Quantum circuit device and its control method

Abstract

To provide a quantum circuit device that can suppress cross-Kerr interactions between qubits and couplers and / or cross-Kerr interactions between qubits. [Solution] The quantum circuit device comprises N qubits (where N is a predetermined integer of 3 or more) coupled by many-body interaction via a coupler, wherein a parameter representing the nonlinearity of at least one of the N qubits has a different sign from the sign of the parameter representing the nonlinearity of the coupler and / or other qubits.

Description

[Technical Field]

[0001] This disclosure relates to a quantum circuit device and a method for controlling the same. [Background technology]

[0002] The LHZ (Lechner, Hauke, Zoller) scheme, one of the quantum annealing methods for solving combinatorial optimization problems, requires a bit interaction called a four-body interaction (Non-Patent Literature 1). Non-Patent Literature 2 discloses a network based on four-body interaction of four qubits and one coupler, as shown in Figure 1, as a physical implementation of the LHZ scheme. Figure 1 is based on Figure 4a of Non-Patent Literature 2. In the example in Figure 1, a configuration is used in which, for example, a Josephson Parametric Oscillator (JPO) is used as the qubit and a Josephson Junction (JJ) is used as the coupler. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Lechner, Hauke, Zoller, "A quantum annealing architecture with all-to-all connectivity from local interactions", Science Advances 23 Oct 2015 Vol 1, Issue 9 :DOI: 10.1126 / sciadv.1500838 [Non-Patent Document 2] Shruti Puri, Christian Kraglund Andersen, Arne L. Grimsmo, Alexandre Blais, "Quantum annealing with a network of all-to-all connected, two-photon driven Kerr nonlinear oscillators", Nature Commun 8, 15785 (2017) [Overview of the initiative] [Problems that the invention aims to solve]

[0004] A qubit is a resonator with nonlinearity. The circuit in Figure 1 has two types of cross-Kerr interactions: a cross-Kerr interaction between qubits and a cross-Kerr interaction between a qubit and a coupler. This cross-Kerr interaction is known to have adverse effects on circuit operation, such as changing the resonant frequency of the qubits.

[0005] This disclosure aims to provide a quantum circuit device and a control method thereof that solves the above-mentioned problems. [Means for solving the problem]

[0006] According to one embodiment of the quantum circuit device of the present disclosure, it comprises N qubits (where N is a predetermined integer of 3 or more) coupled by many-body interaction via a coupler, wherein a parameter representing the nonlinearity of at least one of the N qubits has a different sign from the sign of a parameter representing the nonlinearity of the coupler and / or other qubits.

[0007] According to one embodiment of the present disclosure, a method for controlling a many-body interaction in a quantum circuit device including N qubits (where N is a predetermined integer of 3 or more) coupled in a many-body interaction via a coupler, wherein the sign of a parameter representing the nonlinearity of at least one of the N qubits is set to be different from the sign of a parameter representing the nonlinearity of the coupler and / or other qubits. [Effects of the Invention]

[0008] According to this disclosure, it is possible to suppress cross-Kerr interactions between qubits and couplers and / or cross-Kerr interactions between qubits. [Brief explanation of the drawing]

[0009] [Figure 1] This is a diagram illustrating an example of the disclosure in Non-Patent Document 2. [Figure 2] This figure illustrates an example of some embodiments of the present disclosure. [Figure 3] (A) and (B) are diagrams illustrating some examples of embodiments of the present disclosure, respectively. [Figure 4] This figure illustrates an example of some embodiments of the present disclosure. [Figure 5] This figure illustrates an example of some embodiments of the present disclosure. [Figure 6] (A) and (B) are diagrams illustrating some examples of embodiments of the present disclosure, respectively. [Figure 7] Figures (A), (B), and (C) illustrate, respectively, some examples of embodiments of the present disclosure. [Figure 8] This figure illustrates an example of some embodiments of the present disclosure. [Figure 9] This figure illustrates an example of some embodiments of the present disclosure. [Figure 10] This figure illustrates an example of some embodiments of the present disclosure. [Figure 11]This diagram illustrates one example of several embodiments of the present disclosure, specifically a quantum annealing machine. [Modes for carrying out the invention]

[0010] Embodiments of this disclosure will now be described. According to some embodiments of this disclosure, quantum circuit devices are disclosed in which cross-Kerr interactions between qubits and cross-Kerr interactions between qubits and qubit-couplers are suppressed by combining qubits and couplers with different signs (polarities) of nonlinearity, as will be described in detail below.

[0011] First, as a premise for this disclosure, we will analyze the configuration shown in Figure 1 and explain its challenges in detail. Referring to Figure 1, the quantum circuit device 1 includes four qubits 20-1 to 20-4 and a coupler 21. More specifically, the first qubit 20-1 includes a SQUID 210A in which a member that becomes superconducting at extremely low temperatures (superconducting member) 203A, a Josephson junction 201A, a superconducting member 204A, and a Josephson junction 202A form a loop. The superconducting member 203A is connected to electrode 24A, the superconducting member 204A is connected to ground, and a capacitor 206A (shunt capacitor) is connected in parallel to the SQUID 210A between electrode 24A and ground. During operation, a magnetic flux is generated that penetrates the SQUID 210A by passing a current from a signal source (not shown) through an inductor (magnetic field generating unit) (not shown). The resonant angular frequency ω1 of the first qubit 20-1 is varied according to the magnetic flux passing through SQUID210A. For the second to fourth qubits 20-2 to 20-4, the superconducting members corresponding to the superconducting member 203A of the first qubit 20-1 are 203B to 203D, the Josephson junctions corresponding to the Josephson junction 201A of the first qubit 20-1 are 201B to 201D, the superconducting members corresponding to the superconducting member 204A of the first qubit 20-1 are 204B to 204D, the Josephson junctions corresponding to the Josephson junction 202A of the first qubit 20-1 are 202B to 202D, the SQUIDs corresponding to SQUID210A of the first qubit 20-1 are 210B to 210D, and the capacitors corresponding to the capacitor 206A of the first qubit 20-1 are 206B to 206D. During operation, by passing a current from a signal source (not shown) through an inductor (magnetic field generating unit) (not shown), magnetic flux is generated that penetrates SQUID210B to 210D, and the resonant angular frequencies ω2 to ω4 of the second to fourth qubits 20-2 to 20-4 are varied according to the magnetic flux penetrating SQUID210B to 210D.

[0012] The coupler 21 comprises a Josephson junction 10 and a capacitor 16 connected in parallel between a first electrode (first node) 17 and a second electrode (second node) 18. The first electrode 17 is connected to the first qubit 20-1 and the second qubit 20-2 via coupling capacitors 31A and 31B (capacitive coupling), and the second electrode 18 is connected to the third qubit 20-3 and the fourth qubit 20-4 via coupling capacitors 31C and 31D (capacitive coupling). In the following, unless the qubit number is specifically identified, the sub-number of the reference numeral 20 is removed, and it will be referred to as qubit 20, etc. The same applies to other elements.

[0013] In the circuit shown in Figure 1, there are two types of cross-Kerr interactions (abbreviated as "CKI"): one acting between qubits 20 ("QQ-CKI") and one acting between qubit 20 and coupler 21 ("QC-CKI").

[0014] QQ-CKI is proportional to the sum of the nonlinearities of the 20 qubits. There are 4! / 2! = 4 × 3 / 2 = 6 types of QQ-CKI, and each of them is... (K1+K2) (K1+K3) (K1+K4) (K2+K3) (K2 + K4) It is proportional to (K3 + K4).

[0015] Here, K i (i=1,2,3,4) are parameters (Kerr coefficients) that represent the nonlinearity (Kerr nonlinearity) of the i-th qubit 20-i. i This is also called the nonlinear parameter of the i-th qubit 20-i. i This is the Hamiltonian H of the i-th qubit (JPO) 20-i (i=1,2,3,4) in Figure 1. i When expressed by the following equation (1), TIFF2026142955000002.tif7150…(1) Kerr nonlinearity K ican be made to correspond to.

[0016] In Equation (1), Δ is half the difference between the resonant angular frequency ω of the coupler 21 c and the angular frequency ωp of the i-th pump signal Δ=ω c -(1 / 2)ωp …(2) wherein Εp is the strength of two-photon driving (pump term). a i + and a i are the creation operator and annihilation operator of bosons (photons) in the i-th qubit 20-i, respectively.

[0017] QC-CKI is proportional to the sum of the nonlinearity of the qubits 20 and the nonlinearity of the coupler 21. There are four types of QC-CKI corresponding to the first to fourth qubits 20-1 to 20-4, which are respectively (K1+K g ), (K2+K g ), (K3+K g ), (K4+K g ) are proportional. Here, K g is a parameter (Kerr coefficient) representing the nonlinearity (Kerr nonlinearity) of the coupler 21. K g is also referred to as the nonlinear parameter of the coupler 21.

[0018] As described above, it is known that cross-Kerr interaction adversely affects circuit operation, such as changing the resonant frequency of the qubits 20.

[0019] The above problem is one example. According to the present disclosure, the contribution of the nonlinearity of the qubits 20 in the multi-body interaction between the qubits 20 can be suppressed in various situations without being limited to the above.

[0020] Regarding the circuit shown in Figure 1, according to Non-Patent Literature 2, the conditions for the four-body interaction of the four qubits 20-1 to 20-4 are set, for example, as follows: the angular frequencies ωp,i (i=1,…,4) of the respective pump signals.

[0021] ω p,1 +ω p,2 =ω p,3 +ω p,4 …(3)

[0022] In the Hamiltonian after the rotational wave approximation for the quantum circuit shown in Figure 1, TIFF2026142955000003.tif6150…(4) This leads to a four-body interaction bond of the form (the four-body interaction bond term in the Hamiltonian has a minus sign in equation (4)). In equation (4), a i a i + (i=1,2,3,4) are the annihilation and creation operators for bosons in each qubit, respectively.

[0023] Strength of tetra-body interaction (binding coefficient) g (4) teeth, TIFF2026142955000004.tif9150…(5) It is given by and depends on the nonlinearity of the Josephson junction (JJ) of the coupler and the difference (detuning) between the resonant frequencies of the qubit and the coupler.

[0024] In equation (5), K g This parameter represents the nonlinearity (Kerr nonlinearity) of the coupler 21. g This is also called the nonlinear parameter of the coupler 21. Δ i (i=1,2,3,4) is the resonant angular frequency ω of the coupler 21. c and the resonant angular frequency ω of the i-th qubit i The difference (detune) (=ω c -ω i ) g i(i=1,2,3,4) represents the magnitude (strength) of the connection between the i-th qubit 20-i and the coupler 21.

[0025] From equation (5), TIFF2026142955000005.tif9150…(6) Detuning Δ within the range i If we make it as small as possible, the coupling coefficient g of the four-body interaction (4) The resonant angular frequency ω of each qubit 20 becomes large, and the four-body interaction becomes strong. Therefore, the resonant angular frequency ω of each qubit 20 is large. i (i=1,2,3,4) and the resonant angular frequency ω of the coupler c It needs to be somewhat close to that.

[0026] In equation (5), g i / Δ i Approximating (i=1,2,3,4) with g / Δ, the nonlinear parameter K of the coupler g The fourth term of g / Δ: (g / Δ) 4 This means that a charge is applied.

[0027] From equation (5), the nonlinear parameter K of the coupler 21 is obtained. g Increasing the coefficient of the four-body interaction g (4) However, the nonlinear parameter K of the coupler 21 is large. g This includes (g / Δ) to the power of 4 (g / Δ) which is less than 1. 4 This is the case. Therefore, the coupling coefficient g of the four-body interaction via the coupler 21 is (4) This basically only results in a small value. That is, in the circuit of Figure 1, the coupling coefficient g of the four-body interaction via the coupler 21. (4) It is generally difficult to consider something as large.

[0028] According to this disclosure, in addition to the challenge of suppressing the cross-Kerr interaction described above, the coupling coefficient g of the four-body interaction via the coupler 21 is also addressed. (4) The coefficient h represents the strength of the four-body interaction coupling due to the nonlinearity of qubit 20 (Kerr nonlinearity). (4) By combining these, it is also possible to increase the four-body interaction.

[0029] Figure 2 is a schematic diagram illustrating an example of an embodiment of the present disclosure. In Figure 2, the first to fourth qubits 20-1 to 20-4 are connected to the coupler 21 via coupling capacitors 31A to 31D (capacitive coupling) and coupled by a four-body interaction.

[0030] In Figure 2, for example, • Set the nonlinear parameters K1 to K4 of the first to fourth qubits 20-1 to 20-4 to the same value K, • Nonlinear parameter K of coupler 21 g Set it to -K. In this case, the sum of the nonlinearities of the qubit 20 and the coupler 21 is: (K1 + K g ), (K2+K g ), (K3+K g ), (K4+K g The QC-CKI values ​​proportional to each of these values ​​are all 0.

[0031] While not particularly limited, in Figure 2, for example, the first to fourth qubits 20-1 to 20-4 may be composed of JPOs having SQUIDs, and the coupler 21 may be composed of a JPO including a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement).

[0032] Furthermore, although not particularly limited, for example, the nonlinear parameters K1 to K4 of the first to fourth qubits 20-1 to 20-4 may be set to positive values, and the nonlinear parameter K of the coupler 21 may be set to positive values. g For example, you could set it to a negative value. Alternatively, for example, set the nonlinear parameters K1 to K4 of the first to fourth qubits 20-1 to 20-4 to negative values, and set the nonlinear parameter K of the coupler 21. g For example, this can be set to a positive value. This makes it possible to suppress the influence of the cross-Kerr interaction (QC-CKI) between the qubit 20 and the coupler 21 that contribute to the four-body interaction.

[0033] In Figure 2, the coupler 21 may be configured as a JPO equipped with SNAIL221, for example, as shown in Figure 3(A). SNAIL221 is configured such that a Josephson junction 212 and N (N≧2) Josephson junctions 213-1 to 213-N connected in series are connected in parallel between the first electrode (first node) 17 and the second electrode (second node) 18 (the Josephson junction 212 and Josephson junctions 213-1 to 213-N form a loop). The Josephson energy E of the Josephson junction 212 J2 The Josephson energies E of each Josephson junction 213-1 to 213-N are Jg It is set to α times (0 < α < 1). Since the Josephson energy is proportional to the critical current, the critical current of Josephson junction 212 is the critical current I of Josephson junctions 213-1 to 213-N. cg It is assumed 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 Josephson junction 212 is smaller than the junction sizes of Josephson junctions 213-1 to 213-N, and the junction size of Josephson junction 212 is assumed to be α times (0 < α < 1) the junction size of Josephson junctions 213-1 to 213-N. By connecting Josephson junctions 213-1 to 213-N in series, the nonlinearity is weakened. It should also be noted that the qubit 20 may also be configured in a SNAIL configuration, as shown in Figure 3(B).

[0034] Figure 4 shows an example of the configuration shown in Figure 2. Referring to Figure 4, in the quantum circuit device 1, the first qubit 20-1 includes a SQUID 210A in which a superconducting member 203A, a Josephson junction 201A, a superconducting member 204A, and a Josephson junction 202A form a loop. The superconducting member 203A is connected to electrode 24A, the superconducting member 204A is connected to ground, and a capacitor 206A (shunt capacitor) is connected in parallel to the SQUID 210A between electrode 24A and ground. By passing current through an inductor (not shown), a magnetic flux is generated that penetrates the SQUID 210A, and by varying this magnetic flux, the resonant angular frequency ω1 of the first qubit 20-1 is varied. For the second to fourth qubits 20-2 to 20-4, the superconducting members corresponding to the superconducting member 203A of the first qubit 20-1 are designated as 203B to 203D, the Josephson junctions corresponding to the Josephson junction 201A of the first qubit 20-1 are designated as 201B to 201D, the superconducting members corresponding to the superconducting member 204A of the first qubit 20-1 are designated as 204B to 204D, the superconducting members corresponding to the Josephson junction 202A of the first qubit 20-1 are designated as 202B to 202D, the SQUIDs corresponding to the SQUID 210A of the first qubit 20-1 are designated as 210B to 210D, and the capacitors corresponding to the capacitor 206A of the first qubit 20-1 are designated as 206B to 206D. The electrodes 24A and 24B of the first qubit 20-1 and the second qubit 20-2 are connected to the first electrode (first node) 17 of the coupler 21 via coupling capacitors 31A and 31B, and the electrodes 24C and 24D of the third qubit 20-3 and the fourth qubit 20-4 are connected to the second electrode (second node) 18 of the coupler 21 via coupling capacitors 31C and 31D.

[0035] The coupler 21 includes a parallel circuit of SNAIL 221 and capacitor 16 between the first electrode (first node) 17 and the second electrode 18 (second node). SNAIL 221 includes a first Josephson junction 212-1 and two second Josephson junctions 213-1 and 213-2 connected in series. Of course, the number of second Josephson junctions 213 connected in series is not limited to two.

[0036] The nonlinear parameters K1 to K4 of the first to fourth qubits 20-1 to 20-4 are set to have the same sign, and the nonlinear parameter K of the coupler 21 is set to K g If we set this to have the opposite sign to the nonlinear parameters K1 to K4 of the first to fourth qubits 20-1 to 20-4, (K1+K g ), (K2+K g ), (K3+K g ), (K4+K g The value of (if negative, the absolute value) will be small, and the QC-CKI values ​​proportional to each will also be small.

[0037] Also, K1=K2=K3=K4=K>0,K g = -K < 0 …(7) or, K1=K2=K3=K4=K<0,K g =-K>0 …(8) In that case, (K1+K g )=(K²+K g )=(K3+K g )=(K⁴+K g )=0 …(9) As a result, the proportional QC-CKI values ​​for each become 0.

[0038] Note that the nonlinear parameter K of the i-th qubit 20-i i (i=1,2,3,4) and the nonlinear parameter K of the coupler 21 g It can be broadly divided into a component determined by inductance and a component determined by capacitance, which can be expressed, for example, by the following equation (10). Note that below, K i (i=1,2,3,4) g By reinterpreting it this way, it can be directly applied to the coupler 21.

[0039] TIFF2026142955000006.tif6150…(10)

[0040] In equation (10), p iThe (Participation ratio)(i=1,2,3,4,g) is the ratio of the induced energy stored in the qubit (Josephson junction) to the inductive energy stored in the circuit, and can be expressed, for example, by the following equation (11).

[0041] TIFF2026142955000007.tif13150…(11)

[0042] Here, L iL (i=1,2,3,4) is the structural inductance of the i-th qubit 20-i. L iS (i=1,2,3,4) is the inductance of the SQUID for the i-th qubit 20-i. n iS (i=1,2,3,4) represents the number of SQUIDs in the i-th qubit 20-i (Figure 7(B), Figure 7(C)), L iJ (i=1,2,3,4) is the inductance of the SQUID connected in series with the i-th qubit 20-i or the Josephson junction (Figure 7(A), Figure 7(C)), n iJ (i=1,2,3,4) represents the number of Josephson junctions connected in series in the i-th qubit 20-i (202-1 to 202-N in Figure 3(B)).

[0043] E in equation (10) Ci This can be expressed by the following equation (12). TIFF2026142955000008.tif11150…(12)

[0044] e is an elementary charge, C i This is the effective structural capacitance of qubit 20. For example, it may be the capacitance of the capacitor (shunt capacitor) 206 of the i-th qubit 20-i.

[0045] Figure 5 is a diagram illustrating the structural inductance of qubit 20. The p in equation (11) iThe maximum value for (i=1,2,3,4) is 1. i To bring it closer to its maximum value, the structural inductance L i (The inductance L1 in Figure 5) should be made as small as possible.

[0046] Figures 6(A) and 6(B) show modified versions of the circuit configurations in Figures 3(A) and 3(B). Referring to Figure 6(A), in the coupler 21, a SNAIL 221 and M Josephson junctions 214 may be connected in series between the first electrode (first node) 17 and the second electrode (second node) 18. Referring to Figure 6(B), in the qubit 20, a SNAIL 231 and M (M≧1) Josephson junctions 207 may be connected in series between the electrode 24 and ground.

[0047] As a configuration to change the nonlinearity (Kerr nonlinearity) of the first to fourth qubits 20-1 to 20-4 in Figure 4, configurations such as those shown in Figures 7(A), 7(B), and 7(C) may be used. Figure 7(A) shows a configuration in which M Josephson junctions 207-1 to 207-M ​​are connected in series with a SQUID 210 between electrode 24 and ground. By changing the number M of Josephson junctions 207-1 to 207-M, the nonlinearity (Kerr nonlinearity) of qubit 20 can be changed. For example, as M increases, the nonlinearity decreases. Figure 7(B) shows a configuration in which L SQUIDs 210-1 to 210-L are connected in series between electrode 24 and ground. By changing the number L of SQUIDs 210-1 to 210-L, the nonlinearity (Kerr nonlinearity) of qubit 20 can be changed. As L increases, the nonlinearity decreases. Figure 7(C) shows a configuration in which L SQUIDs 210-1 to 210-L and M Josephson junctions 207-1 to 207-M ​​are connected in series between electrode 24 and ground. By changing the number L of SQUIDs 210-1 to 210-L and the number M of Josephson junctions 207-1 to 207-M, the nonlinearity (Kerr nonlinearity) of the qubit 20 can be changed. A similar configuration may be used for the coupler 21. In this case, the ground and electrode 24 in Figures 7(A), 7(B), and 7(C) are replaced by the first electrode (first node) 17 and the second electrode (second node) 18 of the coupler 21.

[0048] The nonlinear parameter K represents the nonlinearity (Kerr nonlinearity) of qubit 20-i using SNAIL. i (i=1,…,4) is the Hamiltonian H of qubit 20-i. i When the following equation (13) is true, TIFF2026142955000009.tif7150…(13) This is expressed by the following equation (14) (Reference 1). In equation (13), ai+ and ai are the boson creation and annihilation operators in qubit 20-i.

[0049] TIFF2026142955000010.tif11150…(14) ωi is the resonance angular frequency of quantum bit 20-i.

[0050] Similarly, the parameter representing the nonlinearity of the coupler 21 using SNAIL (Kerr coefficient) (nonlinear parameter) K g can be expressed by the following formula (15).

[0051] TIFF2026142955000011.tif11150…(15) ω g is the resonance angular frequency of the coupler 21.

[0052] FIG. 8 is a diagram illustrating an example of a magnetic field characteristic (magnetic field response) 801 of the SNAIL resonance frequency (GHz (Giga-Hertz)) and a magnetic field characteristic (magnetic field response) 802 of the SNAIL Kerr nonlinearity (MHz (Mega-Hertz)). For a Josephson parametric oscillator (JPO) that uses a SNAIL with a negative nonlinear parameter K, the magnitude of the applied magnetic flux reaches a minimum at, for example, the position of the minimum value of the resonance frequency of the quantum bit (magnetic flux Φ=±0.5Φ0 (half-integer), where Φ0 is the flux quantum Φ0= h / 2e). For a JPO that uses a SNAIL with a positive nonlinear parameter K, the magnitude of the applied magnetic flux deviates from ±0.5 (half-integer) (Φ=0.4~-0.4Φ0, 0.6~1.4Φ0, -0.6~-1.4Φ0). Note that for a SQUID, the positive or negative sign of the nonlinear parameter cannot be changed by the applied magnetic field.

[0053] When the nonlinear parameter K of the coupler 21 in FIG. 4 g is set to a negative value, for example, for the SNAIL 221 of the coupler 21, in the magnetic field characteristic (magnetic field response) 802 of the Kerr nonlinearity in FIG. 8, a magnetic field at which the nonlinear parameter K g becomes negative is applied from a magnetic field applying unit (not shown in the figure).

[0054] Figure 9 illustrates a modification of Figure 4 as an example of several embodiments of the present disclosure. In the example of Figure 9, the coupler 21 comprises a SQUID (consisting of Josephson junctions 212 and 213), and the first to fourth qubits 20-1 to 20-4 comprise SNAILs 231A to 231D. In the configuration of Figure 9, for example, the nonlinear parameter K of the coupler 21 is... g The sign of the first and fourth qubits 20-1 and 20-4 may be set to positive, the signs of the nonlinear parameters K1 and K4 of the first and fourth qubits 20-1 and 20-4 may be set to negative, and the signs of the nonlinear parameters K2 and K3 of the second and third qubits 20-2 and 20-3 may be set to negative. In this case, a magnetic field (magnetic field response 802 in Figure 8) is applied to the SNAIL231A and 231D of the first and fourth qubits 20-1 and 20-4 from a magnetic field application unit not shown, such that the magnetic field characteristic 802 of the nonlinear parameters in Figure 8 is negative. The first and fourth qubits (JPO) 20-1 and 20-4, including SNAIL231A and 231D, oscillate (parametric oscillation) by an AC signal capacitively coupled to each of them. For example, an AC signal (with a frequency twice the resonant frequency) capacitively coupled to electrodes 24A and 24D of the first qubit 20-1 and the fourth qubit 20-4, respectively, is supplied from a signal source not shown. Meanwhile, a magnetic field (DC magnetic field + AC magnetic field (with a frequency approximately twice the resonant frequency)) is applied to the second and third qubits 20-2 and 20-3, SQUID210B and 210C, respectively, from a magnetic field application unit not shown, causing them to oscillate (parametric oscillation) at a predetermined resonant frequency.

[0055] The nonlinear parameters K1 to K4 of the first to fourth qubits 20-1 to 20-4 and the nonlinear parameter K of the coupler 21 g If you set it as follows, K2=K3=K>0, K1=K4=-K<0, K g =K>0 …(16) Of the six possible combinations of the sum of the nonlinear parameters of the two qubits 20 related to QQ-CKI, the following four combinations result in 0. (K1+K2)=(K1+K3)=(K2+K4)=(K3+K4)=0 …(17) Further, among the following four combinations of sums of nonlinear parameters of the coupler 21 and quantum bits related to QC-CKI, the following two combinations are 0. (K1+K g )=(K4+K g )=0 …(18)

[0056] As described above, according to the circuit of FIG. 9, QQ-CKI and QC-CKI can be suppressed. Note that formula (16) is K2=K3=K<0,K1=K4=-K>0,K g =K>0 …(19) may also be set as such.

[0057] In FIG. 9, the resonance angular frequencies ω1 to ω4 of the first to fourth quantum bits 20-1 to 20-4 satisfy the following condition: ω1+ω2=ω3+ω4…(20) when the above condition is satisfied, the coupling coefficient h of four-body interaction due to the nonlinearity of the first to fourth quantum bits 20-1 to 20-4 (4) can be expressed by the following formula (21).

[0058] TIFF2026142955000012.tif10150 …(21)

[0059] In formula (21), K i (i=1, 2, 3, 4) is a nonlinear parameter representing the nonlinearity of the i-th quantum bit 20-i. g ij (i≠j=1, 2, 3, 4) represents the strength (magnitude) of coupling between the i-th quantum bit 20-i and the j-th quantum bit 20-j. Δ ij where (i≠j=1, 2, 3, 4) represents the difference between the resonance angular frequency ω of the i-th quantum bit 20-i i and the resonance angular frequency ω of the j-th quantum bit 20-j j , which is ω i -ω j .

[0060] In other words, the coupling coefficient h of the four-body interaction arising from the nonlinearity between qubits. (4) It can be expressed (approximated) as shown in equation (22).

[0061] TIFF2026142955000013.tif17150…(22)

[0062] In equation (22), similar to equation (21), g ij (i, j=1,2,3,4 (j≠i)) represents the strength (magnitude) of the coupling between the j-th qubit 20-j and the i-th qubit 20-j (also called the "coupling constant"), Δ ji (i, j=1,2,3,4 (j≠i)) is the resonant angular frequency ω of the j-th qubit 20-j. j and the resonant angular frequency ω of the i-th qubit 20-i i The difference ω j -ω i And K i (i=1,2,3,4) are the nonlinear parameters of the i-th qubit 20-i.

[0063] In equation (22), the multiplication term is: TIFF2026142955000014.tif17150 is g ij Let (j=1,2,3,4 (j≠i)) be g and Δ ji Let Δ be (j=1,2,3,4 (j≠i)), and K q to g ij / Δ ji If we consider the effective value including the sign (the effective Kerr coefficient remaining after the signs ± cancel each other out), it can be expressed by the following equation (23). TIFF2026142955000015.tif9150…(23)

[0064] In equation (23), TIFF2026142955000016.tif8150…(24) It is said that, under these conditions, by minimizing the difference Δ in the resonant angular frequencies between the two qubits (the i-th and j-th qubits 20-i and 20-j), the value of equation (23) becomes large.

[0065] Furthermore, from equation (23), the parameter K represents the nonlinearity of qubit 20. q Even if we increase the coefficient h of the four-body interaction, (4) It becomes larger. In equation (23), the nonlinear parameter K of qubit 20 is q The cube term of (g / Δ) (<1) is (g / Δ) 3 This is the case. Therefore, the coupling coefficient h of the four-body interaction due to the nonlinearity of qubit 20 is (4) is g in equation (5) (4) Compared to (the coupling coefficient of the four-body interaction between the qubits 20 via the coupler 21), it is relatively easy to make it larger. (4) For example, K q and K g When they are of the same order, the g of equation (5) (4) In some cases, the order of magnitude could be nearly an order of magnitude larger.

[0066] Expanding equation (22) for the first to fourth qubits 20-1 to 20-4 in Figure 9, we can express (approximate) it as the following equation (25).

[0067] TIFF2026142955000017.tif9150…(25)

[0068] In equation (25) above, the conditions for the first to fourth qubits 20-1 to 20-4 to exhibit four-body interaction (conditions relating to resonant angular frequencies ω1 to ω4) are TIFF2026142955000018.tif6150…(26) Let's assume that.

[0069] From equation (26) TIFF2026142955000019.tif6150 TIFF2026142955000020.tif6150 Therefore, TIFF2026142955000021.tif6150…(27) TIFF2026142955000022.tif6150…(28)

[0070] Furthermore, regarding equation (25), Δ ij (=ω i -ω j ) is antisymmetric with respect to the subscripts i and j: Δ ij =-Δ ji …(29) g ij It is symmetric with respect to the subscripts i and j: TIFF2026142955000023.tif6150…(30)

[0071] The coupling constant g between the first and second qubits 20-1 and 20-2, which are coupled to the first electrode 17 (first node) of the coupler 21 via coupling capacitors 31A and 31B. 12 The coupling constant g between the third and fourth qubits 20-3 and 20-4, which are coupled to the second electrode 18 (second node) of the coupler 21 via coupling capacitors 31C and 31D, is also g. 34 This means that when their resonant angular frequencies are close, they are approximated to be equal. TIFF2026142955000024.tif6150…(31)

[0072] The coupling constant g between the first and third qubits 20-1 and 20-3, which are coupled via the coupler 21. 13 The coupling constant g between the first and fourth qubits 20-1 and 20-4, which are coupled via the coupler 21. 14 The coupling constant g between the second and third qubits 20-2 and 20-3, which are coupled via the coupler 21. 23 The coupling constant g between the second and fourth qubits 20-2 and 20-4, which are coupled via the coupler 21. 24 This means that when their resonant angular frequencies are close, they are approximated to be equal. TIFF2026142955000025.tif6150…(32)

[0073] Under the conditions of equations (27) to (32), equation (25) above is: TIFF2026142955000026.tif10150 TIFF2026142955000027.tif10150…(33) Therefore, it can be expressed as equation (34) below.

[0074] TIFF2026142955000028.tif10150…(34)

[0075] From equation (34), for example, K1=K4=-K<0, K2=K3=K>0 …(35a) or, If we set K1=K4=-K>0 and K2=K3=K<0 …(35b), then (K2-K1)>0 and (K3-K4)>0 …(36a) or, (K2-K1)<0, (K3-K4)<0 …(36b) Therefore, the difference in resonant angular frequency Δ 34 and Δ 12 of, Δ 34 >0,Δ 12 >0 …(37a) or, Δ 34 <0,Δ 12 <0 …(37b) By doing so, the numerator (K2-K1)Δ of equation (34) 34 +(K3-K4)Δ 12 The value of (or absolute value if negative) can be increased. That is, the coupling strength h of the four-body interaction due to the nonlinearity of the four qubits 20-1 to 20-4. (4) This can be increased. If we use equation (35a) or equation (35b), then K1+K2=K1+K3=K2+K4=K3+K4=0, and QQ-CKI can be suppressed.

[0076] This h (4) (For example, its absolute value) is the strength g of the four-body coupling between the qubits 20 via the coupler 21 in equation (5). (4) (For example, its absolute value) can be combined with the result of addition or other means to determine the strength of the four-body interaction bond. Note that from equation (34), if K1=K2 and K3=K4, h (4) The result is 0.

[0077] Furthermore, the conditions concerning the resonant angular frequencies ω1 to ω4 between the four qubits 20-1 to 20-4 are TIFF2026142955000029.tif6150…(38) In that case, equation (25) can be expressed as equation (39).

[0078] TIFF2026142955000030.tif10150…(39)

[0079] From equation (39), for example, K1=K4=-K<0, K3=K2=K>0 …(40a) or, K1=K4=-K>0, K2=K3=K<0 …(40b) In that case, (K1-K3)<0, (K4-K2)<0 …(41a) or (K1-K3)>0, (K4-K2)<0 …(41b) Therefore, the difference in resonant angular frequency Δ 24 and Δ 13 of, Δ 24 <0,Δ 13 <0 …(42a) or, Δ 24 >0,Δ 13 >0 …(42b) By doing so, the numerator (K1-K3)Δ of equation (39) 24 +(K4-K2)Δ 13 The value of (or absolute value if negative) can be increased. That is, the coupling strength h of the four-body interaction due to the nonlinearity of the four qubits 20-1 to 20-4. (4) Furthermore, the nonlinear parameter K of the coupler 21 can be increased. g By setting the sign of to be the opposite sign of either K1 or K2, which have opposite signs, at least a portion of the cross-Kerr interaction (QC-CKI) between the qubit 20 and the coupler 21 can be suppressed. Note that in equation (39), when K1=K3 and K4=K2, h (4) The result is 0.

[0080] Furthermore, the conditions for the first to fourth qubits 20-1 to 20-4 to exhibit four-body interaction (conditions relating to resonant angular frequencies ω1 to ω4) TIFF2026142955000031.tif6150…(43) In that case, equation (25) can be expressed as equation (44).

[0081] TIFF2026142955000032.tif10150…(44)

[0082] From equation (44), for example, K1=K3=K>0, K2=K4=-K<0 …(45a) or, K1=K3=K<0, K2=K4=-K>0 …(45b) In that case, (K1-K4)>0, (K3-K2)>0 …(46a) or, (K1-K4)<0, (K3-K2)<0 …(46b) Therefore, the difference in resonant angular frequency Δ 23 and Δ 14 of, Δ 23 >0,Δ 14 >0 …(47a) or, Δ 23 <0,Δ 14 <0 …(47b) By doing so, the numerator term of equation (44) is (K1-K4)Δ 23 +(K3-K2)Δ 14 The value of (or absolute value if negative) can be increased. That is, the coupling strength h of the four-body interaction due to the nonlinearity of the four qubits 20-1 to 20-4. (4) It can be made larger.

[0083] Furthermore, equations (45a), (45b), (46a), and (46b) allow us to suppress some of the QQ-CKI (four out of six combinations of the sum of the nonlinear parameters of the two qubits 20). In addition, the nonlinear parameter K of the coupler 21 g By setting the sign of to be the opposite sign of either K1 or K2, which have opposite signs to each other, it is possible to suppress a portion of QC-CKI (two of the four combinations of nonlinear parameters of the qubit 20 and the coupler 21). Note that in equation (44), when K1=K4 and K3=K2, h (4) The result is 0.

[0084] Figure 10 shows an example of a further modification of Figure 4 as an example of some embodiments of the present disclosure. In the example of Figure 10, the coupler 21 comprises SNAIL221 (consisting of a Josephson junction 212-1 and a parallel circuit of series-connected Josephson junctions 212-2 and 212-3), the first qubit 20-1 and the fourth qubit 20-4 comprise SNAIL231A and 231D, and the second qubit 20-2 and the second qubit 20-3 comprise SQUID210B and 210C.

[0085] The first and fourth qubits (JPOs) 20-1 and 20-4, including SNAIL231A and 231D, oscillate (parametric oscillation) due to an AC signal capacitively coupled to them. For example, an AC signal (with a frequency twice the resonant frequency) capacitively coupled to electrodes 24A and 24D of the first qubit 20-1 and the fourth qubit 20-4, respectively, is supplied from a signal source not shown. Meanwhile, a magnetic field (DC magnetic field + AC magnetic field (with a frequency approximately twice the resonant frequency)) is applied to the second and third qubits 20-2 and 20-3, respectively, from a magnetic field application unit not shown, causing them to oscillate (parametric oscillation) at a predetermined resonant frequency. The coupler 21, including SNAIL221, oscillates due to an AC signal capacitively coupled to the electrodes of SNAIL221, for example. A magnetic field corresponding to the magnetic field characteristics (magnetic field response) 802 shown in Figure 8 is applied to the first and fourth qubits (JPOs) 20-1 and 20-4, including SNAIL231A and 231D, and to the coupler 21, which includes SNAIL221, and the sign (positive or negative) of the nonlinear parameter is set. In the configuration of Figure 10, the nonlinear parameter K of the coupler 21 is g The sign of is negative (-K), the nonlinear parameters K1 and K4 of the first qubit 20-1 and the fourth qubit 20-4 are negative (-K), and the nonlinear parameters K2 and K3 of the second qubit 20-2 and the third qubit 20-3 are negative (-K). を It may be set to a positive value (+K), or vice versa.

[0086] In this case, (K² + K g ), (K3+K g The QC-CKI values ​​proportional to (K1+K) are all 0. However, (K1+K g ), (K4+K g The QC-CKI values ​​that are proportional to each of the above remain.

[0087] Furthermore, the QQ-CKI values ​​proportional to (K1+K2), (K1+K3), (K2+K4), and (K3+K4), respectively, are all 0. However, the QQ-CKI values ​​proportional to (K1+K4) and (K2+K3), respectively, remain. However, it is possible to suppress 2 of the 4 QC-CKI values ​​and 4 of the 6 QQ-CKI values. For simplicity, the nonlinear parameter K of the coupler 21 is used. g We defined the sign of as negative (-K, K>0), the nonlinear parameters K1 and K4 of the first qubit 20-1 and the fourth qubit 20-4 as negative (-K), and the nonlinear parameters K2 and K3 of the second qubit 20-2 and the third qubit 20-3 as positive (+K). However, any combination of values ​​for the nonlinear parameters is acceptable.

[0088] In Figure 10, the first qubit 20-1 to the fourth qubit 20-4 and the coupler 21 may each be configured as JPOs equipped with SNAIL.

[0089] Furthermore, in the configuration shown in Figure 10, the bond strength (bond coefficient) h of the four-body interaction, as expressed by the above-mentioned equations (34), (39), (44), etc. (4) It can manifest.

[0090] Figure 11 illustrates the configuration of a quantum computing device (quantum annealing machine) 300, which includes the four qubits 20-1 to 20-4 and the coupler 21 as a unit according to the above-described embodiment. In Figure 11, the gray circle represents the coupler 21, and the four white circles around it represent the physical qubits, which are qubits 20.

[0091] The Hamiltonian for the all-to-all Ising spin glass model is given by equation (48).

[0092] TIFF2026142955000033.tif14150…(48) (However, σ (i) Z This is logical spin (Pauli matrix), J ijb is the interaction coefficient. i (This refers to the local magnetic field.)

[0093] Equation (48) can be expanded into the Hamiltonian of a physical qubit in the following equation (49), where K = N(N-) / 2 (K = 15 when N = 6).

[0094] TIFF2026142955000034.tif14150…(49)

[0095] The interaction coefficient (matrix) J of the fully coupled Ising spin in equation (48) ij In the Hamiltonian of equation (49), the local magnetic field J acting on the physical qubit is... k This is converted to C in equation (49). l This is a constraint (see Non-Patent Document 1). In Figure 11, Ji and j in Jk=Ji,j attached to each circle (physical qubit) are the same as J in equation (48). ij This corresponds to the following: The four qubits in the bottom row are fixed values, and the solution to the optimal problem is read from the row above.

[0096] In this disclosure, the quantum circuit device may be integrated as a chip. In this case, the substrate may be, for example, 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, while it is preferable for the substrate of the quantum chip to be a single crystal, it may also be polycrystalline or amorphous. The pattern of the wiring layer of the quantum chip may be formed by depositing (depositing) a superconducting material onto the surface of the substrate and then patterning it. As the superconducting material (wiring material) for the wiring and electrodes of the wiring layer of the quantum chip, for example, Nb (niobium) or Al (aluminum) may be used, but it is not limited to these, and any metal that becomes superconducting when cooled to an extremely low temperature may 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, and alloys containing at least one of these. While not particularly limited, a first aluminum film is formed on the surface of the quantum chip substrate by oblique deposition as a Josephson junction and oxidized to form a tunnel oxide film (AlO x ) is formed, and a second aluminum film is formed by oblique deposition from the opposite direction to the previous one, thereby creating a Josephson junction (Al / AlO x / Al) may be formed.

[0097] Although SQUID and SNAIL were used as examples of nonlinear elements for the qubit 20 and coupler 21, ATS (Asymmetrically Threaded SQUID) and STS (Symmetrically Threaded SQUID) may also be used. Alternatively, any other Josephson junction configuration may be used. For example, the qubit 20 may include a transmon composed of one Josephson junction and a capacitor.

[0098] The cross-Kerr interaction (cross-Kerr nonlinear interaction) described above is not limited to superconducting quantum circuits, but can also be applied to cross-Kerr nonlinear interactions between optical cavities and microwaves. That is, although the explanation used JPO as an example of a parametric oscillator (Kerr Parametric Oscillator: KPO) exhibiting the Kerr effect, it is of course possible to use KPOs other than JPO for qubits 20-1 to 20-4.

[0099] [Reference 1] Timo Hillmann, Fernando Quijandria, "Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops", Phys. Rev. Applied 17, 064018 - Published 9 June, 2022

[0100] The embodiments / examples exemplified above are further noted below (but are not limited thereto).

[0101] (Note 1) The quantum circuit device comprises N qubits (where N is a predetermined integer of 3 or more) coupled by many-body interaction via a coupler, wherein a parameter representing the nonlinearity of at least one of the N qubits has a different sign from the parameter representing the nonlinearity of the coupler and / or other qubits.

[0102] (Note 2) In the quantum circuit device of Note 1, the many-body interaction is a four-body interaction involving four qubits where N is 4.

[0103] (Note 3) In the quantum circuit device of Note 1 or 2, the coupler includes at least one of the following: a Josephson junction, a SQUID (Superconducting Quantum Interference Device) containing multiple Josephson junctions in a loop, and a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement) in which at least one Josephson junction and multiple Josephson junctions connected in series are connected in parallel in a loop.

[0104] (Note 4) In any of the quantum circuit devices described in Notes 1 to 3, the qubit includes at least one of the following: a Josephson junction, a SQUID (Superconducting Quantum Interference Device) containing multiple Josephson junctions in a loop, and a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement) in which at least one Josephson junction and multiple Josephson junctions connected in series are connected in parallel within a loop.

[0105] (Note 5) In any of the quantum circuit devices described in Notes 1 to 4, the qubit is capacitively coupled to the coupler.

[0106] (Note 6) In the quantum circuit device of Note 2, the coupling coefficient h of the four-body interaction by the four qubits (4) The coupling coefficient g of the four-body interaction by the coupler of the four qubits. (4) The combined value of these factors acts as the strength of the four-body interaction.

[0107] (Note 7) In any of the quantum circuit devices described in Notes 1 to 6, a quantum computer is constructed by arranging four qubits and a coupler as the basic unit.

[0108] (Note 8) A method for controlling the many-body interaction of a quantum circuit device including N qubits (where N is a predetermined integer of 3 or more) coupled in a many-body interaction via a coupler, wherein the sign of a parameter representing the nonlinearity of at least one of the N qubits is set to be different from the sign of the nonlinear parameter of the coupler and / or other qubits.

[0109] (Note 9) In the method of Note 8, the many-body interaction is a four-body interaction involving four qubits where N is 4.

[0110] Furthermore, the disclosures in Non-Patent Documents 1 and 2 and Reference 1 are incorporated herein by reference. Within the framework of the entire disclosure (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, various combinations or selections of various disclosed elements (including each element of each claim, each element of each embodiment, each element of each drawing, etc.) are possible. In other words, this disclosure naturally includes the entire disclosure, including the claims, and various modifications and alterations that a person skilled in the art could make in accordance with the technical concept. [Explanation of symbols]

[0111] 1 Quantum circuit device 15 Inductors 16 Capacitors 17. First electrode (first node) 18. Second electrode (second node) 19 Electrodes (Nodes) 20, 20A~20E qubits 20-1~20-4 1st to 4th qubits 21 Combiner 24, 24A~24D Electrodes (Coupler connection part) 31, 31A~31D Coupling Capacitors 201, 201A~201D Josephson junction 202, 202A~202D, 202-1~202-N Josephson junctions 203, 203A~203D Superconducting Materials 204, 204A~204D Superconducting Materials 206, 206A~206D Capacitors 207-1~207-M, 212, 213-1~213-N, 214-1~214~M Josephson junction 210, 210A~210D SQUID 221, 231, 231A~231D SNAIL 300 Quantum Computers (Quantum Annealing Machines) 801 Magnetic field characteristics at resonant frequencies 802 Kerr Nonlinear Magnetic Field Characteristics

Claims

1. It comprises N qubits (where N is a predetermined integer greater than or equal to 3) connected by many-body interactions via a coupler, A quantum circuit device in which a parameter representing the nonlinearity of at least one of the N qubits has a different sign from the sign of a parameter representing the nonlinearity of the coupler and / or other qubits.

2. The quantum circuit device according to claim 1, wherein the many-body interaction is a four-body interaction involving four qubits where N is 4.

3. The aforementioned coupler is, Josephson junction, A SQUID (Superconducting Quantum Interference Device) containing multiple Josephson junctions within a loop, and A SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement) consists of at least one Josephson junction and multiple series-connected Josephson junctions connected in parallel within a loop. The quantum circuit device according to claim 2, comprising at least one of the following.

4. The aforementioned qubit is Josephson junction, A SQUID (Superconducting Quantum Interference Device) containing multiple Josephson junctions within a loop, and A SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement) consists of at least one Josephson junction and multiple series-connected Josephson junctions connected in parallel within a loop. A quantum circuit device according to claim 1, comprising at least one of the following.

5. The quantum circuit device according to claim 1, wherein the qubit is capacitively coupled to the coupler.

6. The coupling coefficient h of the four-body interaction by the four qubits （４） The coupling coefficient g of the four-body interaction by the coupler of the four qubits. （４） The quantum circuit device according to claim 2, wherein the combined value of the two functions as the strength of the four-body interaction.

7. The quantum circuit device according to claim 2, wherein the four qubits and the couplers that connect the four qubits are arranged as basic units to constitute a quantum computer.

8. A method for controlling the many-body interaction of a quantum circuit device including N qubits (where N is a predetermined integer of 3 or more) that are coupled via a coupler in a many-body interaction, A control method in which the sign of a parameter representing the nonlinearity of at least one of the N qubits is set to be different from the sign of the nonlinear parameter of the coupler and / or other qubits.

9. The control method according to claim 8, wherein the many-body interaction is a four-body interaction involving four qubits where N is 4.

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