connected to the first superconducting sections 203C and 203D of JPO3(20C) and JPO4(20D), are respectively connected to the third and fourth opposing sections 19A and 19B of the coupler 21 via coupling capacitors 31C and 31D.

[0038] The coupler 21 is A loop circuit 10 is connected to one end 16 (first electrode) and the other end 18 (second electrode) of the coupler 21, and includes multiple Josephson junctions (JJs). • A capacitor 15 connected in parallel to the loop circuit 10, It is equipped with.

[0039] More specifically, the loop circuit 10 is located between one end (first electrode) 16 and the other end (second electrode) 18 of the coupler 21. • The first Josephson junctions 11-1 to 11-n are connected in series, spaced apart from each other, Between one end (first electrode) 16 and the other end (second electrode) 18 of the coupler 21, a second Josephson junction 12 is connected in parallel with the first Josephson junctions 11-1 to 11-n. It is equipped with.

[0040] The magnetic field generating unit 14 consists of a line (inductor) that inductively couples with the loop circuit 10 of the coupler 21, and carries a DC signal supplied from a current control unit (not shown) to the control line 13, generating a magnetic flux Φ that penetrates the loop circuit 10, which includes the first Josephson junctions 11-1 to 11-n and the second Josephson junction 12. ext It generates a magnetic field. One end of the magnetic field generating unit 14 is connected to the control line 13, and the other end is connected to the control line 13. This could be a coplanar superconducting line or superconducting coil, etc., with one end connected to ground.

[0041] In the coupler 21 shown in Figure 4A, the n first Josephson junctions 11-1 to 11-n connected in series are connected such that the ends of n+1 adjacent superconducting lines overlap, and the n overlapping sections consist of tunnel junctions of (one end of the superconducting line) / (insulating film) / (one end of the adjacent superconducting line). The other ends of the 1st and (n+1th)th superconducting lines are connected to one end (first electrode) 16 and the other end (second electrode) 18 of the coupler 21, respectively.

[0042] The coupler connections 24A and 24B of JPO1(20A) and JPO2(20B) are capacitively coupled to one end (first electrode) 16 of the coupler 21, respectively. The coupler connections 24C and 24D of JPO3(20C) and JPO4(20D) are capacitively coupled to the other end (second electrode) 18 of the coupler 21, respectively. In other words, in Figure 4A, the first and second opposing parts 17A and 17B connected to one end (first electrode) 16 of the coupler 21 are capacitively coupled to the coupler connection parts 24A and 24B of JPO1 (20A) and JPO2 (20B) via coupling capacitors 31A and 31B, respectively, and the third and fourth opposing parts 19A and 19B connected to the other end (second electrode) 18 of the coupler 21 are capacitively coupled to the coupler connection parts 24C and 24D of PO3 (20C) and JPO4 (20D) via coupling capacitors 31C and 31D, respectively.

[0043] The capacitance of capacitors 206A to 206D in JPO1 (20A) to JPO4 (20D) is C J The capacitance of capacitor 15 of coupler 21 is C g Let C be the capacitance of the coupled capacitors 31A to 31D.

[0044] In this embodiment, the coupler 21 is configured to increase the coupling coefficient of the tetrabody interaction between JPO1(20A) and JPO4(20D), as will become clear from the following description.

[0045] As shown in Figure 5(A), in the SQUID, the first Josephson junction 11 is the portion (tunnel junction) where the ends of superconducting lines 101-1 and 101-2 are in contact via an insulating film (oxide film), and the second Josephson junction 12 is the portion (tunnel junction) where the ends of superconducting lines 102-1 and 102-2 are in contact via an insulating film (oxide film). The superconducting lines 103 and 104 connected to superconducting lines 101-1, 102-1 and superconducting lines 101-2 and 102-2, respectively, may be made of the same superconducting material as superconducting lines 101-1 and 102-1 and superconducting lines 101-2 and 102-2, or they may be made of different superconducting materials.

[0046] The loop of the SQUID in Figure 5(A) is connected by the magnetic flux Φ. ext If it penetrates, the first and second Joseph If we denote the phase differences between Son junctions 11 and 12 as ψ1 and ψ2, respectively, and ignore the linear inductance of the superconducting line, then the following holds: TIFF0007899883000014.tif10150(2.1)

[0047] In equation (2.1), φ0 is the magnetic flux quantum in equation (1.5) above.

[0048] According to equation (2.1), TIFF0007899883000015.tif10150(2.2)

[0049] The potential energy V(ψ1) of the SQUID loop in Figure 5(A) is given by the following equation. TIFF0007899883000016.tif10150(2.3)

[0050] In equation (2.3), E J1 , E J2 These are the Josephson energies of the first and second Josephson junctions 11 and 12. TIFF0007899883000017.tif9150(2.4)

[0051] I C,i (i=1,2) represents the critical currents of the first and second Josephson junctions 11 and 12.

[0052] As shown in Figure 5(B), the loop circuit 10 of the embodiment consists of an array of n first Josephson junctions 11-1 to 11-n connected in series and spaced apart from each other between nodes n1 and n2, and a second Josephson junction 12 connected in parallel to the array. The n first Josephson junctions 11-1 to 11-n connected in series and spaced apart from each other are, for example, the portions (tunnel junctions) where pairs of adjacent superconducting lines 101-1 to 101-n+1 are in contact with each other via an insulating film (oxide film). Superconducting lines 101-1 and 101-n+1 are connected to superconducting lines 103 and 104, respectively. Superconducting lines 103 and 104 may constitute the first and second electrodes 16 and 18. The second Josephson junction 12 is, as in Figure 5(A), a portion (tunnel junction) where the ends of the superconducting lines 102-1 and 102-2 are in contact with each other via an insulating film (oxide film).

[0053] For an array of n first Josephson junctions 11-1 to 11-n connected in series, if the phase difference between the two ends of the array (between nodes n1 and n2) is ψ1 and the phase difference at the second Josephson junction 12 is ψ2, then equation (2.2) above holds. For an array of 1 to 11-n, the phase difference ψ / n obtained by equally dividing the phase difference ψ1 across the array is taken as the phase difference between the input and output at each Josephson junction 11-1 to 11-n. The potential energy of n first Josephson junctions 11-1 to 11-n connected in series is the individual potential energy of the n first Josephson junctions 11-1 to 11-n. TIFF0007899883000018.tif8150(2.5) It is given by adding n of them together. TIFF0007899883000019.tif8150(2.6)

[0054] However, in equation (2.6) above, the capacitance of each first Josephson junction 11 is ignored. It is known that this holds true in the following case: Let C1 be the capacitance of the first Josephson junction, and the charge energy EC =e 2 Regarding / (2C1) exp{-√(8E Jg / E c )≪1 is In terms of its structure, if we consider the capacitance between the array of the first Josephson junctions 11-1 to 11-n and the ground as Cs, C1 / Cs>>n This is conditional on the following being true (Non-Patent Document 2, Non-Patent Document 3, etc.).

[0055] The loop circuit 10 in Figure 5(B) is connected to the magnetic flux Φ ext If it penetrates, the potential energy is, TIFF0007899883000020.tif10150(2.7)

[0056] Here, the magnetic flux Φ passes through the loop circuit 10. ext of TIFF0007899883000021.tif9150(2.8) Let's assume that.

[0057] In equation (2.8), Φ0 is the magnetic flux quantum. TIFF0007899883000022.tif9150(2.9)

[0058] On the other hand, φ0 is the reduced magnetic quantum flux (irreducible quantity) in equation (1.5) above. It is a magnetic flux particle.

[0059] From equation (2.8), TIFF0007899883000023.tif10150(2.10)

[0060] therefore, From TIFF0007899883000024.tif10150, equation (2.7) is as follows:

[0061] TIFF0007899883000025.tif8150(2.11)

[0062] A Josephson junction has a structure in which a junction barrier layer is sandwiched between two superconductors, and an insulating layer, a non-magnetic metal layer, etc. are used for the barrier layer. In this case, if the critical current of the Josephson junction is I0 and the phase difference across the junction (the phase difference of the wave functions in the two superconductors sandwiching the junction) is ψ, the superconducting current (Josephson current) is TIFF00N7899883000026.tif6150(2.12) expressed as, and when in the ground state (I S = 0), the phase difference ψ is 0 rad (radian). Therefore, it is also called a 0 junction. A Josephson junction using a non-magnetic oxide film (such as AlOx, etc.) as the junction barrier layer is a 0 junction.

[0063] On the other hand, between the first superconductor and the second superconductor, as a barrier layer, in a Josephson junction (ferromagnetic Josephson junction) using a ferromagnetic layer (such as copper-nickel alloy (CuNi), palladium-nickel alloy (PdNi), or ferromagnetic insulator layer), it alternates between 0 junctions and π junctions depending on the film thickness of the ferromagnetic layer.

[0064] Here, a π junction is TIFF0007899883000027.tif6150(2.13) a junction where, and in the ground state, the phase difference is π rad different from that of a 0 junction. For example, when the film thickness dF of the ferromagnetic layer is below a predetermined value t1, it is in the 0 state, and when t1 < dF < t2, it is in the π state. By using a π junction instead of a 0 junction, in a loop including the junction, the phase difference can be shifted by π. In a loop including an odd number of π junctions, the phase difference around the loop is ±π×(odd number).

[0065] ​​Figure 5(C) schematically shows an example of a loop circuit 10 using a π junction. Although not particularly limited, in the example of Figure 5(C), n first Josephson junctions 11-1 to 11-n are 0 junctions, and the second Josephson junction 12 is a π junction. If the phase difference between the ends of the array of n first Josephson junctions 11-1 to 11-n connected in series is ψ1, and the phase difference at the second Josephson junction 12 is ψ2, then when the loop circuit 10 is traversed, an additional phase difference π is generated compared to the phase difference ψ2 - ψ1. Therefore, the following holds true. TIFF0007899883000028.tif6150(2.14) Therefore, the potential energy of the second Josephson junction 12 is, TIFF0007899883000029.tif6150(2.15) Therefore, the potential energy V(ψ1) of the loop circuit 10 is the same as that given in equation (2.11) above. That is, when the loop circuit 10 is configured to include an odd number of π junctions (in Figure 5(C), the π junctions... (1 unit), a magnetic flux Φ is supplied to the loop circuit 10 from the outside. ext Without applying (magnetic flux Φ ext (=0), the loop circuit 10 is subjected to a magnetic flux Φ0 / 2 (or -Φ0 / 2) (where Φ0 (=h / (2e)) is the magnetic flux quantum) This can be made equivalent to the above state. For this reason, when the loop circuit 10 is configured to include an odd number of π junctions, the magnetic field generating unit 14 and control line 13 in Figure 4A are unnecessary, as shown in Figure 4B.

[0066] Here, regarding the potential energy of the loop circuit 10 of the coupler 21 in Figure 4A or Figure 4B, the notations in Figure 5(B) or Figure 5(C) are as follows: ψ1=ψg, E J1 =E Jg ,E J2 =αE Jg (However, assume that 0 < α < 1.)

[0067] Then, equation (2.11) becomes equation (2.16). TIFF0007899883000030.tif9150(2.16)

[0068] In equation (2.16), the Josephson energies E of the first Josephson junctions 11-1 to 11-n are given by Jg teeth TIFF0007899883000031.tif9150(2.17) (I cg (where is the critical current of each first Josephson junction).

[0069] Josephson energy E of the second Josephson junction 12 J2 The Josephson energies E of the first Josephson junctions 11-1 to 11-n Jg It is set to α times (0 < α < 1). Since the Josephson energy is proportional to the critical current, the critical current of the second Josephson junction 12 is equal to the critical currents I of the first Josephson junctions 11-1 to 11-n. cg It is set to be α times (0 < α < 1). The value of the critical current of a Josephson junction is proportional to the junction size (junction area) of the Josephson junction. Therefore, the junction size of the second Josephson junction 12 is smaller than the junction sizes of each of the first Josephson junctions 11-1 to 11-n, and the junction size of the second Josephson junction 12 is set to be α times (0 < α < 1) the junction size of each of the first Josephson junctions 11-1 to 11-n. This is the same when both the n first Josephson junctions 11-1 to 11-n and the second Josephson junction 12 are 0 junctions, and when the n first Josephson junctions 11-1 to 11-n are 0 junctions and the second Josephson junction 12 is a π junction.

[0070] In equation (2.16), we perform a Taylor expansion of cos and ψ g 4 Consider up to (ψ g 6 Ignore higher-order terms do). TIFF0007899883000032.tif11150(2.18)

[0071] however, TIFF0007899883000033.tif9150(2.19) TIFF0007899883000034.tif9150(2.20)

[0072] The first term on the right-hand side of equation (2.18) is a constant term and does not affect the subsequent discussion, so we ignore it. V g (ψ g ) is expressed by the following formula. TIFF0007899883000035.tif11150(2.21)

[0073] When n=1 and α=0, this consists of one first Josephson junction and corresponds to the coupler in Non-Patent Document 1, E Jg (2) =E Jg (4) =E Jg This is the result.

[0074] For n>=2, E Jg (2) ≠E Jg (4) This difference has an impact on the coupling coefficient of the tetrabody interaction. It resonates.

[0075] Figure 6 is a diagram illustrating the four-body interaction of the four JPO1(20A) to JPO4(20D) described with reference to Figures 3 to 5, and corresponds to Figures 4A and 4B. Note that in Figure 6, the magnetic field generating sections 207A to 207D and 14 in Figure 4A are not shown. In Figure 6, 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. JThis represents Josephson energy. TIFF0007899883000036.tif9150(2.22)

[0076] E Jg This represents the Josephson energy of the first Josephson junction 11 of the coupler 21 (Equation (2.17)).

[0077] Magnetic fluxes φ1-φ4, φg1, and φg2 are placed at each node 1-4, g1, and g2 (placed at each node) For information on flux (magnetic flux), see, for example, Non-Patent Document 3. Regarding the circuit in Figure 7... Then we construct the classical Hamiltonian.

[0078] TIFF0007899883000037.tif9150(2.23)

[0079] In equation (2.23), C mat ―1 This is the capacitance connection matrix (6 rows x 6 columns) C in Figure 6. mat This is the inverse matrix of [the given matrix].

[0080] TIFF0007899883000038.tif6150 TIFF0007899883000039.tif6150(2.24)

[0081] TIFF0007899883000040.tif7150(2.25)

[0082] TIFF0007899883000041.tif7150(2.26)

[0083] V(φ) is the sum of the potential energies Vsquid,i (i=1~4) of the SQUIDs in JPOi (i=1~4) and the potential energy Vcoupler of the coupler 21 in equation (2.20). TIFF0007899883000042.tif13150(2.27)

[0084] Vsquid,i (i=1~4) is given by the equation (2.3) for the potential energy of the SQUIDs of JPO1~4, E J1 =E J2 =E J Let's ignore the cos(ψi) term and Φ i When we take out the terms containing / φ0, TIFF0007899883000043.tif10150 (2.28)

[0085] However, Φ i , φ i (i=1~4) represents the external magnetic flux Φ in Figure 6. i and the flux φ of node i i That is the case.

[0086] The Vcoupler is given by equation (2.16) and the flux φ of nodes g1 and g2 in Figure 6. g1 , φ g2 from, TIFF0007899883000044.tif10150(2.29)

[0087] Regarding the Hamiltonian of the circuit shown in Figure 6, following the standard method described in Non-Patent Document 3, etc., the coordinate φ and momentum q are defined by the creation and annihilation operator a of bosons (Cooper pairs) a + Quantize using a. Here, the phase ψ k =φ k / φ0 and the number of bosons (Cooper pairs) n k =q k The function / 2e(k=1,2,3,4,g1,g2) is quantized using the boson creation and annihilation operators.

[0088] TIFF0007899883000045.tif10150(2.30)

[0089] TIFF0007899883000046.tif8150(2.31)

[0090] however, TIFF0007899883000047.tif14150(2.32)

[0091] TIFF0007899883000048.tif14150(2.33)

[0092] In equations (2.32) and (2.33), TIFF0007899883000049.tif14150(2.34)

[0093] TIFF0007899883000050.tif14150(2.35)

[0094] In equation (2.34), E C is the charging energy of capacitor C J and, in equation (2.35), E' [[ID=​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0097] In Equation (2.36), TIFF0007899883000054.tif14150(2.39)

[0098] In Equation (2.37), TIFF0007899883000055.tif14150(2.40)

[0099] The Z in Equation (2.39) and Equation (2.40) g is given below. TIFF0007899883000056.tif14150(2.41)

[0100] The cos(φ i / φ0) in Equation (2.28) is expanded up to the fourth - order Taylor expansion as follows and represented by boson creation and annihilation operators. sons. TIFF0007899883000057.tif11150(2.42)

[0101] In Equation (2.28), for the magnetic flux Φ i through each loop of the SQUID of JPO (i = 1,2,3,4), a pump wave with angular frequency ωp,i is applied so that the following holds. i TIFF0007899883000058.tif6150(2.43)

[0102] Since the function V in Equation (2.29) g is defined by Equation (2.16), it includes cos((φ g1 -φ g2 ) / φ0), which, similar to Equation (2.42), TIFF0007899883000059.tif26156 (2.44)

[0103] The quantized Hamiltonian is expressed as follows.

[0104] TIFF0007899883000060.tif27150 (2.45)

[0105] In equation (2.45), H JPO,i Each JPO i The Hamiltonian for (i=1,2,3,4) is given by equation (2.46). TIFF0007899883000061.tif13150(2.46)

[0106] In equation (2.45), H coupler This is the Hamiltonian of coupler 21, given by equation (2.47) It is given. TIFF0007899883000062.tif14150(2.47)

[0107] In equations (2.46) and (2.47), ω is a i The corresponding JPO resonant angular frequency, ω + , ω - is, a g+ a g- This represents the resonant angular frequency of the corresponding coupler 21. However, the difference in angular frequency between different JPOs is not considered.

[0108] H total This includes the interaction between each JPO and the coupler 21. In equation (2.45), g + and g - This represents the strength of the interaction between each JPO and the two degrees of freedom of the coupler 21.

[0109] Furthermore, in equation (2.45), s1=s2=1, s3=s4=-1 (2.48) That is the case.

[0110] Since each JPO interacts with coupler 21, it can be considered that the JPOs also indirectly interact with each other through their interaction with coupler 21. When the variables are transformed to incorporate the influence of coupler 21 into each JPO, the interaction between JPO1-4 and coupler 21 is transformed into a four-body interaction between the JPOs. In other words, it can be transformed into a Hamiltonian in which the JPOs directly interact with each other. This transformation is expressed as a unitary transformation using the following unitary matrix U.

[0111] TIFF0007899883000063.tif13150(2.49)

[0112] Here, ω, ω + , ω - is a i a g+ a g- This is the corresponding resonant angular frequency (the frequency difference between different JPOs is not considered). Also, g + / (ω-ω + ), g - / (ω-ω - ) is assumed to be less than 1.

[0113] The above unitary transformation is similar to that in Non-Patent Document 1, but differs in that Non-Patent Document 1 only considers one degree of freedom for the coupler. After performing the unitary transformation, the bosons of each JPO are represented in a rotating coordinate system. The rotation frequency of the coordinate system differs for each JPO. For JPO1-4, they are represented in a coordinate system that rotates at half the frequency of the pump signal that generates the magnetic flux passing through the SQUID loop of JPO1-4. The pump frequency differs for each JPO. Due to the transition to the rotating coordinate system, time-oscillating terms appear in the Hamiltonian, but these oscillating terms are averaged on the time scale of interest here, and the positive and negative values ​​cancel each other out, so they can be ignored (rotating wave approximation).

[0114] Due to the difference in the frequency of the pump signals, many of the terms representing the interactions between JPOs and the interaction between JPOs and the coupler 21 oscillate and are therefore ignored for the reasons mentioned above. By focusing on the various transformations and characteristic time scales described above, the strength of the interactions between JPOs that occur through the coupler 21 can be estimated. The Hamiltonian H'total obtained through the above process can be expressed as equation (2.50) below, focusing on the four-body interaction term.

[0115] TIFF0007899883000064.tif15150(2.50)

[0116] In equation (2.50), H' JPO,i (i = 1, 2, 3, 4) are Hamiltonian for JPO1(20A)~JPO4(20D) It's Anne.

[0117] H' coupler This is the Hamiltonian of coupler 21.

[0118] a + k a k (k = 1, 2, 3, 4) are the boson creation and annihilation operators corresponding to JPO1(20A) to JPO4(20D).

[0119] In equation (2.50), g (4) This is a coefficient (bond coefficient) that represents the strength of the tetrabody interaction bond. the law of nature, The ratio of the Josephson energies of the second Josephson junction 12 and the first Josephson junction 11 in the coupler 21 (ratio of the junction sizes of the Josephson junctions) α, The number n of the first Josephson junctions 11 connected in series in the coupler 21, • Capacitance Cg of coupler 21, The coupling capacitance C of the capacitive coupling between coupler 21 and each JPO, • Resonant angular frequency ω of each JPO and resonant angular frequency ω of coupler 21 - And, therefore, it can be expressed by the following equation (2.51).

[0120] TIFF0007899883000065.tif26150(2.51)

[0121] In equation (2.51), the resonant angular frequency ω of each JPO is given by the following equation (2.52). TIFF0007899883000066.tif6150(2.52)

[0122] In equation (2.52), Ec is the capacitance C of each JPO. J This is the charge energy. TIFF0007899883000067.tif11150(2.53)

[0123] E J This represents the Josephson energy of the SQUID for each JPO.

[0124] ω - The resonant angular frequency of the coupler 21 (bosonic operator a g- This is the corresponding resonant angular frequency, and is given by the following equation. TIFF0007899883000068.tif10150(2.54)

[0125] In equation (2.54), E'cg is the equivalent capacitance: C g This is the charge energy of +C, and is given by the following equation. TIFF0007899883000069.tif11150 (2.55)

[0126] In equation (2.54), E Jg (2) The resonant angular frequency of the coupler 21 is given by equation (2.19). It is given by the following equation. TIFF0007899883000070.tif14150 (2.56)

[0127] Resonant angular frequency ω of coupler 21 - While the resonant frequency ω of each JPO depends on n and α, it does not depend on n or α.

[0128] By changing n and α, the resonant angular frequency ω of the coupler 21 can be changed. - As the value of moves away from the resonant angular frequency ω of each JPO, the coupling coefficient g of the four-body interaction changes. (4) It becomes smaller. ω - The value of needs to be adjusted by parameters other than n and α. This is the critical current I of the individual Josephson junctions of coupler 21. cg This can be achieved by adjusting the settings.

[0129] Below, we will consider specific circuit parameter settings and demonstrate the effect of adjusting n and α. Let's consider the following settings.

[0130] TIFF0007899883000071.tif31125

[0131] The parameters of the Josephson junction are adjusted to achieve the above frequencies. The effect is on the coupling coefficient g of the tetrabody interaction. (4) We evaluate it using its absolute value. The reason is as follows:

[0132] The coupling coefficient g of the tetrabody interaction (4) According to equation (2.51), depending on the combination of values ​​of n and α, g (4) The value of can be negative. However, by adjusting another parameter not explicitly stated here, g (4) The sign can be changed.

[0133] Therefore, the coupling coefficient g of the tetrabody interaction (4) The sign is not essential, g (4) It is sufficient to focus only on the absolute value of .

[0134] Figure 7 shows the coupling coefficient g of the tetrabody interaction when only α is changed, for example, when the number n of the first Josephson junctions 11 connected in series in the coupler 21 is 1, 3, 5, and 10 under the above settings. (4)This figure shows the change in the absolute value of g. In Figure 7, the vertical axis is g (4) The absolute value of is divided by h / 2π and shown as a converted value in MHz (megahertz) units (h is Planck's constant (approximately 6.6 × 10⁻³⁴ joules / seconds). Other parameters are fixed to the above settings. In particular, the resonant angular frequency ω of the coupler 21 - It is also fixed in place.

[0135] In Figure 7, the result for n=1 corresponds to the case of the coupler in Non-Patent Document 1 (Figure 1 of this application). At this time, g (4) This is constant regardless of α.

[0136] According to the coupler 21 of the embodiment, n is set to 2 or more, and in the region where the value of α is large, In TIFF0007899883000072.tif6150, the coupling coefficient g of the tetrabody interaction is shown. (4) The absolute value of becomes rapidly larger, exceeding the case where n=1. In other words, the absolute value of the coupling coefficient of the tetrabody interaction can be made larger than disclosed in Non-Patent Document 1.

[0137] As described above, in the above embodiment, a four-body interaction of qubits consisting of JPOs is realized, and in the coupler 21, the coupling coefficient g of the four-body interaction is (4) The parameter n(conclusion) included (Number of first Josephson junctions 11 of the combiner 21) and α (Number of second Josephson junctions 12 and the By adjusting the ratio of Josephson energies of the first Josephson junction 11 and the ratio of junction sizes of the second Josephson junction 12 and the first Josephson junction 11, and in particular, in the range α = < 1 / n, by adjusting the critical current Ic of the Josephson junction, the coupling coefficient g of the four-body interaction is controlled. (4) The absolute value of can be increased.

[0138] The coupling coefficient g of the tetrabody interaction in equation (2.51) (4) This refers to capacitance C, one of the circuit parameters. J, C g Regarding C, factor TIFF0007899883000073.tif12150(2.57) Includes.

[0139] Therefore, in addition to the circuit parameters n and α in the coupler 21, capacitance C J , C g By setting the capacity value of C, the coupling coefficient g of the tetrabody interaction is determined. (4) This can be increased. This is based on the four-body interaction coupling coefficient of the embodiment and is a major difference from Non-Patent Document 2, which deals with two-body interactions.

[0140] For example, the capacitance C of the capacitor 15 of the coupler 21 g By reducing the capacitance C of the coupling capacitors 31A to 31D, the coupling coefficient g of the tetrabody interaction can be reduced. (4) The denominator C g +C becomes smaller, g (4) The value of becomes large.

[0141] Furthermore, the capacitance Cg of capacitor 15 of coupler 21 is the capacitance C of each JPO J To make it smaller compared to [this].

[0142] Furthermore, it realizes the four-body interaction network envisioned in LHZ quantum annealing. To achieve this, it is necessary to weaken the two-body interactions in which only two of the four JPOs interact with each other.

[0143] These two-body interactions are C / C J It is proportional to. In the embodiment, in order to weaken these two-body interactions, the capacitance C of the coupling capacitors 31A to 31D between each JPO and the coupler 21 is set to the capacitance C of each JPO. J Compared to C J Let C be large.

[0144] While Figures 4A and 4B illustrate the configuration of the embodiment as a circuit diagram, the following section will first describe an example of implementation on a quantum chip where a superconducting circuit is formed on a wiring layer on a substrate, and then will also describe the quantum annealing device.

[0145] Figure 8 schematically illustrates an example of the configuration of the coupler 21 (wiring pattern formed on the substrate) when JPO1(20A) to JPO4(20D) in Figure 4A are configured as lumped-parameter types. In Figure 8, each JPO from JPO1(20A) to JPO4(20D) has the configuration of Figure 4A and is configured as a waveguide resonator terminated to ground by SQUID210A to 210D. These waveguide resonators cause parametric oscillation by modulating the magnetic flux passing through each loop of SQUID210A to 210D at a frequency approximately twice the resonant frequency using pump signals (microwaves) from control lines 23A to 23D.

[0146] In JPO1(20A) to JPO4(20D), the coupler connection sections 24A to 24D, which extend from the conductive sections (waveguides made of superconducting material) 205A to 205D connected to the first superconducting sections 203A to 203D of SQUID210A to 210D, are capacitively coupled to the ends of the first and second opposing sections 17B and the third and fourth opposing sections 19A and 19B of the coupler 21.

[0147] The coupler connections 24A to 24D of JPO1(20A) to JPO4(20D) may be configured, for example, as a coplanar waveguide sandwiched on both sides along the longitudinal direction by a ground pattern not shown, with a gap in between. However, it goes without saying that the configuration is not limited to the above.

[0148] In the tetrabody interaction coupler 21, the first electrode 16 has first and second opposing portions 17A and 17B that extend from the first electrode 16 toward the two JPO1 and 2 (20A and 20B) sides, with their ends facing the ends of the coupler connection portions 24A and 24B of JPO1 and 2 (20A and 20B) and capacitively coupling via coupling capacitors 31A and 31B. The second electrode 18, positioned opposite the first electrode 16, has third and fourth opposing portions 19A and 19B that face the ends of the coupler connection portions 24C and 24D of JPO3 and 4 (20C and 20D) and capacitively coupling via coupling capacitors 31C and 31D. Between the first electrode 16 and the second electrode 18, a loop circuit 10 is provided, which includes n first Josephson junctions 11-1 to 11-n connected in series, and a second Josephson junction 12 connected in parallel to the first Josephson junctions 11-1 to 11-n.

[0149] The ends of the first and second opposing portions 17A and 17B extending from the first electrode 16 are capacitively coupled to the ends of the coupler connection portions 24A and 24B of JPO1 and 2 (20A and 20B) facing them respectively, via capacitors (coupling capacitors (C) 31A and 31B). The ends of the third and fourth opposing portions 19A and 19B extending from the second electrode 18 are capacitively coupled to the ends of the coupler connection portions 24C and 24D of JPO3 and 4 (20C and 20D) facing them respectively, via capacitors (coupling capacitors (C) 31C and 31D). There are only gaps between the first and second opposing parts 17A and 17B and the coupling connection parts 24A and 24B that face them respectively, and between the third and fourth opposing parts 19A and 19B and the coupling connection parts 24C and 24D that face them respectively.

[0150] Furthermore, the first and second electrodes 16 and 18 have a capacitance (C) between them. g Capacitive coupling occurs via )15. There is only an air gap between the first and second electrodes 16 and 18.

[0151] In the example of FIG. 8, for simplicity, the first and second opposing portions 17A and 17B, and the third and fourth opposing portions 19A and 19B extend from two sides of the rectangular first electrode 16 and the second electrode 18, respectively. However, it is needless to say that the planar shapes of the first and second electrodes 16 and 18 are not limited to rectangles. The first and second opposing portions 17A and 17B and the third and fourth opposing portions 19A and 19B each have the same rectangular shape (rectangle) in the longitudinal direction in terms of width. However, it is needless to say that the planar shape is not limited to a rectangle.

[0152] In an embodiment, the coupler 21 and JPO1 (20A) to JPO4 (20D) are realized by, for example, a line (wiring) formed of a superconductor on a substrate. Although silicon (Si) is used for the substrate, other electronic materials such as sapphire or compound semiconductor materials (Group IV, III-V, II-VI) may be used. Also, it is desirable that the substrate is a single crystal, but it may be a polycrystal or amorphous. As the material of the line (wiring material), for example, Nb (niobium) or Al (aluminum) is used, but it is not limited thereto. Any metal that becomes a superconducting state when cooled to an extremely low temperature, 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 an alloy containing at least any of these, may be used. Further, in order to minimize thermal noise, the circuit of the coupler is used in a temperature environment of about 10 mK (millikelvin) realized by a refrigerator.

[0153] In FIG. 8, regarding the capacitance value of each capacitor, C J >Cg>C (2.58) may be set.

[0154] In FIG. 8, when an odd number of Josephson junctions among the n first Josephson junctions 11-1 to 11-n of the loop circuit 10 and the second Josephson junction 12 are π junctions, as described above, the phase difference around the loop circuit 10 is ±π×(odd number). That is, without applying an external magnetic flux Φ ext it is possible to bias the loop circuit 10 with a magnetic flux that is an odd multiple of Φ0 / 2 (or -Φ0 / 2) (where Φ0(=h / 2e) is the magnetic flux quantum) without applying an external magnetic flux Φ. Therefore, the control line 13 and the magnetic field generation unit 14 connected to a current control unit (not shown) are unnecessary.

[0155] FIG. 9A is a diagram showing a non-limiting example of the above-described embodiment, and is a diagram schematically showing a non-limiting example of the pattern (planar circuit) of the coupler 21 in FIG. 8. In FIG. 9A, for convenience of drawing preparation, JPO1 to JPO4 each show the respective coupler connection portions 24A to 24D.

[0156] Referring to FIG. 9A, the coupler 21 is arranged surrounded by a ground pattern (ground plane) 40. Also, although not particularly limited, the coupler connection portions 24A to 24D of JPO1 to 4 are surrounded by the ground pattern (ground plane) 40 with gaps on both sides, and the JPO1 to 4 bodies are also arranged surrounded by the ground pattern (ground plane) 40. As schematically shown in FIG.  9A, the coupler 21 is arranged at a gap, for example, on the order of the size of the coupler 21 (from one fraction to several times the order of this size), away from the edge of the ground pattern (ground plane) 40. When the coupler 21 is on the order of 10 to 100 μm (tens to hundreds of μm), the gap interval may be approximately on this order. In FIG. 9A, 41 is a region where no ground pattern is provided and the substrate is exposed.

[0157] In the non-restrictive example shown in Figure 9A, the planar shape of the first electrode 16 is approximately trapezoidal, and its shape is that of an electrode rotated approximately 45 degrees counterclockwise with respect to the horizontal direction of the figure. The first and second opposing portions 17A and 17B of the first electrode 16 extend from the hypotenuse (legs) of the trapezoid towards the left and upward directions of the figure, respectively, toward the coupler connection portions 24A and 24B of JPO1 and JPO2. The planar shape of the second electrode 18 is approximately an inverted trapezoidal shape obtained by rotating the first electrode 16 by 180 degrees, and the third and fourth opposing portions 19A and 19B of the second electrode 18 extend from the hypotenuse towards the right and downward directions of the figure, respectively, toward the coupler connection portions 24C and 24D of JPO3 and JPO4. 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 roughly hexagonal.

[0158] The first electrode 16 has a projection 16C that protrudes downward in the figure near the intersection of one end of the lower base and the hypotenuse, and 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 the lower base and the hypotenuse, and a loop circuit 10, as described with reference to Figure 5(C), is provided 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 second electrode 18 (note that the first Josephson junctions 11-1 to 11-n and the second Josephson junction 12 in Figure 8 are not shown due to the difference in dimensions between the loop circuit 10 and electrodes 16 and 18). In the loop circuit 10, for example, if the second Josephson junction 12 is a π junction and the remaining n first Josephson junctions 11-1 to 11-n are 0 junctions, then a magnetic flux Φ0 / 2 is given through the loop circuit 10. However, the potential energy of the second Josephson junction 12 is given by equation (2.15), and the potential energy V(ψ1) of the loop circuit 10 is the same as the potential energy given by equation (2.11).

[0159] On the other hand, Figure 9B shows that in the loop circuit 10, all n first Josephson junctions 11-1 to 11-n and the second Josephson junction 12 are set to 0 junctions, and the magnetic flux Φ passing through the loop circuit 10 from the magnetic field generating unit 14 isext Coupler 21 when giving =Φ0 / 2 (where Φ0 is the magnetic flux quantum = h / (2e)) This figure schematically shows a non-restrictive example of the pattern (planar circuit). In Figure 9B, a current supplied from a current control unit (not shown) flows through the loop circuit 10, and the magnetic flux Φ ext Control line that generates The control line 13 further has a control line 13. The control line 13 is configured as a line with ground patterns 40 arranged on both sides in the longitudinal direction with gaps in between, and its end functions as a magnetic field generating unit 14 in Figure 8 and is connected to ground (ground pattern 40) in the vicinity of the loop circuit 10. For this reason, in the vicinity of the loop circuit 10, it has a portion 30 that extends the ground pattern 40 inward and brings it closer to the loop circuit 10. The control line 13 has a magnetic flux Φ generated by the magnetic field generating unit 14 (Figure 8) that penetrates the loop circuit 10 ext So that the magnetic flux quantum Φ0 is 1 / 2 (= h / (4e)) A DC current is supplied from a current control unit (not shown).

[0160] In the example shown in Figure 9B, in order to efficiently apply magnetic flux through inductive coupling with the control line 13 (transmission line), the distance between the ground pattern 40 and only the electrodes near the Josephson junction loop circuit 10 of the first electrode 16 and second electrode 18 is partially reduced. By forming the control line 13 near the loop circuit 10, the magnetic flux Φ is applied from very close to the loop circuit 10. ext This allows for the application of [something]. As mentioned above, the ground pattern 40 is Except for the portion 30 that approaches the loop circuit 10, the first and second electrodes 16 and 18 are basically spaced apart, similar to Figure 9A. Note that Figure 9B shows an example where the control line 13 and magnetic field generator 14 from Figure 8 are placed on the same wiring layer as the coupler 21, but the configuration is not limited to this. On the surface of a wiring board (interposer) (not shown) on which the quantum chip, including the coupler 21, is mounted via bumps, the control line 13 and magnetic field generator 14 may be positioned opposite or near the loop circuit 10 of the coupler 21.

[0161] In the coupler 21 with the configuration shown in Figures 9A and 9B, the capacitance C of the capacitors JPO1 (20A) to JPO4 (20D) (201A to 201D in Figure 4A) J Regarding the capacitance Cg of the capacitor of coupler 21 (15 in Figure 4A), and the capacitance C of the coupling capacitor between the coupler connection section 24A-24D of JPO1 (20A) to JPO4 (20D) and the opposing sections 17A, 17B, 19A, 19B of coupler 21 (31A-31D in Figure 4A), C J >C g >C You can also set it to that.

[0162] Furthermore, Non-Patent Document 2 maintains a coupling device comprising a superconducting loop circuit having an array of n first Josephson junctions connected in series and a second Josephson junction connected in parallel with the array. Let us compare the disclosure of the present application described above with the disclosure of Non-Patent Document 2. The following points are common to both.

[0163] The loop circuit structure of coupler 21 is also used as a coupler structure between qubits (or photons) in Non-Patent Document 2.

[0164] The Josephson junction loop circuit is the one where n first Josephson junctions are connected in series. (i) and a second Josephson junction connected in parallel to the array, the Josephson energy of the second Josephson junction being α times that of the first Josephson junction, and an external magnetic flux Φ is supplied to the loop circuit 10. ext Multiply by =h / (4e)=πφ0. By setting α≈1 / n, the interval between qubits The interaction coefficient can be increased.

[0165] There are numerous discrepancies between the disclosure in this application and Non-Patent Document 2.

[0166] For example, the type of interaction generated by the coupler 21 differs. In the present disclosure, the coupler 21 is used to generate a four-body interaction of a qubit (JPO), whereas in Non-Patent Document 2, this coupler is used to generate a two-body interaction of a qubit (Non-Patent Document 2 does not mention a four-body interaction coupler at all). As a result, the differences are as follows.

[0167] In this embodiment, a capacitor is required to distinguish between JPO1 and JPO2, and JPO3 and JPO4, which are connected without a coupler for four-body interaction. In this embodiment, a coupling capacitor is required between the qubit (JPO) and the coupler 21. Non-patent document 2 does not contain a capacitor that corresponds to this.

[0168] Furthermore, the presence or absence of this capacitor results in the following differences.

[0169] In the disclosure of this application, resonance occurs in the coupler 21, whereas in Non-Patent Document 2, resonance in the coupler itself is not considered. Therefore, circuit settings and g (4) ω that appears - What corresponds to This does not appear in Non-Patent Document 2.

[0170] To increase the strength of the four-body interaction (coupling coefficient), the resonant angular frequency ω of coupler 21 - The technique of adjusting (or keeping) the value of [the variable] is unique to this invention.

[0171] Furthermore, Non-Patent Document 2 applies to two-body interactions, which differ from four-body interactions. Therefore, the χ (quarton) in equation (7) of the coupling coefficient of the interaction presented in Non-Patent Document 2 is different from the coupling coefficient g of the four-body interaction in equation (2.51) of the present application described above. (4) In contrast to that Yes, they are.

[0172] In the above disclosure of the present application, the main difference is that it deals with the four-body interaction of qubits, while Non-Patent Document 2 deals with the two-body interaction of qubits. Due to this point, there are differences in the presence or absence of capacitors between the qubits and the coupler, the presence or absence of resonance of the coupler, the necessity of adjusting the resonance frequency of the coupler, and the expression of the interaction coefficient.

[0173] According to this embodiment, in order to increase the coupling coefficient of the four-body interaction in Equation (2.51), in addition to setting the circuit parameters n and α of the coupler 21, for the shunt capacitor C of each JPO's SQUID J , the coupling capacitance C between each JPO and the coupler 21, and the capacitance C of the coupler 21 g Regarding C J >C g >C is set so that the coupling coefficient g of the four-body interaction (4) can be increased.

[0174] Furthermore, the resonance angular frequency ω of each JPO and the resonance angular frequency ω of the coupler 21 - are prevented from approaching too closely. More specifically, for the factor (ωω - ) 2 / (ω - ω - ) 4 in the formula (2.51) for the strength of the four-body interaction, TIFF0007899883000074.tif1249(2.59) When it is set as

[0175] TIFF0007899883000075.tif1355(2.60)

[0176] Figure 10 is a schematic diagram showing the configuration of a quantum computer 300 integrating JPO20s as an example of the configuration of another embodiment. In the configuration shown in Figure 10, each four-body interaction coupler 21 is connected to four JPO20s, as shown in Figures 4A, 4B, and 8. 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 4A, 4B, and 8. In the quantum computer 300, at least one JPO20 is connected to multiple four-body interaction couplers 21. In particular, in the example shown in Figure 10, 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 10, the quantum computer 300 has multiple unit structures, and the JPO20 is shared among multiple unit structures. In the example shown in Figure 10, 13 superconducting nonlinear JPO20s are integrated, but any number of JPO20s can be integrated in the same way. Note that in Figure 10, the current control unit and readout unit are omitted from the illustration to facilitate understanding of the diagram, but as explained with reference to Figure 3, the current control unit and readout unit are used to control and read the JPO20.

[0177] The disclosure of the above embodiments is further noted below (but is not limited to the above).

[0178] (Note 1) The superconducting quantum circuit comprises a first to fourth qubit and a coupler that connects the first to fourth qubits by a four-body interaction. The coupler comprises a loop circuit connected between one end and the other end of the coupler, A capacitor connected in parallel to the aforementioned loop circuit, Equipped with, The aforementioned loop circuit comprises n (where n is a positive integer of 2 or more) first Josephson junctions arranged in series and spaced apart from each other, A second Josephson junction is arranged in parallel with n first Josephson junctions, and the junction size is smaller than that of the first Josephson junctions. It has, The first and second qubits are capacitively coupled to one end of the coupler, The third and fourth qubits are capacitively coupled to the other end of the coupler, respectively. The magnitude of the coupling coefficient of the four-body interaction by the coupler can be set based on circuit parameters that include at least n and the ratio α (0 < α < 1) of the Josephson energy of the second Josephson junction to the Josephson energy of the first Josephson junction.

[0179] (Note 2) In the superconducting quantum circuit described in Appendix 1, the α in the coupler may be set to a predetermined value close to 1 / n within a range smaller than the reciprocal of n, which is 1 / n.

[0180] (Note 3) The aforementioned loop circuit has a magnetic flux of ±Φ0 / 2 × (2k+1) (where Φ0 (=h / (2e)) is the magnetic flux quantum: The state may also be considered as being biased by h (where h is Planck's constant and e is the elementary charge). See Appendix 1 or 2. The superconducting quantum circuit may include a magnetic field generating unit that generates a magnetic flux of Φ0 / 2 or -Φ0 / 2 as a magnetic flux that penetrates the loop circuit of the coupler by passing a DC current from the current control unit.

[0181] (Note 4) In the superconducting quantum circuit described in Appendix 1 or 2, of the n first Josephson junctions and second Josephson junctions of the loop circuit, an odd number (2k+1, where k is a predetermined non-negative integer) The number of junctions may be a π junction and the remainder a 0 junction. With this configuration, the phase difference when the loop circuit is circulated is ±π × (2k+1), and the loop circuit has a magnetic flux of ±Φ0 / 2 × (2k+1) (where Φ0 (=h / (2e)) is the magnetic flux quantum: This is equivalent to a state biased by h (where h is Planck's constant and e is the elementary charge).

[0182] (Note 5) In the superconducting quantum circuit described in any of Appendix 1 to 4, the loop circuit of the coupler comprises a first electrode and a second electrode arranged opposite to each other and spaced apart from the ground pattern within a region surrounded by the ground pattern in a wiring layer on a substrate, The aforementioned n (where n is a positive integer greater than or equal to 2) first Josephson junctions, The above-mentioned second Josephson junction, These are arranged in parallel between the first electrode and the second electrode, The first electrode is, The first electrode extends from a point on the first electrode, separate from the side facing the second electrode, toward the first and second qubits, and each end has a first and second opposing portion that capacitively couples with the ends of the coupler connection portion of the first and second qubits, respectively. The second electrode is, The second electrode may have third and fourth opposing portions that extend from a point on the second electrode that is not facing the first electrode towards the third and fourth qubits, respectively, and whose ends face and capacitively couple with the ends of the coupler connection portions of the third and fourth qubits.

[0183] (Note 6) In the superconducting quantum circuit described in Appendix 5, Each of the first to fourth qubits includes a Josephson parametric oscillator, The Josephson parametric oscillator described above is A SQUID (superconducting quantum interference device) has two Josephson junctions at both ends where the first and second superconducting lines forming the loop intersect. and, A capacitor connected in parallel with the aforementioned SQUID, A transmission line that inductively couples with the aforementioned SQUID and generates a magnetic flux passing through the loop of the SQUID, It has, One of the first and second superconducting lines of the SQUID is at ground potential. The other of the first superconducting line and the second superconducting line of the SQUID is connected to the coupling connection. The system may be configured to parametrically oscillate according to the microwave current supplied to the aforementioned line.

[0184] (Note 7) In the superconducting quantum circuit described in Appendix 6, The circuit parameters that define the coupling coefficients of the four-body interaction are, In addition to α and n, The capacitance value C of the capacitive coupling between the coupler connection portion of the first to fourth qubits and each of the first to fourth opposing portions of the coupler, The capacitance value C of the capacitor connected in parallel to each of the first to fourth qubits' SQUIDs. J , The capacitance value C between the first and second electrodes of the coupler. g Includes, The relative magnitudes of these capacitances are as follows: C J >C g >C It can also be used as a setting.

[0185] (Note 8) In the superconducting quantum circuit described in Appendix 6 or 7, The coupling coefficient of the aforementioned tetrabody interaction is, The aforementioned α and the aforementioned n, The capacitance value C of the capacitive coupling between the coupler connection portion of the first to fourth qubits and each of the first to fourth opposing portions of the coupler, The capacitance value C of the capacitor connected in parallel to each of the loop circuits of the first to fourth qubits. J , The capacitance value C between the first and second electrodes of the coupler. g , The resonant angular frequency ω of the aforementioned coupler - The circuit parameter of the difference ω between the resonant angular frequencies of each qubit. Regarding TIFF0007899883000076.tif13150 The configuration may also be represented as follows:

[0186] (Note 9) A superconducting quantum circuit described in any of the appendices 1 to 8, 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.

[0187] (Note 10) In the superconducting quantum circuit device described in Appendix 9, Having multiple of the aforementioned unit structures, The unit structure may constitute 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.

[0188] Furthermore, the disclosures in Patent Documents 1 and 2 and Non-Patent Documents 1-5 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 in each appendix, each element in each embodiment, each element in each drawing, etc.) are possible. In other words, the present invention naturally includes various modifications and alterations that a person skilled in the art could make in accordance with the full disclosure, including the claims, and the technical concept. [Explanation of symbols]

[0189] 1. Superconducting Quantum Circuits 10 Loop circuits (nonlinear elements) 11, 11-1~11-n First Josephson junction 12. Second Josephson junction 13 Control Line 14 Magnetic field generation unit 15 Capacitors 16 Electrodes (First Electrode) 16C protrusion 17A, 17B First and second opposing sections 18 Electrode (Second Electrode) 19A, 19B Third and fourth opposing sections 20A-20D, 120A-120D Superconducting Qubits (JPO) 21, 121 combiner 122A~122D Readout circuit connection section 23A~23D, 123A~123D Control lines (flux lines) Coupler connection section for 24A~24D and 124A~124D 30 parts (grand pattern protrusions) 31A~31D Capacitors (Coupling Capacitors) 40 Ground (GND) pattern (ground plane) 41 Surface of the substrate 10¹-1 to 10¹-n superconducting lines 102-1, 102-2 superconducting lines 103, 104 Superconducting Lines 110 Nonlinear elements 132A~132D Capacitors 140A~140D Readout Circuit 150A~150D signal generation section 201A, 201B, 201C, 201D First Josephson Junction 202A, 202B, 202C, 202D Second Josephson Junction 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 unit 300 Quantum Computer

Claims

1. The first to fourth qubits, A coupler that connects the first to fourth qubits via a four-body interaction, Equipped with, The aforementioned coupler is, A loop circuit connected between one end and the other end of the coupler, A capacitor connected in parallel to the aforementioned loop circuit, Equipped with, The aforementioned loop circuit is n first Josephson junctions (where n is a positive integer greater than or equal to 2) are arranged in series, spaced apart from each other, A second Josephson junction is arranged in parallel with n first Josephson junctions, and the junction size is smaller than that of the first Josephson junctions. It has, The first and second qubits are capacitively coupled to one end of the coupler, The third and fourth qubits are capacitively coupled to the other end of the coupler, respectively. The magnitude of the coupling coefficient of the four-body interaction by the aforementioned coupler is at least, The aforementioned n and, The ratio α (0 < α < 1) of the Josephson energy of the second Josephson junction to the Josephson energy of the first Josephson junction, A superconducting quantum circuit whose parameters can be freely configured based on the circuit parameters including those mentioned above.

2. The superconducting quantum circuit according to claim 1, wherein in the coupler, α is set to a predetermined value close to 1 / n within a range smaller than the reciprocal of n, 1 / n.

3. A direct current is passed from the current control unit, and the magnetic flux passing through the loop circuit of the coupler is Φ. 0 / 2 or -Φ 0 / 2 (however, Φ 0 The superconducting quantum circuit according to claim 1, comprising a magnetic field generating unit that generates a magnetic flux quantum (= h / (2e) where h is Planck's constant and e is the elementary charge).

4. Of the n first Josephson junctions and second Josephson junctions in the loop circuit, an odd number (2k+1, where k is a predetermined non-negative integer) are designated as π junctions, and the remainder are designated as 0 junctions. The phase difference when the loop circuit is circulated is ±π × (2k+1), and the loop circuit has a magnetic flux of ±Φ without applying a magnetic flux through it. 0 / 2 × (2k + 1) (where Φ 0 The superconducting quantum circuit according to claim 1, wherein it is in a state biased by a magnetic flux quantum (where h / (2e) is Planck's constant and e is the elementary charge).

5. The loop circuit of the coupler comprises a first electrode and a second electrode arranged opposite to each other and spaced apart from the ground pattern within a region surrounded by the ground pattern on the wiring layer of the substrate. The n (where n is a positive integer of 2 or more) first Josephson junctions, The aforementioned second Josephson junction, These are arranged in parallel between the first electrode and the second electrode, 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 superconducting quantum circuit according to claim 1, wherein the second electrode extends from a location separate from the side facing the first electrode toward the third and fourth qubits, and the ends of the second electrode are each 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.

6. Each of the first to fourth qubits includes a Josephson parametric oscillator, The Josephson parametric oscillator described above is A SQUID (superconducting quantum interference device) having two Josephson junctions at both ends where the first and second superconducting lines forming a loop intersect, A capacitor connected in parallel with the aforementioned SQUID, A transmission line that inductively couples with the aforementioned SQUID and generates a magnetic flux passing through the loop of the SQUID, It has, One of the first superconducting line and the second superconducting line of the SQUID is at ground potential. The other of the first superconducting line and the second superconducting line of the SQUID is connected to the coupling connection section. The superconducting quantum circuit according to claim 5, which parametrically oscillates according to the microwave current supplied to the transmission line.

7. The circuit parameters that define the coupling coefficients of the four-body interaction are, In addition to α and n, The capacitance value C of the capacitive coupling between the coupler connection portion of the first to fourth qubits and each of the first to fourth opposing portions of the coupler, The capacitance value C of the capacitor connected in parallel to each of the first to fourth qubits' SQUIDs. Ｊ , The capacitance value C between the first and second electrodes of the coupler. ｇ Includes, The relative magnitudes of these capacitances are C Ｊ >C ｇ >C A superconducting quantum circuit according to claim 6, which is set to the above.

8. The coupling coefficient of the aforementioned tetrabody interaction is, The aforementioned α and the aforementioned n, The capacitance value C of the capacitive coupling between the coupler connection portion of the first to fourth qubits and each of the first to fourth opposing portions of the coupler, The capacitance value C of the capacitor connected in parallel to each of the first to fourth qubits' SQUIDs. Ｊ , The capacitance value C between the first and second electrodes of the coupler. ｇ , The resonant angular frequency ω of the aforementioned coupler - Regarding the circuit parameters of the difference ω between the resonant angular frequencies of each qubit, A superconducting quantum circuit according to claim 6, represented as shown in the image.

9. A superconducting quantum circuit device comprising a superconducting quantum circuit according to any one of claims 1 to 8, A superconducting quantum circuit device comprising a quantum computer having the first to fourth parametrically oscillating qubits and the coupler as unit structures.

10. The quantum computer has a plurality of the unit structures, The superconducting quantum circuit device according to claim 9, wherein the unit structure shares at least one of the first to fourth qubits constituting the unit structure with one or more other unit structures.

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