Superconducting quantum circuit

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

Superconducting quantum circuits

[0001] The present invention relates to superconducting quantum circuits.

[0002] Quantum annealing is a method for solving combinatorial optimization problems, and one of the quantum annealing methods is called the LHZ (Lechner, Hauke, Zoller) method (see, for example, Patent Document 1). To physically implement LHZ quantum annealing, it is necessary to realize the basic element of quantum bits and their network, particularly a network in which four quantum bits interact simultaneously (four-body interaction). One proposed implementation format is to use Josephson parametric oscillators (JPOs) as quantum bits (see, for example, Non-Patent Document 1).

[0003] (a) One of the methods is shown in Figure 1, which can realize four-body interactions with a simple structure. Figure 1 is based on Figure 4a in Non-Patent Document 1. In Figure 1, the resonant angular frequency ω r,i The diagram shows a system in which JPO1 to JPO4 (i=1, 2, 3, 4) interact through a single Josephson junction (JJ). (JPO1 to JPO4 with different resonant angular frequencies are shown in different patterns according to Figure 4 in Non-Patent Document 1.)

[0004] The SQUID (Superconducting Quantum Interference Device) loop of each JPO is driven by a flux pump with adjustable amplitude and frequency. The angular frequency of the pump signal, ω p,k (t)(k=1,2,3,4) is the angular frequency twice the angular frequency of the resonator: 2ω r,i In a Josephson Parametric Amplifier (JPA), there is a threshold of pump strength above which oscillation occurs, with a resonant angular frequency ω r,iThis is called parametric oscillation. Since this specification focuses on resonators that generate parametric oscillation, the JPA in Figure 4 of Non-Patent Document 1 is referred to as JPO.

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

[0006] The angular frequencies of the pump signals of JPO1 to JPO4 are (1.1) and detune the cavity.

[0007] If they are detuned from each other, the central Josephson junction (JJ) is expressed as follows in the rotating coordinate system of the two-photon drive: This gives rise to a bond of the form (1.2).

[0008] This four-body interaction is always active, 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 to 4) is the annihilation operator of the resonance modes (bosons) of JPO1 to 4, a ｉ ＋ (i=1 to 4) is a generation operator.

[0009] G in equation (1.2) is given by: (1.3)

[0010] In equation (1.3), Δ k (k=1,2,3,4) is the mode angular frequency ω of the kth JPO r,k and the mode angular frequency (resonance angular frequency) ω, which is determined by the capacitance and inductance of the central Josephson junction (JJ). c This is the difference (detuning) between (1.4)

[0011] φ0 is the reduced magnetic quantum flux: (1.5) However, is the Dirac constant, (1.6) (h is Planck's constant, 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 the critical current I ｃ is proportional to. (1.7)

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

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

[0016] In Non-Patent Document 1, C is used as the four-body coupling strength in Equations (1.2) and (1.3), but here it is expressed as G to distinguish it from coupling capacitors such as C. In Non-Patent Document 1, the method for strengthening the four-body interaction in the configuration of FIG.

[0017] (b) The other method uses a Josephson Ring Modulator (JRM), as shown in Figure 2. Figure 2 is based on Supplementary Figure 8 of Non-Patent Document 1. Note that in Figure 2, the JPA in Supplementary Figure 8 of Supplementary Note 8 of Non-Patent Document 1 is used as the JPO. A microwave drive signal (capacitor C ｘ and C ｙ(shown by the solid and dashed arrows) activates the four-body phase coupling between JPOs.

[0018] In the example shown in Fig. 2, an unbalanced shunt-type JRM is used to realize tunable four-body interactions. The JRM has two sets of two Josephson junctions (JJs) connected in series in parallel between a first node, which is the junction of JPO1 and JPO2, and a second node, which is the junction of JPO3 and JPO4. The first and second nodes each have a capacitor C ｘ A microwave drive signal is applied via a capacitor C ｙ via the capacitor C ｘ A microwave drive signal is applied to the inverter in opposite phase to the microwave drive signal applied to the inverter.

[0019] In this case, in order to realize the four-body interaction, the oscillation angular frequency satisfied by JPO1 to JPO4 and the angular frequency ω of the drive signal input from the capacitors Cx and Cy are d For example, the combination of (1.9), the drive signal (1.10) (where n is the number of photons in mode z), the rotating wave approximation leads to the Hamiltonian

[0020] (1.11)

[0021] however, (1.12)

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

[0023] As a related art configuration similar to that shown in FIG. 1, for example, Patent Document 2 discloses a circuit using a lumped constant JPO as shown in FIG.

[0024] 3, the system includes four JPOs, JPO1 (120A) to JPO4 (120D), and a coupler 121. The coupler connection parts 124A to 124D of JPO1 (120A) to JPO4 (120D) are capacitively coupled to the coupler 121, which is made up of a Josephson junction (JJ), via capacitors (coupling capacitors) 131A to 131D, respectively. The readout circuit connection parts 122A to 122D of JPO1 (120A) to JPO4 (120D) are capacitively coupled to readout circuits 140A to 140D via capacitors 132A to 132D, respectively. JPO1 (120A) to JPO4 (120D) are connected via control lines 123A-123D to signal generators 150A-150D that generate pump signals for generating magnetic fluxes that penetrate the SQUID loops of JPO1 (120A) to JPO4 (120D). The nonlinear element 110 of the coupler 121 is an element that can be regarded as an LC resonator with a Josephson junction (JJ) as a nonlinear inductance, and the nonlinear element 110 may be a SQUID including two Josephson junctions (JJ).

[0025] Note that a coupler having a circuit similar to the loop circuit in Figure 5(B) described below is disclosed in Non-Patent Document 2. However, the disclosure of Non-Patent Document 2 is not a coupler for four-body interactions of four quantum bits. Differences between the disclosure of the present application and the disclosure of Non-Patent Document 2 will be described in detail in the embodiments.

[0026] International Publication No. 2017 / 001404 International Publication No. 2021 / 014885

[0027] Shruti Puri, et. al., "Quantum annealing with all-to-all connected nonlinear oscillators", Nature Communications 8, 15785 (2017)Yufeng Ye, et. al., "Engineering Purely Nonlinear Coupling between Superconducting Qubits Using a Quarton", PHYSICAL REVIEW LETTERS 127, 050502 (2021)Uri Vool, et. al., "Introduction to Quantum Electromagnetic Circuits", International Journal of Circuit Theory and Applications 45, 897 (2016)T Yamashita, et.al., "Superconducting π qubit with three Josephson junctions", Appl. Phys. Lett. 88, 132501 (2006)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

[0028] Non-Patent Document 1 and Patent Document 2 shown in Figures 1 to 3 do not mention a method for strengthening the four-body interaction. In addition, although the configuration in Figure 2 can adjust the strength of the four-body interaction, it requires a separate external input (a microwave drive signal input in reverse phase to capacitors Cx and Cy).

[0029] The present disclosure has been made in view of the above-mentioned problems, and its purpose is to provide a superconducting quantum circuit equipped with a coupler configured to enable the four-body interaction to be strengthened by changing the circuit parameters.

[0030] According to one aspect of the present disclosure, a superconducting quantum circuit includes first to fourth quantum bits and a coupler that couples the first to fourth quantum bits through four-body interactions. The coupler includes 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 includes n (n is a positive integer of 2 or more) first Josephson junctions that are spaced apart from each other and arranged in series, and second Josephson junctions that are arranged in parallel with the n first Josephson junctions and have a junction size smaller than that of the first Josephson junctions. The first and second quantum bits are each capacitively coupled to one end of the coupler, and the third and fourth quantum bits are each 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 freely 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.

[0031] According to the present disclosure, it is possible to realize a superconducting quantum circuit equipped with a coupler configured to enable the four-body interaction to be strengthened by adjusting the circuit parameters.

[0032] 1A, 1B, and 1C are diagrams illustrating an embodiment; 1C are diagrams illustrating an embodiment; 1D are diagrams illustrating the strength of four-body interactions in an embodiment; 1D are diagrams illustrating an embodiment; 1D are diagrams illustrating an example of a coupler according to an embodiment; 1D are diagrams illustrating another example of a coupler according to an embodiment; 1D are diagrams illustrating an embodiment; 1D are diagrams illustrating an embodiment; 1D are diagrams illustrating an embodiment; 1D are diagrams illustrating an example of a coupler according to ...

[0033] Several embodiments will be described below. Fig. 4A is a diagram illustrating one embodiment. Referring to Fig. 4A, a superconducting quantum circuit 1 includes four JPOs, JPO1 (20A) to JPO4 (20D), and a coupler 21. JPO1 (20A) to JPO4 (20D) are capacitively coupled to the coupler 21 via coupling capacitors 31A to 31D, respectively. In the following embodiments, an example of a lumped constant type JPO will be described, but it goes without saying that each JPO may also be a distributed constant type.

[0034] JPO1 (20A) to JPO4 (20D) each include: SQUIDs (SQUID loops) 210A to 210D in which first superconducting portions 203A to 203D, first Josephson junctions 201A to 201D, second superconducting portions 204A to 204D, and second Josephson junctions 202A to 202D are connected in a ring; magnetic field generating units 207A to 207D each consisting of a line (inductor) that is inductively coupled to the SQUID loops 210A to 210D and that generates a magnetic flux that passes through the SQUID loops 210A to 210D by passing a pump signal that is supplied to control lines 23A to 23D from a signal generating unit (not shown); and capacitors 206A to 206D connected between the first superconducting portions 203A to 203D and the second superconducting portions 204A to 204D.

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

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

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

[0038] The coupler 21 comprises: a loop circuit 10 connected to one end 16 (first electrode) and the other end 18 (second electrode) of the coupler 21 and including a plurality of Josephson junctions (JJs); and a capacitor 15 connected in parallel to the loop circuit 10.

[0039] More specifically, the loop circuit 10 includes: n first Josephson junctions 11-1 to 11-n connected in series and spaced apart from one another between one end (first electrode) 16 and the other end (second electrode) 18 of the coupler 21; and a second Josephson junction 12 connected in parallel with the first Josephson junctions 11-1 to 11-n between the one end (first electrode) 16 and the other end (second electrode) 18 of the coupler 21.

[0040] The magnetic field generating unit 14 is composed of a line (inductor) that is inductively coupled with the loop circuit 10 of the coupler 21, and generates a magnetic flux Φ 1 that passes through the loop circuit 10 including the first Josephson junctions 11-1 to 11-n and the second Josephson junction 12 by supplying a DC signal to the control line 13 from a current control unit (not shown). ext The magnetic field generating unit 14 may be a coplanar superconducting line or a superconducting coil, one end of which is connected to the control line 13 and the other end of which is connected to the ground.

[0041] 4A, the n first Josephson junctions 11-1 to 11-n connected in series are connected so that the ends of the (n+1) adjacent superconducting lines overlap, and the n overlapping portions are formed by tunnel junctions of (one end of a superconducting line) / (insulating film) / (one end of an adjacent superconducting line). The other ends of the first and (n+1)-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 connection parts 24A and 24B of JPO1 (20A) and JPO2 (20B) are capacitively coupled to one end (first electrode) 16 of the coupler 21. The coupler connection parts 24C and 24D of JPO3 (20C) and JPO4 (20D) are capacitively coupled to the other end (second electrode) 18 of the coupler 21. That is, in FIG. 4A , the first and second opposing portions 17A and 17B connected to one end (first electrode) 16 of the coupler 21 are capacitively coupled to the coupler connection portions 24A and 24B of JPO1 (20A) and JPO2 (20B) via coupling capacitors 31A and 31B, respectively, and the third and fourth opposing portions 19A and 19B connected to the other end (second electrode) 18 of the coupler 21 are capacitively coupled to the coupler connection portions 24C and 24D of JPO3 (20C) and JPO4 (20D) via coupling capacitors 31C and 31D, respectively.

[0043] The capacitance of the capacitors 206A to 206D of JPO1 (20A) to JPO4 (20D) is C Ｊ , the capacitance of the capacitor 15 of the coupler 21 is C ｇ , and the capacitance of the coupling capacitors 31A to 31D is C.

[0044] In this embodiment, the coupler 21 is configured to be able to increase the coupling coefficient of the four-body interaction of JPO1 (20A) to JPO4 (20D), as will be apparent from the following description.

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

[0046] The SQUID loop in FIG. 5(A) is a magnetic flux Φ extWhen the superconducting lines penetrate each other, the phase differences between the first and second Josephson junctions 11 and 12 are ψ1 and ψ2, respectively, and the linear inductance of the superconducting lines is ignored, the following holds true: (2.1)

[0047] In equation (2.1), φ ０ is the magnetic flux quantum in equation (1.5) above.

[0048] According to equation (2.1), (2.2)

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

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

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

[0052] As shown in FIG. 5B , the loop circuit 10 of this embodiment includes an array of n first Josephson junctions 11-1 to 11-n connected in series and spaced apart from one another 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 one another are, for example, tunnel junctions where the ends of a pair of adjacent superconducting lines, for n+1 superconducting lines 101-1 to 101-n+1, ​​are in contact with each other via an insulating film (oxide film). The superconducting lines 101-1 and 101-n+1 are connected to superconducting lines 103 and 104, respectively. The superconducting lines 103 and 104 may form first and second electrodes 16 and 18. The second Josephson junction 12 is 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), as in FIG. 5A.

[0053] For an array of n first Josephson junctions 11-1 to 11-n connected in series, the phase difference between both ends of the array (between nodes n1 and n2) is ψ1, and the phase difference at the second Josephson junction 12 is ψ2, and the above equation (2.2) holds. For the array of first Josephson junctions 11-1 to 11-n, the phase difference ψ1 between both ends of the array is equally divided into phase differences ψ / n, which is 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 sum of the individual potential energies of the n first Josephson junctions 11-1 to 11-n. (2.5) is given by adding n times. (2.6)

[0054] However, it is known that the above equation (2.6) holds when the capacitance of each first Josephson junction 11 is ignored. That is, when the capacitance of the first Josephson junction is C1 and the charging energy E C = e 2 In terms of / (2C1), exp{-√(8E Jｇ / E c )<<1 holds, and when the capacitance between the array of the first Josephson junctions 11-1 to 11-n and the ground is Cs, the condition C1 / Cs>>n holds (Non-Patent Documents 2 and 3, etc.).

[0055] The loop circuit 10 in FIG. 5B is connected to a magnetic flux Φ ext When penetrated, the potential energy is (2.7)

[0056] Here, the magnetic flux Φ penetrating the loop circuit 10 ext of (2.8).

[0057] In equation (2.8), Φ ０ is the magnetic flux quantum. (2.9)

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

[0059] From equation (2.8), (2.10)

[0060] therefore, Therefore, equation (2.7) becomes as follows.

[0061] (2.11)

[0062] The Josephson junction has a structure in which a junction barrier layer is sandwiched between two superconductors, and the barrier layer is made of an insulating layer or a non-magnetic metal layer. In this case, the critical current of the Josephson junction is I ０ If the phase difference across the junction (the phase difference between the wave functions in the two superconductors on either side of the junction) is ψ, the superconducting current (Josephson current) is given by (2.12) and the ground state (I S = 0), the phase difference ψ is 0 rad (radian). For this reason, it is also called a zero junction. A Josephson junction that uses a non-magnetic oxide film (such as AlOx) as the junction barrier layer is a zero junction.

[0063] In contrast, in a Josephson junction (ferromagnetic Josephson junction) that uses a ferromagnetic layer (e.g., copper-nickel alloy (CuNi), palladium-nickel alloy (PdNi), or a ferromagnetic insulating layer) as a barrier layer between the first and second superconductors, the junction alternates between a 0 junction and a π junction depending on the thickness of the ferromagnetic layer.

[0064] Here, the π junction is It is a junction that satisfies (2.13), and the phase difference from the 0 junction in the ground state is different by π rad. For example, when the film thickness dF of the ferromagnetic layer is less than or equal to 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, the phase difference can be shifted by π in the loop including the junction. In a loop including an odd number of π junctions, the phase difference around the loop is ±π×(odd number).

[0065] FIG. 5(C) is a diagram schematically showing an example of the loop circuit 10 using a π junction. Although not particularly limited, in the example of FIG. 5(C), n first Josephson junctions 11-1 to 11-n are 0 junctions, and the second Josephson junction 12 is a π junction. For an array of n first Josephson junctions 11-1 to 11-n connected in series, if the phase difference between both ends (between nodes n1 and n2) of the array is ψ1 and the phase difference at the second Josephson junction 12 is ψ2, a phase difference π will be generated additionally with respect to the phase difference ψ2 - ψ1 when going around the loop circuit 10, and the following holds. (2.14) Therefore, the potential energy of the second Josephson junction 12 is (2.15) and the potential energy V(ψ1) of the loop circuit 10 is the same as the above formula (2.11). That is, when the loop circuit 10 has a configuration including an odd number of π junctions (in FIG. 5(C), there is 1 π junction), without applying an external magnetic flux Φ ext to the loop circuit 10 (magnetic flux Φ ext = 0), it can be made equivalent to the state where the loop circuit 10 is biased with a magnetic flux Φ0 / 2 (or -Φ0 / 2) (where Φ0(=h / (2e)) is the magnetic flux quantum). Therefore, when the loop circuit 10 has a configuration including an odd number of π junctions, as shown in FIG. 4B, the magnetic field generation unit 14 and the control line 13 in FIG. 4A are unnecessary.

[0066] Here, regarding the potential energy of the loop circuit 10 of the coupler 21 in FIG. 4A or FIG. 4B, each notation in FIG. 5(B) or FIG. 5(C) is ψ1 = ψg, E Ｊ１ = E Ｊｇ, E Ｊ２ = αE Ｊｇ (where 0<α<1).

[0067] Then, equation (2.11) becomes the following equation (2.16). (2.16)

[0068] In equation (2.16), the Josephson energy E of each of the first Josephson junctions 11-1 to 11-n is Ｊｇ teeth (2.17) (I ｃｇ is the critical current of each first Josephson junction).

[0069] The Josephson energy E of the second Josephson junction 12 Ｊ２ is the Josephson energy E of each of the first Josephson junctions 11-1 to 11-n. Ｊｇ Since the Josephson energy is proportional to the critical current, the critical current of the second Josephson junction 12 is set to be α times (0<α<1) the critical current I of each of the first Josephson junctions 11-1 to 11-n. ｃｇ The critical current value 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 size of each of the first Josephson junctions 11-1 to 11-n, and the junction size of the second Josephson junction 12 is α times (0<α<1) the junction size of each of the first Josephson junctions 11-1 to 11-n. This is true whether the n first Josephson junctions 11-1 to 11-n and the second Josephson junction 12 are all 0 junctions or whether 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), cos is expanded by Taylor to obtain ψ g ４ Consider up to (ψ g 6 (ignore subsequent higher-order terms). (2.18)

[0071] however, (2.19) (2.20)

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

[0073] When n=1 and α=0, this consists of one first Josephson junction, which corresponds to the coupler of [1], and E Ｊｇ (2) = E Ｊｇ (4) = E Ｊｇ This becomes:

[0074] For n>=2, E Ｊｇ (2) ≠E Ｊｇ (4) This difference affects the coupling coefficient of the four-body interaction.

[0075] 6 is a diagram for explaining the four-body interactions of the four JPO1 (20A) to JPO4 (20D) described with reference to FIGS. 3 to 5, and corresponds to FIGS. 4A and 4B. Note that the magnetic field generating units 207A to 207D and 14 in FIG. 4A are not shown in FIG. 6. In FIG. 6, Josephson junctions are indicated by a symbol consisting of an x ​​surrounded by a square, and the Φ １ ~Φ ４ represents the magnetic flux passing through each SQUID loop. Ｊ represents the Josephson energy. (2.22)

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

[0077] Magnetic fluxes φ1 to φ4, φg1, and φg2 are placed at the nodes 1 to 4, g1, and g2, respectively (for details on the fluxes (magnetic fluxes) placed at each node, see, for example, Non-Patent Document 3). A classical Hamiltonian is established for the circuit in FIG.

[0078] (2.23)

[0079] In equation (2.23), C mat ―１ is the capacitance connection matrix (6 rows and 6 columns) C mat is the inverse matrix of

[0080] (2.24)

[0081] (2.25)

[0082] (2.26)

[0083] V(φ) is the sum of the potential energy Vsquid,i (i=1 to 4) of the SQUID of JPOi (i=1 to 4) and the potential energy Vcoupler of the coupler 21 of equation (2.20). (2.27)

[0084] Vsquid,i (i = 1 to 4) is the potential energy of the SQUIDs of JPO1 to 4 in equation (2.3), E Ｊ１ = E Ｊ２ = E Ｊ and ignore the term cos(ψi) and ｉ Taking out the terms including / φ0, (2.28)

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

[0086] Vcoupler is calculated by equation (2.16) and the flux φ at nodes g1 and g2 in FIG.g1 , φ g2 from, (2.29)

[0087] Regarding the Hamiltonian of the circuit shown in FIG. 6, the coordinate φ and momentum q are calculated as the boson (Cooper pair) creation and annihilation operator a ＋ , a, where the phase ψ ｋ =φ ｋ / φ ０ and the number of bosons (Cooper pairs) n ｋ =q ｋ / 2e (k=1,2,3,4,g1,g2) is quantized using boson creation and annihilation operators.

[0088] (2.30)

[0089] (2.31)

[0090] however, (2.32)

[0091] (2.33)

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

[0093] (2.35)

[0094] In equation (2.34), E C is the capacitor C Ｊ In equation (2.35), E' Ｃｇ represents the effective energy that takes into account the effect of coupling with the JPO in addition to the charging energy of the capacitor Cg of the coupler 21.

[0095] a ＋ ｋ and a ｋ (k=1,2,3,4,g1,g2) are the boson creation and annihilation operators. The coupler 21 has two flux degrees of freedom φｇ１ , φ ｇ２ There is.

[0096] ^ψ k and ｋ , a ｋ The following operators are defined for (k=g1, g2). (2.36) (2.37) (2.38)

[0097] In equation (2.36), (2.39)

[0098] In equation (2.37), (2.40)

[0099] Z in equation (2.39) and equation (2.40) ｇ is given by: (2.41)

[0100] cos(φ) in equation (2.28) i / φ0) is expanded to fourth order by Taylor and expressed as boson creation and annihilation operators as follows: (2.42)

[0101] In equation (2.28), JPO ｉ Magnetic flux Φ passing through each SQUID loop (i=1,2,3,4) ｉ A pump wave of angular frequency ωp,i is applied such that: (2.43)

[0102] Function V in equation (2.29) g is defined by equation (2.16), so cos((φ g1 -φ g2 ) / φ ０ ), which, like equation (2.42), (2.44)

[0103] The quantized Hamiltonian is given by:

[0104] (2.45)

[0105] In equation (2.45), H ＪＰＯ，ｉ Each JPO ｉ (i=1,2,3,4) Hamiltonian, given by the following equation (2.46): (2.46)

[0106] In equation (2.45), H coupler is the Hamiltonian of the coupler 21 and is given by the following equation (2.47). (2.47)

[0107] In equations (2.46) and (2.47), ω is a ｉ The resonant angular frequency of the JPO corresponding to ＋ , ω － is a ｇ＋ , a ｇ－ where the difference in angular frequency between different JPOs is not taken into consideration.

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

[0109] Also, in equation (2.45), s １ =s ２ = 1, s ３ =s ４ =-1 (2.48).

[0110] Since each JPO interacts with the coupler 21, it is thought that the JPOs also indirectly interact with each other through their interactions with the coupler 21. If a variable transformation is performed to incorporate the influence of the coupler 21 into each JPO, the interactions between JPOs 1 to 4 and the coupler 21 are transformed into four-body interactions between the JPOs. In other words, the Hamiltonian can be transformed into one in which the JPOs interact directly with each other. This transformation is expressed as a unitary transformation using the following unitary matrix U:

[0111] (2.49)

[0112] where ω, ω ＋ , ω － Haa ｉ , a ｇ＋ , a ｇ－ is the resonant angular frequency corresponding to (the frequency difference between different JPOs is not taken into account). ＋ / (ω-ω ＋ ), g － / (ω-ω － ) is 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 considers only one degree of freedom of 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 is different for each JPO. JPOs 1 to 4 are represented in a coordinate system that rotates at half the frequency of the pump signal that generates the magnetic flux penetrating the SQUID loops of JPOs 1 to 4. The pump frequency is different for each JPO. The transition to a rotating coordinate system introduces time-oscillating terms into the Hamiltonian, but these oscillating terms can be ignored because they are averaged over the time scale of interest here and positive and negative values ​​cancel each other out (rotating wave approximation).

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

[0115] (2.50)

[0116] In equation (2.50), H' JPO,i (i = 1, 2, 3, 4) is the Hamiltonian of JPO1 (20A) to JPO4 (20D).

[0117] H' coupler is the Hamiltonian of the 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) is a coefficient (coupling coefficient) representing the strength of coupling of the four-body interaction; a ratio α 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); the number n of the first Josephson junctions 11 connected in series in the coupler 21; a capacitance Cg of the coupler 21; a coupling capacitance C of the capacitive coupling between the coupler 21 and each JPO; and a resonant angular frequency ω of each JPO and a resonant angular frequency ω of the coupler 21. － and, the following equation (2.51) is obtained:

[0120] (2.51)

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

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

[0123] E Ｊ is the Josephson energy of the SQUID of each JPO.

[0124] ω － is the resonant angular frequency of the coupler 21 (boson operator a ｇ－ (resonant angular frequency corresponding to the (2.54)

[0125] In equation (2.54), E'cg is the combined capacitance: C ｇ +C charging energy, given by the following formula: (2.55)

[0126] In equation (2.54), E Ｊg （２） is given by equation (2.19), and the resonant angular frequency of the coupler 21 is given by the following equation: (2.56)

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

[0128] By changing n and α, the resonant angular frequency ω of the coupler 21 － When the value of is far from the resonant angular frequency ω of each JPO, the coupling coefficient g （４） becomes smaller. ω － The value of must be adjusted by parameters other than n and α. This is because the critical current I of each Josephson junction in the coupler 21 ｃｇ This can be achieved by adjusting the

[0129] Below, we consider specific circuit parameter settings and show the effect of adjusting n and α. Consider the following settings.

[0130]

[0131] The parameters of the Josephson junction are adjusted to realize the above frequency. The effect is due to the coupling coefficient g （４） The reason is as follows:

[0132] Coupling coefficient g of four-body interaction （４） According to equation (2.51), depending on the combination of n and α, （４） However, by adjusting other parameters not explicitly mentioned here, the value of g （４） The sign of can be changed.

[0133] Therefore, the coupling coefficient of the four-body interaction g （４） The sign of g is not essential, （４） It is sufficient to look only at the absolute value of

[0134] FIG. 7 shows the relationship between the coupling coefficient g of the four-body interaction when only α is changed, when the number n of the first Josephson junctions 11 connected in series in the coupler 21 is set to 1, 3, 5, and 10 under the above setting. （４） 7 is a graph showing the change in the absolute value of g （４） The absolute value of is divided by h / 2π and is expressed as a converted value in units of MHz (megahertz) (h is Planck's constant (approximately 6.6×10^(-34) joule seconds). The other parameters are fixed to the above set values. In particular, the resonant angular frequency ω － is also fixed.

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

[0136] According to the coupler 21 of the embodiment, n is set to 2 or more, and in a region where the value of α is large, particularly , the coupling coefficient of the four-body interaction g （４）The absolute value of the coupling coefficient of the four-body interaction can be increased significantly compared to the case where n = 1.

[0137] As described above, in the above embodiment, four-body interaction of quantum bits consisting of JPOs is realized, and the coupling coefficient g of the four-body interaction is calculated in the coupler 21. （４） The parameters n (the number of first Josephson junctions 11 in the coupler 21) and α (the ratio of the Josephson energies of the second Josephson junctions 12 and the first Josephson junctions 11, and the ratio of the junction sizes of the second Josephson junctions 12 and the first Josephson junctions 11) included in the above equation are adjusted, and in particular, within the range of α=<1 / n, the change in the resonant frequency of the coupler 21 caused by the change in α is avoided by adjusting the critical current Ic of the Josephson junctions, thereby making it possible to reduce the coupling coefficient g （４） The absolute value of can be increased.

[0138] Coupling coefficient g of the four-body interaction in equation (2.51) （４） is the capacitance C Ｊ , C ｇ , C, the factor (2.57).

[0139] Therefore, in addition to the circuit parameters n and α in the coupler 21, the capacitance C Ｊ , C ｇ , by setting the capacitance value of C, the coupling coefficient g of the four-body interaction （４） 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 four-body interaction （４） The denominator of C ｇ +C becomes smaller, and g （４） The value of becomes large.

[0141] Furthermore, the capacitance Cg of the capacitor 15 of the coupler 21 is set to the capacitance C of each JPO. Ｊ Make it smaller than.

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

[0143] These two-body interactions are C / C Ｊ 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 proportional to the capacitance C of each JPO. Ｊ Make it smaller than C Ｊ / C is large.

[0144] In Figures 4A and 4B, the configuration of the embodiment is described as a circuit diagram, but below we will explain an example of implementation on a quantum chip in which a superconducting circuit is formed in a wiring layer on a substrate, and then we will also explain the quantum annealing device.

[0145] Fig. 8 is a diagram showing a schematic example of the configuration of coupler 21 (wiring pattern formed on a substrate) when JPO1 (20A) to JPO4 (20D) in Fig. 4A are configured as lumped-element type. In Fig. 8, each of JPO1 (20A) to JPO4 (20D) has the configuration shown in Fig. 4A and is configured as a waveguide resonator terminated to ground by SQUIDs 210A to 210D, respectively. This waveguide resonator generates parametric oscillation by modulating the magnetic flux passing through each loop of SQUIDs 210A 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), coupler connection portions 24A to 24D extending from conductive portions (waveguides made of superconducting material) 205A to 205D connected to first superconducting portions 203A to 203D of SQUIDs 210A to 210D are capacitively coupled to the ends of first and second opposing portions 17B and third and fourth opposing portions 19A and 19B of coupler 21.

[0147] The coupler connection sections 24A to 24D of JPO1 (20A) to JPO4 (20D) may be configured, for example, as coplanar waveguides sandwiched between ground patterns (not shown) on both sides along the longitudinal direction with gaps between them, but of course, they are not limited to the above configuration.

[0148] The four-body interaction coupler 21 has first and second opposing portions 17A and 17B extending from the first electrode 16 toward the two JPOs 1 and 2 (20A and 20B), and the ends of the first and second opposing portions 17A and 17B face the ends of the coupler connection portions 24A and 24B of the JPOs 1 and 2 (20A and 20B) and are capacitively coupled via coupling capacitors 31A and 31B. The second electrode 18, which faces the first electrode 16, has third and fourth opposing portions 19A and 19B face the ends of the coupler connection portions 24C and 24D of the JPOs 3 and 4 (20C and 20D) and are capacitively coupled 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 via capacitors (coupling capacitors (C) 31A and 31B) to the ends of the coupler connection portions 24A and 24B of the JPOs 1 and 2 (20A and 20B) facing these portions, respectively. The ends of the third and fourth opposing portions 19A and 19B extending from the second electrode 18 are capacitively coupled via capacitors (coupling capacitors (C) 31C and 31D) to the ends of the coupler connection portions 24C and 24D of the JPOs 3 and 4 (20C and 20D) facing these portions, respectively. There are only gaps between the first and second opposing portions 17A and 17B and the coupler connection portions 24A and 24B facing them, respectively, and between the third and fourth opposing portions 19A and 19B and the coupler connection portions 24C and 24D facing them, respectively.

[0150] The first and second electrodes 16 and 18 are connected to each other by a capacitor (C ｇThe first and second electrodes 16, 18 are capacitively coupled via a capacitive coupling element 15. There is only an air gap between the first and second electrodes 16, 18.

[0151] 8, for simplicity, first and second opposing portions 17A, 17B and third and fourth opposing portions 19A, 19B extend from two side edges of rectangular first electrode 16 and second electrode 18, respectively, but it goes without saying that the planar shapes of first and second electrode 16 and electrode 18 are not limited to rectangular. First and second opposing portions 17A, 17B and third and fourth opposing portions 19A, 19B are each rectangular (oblong) with the same width in the longitudinal direction, but it goes without saying that the planar shapes are not limited to rectangular.

[0152] In the embodiment, the coupler 21 and JPO1 (20A) to JPO4 (20D) are realized by, for example, lines (wiring) formed of a superconductor on a substrate. The substrate is made of silicon (Si), 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 of the lines (wiring material) 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), titanium nitride, molybdenum (Mo), tantalum (Ta), tantalum nitride, or an alloy containing at least one of these metals. In addition, in order to minimize thermal noise, the coupler circuit is used in a temperature environment of about 10 mK (millikelvin) realized by a refrigerator.

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

[0154] 8, when an odd number of Josephson junctions among the n first Josephson junctions 11-1 to 11-n and the second Josephson junction 12 in the loop circuit 10 are π junctions, the phase difference circulating around the loop circuit 10 is ±π×(odd number), as described above. ext The loop circuit 10 can be biased 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 a current. Therefore, the control line 13 and magnetic field generator 14 connected to the current control unit (not shown) are not required.

[0155] Fig. 9A is a diagram showing a non-limiting example of the embodiment described above, and is a diagram showing a non-limiting example of the pattern (planar circuit) of the coupler 21 of Fig. 8. For convenience of drawing, Fig. 9A shows coupler connection portions 24A to 24D of JPO1 to JPO4, respectively.

[0156] Referring to FIG. 9A , the coupler 21 is disposed surrounded by a ground pattern (ground surface) 40. Although not particularly limited, the coupler connection sections 24A-24D of JPOs 1-4 are surrounded by ground patterns (ground surfaces) 40 on both sides with gaps between them, and the JPOs 1-4 themselves are also disposed surrounded by the ground pattern (ground surface) 40. As shown schematically in FIG. 9A , the coupler 21 is disposed away from the edge of the ground pattern (ground surface) 40 by a gap approximately the size of the coupler 21 (on the order of a fraction to several times that size). When the coupler 21 is on the order of 10-100 μm (several tens to several hundred μm), the gap spacing may be approximately on this order. In FIG. 9A , 41 denotes a region where no ground pattern is provided and the substrate is exposed.

[0157] 9A , the planar shape of the first electrode 16 is generally trapezoidal and rotated approximately 45 degrees counterclockwise relative to the horizontal direction of the drawing. The first and second opposing portions 17A and 17B of the first electrode 16 extend from the hypotenuse (leg) of the trapezoid toward the left and top of the drawing toward the coupler connection portions 24A and 24B of JPO1 and JPO2, respectively. The planar shape of the second electrode 18 is generally an inverted trapezoid rotated 180 degrees from the first electrode 16, and the third and fourth opposing portions 19A and 19B of the second electrode 18 extend from the hypotenuse toward the right and bottom of the drawing toward the coupler connection portions 24C and 24D of JPO3 and JPO4, respectively. The first electrode 16 and the second electrode 18 are disposed so that the bases of their respective trapezoids face each other, and the planar shape of the electrodes together with the main body excluding the facing portions is approximately hexagonal.

[0158] The first electrode 16 has a protrusion 16C protruding downward in the figure near the intersection of one end of the lower base and the oblique side, and the second electrode 18 has a cut portion 18C cut off so as to be parallel to the protrusion 16C of the first electrode 16 near the intersection of one end of the lower base and the oblique side, and the loop circuit 10 described with reference to FIG. 5C is provided between the protrusion 16C near the intersection of one end of the lower base of the first electrode 16 and the oblique side, and the cut portion 18C near the intersection of one end of the lower base of the second electrode 18 and the oblique side (note that the first Josephson junctions 11-1 to 11-n and the second Josephson junction 12 in FIG. 8 are not shown due to the difference in dimensions between the loop circuit 10 and the 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, even if a magnetic flux Φ0 / 2 is not applied to pass through the loop circuit 10, 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 becomes the same potential energy as equation (2.11).

[0159] On the other hand, FIG. 9B shows a state in which the n first Josephson junctions 11-1 to 11-n and the second Josephson junction 12 in the loop circuit 10 are all zero junctions, and the magnetic flux Φ ext9B is a diagram showing a non-limiting example of a pattern (planar circuit) of the coupler 21 when a magnetic flux Φ 0 / 2 (Φ 0 is a magnetic flux quantum = h / (2e)) is applied. ext The control line 13 is configured as a line with ground patterns 40 arranged on both sides of the control line 13 in the longitudinal direction with a gap therebetween, and its ends function as the magnetic field generating unit 14 in FIG. 8 and are connected to the ground (ground pattern 40) near the loop circuit 10. Therefore, near the loop circuit 10, the control line 13 has a portion 30 that causes the ground pattern 40 to protrude inward and approach the loop circuit 10. The control line 13 is connected to the magnetic flux Φ , which is generated by the magnetic field generating unit 14 (FIG. 8) and passes through the loop circuit 10. ext A direct current is supplied from a current control unit (not shown) so that the magnetic flux quantum Φ0 is 1 / 2 (=h / (4e)).

[0160] In the example shown in FIG. 9B , in order to efficiently apply a magnetic flux by inductive coupling with the control line 13 (line), the distance between the ground pattern 40 and only the electrodes in the vicinity of the Josephson junction loop circuit 10 among the first electrode 16 and the second electrode 18 is partially reduced, and by forming the control line 13 in the vicinity of the loop circuit 10, the magnetic flux Φ ext 9A , except for the portion 30 that is close to the loop circuit 10. While FIG. 9B shows an example in which the control line 13 and the magnetic field generator 14 of FIG. 8 are arranged on the same wiring layer as the coupler 21, the present invention is not limited to this configuration. Alternatively, the control line 13 and the magnetic field generator 14 may be provided at a position facing the loop circuit 10 of the coupler 21 or in the vicinity thereof on the surface of a wiring substrate (interposer) (not shown) on which a quantum chip including the coupler 21 is flip-chip mounted via bumps.

[0161] In the coupler 21 having the configuration shown in FIGS. 9A and 9B, the capacitance C Ｊ , the capacitance Cg of the capacitor (15 in FIG. 4A) of the coupler 21, the capacitance C of the coupling capacitor (31A-31D in FIG. 4A) between the coupler connection parts 24A-24D of JPO1 (20A) to JPO4 (20D) and the opposing parts 17A, 17B, 19A, 19B of the coupler 21, Ｊ >C ｇ >C.

[0162] Incidentally, Non-Patent Document 2 maintains a coupling device including an array of n first Josephson junctions connected in series and a superconducting loop circuit including a second Josephson junction connected in parallel to the array. The disclosure of the present application and the disclosure of Non-Patent Document 2 are compared. The following points are common to both documents.

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

[0164] The loop circuit of the Josephson junction includes an array in which n first Josephson junctions are connected in series, and one second Josephson junction connected in parallel to the array, the Josephson energy of the second Josephson junction is α times that of the first Josephson junction, and an external magnetic flux Φ ext = h / (4e) = πφ ０ By setting α≒1 / n, the interaction coefficient between quantum bits can be increased.

[0165] There are a number of differences between the disclosure of this application and that of Non-Patent Document 2.

[0166] For example, the types of interactions generated by the coupler 21 are different. In the present disclosure, the coupler 21 is used to generate four-body interactions of quantum bits (JPOs), whereas in Non-Patent Document 2, this coupler is used to generate two-body interactions of quantum bits (Non-Patent Document 2 does not mention four-body interaction couplers 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 between JPO3 and JPO4, which are connected without a coupler for four-body interactions in between. In this embodiment, a coupling capacitor is required between the quantum bit (JPO) and coupler 21. Non-Patent Document 2 does not have a corresponding capacitor.

[0168] The presence or absence of this capacitor also results in the following differences.

[0169] In the disclosure of the present application, resonance occurs in the coupler 21, whereas in Non-Patent Document 2, resonance of the coupler itself is not considered. （４) ω appears in － Nothing corresponding to this appears in Non-Patent Document 2.

[0170] In order to increase the strength of the four-body interaction (coupling coefficient), the resonant angular frequency ω － The technique of adjusting the value of (preventing it from changing) is unique to this application.

[0171] Furthermore, in Non-Patent Document 2, the coupler is applied to two-body interactions, which is different from four-body interactions. Therefore, the coupling coefficients of the interactions presented in Non-Patent Document 2, such as χ(quarton) in Equation (7), are different from the coupling coefficients of the four-body interactions in Equation (2.51) of the present application. （４） It is completely different from.

[0172] As described above, the main difference is that the disclosure of the present application deals with four-body interactions of qubits, while Non-Patent Document 2 deals with two-body interactions of qubits. As a result, there are differences in the presence or absence of a capacitor between the qubit and the coupler, the presence or absence of resonance in the coupler, the necessity of adjusting the resonant frequency of the coupler, and the expressions for the interaction coefficients.

[0173] In order to increase the coupling coefficient of the four-body interaction in equation (2.51), according to this embodiment, in addition to setting the circuit parameters n and α of the coupler 21, the shunt capacitor C 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 By setting it to >C, the coupling coefficient g （４） can be made large.

[0174] Furthermore, the resonant angular frequency ω of each JPO and the resonant angular frequency ω of the coupler 21 are － More specifically, the factor (ωω) in the four-body interaction strength formula (2.51) － ) ２ / (ω-ω － ) ４ Regarding (2.59), for example, δ is set to satisfy the following condition:

[0175] (2.60)

[0176] FIG. 10 is a schematic diagram showing the configuration of a quantum computer 300 integrating JPOs 20 as a configuration example of another embodiment. In the configuration shown in FIG. 10 , each four-body interaction coupler 21 is connected to four JPOs 20, as shown in FIGS. 4A , 4B , and 8 . Each JPO 20 is connected to one to four four-body interaction couplers 21, and the JPO 20 is shared and arranged among multiple unit structures, thereby arranging the unit structures shown in FIGS. 4A , 4B , 8 , etc. In the quantum computer 300, at least one JPO 20 is connected to multiple four-body interaction couplers 21. In particular, in the example shown in FIG. 10 , at least one JPO 20 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 JPOs 20, each connected to one to four four-body interaction couplers 21. The number of four-body interaction couplers 21 connected to each JPO 20 corresponds to the number of unit structures to which the JPO 20 is shared. Thus, in the example shown in FIG. 10 , the quantum computer 300 has multiple unit structures, and the JPO 20 is shared by multiple unit structures. In the example shown in FIG. 10 , 13 superconducting nonlinear JPOs 20 are integrated, but any number of JPOs 20 can be integrated in a similar manner. Note that the current control unit and readout unit are omitted in FIG. 10 to facilitate understanding of the drawing. However, as described with reference to FIG. 3 , the JPOs 20 are controlled and readout using the current control unit and readout unit.

[0177] The disclosure of the above embodiment is supplemented as follows (however, it goes without saying that the disclosure is not limited to the following).

[0178] (Supplementary Note 1) A superconducting quantum circuit comprises first to fourth quantum bits and a coupler that couples the first to fourth quantum bits through four-body interaction, the coupler comprising 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 that are spaced apart from each other and arranged in series, and a second Josephson junction that is arranged in parallel with the n first Josephson junctions and has a junction size smaller than that of the first Josephson junctions, the first and second quantum bits are each capacitively coupled to the one end of the coupler, and the third and fourth quantum bits are each capacitively coupled to the other end of the coupler, The magnitude of the coupling coefficient of the four-body interaction by the coupler can be freely set based on circuit parameters including 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] (Supplementary Note 2) In the superconducting quantum circuit according to Supplementary Note 1, in the coupler, α may be set to a predetermined value that is smaller than the reciprocal 1 / n of n and close to 1 / n.

[0180] (Supplementary Note 3) The loop circuit may be biased with a magnetic flux ±Φ0 / 2×(2k+1) (where Φ0 (=h / (2e)) is a magnetic flux quantum: h is Planck's constant, and e is an elementary charge). The superconducting quantum circuit described in Supplementary Note 1 or 2 may include a magnetic field generation unit that applies a direct current from a current control unit to generate Φ0 / 2 or −Φ0 / 2 as a magnetic flux that penetrates the loop circuit of the coupler.

[0181] (Supplementary Note 4) In the superconducting quantum circuit described in Supplementary Note 1 or 2, an odd number (2k+1, k is a predetermined non-negative integer) of the n first Josephson junctions and the n second Josephson junctions in the loop circuit may be π junctions, and the remaining may be 0 junctions. With this configuration, the phase difference when going around the loop circuit is ±π×(2k+1), and without applying a magnetic flux that penetrates the loop circuit, the loop circuit becomes equivalent to a state biased with a magnetic flux ±Φ0 / 2×(2k+1) (where Φ0 (=h / (2e)) is a magnetic flux quantum: h is Planck's constant, and e is an elementary charge).

[0182] (Supplementary Note 5) In the superconducting quantum circuit according to any one of Supplementary Notes 1 to 4, the loop circuit of the coupler comprises a first electrode and a second electrode arranged opposite each other and spaced apart from a ground pattern in a region surrounded by the ground pattern in a wiring layer on a substrate, the n (n is a positive integer of 2 or more) first Josephson junctions and the n second Josephson junctions are respectively arranged in parallel between the first electrode and the second electrode, the first electrode comprises first and second opposing portions extending from a position of the first electrode different from the side opposing the second electrode toward the first and second quantum bits, and the ends of the first electrode are respectively opposed to and capacitively coupled with ends of the coupler connection portions of the first and second quantum bits, and the second electrode The second electrode may include third and fourth opposing portions that extend from a position on the second electrode other than the side facing the first electrode toward the third and fourth quantum bits, and whose ends face and capacitively couple with ends of the coupler connection portions of the third and fourth quantum bits, respectively.

[0183] (Supplementary Note 6) In the superconducting quantum circuit described in Supplementary Note 5, each of the first to fourth quantum bits includes a Josephson parametric oscillator, the Josephson parametric oscillator having: a SQUID (superconducting quantum interference device) having two Josephson junctions at both ends of a crossing between a first superconducting line and a second superconducting line that form a loop; a capacitor connected in parallel to the SQUID; and a line that is inductively coupled to the SQUID and generates a magnetic flux that penetrates the loop of the SQUID; one of the first superconducting line and the second superconducting line of the SQUID is set to ground potential; and the other of the first superconducting line and the second superconducting line of the SQUID is connected to the coupler connection portion, and the oscillator may be configured to parametrically oscillate in accordance with a microwave current supplied to the line.

[0184] (Supplementary Note 7) In the superconducting quantum circuit according to Supplementary Note 6, the circuit parameters that define the coupling coefficient of the four-body interaction include, in addition to α and n, a capacitance value C of the capacitive coupling between the coupler connection part of the first to fourth quantum bits and each of the first to fourth opposing parts of the coupler, and a capacitance value C of the capacitor connected in parallel to the SQUID of each of the first to fourth quantum bits. Ｊ , the value C of the capacitance between the first and second electrodes of the coupler ｇ The relationship between these capacitances is as follows: C Ｊ >C ｇ >C.

[0185] (Supplementary Note 8) In the superconducting quantum circuit according to Supplementary Note 6 or 7, the coupling coefficient of the four-body interaction is determined by: the α and the n; a capacitance value C of the capacitive coupling between the coupler connection part of the first to fourth quantum bits and each of the first to fourth opposing parts of the coupler; and a capacitance value C of the capacitor connected in parallel to the loop circuit of each of the first to fourth quantum bits. Ｊ, the value C of the capacitance between the first and second electrodes of the coupler ｇ , the resonant angular frequency ω of the coupler - and the circuit parameters of the difference ω in the resonant angular frequency of each quantum bit, The configuration may be expressed as follows.

[0186] (Supplementary Note 9) A superconducting quantum circuit device, wherein the superconducting quantum circuit according to any one of Supplementary Notes 1 to 8 constitutes a quantum computer having, as unit structures, the first to fourth quantum bits that perform Josephson parametric oscillation and the coupler.

[0187] (Supplementary Note 10) The superconducting quantum circuit device described in Supplementary Note 9 may comprise a quantum computer having a plurality of the unit structures, wherein the unit structures share at least one quantum bit among the first to fourth quantum bits constituting the unit structures with one or more other unit structures.

[0188] The disclosures of Patent Documents 1 and 2 and Non-Patent Documents 1-5 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 appendix, each element of each example, each element of each drawing, etc.) are possible within the scope of the claims of the present invention. In other words, the present invention naturally includes various modifications and alterations that would be possible for a person skilled in the art in accordance with the entire disclosure, including the scope of the claims, and the technical ideas thereof.

[0189] 1 Superconducting quantum circuit 10 Loop circuit (nonlinear element) 11, 11-1 to 11-n First Josephson junction 12 Second Josephson junction 13 Control line 14 Magnetic field generating unit 15 Capacitor 16 Electrode (first electrode) 16C Protrusion 17A, 17B First and second opposing portions 18 Electrode (second electrode) 19A, 19B Third and fourth opposing portions 20A to 20D, 120A to 120D Superconducting quantum bit (JPO) 21, 121 Coupler 122A to 122D Readout circuit connection portion 23A to 23D, 123A to 123D Control line (flux line) 24A to 24D, 124A to 124D Coupler connection portion 30 Portion (ground pattern protruding portion) 31A to 31D Capacitor (coupling capacitor) 40 Ground (GND) pattern (ground plane) 41 Surface of substrate 101-1 to 101-n Superconducting lines 102-1, 102-2 Superconducting lines 103, 104 Superconducting lines 110 Nonlinear elements 132A to 132D Capacitors 140A to 140D Readout circuits 150A to 150D Signal generation units 201A, 201B, 201C, 201D First Josephson junctions 202A, 202B, 202C, 202D Second Josephson junctions 203A, 203B, 203C, 203D First superconducting section 204A, 204B, 204C, 204D Second superconducting section 205A, 205B, 205C, 205D Conductive portion 206A, 206B, 206C, 206D Capacitor 207A, 207B, 207C, 207D Magnetic field generating portion 300 Quantum computer

Claims

1. First to fourth quantum bits; a coupler that couples the first to fourth quantum bits through a four-body interaction; Equipped with The coupler comprises: a loop circuit connected between one end and the other end of the coupler; A capacitor connected in parallel to the loop circuit; Equipped with The loop circuit includes: n (n is a positive integer equal to or greater than 2) first Josephson junctions arranged in series and spaced apart from one another; a second Josephson junction arranged in parallel with the n first Josephson junctions and having a junction size smaller than that of the first Josephson junctions; having the first and second quantum bits are capacitively coupled to the one end of the coupler, the third and fourth quantum bits are capacitively coupled to the other end of the coupler, The magnitude of the coupling coefficient of the four-body interaction by the coupler is at least The n, a ratio α (0<α<1) between the Josephson energy of the second Josephson junction and the Josephson energy of the first Josephson junction; The superconducting quantum circuit can be freely set based on circuit parameters including:

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

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

4. Among the n number of the first Josephson junctions and the n number of the second Josephson junctions in the loop circuit, an odd number (2k+1, k is a predetermined non-negative integer) are π junctions, and the remaining are 0 junctions, The phase difference when going around the loop circuit is ±π×(2k+1), and the loop circuit has a magnetic flux of ±Φ 0 / 2 × (2k + 1) (where Φ 0 2. The superconducting quantum circuit of claim 1, wherein the superconducting quantum circuit is biased with a magnetic flux quantum (=h / (2e)), where h is Planck's constant and e is an elementary charge.

5. the loop circuit of the coupler includes a first electrode and a second electrode disposed opposite each other and spaced apart from the ground pattern in a region surrounded by the ground pattern in a wiring layer on a substrate; the n (n is a positive integer of 2 or more) first Josephson junctions; the second Josephson junction; are disposed in parallel between the first electrode and the second electrode, The first electrode is a first electrode extending from a position other than the side facing the second electrode to the first and second quantum bit sides, the first electrode and the second electrode extending from the second electrode to the first and second quantum bit sides, the first and second opposing portions each having an end facing an end of a coupler connection portion of the first and second quantum bit, and capacitively coupled to the end of the coupler connection portion of the first and second quantum bit, The second electrode is 2. The superconducting quantum circuit device according to claim 1, further comprising third and fourth opposing portions each extending from a position of the second electrode other than the side facing the first electrode toward the third and fourth quantum bit sides, the ends of which face and capacitively couple with the ends of the coupler connection portions of the third and fourth quantum bits, respectively.

6. each of the first to fourth quantum bits includes a Josephson parametric oscillator; The Josephson parametric oscillator comprises: a SQUID (superconducting quantum interference device) having two Josephson junctions at both ends of a crossing between a first superconducting line and a second superconducting line that form a loop; a capacitor connected in parallel to the SQUID; a line that is inductively coupled to the SQUID to generate a magnetic flux that penetrates the loop of the SQUID; having one of the first superconducting line and the second superconducting line of the SQUID is set to a ground potential; the other of the first superconducting line and the second superconducting line of the SQUID is connected to the coupler connection portion; 6. The superconducting quantum circuit according to claim 5, which parametrically oscillates in accordance with a microwave current supplied to the line.

7. The circuit parameters defining the coupling coefficient of the four-body interaction are In addition to the α and the n, a 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 counter portions of the coupler; The capacitance value C of the capacitor connected in parallel to the SQUID of each of the first to fourth quantum bits Ｊ , The value of the capacitance between the first and second electrodes of the coupler, C ｇ Including, The relationship between these capacitances is C Ｊ >C ｇ >C 7. The superconducting quantum circuit of claim 6, wherein the

8. The coupling coefficient of the four-body interaction is The α and the n, a 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 counter portions of the coupler; The capacitance value C of the capacitor connected in parallel to the SQUID of each of the first to fourth quantum bits Ｊ , The value of the capacitance between the first and second electrodes of the coupler, C ｇ , The resonant angular frequency ω of the coupler - Regarding the circuit parameters of the difference ω between the resonant angular frequencies of the quantum bits and The superconducting quantum circuit of claim 6 ,

9. The superconducting quantum circuit device according to any one of claims 1 to 8, a quantum computer having, as unit structures, the first to fourth quantum bits which undergo Josephson parametric oscillation and the coupler;

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

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