Quantum circuit device and its control method

Abstract

To provide a quantum circuit device that eliminates the need for adjustments such as setting the resonant frequency of the coupler, and can increase the coupling strength of, for example, a four-body interaction. [Solution] The quantum circuit device has N qubits (where N is a predetermined integer of 3 or more) connected by many-body interactions, and the number of qubits to which nonlinearity contributes to the many-body interaction is M (1 ≤ M

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 used to solve combinatorial optimization problems, requires a bit-to-bit interaction called a four-body interaction (Non-Patent Literature 1). Non-Patent Literature 2 discloses a physical implementation of the LHZ scheme, for example, a network with four qubits and one coupler using a four-body interaction, as shown in Figure 1. Figure 1 is based on Figure 4a of Non-Patent Literature 2. In the example in Figure 1, for example, Josephson parametric oscillators (JPOs) are used as qubits, and a configuration is used that includes, for example, a Josephson junction (JJ) 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)

Summary of the Invention

Problems to be Solved by the Invention

[0004] The quantum circuit device illustrated in FIG. 1 includes a coupler having a nonlinear element such as a Josephson junction. Additional measuring equipment, waveguide design, or the like is required for setting, adjusting, or the like of the resonance frequency of the coupler. Further, when attempting to increase the coupling coefficient of four-body interaction, manufacturing difficulties arise, for example, due to differences in parameters of Josephson junctions used for qubits and the coupler.

[0005] An object of the present disclosure is to provide a quantum circuit device and a control method thereof that solve the above problems.

Means for Solving the Problems

[0006] According to one aspect of the quantum circuit device of the present disclosure, for N qubits (N is a predetermined integer of 3 or more) coupled by many-body interaction, the configuration is such that the number of qubits to which nonlinearity contributes in the many-body interaction is limited to M (1≤M<N), and / or one or more qubits among the N qubits have a configuration in which the sign of a parameter representing the nonlinearity of the qubit is set to either positive or negative so as to increase the coupling strength of the many-body interaction.

[0007] According to the method of one aspect of the present disclosure, for N qubits (N is a predetermined integer of 3 or more) coupled by multi-body interaction, limiting the number of qubits to which non-linearity contributes in the multi-body interaction to M (1≦M<N), and / or setting the sign of a parameter representing non-linearity of one or more qubits among the N qubits to either positive or negative so as to increase the coupling strength of the multi-body interaction. [Effect of the Invention]

[0008] According to the present disclosure, adjustments such as setting of the resonant frequency of a coupler are not required, and for example, the coupling coefficient of 4-body interaction can be increased. BRIEF DESCRIPTION OF DRAWINGS

[0009] [Figure 1] It is a diagram explaining an example of the disclosure in Non-Patent Document 2. [Figure 2] It is a diagram explaining the configuration of at least one example of some embodiments of the present disclosure. [Figure 3] It is a diagram explaining the configuration of at least one example of some embodiments of the present disclosure. [Figure 4] It is a diagram explaining the configuration of at least one example of some embodiments of the present disclosure. [Figure 5] It is a diagram explaining the configuration of at least one example of some embodiments of the present disclosure. [Figure 6] It is a diagram explaining at least one example of some embodiments of the present disclosure. [Figure 7] It is a diagram explaining at least one example of some embodiments of the present disclosure. [Figure 8] It is a diagram explaining at least one example of some embodiments of the present disclosure. [Figure 9] It is a diagram explaining the configuration of at least one example of some embodiments of the present disclosure. [Figure 10] (A) to (C) are diagrams respectively explaining the configuration of at least one example of some embodiments of the present disclosure. [Figure 11](A) and (B) are figures illustrating at least one example of several embodiments of the present disclosure. [Figure 12] This figure illustrates at least one example of several embodiments of the present disclosure. [Modes for carrying out the invention]

[0010] Embodiments of this disclosure will now be described. First, as a premise of this disclosure, the configuration of Figure 1 will be analyzed and its problems will be explained 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 an 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 the electrode 24A and ground. During operation, a magnetic flux penetrating the SQUID 210A is generated 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 superconducting members 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 D, 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.

[0011] 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.

[0012] In relation to the circuit in Figure 1, Non-Patent Literature 2 states that the angular frequencies of the pump signals for the first to fourth qubits 20-1 to 20-4 (JPO1 to JPO4) are set as follows, for example: ω p,1 +ω p,2 =ω p,3 +ω p,4 …(1)

[0013] ωp,i (i=1,2,3,4) is the angular frequency of the pump signal supplied to the i-th qubit 20-i. As the pump signal to the i-th qubit 20-i (i=1,2,3,4), an AC signal with an angular frequency approximately twice the resonant angular frequency ωi of that i-th qubit 20-i is supplied.

[0014] For the circuit in Figure 1, in the Hamiltonian after the rotational wave approximation, the coupling term of the four-body interaction via the coupler 21 of the four qubits 20-1 to 20-4 is given by the following equation (2) (see, for example, Non-Patent Document 2).

[0015] TIFF2026142953000002.tif6150…(2)

[0016] In equation (2), a i a i +where (i=1,2,3,4) are respectively the boson annihilation operator and creation operator for each qubit. In Non-Patent Document 2, the coupling term of the four-body interaction in the Hamiltonian is given a negative sign in formula (2).

[0017] In formula (2), the strength (coupling coefficient) g of the four-body interaction (4) is TIFF2026142953000003.tif9150…(3) given by , and depends on the nonlinearity of the Josephson junction 10 (JJ) of the coupler 21 and the difference (detuning) between the resonance frequencies of the qubits 20-1 to 20-4 and the coupler 21.

[0018] In formula (3), K g is a parameter (Kerr coefficient) representing the nonlinearity of the coupler 21. K g is also referred to as the nonlinear parameter of the coupler 21. Δ i (i=1,2,3,4) is the difference (detuning) between the resonance angular frequency ω of the coupler 21 c and the resonance angular frequency ω of the i-th qubit 20-i i (=ω c -ω i ). g i (i=1,2,3,4) represents the magnitude (strength) of coupling between the i-th qubit 20-i and the coupler 21.

[0019] From formula (3), TIFF2026142953000004.tif9150…(4) within the range of detuning Δ i if the detuning Δ is made as small as possible, the coupling coefficient g of the four-body interaction (4) becomes larger, and the four-body interaction becomes stronger. Therefore, the resonance angular frequency ω of each qubit 20-i i (i=1,2,3,4) and the resonance angular frequency ω of the coupler 21 c need to be close to each other to a certain extent.

[0020] In formula (3), each g i / Δi Approximating (i=1,2,3,4) with g / Δ, TIFF2026142953000005.tif9150…(5) g in equation (3) (4) The nonlinear parameter K of the coupler 21 is g The fourth term of g / Δ: (g / Δ) 4 This means that a charge is applied.

[0021] From equation (3), 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 is (4) This basically only results in a small value. That is, in the circuit in Figure 1, the coupling coefficient g of the four-body interaction (4) It is generally difficult to consider something as large.

[0022] Furthermore, when a Josephson junction 10, which is a nonlinear element, is used as a fixed-frequency coupler 21, as shown in the circuit of Figure 1, its resonant frequency depends on the critical current value of the Josephson junction 10. Therefore, it is necessary to fabricate a Josephson junction with a critical current value close to the desired value (design value).

[0023] On the other hand, if the coupler 21 is not a fixed-frequency type but is a variable-frequency coupler equipped with, for example, a SQUID (superconducting quantum interference device), then it is necessary to route input / output lines to read out the coupler's frequency and bias lines for frequency change (adjustment) (for example, lines that supply bias signals to generate the bias magnetic flux applied to the SQUID).

[0024] In addition to arranging these lines on a chip that integrates the network of qubits 20 and couplers 21, measurement wiring, cables, signal sources, and measuring instruments are required outside of the chip. Furthermore, a certain level of precision is required in adjusting the difference in resonant frequencies between the coupler and the qubits.

[0025] The above problem is merely one example, but according to this disclosure, it is possible to enable the manifestation of many-body interactions due to the nonlinearity of qubits without the use of a coupler in various situations, not limited to the above, and to set the strength of the many-body interaction coupling to a desired value.

[0026] Figure 2 illustrates an example of several embodiments of the present disclosure. As shown in Figure 2, four-body interactions between qubits can occur even in configurations without couplers.

[0027] Referring to Figure 2, 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 Josephson junctions 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, 24B, 24C, and 24D of the first qubit 20-1, the second qubit 20-2, the third qubit 20-3, and the fourth qubit 20-4 are connected to a common node n1 via coupling capacitors 31A, 31B, 31C, and 31D, respectively. During operation, current from a signal source (not shown) is passed through an inductor (magnetic field generator) (not shown), generating magnetic fluxes that penetrate SQUIDs 210B to 210D. The resonant angular frequencies ω2 to ω4 of the second to fourth qubits 20-2 to 20-4 are varied according to the magnetic fluxes that penetrate SQUIDs 210B to 210D.

[0028] Four-body interactions arise, for example, from the nonlinearity (Kerr nonlinearity) of four qubits 20-1 to 20-4. In this case, the coupling coefficient h represents the strength of the four-body interaction. (4) It is given (approximated) by the following equation (6).

[0029] TIFF2026142953000006.tif10150 …(6)

[0030] In equation (6), g ij (i≠j=1,2,3,4) represents the strength (magnitude) of the connection between the i-th qubit 20-i and the j-th qubit 20-j. Δ ij The value (i≠j=1,2,3,4) represents the difference ωi-ωj between the resonant angular frequency ωi of the i-th qubit 20-i and the resonant angular frequency ωj of the j-th qubit 20-j. 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 qubit 20-i.

[0031] K i This is the Hamiltonian H of the i-th qubit (JPO) 20-i (i=1,2,3,4) in Figure 2. i When expressed by the following equation (7), TIFF2026142953000007.tif7150…(7) Kerr nonlinearity K i It may be made to correspond to this.

[0032] In equation (7), Δ is the resonant angular frequency ω of the coupler 21. c and the difference of 1 / 2 of the angular frequency ωp of the i-th pump signal Δ=ω c -(1 / 2)ωp …(8) That is the case. Ep is the strength of the 2-photon drive (pump term). i + and a i These are the creation and annihilation operators for the boson (photon) in the i-th qubit, 20-i.

[0033] Here, the four-body interaction between the four qubits 20-1 to 20-4 arises not through the coupler 21, but from the nonlinearity of qubit 20. Referring again to Figure 2, the coupling coefficient h of the four-body interaction arising from the nonlinearity between qubits. (4) It can be expressed (approximated) as, for example, in equation (9).

[0034] TIFF2026142953000008.tif17150…(9)

[0035] In equation (9), similar to equation (6), 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 That is the case. K i (i=1,2,3,4) are the nonlinear parameters of the i-th qubit 20-i.

[0036] Here, in equation (9), the multiplication term is: Regarding TIFF2026142953000009.tif17150, 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 (10). TIFF2026142953000010.tif9150…(10)

[0037] In equation (10), TIFF2026142953000011.tif8150…(11) 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 (11) becomes large.

[0038] From equation (11), the parameter K represents the nonlinearity of qubit 20. q Even if we increase the coefficient h of the four-body interaction, (4) The value becomes larger. In equation (11), 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) This is g in Figure 1. (4) Compared to that, it is relatively easy to enlarge. (4) For example, K q and K g When they are of the same order, the g of equation (3) (4) In some cases, the order of magnitude could be nearly an order of magnitude larger.

[0039] Furthermore, equation (9), which represents the four-body interaction due to the nonlinearity of the qubit 20, does not involve the degrees of freedom of the coupler 21 (parameters related to the coupler 21). Therefore, adjustment of the resonant frequency of the coupler 21, etc., is not necessary to strengthen the four-body interaction. In other words, the coupler 21 does not need to include nonlinear elements such as Josephson junctions or SQUIDs, and can be constructed with linear elements. When the coupler 21 is constructed with linear elements, there is no need for a signal source to vary the frequency of the coupler 21, control lines and input / output lines, or measuring equipment. Note that although the degrees of freedom of the coupler 21 (parameters related to the coupler 21, etc.) do not involve the four-body interaction due to the nonlinearity between the qubits 20 in equation (9), this does not preclude constructing the coupler 21 with nonlinear elements. Also, when the coupler 21 generates all interactions, including the four-body interaction, the interaction represented by equation (3) and the four-body interaction represented by equation (9) can coexist.

[0040] In equation (9), if we focus on i=1, that is, the first qubit 20-1 in Figure 2, • The difference in resonant angular frequencies between the second qubit 20-2 and the first qubit 20-1 Δ 21 (=ω2-ω1) and the strength g of the coupling between the first qubit 20-1 and the second qubit 20-2 12 , • The difference in resonant angular frequencies between the third qubit 20-3 and the first qubit 20-1 Δ 31 (=ω3-ω1) and the strength g of the coupling between the first qubit 20-1 and the third qubit 20-3. 13 and, • The difference in resonant angular frequencies between the fourth qubit 20-4 and the first qubit 20-1 Δ 41 (=ω4-ω1) and the strength g of the coupling between the first qubit 20-1 and the fourth qubit 20-4. 14 and 、 Regarding this, the multiplication term for i=1 in equation (9) is TIFF2026142953000012.tif9150…(12) This is the result. Equation (9) is a generalization of equation (12).

[0041] Expanding equation (9) for the first to fourth qubits 20-1 to 20-4 in Figure 2, we can express it as the following equation (13).

[0042] TIFF2026142953000013.tif9150…(13)

[0043] In equation (13) 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 TIFF2026142953000014.tif6150…(14) Let's assume that.

[0044] From equation (14) TIFF2026142953000015.tif6150 TIFF2026142953000016.tif6150 Therefore, TIFF2026142953000017.tif6150…(15) TIFF2026142953000018.tif6150…(16)

[0045] Furthermore, regarding equation (13), Δ ij (=ω i -ω j ) is the opposite with respect to the subscripts i and j: Δ ij =-Δ ji …(17) g ij It is symmetric with respect to the subscripts i and j: TIFF2026142953000019.tif6150…(18)

[0046] 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. TIFF2026142953000020.tif6150…(19)

[0047] 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. TIFF2026142953000021.tif6150…(20)

[0048] Under the conditions of formulas (15) to (20), the above formula (13) is TIFF2026142953000022.tif10150 TIFF2026142953000023.tif10150…(21) from which formula (6), reprinted below, is derived. TIFF2026142953000024.tif10150…(6)

[0049] From formula (6), when the nonlinear parameter K₁ of the first quantum bit 20-1 is equal to the nonlinear parameter K₂ of the second quantum bit 20-2, and the nonlinear parameter K₃ of the third quantum bit 20-3 is equal to the nonlinear parameter K₄ of the fourth quantum bit 20-4, that is, K₂=K₁, K₃=K₄…(22) holds, h (4) becomes 0.

[0050] From formula (6), in order for the coefficient h of the four-body interaction due to the nonlinearity of the first to fourth quantum bits 20-1 to 20-4 (4) to obtain a non-zero value, it is necessary to prepare nonlinear parameters K i (i=1, 2, 3, 4) with different values.

[0051] In formula (6), by changing the sign (positive / negative) setting of any one (including a plurality of) of the nonlinear parameters K i (i=1, 2, 3, 4) of the first to fourth quantum bits 20-1 to 20-4, for example, ((K₂-K₁)>0 and Δ 34 >0) and ((K₃-K₄)>0 and Δ 12 >0) …(23a) ((K₂-K₁)>0 and Δ 34 <0) and ((K₃-K₄)>0 and Δ 12 <0) …(23b) ((K₂-K₁)<0 and Δ 34 >0) and ((K₃-K₄)<0 and Δ 12 >0) …(23c) ((K2-K1)<0 and Δ 34 <0) and ((K3-K4)<0 and Δ 12 <0) …(23d) ((K2-K1)<0 and Δ 34 >0) and ((K3-K4)>0 and Δ 12 <0) …(23e) ((K2-K1)>0 and Δ 34 <0) and ((K3-K4)<0 and Δ 12 >0) …(23f) For any one of the above cases, when the nonlinear parameters K1 to K4 of the first to fourth qubits 20-1 to 20-4 and the difference Δ between resonance angular frequencies 34 and Δ 12 are appropriately set, the coefficient h of the four-body interaction in equation (6) (4) will not be 0.

[0052] When nonlinear parameters K2 and K1 have the same sign, and nonlinear parameters K3 and K4 have the same sign, the value of (K2-K1) (the absolute value if negative) and the value of (K3-K4) (the absolute value if negative) become small.

[0053] In equations (23a) and (23b), setting the signs of nonlinear parameters K2 and K3 to be positive and the signs of nonlinear parameters K1 and K4 to be negative increases the coefficient h of the four-body interaction (4) (when h (4) is a negative value, the absolute value increases).

[0054] In equations (23c) and (23d), setting the signs of nonlinear parameters K2 and K3 to be negative and the signs of nonlinear parameters K1 and K4 to be positive increases the coefficient h of the four-body interaction (4) (when h (4) is a negative value, the absolute value increases).

[0055] In equation (23e), setting the sign of nonlinear parameter K2 to be negative, the sign of nonlinear parameter K1 to be positive, the sign of nonlinear parameter K3 to be positive, and the sign of nonlinear parameter K4 to be negative increases the coefficient h of the four-body interaction (4)(h (4) If the value is negative, the absolute value will be large.

[0056] In equation (23f), by setting the sign of the nonlinear parameter K2 to positive, the sign of the nonlinear parameter K1 to negative, the sign of the nonlinear parameter K3 to negative, and the sign of the nonlinear parameter K4 to positive, the coefficient h of the four-body interaction is obtained. (4) (h (4) If the value is negative, the absolute value will be large.

[0057] As described above, the coefficient h of the four-body interaction in equation (6) (4) To obtain a non-zero value, we need a nonlinear parameter K with different values. i We need to prepare (i=1,2,3,4).

[0058] Furthermore, in Figure 2, the conditions for the four-body interaction with respect to the resonant angular frequencies ω1~ω4 of the four qubits are TIFF2026142953000025.tif6150…(24) In that case, equation (13) can be expressed as equation (25).

[0059] TIFF2026142953000026.tif10150…(25)

[0060] From equation (25), for example, K1=K4=K>0, K2=K3=-K<0 …(26a) or, K1=K4=K<0, K3=K2=-K>0 …(26b) In that case, for example, (K1-K3)>0, (K4-K2)>0 …(27a) or, (K1-K3)<0, (K4-K2)<0 …(27b) Therefore, the difference in resonant angular frequency Δ 24 and Δ 13 of, Δ 24 >0, Δ 13 >0 …(28a) or, Δ 24 <0, Δ 13 <0 …(28b) By doing so, the numerator (K1-K3)Δ of equation (25) 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 of either K1 or K2, which have opposite signs, at least a portion of the cross-Kerr interaction between the qubit 20 and the coupler 21 (two out of four combinations of the sum of the nonlinear parameters of the qubit 20 and the coupler 21) can be suppressed. The cross-Kerr interaction between the qubit 20 and the coupler 21 is abbreviated as "QC-CKI". Note that in equation (25), when K1=K3 and K4=K2, h (4) The result is 0.

[0061] Furthermore, the conditions for the four-body interaction with respect to the resonant angular frequencies ω1~ω4 of the four qubits are TIFF2026142953000027.tif6150…(29) In that case, equation (13) can be expressed as equation (30).

[0062] TIFF2026142953000028.tif10150…(30)

[0063] From equation (30), for example, K1=K3=K>0, K2=K4=-K<0 …(31a) or, K1=K3=K<0, K2=K4=-K>0 …(31b) In that case, for example, (K1-K4)>0, (K3-K2)>0 …(32a) or, (K1-K4)<0, (K3-K2)<0 …(32b) Therefore, the difference in resonant angular frequency Δ23 and Δ 14 of, Δ 23 >0,Δ 14 >0 …(33a) or, Δ 23 <0,Δ 14 <0 …(33b) By doing so, the numerator term of equation (30) 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) This can be made larger. Also, from equations (31a) and (31b), it is possible to suppress a portion of the cross-Kerr interaction between the qubits 20 (abbreviated as "QQ-CKI") (four out of six combinations of the sum of the nonlinear parameters of the two qubits 20). 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 to each other, it is possible to suppress a portion of the cross-Kerr interaction (QC-CKI) between the qubit 20 and the coupler 21 (two out of four combinations of the sum of the nonlinear parameters of the qubit 20 and the coupler 21). Note that in equation (30), when K1=K4 and K3=K2, h (4) The result is 0.

[0064] Figure 3 is a schematic diagram illustrating some examples of embodiments of the present disclosure. Referring to Figure 3, the quantum circuit device 1 comprises first to fourth qubits 20-1 to 20-4, each equipped with a nonlinear resonant circuit. In Figure 2, an example is shown in which four qubits are coupled via a coupler 21 in a four-body interaction, corresponding to Figure 1, but a three-body interaction, a five-body interaction, or the like may also be used.

[0065] In Figure 3, the first and second qubits 20-1 and 20-2 are connected to the common node n1 via coupling capacitors 31A and 31B, respectively (capacitive coupling), and the third qubit 20-3 is connected to the common node n1 via coupling capacitor 31C (capacitive coupling). The fourth qubit 20-4 is DC-coupled to the common node n1. In the quantum circuit device 1 of Figure 3, only the nonlinearity of the fourth qubit 20-4 contributes to the four-body interaction. Since the circuit in Figure 3 does not include a coupler, there is no cross-Kerr interaction (QC-CKI) between the qubit 20 and the coupler.

[0066] Figure 4 shows the first to fourth qubits 20-1 to 20-4 in Figure 3 configured with JPO. The first to fourth qubits 20-1 to 20-4 in Figure 3 are identical to the first to fourth qubits 20-1 to 20-4 described with reference to Figures 1 and 2, so their description is omitted. The electrodes 24A to 24C of the first to third qubits 20-1 to 20-3 are connected to the common node n1 via coupling capacitors 31A and 31B, respectively (capacitive coupling), while the electrode 24D of the fourth qubit 20-4 is directly connected to the common node n1 by wiring, etc. (DC coupling). In this case, the coupling strength (h) due to the four-body interaction caused by the nonlinearity of qubit 20 (4) In this case, only the nonlinear parameter of the fourth qubit 20-4 is affected.

[0067] In Figure 4, the coupling coefficient h of the four-body interaction due to the nonlinearity of qubit 20 is shown. (4) From equation (13), it can be expressed by the following equation (34).

[0068] TIFF2026142953000029.tif10150…(34)

[0069] In equation (34), the nonlinearity of the first, second, and third qubits 20-1, 20-2, and 20-3 is given by the strength of the coupling due to the four-body interaction (coupling coefficient) h. (4) Since it does not contribute to the equation, any value can be taken. For example, the nonlinear parameters of the four qubits 20-1 to 20-4 may be the same, i.e., K1=K2=K3=K4.

[0070] In this case, the first to fourth qubits 20-1 to 20-4 may have the same layout and configuration. The configuration in Figure 4, compared to the circuit in Figure 2, significantly simplifies the setting of the nonlinearity of the first to fourth qubits 20-1 to 20-4 by changing the connection configuration of the coupling capacitor between the qubit 20 and the common node n1.

[0071] Note that, as with Figure 3, QC-CKI does not exist in Figure 4 because it does not include a coupler. 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). For example, K1=K2=K3=-K4…(35) By doing so, (K1+K4), (K2+K4), and (K3+K4) become 0, and the contribution (influence) of QQ-CKI to the four-body interaction can be suppressed.

[0072] Figure 5 illustrates another example of some embodiments of the present disclosure. In this quantum circuit device 1, the nonlinear parameter K1 of the first qubit 20-1 and the nonlinear parameter K4 of the fourth qubit 20-4 contribute to the four-body interaction (four-body interaction due to the nonlinearity of qubit 20).

[0073] By extracting the terms for the nonlinear parameter K1 and the nonlinear parameter K4 from equation (13), we derive the following equation (36).

[0074] TIFF2026142953000030.tif10150…(36)

[0075] In equation (36), there is no canceling effect of the nonlinearity of qubit 20, and the nonlinear parameter K1 of qubit 20-1 and the nonlinearity parameter K4 of the fourth qubit 20-4 have a difference in resonant angular frequency Δ 34 and Δ 12 The weights are added together. The second qubit 20-2 and the third qubit 20-3 are connected to each other via the ground-terminated first qubit 20-1 and fourth qubit 20-4, respectively, and the nonlinear shape of the second qubit 20-2 and the third qubit 20-3 contributes little to (negligible to) the four-body interaction.

[0076] From equation (36), (Δ 34 =ω3-ω4>0) and (Δ 12 =ω1-ω2>0) …(37a) or (Δ 34 =ω3-ω4<0) and (Δ 12 =ω1-ω2<0) …(37b) In this case, the sign of the nonlinear parameter K1 of the first qubit 20-1 may be the same as the sign of the nonlinear parameter K4 of the fourth qubit 20-4.

[0077] (Δ 34 =ω3-ω4>0)and (Δ 12 =ω1-ω2<0) …(37c) (Δ 34 =ω3-ω4<0) and (Δ 12 =ω1-ω2>0) …(37d) In either case, the nonlinear parameter K1 of the first qubit 20-1 and the nonlinear parameter K4 of the fourth qubit 20-4 may have opposite signs (when one is positive, the other is negative).

[0078] According to this disclosure, it is possible to enable many-body interactions between qubits in various situations, not limited to those described above, and to simplify the setting of the interaction strength, i.e., the coupling coefficient.

[0079] The nonlinear parameter K represents the nonlinearity of the first to fourth qubits 20-1 to 20-4. i (i=1,2,3,4) has two main components: one determined by inductance and the other by capacitance, which can be expressed, for example, by the following equation (38).

[0080] TIFF2026142953000031.tif6150…(38)

[0081] In equation (38), p i The (Participation ratio) 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 (39). TIFF2026142953000032.tif21153…(39) 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 10(B), (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 10(A), (C)). n iJ (q=1,2,3,4) is the number of Josephson junctions (Figure 7) connected in series in the i-th qubit 20-i.

[0082] E in equation (38) Ci This is given by equation (40). TIFF2026142953000033.tif11150…(40)

[0083] e is an elementary charge, Ci 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.

[0084] Figure 6 is a diagram illustrating the structural inductance of a qubit. The p in equation (39) i The 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 6) should be made as small as possible.

[0085] The qubit 20 may be configured as a JPO equipped with a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement) as a nonlinear element, as shown in Figure 7. SNAIL231 may be configured with a small Josephson junction 201 and N large Josephson junctions 202-1 to 202-N connected in series in parallel. The Josephson energy E of the Josephson junction 201 J The Josephson energies E of each Josephson junction 202-1 to 202-N are J 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 201 is the critical current I of Josephson junctions 202-1 to 202-N. c 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 202 is smaller than the junction sizes of Josephson junctions 202-1 to 202-N, and the junction size of Josephson junction 201 is assumed to be α times (0 < α < 1) the junction size of Josephson junctions 202-1 to 202-N. By connecting Josephson junctions 202-1 to 202-N in series, the nonlinearity is weakened.

[0086] The nonlinear parameter K represents the nonlinearity (Kerr nonlinearity) of the i-th qubit 20-i using SNAIL. i(i=1,…,4) is the Hamiltonian H of qubit 20-i. i When the following equation (41) is true, TIFF2026142953000034.tif7150…(41) It is expressed by the following equation (42) (Reference 1). Note that in equation (41), a i + and a i These are the boson creation and annihilation operators for the i-th qubit, 20-i.

[0087] TIFF2026142953000035.tif11150…(42) ω i This is the resonant angular frequency of qubit 20-i.

[0088] Similarly, the parameter (Kerr coefficient) (nonlinear parameter) K represents the nonlinearity of the coupler 21 using SNAIL. g This can be expressed by the following equation (43).

[0089] TIFF2026142953000036.tif11150…(43) ω g This is the resonant angular frequency of the coupler 21.

[0090] Figure 8 shows an example of the magnetic field characteristics 801 at the resonant frequency (GHz (Giga-Hertz)) of SNAIL and the magnetic field characteristics 802 at the Kerr nonlinearity (nonlinear parameter) (MHz (Mega-Hertz)) of SNAIL. In a JPO using a SNAIL with a negative nonlinear parameter K, the magnitude of the applied magnetic flux is minimized at the position of the minimum value of the resonant frequency of the qubit (magnetic flux Φ = ±0.5Φ0 (half integer) (magnetic flux quantum Φ0 = h / 2e)). In a JPO using a SNAIL with a positive nonlinear parameter K, the magnitude of the applied magnetic flux deviates from ±0.5 (half integer) (Φ = 0.4 to -0.4Φ0, 0.6 to 1.4Φ0, -0.6 to -1.4Φ0). Note that the sign (positive or negative) of the nonlinear parameter in SQUID cannot be changed by the applied magnetic field.

[0091] The above disclosure also applies to the circuit in Figure 2. Figure 9 shows a configuration in the circuit of Figure 2 in which the first qubit 20-1 and the fourth qubit 20-4 are composed of JPOs including SNAIL231A and 231D, and the second qubit 20-2 and the third qubit 20-3 are composed of JPOs including SQUID210B and 210C. The JPOs including SNAIL231A and 231D oscillate (parametric oscillation) with a capacitively coupled AC signal. For example, an AC signal (with a frequency twice the resonant frequency) that capacitively couples 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.

[0092] The nonlinear parameters K1 and K2 of the first qubit 20-1 and the second qubit 20-2 may be set to opposite signs (for example, K2 being positive and K1 being negative), and the nonlinear parameters K3 and K4 of the third qubit 20-3 and the fourth qubit 20-4 may be set to opposite signs (for example, K3 being positive and K4 being negative). For example, K2>0, K1=-K2<0, K3>0, K4=-K3<0 …(44) In this case, (K1+K2) and (K3+K4) are set to 0, and the values ​​of (K1+K3) and (K2+K4) are smaller than when they have the same sign, because K1 and K3 have opposite signs, and K3 and K4 have opposite signs, thus suppressing QQ-CKI.

[0093] The first qubit 20-1 and the fourth qubit 20-4, SNAIL231A and 231D, are supplied with magnetic fields ψ1 and ψ4 (magnetic field characteristics 802 in Figure 8) such that the signs of the nonlinear parameters K1 and K4 are negative, respectively, from a magnetic field generator (an inductor component with one end connected to a signal line and the other to ground). The first and fourth qubits (JPO) 20-1 and 20-4, including SNAIL231A and 231D, oscillate (parametric oscillation) in response to a capacitively coupled AC signal. For example, an AC signal (with a frequency twice the resonant frequency) is supplied from a signal source (not shown) to capacitively couple to electrodes 24A and 24D of the first qubit 20-1 and the fourth qubit 20-4, respectively. 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.

[0094] Furthermore, for example, if (K2-K1) is positive and (K3-K4) is positive, the difference Δ of the resonant angular frequency 34 and Δ 12 By setting the values ​​to have the same sign, the bond coefficient h of the four-body interaction in equation (6) can be determined. (4) (K2-K1)Δ 34 +(K3-K4)Δ 12 The value (or absolute value if negative) can be increased.

[0095] Furthermore, configurations that change the nonlinearity of the first to fourth qubits 20-1 to 20-4 may be as shown in Figures 10(A), 10(B), and 10(C). Figure 10(A) shows a configuration in which M Josephson junctions 207-1 to 207-M ​​are connected in series with a SQUID 210 between the power supply 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 10(B) shows a configuration in which L SQUIDs 210-1 to 210-L are connected in series between the power supply 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. For example, as L increases, the nonlinearity decreases. Figure 10(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 the power supply 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.

[0096] The quantum circuit device 1, consisting of four qubits 20-1 to 20-4 connected to the common node n1 of the embodiment described with reference to Figures 3 and 4, may be represented as shown by reference numeral 11 in Figure 11(A), or as shown by reference numeral 12. In the circuit of reference numeral 12, the double lines between the qubits indicated by circles represent transmission lines (wiring) with coupling capacitors.

[0097] Figure 11(B) is a diagram illustrating the configuration of a four-unit quantum computing device (quantum annealing machine) 300. It shows a configuration that extends the circuit configuration of the embodiment described with reference to Figures 3 and 4, etc., to include multiple bits. As shown in Figure 11(B), the basic circuit can be expanded to construct a large-scale circuit. In Figure 11(B), each circle represents a physical qubit, specifically a qubit 20.

[0098] The Hamiltonian for the all-to-all Ising spin glass model is given by equation (45).

[0099] TIFF2026142953000037.tif14150…(45) (However, σ (i) Z This is logical spin (Pauli matrix), J ij b is the interaction coefficient. i (This refers to the local magnetic field.)

[0100] Equation (45) can be expanded into the Hamiltonian of physical qubits as follows, where K = N(N-) / 2 (when N=6, K=15).

[0101] TIFF2026142953000038.tif14150…(46)

[0102] In other words, the interaction coefficient (matrix) J of a fully connected Ising spin ij In the Hamiltonian of equation (46), the local magnetic field J acting on the physical qubit is... k It is converted to C of equation (46). l This is a constraint (see Non-Patent Document 1). In Figure 11(B), the two numbers attached to each circle (physical qubit) are two logical bits (J in equation (45)). ij This represents ij). Nine distinct frequencies are provided to prevent extraneous four-body interactions, and the numbers 1-9 within each circle (physical qubit) represent the labels of these nine distinct frequencies. The four qubits in the lowest row are fixed values, and the solution to the optimal problem is read out from the rows above them.

[0103] Figure 11(B) shows that the quantum annealing machine 300 is equivalent to Figure 12, which illustrates a physical implementation of the LHZ method (number of logical bits N=6, number of physical bits=15) disclosed in Non-Patent Documents 1 and 2. Figure 12 is a diagram illustrating the configuration of a quantum computing device (quantum annealing machine) 300 that includes four qubits 20-1 to 20-4 and a coupler 21 as a unit. The gray circle represents the coupler 21, and the four white circles around it represent the physical qubits, which are qubits 20. In Figure 12, the four nearest qubits 20 are coupled to the coupler 21 via a four-body interaction, forming a unit. Figure 12 corresponds to a fully connected quantum annealing machine, where the four qubits in the bottom row are fixed values, and the solution to the optimal problem is read out from the row above.

[0104] 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.

[0105] Although SQUIDs and SNAILs have been described as examples of nonlinear elements for the qubits 20 and the couplers 21, ATS (Asymmetrically Threaded SQUID) or STS (Symmetrically Threaded SQUID) may also be used. Alternatively, any other configuration of Josephson junctions may be used. For example, the qubit 20 may also include a transmon constituted by one Josephson junction.

[0106] Furthermore, the cross-Kerr interaction (cross-Kerr nonlinear interaction) described above is not limited to superconducting quantum circuits, and can also be applied to cross-Kerr nonlinear interaction between an optical cavity and microwaves. That is, although JPOs have been described as examples of Kerr parametric oscillators (KPOs) having the Kerr effect, it goes without saying that the qubits 20-1 to 20-4 may be KPOs other than JPOs.

[0107] [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

[0108] The embodiments / examples exemplified above are additionally noted as follows (but are not limited to the following).

[0109] (Additional Note 1) A quantum circuit device has a configuration in which, for N qubits (N is a predetermined integer of 3 or more) coupled by multi-body interaction, the number of qubits to which nonlinearity contributes to the multi-body interaction is limited to M (1≦M<N), and / or One or more of the N qubits have a configuration in which the sign of a parameter representing the nonlinearity of the qubit is set to either positive or negative, such that the strength of the coupling of the many-body interaction is increased.

[0110] (Note 2) In the quantum circuit device of Note 1, the many-body interaction is a four-body interaction with N = 4, and one of the four qubits is DC-coupled to a common node, while the remaining qubits are capacitively coupled to the common node.

[0111] (Note 3) In the quantum circuit device of Note 1 or 2, the many-body interaction is a four-body interaction where N is 4, and the opposing first qubit and fourth qubit are connected via a first capacitor, the first qubit is connected to the adjacent second qubit and third qubit via a second capacitor and a third capacitor, respectively, and the fourth qubit is connected to the adjacent second qubit and third qubit via a fourth capacitor and a fifth capacitor.

[0112] (Note 4) In the quantum circuit device of Note 1 or 2, the coefficient h represents the strength of the coupling of the four-body interaction in which at least one of the four qubits is configured such that the i-th qubit is DC-coupled to the common node. (4) The following is an approximate formula: TIFF2026142953000039.tif10150 (However, g ij This is the strength of the coupling between the i-th and j-th qubits (i=1, j=2, 3), Δ li , Δ mi , Δ ni These are the differences in the resonant angular frequencies of the l, m, and nth qubits and the i-th qubit (l, m, n = 1, 2, 3, 4, l ≠ m ≠ n ≠ i), respectively. i (where is a parameter representing the nonlinearity of the i-th qubit).

[0113] (Note 5) In the quantum circuit device of Note 2, the coefficient h represents the strength of the coupling of the four-body interaction by the four qubits. (4) However, it is expressed as a combination of a term containing the difference in parameters representing the nonlinearity of two qubits and a term containing the difference in parameters representing the nonlinearity of the remaining two qubits, where the signs of the parameters representing the nonlinearity of the two qubits are set to be opposite signs, and the signs of the parameters representing the nonlinearity of the remaining two qubits are set to be opposite signs.

[0114] (Note 6) In the quantum circuit device of Note 2, the sign of parameter K1, which represents the nonlinearity of the first of the four qubits, is set to the opposite sign of parameter K2, which represents the nonlinearity of the second qubit. The parameter K4 representing the nonlinearity of the fourth qubit is set to have the opposite sign to the parameter K3 representing the nonlinearity of the third qubit. The difference Δ between the resonant angular frequency ω3 of the third qubit and the resonant angular frequency ω4 of the fourth qubit 34 The difference Δ between the resonant angular frequency ω1 of the first qubit and the resonant angular frequency ω2 of the second qubit. 12 Regarding (K2-K1)Δ 34 (K3-K4)Δ 12 The values ​​and signs of the parameters K1 to K4 representing the nonlinearity are set such that the sum of the two is large.

[0115] (Note 7) In any of the quantum circuit devices described in Notes 1 to 6, four qubits are arranged as the basic unit to constitute a quantum computer.

[0116] (Supplementary Note 8) In the quantum circuit device according to any one of Supplementary Notes 1 to 7, the quantum bit comprises at least any one of a Josephson junction, a SQUID (Superconducting Quantum Interference Device), and a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement) in which at least one Josephson junction and a plurality of Josephson junctions connected in series are connected in parallel within a loop.

[0117] (Supplementary Note 9) A method of controlling a quantum circuit device comprises, for N quantum bits (N is a predetermined integer of 3 or more) coupled by multi-body interaction, limiting the number of quantum bits to which nonlinearity contributes in said multi-body interaction to M (1≤M<N), and / or setting a sign of a parameter representing nonlinearity of one or more quantum bits among said N quantum bits to either positive or negative so as to increase the coupling strength of said multi-body interaction.

[0118] (Supplementary Note 10) In the method of controlling a quantum circuit device according to Supplementary Note 9, said multi-body interaction is a 4-body interaction where N is 4.

[0119] It is to be noted that the disclosures of Non-Patent Documents 1, 2 and Reference 1 are incorporated herein by reference. Within the scope of the entire disclosure (including the scope of claims), modifications and adjustments of the embodiments or examples can be further made based on the basic technical idea thereof. Also, 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 within the scope of the claims. That is, the present disclosure naturally includes various variations and modifications that can be made by those skilled in the art according to the entire disclosure including the scope of claims and the technical idea thereof. Description of Reference Signs

[0120] 1 Quantum circuit device 10 Josephson junction 11, 12 Circuit (circuit representation) 15 Inductors 16 Capacitors 17. First electrode (first node) 18. Second electrode (second node) 20, 20A~20E qubits 20-1~20-4 1st to 4th qubits 21 Combiner 24, 24A~24D Electrodes (Coupler connection part) 31, 31A~31C coupled 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 ​​Josephson junction 210, 210', 210A~210D, 210-1~210-L SQUID 231, 231A, 231D SNAIL 300 Quantum Computers (Quantum Annealing Machines) 801 Magnetic field characteristics (magnetic field response) at resonant frequency 802 Nonlinear magnetic field characteristics (magnetic field response)

Claims

1. For N qubits (where N is a predetermined integer greater than or equal to 3) connected by many-body interactions, A configuration in which the number of qubits to which nonlinearity contributes to the many-body interaction is limited to M (1 ≤ M < N), and / or, A quantum circuit device having a configuration in which one or more of the N qubits are configured such that the sign of a parameter representing the nonlinearity of the qubit is set to either positive or negative, thereby increasing the strength of the coupling of the many-body interaction.

2. The aforementioned many-body interaction is a four-body interaction in which N is 4. The quantum circuit device according to claim 1, wherein one of the four qubits is DC-coupled to a common node, and the remaining qubits are capacitively coupled to the common node.

3. The aforementioned many-body interaction is a four-body interaction in which N is 4. The opposing first and fourth qubits are connected via the first capacitor. The first qubit is connected to the adjacent second qubit and third qubit via the second and third capacitors, respectively. The quantum circuit device according to claim 1, wherein the fourth qubit is connected to the adjacent second qubit and third qubit via a fourth capacitor and a fifth capacitor.

4. The coefficient h represents the strength of the coupling in the four-body interaction, in which at least one of the four qubits, the i-th qubit, is DC-coupled to the common node. (4) The approximate formula is as follows: (However, g iｊ This is the strength of the coupling between the i-th and j-th qubits (i=1, j=2, 3), Δ li , Δ mi , Δ ni These are the differences in the resonant angular frequencies of the l, m, and nth qubits and the i-th qubit (l, m, n = 1, 2, 3, 4, l ≠ m ≠ n ≠ i), respectively, K i The quantum circuit device according to claim 2, wherein is a parameter representing the nonlinearity of the i-th qubit.

5. The coefficient h represents the strength of the coupling of the four-body interaction between the four qubits. (4) However, it can be expressed as a composition of a term containing the difference in parameters representing the nonlinearity of two qubits and a term containing the difference in parameters representing the nonlinearity of the remaining two qubits. The signs of the parameters representing the nonlinearity of each of the two qubits are set to be opposite signs to each other. The quantum circuit device according to claim 2, wherein the signs of the parameters representing the nonlinearity of each of the remaining two qubits are set to be opposite signs to each other.

6. Parameter K representing the nonlinearity of the first qubit among the four qubits 1 has a sign opposite to that of parameter K representing the nonlinearity of the second qubit 2 , Parameter K represents the nonlinearity of the fourth qubit. ４ The parameter K represents the nonlinearity of the third qubit. 3 And the opposite sign, The resonant angular frequency ω of the third qubit ３ and the resonant angular frequency ω of the fourth qubit ４ The difference Δ 34 And the resonant angular frequency ω of the first qubit. １ and the resonant angular frequency ω of the second qubit ２ The difference Δ １２ Regarding (K 2 -K 1 )Δ 34 and (K 3 -K 4 )Δ １２ The parameter K representing the nonlinearity is set such that the sum with is large. １ ~K 4 The quantum circuit device according to claim 2, wherein the value and sign are set.

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

8. 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 any one of claims 1 to 7, comprising at least one of the above.

9. For N qubits (where N is a predetermined integer greater than or equal to 3) connected by many-body interactions, Restricting the number of qubits to which nonlinearity contributes to the many-body interaction to M (1 ≤ M < N), and / or, The sign of the parameter representing the nonlinearity of one or more of the N qubits is set to either positive or negative so as to increase the strength of the coupling of the many-body interaction. A method for controlling a quantum circuit device, including the control of the device.

10. The control method for a quantum circuit device according to claim 9, wherein the many-body interaction is a four-body interaction with N = 4.

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