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, while eliminating the need for bias lines or input / output lines for frequency tuning.SOLUTION: The quantum circuit device includes a coupler composed of linear elements and 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) scheme is known as one of the quantum annealing schemes that solves combinatorial optimization problems (Reference 1). Non-Patent Document 1 discloses a network based on four-body interactions of quantum bits and couplers, as shown in Figure 1, as a physical implementation of the LHZ scheme. Figure 1 is a diagram based on Figure 4a in Non-Patent Document 1. In the example of Figure 1, a Josephson Parametric Oscillator (JPO), for example, is used as the quantum bit, and a nonlinear element such as a Josephson Junction (JJ), for example, is used as the coupler. [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] To obtain a four-body interaction large enough for quantum annealing to work, for example, The frequency difference between the resonant frequency of the qubit and the resonant frequency of the coupler, The coupler must meet certain (desired) conditions regarding its nonlinearity, etc. In a configuration using a nonlinear element such as a Josephson junction as a coupler, as shown in Figure 1, it is generally not easy to design and manufacture a coupler equipped with a Josephson junction that satisfies these conditions. Furthermore, in the case of a frequency-tunable coupler, its adjustment (calibration, etc.) requires time and effort. A frequency-tunable coupler requires the installation of bias lines for frequency adjustment and input / output lines for frequency readout, as well as the preparation of new measuring equipment and wiring.

[0005] One of the objectives of the present disclosure is to provide a quantum circuit device and a control method for a coupler that can exhibit many-body interactions between multiple quantum bits, which eliminates the need for bias lines or input / output lines for frequency adjustment and allows the strength of the many-body interactions to be freely set to a desired value. [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, the coupler being configured with linear elements, and the nonlinearity of at least one of the first to third quantum bits being set to be different from the nonlinearity of the other quantum bits. [Effects of the Invention]

[0008] According to the present disclosure, a coupler that couples quantum bits through many-body interactions does not require bias lines for frequency adjustment or input / output lines for frequency readout, and the strength of the many-body interactions can be freely set to a desired value. [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] 1A and 1B are diagrams illustrating examples of quantum bits according to the present disclosure. [Figure 8] 1A and 1B are diagrams for schematically explaining examples of layouts according to the present disclosure. [Figure 9] 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 10] 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. 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 i When 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 iWhen 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: TIFF2025141607000002.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. TIFF2025141607000003.tif6150…(2-a) TIFF2025141607000004.tif6150…(2-b)

[0013] Four-body interaction strength (coupling coefficient) g (4) teeth, TIFF2025141607000005.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 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) between c -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), TIFF2025141607000006.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 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 of the coupler is 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] When a Josephson junction is used as a frequency-fixed coupler, its resonant frequency depends on the critical current value of the Josephson junction, and therefore it is necessary to fabricate a Josephson junction with a critical current value close to the desired value (design value).

[0019] On the other hand, if the coupler is not a fixed-frequency type but, for example, a variable-frequency type equipped with a SQUID, it will be necessary to route input / output lines to read out the coupler's frequency and bias lines for frequency change (adjustment) (for example, a line supplying a bias signal to generate a bias magnetic flux to be applied to the SQUID). In addition to placing these lines on a chip that integrates a network of quantum bits and couplers, measurement wiring and cables, signal sources, and measuring instruments will also be required outside the chip. Furthermore, a certain level of precision is required to adjust the difference in resonant frequency between the coupler and quantum bits.

[0020] 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 simplify the setting of the strength of the interaction, i.e., the coupling coefficient.

[0021] According to the present disclosure, by using a coupler (also called a "linear coupler") composed of linear elements (linear circuits) for coupling between quantum bits, rather than a coupler using nonlinear elements such as Josephson junctions or SQUIDs, as shown in Figure 1, requirements such as design tolerance, frequency adjustment, and calibration that are required when using nonlinear elements in a coupler are relaxed, and furthermore, the nonlinearity of the four quantum bits makes it possible to set the strength of the four-body interaction to a desired value.

[0022] Linear elements typically include inductors and capacitors. However, in cases where a network of quantum bits and couplers is integrated on a wiring layer of a chip (such as a quantum chip or wiring chip), the capacitance component between the wiring (for example, between opposing electrodes or between an electrode and ground) constitutes a capacitor. In this disclosure, linear elements include, for example, circuit elements patterned on a wiring layer of a chip, but do not necessarily mean that they are discrete components or discrete devices separate from the chip.

[0023] 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.

[0024] 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).

[0025] The coupler 21 includes a capacitor, an inductor, or a parallel resonant circuit of an inductor and a capacitor as a linear element connected between the first electrode and the second electrode.

[0026] Each of the first to fourth quantum bits 20-1 to 20-4 may include at least one Josephson junction and a capacitor (shunt capacitor) connected in parallel between an electrode and ground.

[0027] Each of the first to fourth quantum bits 20-1 to 20-4 may be configured to include at least one SQUID and a capacitor (shunt capacitor) connected in parallel between an electrode and ground.

[0028] 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.

[0029] In the present disclosure, at least one of the nonlinear parameters K1 to K4 of the first to fourth quantum bits 20-1 to 20-4 is preferably set to a value different from the others. K1 to K4 may all be set to different values.

[0030] 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 large, and the difference (δ 12 =ω1-ω2), 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 four-body interaction between the first to fourth quantum bits 20-1 to 20-4 may be set by adjusting the absolute value |δ of the difference between the resonant frequencies. 12 | and |δ 34 By making both | large, the four-body interactions between the first to fourth quantum bits 20-1 to 20-4 may be strengthened.

[0031] 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 in accordance with the condition for the four-body interaction will be different from the combination described above.

[0032] 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.

[0033] 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) In this 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.

[0034] 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.

[0035] 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 capacitively coupled to the first electrode 17 (first node) of the coupler 21 via a coupling capacitor 31A. The electrode 24A may include a connection (coupler connection) that capacitively couples 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 capacitively coupled to the first electrode 17 (first node) of the coupler 21 via a coupling capacitor 31B. Electrode 24B may include a connection (coupler connection) that capacitively couples 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 is capacitively coupled to second electrode 18 (second node) of coupler 21 via coupling capacitor 31C. Electrode 24C may include a connection (coupler connection) that capacitively couples 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 is capacitively coupled to second electrode 18 (second node) via coupling capacitor 31D. Electrode 24D may include a connection portion (coupler connection portion) that capacitively couples to second electrode 18 of coupler 21. In the following, when the individual quantum bits of first to fourth quantum bits 20-1 to 20-4 are not specified, they will be simply referred to as quantum bit 20 without the suffix number, and similarly, they will be referred to as Josephson junction 201, capacitor 206, etc.

[0036] In coupler 21, a parallel resonant circuit of inductor 15 and capacitor 16 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.

[0037] 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, which is formed by a loop of superconducting material 203A, Josephson junction 201A, superconducting material 204A, and Josephson junction 202A. 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.

[0038] 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: TIFF2025141607000007.tif17150…(8)

[0039] 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 jth quantum bit 20-j j and the resonant angular frequency ω of the i-th qubit 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 ith quantum bit 20-i.

[0040] where in equation (8), the multiplication term: Regarding TIFF2025141607000008.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 ±), It can be expressed as TIFF2025141607000009.tif10150. …(9)

[0041] In equation (9), TIFF2025141607000010.tif9150…(10) Under this condition, by making the difference δ in the resonant angular frequency between two quantum bits (i-th and j-th quantum bits 20-i and 20-j) as small as possible, the value of equation (9) becomes large.

[0042] From equation (9), the parameter K, which represents the nonlinearity of the quantum bit 20, q Even if we increase the coefficient of four-body interaction h (4) becomes larger.

[0043] In equation (3), the coefficient of the four-body interaction g (4) The nonlinearity parameter (Kerr coefficient) of the coupler is g Then, the fourth power term (g / Δ) (<1) 4 For example, in the example disclosed in Non-Patent Document 1, when g / Δ is 0.12, (g / Δ) 4 The result is ~0.00021.

[0044] On the other hand, in equation (9), the nonlinear parameter K of the quantum bit 20 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.

[0045] Furthermore, equation (8), which expresses the four-body interaction due to the nonlinearity between the quantum bits 20, does not involve the degrees of freedom of the coupler 21 (parameters related to the coupler 21). Therefore, there is no need to adjust the resonant frequency of the coupler 21 to strengthen the four-body interaction. In other words, the coupler 21 does not need to include a nonlinear element (such as a Josephson junction or a SQUID), and can be configured with a linear element. When the coupler 21 is configured with a linear element, there is no need to install a signal source for varying the frequency of the coupler 21, control lines, input / output lines, or measuring equipment. Note that although equation (8), which expresses the four-body interaction, does not involve the degrees of freedom of the coupler 21 (parameters related to the coupler 21), this does not preclude the coupler 21 from being configured with a nonlinear element. Furthermore, when the coupler generates all interactions, including the four-body interaction, the four-body interaction expressed by equation (8) can coexist.

[0046] 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 TIFF2025141607000011.tif10150…(11) Equation (9) is a generalization of equation (11).

[0047] 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. TIFF2025141607000012.tif10150…(12)

[0048] In the above equation (12), the condition for four-body interaction is TIFF2025141607000013.tif6150…(13) Let's say.

[0049] From equation (13), TIFF2025141607000014.tif6150 TIFF2025141607000015.tif6150Therefore, TIFF2025141607000016.tif6150…(14) TIFF2025141607000017.tif6150…(15)

[0050] Furthermore, regarding equation (12), δ ij (=ω i -ω j ) is antisymmetric with respect to the indices i and j: TIFF2025141607000018.tif6150…(16) h ij is symmetric with respect to the indices i and j: TIFF2025141607000019.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. TIFF2025141607000020.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. TIFF2025141607000021.tif6150…(19)

[0053] Under the above conditions (14) to (19), the above equation (12) becomes: TIFF2025141607000022.tif10150 TIFF2025141607000023.tif10150 Therefore, it is expressed by the following equation (20). TIFF2025141607000024.tif10150…(20)

[0054] In equation (20), if the nonlinearities K1 to K4 of the first to fourth quantum bits 20-1 to 20-4 are all the same, then K2 = K1, K3 = K4…(21) and h (4) = 0. In this case, the four-body interactions resulting from the nonlinearity of the first to fourth quantum bits 20-1 to 20-4 are cancelled out (turned off).

[0055] Furthermore, from equation (20), the absolute values ​​|K1-K2| and |K4-K3| are set to large values ​​(above a predetermined value), and δ 34 and δ 12 By making large, including the sign, h (4)The value (absolute value) becomes large, and a large four-body interaction can be obtained. For example, when (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, let 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, as well as 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 achieved.

[0057] In each qubit 20 of the 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. For this reason, 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 respectively, for example, ω1>ω2 and ω3>ω4 may be achieved. When the DC bias current value is large, 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 both large values (equal to or greater than a predetermined value), and when K1>K2 and K4<K3, δ 34 may be a large positive value, and δ 12 may be a negative value with a large absolute value. Alternatively, δ 34 may be a negative value with a large absolute value, and δ 12 may be a large positive value.

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

[0060] Also, in equation (20), if either one of the absolute values |K2 - K1| and |K3 - K4| is a large value and the other is a small value, the difference δ 34 in the resonance angular frequencies between the third qubit 20-3 and the fourth qubit 20-4, and the difference δ 12 in the resonance angular frequencies between the first qubit 20-1 and the second qubit 20-2 require less adjustment effort.

[0061] Alternatively, in equation (20), set |K1 - K2| and |K4 - K3| to predetermined values in advance, and by adjusting the difference δ 34 in the resonance angular frequencies between the third qubit 20-3 and the fourth qubit 20-4, and the difference δ 12 in the resonance angular frequencies between the first qubit 20-1 and the second qubit 20-2, h (4) can be set to 0 to cancel out the four-body interaction due to the non-linearity of the qubit 20. In this case, the adjustment of the resonance frequency differences δ 34 and δ 12 can be performed, for example, by reading out the frequencies of the first to fourth qubits २०-१~२०-४ in FIG. 4 from an input / output line (not shown), measuring them with a measuring instrument (not shown), and variably setting the DC bias current and microwave current from a signal source (not shown) for adjustment (calibration).

[0062] <9000514>By changing the conditions of the four-body interaction of the first to fourth qubits 20-1~20-4, even if the first to fourth qubits 20-1~20-4 have the same design, the strength of the four-body interaction can be switched.

[0063] For example, in equation (20), when K1 = K4 > K2 = K3, δ34 and δ 12 By appropriately adjusting , the four-body interaction can be strengthened. That is, equation (20) becomes the following equation (22). TIFF2025141607000025.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, δ 34 +δ 12 =(ω3-ω4)+(ω1-ω2) …(twenty three) Therefore, it may be set so that ω3>ω4 and ω1>ω2.

[0065] In addition, the conditions for the four-body interaction between the four qubits are TIFF2025141607000026.tif6150…(24) In this case, from equation (24), TIFF2025141607000027.tif6150 TIFF2025141607000028.tif6150Therefore, TIFF2025141607000029.tif6150…(25) TIFF2025141607000030.tif6150…(26)

[0066] From equations (25), (26) and equations (18), (19), equation (12) becomes: TIFF2025141607000031.tif15153 TIFF2025141607000032.tif10150 and is simplified as follows: TIFF2025141607000033.tif10150…(27)

[0067] From equation (27), taking the absolute values |K1 - K3| and |K4 - K2| to be large values (greater than or equal to a predetermined value), and δ 24 and δ 13 to be 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) between the resonance angular frequencies of the first qubit 20-1 and the third qubit 20-3 can both be large positive values, or both can be negative values with large absolute values. That is, ω2 > ω4 and ω1 > ω3, or ω2 < ω4 and ω1 < ω3 may be used.

[0068] As other controls, for the case where the condition of the four-body interaction is ω1 + ω2 = ω3 + ω4, the various controls described above regarding the non-linear parameters of the qubits and the difference δij in the resonance angular frequencies between the qubits are similarly applicable for the case of ω1 + ω3 = ω2 + ω4 by changing 2 to 3 and 3 to 2 with respect to the qubit numbers.

[0069] Furthermore, regarding the condition of the four-body interaction between the four qubits TIFF2025141607000034.tif6150…(28) it may be replaced with. In this case, from equation (28), TIFF2025141607000035.tif6150 TIFF2025141607000036.tif6150Therefore, TIFF2025141607000037.tif6150 …(29) TIFF2025141607000038.tif6150…(30)

[0070] From equations (29), (30) and equations (18), (19), equation (12) becomes TIFF2025141607000039.tif17156 TIFF2025141607000040.tif10150 This can be simplified as follows: TIFF2025141607000041.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, TIFF2025141607000042.tif10150…(32) In equation (32), the difference in resonant angular frequency 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 Regarding, for example, if K4>K1, 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 the quantum bit 20, multiple Josephson junctions 201 are connected in series (the number of Josephson junctions connected in series is changed). The configuration (geometric structure, layout) of the quantum bit electrodes and the like is left unchanged, but the junction structure (geometry, etc.) of the Josephson junctions is changed. (II) Changing the structural capacitance and inductance of the quantum bit 20. (III) Changing the resonant frequency of qubit 20, if the resonant frequency is tunable.

[0075] Specific examples of (I) to (III) above will be explained below.

[0076] (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 are connected in series between the electrode 24 and ground, and a capacitor 206 is 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.

[0077] 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).

[0078] As another example of connecting multiple Josephson junctions in series, a configuration may be used, as shown in FIG. 6(A) 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. For example, when the nonlinear parameters K1 through K4 of first through fourth quantum bits 20-1 through 20-4 are set to satisfy the relationship 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. 6(A), 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.

[0079] 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.

[0080] Alternatively, as yet another example of connecting multiple Josephson junctions in series, a configuration may be used in which L SQUIDs 210-1 to 210-L and M Josephson junctions 207-1 to 207-M ​​are connected in series between electrode 24 and ground, as shown in Fig. 6(C) as quantum bit 20D. When the nonlinear parameters of quantum bits 20D are to be different, at least one of the number L of L SQUIDs 210 connected in series and the number M of M Josephson junctions 207 connected in series may be made different in quantum bit 20C of Fig. 6(C). When the nonlinear parameters of quantum bits 20D are to be the same, the number L of L SQUIDs 210 connected in series and the number M of M Josephson junctions 207 connected in series may be made the same.

[0081] 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. When the nonlinear parameters K1 through K4 of the first through fourth quantum bits 20-1 through 20-4 are set to, for example, K1=K4>K2=K3, the second quantum bit 20-2 and the third quantum bit 20-3 in FIG. 4 may be configured with quantum bit 20E in FIG. 6(D), and the first quantum bit 20-1 and the fourth quantum bit 20-4 may remain as configured in FIG. 4.

[0082] 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.

[0083] (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: TIFF2025141607000043.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.

[0084] 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.

[0085] In equation (9), the nonlinear parameter K of the quantum bit 20 q (q=1,2,3,4) can be broadly divided into components determined by inductance and components determined by capacitance. TIFF2025141607000044.tif6150…(36) where E cq is the charging energy of qubit 20.

[0086] 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: TIFF2025141607000045.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)).

[0087] 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.

[0088] Coupling coefficient K of four-body interactions with qubits q is essentially the structural capacitance C of qubit 20 q is decided. TIFF2025141607000046.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.

[0089] By reducing the capacitance of capacitor 206, the nonlinear parameter K of qubit 20 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.

[0090] 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. TIFF2025141607000047.tif10150 TIFF2025141607000048.tif10150 TIFF2025141607000049.tif11150…(39)

[0091] 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 between them. 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.

[0092] 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.

[0093] 8(B) is a diagram for explaining 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 bit 20-1 to fourth quantum bit 20-4 are set to different values, but the arm width, arm length, etc. of one quantum bit among first quantum bit 20-1 to fourth quantum bit 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 geometrical 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-shaped configuration shown in Fig. 8(B), which is a non-limiting example.

[0094] 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.

[0095] (III) If the quantum bit is frequency variable, the resonant angular frequency is changed. In the example shown in FIG. 4, if 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 the SQUIDs 210A to 210D from magnetic field application units (not shown) provided near the SQUIDs 210A to 210D of the first to fourth quantum bits 20-1 to 20-4. In this case, the nonlinearity of the quantum bits does not change drastically, and from equation (8), it can be seen that the coupling coefficient h of the four-body interaction due to the nonlinearity of the quantum bit 20 (4) However, as the resonant frequencies (operating points) of the first to fourth quantum bits 20-1 to 20-4, the coupling coefficient h (4) If there is a frequency range in which the value of changes relatively frequently, by selecting this frequency range, 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 can be varied by changing the magnetic flux applied to each loop of SQUIDs 210A to 210D (by changing the value of the direct current flowing through the magnetic flux generating section).

[0096] 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 12When 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.

[0097] 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).

[0098] 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.

[0099] Fig. 9 is a diagram showing one modification of Fig. 3. Referring to Fig. 9, coupler 21 has a configuration in which capacitor 16 is connected between first electrode (first node) 17 and second electrode 18 (second node). Capacitor 16 may be configured as the capacitance of the gap between first electrode (first node) 17 and second electrode 18 (second node). In this case, capacitor 16 may be configured as an interdigital capacitor in which protruding portions are nested on the opposing sides of first electrode 17 and second electrode 18.

[0100] Figure 10 is a diagram showing a modification of Figure 3. Referring to Figure 10, coupler 21 has a configuration in which inductor 15 is connected between first electrode (node) 17 and second electrode 18. Inductor 15 may be formed by wiring a coplanar waveguide in a meander shape between first electrode (first node) 17 and second electrode 18 (second node).

[0101] In the examples of Figures 9 and 10, as in the example of Figure 3, 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 of the above-mentioned techniques (I) to (III), or a combination of at least two of these techniques.

[0102] 11 and 12 are diagrams showing modifications of FIG. 4 (qubit 20 includes SQUID 210), in which coupler 21 is configured with capacitor 16 and inductor 15, respectively. In the examples of FIGS. 11 and 12, as in the example of FIG. 4, the nonlinearity of at least one of four qubits 20 may be made different from the nonlinearity of the other qubits by using the above-mentioned techniques (I) to (III), or a combination of at least two of these. In FIG. 12, the first to fourth qubits 20-1 to 20-4 may have the same number of Josephson junctions connected in series, or at least one of the structural inductance and the structural capacitance, and the magnetic flux passing through SQUIDs 210A to 210D may be made different to vary the resonant frequency.

[0103] Figure 13 is a diagram showing a variation of Figure 3. Referring to Figure 13, 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.

[0104] Fig. 14 is a diagram showing a modification of Fig. 4. Referring to Fig. 14, 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. 13 and 14, 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.

[0105] FIG. 15 is a schematic diagram illustrating an example of the configuration of a superconducting quantum computer 300 (quantum annealing machine). In the example of FIG. 15, 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 called 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. 15, the superconducting quantum computer 300 has multiple unit structures, and the quantum bit 20 is shared among the multiple unit structures. In the example shown in FIG. 15, 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. 15. The configuration of FIG. 15 is suitable for a network using the LHZ (Lechner, Hauke, Zoller) method, which is one of the quantum annealing methods.

[0106] 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).

[0107] [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

[0108] Some embodiments disclosed above are summarized as follows (but are not limited to):

[0109] (Supplementary Note 1) A quantum circuit device includes a coupler configured with linear elements and at least three or more quantum bits coupled by a many-body interaction via the coupler, At least one of the at least three or more qubits has a nonlinearity different from that of the other qubits.

[0110] (Supplementary Note 2) In the quantum circuit device of Supplementary Note 1, the many-body interaction is a four-body interaction involving four quantum bits.

[0111] (Supplementary Note 3) In the quantum circuit device of Supplementary Note 1 or 2, the coupler includes a capacitor and / or an inductor as the linear element.

[0112] (Supplementary Note 4) In the quantum circuit device of any one of Supplementary Notes 1 to 3, the quantum bit includes at least one Josephson junction and a capacitor connected in parallel between an electrode and a ground.

[0113] (Supplementary Note 5) In the quantum circuit device of any one of Supplementary Notes 1 to 3, the quantum bit includes a SQUID (Superconducting Quantum Interference Device) including a plurality of Josephson junctions in a loop, and a capacitor.

[0114] (Supplementary Note 6) In the quantum circuit device of any one of Supplementary Notes 1 to 5, the quantum bits are capacitively coupled to the coupler.

[0115] (Supplementary Note 7) In any one of Supplementary Notes 1 to 6, the coupling coefficient h of the four-body interaction by the four qubits (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.

[0116] (Appendix 8) In the quantum circuit device of Appendix 7, the coupling coefficient h of the four-body interaction by the four qubits(4) teeth, TIFF2025141607000050.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.

[0117] (Supplementary Note 9) In the quantum circuit device of Supplementary Note 2 to 8, the four-body interaction conditions for the first to fourth resonance angular frequencies ω1, ω2, ω3, 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. ) for the four-body interaction of the four qubits, (4) is 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 =ωn -ω m It is determined according to the setting values ​​of each of the above.

[0118] (Supplementary Note 10) In the quantum circuit device of Supplementary Note 9, when the condition of the four-body interaction is ω1 + ω2 = ω3 + ω4, 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.

[0119] (Appendix 11) In the quantum circuit device of Appendix 9, when the condition of the four-body interaction is ω1 + ω2 = ω3 + ω4, 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.

[0120] (Supplementary Note 12) In the quantum circuit device of Supplementary Note 9, when the condition of the four-body interaction is ω1+ω2=ω3+ω4, the strength of coupling between at least one of the four quantum bits and another quantum bit is made different from the strength of coupling between the one quantum bit and yet another quantum bit.

[0121] (Supplementary Note 13) In the quantum circuit device of Supplementary Note 4, the number of Josephson junctions connected in series included in the at least one quantum bit is different from the number of the other quantum bits.

[0122] (Supplementary Note 14) In the quantum circuit device of Supplementary Note 5, 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.

[0123] (Appendix 15) In the quantum circuit device of any one of Appendices 1 to 14, 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.

[0124] (Supplementary Note 16) In the quantum circuit device of Supplementary Notes 1 to 15, 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.

[0125] (Supplementary Note 17) In the quantum circuit device of any one of Supplementary Notes 1 to 16, the resonant frequency of the at least one quantum bit is set to a value different from that of the other quantum bits.

[0126] (Appendix 18) A method for controlling the strength of coupling in which at least first to third quantum bits interact with each other via a coupler, the coupler being configured with a linear element; 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.

[0127] (Supplementary Note 19) In the control method of Supplementary Note 18, the many-body interaction is a four-body interaction between four quantum bits.

[0128] (Supplementary Note 20) In the control method of Supplementary Note 18 or 19, the coupler includes a capacitor and / or an inductor as the linear element.

[0129] 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]

[0130] 1 Quantum circuit device 15 Inductors 16 Capacitors 17 First electrode (first node) 18 Second electrode (second node) 19 electrodes (nodes) 20, 20A-20E qubits 20-1~20-4 1st to 4th 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 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 junctions 210, 210', 210A~210D SQUID 300 Superconducting Quantum Computer

Claims

1. a coupler composed of linear elements; At least three or more qubits coupled by many-body interactions via the coupler; Including, A quantum circuit device, wherein at least one of the at least three or more quantum bits has a nonlinearity different from that of the other quantum bits.

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

3. The quantum circuit device according to claim 1 , wherein the coupler includes a capacitor and / or an inductor as the linear element.

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

5. 2. The quantum circuit device according to claim 1, wherein the quantum bit includes a SQUID (Superconducting Quantum Interference Device) including a plurality of Josephson junctions in a loop, and a capacitor.

6. The quantum circuit device according to claim 3 , wherein the quantum bit is capacitively coupled to the coupler.

7. 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 resonance angular frequency ω between the jth quantum bit and the ith quantum bit (i, j = 1, ..., 4, where j ≠ i) ｊ and ω ｉ The difference ω ｊ -ω ｉ , K ｉ 3. The quantum circuit device according to claim 2, wherein i=1, . . . , 4 is a parameter representing the nonlinearity of the i-th quantum bit.

8. The first to fourth resonance angular frequencies ω of the first to fourth quantum bits among the four quantum bits １ , ω ２ , ω ３ , ω ４ The four-body interaction condition for oh １ +oh l =ω m +oh 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. ) for the four-body interaction by the four qubits, （４） teeth, The nonlinear parameter K of the first qubit of the four qubits １ and the nonlinear parameter K of the lth qubit ｌ and the nonlinear parameter K of the nth qubit ｎ and the nonlinear parameter K of the mth qubit ｍ and the resonant angular frequency ω of the first quantum bit １ and the resonant angular frequency ω of the first quantum bit ｌ The difference δ １１ =ω １ -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 3. The quantum circuit device according to claim 2, wherein the value is determined in accordance with the set values ​​of the above.

9. 5. The quantum circuit device according to claim 4, wherein the number of Josephson junctions and / or the number of SQUIDs connected in series included in at least one of the quantum bits is different from that of the other quantum bits.

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: The coupler is configured with linear elements; 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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