Superconducting quantum circuits

Abstract

This superconducting quantum circuit is provided with a coupler (21) that couples a first through fourth quantum bits (20A to 20D) by a four-body interaction, the coupler comprising first and second electrodes (16, 18) and a Josephson junction (10) cross-linking the first and second electrodes. The first through fourth quantum bits comprise a resonator including a loop circuit (210A to 210D) and a capacitor (206A to 206D) connected in parallel to the loop circuit. In the loop circuit (210A to 210D), a first superconducting line (203A to 203D), a first Josephson junction (201A to 201D), a second superconducting line (204A to 204D), and a second Josephson junction (202A to 202D) are connected in a ring. The first and second quantum bits are capacitively coupled to the first electrode, and the third and fourth quantum bits are capacitively coupled to the second electrode. The capacitance C of the capacitive coupling between the first through fourth quantum bits and the coupler, the capacitance CJ of the capacitor connected in parallel to the first through fourth quantum bits, and the capacitance Cg between the first and second electrodes of the coupler are set to CJ>Cg>C.

Description

[Technical Field]

[0001] The present invention relates to superconducting quantum circuits. [Background technology]

[0002] Quantum annealing is a method for solving combinatorial optimization problems, and one of the quantum annealing methods is called the LHZ (Lechner, Hauke, Zoller) method (see, for example, Patent Document 1). In order to physically implement LHZ quantum annealing, it is necessary to realize the basic element of quantum bits and their network, in particular a network in which four quantum bits interact simultaneously (four-body interaction).

[0003] As one implementation format, a method has been proposed in which a Josephson Parametric Oscillator (JPO) is used as a quantum bit (see, for example, Non-Patent Document 1, Patent Document 3, etc.).

[0004] (a) One of the methods is shown in Figure 1A, which can realize four-body interactions with a simple structure. Figure 1A is based on Figure 4a in Non-Patent Document 1. is the resonant angular frequency ω r,i The figure shows a system in which JPO1 to JPO4 (i=1, 2, 3, 4) interact through a single Josephson junction (JJ) (JPO1 to JPO4 with different resonant angular frequencies are shown in different patterns according to Figure 4 in Non-Patent Document 1).

[0005] The SQUID (superconducting quantum interference device) loops at each JPO are: It is driven by a flux pump with adjustable amplitude and frequency. The angular frequency of the pump signal ω p,k (t) (k=1,2,3,4) is twice the angular frequency of the resonator: 2ω r,i It is said to be close. Joseph In a Josephson Parametric Amplifier (JPA), the pump There is a threshold value for the strength of , and when it exceeds this threshold, oscillation occurs, and even in the absence of an input signal, the resonant angular frequency ω r,i This is called parametric oscillation. In this specification, the object is a resonator that generates parametric oscillation, so in Figure 1A, the JPA in Figure 4 of Non-Patent Document 1 is expressed as JPO.

[0006] The local four-body coupling is realized by the nonlinear inductance of the central Josephson junction JJ.

[0007] The angular frequency of the pump signal of JPO1 to JPO4 is ω p,1 (t)+ω p,2 (t)=ω p,3 (t)+ω p,4 (t) (1.1) and detune the resonator. If they are detuned from each other, the central Josephson junction (JJ) is -C(a1 + a2 + a3a4+a4 + a3 + a2a1) (1.2) This four-body interaction is always active, and its strength G depends on the nonlinearity of the Josephson junction (JJ) and the detuning of the resonator consisting of the JPO and the Josephson junction. In addition, a i (i=1~4) is the annihilation operator of the resonance modes (bosons) of JPO1~4, a i + (i= 1~4) are generation operators.

[0008] G=E j (φ c 4 / φ04 ){(g1g2g3g4) / (Δ1Δ2Δ3Δ4)} (1.3)

[0009] In equation (1.3), Δ k (k=1,2,3,4) is the mode angular frequency ω of the kth JPO r,k and the mode angular frequency (resonance angle) determined by the capacitance and inductance of the central Josephson junction JJ. frequency)ω c This is the difference (detuning) between Δ k =ω c -ω r,k (k=1,2,3,4) (1.4) φ0=(h / 2π)(2e) is the magnetic flux quantum (e is the elementary charge), φ c is the standard deviation of the zero-point flux fluctuation of the JJ mode It's the difference. E J is the Josephson energy at the center, which is proportional to the critical current Ic of the Josephson junction. g k (k=1,2,3,4) is the mode of the kth JPO and the Josephson junction in the central coupler. Represents the size of the bond. g k =φ0 2 e 2 / 2Cφ c φ k (1.5) φ k (k=1,2,3,4) is the zero-point flux fluctuation of the JPO mode, C is the capacitance of the coupling capacitor between the coupler and the qubit. In Non-Patent Document 1, C is used as the four-body coupling strength in Equations (1.2) and (1.3), but to distinguish it from the coupling capacitor C, G It states that:

[0010] In Non-Patent Document 1, it is not clear how to strengthen the four-body interaction with respect to the configuration of FIG. 1A.

[0011] (b) The other method uses a Josephson Ring Modulator (JRM), as shown in Figure 1B. Figure 1B is based on Supplementary Figure 8 of Non-Patent Document 1. Note that in Figure 1B, JPA in Supplementary Figure 8 of Supplementary Note 8 of Non-Patent Document 1 is replaced with JPO. Microwave drive signal (capacitor C x and C y The four-body coupling between the JPOs is activated by the unbalanced shunt-type JRM. The adjustable four-body interaction is realized by using an unbalanced shunt-type JRM. The JRM consists of two sets of two Josephson junctions (JJs) connected in series in parallel between the first node, which is the junction of JPO1 and JPO2, and the second node, which is the junction of JPO3 and JPO4. The first and second nodes are connected by a capacitor C x A microwave drive signal is applied via the junctions, and a capacitor C is connected to each of the two parallel-connected Josephson junctions (JJs). y via capacitor C x A microwave drive signal is applied to the inverter in opposite phase to the microwave drive signal applied to the inverter.

[0012] In this case, to realize the four-body interaction, the oscillation angular frequency satisfied by JPO1 to JPO4 and the angular frequency ω of the drive signal input from the capacitors Cx and Cy are d For example, the combination of ω d =ω p,1 +ω p,2 +ω p,3 -ω p,4 (1.6) If , the drive signal 2Φ Z (√n)cos (ωd t) (1.7) For this, the following Hamiltonian is derived:

[0013] H plaquette ≒Σ<k=1,4> [H JPO,k -{(g x k ) 2 / Δ x k}a k + a k ]-C jrm (a1 + a2 + a3 + A4+A4 + a3a2a1) (1.8)

[0014] however, C jrm =E J (√n){φx 4 φz / (4φ0 5 )}(g1g2g3g4) / (Δ1Δ2Δ3Δ4) (1.9)

[0015] The second term on the right hand side of equation (1.8) is the four-body interaction term. √n is proportional to the microwave drive strength.

[0016] As a related art configuration similar to that shown in Fig. 1A, for example, Patent Document 2 discloses a circuit using lumped-element JPOs, as shown in Fig. 2. The circuit includes four JPOs, JPO1 (120A) through JPO4 (120D), and a coupler 121. Coupler connection sections 124A through 124D of JPO1 (120A) through JPO4 (120D) are capacitively coupled to the coupler 121, which is made up of Josephson junctions (JJ), via capacitors (coupling capacitors) 131A through 131D, respectively. Readout circuit connection sections 122A through 122D of JPO1 (120A) through JPO4 (120D) are capacitively coupled to readout circuits 140A through 140D via capacitors 132A through 132D, respectively. JPO1 (120A) to JPO4 (120D) are connected via control lines 123A-123D to signal generators 150A-150D, which generate pump signals for generating magnetic fluxes that pass through the SQUID loops of JPO1 (120A) to JPO4 (120D). The nonlinear element 110 of the coupler 121 is an element that can be regarded as an LC resonator with a Josephson junction (JJ) as a nonlinear inductance, and the nonlinear element 110 may be a SQUID including two Josephson junctions (JJ). [Prior art documents] [Patent documents]

[0017] [Patent Document 1] International Publication No. 2017 / 001404 [Patent Document 2] International Publication No. 2021 / 014885 [Patent Document 3] U.S. Patent No. 10,262,276 [Non-patent literature]

[0018] [Non-Patent Document 1] Puri, et. al., "Quantum annealing with all-to-all connected nonlinear oscillators", Nature Communications 8, 15785 (2017) [Non-patent document 2] "Introduction to Quantum Electromagnetic Circuits", International Journal of Circuit Theory and Applications 45, 897 (2016) [Non-patent document 3] Z. Wang et al., "Quantum Dynamics of a Few-Photon Parametric Oscillator", Physical Review X 9, 021049 (2019) Summary of the Invention [Problem to be solved by the invention]

[0019] Non-Patent Document 1 and Patent Document 2, which are shown in Figures 1A and 2, do not mention any method for strengthening the four-body interaction. In addition, the configuration in Figure 1B can adjust the strength of the four-body interaction, but requires a separate external input (microwave drive signals input in opposite phase to capacitors Cx and Cy).

[0020] The present disclosure has been devised in view of the above-mentioned problems, and aims to provide a superconducting quantum circuit configured to enable the four-body interaction to be strengthened by the circuit configuration itself, without requiring any additional external input. [Means for solving the problem]

[0021] According to one aspect of the present disclosure, there is provided a quantum computer comprising first to fourth quantum bits and a coupler that couples the first to fourth quantum bits through four-body interaction, the coupler including first and second electrodes that are arranged opposite to each other, and a nonlinear element that includes a Josephson junction and bridges the first and second electrodes, each of the first to fourth quantum bits comprising a resonator including a loop circuit in which a first superconducting line, a first Josephson junction, a second superconducting line, and a second Josephson junction are connected in a circular manner, and a capacitor connected in parallel to the loop circuit, the first and second quantum bits are capacitively coupled to the first electrode of the coupler, and the third and fourth quantum bits are capacitively coupled to the second electrode of the coupler, and a capacitance value C of the capacitive coupling between the first to fourth quantum bits and the coupler, a capacitance value C of the capacitor connected in parallel to the loop circuit of the first to fourth quantum bits, J , the value of the capacitance between the first and second electrodes of the coupler, C g The magnitude relationship between these is C J >C g It is set to C. [Effects of the Invention]

[0022] According to the present disclosure, a superconducting quantum circuit is provided that has a configuration that makes it possible to strengthen the four-body interaction using the circuit configuration itself, without requiring any additional external input. [Brief explanation of the drawings]

[0023] [Figure 1A] FIG. 1 is a diagram illustrating a related art. [Figure 1B] FIG. 1 is a diagram illustrating a related art. [Figure 2] FIG. 1 is a diagram illustrating a related art. [Figure 3] FIG. 1 is a diagram illustrating an embodiment. [Figure 4] FIG. 1 is a diagram illustrating an embodiment. [Figure 5] FIG. 1 is a diagram illustrating an embodiment. [Figure 6] FIG. 1 is a diagram illustrating an embodiment. [Figure 7] FIG. 1 is a diagram illustrating an example. [Figure 8] FIG. 10 is a diagram schematically illustrating a modified example. [Figure 9] FIG. 10 is a diagram schematically illustrating a modified example. [Figure 10] FIG. 1 is a diagram illustrating an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0024] An embodiment of the present disclosure will now be described. FIG. 3 is a diagram illustrating the circuit configuration of the embodiment. The readout circuits connected to each JPO shown in FIG. 2 are omitted from FIG. 3. In this embodiment, the resonant frequencies of each JPO and the coupler are made closer to each other to strengthen the four-body interaction, provided that the resonant frequencies are made closer to each other within a range that satisfies the conditions described below. Furthermore, conditions are imposed on the capacitance to prevent the strengthening of unnecessary interactions other than the four-body interaction.

[0025] The embodiment provides circuit parameter dependency of four-body interaction and conditions for parameter setting to enhance the four-body interaction.

[0026] 3, the system includes four JPO1 (20A) to JPO4 (20D) and a coupler 21, and JPO1 (20A) to JPO4 (20D) are capacitively coupled to the coupler 21 via coupling capacitors 31A to 31D, respectively. In the following embodiments, each JPO is of a lumped constant type, but it goes without saying that it may also be of a distributed constant type.

[0027] The coupler 21 has a nonlinear element 10 including a Josephson junction (JJ), and a capacitor 15 is connected in parallel to the nonlinear element 10 .

[0028] JPO1 (20A) to JPO4 (20D) include SQUIDs (SQUID loops) 210A to 210D in which first superconducting portions 203A to 203D, first Josephson junctions 201A to 201D, second superconducting portions 204A to 204D, and second Josephson junctions 202A to 202D are connected in a circular configuration, magnetic field generating portions 207A to 207D that generate magnetic fluxes that penetrate the SQUID loops 210A to 210D by supplying pump signals supplied to control lines 23A to 23D from a signal generating portion (not shown), and the first superconducting portions 203A to 203D. The first superconducting portions 203A to 203D and the second superconducting portions 204A to 204D are provided with capacitors 206A to 206D connected between them, and the second superconducting portions 204A to 204D are connected to ground, the first superconducting portions 203A and 203B of JPO1 (20A) and JPO2 (20B) are connected to one end of the coupler 21 via coupling capacitors 31A and 31B, and the first superconducting portions 203C and 203D of JPO3 (20C) and JPO4 (20D) are connected to the other end of the coupler 21 via coupling capacitors 31C and 31D, respectively.

[0029] The capacitance of capacitors 206A to 206D of JPO1 (20A) to JPO4 (20D) is C J , the capacitance of the coupler capacitor 15 is C g The capacitance of the coupling capacitors 31A to 31D is C.

[0030] FIG. 4 is a schematic diagram illustrating an example of the configuration (wiring pattern) of a coupler 21, as an example of FIG. 3, in which JPO1-JPO4 are configured as lumped constants. The coupler 21 includes first and second electrodes 16 and 18 (made of superconducting materials) bridged by a nonlinear element 10. The first electrode 16 includes first and second opposing portions 17A and 17B (made of superconducting materials) extending toward JPO1 (20A) and JPO2 (20B), respectively. The second electrode 18 includes third and fourth opposing portions 19A and 19B (made of superconducting materials) extending toward JPO3 (20C) and JPO4 (20D), respectively. In the coupler 21 of FIG. 4, a capacitor 15 shunt-connected (in parallel) to the Josephson junction (JJ) corresponds to the capacitance between the opposing first and second electrodes 16 and 18. In FIG. 4, the ground pattern (ground surface) surrounding the first and second electrodes 16 and 18 is omitted.

[0031] JPO1 (20A) to JPO4 (20D) are configured as waveguide resonators terminated to ground by SQUIDs 210A to 210D, respectively, and the waveguide resonators generate parametric oscillation by modulating the magnetic flux passing through the SQUID loops 210A to 210D at a frequency approximately twice the resonant frequency using pump signals (microwaves) from control lines 23A to 23D.

[0032] In JPO1 (20A) and JPO2 (20B), the ends (corresponding to coupler connecting portions 24A and 24B in FIG. 3) of conductive portions (waveguides made of superconducting material) 205A and 205B connected to first superconducting portions 203A and 203B of SQUIDs 210A and 210B are capacitively coupled to the ends of first and second opposing portions 17A and 17B of first electrode 16 of coupler 21. Capacitance value C of coupling capacitors 31A and 31B is the capacitance between the ends of conductive portions (waveguides) 205A and 205B and the ends of first and second opposing portions 17A and 17B of first electrode 16 of coupler 21. In JPO3 (20C) and JPO4 (20D), the ends (corresponding to coupler connecting portions 24C and 24D in FIG. 3) of conductive portions (waveguides) 205C and 205D connected to first superconducting portions 203C and 203D of SQUIDs 210C and 210D are capacitively coupled to the ends of third and fourth opposing portions 19A and 19B of second electrode 18 of coupler 21. Capacitance value C of coupling capacitors 31C and 31D is the capacitance between the ends of conductive portions (waveguides) 205C and 205D and the ends of third and fourth opposing portions 19A and 19B of second electrode 18 of coupler 21. The capacitors 206A to 206D of JPO1 (20A) to JPO4 (20D) correspond to the capacitance between the first superconducting portions 203A to 203D of the SQUIDs 210A to 210D and the ground. In FIG. 4, the ground patterns (ground planes) on both sides of the conductive portions (coplanar waveguides) 205A to 205D of JPO1 (20A) to JPO4 (20D) are omitted. .

[0033] According to an embodiment, C J >C g >C (2.1) Let's say.

[0034] Furthermore, by bringing the resonant angular frequency ω of each of the JPOs JPO1 (20A) to JPO4 (20D) and the resonant angular frequency of the coupler 21 closer together, the strength of the four-body interaction (magnitude of the coupling constant) can be set large.

[0035] The four-body interaction strength (coupling constant) g of JPO1(20A)~JPO4(20D) (4)of The derivation is outlined below (details will be given later).

[0036] Following the standard method in this field (e.g., Non-Patent Document 2), we set the magnetic flux degrees of freedom in the circuit. One magnetic flux degree of freedom is set for each JPO and two for the coupler. Using this, we write down the Hamiltonian of the classical circuit. We then quantize the Hamiltonian using the standard method (Non-Patent Document 2). The quantized Hamiltonian H total is expressed as the following equation (2.1): In this specification, as in Patent Document 2, the notation of ^H with a hat is not used as the quantized Hamiltonian.

[0037] TIFF0007786560000001.tif49170 (2.2)

[0038] In equation (2.2), H JPO,i Each JPO i Hamiltonian for (i=1,…,4), H coupler represents the Hamiltonian of the coupler 21.

[0039] a i , a i + represent the boson creation and annihilation operators corresponding to JPOi (i=1,…,4), respectively (in this specification, no hat is attached to the creation and annihilation operators).

[0040] The coupler 21 has two flux degrees of freedom, so there are two modes of bosons in the coupler 21. They are the boson creation and annihilation operators a g+ , a g+ + , a g- , a g- + are expressed by

[0041] H total includes the interaction of each JPO with the coupler 21.

[0042] g + and g - are the strengths of interaction between each JPO and the two degrees of freedom of the coupler 21. These can be expressed by circuit parameters.

[0043] s i teeth, s1=s2=1, s3=s4=-1 (2.3) is.

[0044] Since each JPO interacts with the coupler 21, it is thought that the JPOs also indirectly interact with each other through their interactions with the coupler 21. If we transform the variables so that the influence of the coupler 21 is incorporated into each JPO, the interaction between each JPO and the coupler 21 is transformed into a four-body interaction between the JPOs.

[0045] In other words, we can transform it into a Hamiltonian in which the JPOs directly interact with each other. This variable transformation is expressed as a unitary transformation using the unitary matrix U in the following equation (2.4).

[0046] TIFF0007786560000002.tif18145 (2.4)

[0047] where ω, ω + , ω - is a i , a g+ , a g- where the difference in angular frequency between different JPOs is not taken into consideration.

[0048] Also TIFF0007786560000003.tif9150 (2.5) and, TIFF0007786560000004.tif9150 (2.6) is assumed to be less than 1. In particular, the absolute value of equation (2.6) is the same as g', which will be discussed later.

[0049] After performing the unitary transformation, the bosons of each JPO are represented in a rotating coordinate system. The frequency of rotation of the coordinate system is different for each JPO. i (i=1,…,4) is JPO i applied to the SQUID loop The frequency of the pump signal is expressed by a coordinate system that rotates at half the frequency of the pump signal applied to the magnetic field generating units 207A to 207D to generate the magnetic flux. i (i=1,..,4).

[0050] The transition to a rotating coordinate system introduces time-oscillating terms into the Hamiltonian. These oscillatory terms average out over the time scales of interest, and their positive and negative values ​​cancel out, making them negligible (rotating wave approximation). Due to the frequency difference of the pump signals, many of the terms representing the interactions between the JPOs and between the JPO and the coupler 21 oscillate, and these terms can be ignored.

[0051] However, there are also non-oscillatory interaction terms, which remain. Note that the transition to a rotating frame and the rotating wave approximation are standard methods for focusing on the behavior of JPOs on characteristic time scales.

[0052] By focusing on the various transformations and characteristic time scales mentioned above, we can estimate the strength of the interaction between JPOs that occurs through the coupler.

[0053] Hamiltonian H' obtained through the above process total can be expressed as the following equation (2.7).

[0054] TIFF0007786560000005.tif45153 (2.7)

[0055] In equation (2.7), H' JPO,i and H'coupler are H JPO,i and H coupler is the converted form.

[0056] In equation (2.7), g (4) is the strength of the four-body interaction (coupling constant), and is expressed by the following equation (2.8) using the circuit parameters.

[0057] TIFF0007786560000006.tif17102 (2.8)

[0058] In equation (2.8), ω and ω - are the resonant angular frequencies of the JPO and coupler 21, respectively. C J , C g , C are the capacitance values ​​of the capacitors (206A to 206D) of each JPO, the capacitor (15) of the coupler 21, and the coupling capacitors (31A to 31D) between each JPO and the coupler 21, respectively, as described above. e is the elementary charge (approximately 1.6 × 10 (-19) Coulomb).

[0059] According to this embodiment, the four-body interaction strength (coupling constant) expressed by equation (2.8) can be calculated, for example, by the following method: (4) can be made larger.

[0060] <Condition 1>: The resonant angular frequency ω of each JPO and the resonant angular frequency ω of the coupler 21 - Bring it closer.

[0061] However, g in equation (2.8) (4) The interaction between each JPO and the coupler 21 is as follows: It is derived assuming that the parameter g' given in equation (2.9) is sufficiently smaller than 1 (g' is a dimensionless quantity).

[0062] TIFF0007786560000007.tif18108 (2.9)

[0063] In an embodiment, the value of g' is kept small while the four-body coupling constant g (4) of Make it bigger.

[0064] <Condition 2>: The resonant angular frequency ω of each JPO and the resonant angular frequency ω of the coupler 21 - Don't get too close.

[0065] More specifically, TIFF0007786560000008.tif1249 (2.10) Then, δ is set to satisfy the following condition:

[0066] TIFF0007786560000009.tif1355 (2.11)

[0067] At this time, g'<1 (2.12) This becomes:

[0068] <Condition 3>: Capacitance C of coupler 21 g The capacitance C of each JPO J The coupling constant g (4) is expressed by the following equation (2.13).

[0069] TIFF0007786560000010.tif1686 (2.13)

[0070] While keeping g' small, the coupling constant g (4) To increase the capacitance Cg of the capacitor 15 of the coupler 21 and the capacitance C of the coupling capacitors 31A to 31D must be reduced.

[0071] One of the circuit parameters that characterizes each JPO is the capacitor C J Therefore, the capacitance Cg of the capacitor 15 of the coupler 21 is J However, note that Cg is also included in g' in equation (2.9).

[0072] Coupling constant g of four-body interactions (4) To increase the capacitance Cg, it is necessary to reduce the capacitance Cg of the coupling capacitors 31A to 31D as well. However, since this overlaps with condition 4 described later, only the capacitance Cg of the capacitor 15 of the coupler 21 will be considered below.

[0073] In addition, we have realized a network of four-body interactions, which is assumed in LHZ quantum annealing. To achieve this, it is necessary to weaken the two-body interaction in which only two of the four JPOs interact.

[0074] The strength of the two-body interactions between JPO1 and JPO2, and between JPO3 and JPO4 in Figures 3 and 4 are both expressed by the following equation (2.14):

[0075] TIFF0007786560000011.tif14112 (2.14)

[0076] The strength of the two-body interactions between JPO1 and JPO3, JPO1 and JPO4, JPO2 and JPO3, and JPO2 and JPO4 are all expressed by the following equation (2.15).

[0077] TIFF0007786560000012.tif16130 (2.15)

[0078] In the embodiment, the following conditions are satisfied to weaken these two-body interactions.

[0079] <Condition 4>: The capacitance C of the coupling capacitors 31A to 31D between each JPO and the coupler 21 is set to the capacitance C of each JPO. J Make it smaller than .

[0080] Qualitatively, the four-body interaction can be strengthened by satisfying conditions 1 to 4. The following settings satisfy the above four conditions 1 to 4.

[0081] JPO frequency ω / (2π): 10GHz (gigahertz) Frequency ω of coupler 21 - / (2π):9.98GHz Capacitance C of each JPO J :1000fF(femtofarad) Capacitance C of coupler 21 g :200fF Coupling capacitance C between each JPO and coupler 21: 1 fF

[0082] The Josephson junction is adjusted to achieve the above frequency.

[0083] In this setting, Four-body interaction strength: g (4) / (2π) is TIFF0007786560000013.tif844 (Dirac constant TIFF0007786560000014.tif1884 h is Planck's constant)

[0084] The parameter g' in equation (2.9) (which is assumed to be sufficiently smaller than 1) is approximately The result is 0.28.

[0085] Four-body interaction strength (coupling constant) g (4) / (2π): TIFF0007786560000015.tif767 is the strength of the four-body interaction calculated in the setting of Non-Patent Document 1: TIFF0007786560000016.tif938 That is, in the above equation (1.3), E j / (2π)=600GHz,φ c =0.12φ0 , g k / Δ k When the .lambda. .gtoreq.0.12, C / (2.pi.)=63 kHz (see the explanation of equation (23) in Supplementary Note 6 of Non-Patent Document 1).

[0086] FIG. 5 shows the capacitance C of the coupler 21. g The coupling constant g when only (4) and g 5 shows the change in g'. (4) / (2π) and g' / (2π) are shown in Figure 5. In this case, the frequency ω of the coupler 21 - / (2π) is fixed at the above setting (9.98GHz).

[0087] The capacitance C of the coupler 21 g By reducing the value of g, the strength of the four-body interaction (coupling constant) (4) The strengthening of the four-body interaction can be interpreted as follows.

[0088] In the superconducting quantum circuit of the above embodiment, the four-body interaction of the JPO is as follows: · Interaction between JPO and coupler 21, · Nonlinearity when quantizing the combiner 21, This is achieved through two elements:

[0089] Capacitor C of coupler 21 g Reducing increases the nonlinearity and, consequently, the four-body interaction.

[0090] To keep g' in equation (2.9) small, the interaction between the JPO and the coupler 21 is not strong, but instead the capacitor C g By reducing , the four-body interaction is strengthened.

[0091] As described above, in the embodiment, the circuit parameters are adjusted in consideration of the above conditions, and the coupling constant g (4) By substituting this into equation (2.8), it is possible to realize a circuit in which the four-body interaction is strong and the other interactions, i.e., the two-body interaction in which two of the four JPOs interact with each other, are weak.

[0092] <Configuration example 1> FIG. 6 is a diagram showing a non-limiting example of the above-described embodiment, and is a diagram showing a schematic diagram of a non-limiting example of a wiring pattern (planar circuit) of a superconducting quantum circuit fabricated on a substrate such as silicon.

[0093] FIG. 6 shows a planar configuration of a coupler 21 in which four quantum bits are configured by four lumped constant type JPO1 (20A) to JPO4 (20D), and these four quantum bits are coupled by four-body interaction.

[0094] Lumped-element type JPO1 (20A) to JPO4 (20D) are linear (not nonlinear) impedance converters. It consists of a resonator made up of nonlinear elements including inductance and capacitance components and Josephson junctions.

[0095] In the embodiment, the coupler 21 and JPO1 to JPO4 are realized by, for example, lines (wiring) formed on a substrate using a superconductor. Silicon (Si) is used for the substrate, but other electronic materials such as sapphire or compound semiconductor materials (Group IV, Group III-V, Group II-VI) may also be used. While a single crystal substrate is preferable, polycrystalline or amorphous substrates may also be used. The material for the lines (wiring material) may be, for example, niobium (Nb) or aluminum (Al). However, the material 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), molybdenum (Mo), tantalum (Ta), tantalum nitride, or an alloy containing at least one of these metals. In addition, to achieve a superconducting state, the coupler circuit is used in a temperature environment of about 10 mK (millikelvin) achieved by a refrigerator.

[0096] Referring to FIG. 6, the planar shape of the first electrode 16 is a substantially trapezoidal shape rotated approximately 45 degrees counterclockwise. The first and second opposing portions 17A and 17B of the first electrode 16 extend from near the intersection of the trapezoid's upper base and hypotenuse (leg) toward the left and upward, respectively, toward the locations where the JPOs 20A and 20B are to be disposed. The planar shape of the second electrode 18 is an inverted trapezoid rotated approximately 135 degrees clockwise. The third and fourth opposing portions 19A and 19B of the second electrode 18 extend from near the intersection of the trapezoid's upper base and hypotenuse (leg) toward the right and downward, respectively, toward the locations where the JPOs 20C and 20D are to be disposed. The first electrode 16 and the second electrode 18 are disposed so that the bases of their respective trapezoids face each other, and the planar shape of the electrodes together with the main body excluding the facing portions is a shape that is approximately hexagonal.

[0097] The first electrode 16 has a protrusion 16C protruding downward in the figure near the intersection of one end of the lower base and the oblique side, and the second electrode 18 has a cut portion 18C cut off parallel to the protrusion 16C of electrode 16 near the intersection of one end of the lower base and the oblique side, and a nonlinear element 10 such as a SQUID is provided in the gap between the protrusion 16C near the intersection of one end of the lower base of the first electrode 16 and the oblique side and the cut portion 18C near the intersection of one end of the lower base of the first electrode 16 and the oblique side. The configuration in Figure 6 aims to make the arrangement area compact by using an obliquely arranged electrode configuration.

[0098] JPO1 (20A) to JPO4 (20D) are composed of coplanar waveguides 25A, 25B, 25C, and 25D and SQUIDs 26A, 26B, 26C, and 26D, respectively, and are microwave LC resonant circuits consisting of the linear inductance and capacitance components of the coplanar waveguides 25A, 25B, 25C, and 25D and the nonlinear inductance and capacitance components of the SQUIDs 26A, 26B, 26C, and 26D. The resonant frequency can be adjusted by applying a DC (direct current) current to control lines 23A, 23B, 23C, and 23D inductively coupled to SQUIDs 26A, 26B, 26C, and 26D. Furthermore, by passing an AC (alternating current) current through the control lines 23A, 23B, 23C, and 23D of JPO1 (20A) to JPO4 (20D), parametric oscillation can be induced.

[0099] JPO1 (20A) to JPO4 (20D) are capacitively coupled to connection sections (I / O waveguides) 22A to 22D with the readout circuit via capacitors 32A to 32D. Fig. 6 shows a portion of each of the connection sections (I / O coplanar waveguides) 22A, 22B, 22C, and 22D with the readout circuit. The wiring patterns of the connection sections (I / O coplanar waveguides) 22A to 22D may be extended to, for example, the periphery of the chip and connected to, for example, a wiring board (not shown) via bump electrodes. Furthermore, they may be connected to a measuring device or the like outside the refrigerator via readout wiring or the like. Note that the capacitor 15 in Fig. 4 is omitted in Fig. 6.

[0100] 6, for the control lines 23A, 23B, 23C, and 23D configured as coplanar waveguides, air bridge wirings 27A, 27B, 27C, and 27D are provided overhead on the wiring layer to stabilize the potential (uniformize the charge distribution) of the ground plane (ground pattern) 40 surrounding the JP0s 20A, 20B, 20C, and 20D. The control lines 23A, 23B, 23C, and 23D may also be connected to a wiring board (not shown) via bump electrodes (not shown) in the chip periphery, for example, and connected to a signal generating device (current control unit) outside the refrigerator.

[0101] In FIG. 6, a cross section of line AA perpendicular to the control line 23D is shown in a balloon. The cross sections of the control lines 23A to 23D have the same configuration. For example, a wiring layer is formed on the surface of a substrate 42 made of silicon, and the above-mentioned JPOs 20 (20A to 20D) and the central coupler (21) are formed on this wiring layer. The control line 23D is made of a coplanar waveguide in the same wiring layer as this wiring layer. As shown in FIG. 6, ground patterns 40-1 and 40-2 are arranged on both sides of the control line 23D (wiring) in the longitudinal direction, with a gap therebetween, and an arch-shaped air bridge wiring 27D made of a superconducting material (e.g., Al) is provided so as to straddle the control line 23D from above. The air bridge wiring structure for the ground pattern 40 eliminates the division of the ground pattern into two sides 40-1 and 40-2 by the control lines 23 (23A to 23D) made of coplanar waveguides, and stabilizes the potential of the ground plane (ground pattern) 40 surrounding the JPOs 20A, 20B, 20C, and 20D. In FIG. 6, as a non-limiting example, the connection sections (I / O coplanar waveguides) 22A to 22D with the readout circuit are configured to have air bridge wirings 28A, 28B, 28C, and 28D wired overhead on the wiring layer, respectively, similar to the control lines 23A to 23D. The air bridge wirings 28A to 28D of the connection sections (I / O coplanar waveguides) 22A to 22D also have the same cross-sectional configuration.

[0102] The capacitance C of the capacitors (206A to 206D in FIG. 3) between the waveguides 25A to 25D and the ground in JPO1 (20A) to JPO4 (20D) J Regarding the capacitance Cg of the capacitor 15 (the capacitor between the first and second electrodes 16 and 18) shunt-connected to the nonlinear element 10 of the coupler 21, the capacitance C of the coupling capacitor (31A, 31B in FIG. 3) between the coupler connection parts 24A, 24B of the waveguides 25A, 25B of the JPO1 (20A) and JPO2 (20B) and the first and second opposing parts 17A, 17B of the first electrode 16 of the coupler 21, and the capacitance C of the capacitor (31C, 31D in FIG. 3) between the coupler connection parts 24C, 24D of the waveguides 25C, 25D of the JPO3 (20C) and JPO4 (20D) and the third and fourth opposing parts 19A, 19B of the second electrode 18 of the coupler 21, C J >C g >C Moreover, by bringing the resonant angular frequency ω of each of the JPO1 (20A) to JPO4 (20D) and the resonant angular frequency of the coupler 21 closer to each other, the strength of the four-body interaction can be set to be large.

[0103] The lengths (widths) of the opposing sides of the first and second electrodes 16 and 18 of the coupler 21 are longer than the widths of the coupler connection portions 24A to 24D of the waveguides 25A to 25D of the JPO1 (20A) to JPO4 (20D) that face the respective ends of the first and second facing portions 17A and 17B and the third and fourth facing portions 19A and 19B of the coupler 21. The gaps (caps) of the sides facing each other are smaller than the gaps between the ends of the coupler connection parts 24A, 24B, coupler connection parts 24C, 24D and the first and second facing parts 17A, 17B and the third and fourth facing parts 19A, 19B facing these parts, respectively. Therefore, from FIG. 6 which shows a schematic example of the wiring pattern, it can be seen that the capacitances C of the coupling capacitors 31A to 31D between the waveguides 25A, 25B of JPO1 (20A) and JPO2 (20B) and the waveguides 25C, 25D of JPO3 (20C) and JPO4 (20D) and the first and second facing parts 17A, 17B and the third and fourth facing parts 19A, 19B are smaller than the capacitance C between the electrodes 16 and 18 of the coupler 21. g It can be seen that the capacitance C of each of the cross-shaped waveguides 25A to 25D (coplanar waveguides) of JPO1 (20A) to JPO4 (20D) is smaller than the capacitance C of the capacitor 15 connected in parallel to the nonlinear element 10. It can be seen that the length of the side facing the ground plane (ground pattern) 40 across the gap in each of the cross-shaped waveguides 25A to 25D (coplanar waveguides) of JPO1 (20A) to JPO4 (20D) is several times longer than the length of the facing sides of the first and second electrodes 16 and 18. For this reason, in FIG. 6, the capacitance C of each of JPO1 (20A) to JPO4 (20D) is J (206A to 206D in FIG. 3) represent the capacitance C between the first and second electrodes 16 and 18 of the coupler 21. g It can be seen that this is larger than (15 in Figure 3).

[0104] Four-body interaction strength g (4) The coupler (four-body interaction coupler) 21 and the JPO (20A~ Therefore, by adjusting the resonant frequencies of the JPOs (20A to 20D) and the coupler 21, it is possible to control the coupling strength of the four-body interaction.

[0105] The first and second electrodes 16, 18 of coupler 21 are coupled by capacitor 15, and are also coupled to JPOs 20A, 20B, 20C, and 20D via coupling capacitors 31A, 31B, 31C, and 31D, respectively, and are entirely surrounded by a ground pattern (ground surface) 40. First and second opposing portions 17A, 17B and third and fourth opposing portions 19A, 19B of coupler 21, which are capacitively coupled to JPOs 20A, 20B, and JPOs 20C, 20D, respectively, protrude from first electrode 16 and second electrode 18 toward ground pattern 40, and can be coupled to coupler connecting portions 24A, 24B and coupler connecting portions 24C, 24D of JPOs 20A, 20B, and JPOs 20C, 20D at locations distant from first electrode 16 and second electrode 18.

[0106] The stray capacitance between the ground pattern 40 and the portions of the first and second electrodes 16, 18 other than the coupling capacitors 31A to 31D is reduced by providing a large gap (similar in size to the coupler 21) where no superconductor is deposited, for example, a total length on the order of 100 μm (micrometers).

[0107] The capacitor 15 between the first and second electrodes 16, 18 strengthens the four-body interaction coupler 21 against disturbances such as charge noise. Also, reducing the stray capacitance of the first and second electrodes 16, 18 has the effect of strengthening the four-body interaction. The coupling strength of the four-body interaction by the coupler 21 capacitively coupled to each JPO is reduced by the self-capacitance (C g 6, the coupler 21 is disposed at a distance, for example, approximately the same as the distance between the coupler 21 and the edge of the ground plane (ground pattern) 40 that surrounds the coupler 21, thereby reducing the stray capacitance of the coupler 21.

[0108] <Configuration example 2> FIG. 7 is a diagram illustrating another non-limiting example of a coupler (four-body interaction coupler) 21. In FIG. 7, quantum bits (JPOs) 20A-20B are omitted, and a planar circuit corresponding to the coupler 21 of FIG. 4 is illustrated. Referring to FIG. 7, in this modified coupler 21, the first electrode 16 has sides bent at right angles (horizontal side 16A, vertical side 16B), and the second electrode 18 also has sides bent at right angles (horizontal side 18A, vertical side 18B). The vertical sides 16B, 18B of the first and second electrodes 16, 18 face each other, and the horizontal sides 16A, 18A also face each other. The first electrode 16 has n extensions 16D (seven in FIG. 7) extending from the vertical side 16B toward the vertical side 18B of the second electrode 18 at predetermined intervals parallel to the horizontal side 16A, forming a comb-tooth pattern. The second electrode 18 also has n extensions 18D extending from the vertical side 18B toward the vertical side 16B of the first electrode 16 in parallel with the horizontal side 18A at predetermined intervals, forming a comb-teeth pattern. The extensions 16D and 18D corresponding to the comb teeth are arranged opposite each other in a nested manner. Here, the capacitance between adjacent extensions 16D and 18D, the capacitance between the horizontal side 16A and the extension 18D facing it, and the capacitance between the horizontal side 18A and the extension 16D facing it are all set to the same value C a The capacitance C1 between the horizontal side 16A and the horizontal side 18A is the capacitance C a ) can be approximated by a configuration of 2n+1 parallel connected transistors, C1= (2n+1)×C a (2.16) This becomes:

[0109] Here, assuming that the comb-tooth-shaped extension portions 16D, 18D arranged opposite to each other in a nested manner are not provided, the distance between the horizontal sides 16A, 18A is (2n+1) times or more larger than the distance between the opposing extension portions 16D, 18D in FIG. 7, the capacitance C2 between the horizontal sides 16A, 18A is as follows: C2< C a / (2n+1) (2.17) holds true.

[0110] Therefore, the capacitance C1 of the first and second electrodes 16, 18 in the structure in which the comb teeth are nested and arranged facing each other is roughly calculated as (2n+1) times the capacitance C2 in the case where this structure is not adopted. 2 It will be more than double.

[0111] By configuring the capacitor between the first and second electrodes 16, 18 in a comb shape, the capacitance between the first and second electrodes 16, 18 increases, and the effects of voltage fluctuations due to electric field noise can be more effectively reduced, thereby achieving stable four-body interaction coupling.

[0112] The vertical side 16B of the first electrode 16 is provided with a first opposing portion 17A corresponding to the coupler connection portion 24A of the JPO 20A, and the horizontal side 16A of the first electrode 16 is provided with a second opposing portion 17B corresponding to the coupler connection portion 24B of the JPO 20B. The first and second opposing portions 17A and 17B each consist of a U-shaped portion and a portion connecting this to the first electrode 16. The coupler connection portions 24A and 24B, which are made of coplanar waveguides, are arranged between the U-shaped portions of the first and second opposing portions 17A and 17B.

[0113] Additionally, the vertical side 18B of the second electrode 18 is provided with a third opposing portion 19A corresponding to the coupler connection portion 24C of the JPO 20C, and the horizontal side 18B of the second electrode 18 is provided with a fourth opposing portion 19B corresponding to the coupler connection portion 24D of the JPO 20D. The third and fourth opposing portions 19A and 19B each consist of a U-shaped portion and a portion connecting this to the main body of the electrode 18. Coplanar waveguide type coupler connection portions 24C and 24D are disposed between the U-shaped portions of the third and fourth opposing portions 19A and 19B, respectively.

[0114] A nonlinear element 10 consisting of a SQUID is connected to the gap between the end of the vertical side 16B of the first electrode 16 and the end of the horizontal side 18A of the second electrode 18. The SQUID constituting the nonlinear element 10 bridges the first electrode 16 (end of the vertical side 16B) and the second electrode 18 (end of the horizontal side 18A). In FIG. 7, the first electrode 16 (end of the vertical side 16B) and the second electrode 18 (end of the horizontal side 18A) bridged by the SQUID indicated by reference numeral 10 are shown as a SQUID bridge section, surrounded by a dashed circle and designated by reference numeral 29. A control line 51 is further provided to apply a magnetic flux to this SQUID from within the same plane. A frequency-tunable coupler is provided by varying the current (e.g., DC current) flowing through the control line 51. An external magnetic flux given from the current control section via a control line 51 passes through the SQUID loop of the four-body interaction coupler 21 and varies the effective self-inductance of the SQUID loop, thereby varying the resonant frequency.

[0115] 7, in order to efficiently apply magnetic flux from the control line 51 by inductive coupling, the distance between the ground (ground pattern 40) and only the first electrode 16 and the second electrode 18 near the SQUID bridge portion 29 is reduced, and the control line 51 is formed near the SQUID bridge portion 29, thereby enabling external magnetic flux to be applied from very close to the SQUID bridge portion 29. As described above, since it is generally preferable that the ground pattern 40 be spaced apart from the first and second electrodes 16 and 18, the length of the portion 30 (ground pattern protrusion) where the ground pattern 40 is protruded inward near the SQUID bridge portion 29 is preferably ¼ or less of the perimeter of the inner periphery of the ground pattern 40 surrounding the electrodes 16 and 18. It may be more preferably ⅙ or less, and even more preferably ⅛ or less.

[0116] In the coupler 21 of this configuration, the capacitance C JRegarding the capacitance Cg of the capacitor (15 in FIG. 3) of the coupler 21, and the capacitance C of the coupling capacitors (31A-31D in FIG. 3) between the coupler connection parts 24A-24D of JPO1 (20A) to JPO4 (20D) and the opposing parts 17A, 17B, 19A, and 19B of the coupler 21, C J >C g >C Let's say.

[0117] <Configuration example 3> Fig. 8 is a diagram illustrating yet another non-limiting example of a coupler (four-body mutual coupler) 21. In Fig. 8, the quantum bits (JPOs) 20A-20B are omitted, and a planar circuit corresponding to the coupler 21 of Fig. 4 is illustrated. Referring to Fig. 8, a ground pattern 40 is configured to run through between first and second opposing portions 17A, 17B and third and fourth opposing portions 19A, 19B of the first and second comb-shaped electrodes 16, 18 and coupler connecting portions 24A, 24B, 24C, and 24D of the JPOs 20A, 20B, 20C, and 20D. For example, coupler connection parts 24A, 24B, 24C, and 24D of JPOs 20A, 20B, 20C, and 20D are connected to ground via capacitors 31A-2, 31B-2, 31C-2, and 31D-2, and the first and second opposing parts 17A, 17B and the third and fourth opposing parts 19A, 19B corresponding to coupler connection parts 24A, 24B, 24C, and 24D, respectively, are connected to ground via capacitors 31A-1, 31B-1, 31C-1, and 31D-1, respectively. The coupler connection parts 24A, 24B of the JPOs 20A, 20B are shielded (electrostatically shielded) from the first and second opposing parts 17A, 17B by ground (ground pattern 40), and the coupler connection parts 24C, 24D of the JPOs 20C, 20D are shielded (electrostatically shielded) from the third and fourth opposing parts 19A, 19B by ground (ground pattern 40). Therefore, the capacitances between the coupler connection parts 24A, 24B of the JPOs 20A, 20B and the first and second opposing parts 17A, 17B, and the capacitances between the coupler connection parts 24C, 24D of the JPOs 20C, 20D and the third and fourth opposing parts 19A, 19B function as coupling capacitors 31A to 31D with smaller capacitances than in a configuration where there is no ground pattern between the coupler connection parts and the opposing parts of the JPOs (Figure 7).

[0118] In the coupler 21 of this configuration, the capacitance C J Regarding the capacitance Cg of the capacitor (15 in FIG. 3) of the coupler 21, and the capacitance C of the coupling capacitors (31A to 31D in FIG. 3) between the coupler connection parts 24A to 24D of JPO1 (20A) to JPO4 (20D) and the opposing parts 17A, 17B, 19A, and 19B of the coupler 21, C J >C g >C Let's say.

[0119] <Another embodiment> FIG. 10 is a schematic diagram showing the configuration of a quantum computer 200 integrating JPOs 20 as a configuration example of another embodiment. In the configuration shown in FIG. 10 , each four-body interaction coupler 21 is connected to four JPOs 20, as shown in FIGS. 4 and 6 . Each JPO 20 is connected to one to four four-body interaction couplers 21, and the JPO 20 is shared and arranged among multiple unit structures, thereby arranging the unit structures shown in FIGS. 3 , 4 , 6 , etc. In the quantum computer 200, at least one JPO 20 is connected to multiple four-body interaction couplers 21. In particular, in the example shown in FIG. 10 , at least one JPO 20 is connected to four four-body interaction couplers 21. The quantum computer 200 can also be described as follows. The quantum computer 200 has multiple JPOs 20, and each JPO 20 is connected to one to four four-body interaction couplers 21. The number of four-body interaction couplers 21 connected to each JPO 20 corresponds to the number of unit structures to which the JPO 20 is shared. Thus, in the example shown in FIG. 10 , the quantum computer 200 has multiple unit structures, and the JPO 20 is shared by multiple unit structures. While the example shown in FIG. 10 integrates 13 superconducting nonlinear JPOs 20, any number of JPOs 20 can be integrated in a similar manner. Note that the current control unit and readout unit are omitted in FIG. 10 for ease of understanding. However, as described with reference to FIG. 2 and other figures, the JPOs 20 are controlled and readout using the current control unit and readout unit.

[0120] < On the derivation of the above formula for the four-body interaction > The derivation of the above formula will be explained below. As described in Non-Patent Document 2, Fig. 9 is a diagram corresponding to Fig. 3. In Fig. 9, Josephson junctions are indicated by symbols each consisting of an x ​​surrounded by a square, and Φ1 to Φ4 in the SQUID loops 210A to 210D of JPO1 to JPO4 represent magnetic fluxes passing through each SQUID loop. EJ attached to the two Josephson junctions in the SQUID loops 210A to 210D of JPO1 to JPO4 represents the Josephson energy.

[0121] <1. Classical Hamiltonian > As shown in FIG. 9, magnetic fluxes φ1 to φ4, φg1, and φg2 are placed at the nodes 1 to 4, g1, and g2, respectively.

[0122] In a circuit of an inductor (a Josephson junction can be considered a nonlinear inductor) and a capacitor (a non-dissipative circuit), the time derivative of the magnetic flux φ is V=-dφ / dt (Faraday's law), so the energy of the capacitance branch (voltage V across both ends) is E=(1 / 2)CV. 2 teeth,

[0123] TIFF0007786560000017.tif12108 (3.1)

[0124] The capacitor energy can be treated as kinetic energy. Let φ be a vector (6-dimensional vector) with φ1 to φ4, φg1, and φg2 as elements.

[0125] TIFF0007786560000018.tif5030 (3.2)

[0126] In FIG. 9, the energy (kinetic energy) of the capacitor branch is given by the following equation (3.3).

[0127] TIFF0007786560000019.tif9150 (3.3)

[0128] where C mat is expressed by the capacitance blank in Figure 9 as shown in the following equation (3.4): This is the circuit matrix (a matrix of 6 rows and 6 columns).

[0129] TIFF0007786560000020.tif57170 (3.4)

[0130] matrix C mat Element C in the kth row and kth column (k=1~4) of J +C is the two capacitors C and C connected in parallel to node k (k=1 to 4). J is the combined capacitance of the matrix C mat of the kth row and kth column (k=5,6) element C J +2C is the capacitance of three capacitors C, C, C connected in parallel to node k (k=5,6). J of The composite capacitance is the matrix C mat The i-th row and j-th column (i≠j, i,j=1 to 6) of is the capacitance between nodes i and j (the sign indicates the directionality of the capacitor branch).

[0131] The Lagrangian for the circuit in Figure 9 is given by the following equation (3.5):

[0132] TIFF0007786560000021.tif9150 (3.5)

[0133] In equation (3.5), V(φ) is the potential energy, given by the following equation (3.6): TIFF0007786560000022.tif14150 (3.6)

[0134] however, TIFF0007786560000023.tif10150 (3.7) TIFF0007786560000024.tif9150 (3.8)

[0135] E J are the Josephson energies of JPO1 to JPO4. E Jg is the Josephson energy of the coupler 21. Φ i is JPO i The magnetic flux passing through the SQUID loop (i=1,…,4) is

[0136] φ g1 -φ g2 is the magnetic flux passing through the coupler 21 (the difference between the magnetic fluxes at nodes g1 and g2).

[0137] Lagrangian kinetic energy TIFF0007786560000025.tif9150 (3.9) is represented by the vector q.

[0138] TIFF0007786560000026.tif10150 (3.10)

[0139] q1,q2,q3,q4,q g1 ,q g2 is the charge at each node. t is the transpose operator. matrix C mat Assuming that is normal, from equation (3.10), TIFF0007786560000027.tif6150(3.11)

[0140] Therefore, the kinetic energy in equation (3.9) can be calculated using the vector q as follows: TIFF0007786560000028.tif9150 (3.12) This can be expressed as:

[0141] In equation (3.12), I is a 6x6 identity matrix. The last equation in equation (3.12) is the matrix C mat is a symmetric matrix (component c ij (i,j=1,…,6) is the index i, j Regarding c ij =c ji ) and C mat Inverse matrix C of mat -1 It is also assumed that C is a symmetric matrix. mat C mat -1 =I, and taking the transpose of both sides, (C mat -1 ) t C mat t =I, C mat Since is a symmetric matrix, (C mat -1 ) t C mat =I. matrix C mat -1 Multiplying by (C mat -1 ) t =C mat -1 Therefore, equation (3.12) holds. stand.

[0142] Assuming that the potential energy remains a function (nonlinear function) of the vector φ, the Hamiltonian is given by:

[0143] TIFF0007786560000029.tif9150 (3.13)

[0144] 6-by-6 matrix C mat Inverse matrix C of mat -1 Specifically, the Hamiltonian H is given by the following equation (3.14). TIFF0007786560000030.tif104170 (3.14)

[0145] however, C'=C / C J (3.15)

[0146] C"=C / C g (3.16)

[0147] TIFF0007786560000031.tif9150 (3.17)

[0148] s1=s2=1, s3=s4=-1 (3.18) is.

[0149] In equation (3.14), the bottom line is C'≪1 (3.19) It is assumed that:

[0150] If O(C') is ignored, the product of the degrees of freedom of JPO does not appear. The details of the calculation are as follows: See section A.1 of the appendix.

[0151] <2. Quantization > The variables φ and q of the classical Hamiltonian are transformed into operators as follows: Replace the Hamiltonian by a function of the operator (quantization of the Hamiltonian). TIFF0007786560000032.tif3384(4.1) TIFF0007786560000033.tif14150 (4.2) TIFF0007786560000034.tif14150 (4.3)

[0152] k=1,2,3,4,g1,g2, and a + k and a k is the boson creation and annihilation operator. e is the elementary charge (elementary charge ) In this case, the exchange relationship of the following equation (4.4) holds. TIFF0007786560000035.tif6150 (4.4)

[0153] TIFF0007786560000036.tif1493 (4.5)

[0154] TIFF0007786560000037.tif16105 (4.6)

[0155] In equations (4.5) and (4.6), TIFF0007786560000038.tif11150(4.7) TIFF0007786560000039.tif11150where TIFF0007786560000040.tif11150 (4.8)

[0156] Since Z1 and Z2 are equal, TIFF0007786560000041.tif6150 (4.9)

[0157] TIFF0007786560000042.tif6150 (4.10) Let's say. TIFF0007786560000043.tif6150 (4.11)

[0158] TIFF0007786560000044.tif14150 (4.12)

[0159] TIFF0007786560000045.tif9150 (4.13)

[0160] TIFF0007786560000046.tif14150(4.14)

[0161] In equations (4.11) and (4.13), TIFF0007786560000047.tif10150 (4.15)

[0162] In equations (4.12) and (4.14), TIFF0007786560000048.tif14150 (4.16)

[0163] The following holds as commutators (commutation relations) of operators:

[0164] TIFF0007786560000049.tif6150(4.17) TIFF0007786560000050.tif6150 (4.18)

[0165] Therefore, by quantizing the classical Hamiltonian as above, we obtain the following: The quantized Hamiltonian has H instead of hat Q It is written as follows. TIFF0007786560000051.tif112170 (4.19)

[0166] Ignore O(C') and calculate cos(φi / φ0) were expanded, higher-order terms were ignored.

[0167] next, TIFF0007786560000052.tif6150 (4.20) The quantized Hamiltonian H Q As a result, the following equation (4.21) is derived. TIFF0007786560000053.tif55170 (4.21)

[0168] however, TIFF0007786560000054.tif6150 (4.22)

[0169] TIFF0007786560000055.tif14150

[0170] (4.23) TIFF0007786560000056.tif10150 (4.24)

[0171] TIFF0007786560000057.tif14150 (4.25)

[0172] TIFF0007786560000058.tif14150 (4.26)

[0173] However, the constant term has been omitted from equation (4.21).

[0174] Also, δE J is treated as small, and δE J φ 4 Z was ignored.

[0175] Furthermore, on the right-hand side of equation (4.23), C′(=C / C J ) quantities of that magnitude are ignored.

[0176] Next, for the Hamiltonian in equation (4.21), we use the unitary matrix U g Perform a unitary transformation using

[0177] TIFF0007786560000059.tif22170 (4.27)

[0178] In equation (4.27), TIFF0007786560000060.tif9150 (4.28)

[0179] TIFF0007786560000061.tif9150 (4.29)

[0180] s i is given by equation (3.18).

[0181] This unitary transformation is due to the interaction between JPO1-4 and coupler 21 in HQ ( TIFF0007786560000062.tif6150 etc.) is used as the creation / destruction operator a + i / a i The conversion is to incorporate it into the following:

[0182] In other words, this is a transformation that incorporates the influence of the coupler 21 into JPO1 to JPO4 in a perturbative manner.

[0183] After this unitary transformation, the creation / annihilation operator a + i / a i with frequency ω p,i / 2 rotated coordinate system (<Note 1> :After the above unitary transformation, this a iis the degree of freedom of each JPO incorporating the influence of the coupler 21 perturbatively).

[0184] TIFF0007786560000063.tif7150 (4.30)

[0185] TIFF0007786560000064.tif13150 (4.31) However, the angular frequencies of the pump signals of JPO1 to JPO4 must satisfy the following equation (4.32):

[0186] TIFF0007786560000065.tif6150 (4.32)

[0187] And for the time scale of interest, ω p,k is large enough to ignore the vibrational term A rotating wave approximation is performed.

[0188] At this time, TIFF0007786560000066.tif9150 (4.33) is used.

[0189] Also, O(g' + 2 ) are ignored as small quantities. However, g'_ 4 / C g is another term (e.g. For example, the following Δ i ) and cannot be ignored.

[0190] In this case, the following Hamiltonian H' Q The details of the calculation are given in Section A.2.

[0191] TIFF0007786560000067.tif44170 (4.34)

[0192] In equation (4.34), TIFF0007786560000068.tif9150 (4.35)

[0193] TIFF0007786560000069.tif6150 (4.36)

[0194] TIFF0007786560000070.tif11150 (4.37)

[0195] TIFF0007786560000071.tif6150 (4.38)

[0196] TIFF0007786560000072.tif6150 (4.39)

[0197] TIFF0007786560000073.tif6150 (4.40)

[0198] TIFF0007786560000074.tif10150 (4.41)

[0199] g' + , g' - , g (4) are the circuit parameters and the resonant angular frequencies ω and ω - is expressed as follows:

[0200] TIFF0007786560000075.tif14150 (4.42)

[0201] TIFF0007786560000076.tif16150 (4.43)

[0202] TIFF0007786560000077.tif13150 (4.44)

[0203] The result of Non-Patent Document 1 corresponding to equation (4.44) is that capacitance C → 0 and g (4 ) diverges to infinity, which is physically strange. The strength of the interaction is proportional to g1g2g3g4 (equation (1.3) above), and each gk (k=1 to 4) is expressed as (1 / C) with respect to the coupling capacitor C between the coupler and the quantum bit (equation (1.5) above).When the coupling capacitor C → 0, the strength of the four-body interaction in equation (1.3) above diverges to infinity.

[0204] <3. Conclusion> In the circuit shown in Figure 9, each JPO interacts with another JPO through the coupler 21. To represent this as a direct interaction between JPOs, in this embodiment, the influence of the coupler 21 is perturbatively incorporated into the JPO. The JPO incorporating the influence of the coupler 21 realizes a four-body interaction. The following conditions were imposed in the calculation process:

[0205] (1) C / CJ << 1

[0206] (2) g' given by equations (4.43) and (4.44), respectively + and g'_, |g' + |,|g'_|<<1 (see Note 2 below).

[0207] (3) Angular frequency of the pump signal ω p,k (k=1,2,3,4) are significantly different, and the rotating wave approximation It is established.

[0208] These conditions have the following physical meaning:

[0209] Condition (1) weakens the direct interaction between the JPOs without the intervention of the coupler 21.

[0210] Condition (2) ensures that the influence of the coupler 21 does not become too strong and that the behavior does not deviate from that of the original JPO.

[0211] Condition (3) weakens interactions other than the four-body interaction between JPOs that incorporates the influence of the coupler 21 (two-body interactions between JPOs, and interactions between JPOs and the coupler 21).

[0212] When the above conditions are satisfied, the effective Hamiltonian of the circuit is given by equation (4.34), and the coupling coefficient g of the four-body interaction of the JPO is (4) is given by equation (4.44).

[0213] <Note 2> however, TIFF0007786560000078.tif832 And C / Cg<<1 When

[0214] TIFF0007786560000079.tif31170 (4.45)

[0215] Since |g'_|≪1 (4.46) is a sufficient condition.

[0216] <Addendum> The following provides a supplementary explanation of the above derivation process in detail.

[0217] <A: calculation >

[0218] <A.1 capacitance > C in equation (3.4) mat -1 is the matrix C mat is the inverse matrix of the inverse matrix, and the value of element (i,j) of the inverse matrix is ​​C ij -1 is as follows, where Cmat -1 Since is a symmetric matrix, the upper triangular part of the matrix (including the diagonal elements) C ij -1 Only (j>=i) is shown.

[0219] TIFF0007786560000080.tif27170 (A.1)

[0220] TIFF0007786560000081.tif35170 (A.2)

[0221] TIFF0007786560000082.tif24170 (A.3)

[0222] TIFF0007786560000083.tif30170 (A.4)

[0223] TIFF0007786560000084.tif33170 (A.5)

[0224] TIFF0007786560000085.tif33170 (A.6)

[0225] TIFF0007786560000086.tif42170 (A.7)

[0226] This gives the Hamiltonian (classical Hamiltonian) as follows: TIFF0007786560000087.tif149170 (A.8)

[0227] however, TIFF0007786560000088.tif9150 (A.9)

[0228] s1=s2=1, s3=s4=―1 (A.10)

[0229] C':=C / C J (A.11)

[0230] C":=C / C g (A.12)

[0231] and assume that C'<<1.

[0232] TIFF0007786560000089.tif39170 (A.13)

[0233] TIFF0007786560000090.tif48170 (A.14)

[0234] TIFF0007786560000091.tif51128 (A.15)

[0235] TIFF0007786560000092.tif47170 (A.16)

[0236] TIFF0007786560000093.tif47170 (A.17)

[0237] TIFF0007786560000094.tif35170 (A.18)

[0238] TIFF0007786560000095.tif37170 (A.19)

[0239] and the following equation (A.20) is derived as the Hamiltonian H.

[0240] TIFF0007786560000096.tif75170 (A.20)

[0241] <A.2 unitary transformation > Next, we consider how each operator is transformed by the unitary transformation matrix Ug [equation (4.27)].

[0242] TIFF0007786560000097.tif23170 (A.21)

[0243] However, s i is as shown in equation (3.18).

[0244] TIFF0007786560000098.tif6150 (A.22) Let's say.

[0245] f i (1) can be found. To do this, f i (λ) is expanded by Taylor expansion around λ=0, and λ= Let's say it's 1. TIFF0007786560000099.tif10150 (A.23) and TIFF0007786560000100.tif7150 (A.24) Take advantage of the fact that

[0246] For these calculations, the following relations (A.25) to (A.28) are used. TIFF0007786560000101.tif6150 (A.25)

[0247] TIFF0007786560000102.tif6150 (A.26)

[0248] TIFF0007786560000103.tif13150 (A.27)

[0249] TIFF0007786560000104.tif13150 (A.28)

[0250] From these relations, we obtain the following equations (A.29) to (A.34), where O(g' + 3 ) etc. They are ignoring me. TIFF0007786560000105.tif24170 (A.29)

[0251] TIFF0007786560000106.tif25170 (A.30)

[0252] TIFF0007786560000107.tif26170 (A.31)

[0253] TIFF0007786560000108.tif25170 (A.32)

[0254] TIFF0007786560000109.tif30143 (A.33)

[0255] TIFF0007786560000110.tif25134 (A.34)

[0256] Conversion to a rotating coordinate system U ωp / 2 Also perform [Equation (4.31)].

[0257] Then, by two transformations, for example, a + i a i is transformed as follows:

[0258] TIFF0007786560000111.tif62170 (A.35)

[0259] Here, the vibration term is exp(iω p,i t) such that each frequency ω p,i It is a term that oscillates in and is ignored in the rotating wave approximation.

[0260] Below, we consider the quantized Hamiltonian H Q The transformation of each of the other terms in [Equation (4.21)] is shown below. However, H Q In ω, ω + , the term with ω_ as a coefficient (a + g+ a g+ etc.), after conversion, g' + 2 ya g' - 2 Specifically, we show the terms up to the coefficient (a g _+a + g _) 4 Conversion of Well, g_' 4 The coefficients of the other terms are shown in detail. + 2 ) etc. The conversion is as follows:

[0261] TIFF0007786560000112.tif24170 (A.36)

[0262] where: TIFF0007786560000113.tif19170 (A.37) I used.

[0263] TIFF0007786560000114.tif18170 (A.38)

[0264] TIFF0007786560000115.tif49170 (A.39)

[0265] TIFF0007786560000116.tif43170 (A.40)

[0266] TIFF0007786560000117.tif49170 (A.41)

[0267] TIFF0007786560000118.tif34170 (A.42)

[0268] TIFF0007786560000119.tif48170 (A.43) TIFF0007786560000120.tif148170 (A.44)

[0269] however, TIFF0007786560000121.tif10150 (A.45)

[0270] TIFF0007786560000122.tif111170 (A.46) Therefore, substituting this into the above equation (A.44), we get

[0271] TIFF0007786560000123.tif51170 (A.47)

[0272] Next, using equations (A.35), (A.39), (A.40), (A.41), and (A.43), H Q The following sum in [Equation (4.21)] is TIFF0007786560000124.tif17170 (A.48) Consider the unitary transformation of

[0273] however, TIFF0007786560000125.tif9150 (A.49)

[0274] TIFF0007786560000126.tif9150 (A.50) TIFF0007786560000127.tif13150 (A.51) Note that from now on, O(g' 2 ) and ignore all vibrational terms.

[0275] TIFF0007786560000128.tif142170 (A.52)

[0276] By equations (A.34), (A.36), (A.42), (A.47), and (A.52), the quantized Hamiltonian H Q The unitary transformation of [Equation (4.21)] is obtained as [Equation (4.31)].

[0277] TIFF0007786560000129.tif201170 (A.53)

[0278] In deriving equation (A.53), the following equations (A.54) to (A.62) are used.

[0279] TIFF0007786560000130.tif9150 (A.54)

[0280] TIFF0007786560000131.tif6150 (A.55)

[0281] TIFF0007786560000132.tif11150 (A.56)

[0282] TIFF0007786560000133.tif6150 (A.57)

[0283] TIFF0007786560000134.tif6150 (A.58)

[0284] TIFF0007786560000135.tif6150 (A.59)

[0285] TIFF0007786560000136.tif6150 (A.60)

[0286] TIFF0007786560000137.tif10150(A.61)

[0287] however, TIFF0007786560000138.tif9150 (A.62)

[0288] In addition, a g+ , a + g+ is a i , a + i Since it is not a product of a, there is no need to pay attention to it. g + , a + g+ Eliminating the term, we obtain equation (4.34).

[0289] The general flow of the derivation of the four-body interaction of the JPO mentioned above can be said to be similar to that of the research by Puri et al. [Non-Patent Document 1]. However, the details of the derivation process are completely different, and the final results are also different. It can be said that the results obtained in this specification are physically more natural. The circuit analyzed by Puri et al. [Non-Patent Document 1] is basically the same as that shown in Figure 9. However, in Non-Patent Document 1, the capacitance C J Furthermore, in the derivation process, Non-Patent Document 1 does not show the Hamiltonian of a classical circuit. g+ , a + g+ Therefore, in Non-Patent Document 1, the unitary matrix for the transformation that incorporates the JPO-coupler interaction into the JPO is different from the above equation (4.27) in this specification.

[0290] In the analysis by Puri et al. (Non-Patent Document 1), g' in the above equation (4.42) of this specification + There is no equivalent.

[0291] In the analysis by Puri et al. (Non-Patent Document 1), in the limit where the JPO and the coupler become independent (each JPO In the capacitance C between O and the coupler, g (4) diverges to infinity, which is physically incorrect. C → 0 should be the limit where the approximation improves, so it is odd that the analysis breaks down here.

[0292] g in the above formula (4.44) (4) is the capacitance C→0, g (4) →0. Therefore, it can be said that there is a leap in the derivation process of Puri et al.

[0293] The disclosures of the above Patent Documents 1 to 3 and Non-Patent Documents 1 to 3 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]

[0294] 10, 110 Nonlinear elements 15 Capacitor 16 electrode (first electrode) 16A, 18A horizontal side 16B, 18B Vertical side 16C protrusion 16D, 18D extension 17A, 17B First and second opposing parts 18 electrode (second electrode) 18C cut section 19A, 19B Third and fourth opposing parts 20A~20D, 120A~120D Superconducting Qubit (JPO) 21, 121 combiner 22A to 22D, 122A to 122D Readout circuit connection parts 23A~23D, 123A~123D Control lines (flux lines) 24A~24D, 124A~124D Coupler connection 25A~25D coplanar waveguide 26A~26D Nonlinear elements (SQUID) 27A~27D Air bridge wiring 28A~28D Air bridge wiring 29 SQUID crosslinking part 30 parts (ground pattern protrusions) 31A~31D Capacitors (coupling capacitors) 32A~32D capacitors 40, 40-1, 40-2 Ground (GND) pattern (ground plane) 41 Surface of the board 42 Substrate (silicon substrate) 43A~43D, 44A, 44B Gap (gap width) 51 Control Line 140A~140D Readout circuit 150A~150D signal generation section 200 Quantum Computer 201A, 201B, 201C, 201D First Josephson junctions 202A, 202B, 202C, 202D Second Josephson junction 203A, 203B, 203C, 203D First superconducting section 204A, 204B, 204C, 204D Second superconducting section 205A, 205B, 205C, 205D Conductive part 206A, 206B, 206C, 206D capacitors 207A, 207B, 207C, 207D Magnetic field generation section 210A, 210B, 210C, 210D SQUID (SQUID loop)

Claims

1. first through fourth quantum bits; a coupler that couples the first to fourth quantum bits through a four-body interaction; Equipped with the coupler includes first and second electrodes arranged opposite to each other, and a nonlinear element including a Josephson junction and bridging the first and second electrodes; Each of the first to fourth quantum bits is a resonator including a loop circuit in which a first superconducting line, a first Josephson junction, a second superconducting line, and a second Josephson junction are connected in a circular configuration, and a capacitor connected in parallel with the loop circuit, the first superconducting line side of the loop circuit being connected to a conductive part, and the second superconducting line of the loop circuit being connected to ground; an end of the conductive portion of the first quantum bit and an end of the conductive portion of the second quantum bit are capacitively coupled to the first electrode of the coupler; an end of the conductive portion of the third quantum bit and an end of the conductive portion of the fourth quantum bit are capacitively coupled to the second electrode of the coupler; a capacitance value C of the capacitive coupling between the ends of the conductive portions of the first through fourth qubits and the coupler; The capacitance value C of the capacitor connected in parallel to the loop circuit of each of the first to fourth quantum bits Ｊ , The value of the capacitance between the first and second electrodes of the coupler, C ｇ The relationship between these is as follows: C Ｊ >C ｇ >C Superconducting quantum circuits are set to.

2. The strength of the four-body interaction is a numerator including the product of the fourth power of C and the square of the product of the resonant angular frequency of the coupler and the resonant angular frequency of each quantum bit; Said C Ｊ and the square of C ｇ a denominator including the product of the cube of the sum of C and the fourth power of the difference between the resonant angular frequency of the coupler and the resonant angular frequency of each quantum bit; is expressed as Said C ｇ C Ｊ 2. The superconducting quantum circuit according to claim 1, wherein the strength of the four-body interaction is set to be large by making it smaller than

3. The C Ｊ 3. The superconducting quantum circuit according to claim 1, wherein the two-body interaction between the two quantum bits is weakened by making the two-body interaction smaller than .

4. The resonant angular frequency ω of the quantum bit and the resonant angular frequency ω of the coupler － The ratio of oh / oh － =1±δ Regarding δ>C / [4√{C Ｊ (C ｇ +C)}] to change the ω to the ω － 3. The superconducting quantum circuit according to claim 1, wherein

5. In each of the first to fourth quantum bits, the resonator is terminated by the loop circuit, 5. The superconducting quantum circuit according to claim 1, further comprising a magnetic field generating unit that applies a pump signal to generate a magnetic flux that intersects with the loop circuit and causes the resonator to oscillate parametrically.

6. In each of the first to fourth quantum bits, the conductive portion is a waveguide made of a superconducting material, 5. The superconducting quantum circuit according to claim 1, wherein the capacitor connected in parallel with the loop circuit is formed by stray capacitance between the waveguide and ground.

7. 5. The superconducting quantum circuit according to claim 1, wherein in the coupler, the nonlinear element includes a SQUID (superconducting quantum interference device).

8. The superconducting quantum circuit according to any one of claims 1 to 7, a superconducting quantum circuit that constitutes a quantum computer having, as unit structures, the first to fourth quantum bits that undergo Josephson parametric oscillation and the coupler;

9. The unit structure has a plurality of units, 9. The superconducting quantum circuit according to claim 8, wherein the unit structure constitutes a quantum computer in which at least one of the first to fourth quantum bits constituting the unit structure is shared with one or more other unit structures.

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