Quantum circuit device and its control method

Abstract

The present invention provides a quantum circuit device that suppresses 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) connected to a common node and coupled by many-body interaction, wherein the N qubits include at least one qubit whose nonlinearity contributes to the many-body interaction, and one or more qubits whose nonlinearity does not contribute to the many-body interaction.

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) [Overview of the project] [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 solve the above-mentioned problems. [Means for solving the problem]

[0006] According to one embodiment of the present disclosure, a quantum circuit device has N qubits (where N is a predetermined integer of 3 or more) connected to a common node and coupled by a many-body interaction, wherein the N qubits include at least one qubit whose nonlinearity contributes to the many-body interaction, and one or more qubits whose nonlinearity does not contribute to the many-body interaction.

[0007] According to one embodiment of the present disclosure, a method for controlling a quantum circuit is provided, wherein N qubits (where N is a predetermined integer of 3 or more) connected to a common node and coupled by many-body interactions are composed of at least one qubit whose nonlinearity contributes to the many-body interaction, and the remaining qubits being one or more qubits whose nonlinearity does not contribute to the many-body interaction. [Effects of the Invention]

[0008] This disclosure makes it 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 the configuration of at least one example of several embodiments of the present disclosure. [Figure 3] This figure illustrates the configuration of at least one example of several embodiments of the present disclosure. [Figure 4] This figure illustrates the configuration of at least one example of several embodiments of the present disclosure. [Figure 5] This figure illustrates the configuration of at least one example of several embodiments of the present disclosure. [Figure 6] This figure illustrates at least one example of several embodiments of the present disclosure. [Figure 7] This figure illustrates the configuration of at least one example of several embodiments of the present disclosure. [Figure 8] This figure illustrates the configuration of at least one example of several embodiments of the present disclosure. [Figure 9] (A) through (C) are diagrams illustrating the configuration of at least one example of several embodiments of the present disclosure. [Figure 10] (A) and (B) are figures illustrating at least one example of several embodiments of the present disclosure. [Figure 11]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. According to some embodiments of this disclosure, as detailed below, for example, with respect to four qubits coupled in a four-body interaction, the number of qubits to which nonlinearity contributes to the four-body interaction is limited (suppressed) by coupling capacitance or circuit structure. Furthermore, according to this disclosure, a quantum circuit device in which cross-Kerr interaction is suppressed is disclosed by appropriately combining qubits with different signs (polarities) of nonlinearity.

[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), TIFF2026142952000002.tif7150…(1) Kerr nonlinearity K ican be made to correspond.

[0016] In formula (1), Δ is the resonant angular frequency ω of the coupler 21 c and a half of the angular frequency ωp of the i-th pump signal Δ=ω c -(1 / 2)ωp …(2) where Εp is the intensity of two-photon driving (pump term). a i + and a i are the creation operator and annihilation operator for a boson (photon) 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, each of which is (K1+K g ), (K2+K g ), (K3+K g ), (K4+K g ) is 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 a nonlinear parameter of the coupler 21.

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

[0019] The above problem is one example; according to the present disclosure, not limited to the above, in various situations, the contribution of the nonlinearity of the qubits 20 in the multi-body interaction between the qubits 20 can be suppressed.

[0020] Figure 2 is a schematic diagram illustrating an example of the present disclosure. Referring to Figure 2, 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 the four qubits 20-1 to 20-4 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.

[0021] In Figure 2, the first and second qubits 20-1 and 20-2 are commonly connected to node n1 via coupling capacitors 31A and 31B, the third qubit 20-3 is commonly connected to node n1 via coupling capacitor 31C, and the fourth qubit 20-4 is DC-coupled to node n1 (connected by direct wiring, etc.). Node n1, to which the first to fourth qubits 20-1 to 20-4 are commonly connected, is also called the common node. In the circuit of Figure 2, in quantum circuit device 1, only the nonlinearity of the fourth qubit 20-4 contributes to the four-body interaction. Furthermore, since the circuit of Figure 2 does not include a coupler, QC-CKI does not exist.

[0022] Figure 3 shows an example of the circuit in Figure 2. In Figure 3, the configuration of the first to fourth qubits 20-1 to 20-4 is the same as in Figure 1, and its explanation is omitted. Referring to Figure 3, the coupler 21 of Figure 1 is not provided, and the first to third qubits 20-1 to 20-3 are capacitively coupled (AC coupled) to the common node n1 via coupling capacitors 31A to 31C, while the fourth qubit 20-4 is DC coupled (DC coupled) to the common node n1. In quantum circuit device 1, only the nonlinearity of the fourth qubit 20-4 (Kerr nonlinearity) affects the coupling strength (h) due to the four-body interaction caused by the nonlinearity of qubit 20. (4) ) contributes to.

[0023] The strength of the four-body interaction coupling due to the nonlinearity of qubit 20 is h (4) This can be expressed (approximated) by, for example, the following equation (3).

[0024] TIFF2026142952000003.tif10150…(3)

[0025] In equation (3), g ij This represents the interaction between the i-th qubit 20-i and the j-th qubit 20-j (i≠j=1,2,3,4). In equation (3), g12 and g13 appear. Δ ij This represents the difference in resonant angular frequencies between the i-th qubit 20-i and the j-th qubit 20-j (i≠j=1,2,3,4). In equation (3), Δ13, Δ14, and Δ34 appear. K4 is the nonlinear parameter of the fourth qubit, 20-4.

[0026] In equation (3), the nonlinear parameters K1, K2, and K3 of the first, second, and third qubits 20-1, 20-2, and 20-3 are the coupling strength (coupling coefficient) h due to the four-body interaction. (4) It does not contribute to this. Therefore, these nonlinear parameters K1, K2, and K3 can take any value. For example, the nonlinear parameters of the first to fourth qubits 20-1 to 20-4 can be made identical, i.e., K1=K2=K3=K4.

[0027] In this case, the first to fourth qubits 20-1 to 20-4 may have the same nonlinear parameters K1 to K4, as well as the same layout and configuration. Note that, as explained with reference to Figure 2, since no coupler is included in Figure 3, QC-CKI does not exist.

[0028] Regarding the nonlinear parameters K1 to K4 of the first to fourth qubits 20-1 to 20-4, for example, K1=K2=K3=K, K4=-K …(4) By setting it as follows, (K1+K4) (K2 + K4) (K3+K4) is 0 in all cases, canceling out QQ-CKI and suppressing the contribution (influence) of QQ-CKI to the four-body interaction. Alternatively, by making K4 have the opposite sign to K1, K2, and K3, the values ​​of (K1+K4), (K2+K4), and (K3+K4) can be reduced.

[0029] Here, the four-body interaction between the four qubits 20 arises not from the coupler 21, but from the nonlinearity of the qubits 20 (Kerr nonlinearity). Referring again to Figure 3, the coupling coefficient h of the four-body interaction arising from the nonlinearity between the qubits 20. (4) For example, it can be expressed (approximated) as follows:

[0030] TIFF2026142952000004.tif17150…(5)

[0031] In equation (5), 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 ji (i≠j=1,2,3,4) 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.

[0032] Here, in equation (5), the multiplication term is: TIFF2026142952000005.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 (6). TIFF2026142952000006.tif9150…(6)

[0033] In equation (6), TIFF2026142952000007.tif8150…(7) It is said that, under these conditions, by minimizing the difference Δ between the resonant angular frequencies of the two qubits 20, the value of equation (7) becomes large.

[0034] Furthermore, from equation (6), 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 (6), the nonlinear parameter K of qubit 20 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) As explained below, Figure 1 g (4) Compared to that, it's relatively easier to enlarge.

[0035] Note that the strength (coefficient of bonding) of the four-body interaction shown in Figure 1 is g. (4) This is given, for example, by the following equation (8) (Non-Patent Document 2).

[0036] TIFF2026142952000008.tif9150…(8)

[0037] Here, K g This is a parameter (nonlinear parameter) that represents the nonlinearity of the coupler 21. Δ i (i=1,2,3,4) is the resonant angular frequency ω of the coupler. c and the resonant angular frequency ω of the i-th qubit 20-i 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.

[0038] From equation (8), TIFF2026142952000009.tif9150…(9) 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 becomes large, and the four-body interaction becomes strong. Therefore, the resonant angular frequency ω of each qubit i (i=1,2,3,4) and the resonant angular frequency ω of the coupler c It needs to be somewhat close to this. In equation (8), g i / Δ i Approximating (i=1,2,3,4) with g / Δ, the strength of the four-body interaction coupling via the coupler 21 is given by the nonlinear parameter K of the coupler 21. g The fourth term of (g / Δ): (g / Δ) 4 This means that the nonlinear parameter K of the coupler 21 is multiplied. g (g / Δ) to the power of 4 (g / Δ) less than 1 4 Because of this, the bond coefficient g of the four-body interaction in equation (8) (4) Basically, it will only result in a small value.

[0039] Equation (3), which represents the four-body interaction due to the nonlinearity between the four qubits 20, does not involve parameters related to the coupler (e.g., 21 in Figure 1). Therefore, adjustment of the resonant frequency of the coupler 21 in Figure 1 is not necessary to strengthen the four-body interaction. Furthermore, the installation of a signal source for varying the coupler frequency, control lines, input / output lines, and measuring instruments is unnecessary. Although equation (3), which represents the four-body interaction, does not involve parameters related to the coupler, if the coupler generates an interaction that includes a four-body interaction, the four-body interaction represented by equation (3) can coexist. In this case, the strength of the four-body interaction coupling is h (4) +g (4) (h (4) The absolute value and g (4) (This can also be done by adding the absolute values.)

[0040] In equation (5), if we focus on i=1, that is, the first qubit 20-1 in Figure 3, • 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 (5) is given as follows: TIFF2026142952000010.tif9150…(10)

[0041] Expanding equation (5) for the first to fourth qubits 20-1 to 20-4 in Figure 3, we obtain the following equation (11).

[0042] TIFF2026142952000011.tif10150…(11)

[0043] Equation (5) is a generalization of equation (11).

[0044] In equation (11) 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, TIFF2026142952000012.tif6150…(12) Let's assume that.

[0045] From equation (12) TIFF2026142952000013.tif6150 TIFF2026142952000014.tif6150

[0046] therefore, TIFF2026142952000015.tif6150…(13)

[0047] Here, the coupling constant g between the first and second qubits 20-1 and 20-2 is 12 And the coupling constant g between the third and fourth qubits 20-3 and 20-4. 34 This means that when their resonant angular frequencies are close, they are approximated to be equal. TIFF2026142952000016.tif6150…(14)

[0048] Furthermore, the coupling constant g between the first and third qubits 20-1 and 20-3, which are connected via a node (common node) n1, is also a coupling constant. 13 The coupling constant g between the first and fourth qubits 20-1 and 20-4, which are connected via node n1. 14 The coupling constant g between the second and third qubits 20-2 and 20-3, which are connected via node n1. 23 The coupling constant g between the second and fourth qubits 20-2 and 20-4, which are connected via node n1. 24 This means that when their resonant angular frequencies are close together, they are considered to be equal. TIFF2026142952000017.tif6150…(15) twist, TIFF2026142952000018.tif6150…(16) TIFF2026142952000019.tif6150…(17)

[0049] Using equations (13) through (17), we can see that equation (3), which is reproduced below, can be derived from the fourth term on the right-hand side of equation (9).

[0050] TIFF2026142952000020.tif10150…(3)

[0051] Furthermore, the nonlinear parameter K of the qubit 20-i (i=1,2,3,4) i 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 (18).

[0052] TIFF2026142952000021.tif11153 …(18)

[0053] In equation (18), 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, as follows:

[0054] TIFF2026142952000022.tif18153…(19)

[0055] 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 9(B)), 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 9(A), Figure 9(C)), n iJ (q=1,2,3,4) is the number of Josephson junctions connected in series in the i-th qubit 20-i.

[0056] E in equation (18) Ci This is given by equation (20). TIFF2026142952000023.tif11150…(20)

[0057] Here, e is the elementary charge, and C i is the effective structural capacitance of the qubit 20. For example, it may be the capacitance of a capacitor (shunt capacitor) 206 of the i-th qubit 20-i.

[0058] FIG. 4 is a diagram explaining the structural inductance of the SQUID 210 of the qubit 20. p in formula (19) i (i=1,2,3,4) has a maximum value of 1. p i to bring p close to the maximum value, the structural inductance L i (inductance L1 in FIG. 4) is made as small as possible.

[0059] At least one of the four qubits 20 in FIG. 2 may be configured with a JPO including a SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement) as shown in FIG. 5. Referring to FIG. 5, the SNAIL 231 may be configured to include N (N≧1) Josephson junctions 202-1 to 202-N connected in series in parallel with a small Josephson junction 201. The Josephson energy E of the Josephson junction 201 J is α times the respective Josephson energy E of the Josephson junctions 202-1 to 202-N J (0<α<1). Since the Josephson energy is proportional to the critical current, the critical current of the Josephson junction 201 is α times the respective critical current I of the Josephson junctions 202-1 to 202-N c (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. Accordingly, the junction size of the Josephson junction 201 is smaller than the respective junction size of the Josephson junctions 202-1 to 202-N, and the junction size of the Josephson junction 201 is α times the respective junction size of the Josephson junctions 202-1 to 202-N (0<α<1). Connecting the Josephson junctions 202-1 to 202-N in series reduces nonlinearity.

[0060] 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 expressed by the following equation (21), TIFF2026142952000024.tif7150…(21) This is expressed by equation (22) below (Reference 1). In equation (21), ai+ and ai are the boson creation and annihilation operators in qubit 20-i.

[0061] TIFF2026142952000025.tif11150…(22) ω i This is the resonant angular frequency of qubit 20-i.

[0062] 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 (23).

[0063] TIFF2026142952000026.tif11150…(23) ω g This is the resonant angular frequency of the coupler 21.

[0064] Figure 6 shows an example of the magnetic field characteristics (magnetic field response) 601 of SNAIL at its resonant frequency (GHz (Giga-Hertz)) and the magnetic field characteristics (magnetic field response) 602 of SNAIL at its Kerr nonlinearity (MHz (Mega-Hertz)). A JPO using a SNAIL with a negative nonlinear parameter K will have a minimum magnitude of applied magnetic flux at the position of the minimum value of the qubit's resonant frequency (magnetic flux Φ = ±0.5Φ0 (half integer) (magnetic flux quantum Φ0 = h / 2e)). A JPO using a SNAIL with a positive nonlinear parameter K will have an applied magnetic flux magnitude outside of ±0.5 (half integer) (Φ = 0.4 to -0.4Φ0, 0.6 to 1.4Φ0, -0.6 to -1.4Φ0). Note that the sign of the nonlinear parameter in SQUID cannot be changed by the applied magnetic field.

[0065] Incidentally, the above-described approach (cancellation of nonlinear parameters by positive and negative nonlinear parameters) can also be applied to the circuit in Figure 1 equipped with the coupler 21. As previously mentioned, in Figure 1 there are six types of QQ-CKI proportional to (K1+K2), (K1+K3), (K1+K4), (K2+K3), (K2+K4), and (K3+K4).

[0066] K1=K4=-K, K2=K3=K …(24) If we set it as follows, (K1+K2) (K1+K3) (K2 + K4) It can be seen that the four types proportional to (K3 + K4) cancel each other out nicely. However, two types remain that are proportional to (K1+K4) and (K2+K3).

[0067] Figure 7 shows an example in the circuit of Figure 3 in which the fourth qubit 20-4 is constructed using a JPO with SNAIL, and the first qubit 20-1, the second qubit 20-2, and the third qubit 20-3 are constructed using JPOs with SQUID. By setting the nonlinear parameters of the first to third qubits 20-1 to 20-3 to K1=K2=K3=K (for example, positive values) and the nonlinear parameter of the fourth qubit 20-4 to K4=-K (negative value), (K1+K4), (K2+K4), and (K3+K4) all become 0, and it can be seen that QQ-CKI cancels out well.

[0068] Figure 8 shows an example of a configuration that reduces the effects of cross-Kerr interaction compared to the circuit configuration in Figure 1. Referring to Figure 8, the first qubit 20-1 and the fourth qubit 20-4 of Figure 1 are configured as JPOs equipped with SNAIL, and the second qubit 20-2 and the third qubit 20-3 are configured as JPOs equipped with SQUID. By setting the nonlinear parameters of the second and third qubits 20-2 and 20-3 to K2=K3=K (for example, positive values), and the nonlinear parameters of the first and fourth qubits 20-1 and 20-4 to K1=K4=-K (negative values), (K1+K2), (K1+K3), (K2+K4), all (K3+K4) equal 0, so that 4 out of 6 combinations of the sum of nonlinear parameters of the two qubits 20 can be effectively canceled out. Further, let the nonlinear parameter K of the coupler 21 g be K, whereby (K1+K g ), (K4+K g ) are all equal to 0, so that 2 out of 4 combinations of the sum of nonlinear parameters of the qubit 20 and the coupler 21 can be effectively canceled out.

[0069] In FIG. 8, the applied magnetic field (magnetic flux) applied to the SNAILs 231A and 231D of the first and fourth qubits 20-1 and 20-4 is set to a magnetic field (magnetic field characteristic 602 in FIG. 6) where nonlinearity becomes a negative value in the magnetic field characteristic (magnetic field response) 602 of the nonlinear parameter of the SNAIL structure shown in FIG. 6. The first and fourth qubits (JPOs) 20-1 and 20-4 including the SNAILs 231A and 231D oscillate (parametric oscillation) by capacitively coupled AC signals. For example, AC signals (having a frequency twice the resonant frequency) capacitively coupled to the electrode 24A of the first qubit 20-1 and the electrode 24D of the fourth qubit 20-4 are supplied from a signal source (not shown). On the other hand, a magnetic field (DC magnetic field + AC magnetic field with a frequency approximately twice the resonant frequency) is applied to the SQUIDs 210B and 210C of the second and third qubits 20-2 and 20-3 respectively from a magnetic field applying unit (not shown), causing oscillation (parametric oscillation) at a predetermined resonant frequency.

[0070] In the configuration of FIG. 8, the coupling strength h of the four-body interaction caused by the nonlinearity of the qubits 20 (4) (for example, formula (9)) and the coupling strength g of the four-body interaction of the qubits 20 via the coupler 21 (4) (for example, formula (8)) may be combined to serve as the coupling strength of the four-body interaction.

[0071] Furthermore, configurations such as those shown in Figures 9(A), 9(B), and 9(C) may be used to change the nonlinearity in the first to fourth qubits 20-1 to 20-4. Figure 9(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 9(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. As L increases, the nonlinearity decreases. Figure 9(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.

[0072] The quantum circuit device 1, consisting of four qubits 20-1 to 20-4 connected to the common node n1 of the above embodiment described with reference to Figures 2 and 3, may be represented as shown by reference numeral 11 in Figure 10(A), or as shown by reference numeral 12. In the circuit of reference numeral 12, the double lines between qubits indicated by white circles represent transmission lines (wiring) with coupling capacitors.

[0073] Figure 10(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 2, 3, and 7, etc., to a multi-bit configuration. As shown in Figure 10(B), the basic circuit can be expanded to construct a large-scale circuit. In Figure 10(B), each circle represents a physical qubit, specifically a qubit 20.

[0074] The Hamiltonian for the all-to-all Ising spin glass model is given by the following:

[0075] TIFF2026142952000027.tif14150…(25) (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.)

[0076] Equation (25) can be expanded into the Hamiltonian of physical qubits in the following equation (26) by setting K = N(N-1) / 2 (when N=6, K=15).

[0077] TIFF2026142952000028.tif14150…(26)

[0078] In other words, the interaction coefficient (matrix) J of a fully connected Ising spin ij In the Hamiltonian of equation (26), the local magnetic field J acting on the physical qubit is... k This is converted to C in equation (26). l This is a constraint (see Non-Patent Document 1). In Figure 10(B), the two numbers attached to each circle (physical qubit) are two logical bits (J in equation (25)). ij This represents ij). Nine distinct frequencies are provided to avoid extraneous four-body interactions, and the numbers 1-9 within each circle (physical qubit) represent the labels of these nine distinct frequencies. The bottom four qubits are fixed values, and the solution to the optimal problem is read out from the rows above them.

[0079] Figure 10(B) shows that the quantum annealing machine 300 is equivalent to Figure 11, 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, 2, etc. Figure 11 is a diagram illustrating the configuration of a quantum computing device (quantum annealing machine) 300 that includes four qubits 20 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 20. In Figure 11, the four nearest qubits 20 are coupled to the coupler 21 via a four-body interaction to form a unit. Figure 11 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.

[0080] 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.

[0081] 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.

[0082] Furthermore, the 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. In other words, although the JPO was used as an example of a 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.

[0083] [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

[0084] The embodiments / examples exemplified above are further noted below (but are not limited thereto).

[0085] (Note 1) The quantum circuit device has N qubits (where N is a predetermined integer of 3 or more) connected to a common node and coupled by many-body interaction, and the N qubits include at least one qubit whose nonlinearity contributes to the many-body interaction, and one or more qubits whose nonlinearity does not contribute to the many-body interaction.

[0086] (Note 2) In the quantum circuit device of Note 1, N is set to 4, the many-body interaction is a four-body interaction, and of the four qubits, at least one qubit is DC-coupled to the common node, and the remaining qubits are capacitively coupled to the common node.

[0087] (Note 3) In the quantum circuit device of Note 1 or 2, the qubit includes a SQUID (Superconducting Quantum Interference Device) which contains a plurality of Josephson junctions in the loop.

[0088] (Note 4) In any of the quantum circuit devices described in Notes 1 to 3, the coupling coefficient h of the four-body interaction is configured such that at least one of the four qubits is the i-th qubit, which is DC-coupled to the common node. (4) The following is an approximate formula: TIFF2026142952000029.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 between 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 (where is the parameter representing the i-th nonlinearity).

[0089] (Note 5) In any of the quantum circuit devices described in Notes 1 to 4, for the N qubits, at least one pair of qubits in the N(N-1) / 2 combinations of qubits has a nonlinearity of positive and negative polarity, and the cross-Kerr interaction between the two qubits is set to 0.

[0090] (Note 6) The quantum circuit device of Note 1 has N qubits (where N is a predetermined integer of 3 or more) coupled by many-body interaction via a coupler, and for the N qubits, at least one pair of qubits in the combination of two qubits N(N-1) / 2 has a nonlinearity of positive and negative polarity, and the cross-Kerr interaction of the two qubits is set to 0.

[0091] (Note 7) In any of the quantum circuit devices described in Notes 1 to 6, at least one of the N qubits includes 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.

[0092] (Note 8) In any of the quantum circuit devices described in Notes 1 to 7, A quantum computer is constructed by arranging four qubits, which are the basic units, in a lattice pattern.

[0093] (Note 9) The control method for quantum circuits is: N qubits (where N is a predetermined integer greater than or equal to 3) connected to a common node and coupled by many-body interactions, At least one qubit whose nonlinearity contributes to the many-body interaction, The remainder consists of one or more qubits whose nonlinearity does not contribute to the many-body interaction.

[0094] (Note 10) The control method for the quantum circuit in Note 9 is: Let N be 4, and the many-body interaction be a four-body interaction. Of the four qubits, at least one qubit is DC-coupled to the common node, and the remaining qubits are AC-coupled to the common node.

[0095] Furthermore, the disclosures in Non-Patent Documents 1 and 2 and Reference 1 are incorporated herein by reference. Within the framework of the full disclosure of the present invention (including the claims), further modifications and adjustments to the embodiments or examples are possible based on the fundamental technical concept. Also, within the framework of the claims of the present invention, various combinations or selections of various disclosed elements (including each element of each claim, each element of each embodiment, each element of each drawing, etc.) are possible. In other words, the present invention naturally includes the full 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]

[0096] 1 Quantum circuit device 10 Josephson junction 11, 12 circuit (circuit representation) 16 Capacitors (Cg) 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, 210A~210D, 210-1~210-L SQUID 231, 231A, 231D SNAIL 300 Quantum Computers (Quantum Annealing Machines) 601 Magnetic field characteristics (magnetic field response) at resonant frequency 602 Nonlinear magnetic field characteristics (magnetic field response)

Claims

1. It has N qubits (where N is a predetermined integer of 3 or more) connected to a common node and coupled by many-body interactions, The aforementioned N qubits At least one qubit whose nonlinearity contributes to the many-body interaction, One or more qubits in which the aforementioned nonlinearity does not contribute to the many-body interaction, A quantum circuit device, including one.

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

3. The quantum circuit device according to claim 1, wherein the qubit includes a SQUID (Superconducting Quantum Interference Device) containing a plurality of Josephson junctions within a loop.

4. The coupling coefficient h of 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 given by the i-th nonlinearity parameter.

5. The quantum circuit device according to claim 1, wherein, with respect to the N qubits, at least one pair of qubits in the combination N(N-1) / 2 of two qubits has a nonlinearity of positive and negative polarity, and the cross-Kerr interaction of the two qubits is set to 0.

6. It has N qubits (where N is a predetermined integer of 3 or more) that are coupled by many-body interactions via a coupler, A quantum circuit device comprising the aforementioned N qubits, wherein, among the combinations of two qubits N(N-1) / 2, at least one pair of qubits has a nonlinearity of positive and negative polarity, and the cross-Kerr interaction between the two qubits is set to zero.

7. Of the N qubits, at least one qubit is The quantum circuit device according to claim 1, comprising 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.

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

9. N qubits (where N is a predetermined integer greater than or equal to 3) connected to a common node and coupled by many-body interactions, At least one qubit whose nonlinearity contributes to the many-body interaction, A method for controlling a quantum circuit, wherein the remainder is composed of one or more qubits whose nonlinearity does not contribute to the many-body interaction.

10. Let N be 4, and the many-body interaction be a four-body interaction. A method for controlling a quantum circuit according to claim 9, wherein at least one of the four qubits is DC-coupled to the common node, and the remaining qubits are capacitively coupled to the common node.

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