Quantum circuit device and control method

Abstract

To provide a quantum circuit device that enables the strength of many-body interactions to be freely set, utilizing a coupler capable of developing such interactions between a plurality of quantum bits.SOLUTION: The quantum circuit device includes at least three or more quantum bits coupled via a coupler through many-body interactions, and at least one of at least three or more quantum bits possesses a nonlinearity distinct from that of the other quantum bits.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a quantum circuit device and a control method. [Background technology]

[0002] The LHZ (Lechner, Hauke, Zoller) method is known as one of the quantum annealing methods used to solve combinatorial optimization problems (see, for example, Reference 1). To implement LHZ quantum annealing, a network of qubits and couplers, particularly a network based on four-body interactions, is used. In four-body interactions, the four qubits closest to a coupler act through the coupler. A method has been proposed in which Josephson parametric oscillators (JPOs) are used as qubits (see, for example, Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Puri, et. al., "Quantum annealing with all-to-all connected nonlinear oscillators", Nature Communications 8, 15785 (2017) Summary of the Invention [Problem to be solved by the invention]

[0004] A quantum bit can also be considered a resonator with nonlinearity. To obtain a four-body interaction large enough for annealing, two conditions are required: the frequency difference between the quantum bit and the coupler must be small to a certain extent, and the coupler must have a large nonlinearity.

[0005] An object of the present disclosure is to provide a quantum circuit device and a control method that allow for freely setting the strength of many-body interactions with respect to a coupler that can exhibit many-body interactions between multiple quantum bits. [Means for solving the problem]

[0006] According to the present disclosure, a quantum circuit device includes a coupler composed of linear elements and at least three or more quantum bits coupled by a many-body interaction via the coupler, and at least one of the at least three or more quantum bits is configured to have nonlinearity different from that of the other quantum bits.

[0007] According to the present disclosure, there is provided a method for controlling the strength of coupling in which at least first to third quantum bits interact with each other through a coupler, in which the nonlinearity of at least one of the first to third quantum bits is set to be different from the nonlinearity of the other quantum bits. [Effects of the Invention]

[0008] According to the present disclosure, with respect to a coupler capable of generating many-body interactions between a plurality of quantum bits, the strength of the many-body interactions can be freely set. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 10 is a diagram illustrating an example of a comparative example. [Figure 2] FIG. 1 is a diagram illustrating an example of a configuration of the present disclosure. [Figure 3] FIG. 1 is a diagram illustrating an example of a configuration of the present disclosure. [Figure 4] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 5] FIG. 1 is a diagram illustrating a configuration of the present disclosure. [Figure 6] 1A to 1D are diagrams illustrating the configuration of the present disclosure. [Figure 7] FIG. 1 is a diagram illustrating a configuration of the present disclosure. [Figure 8] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 9] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 10] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 11] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 12] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 13] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 14] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 15] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 16] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 17] FIG. 10 is a diagram illustrating another example of the configuration of the present disclosure. [Figure 18] FIG. 1 is a diagram illustrating a quantum computer according to the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0010] An embodiment of the present disclosure will be described. First, in relation to the above-mentioned problems, further analysis by the inventor of the present application regarding the disclosure of FIG. 1 will be provided below. In FIG. 1, the JPA (Josephson Parametric Amplifier) ​​in Non-Patent Document 1 is denoted as JPO because it functions as a parametric oscillator. Four quantum bits (JPO1 to JPO4) are provided with SQUIDs (Superconducting Quantum Interference Devices) including multiple Josephson junctions (JJs) in a loop, and are driven by magnetic flux from a magnetic field application unit (not shown). In the quantum bits (JPO1 to JPO4), coplanar waveguides (CPW) facing each other via the SQUIDs are electrodes / transmission paths. In each quantum bit, the angular frequency ω of the pump signal is p,i (i=1,2,3,4) is the resonant angular frequency ω of the quantum bit i twice the angular frequency 2ω iWhen the pump signal strength exceeds a threshold, the quantum bit oscillates at a resonant angular frequency ω i (This is called "parametric oscillation")

[0011] In Non-Patent Document 1, as a condition for the four-body interaction of the four quantum bits (JPO1 to JPO4), the angular frequencies of the respective pump signals are set, for example, as follows: ω p,1 +ω p,2 =ω p,3 +ω p,4 …(1) In Non-Patent Document 1, the resonant angular frequency of the quantum bit is ω k ≠ω m (k≠m, k, m=1,2,3,4). In equation (1), ω p,k ≠ω p,m When k≠m, k, m=1,2,3,4, the angular frequency ω is half the pump frequency that drives the qubit. p,i / 2 and the quantum bit resonance frequency ω i When the difference between (i=1, 2, 3, 4) is the same for all quantum bits, the quantum bit resonance frequencies are detuned from each other. In Figure 1, four quantum bits (JPO1 to JPO4) with different resonance angular frequencies are shown with different patterns in accordance with Figure 4 in Non-Patent Document 1. In addition to Equation (1), the following four-body interaction conditions (pump frequency conditions) for the four quantum bits (JPO1 to JPO4) can be satisfied: ω p,1 +ω p,3 =ω p,2 +ω p,4 …(1-a) or, ω p,1 +ω p,4 =ω p,2 +ω p,3 …(1-b) It is possible that, etc. In order to generate four-body interactions, it is not necessary for all four qubits to be detuned from each other, but in order to avoid unnecessary two-body interactions, when the difference between half the pump frequency and the resonant frequency is equal for all qubits, the resonant frequencies of the qubits must be detuned from each other.

[0012] In the case of equation (1), the coupler is expressed in the rotating coordinate system as follows: TIFF2025141608000002.tif6150…(2) (The coupling term of the four-body interaction in the Hamiltonian has a minus sign in equation (2).) In equation (2), a i , a i + (i=1,2,3,4) are the annihilation and creation operators of the bosons in each quantum bit, respectively. When the four-body interaction conditions are equations (1-a) and (1-b), the coupling of the four-body interaction in equation (2) is expressed by the following equations. TIFF2025141608000003.tif6150…(2-a) TIFF2025141608000004.tif6150…(2-b)

[0013] Four-body interaction strength (coupling coefficient) g (4) teeth, TIFF2025141608000005.tif9150…(3) and depends on the nonlinearity of the Josephson junctions (JJs) in the coupler and the difference (detuning) in the resonant frequencies of the qubit and the coupler.

[0014] In equation (3), K g is the fourth-order nonlinear parameter (Kerr coefficient) of the coupler. 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 ith qubit i The difference (detuning) betweenc -ω i ) g i (i=1,2,3,4) represents the magnitude of the coupling between the ith quantum bit and the coupler.

[0015] From equation (3), TIFF2025141608000006.tif9150…(4) Detuning Δ i If we make as small as possible, the coupling coefficient g (4) becomes large, and the four-body interaction becomes stronger. Therefore, the resonant angular frequency ω r,i (i=1,2,3,4) and the resonant angular frequency ω of the coupler c It needs to be fairly close to that.

[0016] In equation (3), g i / Δ i (i=1,2,3,4) is approximated by g / Δ, and the nonlinear parameter K g The fourth power term of g / Δ: (g / Δ) 4 This means that the following is applied.

[0017] From equation (3), the nonlinear parameter K g If we increase the coupling coefficient g (4) However, the nonlinear parameter K g is multiplied by the fourth power (g / Δ)^4, which is less than 1, so the coupling coefficient g (4) is basically a small value.

[0018] The above problem is one example, but according to the present disclosure, it is possible to realize many-body interactions between quantum bits in various situations, not limited to the above, and to set the strength of the interaction to a desired value.

[0019] According to the present disclosure, the coupling between quantum bits may be performed by a coupler using a nonlinear element such as a Josephson junction or a SQUID, as shown in Figure 1. Alternatively, the coupler may be a coupler configured with linear elements (also called a "linear coupler").

[0020] Fig. 2 is a diagram illustrating a schematic diagram of an example of the present disclosure. Referring to Fig. 2, a quantum circuit device 1 includes first to fourth quantum bits 20-1 to 20-4, each of which includes a nonlinear resonant circuit, and a coupler 21 that couples these quantum bits through a four-body interaction. Note that Fig. 2 shows an example in which four quantum bits are coupled through the coupler 21 by a four-body interaction, corresponding to Fig. 1, but three-body interaction, five-body interaction, etc. may also be used.

[0021] 2, first and second quantum bits 20-1 and 20-2 are connected to one end (first electrode) of coupler 21 at ports 1 and 2 (p1 and p2), and third and fourth quantum bits 20-3 and 20-4 are connected to the other end (second electrode) of coupler 21 at ports 3 and 4 (p3 and p4). The first and second quantum bits 20-1 and 20-2 may be capacitively coupled to one end of coupler 21 at ports 1 and 2 (p1 and p2), and the third and fourth quantum bits 20-3 and 20-4 may be capacitively coupled to the other end of coupler 21 at ports 3 and 4 (p3 and p4). Alternatively, the first and second quantum bits 20-1 and 20-2 may be directly connected (DC coupled) by wiring to one end of the coupler 21 at ports 1 and 2 (p1 and p2), and the third and fourth quantum bits 20-3 and 20-4 may be directly connected (DC coupled) by wiring to the other end of the coupler 21 at ports 3 and 4 (p3 and p4).

[0022] The coupler 21 includes a Josephson junction or a SQUID as a nonlinear element.

[0023] Each of the first to fourth quantum bits 20-1 to 20-4 may include at least one Josephson junction and a capacitor connected in parallel between an electrode and ground.

[0024] Each of the first to fourth quantum bits 20-1 to 20-4 may include at least one SQUID and a capacitor connected in parallel between an electrode and ground.

[0025] 2, K1 to K4 attached to the first to fourth quantum bits 20-1 to 20-4, respectively, represent the nonlinear parameters of the first to fourth quantum bits 20-1 to 20-4. In the following, as the conditions for the four-body interaction of the first to fourth quantum bits 20-1 to 20-4, the respective resonant angular frequencies ω i For (i=1,2,3,4), the pump frequency ω p,i When the difference between half of (i=1,2,3,4) and the resonant angular frequency is equal for all quantum bits, for example, corresponding to equation (1), ω1+ω2=ω3+ω4…(5) The first to fourth quantum bits 20-1 to 20-4 may be detuned from one another.

[0026] In the present disclosure, preferably, at least one of the nonlinear parameters K1 to K4 of the first through fourth quantum bits 20-1 to 20-4 is set to a value different from the others. The nonlinear parameters K1 to K4 of the first through fourth quantum bits 20-1 to 20-4 may all be different values. The magnitudes of the nonlinear parameters K1 to K4 of the first through fourth quantum bits 20-1 to 20-4 may be 1 kHz (kiloherz) or greater, preferably 10 kHz or greater, and more preferably approximately 0.1 to 100 MHz (megaherz). Furthermore, the magnitude of the difference in the nonlinear parameters of a quantum bit whose nonlinear parameters are set to a value different from the others may be 1 kHz or greater, preferably 10 kHz or greater, and more preferably 0.1 MHz to 10 MHz.

[0027] For example, the absolute value |K1-K2| of the difference between the nonlinear parameters K1 and K2 of the first quantum bit 20-1 and the second quantum bit 20-2 and the absolute value |K3-K4| of the difference between the nonlinear parameters K3 and K4 of the third quantum bit 20-3 and the fourth quantum bit 20-4 are both set to be large, and the difference (δ 12 =ω1-ω2) and the difference between the resonant angular frequency ω3 of the third quantum bit 20-3 and the resonant angular frequency ω4 of the fourth quantum bit 20-4 (δ 34 For example, the absolute value of the difference in the resonant frequencies |δ 12 | and |δ 34 By making both | large, the four-body interaction between the first to fourth quantum bits 20-1 to 20-4 may be strengthened.

[0028] Alternatively, the four-body interaction between the first to fourth quantum bits 20-1 to 20-4 may be strengthened by increasing either |K1-K2| or |K3-K4| and decreasing the other. Here, based on equation (5) which is the condition for the four-body interaction, the values ​​of the nonlinear parameters are shifted between the set of nonlinear parameters K1 and K2 between the first quantum bit 20-1 and the second quantum bit 20-2 and the set of nonlinear parameters K3 and K4 between the third quantum bit 20-3 and the fourth quantum bit 20-4. However, the combination of nonlinear parameters that strengthens the four-body interaction will be different from the above combination depending on the condition for the four-body interaction.

[0029] As a condition for the four-body interaction of the first to fourth quantum bits 20-1 to 20-4, the respective resonance angular frequencies ω i For (i=1,2,3,4), the pump frequency ω p,i When the difference between half of (i=1,2,3,4) and the resonant angular frequency is equal for all quantum bits, for example, corresponding to equation (1-a), ω1+ω3=ω2+ω4…(6) In this case, the absolute value |K1-K3| of the difference between the nonlinear parameters K1 and K3 of the third quantum bit 20-3 and the first quantum bit 20-1 and the absolute value |K2-K4| of the difference between the nonlinear parameters K2 and K4 of the second quantum bit 20-2 and the fourth quantum bit 20-4 are both set to be large, and the difference (δ 13 =ω1-ω3), the difference between the resonant angular frequency ω2 of the second quantum bit 20-2 and the resonant angular frequency ω4 of the fourth quantum bit 20-4 (δ 24 =ω2-ω4), the four-body interactions between first to fourth quantum bits 20-1 to 20-4 may be strengthened.

[0030] As a condition for the four-body interaction of the first to fourth quantum bits 20-1 to 20-4, the respective resonance angular frequencies ω i For (i=1,2,3,4), the pump frequency ω p,i When the difference between half of (i=1,2,3,4) and the resonant angular frequency is equal for all quantum bits, for example, corresponding to equation (1-b), ω1+ω4=ω2+ω3…(7) If this is the case, the absolute value |K1-K4| of the difference between the nonlinear parameters K1 and K4 of the first quantum bit 20-1 and the fourth quantum bit 20-4 and the absolute value |K2-K3| of the difference between the nonlinear parameters K2 and K3 of the second quantum bit 20-2 and the third quantum bit 20-3 are both set to be large, and the difference (δ 14 =ω1-ω4), the difference between the resonant angular frequency ω2 of the second quantum bit 20-2 and the resonant angular frequency ω3 of the third quantum bit 20-3 (δ 23 =ω2-ω3), the four-body interactions between first to fourth quantum bits 20-1 to 20-4 may be strengthened.

[0031] Furthermore, the four-body interaction due to the nonlinearity of the quantum bits 20 may be cancelled (turned off) by making K1 to K4 of the first to fourth quantum bits 20-1 to 20-4 the same or by adjusting the difference in the resonant frequencies of the two quantum bits 20. However, if there is a difference between half the pump frequency and the resonant angular frequency, the four-body interaction is not necessarily cancelled out.

[0032] FIG. 3 is a diagram illustrating an example of the present disclosure. FIG. 3 schematically illustrates an example of a quantum circuit device 1 in which the quantum bit 20 is a superconducting quantum bit. Referring to FIG. 3, the first quantum bit 20-1 includes a Josephson junction 201A and a capacitor 206A connected in parallel between an electrode 24A and ground. The electrode 24A of the first quantum bit 20-1 is connected to a first electrode 17 (first node) of the coupler 21 via a coupling capacitor 31A. The electrode 24A may include a connection portion that connects to the first electrode 17 of the coupler 21. The second quantum bit 20-2 includes a Josephson junction 201B and a capacitor 206B connected in parallel between an electrode 24B and ground. The electrode 24B of the second quantum bit 20-2 is connected to the first electrode 17 (first node) of the coupler 21 via a coupling capacitor 31B. Electrode 24B may include a connection portion that connects to first electrode 17 of coupler 21. Third qubit 20-3 includes Josephson junction 201C and capacitor 206C connected in parallel between electrode 24C and ground. Electrode 24C of third qubit 20-3 connects to second electrode 18 (second node) of coupler 21 via coupling capacitor 31C. Electrode 24C may include a connection portion that connects to second electrode 18 of coupler 21. Fourth qubit 20-4 includes Josephson junction 202D and capacitor 206D connected in parallel between electrode 24D and ground. Electrode 24D of fourth qubit 20-4 connects to second electrode 18 (second node) via coupling capacitor 31D. Electrode 24D may include a connection portion that connects to second electrode 18 of coupler 21. When the first to fourth quantum bits 20-1 to 20-4 are not to be individually identified, the sub-numbers are removed and they are referred to as quantum bits 20, Josephson junctions 201, capacitors 206, and so on.

[0033] In coupler 21, Josephson junction 10 is connected between first electrode 17 and second electrode 18. First electrode 17 and second electrode 18 are arranged facing each other at a distance in coupler 21, and first electrode 17 may have first and second connection portions (not shown) that are capacitively coupled to electrodes 24A and 24B of first and second quantum bits 20-1 and 20-2, respectively, and second electrode 18 may have third and fourth connection portions (not shown) that are capacitively coupled to electrodes 24C and 24D of third and fourth quantum bits 20-3 and 20-4, respectively.

[0034] The four-body interaction between quantum bits arises from the nonlinearity of the quantum bits.

[0035] 3, quantum bit 20, which is composed of a parallel circuit of Josephson junction 201 and capacitor 206, has a fixed frequency. However, as shown in Fig. 4, it may also be a frequency-variable quantum bit composed of a parallel circuit of a SQUID and a capacitor. Referring to Fig. 4, in quantum circuit device 1, first quantum bit 20-1 includes SQUID 210A in which superconducting material 203A, Josephson junction 201A, superconducting material 204A, and Josephson junction 202A form a loop. Superconducting material 203A is connected to electrode 24A, and superconducting material 204A is connected to ground. Capacitor 206A (shunt capacitor) is connected in parallel to SQUID 210A between electrode 24A and ground. A magnetic flux passing through SQUID 210A is generated by passing a current through an inductor (not shown). By varying this magnetic flux, the resonant angular frequency ω1 of first quantum bit 20-1 can be varied. In the second to fourth quantum bits 20-2 to 20-4, the superconducting members corresponding to the superconducting member 203A of the first quantum bit 20-1 are designated 203B to 203D, the Josephson junctions corresponding to the Josephson junction 201A of the first quantum bit 20-1 are designated 201B to 201D, the superconducting members corresponding to the superconducting member 204A of the first quantum bit 20-1 are designated 204B to 204D, the superconducting members corresponding to the Josephson junction 202A of the first quantum bit 20-1 are designated 202B to 202D, the SQUIDs corresponding to the SQUID 210A of the first quantum bit 20-1 are designated 210B to 210D, and the capacitors corresponding to the capacitor 206A of the first quantum bit 20-1 are designated 206B to 206D.

[0036] In this disclosure, the four-body interaction between the four qubits arises from the nonlinearity of qubit 20, not coupler 21. Referring again to FIG. 2, the coupling coefficient h of the four-body interaction arising from the nonlinearity between the qubits is (4) For example, it can be expressed as follows: TIFF2025141608000007.tif17150…(8)

[0037] In equation (8), h ij(i, j=1,2,3,4 (j≠i)) represents the strength (magnitude) of the coupling between the jth quantum bit 20-i and the ith quantum bit 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 quantum bit 20-j j and the resonant angular frequency ω of the ith quantum bit 20-i i The difference ω j -ω i is. K i (i=1, 2, 3, 4) is a parameter (Kerr coefficient) representing the nonlinearity of the i-th quantum bit 20-i.

[0038] where in equation (8), the multiplication term: Regarding TIFF2025141608000008.tif17150, h ij (j=1,2,3,4 (j≠i)) is h, δ ji (j=1,2,3,4 (j≠i)) is δ, and K q h ij / δ ji If we take the effective value including the sign of (the effective Kerr coefficient remaining after canceling with the sign ±), TIFF2025141608000009.tif10150…(9) This can be expressed as:

[0039] In equation (9), TIFF2025141608000010.tif9150…(10) Under this condition, the value of equation (9) becomes large by making the difference δ in the resonant angular frequency between two quantum bits (the i-th and j-th quantum bits 20-i and 20-j) as small as possible.

[0040] From equation (9), the parameter K, which represents the nonlinearity of the qubit 20, q Even if we increase the coefficient of four-body interaction h (4) becomes larger.

[0041] In equation (3), the coefficient of the four-body interaction g(4) as the nonlinearity parameter (Kerr coefficient) of the coupler, K g Then, the fourth power term (g / Δ) (<1) 4 is hanging.

[0042] On the other hand, in equation (9), the nonlinear parameter K q , the cube term (h / δ) (<1) 3 Therefore, the coupling coefficient h of the four-body interaction due to the nonlinearity of the quantum bit 20 (4) is g in Eq. (3). (4) It is relatively easy to make it larger than h. (4) For example, K q and K. g When are of the same order, g in Eq. (3) (4) In some cases, the order of magnitude may be nearly an order of magnitude larger than the above.

[0043] In addition, in equation (8), when i=1, that is, focusing on the first quantum bit 20-1 in FIG. 2, The difference δ between the resonant angular frequencies of the second quantum bit 20-2 and the first quantum bit 20-1 21 (=ω2-ω1) and the coupling strength h between the first qubit 20-1 and the second qubit 20-2. 12 , The difference δ between the resonant angular frequencies of the third quantum bit 20-3 and the first quantum bit 20-1 31 (=ω3-ω1) and the coupling strength h between the first qubit 20-1 and the third qubit 20-3. 13 and, The difference δ between the resonant angular frequencies of the fourth quantum bit 20-4 and the first quantum bit 20-1 41 (=ω4-ω1) and the coupling strength h between the first qubit 20-1 and the fourth qubit 20-4. 14 and 、 Regarding i=1 in equation (8), the multiplication term is TIFF2025141608000011.tif10150. This is generalized as equation (9).

[0044] Furthermore, the degree of freedom of the coupler 21 (parameters related to the coupler 21) is not involved in equation (8), which expresses the four-body interaction due to the nonlinearity between the quantum bits 20. Therefore, the coupler 21 may be configured with linear elements. When the coupler 21 is configured with linear elements, the coupling coefficient of the four-body interaction is h (4) Only.

[0045] On the other hand, when the coupler 21 includes a nonlinear element such as a Josephson junction 10, the strength of the four-body interaction is expressed by the coupling coefficient in equation (3). The strength of the four-body interaction (four-body interaction due to coupler 21) represented by TIFF2025141608000012.tif9150 also acts simultaneously. In this case, the strength of the four-body interaction is effectively h (4) and g (4) and can be expressed as the following equation (11), for example. TIFF2025141608000013.tif6150…(11) In equation (11), h (4) The magnitude (absolute value) of g (4) It may be an addition of the magnitude (absolute value) of

[0046] When formula (8) is expanded for the first to fourth quantum bits 20-1 to 20-4 in FIG. 2, the following formula (12) is obtained. TIFF2025141608000014.tif10150…(12)

[0047] In equation (12), the four-body interaction condition is TIFF2025141608000015.tif6150…(13) Let's say.

[0048] From equation (13), TIFF2025141608000016.tif6150 TIFF2025141608000017.tif6150Therefore, TIFF2025141608000018.tif6150…(14) TIFF2025141608000019.tif6150…(15)

[0049] Furthermore, regarding equation (12), δ ij (=ω i -ω j ) is antisymmetric with respect to the indices i and j: TIFF2025141608000020.tif6150…(16)

[0050] h ij is symmetric with respect to the indices i and j: TIFF2025141608000021.tif6150…(17)

[0051] The coupling constant h between the first and second quantum bits 20-1 and 20-2 coupled to the first electrode 17 (first node) of the coupler 21 via the coupling capacitors 31A and 31B is 12 and a coupling constant h between the third and fourth quantum bits 20-3 and 20-4, which are coupled to the second electrode 18 (second node) of the coupler 21 via the coupling capacitors 31C and 31D. 34 are approximately equal to each other when their resonant angular frequencies are close to each other. TIFF2025141608000022.tif6150…(18)

[0052] The coupling constant h between the first and third quantum bits 20-1 and 20-3 coupled via the coupler 21 13 and a coupling constant h between the first and fourth quantum bits 20-1 and 20-4 coupled via the coupler 21. 14 and a coupling constant h between the second and third quantum bits 20-2 and 20-3 coupled via the coupler 21. 23 and a coupling constant h between the second and fourth quantum bits 20-2 and 20-4 coupled via the coupler 21. 24 are approximately equal to each other when their resonant angular frequencies are close to each other. TIFF2025141608000023.tif6150…(19)

[0053] Under the conditions of (14) to (19) above, the above formula (12) is TIFF2025141608000024.tif10150 TIFF2025141608000025.tif10150 From, it is represented by the following formula (20). TIFF2025141608000026.tif10150…(20)

[0054] In formula (20), assuming that the nonlinearities K1 to K4 of the first to fourth qubits 20-1 to 20-4 are all the same, K2 = K1, K3 = K4…(21) and h (4) = 0. In this case, the four-body interaction generated from the nonlinearities of the first to fourth qubits 20-1 to 20-4 is canceled (turned off).

[0055] Also, from formula (20), by making the absolute values |K1 - K2| and |K4 - K3| each a large value (greater than or equal to a predetermined value), and making δ 34 and δ 12 large including the sign, the value (absolute value) of h (4) becomes large, and a large four-body interaction can be obtained. For example, in the case of (K1 > K2 and K4 > K3), or (K1 < K2 and K4 < K3), the difference δ 12 (= ω1 - ω2) between the resonance angular frequencies of the first qubit 20-1 and the second qubit 20-2, and the difference δ 34 (= ω3 - ω4) between the resonance angular frequencies of the third qubit 20-3 and the fourth qubit 20-4 may both be large positive values, or both may be negative values with large absolute values. That is, ω1 > ω2 and ω3 > ω4, or ω1 < ω2 and ω3 < ω4.

[0056] In each qubit 20 of FIG. 3, the resonance frequency is fixed. This resonance frequency is based on, for example, the inductance of the electrode 24 and the capacitance of the capacitor 206, and the inductance and capacitance of the Josephson junction 201 itself. Therefore, by setting these circuit parameters, for example, ω1>ω2 and ω3>ω4 may be satisfied.

[0057] In each qubit 20 of qubits 20-1 to 20-4 in FIG. 4, the resonance frequency is varied by the magnetic flux passing through the loop of the SQUID 210. Therefore, the configurations and circuit parameters of the first to fourth qubits 20-1 to 20-4 are the same, and by varying the DC bias current applied from a magnetic field application unit (not shown) to the first to fourth qubits 20-1 to 20-4, for example, ω1>ω2 and ω3>ω4 may be satisfied. When the DC bias current value is increased, the magnetic flux passing through the loop of the SQUID 210 of the qubit 20 increases.

[0058] In Equation (20), when |K1 - K2| and |K4 - K3| are each set to a large value (equal to or greater than a predetermined value), and when K1>K2 and K4<K3, δ 34 may be set to a large positive value, and δ 12 may be set to a negative value with a large absolute value. Alternatively, δ 34 may be set to a negative value with a large absolute value, and δ 12 may be set to a large positive value.

[0059] In Equation (20), when |K1 - K2| and |K4 - K3| are each set to a large value (equal to or greater than a predetermined value), and when K1<K2 and K4>K3, δ 34 may be set to a negative value with a large absolute value, and δ 12 may be set to a large positive value. Alternatively, δ 34 may be set to a large positive value, and δ 12 may be set to a negative value with a large absolute value.

[0060] Also, in Equation (20), if either |K2 - K1| or |K3 - K4| is set to a large value and the other is set to a small value, the difference δ in the resonance angular frequencies of the third qubit 20-3 and the fourth qubit 20-434 and the difference δ between the resonance angular frequencies of the first quantum bit 20-1 and the second quantum bit 20-2 12 This reduces the effort required for adjustment.

[0061] Alternatively, in equation (20), |K1-K2| and |K4-K3| are set to predetermined values ​​in advance, and the difference δ between the resonant angular frequencies of the third quantum bit 20-3 and the fourth quantum bit 20-4 is 34 and the difference δ between the resonant angular frequencies of the first quantum bit 20-1 and the second quantum bit 20-2. 12 By adjusting (4) can be set to 0 to cancel the four-body interaction due to the nonlinearity of the quantum bit 20. In this case, the difference in the resonant frequencies δ 34 and δ 12 The adjustment may be performed (calibrated) by, for example, reading out the frequencies of the first to fourth quantum bits 20-1 to 20-4 in FIG. 4 from an input / output line (not shown), measuring them with a measuring device (not shown), and variably setting the DC bias current or microwave current from a signal source (not shown).

[0062] By changing the conditions of the four-body interaction of first to fourth quantum bits 20-1 to 20-4, it is possible to switch the strength of the four-body interaction even if first to fourth quantum bits 20-1 to 20-4 have the same design.

[0063] For example, in equation (20), if K1=K4>K2=K3, then δ 34 and δ 12 By appropriately adjusting the equation, the four-body interaction can be strengthened. That is, equation (20) becomes the following equation (22). TIFF2025141608000027.tif10150…(22)

[0064] From equation (22), K1>K2, for example, δ 34 +δ 12 By setting the absolute value of to a large value, h (4) The absolute value of becomes large, and the four-body interaction can be strengthened. For example, δ34 +δ 12 =(ω3 - ω4)+(ω1 - ω2) …(23) Thus, it may be set such that ω3 > ω4 and ω1 > ω2.

[0065] Also, the condition of the four-body interaction between the four qubits TIFF2025141608000028.tif6150…(24) may be set as follows. In this case, from Equation (24), TIFF2025141608000029.tif6150 TIFF2025141608000030.tif6150 Therefore, TIFF2025141608000031.tif6150…(25) TIFF2025141608000032.tif6150…(26)

[0066] From Equations (25), (26) and Equations (18), (19), the above Equation (12) is TIFF2025141608000033.tif10150 TIFF2025141608000034.tif10150 and is simplified as follows. TIFF2025141608000035.tif10150…(27)

[0067] [[ID=三十九]]From Equation (27), by making the absolute values |K1 - K3| and |K4 - K2| each a large value (greater than or equal to a predetermined value), and making δ 24 and δ 13 large including their signs, the value (absolute value) of h (4) becomes large, and a large four-body interaction can be obtained. For example, in the case of (K1 > K3 and K4 > K2), or (K1 < K3 and K4 < K2), the difference δ 24 (= ω2 - ω4) between the resonance angular frequencies of the second qubit 20-2 and the fourth qubit 20-4, and the difference δ 13(=ω1-ω3) may both be large positive values, or may both be large negative values ​​with large absolute values. That is, ω2>ω4 and ω1>ω3, or ω2<ω4 and ω1<ω3.

[0068] In addition to the above, the nonlinear parameter of the qubit when the four-body interaction condition is ω1+ω2=ω3+ω4 and the difference in resonant angular frequency between the qubits, δ ij The various controls described above also apply to the case where ω1 + ω3 = ω2 + ω4 by replacing the quantum bit numbers by 2 and 3.

[0069] Furthermore, the condition for the four-body interaction between the four qubits is TIFF2025141608000036.tif6150…(28) In this case, from equation (28), TIFF2025141608000037.tif6150 TIFF2025141608000038.tif6150 therefore, TIFF2025141608000039.tif6150…(29) TIFF2025141608000040.tif6150…(30)

[0070] From equations (29), (30) and equations (18), (19), the above equation (12) becomes: TIFF2025141608000041.tif10150 From TIFF2025141608000042.tif10150, it is simplified as follows: TIFF2025141608000043.tif10150…(31)

[0071] In equation (31), if K1=K4 and K2=K3, the difference δ between the resonant frequencies of the first to fourth quantum bits 20-1 to 20-4 is 23 , δ 14 Without adjusting for h(4) becomes 0, and the four-body interaction due to the nonlinearity of the qubit is cancelled out.

[0072] In equation (31), if K1=K2 and K3=K4, TIFF2025141608000044.tif10150…(32) In equation (32), δ 23 =δ 14 In the case of h (4) becomes 0, and the four-body interaction due to the nonlinearity of the quantum bit is cancelled out. Note that in equation (32), the difference in the resonant angular frequency δ 23 and δ 14 For example, if K4>K1, then δ 23 -δ 14 >0, i.e., δ 23 -δ 14 =(ω2-ω3)+(ω4-ω1)>0 …(33) Therefore, for example, by setting ω2>ω3 and ω4>ω1, h (4) is a positive value.

[0073] In first to fourth quantum bits 20-1 to 20-4, the nonlinearity may be changed, for example, as follows.

[0074] (I) In a quantum bit, multiple Josephson junctions are connected in series (changing the number of Josephson junctions connected in series). The configuration (geometric structure, layout) of the quantum bit electrodes is left unchanged, but the junction structure (geometry, etc.) of the Josephson junctions is changed. (II) Changing the capacitance and inductance of the quantum bit structure. (III) Changing the resonant frequency of the quantum bit, if the resonant frequency is tunable.

[0075] (I) As an example of connecting multiple Josephson junctions in series without changing the structure of the electrode 24 of the quantum bit 20, for example, as shown in FIG. 5 as quantum bit 20A, N (N>1) Josephson junctions 201-1 to 201-N may be connected in series between the electrode 24 and ground, and a capacitor 206 may be provided in parallel with the N Josephson junctions 201-1 to 201-N between the electrode 24 and ground. When Josephson junctions are connected in series, nonlinearity is weakened. When the nonlinear parameters of two quantum bits 20 in FIG. 3 are made different, the number N of Josephson junctions connected in series in FIG. 5 may be made different from each other. When the nonlinear parameters are made the same, the number N of Josephson junctions connected in series may be made the same. However, in FIG. 5, if the junction size of each of the N Josephson junctions 201-1 to 201-N is set to be the same as that of the Josephson junction 201 of the quantum bit 20 of FIG. 3, the resonant frequency will deviate from the resonant frequency of the quantum bit 20 of FIG. 3, and therefore the junction size may be adjusted.

[0076] Regarding the nonlinear parameters K1 to K4 of the first to fourth quantum bits 20-1 to 20-4, for example, K1=K4>K2=K3…(34) 5, as an example, second qubit 20-2 and third qubit 20-3 in Fig. 3 may be configured with qubit 20A in Fig. 5, and first qubit 20-1 and fourth qubit 20-4 may remain as configured in Fig. 3 (corresponding to N=1 in Fig. 5). Alternatively, first to fourth qubits 20-1 to 20-4 in Fig. 3 may be configured with qubit 20A in Fig. 5, and the number of series-connected Josephson junctions in second qubit 20-2 and third qubit 20-3 (the same number in second qubit 20-2 and third qubit 20-3) may be set to be greater than the number of series-connected Josephson junctions in first qubit 20-1 and fourth qubit 20-1 (the same number in first qubit 20-1 and fourth qubit 20-4).

[0077] As another example of connecting multiple Josephson junctions in series, a configuration may be used, as shown in FIG. 6A as quantum bit 20B, which includes a SQUID 210 and M series-connected Josephson junctions 207-1 through 207-M ​​between electrode 24 and ground. When Josephson junctions are connected in series, the nonlinearity is weakened. To vary the nonlinearity of quantum bit 20B, the number M of series-connected Josephson junctions 207 may be varied. When the nonlinear parameters K1 through K4 of first through fourth quantum bits 20-1 through 20-4 are set to, for example, K1=K4>K2=K3, second quantum bit 20-2 and third quantum bit 20-3 in FIG. 4 may be configured with quantum bit 20B in FIG. 6A, and first quantum bit 20-1 and fourth quantum bit 20-4 may remain as configured in FIG. 4. Second qubit 20-2 and third qubit 20-3 have less nonlinearity than first qubit 20-1 and fourth qubit 20-4.

[0078] As another example of connecting multiple Josephson junctions in series, a configuration may be used in which L SQUIDs 210-1 to 210-L are connected in series between electrode 24 and ground, as shown as quantum bit 20C in FIG. 6(B). When the nonlinearity of quantum bit 20C is to be varied, the number L of SQUIDs 210 connected in series may be varied. For example, when setting K1=K4>K2=K3, second quantum bit 20-2 and third quantum bit 20-3 in FIG. 4 may be configured with quantum bit 20C in FIG. 6(B), and first quantum bit 20-1 and fourth quantum bit 20-4 may remain configured as in FIG. 4.

[0079] 6(C) as quantum bit 20D, at least one of the number L of SQUIDs 210 connected in series and the number M of Josephson junctions 207 connected in series may be different.

[0080] Alternatively, as yet another example of connecting multiple Josephson junctions in series, a SQUID 210′ ​​may be configured with N (N≧1) Josephson junctions 202-1 through 202-N connected in series in parallel with Josephson junction 201, as shown as quantum bit 20E in FIG. 6(D). When Josephson junctions are connected in series, nonlinearity is weakened. For example, if the nonlinear parameters K1 through K4 of first through fourth quantum bits 20-1 through 20-4 are set to K1=K4>K2=K3, then second quantum bit 20-2 and third quantum bit 20-3 in FIG. 4 may be configured with quantum bit 20E in FIG. 6(D), and first quantum bit 20-1 and fourth quantum bit 20-4 may remain as configured in FIG. 4.

[0081] Although not shown, as a further modification of FIGS. 6(A) to 6(D), the SQUID 210 of FIG. 6(A) may be replaced with the SQUID 210' of FIG. 6(D), and the SQUID 210' and N Josephson junctions 202-1 to 202-N connected in series may be provided between the electrode 24 and ground. Alternatively, the SQUIDs 210-1 to 210-L of FIG. 6(B) may be replaced with the SQUID 210' of FIG. 6(D). The SQUIDs 210-1 to 210-L of FIG. 6(C) may be replaced with the SQUID 210' of FIG. 6(D). The present disclosure is not limited to the above modifications, and the quantum bit 20 may include other combinations of Josephson junctions and SQUIDs.

[0082] (II) In a quantum bit including a Josephson junction, the nonlinearity between quantum bits may be changed by changing the structural capacitance and inductance of the quantum bit 20. FIG. 7(A) is a diagram illustrating the structural inductance using the quantum bit 20 of FIG. 3 as an example. The inductance L1 connected in series to the Josephson junction 201 represents the inductance component of the electrode 24. The capacitance C between the electrode 24 and the ground corresponds to the capacitor 206 connected in parallel to the Josephson junction 201. The Josephson junction 201 has its own capacitance C J and the nonlinear inductance component L J If the current flowing through the Josephson junction 201 is I, the critical current is Ic, and Φ is the magnetic flux quantum, then the nonlinear inductance L of the Josephson junction 201 is J For example, it can be expressed as follows: TIFF2025141608000045.tif11150…(35) This nonlinear inductance L J This makes the potential energy anharmonic, the levels are no longer spaced at regular intervals, and a two-level quantum bit is realized.

[0083] Figure 7(B) is a diagram explaining the structural capacitance and structural inductance using the quantum bit 20 of Figure 3 as an example. Inductance L1 connected in series to SQUID 210 represents the inductance component of electrode 24. Capacitance C between electrode 24 and ground corresponds to capacitor 206 connected in parallel to SQUID 210. Note that Josephson junction 201 has its own capacitance component in addition to the nonlinear inductance component. The structural inductance of quantum bit 20 is L1, and the structural capacitance is 206.

[0084] In equation (9), the nonlinear parameter K of the qubit 20 q (q=1,2,3,4) can be broadly divided into components determined by inductance and components determined by capacitance. TIFF2025141608000046.tif6150…(36) where E cq is the charging energy of qubit 20.

[0085] p q The participation ratio is the ratio of the inductive energy stored in the quantum bit (Josephson junction) to the inductive energy stored in the circuit, and can be expressed, for example, as follows: TIFF2025141608000047.tif13150…(37) where: L qL (q=1,2,3,4) is the structural inductance of the qth qubit 20-q, L qS (q=1,2,3,4) is the inductance of the SQUID of the qth qubit 20-q, n qS (q=1,2,3,4) is the number of SQUIDs in the q-th quantum bit 20-q (L in Figure 6(B) and (C)). L qJ (q=1,2,3,4) is the inductance of the Josephson junction connected in series with the SQUID in the qth qubit 20-q, n qJ (q=1, 2, 3, 4) is the number of Josephson junctions connected in series in the qth quantum bit 20-q (M in FIGS. 6(A) and 6(C)).

[0086] p in equation (37) q The maximum value of (q=1,2,3,4) is 1. q To approach the maximum value, the structural inductance L q (Inductance L1 in Figures 7(A) and (B)) should be made as small as possible.

[0087] Coupling coefficient K of four-body interactions with qubits q is essentially the structural capacitance C of qubit 20 q is decided. TIFF2025141608000048.tif11150…(38) where e is the elementary charge and C q is the effective structural capacitance of the qubit 20, specifically the capacitance of the capacitor (shunt capacitor) 206 of the qth qubit 20.

[0088] By reducing the capacitance of capacitor 206, the nonlinear parameter K q (q=1,2,3,4) is set to large, and the coupling coefficient h (4) In this case, although the geometric structure of the electrodes 24 of the quantum bit 20 and the like changes, the nonlinearity can be significantly changed.

[0089] Here, the structure of the electrodes of the quantum bit 20 is changed to change the coupling constant h between the first quantum bit 20-1 and the third quantum bit 20-3. 13 and the coupling constant h between the first qubit 20-1 and the fourth qubit 20-4. 14 are different, and the coupling constant h 13 and the coupling constant h between the second qubit 20-2 and the third qubit 20-3. 23If they differ, then equation (19) does not hold, and the following is derived from equation (12) above. TIFF2025141608000049.tif10150 TIFF2025141608000050.tif10150 TIFF2025141608000051.tif11150…(39)

[0090] 8A is a schematic plan view illustrating a portion of the wiring layer of the quantum chip. FIG. 8A also shows a non-limiting example of the pattern shape of the quantum bit 20. The electrodes 24A to 20D of the first to fourth quantum bits 20-1 to 20-4 have a cross-shaped electrode structure with four arms extending in all directions from the center, and are surrounded by a ground plane 101 with a gap 102 in between. The gap 102 between the electrodes 24A to 20D and the ground plane 101 constitutes the capacitance component of the capacitor 206. The gap 102 is free of ground or wiring patterns, and the substrate surface of the quantum chip is exposed. The tip of one of the four arms of each of the electrodes 24A to 20D serves as a coupler connection portion and is capacitively coupled to the coupler 21 via the gap 102. A gap 102 between the tip of the arm of each of electrodes 24A to 24D that faces the electrode (not shown) of coupler 21 and the electrode (not shown) of coupler 21 constitutes the capacitance of coupling capacitors 31A to 31D.

[0091] 8A, electrodes 24A-20D of each of first through fourth quantum bits 20-1-20-4 have the same shape. SQUIDs 210A-210D are bridged between each of electrodes 24A-20D of each of first through fourth quantum bits 20-1-20-4 and opposing ground surface 101. For simplicity, in the example of FIG. 8A, SQUIDs 210A-210D are connected between the end of the arm opposite to the arm coupled to coupler 21 and opposing ground surface 101 in cross-shaped electrodes 24A-20D of each of first through fourth quantum bits 20-1-20-4. However, SQUIDs 210A-210D may be connected between one longitudinal side of the arm and opposing ground surface 101. For example, when the tips of the arms of cross-shaped electrodes 24A-24D are coupled to different couplers 21, SQUIDs 210 are connected between the sides of the arms and the opposing ground plane 101. In Fig. 8(A), in the first to fourth quantum bits 20-1-20-4, SQUIDs 210A-210D may be Josephson junctions 201A-201D as shown in Fig. 3. It should be noted that the electrode structure of quantum bit 20 is not limited to the cross shape shown in Fig. 8(A), which is a non-limiting example.

[0092] 8(B) is a diagram illustrating an example of changing the geometric shape of the structural inductance and structural capacitance of a quantum bit, and is a diagram schematically illustrating an example in which the structure of electrodes 24 of quantum bits 20-1 to 20-4 is changed from that of FIG. 8(A). Note that capacitors 206A to 206D and coupling capacitors 31A to 31D shown in FIG. 8(A) are not shown in FIG. 8(B). Referring to FIG. 8(B), the first quantum bit 20-1 and the fourth quantum bit 20-4 differ in the arm width W1 of electrode 24A and the arm width W4 of electrode 24D, and the second quantum bit 20-2 and the third quantum bit 20-3 differ in the arm width W2 of electrode 24B and the arm width W3 of electrode 24C. When the arm width W of electrode 24 is widened and the gap (slot width) with the ground surface is narrowed, the capacitance (structural capacitance) of capacitor 206 between electrode 24 and ground also differs. Note that in FIG. 8(B), for the sake of explanation, arm widths W1 to W4 of electrodes 24A to 24D of first quantum bits 20-1 to fourth quantum bits 20-4 are set to different values, but the arm width, arm length, etc. of one quantum bit among first quantum bits 20-1 to fourth quantum bits 20-4 may be different from the electrodes of the other quantum bits. The capacitances (structural capacitances) of capacitors 206A and 206D between electrode 24A and ground and between electrode 24D and ground differ between first quantum bit 20-1 and fourth quantum bit 20-4, and changing the setting of the geometric shape of the electrode structure also results in different inductance components of electrodes 24A and 24D. The capacitances of capacitors 206A and 206C between electrode 24A and ground and between electrode 24C and ground are different between first quantum bit 20-1 and third quantum bit 20-3, and the inductance components of electrodes 24A and 24C are also different. As a result, the coupling h between first quantum bit 20-1 and third quantum bit 20-3 13 is the coupling h between the first qubit 20-1 and the fourth qubit 20-4 (which has a different electrode structure from that of the third qubit 20-3). 14 In addition, the coupling h between the first quantum bit 20-1 and the third quantum bit 20-3 is 13is the coupling h between the second qubit 20-2 (which has a different electrode structure from the first qubit 20-1) and the third qubit 20-3. 23 The configuration of Fig. 8(B) corresponds to the above-mentioned formula (39). It should be noted that the electrode structure of the quantum bit 20 is not limited to the cross shape shown in Fig. 8(B), which is a non-limiting example.

[0093] 8(A) and 8(B) , in the present disclosure, the quantum chip substrate is made of, 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, the quantum chip substrate is preferably single-crystal, but may also be polycrystalline or amorphous. The pattern of the wiring layer of the quantum chip may be formed by depositing (evaporating) a superconducting material on the surface of the substrate and patterning it. The superconducting material (wiring material) for the wiring and electrodes of the quantum chip wiring layer may be, for example, niobium (Nb) or aluminum (Al). However, this is not limited to these. Any metal that becomes superconducting when cooled to a cryogenic temperature may also be used, such as niobium nitride, indium (In), lead (Pb), tin (Sn), rhenium (Re), palladium (Pd), titanium (Ti), titanium nitride, molybdenum (Mo), tantalum (Ta), tantalum nitride, and alloys containing at least one of these. Although not particularly limited, as a Josephson junction, a first aluminum film is formed on the surface of the quantum chip substrate by oblique deposition and oxidized to form a tunnel oxide film (AlO x ) and then a second aluminum film is formed by oblique evaporation from the opposite direction to the previous one, forming a Josephson junction (Al / AlO x / Al) may be formed.

[0094] (III) As shown in FIG. 4, when the first to fourth quantum bits 20-1 to 20-4 include SQUIDs 210A to 210D and the resonant frequency is adjustable, the resonant angular frequencies ω1 to ω4 of the first to fourth quantum bits 20-1 to 20-4 may be changed. For example, referring to FIG. 8(A), in the first to fourth quantum bits 20-1 to 20-4, the resonant frequencies of the first to fourth quantum bits 20-1 to 20-4 are adjusted by changing the magnetic flux applied to each loop of the SQUIDs 210A to 210D. In this case, the nonlinearity does not change significantly. In addition, the coupling coefficient h of the four-body interaction (4) By selecting a frequency range in which the value of changes relatively frequently, the coupling coefficient h (4) 8(A), the structures of electrodes 24A to 24D of first to fourth quantum bits 20-1 to 20-4 and Josephson junctions 201A to 201D are the same, but the resonant frequencies of first to fourth quantum bits 20-1 to 20-4 are changed by changing the magnetic flux applied to each loop of SQUIDs 210A to 210D (changing the value of the direct current flowing through the magnetic flux generating section).

[0095] In addition, when K1=K4>K2=K3, h (4) In equation (22), the difference δ between the resonant angular frequencies of the third quantum bit 20-3 and the fourth quantum bit 20-4 in FIG. 34 (=ω3-ω4) and the difference δ between the resonant angular frequencies of the first quantum bit 20-1 and the second quantum bit 20-2 12 When adjusting (=ω1-ω2) or the like, the magnetic fluxes applied to the SQUIDs 210A to 210D of the first to fourth quantum bits 20-1 to 20-4 in FIG. 8(A) may be changed.

[0096] Of course, the control of the four-body interaction due to the nonlinearity of the quantum bit does not necessarily have to be performed by selecting one of the above (I) to (III), but may be performed by combining two or three of the above (I) to (III).

[0097] As described above, the coupling coefficient h of the four-body interaction by the first to fourth quantum bits 20-1 to 20-4 is (4) However, for three or more quantum bits, multi-body interactions (three-body interactions, five- to eight-body interactions, etc.) can be similarly exhibited.

[0098] FIG. 9 is a diagram showing one modification of FIG. 3. Coupler 21 has a configuration in which SQUID 220 and capacitor 16 are connected in parallel between first electrode (first node) 17 and second electrode 18 (second node). The resonant frequency of coupler 21 is varied by changing the strength of the magnetic field applied to the loop of SQUID 220 from a magnetic field application unit (not shown). In the example of FIG. 9, as in the example of FIG. 3, the nonlinearity of quantum bit 20 may be made different from the others by any of the above methods (I) to (III). In the case of FIG. 9, the strength of the four-body interaction of quantum bits 20-1 to 20-4 is h (4) and g (4) (Equation (3)) (for example, h (4) The size of g (4) (This can be expressed as the sum of the magnitudes of the

[0099] FIG. 10 is a diagram illustrating a modification of FIG. 4. Referring to FIG. 10, coupler 21 has a configuration in which SQUID 220 and capacitor 16 are connected between first electrode (first node) 17 and second electrode 18 (second node). In the example of FIG. 10, as in the example of FIG. 4, the nonlinearity of quantum bit 20 may be varied using any of the methods (I) to (III) described above. That is, at least one of the number of series-connected Josephson junctions, the structural inductance, and the structural capacitance may be made the same among first to fourth quantum bits 20-1 to 20-4, and the magnetic flux passing through SQUIDs 210A to 210D may be varied to vary the resonant frequency. Furthermore, the resonant frequency of coupler 21 can be varied by changing the strength of the magnetic field applied to the loop of SQUID 220 from a magnetic field application unit (not shown).

[0100] 11 is a diagram illustrating a non-limiting example of a coupler 21 having an interdigital capacitor structure. The coupler 21 is configured by arranging an L-shaped first electrode 17 and a second electrode 18, each having a vertical side and a horizontal side, with the vertical sides facing each other and the horizontal sides facing each other, and each of the first electrode 17 and the second electrode 18 has a shape in which rod-shaped (comb-like) electrodes protruding from the vertical side toward the vertical side of the opposing electrode are combined in a staggered manner. A SQUID 220 is connected in the gap between the horizontal side of the first electrode 17 and the vertical side of the second electrode 18. The vertical and horizontal sides of the first electrode 17 are provided with connection portions A and B (protruding portions) that are capacitively coupled to electrode 24A of the first quantum bit 20-1 and electrode 24B of the second quantum bit 20-2, respectively, as shown in Figures 9 and 10. The horizontal and vertical sides of the second electrode 18 are provided with connection portions C and D (protruding portions) that are capacitively coupled to electrode 24C of the third quantum bit 20-3 and electrode 24D of the fourth quantum bit 20-4, respectively, as shown in Figures 9 and 10. Near the SQUID 220, an end of a coplanar control line (pump line) is connected to the GND plane as a magnetic field application unit that generates a magnetic flux that passes through the loop of the SQUID 220. In other words, an end of an IO line that is capacitively coupled to the second electrode 18 is disposed opposite the horizontal side of the second electrode 18. In areas other than the area where the end of the pump line inductively coupled to SQUID 220 is disposed and the area where the end of the IO line capacitively coupled to the horizontal side of second electrode 18 is disposed, a gap of a predetermined width is provided between first electrode 17, second electrode 18 and the surrounding ground (GND) plane 101. The substrate surface of the quantum chip is exposed in each gap between first and second electrodes 17, 18, the IO line of the coplanar waveguide, and the pump line. It goes without saying that coupler 21 is not limited to the pattern shown in FIG.

[0101] FIG. 12 is a diagram showing a modification of FIG. 3. Referring to FIG. 12, coupler 21 of FIG. 3 is configured with a linear element (LC resonant circuit). Inductor 15 and capacitor 16 are connected in parallel between first electrode 17 and second electrode 18. In the example of FIG. 12, the strength of the four-body interaction of quantum bits 20-1 to 20-4 is determined by the nonlinearity of the quantum bits. (4)In the case of the example of FIG. 12, as in the example of FIG. 3, the nonlinearity of at least one quantum bit 20 may be made different from that of the other quantum bits by any of the above-mentioned methods (I) to (III). In the configuration of FIG. 12, the strength of the four-body interaction of the four quantum bits is determined by the nonlinearity of the quantum bits, h (4) However, the requirements for design tolerance, frequency adjustment, calibration, etc., which are required when a nonlinear element such as a Josephson junction or SQUID is used in the coupler 21, are relaxed.

[0102] FIG. 13 is a diagram showing a modification of FIG. 4. Referring to FIG. 13, coupler 21 in FIG. 4 is configured with a linear element (an LC resonant circuit of inductor 15 and capacitor 16) as in FIG. 12. In the example of FIG. 13, the strength of the four-body interaction of quantum bits 20-1 to 20-4 is also h (4) As in the example of FIG. 4, the nonlinearity of at least one quantum bit 20 may be made different from that of the other quantum bits by any of the methods (I) to (III) described above. In the configuration of FIG. 13, the strength of the four-body interaction of the four quantum bits is determined by the nonlinearity of the quantum bits, h (4) However, the requirements for design tolerance, frequency adjustment, calibration, etc., which are required when a nonlinear element such as a Josephson junction or SQUID is used in the coupler 21, are relaxed.

[0103] Fig. 14 is a diagram showing a modification of Fig. 3. Referring to Fig. 14, coupler 21 of Fig. 3 is configured with a linear element (capacitor 16). In the example of Fig. 14, the strength of the four-body interaction of quantum bits 20-1 to 20-4 is h (4) 14, similarly to the example of FIG. 3, the nonlinearity of at least one of the four quantum bits 20 may be made different from the nonlinearities of the other quantum bits 20 by using any one of the above-described techniques (I) to (III), or a combination of at least two of these techniques.

[0104] Fig. 15 is a diagram showing a modification of Fig. 4. Referring to Fig. 15, coupler 21 of Fig. 4 is configured with a linear element (capacitor 16). In the example of Fig. 15, the strength of the four-body interaction of quantum bits 20-1 to 20-4 is h (4) 15, as in the example of FIG. 4, the nonlinearity of at least one of the four quantum bits 20 may be made different from the nonlinearity of the other quantum bits by using any one of the above-mentioned methods (I) to (III), or a combination of at least two of these methods. Also, the resonant frequency may be varied by making the magnetic flux passing through the SQUIDs 210A to 210D different.

[0105] Figure 16 is a diagram showing a variation of Figure 3. Referring to Figure 16, first and second quantum bits 20-1 and 20-2 are connected to a common node via coupling capacitors 31A and 31B, respectively, and third and fourth quantum bits 20-3 and 20-4 are connected to a common node via coupling capacitors 31C and 31D, respectively.

[0106] Fig. 17 is a diagram showing a modification of Fig. 4. Referring to Fig. 17, first and second quantum bits 20-1 and 20-2 are connected to a common node via coupling capacitors 31A and 31B, respectively, and third and fourth quantum bits 20-3 and 20-4 are connected to a common node via coupling capacitors 31C and 31D, respectively. In Figs. 16 and 17, the node to which four quantum bits 20-1 to 20-4 are commonly connected via coupling capacitors 31A to 31D may be referred to as coupler 21.

[0107] As a further variation of Figure 3, coupler 21 may be configured between first and second electrodes 17, 18, with multiple Josephson junctions connected in series in parallel with capacitor 16, similar to quantum bit 20 of Figure 5, for example.

[0108] 4, coupler 21 may have a configuration similar to that of quantum bits 20B to 20E in FIGS. 6(A) to 6(D). In this case, in quantum bits 20B to 20E in FIGS. 6(A) to 6(D), the node connected to ground and the node connected to coupling capacitors 31A to 31D correspond to first electrode 17 (first node) and second electrode 18 (second node) of coupler 21, respectively. In the present disclosure, coupler 21 is not limited to the above modification and may include other combinations of Josephson junctions and SQUIDs.

[0109] The strength of the four-body interaction (coupling coefficient) g in Eq. (3) (4) The nonlinear parameter K g is composed of a component determined by inductance and a component determined by capacitance, as shown in the following equation. TIFF2025141608000052.tif6150…(40) where E cq is the charging energy of the coupler 21.

[0110] p g The participation ratio is the ratio of the inductive energy stored in the quantum bit (Josephson junction) to the inductive energy stored in the circuit, and can be expressed, for example, as follows: TIFF2025141608000053.tif13150…(41) where: L gL is the structural inductance, L gS is the inductance of the SQUID, n gS is the number of SQUIDs (corresponding to L when the coupler 21 is configured according to Figs. 6(B) and (C)), L gJ is the inductance of the Josephson junction connected in series with the SQUID, n gJis the number of Josephson junctions connected in series (corresponding to M when the coupler 21 is configured in accordance with FIG. 5 or in accordance with FIGS. 6(A) and 6(C)).

[0111] p g The maximum value of p is 1. g To approach the maximum value, the structural inductance Lg (the inductance component of the electrodes of the coupler 21) is made as small as possible.

[0112] Coupling coefficient K of the four-body interaction by coupler 21 g is basically the structural capacitance C of the coupler 21 g is decided. TIFF2025141608000054.tif11150…(42) where C g is the effective structural capacitance of the qubit 20, e.g., the capacitance of the capacitor 16 of the coupler 21 in FIG. 4. For example, by reducing the capacitance of the capacitor 16, the nonlinear parameter K g Increase the coupling coefficient g (4) can be made larger.

[0113] FIG. 18 is a diagram schematically illustrating an example of the configuration of a superconducting quantum computer 300 (quantum annealing machine). In the example of FIG. 18, each coupler 21 couples four adjacent quantum bits 20 through four-body interactions. A coupler 21 and its four adjacent quantum bits 20 form a unit structure (also referred to as a plaquette). In the superconducting quantum computer 300, at least one quantum bit 20 is connected to multiple couplers 21. In the example shown in FIG. 18, the superconducting quantum computer 300 has multiple unit structures, and the quantum bit 20 is shared by the multiple unit structures. In the example shown in FIG. 18, 13 quantum bits 20 are integrated, but any number of quantum bits may be integrated in a similar manner. Note that signal sources and readout units are omitted in FIG. 18. The configuration of FIG. 18 is suitable for a network using the LHZ (Lechner, Hauke, Zoller) method, which is one of the quantum annealing methods.

[0114] In the present disclosure, couplers and the like are not limited to lumped constant circuits (such as superconducting LC resonators), but can also be applied to distributed constant types (such as coplanar type superconducting transmission line resonators).

[0115] [Reference 1] Wolfgang Lechner, Philipp Hauke, and Peter Zoller, "A quantum annealing architecture with all-to-all connectivity from local interactions", SCIENCE ADVANCES 23 Oct 2015 Vol 1, Issue 9

[0116] Some embodiments disclosed above are summarized as follows (but are not limited to):

[0117] (Supplementary Note 1) A quantum circuit device includes at least three or more quantum bits coupled by a many-body interaction via a coupler, and at least one of the at least three or more quantum bits has a nonlinearity different from that of the other quantum bits.

[0118] (Supplementary Note 2) In the quantum circuit device of Supplementary Note 1, the coupler includes a nonlinear element.

[0119] (Supplementary Note 3) In the quantum circuit device of Supplementary Note 1 or 2, the many-body interaction is a four-body interaction involving four quantum bits.

[0120] (Supplementary Note 4) In the quantum circuit device of any one of Supplementary Notes 1 to 3, the coupler includes a Josephson junction as a nonlinear element.

[0121] (Supplementary Note 5) In the quantum circuit device of any one of Supplementary Notes 1 to 4, the coupler includes a SQUID (Superconducting Quantum Interference Device) as a nonlinear element.

[0122] (Supplementary Note 6) In the quantum circuit device of any one of Supplementary Notes 1 to 5, the quantum bit includes a Josephson junction and a capacitor.

[0123] (Supplementary Note 7) In the quantum circuit device of any one of Supplementary Notes 1 to 3, the quantum bit includes a SQUID including a plurality of Josephson junctions in a loop, and a capacitor.

[0124] (Supplementary Note 8) In the quantum circuit device of any one of Supplementary Notes 1 to 5, the nonlinear parameter of the quantum bit is 1 kHz (kiloherz) or more. The difference between the nonlinear parameter of the quantum bit whose nonlinearity differs from that of other quantum bits and the nonlinear parameters of the other quantum bits is 1 kHz or more.

[0125] (Supplementary Note 9) In the quantum circuit device of any one of Supplementary Notes 1 to 8, the quantum bits are capacitively coupled to the coupler.

[0126] (Supplementary Note 10) In any one of the quantum circuit devices of Supplementary Note 1 to Supplementary Note 9, the coupling coefficient h of the four-body interaction by the four quantum bits (4) focuses on one of the four qubits, and defines the strength of the coupling between the one qubit and the other qubit as h, The difference between the resonant frequency of the one quantum bit and the resonant frequency of the other quantum bit is δ. The parameter representing the nonlinearity of one quantum bit is K q As, (h / q) 3 K q Includes the section.

[0127] (Supplementary Note 11) In the quantum circuit device of any one of Supplementary Note 1 to 10, the coupling coefficient h of the four-body interaction by the four qubits (4) and the coupling coefficient g of the four-body interaction by the coupler of the four qubits (4) The combined value (e.g., h (4) and g (4) The sum of the magnitudes of the four-body interactions acts as the strength of the four-body interaction.

[0128] (Supplementary Note 12) In the quantum circuit device of any one of Supplementary Note 1 to 11, a coupling coefficient g of the four-body interaction by the coupler of the four quantum bits (4) teeth, The coupling strength between one of the four qubits and the coupler is g, The difference between the resonant frequency of the one quantum bit and the resonant frequency of the coupler is Δ, The parameter representing the nonlinearity of the coupler is K g For the four qubits, (g / Δ) 4 K g Including the term The coupling coefficient g of the four-body interaction of the four qubits by the coupler (4) and the coupling coefficient h of the four-body interaction by the four qubits (4) The combined value acts as the strength of the four-body interaction.

[0129] (Supplementary Note 13) In any one of the quantum circuit devices of Supplementary Note 1 to 12, a coupling coefficient h of the four-body interaction by the four quantum bits (4) teeth, TIFF2025141608000055.tif17150 (however, h ij is the strength of the coupling between the ith qubit and the jth qubit (i,j=1,...,4 where j≠i), δ ji is the resonant angular frequency ω between the jth qubit and the ith qubit (i,j=1,...,4 where j≠i) j and ω i The difference ω j -ω i is. K i (i=1,...,4) is a parameter that represents the nonlinearity of the i-th quantum bit.

[0130] (Supplementary Note 14) In the quantum circuit device of Supplementary Note 1 to 13, the four-body interaction conditions for the first to fourth resonance angular frequencies ω1, ω2, ω3, and ω4 of the first to fourth quantum bits among the four quantum bits are ω1+ω l =ω m +ω n (However, l, m, and n are When l is 2, m and n are 3 and 4, respectively. When l is 3, m and n are 2 and 4, respectively. When l is 4, m and n are 2 and 3, respectively. Regarding The coupling coefficient h of the four-body interaction of the four qubits (4) teeth, The nonlinear parameter K1 of the first qubit and the nonlinear parameter K of the lth qubit of the four qubits l and the nonlinear parameter K of the nth qubit n and the nonlinear parameter K of the mth qubit m and the difference between the resonant angular frequency ω1 of the first quantum bit and the resonant angular frequency ω of the l quantum bit l The difference δ 11 =ω1-ω l and the resonant angular frequency ω of the nth quantum bit n and the resonance angular frequency ω of the mth quantum bit n The difference δ nm =ω n -ω m It is determined according to the setting values ​​of each of the above.

[0131] (Supplementary Note 15) In any one of the quantum circuit devices of Supplementary Note 1 to 14, a coupling coefficient g of the four-body interaction by the coupler of the four quantum bits (4) teeth, TIFF2025141608000056.tif21153 (However, g i is the strength of the coupling between the ith (i=1,2,3,4) qubit and the coupler, Δ i is the i-th (i=1, 2, 3, 4) quantum bit resonance angular frequency ω i and the resonant angular frequency ω of the coupler r The difference between K g is a parameter that represents the nonlinearity of the coupler.

[0132] (Supplementary Note 16) In the quantum circuit device of Supplementary Note 13, the conditions of the four-body interaction regarding first to fourth resonant frequencies ω1, ω2, ω3, ω4 of first to fourth quantum bits among the four quantum bits include at least ω1+ω2=ω3+ω4; The coupling coefficient h of the four-body interaction of the four qubits (4) teeth, The difference between the nonlinear parameter K1 of the first qubit and the nonlinear parameter K2 of the second qubit of the four qubits; the difference between the nonlinear parameter K3 of the third qubit and the nonlinear parameter K4 of the fourth qubit; The difference δ between the resonant frequency ω1 of the first quantum bit and the resonant frequency ω2 of the second quantum bit 12 and, The difference δ between the resonant frequency ω3 of the third quantum bit and the resonant frequency ω4 of the fourth quantum bit 34 It is determined according to the setting values ​​of each of the above.

[0133] (Supplementary Note 17) In the quantum circuit device of Supplementary Note 13, the absolute value of the difference between the nonlinear parameters K1 and K2 of the first quantum bit and the second quantum bit, and the absolute value of the difference between the nonlinear parameters K3 and K4 of the third quantum bit and the fourth quantum bit are each set to a predetermined value or more; Regarding the absolute value of the difference between the nonlinear parameters K1 and K2 of the first quantum bit and the second quantum bit, and the absolute value of the difference between the nonlinear parameters K3 and K4 of the third quantum bit and the fourth quantum bit, one is set to be large and the other is set to be small.

[0134] (Appendix 18) In the quantum circuit device of Appendix 13, the nonlinear parameters K1 and K4 of the first quantum bit and the fourth quantum bit are set to be the same, the nonlinear parameters K2 and K3 of the second quantum bit and the third quantum bit are set to be the same, and the nonlinear parameter K2 of the second quantum bit is set to be larger than the nonlinear parameter K1 of the first quantum bit.

[0135] (Supplementary Note 19) In the quantum circuit device of Supplementary Note 13, the conditions of the four-body interaction regarding the first to fourth resonant frequencies ω1, ω2, ω3, ω4 of the first to fourth quantum bits among the four quantum bits are as follows: Let ω1+ω4=ω2+ω3, Of the four quantum bits, the strength of the coupling between at least one quantum bit and another quantum bit is made different from the strength of the coupling between the one quantum bit and yet another quantum bit.

[0136] (Supplementary Note 20) In the quantum circuit device of any one of Supplements 1 to 19, the number of Josephson junctions connected in series included in at least one of the quantum bits is different from the number of Josephson junctions included in the other quantum bits.

[0137] (Supplementary Note 21) In the quantum circuit device of any one of Supplementary Notes 1 to 19, the number of SQUIDs connected in series included in the at least one quantum bit is different from the number of SQUIDs included in the other quantum bits.

[0138] (Appendix 22) In the quantum circuit device of any one of Appendices 1 to 19, at least one of the number of SQUIDs connected in series and the number of Josephson junctions connected in series included in at least one of the quantum bits is different from the other quantum bits.

[0139] (Supplementary Note 23) In the quantum circuit device of any one of Supplementary Notes 1 to 22, the value of structural inductance and / or capacitance included in the at least one quantum bit is different from that of the other quantum bits.

[0140] (Supplementary Note 24) In the quantum circuit device of any one of Supplementary Notes 1 to 23, the resonant frequency of the at least one quantum bit is set to a value different from that of the other quantum bits.

[0141] (Supplementary Note 25) A method for controlling the strength of coupling in which at least first to third quantum bits interact with each other via a coupler, comprising: The nonlinearity of at least one of the first to third quantum bits is set to be different from the nonlinearity of the other quantum bits.

[0142] (Supplementary Note 26) In the control method of Supplementary Note 25, the many-body interaction is a four-body interaction between four quantum bits.

[0143] (Supplementary Note 27) In the control method of Supplementary Note 25 or 26, the coupler includes a nonlinear element.

[0144] The disclosures of Non-Patent Document 1 and Reference Document 1 are incorporated herein by reference. Modifications and adjustments of the embodiments and examples are possible within the scope of the entire disclosure of the present invention (including the scope of the claims), and further based on the basic technical ideas thereof. Furthermore, various combinations and selections of the various disclosed elements (including each element of each claim, each element of each example, each element of each drawing, etc.) are possible within the scope of the claims of the present invention. In other words, the present invention naturally includes various modifications and alterations that would be possible for a person skilled in the art based on the entire disclosure, including the scope of the claims, and the technical ideas thereof. [Explanation of symbols]

[0145] 1 Quantum circuit device 10 Josephson junction 15 Inductors 16 Capacitors 17 First electrode (first node) 18 Second electrode (second node) 19 Electrodes (transmission lines, nodes) 20, 20A-20E qubits 20-1~20-4 1st to 4th quantum bits 21 Combiner (linear combiner) 24, 24A to 24D Electrodes (coupler connection parts) 31, 31A~31D Coupling capacitors 101 Ground (ground surface) 102 Gap 201, 201A-201D, 221 Josephson junction 202, 202A-202D, 202-1-202-N, 222 Josephson junction 203, 203A-203D, superconducting materials 204, 204A-204D, superconducting materials 206, 206A~206D capacitors 207-1~207-M ​​Josephson junctions 210, 210A-210D, 220 SQUID 300 Superconducting Quantum Computer

Claims

1. at least three qubits coupled by a many-body interaction via a coupler; A quantum circuit device, wherein at least one of the at least three quantum bits has a nonlinearity different from the nonlinearities of the other quantum bits.

2. The quantum circuit device according to claim 1 , wherein the coupler includes a nonlinear element.

3. The quantum circuit device according to claim 1 , wherein the many-body interaction is a four-body interaction involving four quantum bits.

4. 3. The quantum circuit device according to claim 2, wherein the coupler includes a Josephson junction as the nonlinear element.

5. The quantum circuit device according to claim 1 , wherein the quantum bit includes a Josephson junction and a capacitor.

6. 2. The quantum circuit device according to claim 1, wherein the nonlinear parameter of the quantum bit is 1 kHz (kiloherz) or more, and the difference between the nonlinear parameter of the quantum bit whose nonlinearity differs from that of other quantum bits and the nonlinear parameters of the other quantum bits is 1 kHz or more.

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

8. The coupling coefficient h of the four-body interaction by the four qubits （４） teeth, (However, h ｉｊ is the strength of the coupling between the ith qubit and the jth qubit (i, j = 1, ..., 4 where j ≠ i), δ ｊi is the resonant angular frequency ω between the i-th qubit and the j-th qubit (i, j = 1, ..., 4, where j ≠ i) ｉ and ω ｊ The difference ω ｊ -ω ｉ , K ｉ 2. The quantum circuit device according to claim 1, wherein i=1, . . . , 4 is a parameter representing the nonlinearity of the i-th quantum bit.

9. The coupling coefficient h of the four-body interaction by the four qubits （４） and a coupling coefficient g of the four-body interaction by the coupler of the four qubits. （４） 9. The quantum circuit device according to claim 8, wherein a combined value of the above functions as the strength of the four-body interaction.

10. A method for controlling strength of coupling in which at least first to third quantum bits interact with each other via a coupler, comprising: A control method for setting the nonlinearity of at least one of the first to third quantum bits to be different from the nonlinearity of the other quantum bits.

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