Resonators, oscillators, and quantum computers

Abstract

To provide a resonator, an oscillator, and a quantum computer capable of suppressing the area occupied by a circuit.SOLUTION: A resonator (100) has a loop circuit (110) in which a first superconducting line (101), a first Josephson junction (103), a second superconducting line (102), and a second Josephson junction (104) are connected to one another in a circular manner and a capacitor (120). The capacitor (120) and the loop circuit (110) are connected in a circular manner.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a resonator, an oscillator, and a quantum computer, and more particularly to a resonator, an oscillator, and a quantum computer using a superconducting circuit. [Background technology]

[0002] Research is being conducted on circuits using superconducting elements. For example, Patent Document 1 discloses a high-frequency oscillator using a superconducting element. In addition, in recent years, research is being conducted on quantum computers using superconducting elements. For example, Patent Document 2 and Non-Patent Document 1 propose a quantum computer using a network of nonlinear oscillators. The nonlinear oscillators used in these quantum computers are required to have moderate nonlinearity and the lowest possible loss. Here, the nonlinearity of the nonlinear oscillator is quantified by a nonlinear coefficient. The nonlinear coefficient is a coefficient defined by the coefficient of the nonlinear term of the Hamiltonian of the nonlinear oscillator, as will be described later. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 09-139528 [Patent Document 2] JP 2017-73106 A [Non-patent literature]

[0004] [Non-Patent Document 1] S. Puri, et al., “Quantum annealing with all-to-all connected nonlinear oscillators,” Nature Comm., 2017. Summary of the Invention [Problem to be solved by the invention]

[0005] The above-mentioned Patent Document 2 and Non-Patent Document 1 describe the configuration of a quantum computer using a distributed constant type Josephson parametric oscillator as a nonlinear oscillator. The distributed constant type Josephson parametric oscillator is composed of a distributed constant type resonator and a Josephson junction. This distributed constant type resonator has a length on a circuit board that is approximately the same as the wavelength of an electromagnetic wave corresponding to the oscillation frequency of the parametric oscillator. The circuit board referred to here refers to a board on which a Josephson parametric oscillator is formed. In general, this oscillation frequency is, for example, about 10 GHz, so the length of a distributed constant type resonator corresponding to this frequency is on the order of millimeters. For this reason, the length of the distributed constant type resonator becomes very long.

[0006] On the other hand, to realize a practical quantum computer, it is necessary to integrate several thousand nonlinear oscillators on a chip of a few millimeters square, but the distributed constant type Josephson parametric oscillator has a problem that it is not suitable for such integration because the resonator occupies too large an area.

[0007] An object of the present disclosure is to provide a resonator, an oscillator, and a quantum computer that can reduce the area occupied by the circuit. [Means for solving the problem]

[0008] The resonator according to the embodiment includes: 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; A capacitor; having The capacitor and the loop circuit are connected in a ring shape. Effect of the Invention

[0009] According to the above-mentioned configuration, it is possible to provide a resonator, an oscillator, and a quantum computer that can reduce the area occupied by the circuit. [Brief description of the drawings]

[0010] [Figure 1] FIG. 2 is a schematic diagram illustrating an example of a lumped constant Josephson parametric oscillator according to the first embodiment. [Diagram 2] FIG. 11 is a schematic diagram showing a configuration of a Josephson parametric oscillator according to a second embodiment. [Diagram 3] FIG. 11 is a schematic diagram showing a configuration for controlling and reading out an oscillator according to a second embodiment. [Figure 4] FIG. 13 is a schematic diagram showing a configuration of a Josephson parametric oscillator according to a third embodiment. [Diagram 5] 13 shows a configuration for controlling and reading out an oscillator according to a third embodiment. [Figure 6] FIG. 11 is a schematic diagram showing the configuration of a quantum computer using the oscillator shown in the second or third embodiment. [Figure 7] FIG. 1 is a schematic diagram showing the configuration of a quantum computer in which an oscillator is integrated. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] The details of the embodiments will be described below. The resonator according to the embodiments is realized, for example, by a line (wiring) formed of a superconductor on a silicon substrate. For example, Nb (niobium) or Al (aluminum) is used as the material of this line, but any other metal that becomes superconducting when cooled to an extremely low temperature, such as Mo (molybdenum) or Ta (tantalum), may be used. In order to realize the superconducting state, the resonator circuit is used in a temperature environment of, for example, about 10 mK (millikelvin) realized by a refrigerator. In the following description, a Josephson junction refers to an element having a structure in which a thin insulating film is sandwiched between a first superconductor and a second superconductor.

[0012] <First embodiment> As described above, a distributed constant type Josephson parametric oscillator is unsuitable for integration because the area occupied by the resonator is too large. In order to solve this problem and realize a practical quantum computer, it is necessary to realize a lumped constant type Josephson parametric oscillator. The lumped constant type Josephson parametric oscillator can be realized, for example, by a circuit as shown in FIG. 1. FIG. 1 is a schematic diagram showing an example of a lumped constant type Josephson parametric oscillator 10 according to a first embodiment.

[0013] As shown in FIG. 1, the Josephson parametric oscillator 10 includes a resonator 100 and a magnetic field generating unit 200. The resonator 100 includes a loop circuit 110 and a capacitor 120. The loop circuit 110 includes a first superconducting line 101 that connects a first Josephson junction 103 and a second Josephson junction 104, and a second superconducting line 102 that connects the first Josephson junction 103 and the second Josephson junction 104. In other words, the resonator 100 includes a loop circuit 110 in which the first superconducting line 101 and the second superconducting line 102 are connected by the first Josephson junction 103 and the second Josephson junction 104, and a capacitor 120. As shown in FIG. 1, the loop circuit 110 is configured by connecting the first superconducting line 101, the first Josephson junction 103, the second superconducting line 102, and the second Josephson junction 104 in a circular manner. In other words, in loop circuit 110, a loop is formed by connecting first superconducting line 101 and second superconducting line 102 via first Josephson junction 103 and second Josephson junction 104. In other words, loop circuit 110 can also be called a DC-SQUID (superconducting quantum interference device).

[0014] The loop circuit 110 is shunted by the capacitor 120. That is, the first portion 105 of the first superconducting line 101 and the second portion 106 of the second superconducting line 102 are shunted by the capacitor 120. In other words, the resonator 100 has the input / output end of the DC-SQUID shunted by the capacitor 120. That is, it can be said that a loop circuit is configured in which the loop circuit 110 is incorporated on the line of the loop by connecting the capacitor 120 and the loop circuit 110 in a ring shape. In the following description, a circuit for shunting may be referred to as a shunt circuit. Here, the first portion 105 is an arbitrary portion of the first superconducting line 101. That is, the position of the first portion 105 in the first superconducting line 101 is not particularly limited. Similarly, the second portion 106 is an arbitrary portion of the second superconducting line 102. That is, the position of the second portion 106 in the second superconducting line 102 is not particularly limited.

[0015] The magnetic field generating unit 200 is a circuit that generates an AC magnetic field and applies the AC magnetic field to the loop circuit 110. The magnetic field generating unit 200 is a circuit through which an AC current flows, and generates an AC magnetic field by the AC current. More specifically, a current in which a DC current and an AC current are superimposed flows through the magnetic field generating unit 200. As will be described later, the magnitude of the magnetic flux and the oscillation frequency (resonant frequency) are controlled by the magnitude of the DC current. Although the magnetic field generating unit 200 is represented by one wire in FIG. 1, it may be configured by two wires, with a DC current flowing through one wire and an AC current flowing through the other wire.

[0016] When an AC magnetic field twice the resonant frequency of the resonator 100 is applied to the loop circuit 110 by passing an AC current through the magnetic field generating unit 200, the Josephson parametric oscillator 10 oscillates at the resonant frequency (i.e., an oscillation frequency 0.5 times the frequency of the AC magnetic field). This type of oscillation is called parametric oscillation. In this way, a lumped constant oscillator can be configured according to the configuration shown in Fig. 1. A lumped constant oscillator does not require a resonator with a length approximately equal to the wavelength of the electromagnetic wave corresponding to the oscillation frequency, so the area occupied by the circuit can be reduced.

[0017] As described above, according to the first embodiment, a resonator and an oscillator capable of suppressing the area occupied by the circuit can be realized. Here, the Josephson parametric oscillator 10 shown in FIG. 1 can be used in the quantum computer described in the above-mentioned Patent Document 2 or Non-Patent Document 1. However, as described later, it is not easy to reduce the nonlinear coefficient while keeping the loss small, so that there is a risk that the desired performance cannot be obtained when used in the quantum computer described in the above-mentioned Patent Document 2 or Non-Patent Document 1. That is, if the nonlinear coefficient can be reduced to an appropriate value required for a quantum computer while suppressing the loss, a quantum computer with better performance can be provided. Hereinafter, it will be specifically described that it is not easy to reduce the nonlinear coefficient while keeping the loss small in the Josephson parametric oscillator 10 shown in FIG. 1. In the following description, the Josephson parametric oscillator may be referred to as a nonlinear oscillator.

[0018] The Hamiltonian H of the lumped constant Josephson parametric oscillator 10 shown in FIG.

[0019]

number

[0020] In equation (1), h is the Planck constant and f J0 is the oscillation frequency of the nonlinear oscillator. † is a creation operator. a is an annihilation operator. Also, E C is expressed by the following equation (2).

[0021]

number

[0022] In equation (2), e is the elementary charge, C r is the capacitance of the capacitor 120 used in the shunt.

[0023] Also, f in equation (1) J0 is expressed by the following equation (3).

[0024]

number

[0025] In equation (3), C J is the capacitance of the first Josephson junction 103 and the second Josephson junction 104. On the other hand, in equation (3), L J is the equivalent inductance of the loop circuit 110, and is defined by the following equation (4).

[0026]

number

[0027] In equation (4), I C is the critical current value of the first Josephson junction 103 and the second Josephson junction 104, Φ is the magnetic flux applied to the loop circuit 110, and Φ is the magnetic flux quantum (approximately 2.07×10 -15 As can be seen from equation (4), the equivalent inductance L J can be changed by changing the magnetic flux Φ applied to the loop circuit 110. The magnetic flux Φ can be changed by changing the magnitude of the current passed through the magnetic field generating unit 200. More specifically, it can be changed by the magnitude of the direct current superimposed on the alternating current passed through the magnetic field generating unit 200. Furthermore, as can be seen from equations (3) and (4), the oscillation frequency can be controlled by the magnitude of the current passed through the magnetic field generating unit 200.

[0028] As described above, the nonlinear coefficient of a nonlinear oscillator is defined by the coefficient of the nonlinear term of the Hamiltonian of the nonlinear oscillator. In this disclosure, the nonlinear coefficient K of a nonlinear oscillator is defined as 12 times the absolute value of the coefficient of the nonlinear term of the Hamiltonian of the nonlinear oscillator divided by the Planck constant h. In the Hamiltonian of equation (1), the second term, i.e., (a † +a) 4 The term is the nonlinear term. Therefore, the nonlinear coefficient K of the nonlinear oscillator shown in Figure 1 is expressed as the following equation (5).

[0029]

number

[0030] From equation (5), the nonlinear coefficient K of the nonlinear oscillator shown in FIG. 1 is the capacitance C r It can be seen that it is determined by the value of

[0031] Incidentally, when fabricating the quantum computer described in Patent Document 2 or Non-Patent Document 1, the oscillation frequency of the nonlinear oscillator is preferably 5 GHz or more and 40 GHz or less. This is for the following reasons. At frequencies lower than 5 GHz, there is a problem that the probability of malfunction of the quantum computer due to thermal noise increases to a non-negligible extent. At frequencies higher than 40 GHz, the high-frequency electronic devices and high-frequency electronic components required to operate the quantum computer become very expensive. For this reason, it is preferable to use an oscillation frequency of 5 GHz or more and 40 GHz or less.

[0032] The critical current value I of the first Josephson junction 103 and the second Josephson junction 104 constituting the nonlinear oscillator is C It is preferable that the value of is 10 nA or more and 0.1 mA or less. This is for the following reason. If it is less than 10 nA, the output signal of the nonlinear oscillator is too small to be read out. If it is more than 0.1 mA, the equivalent inductance L J becomes smaller, so that the given oscillation frequency f J0In order to achieve this, the capacitance C r As a result, there is a problem that the loss of the nonlinear oscillator increases to a non-negligible extent. J The smaller the I in equation (4), the C The larger the L J This can be seen from the fact that the given oscillation frequency f J0 To achieve this, the capacitance C r The reason why we need to increase the value of L in Eq. (3) is that J To reduce C r If the f is not increased, J0 This can be seen from the fact that the capacitance C r The reason why losses increase as capacitance increases is as follows: to fabricate a large capacitance in an area small enough for an integrated circuit, a laminated capacitor is required, but with current technology it is difficult to fabricate a dielectric layer with low losses in a laminated capacitor. Here, the dielectric layer refers to the layer of dielectric material formed between the two electrodes of a capacitor. In order to sufficiently reduce losses, the capacitance C r It is preferable that the capacitance is 1 pF or less.

[0033] On the other hand, in a quantum computer, the nonlinear coefficient K is preferably 1 MHz or more and 10 MHz or less. This is for the following reason. If the nonlinear coefficient K is smaller than 1 MHz, the time required for quantum computation becomes too long, and the quantum computation cannot be completed while the quantum computer maintains the quantum state. Also, if the nonlinear coefficient K is larger than 10 MHz, the output signal of the nonlinear oscillator becomes small, and it becomes difficult to read the output signal.

[0034] Critical current I of Josephson junctions C If the current is 10 nA or more and 0.1 mA or less, the equivalent inductance L JFrom equation (4), it is 1.85 pH or more and 18.5 nH or less. In the calculation, the value of Φ in equation (4) was set to 0.3Φ0. The reason for setting the value of Φ to 0.3Φ0 is that if Φ is too small, the nonlinear oscillator will not oscillate easily, while if Φ is too large, it will become sensitive to magnetic field noise and the oscillation frequency will become unstable, so it is preferable to operate the oscillator with Φ of about 0.3Φ0. Also, the capacitance C of the Josephson junction J With current element manufacturing technology, the L J and C. J For a value of f = 1, the oscillation frequency f J0 Capacitance C that makes the frequency range 5GHz or more and 40GHz or less r can be calculated using equation (3). r In this case, the nonlinear coefficient K can be calculated using equation (5). In actual calculations, the nonlinear coefficient K of the Josephson parametric oscillator 10 in FIG. 1 does not fall within the range of 1 MHz or more and 10 MHz or less. Or, even if the nonlinear coefficient K falls within the range of 1 MHz or more and 10 MHz or less, the capacitance C r becomes larger than 1pF.

[0035] As described above, when trying to realize a desirable oscillation frequency using a Josephson junction with a desirable critical current value, it is not necessarily easy to achieve both the appropriate nonlinearity and low loss required for a quantum computer. Therefore, there is a demand for realizing a new lumped constant Josephson parametric oscillator that can achieve both the appropriate nonlinearity and the lowest possible loss required for a quantum computer.

[0036] Hereinafter, a specific description will be given of a configuration that can suppress the area occupied by the circuit while achieving both moderate nonlinearity and low loss. In the following description, the same components as those already described will be designated by the same reference numerals, and detailed descriptions will be omitted as appropriate. Also, redundant descriptions of the definitions of variables in the formulas will be omitted as appropriate.

[0037] The second and third embodiments described below have in common that the loop circuit 110 is shunted by a capacitor and a linear inductor. However, in the second embodiment, the capacitor and the linear inductor used for the shunt are connected in series. In contrast, in the third embodiment, the capacitor and the linear inductor used for the shunt are connected in parallel.

[0038] Second Embodiment FIG. 2 is a schematic diagram showing the configuration of a superconducting nonlinear oscillator (Josephson parametric oscillator) according to the second embodiment. As shown in FIG. 2, the oscillator 20 includes a resonator 300 and a magnetic field generating unit 200. The resonator 300 includes a loop circuit 110, a capacitor 120, and a linear inductor 130. The loop circuit 110 includes a first superconducting line 101 connecting the first Josephson junction 103 and the second Josephson junction 104, and a second superconducting line 102 connecting the first Josephson junction 103 and the second Josephson junction 104. In other words, the resonator 300 includes a loop circuit 110 in which the first superconducting line 101 and the second superconducting line 102 are connected by the first Josephson junction 103 and the second Josephson junction 104, a capacitor 120, and a linear inductor 130.

[0039] In the resonator 300, the loop circuit 110 is shunted by a circuit in which the capacitor 120 and the linear inductor 130 are connected in series. That is, the first portion 105 of the first superconducting line 101 and the second portion 106 of the second superconducting line 102 are shunted by the capacitor 120 and the linear inductor 130 connected in series. In other words, the resonator 300 is shunted by the capacitor 120 and the linear inductor 130 connected in series to the input / output ends of the DC-SQUID. That is, it can be said that a loop circuit in which the loop circuit 110 is incorporated on the line of the loop is configured by connecting the series circuit consisting of the capacitor 120 and the linear inductor 130 to the loop circuit 110 in a ring shape. Note that, as shown in FIG. 2, one end of the loop circuit may be grounded.

[0040] The magnetic field generating unit 200 and the resonator 300 are magnetically coupled via mutual inductance. In other words, the magnetic field generating unit 200 and the resonator 300 are inductively coupled. In the configuration of FIG. 2, parametric oscillation is also realized by generating an AC magnetic field. That is, when an AC magnetic field twice the resonant frequency of the resonator 300 is applied to the loop circuit 110 by passing an AC current through the magnetic field generating unit 200, the oscillator 20 oscillates at the resonant frequency (i.e., an oscillation frequency 0.5 times the frequency of the AC magnetic field). The frequency of the AC magnetic field is equal to the frequency of the AC current. Also, in this embodiment, as can be seen from equation (4) and equation (8) described later, the oscillation frequency can be controlled by the magnitude of the current passed through the magnetic field generating unit 200. Although the magnetic field generating unit 200 is represented by one wire in FIG. 2, it may be configured by two wires, with a DC current passed through one wire and an AC current passed through the other wire.

[0041] The Hamiltonian H of the oscillator 20 shown in FIG. 2 (the Hamiltonian H of the resonator 300) is expressed by the following equation (6).

[0042]

number

[0043] In equation (6), L r is the inductance of the linear inductor 130. Also, f0 is the oscillation frequency of the oscillator 20. In the Hamiltonian H of the equation (6), the second term, i.e., (a † +a) 4 The term is a nonlinear term. Therefore, the nonlinear coefficient K of the oscillator 20 of this embodiment is expressed by the following equation (7).

[0044]

number

[0045] In equation (7), L r If = 0, the nonlinear coefficient K is expressed by the same formula as formula (5). This corresponds to the fact that removing the linear inductor 130 from the oscillator 20 of this embodiment results in the nonlinear oscillator shown in FIG. 1. In other words, the oscillator 20 of this embodiment is an oscillator in which the linear inductor 130 is inserted into the nonlinear oscillator of FIG. 1. As can be seen from formula (7), the inductance L of the linear inductor 130 r The larger the nonlinear coefficient K, the smaller the nonlinear coefficient K. Therefore, in the oscillator 20 of this embodiment, the capacitance C r Therefore, it is possible to reduce the nonlinear coefficient K to a suitable value required for a quantum computer without increasing the loss of the nonlinear oscillator.

[0046] The oscillation frequency f0 of the oscillator 20 of this embodiment shown in FIG. 2 is expressed by the following formula (8). In formula (8), the capacitance C J is neglected because the effect of the capacitance of the Josephson junction is negligible in the circuit of Figure 2.

[0047]

number

[0048] In this embodiment, the oscillation frequency f0 of the oscillator 20 is preferably 5 GHz or more and 40 GHz or less. C The value of is preferably 10 nA or more and 0.1 mA or less.

[0049] Critical current I of Josephson junctions C If the current is 10 nA or more and 0.1 mA or less, the equivalent inductance L J From equation (4), it is 1.85 pH or more and 18.5 nH or less. In addition, the calculation was performed by setting the value of Φ in equation (4) to 0.3Φ0. When the equivalent inductance is 1.85 pH or more and 18.5 nH or less, the inductance L that can set the oscillation frequency f0 of the oscillator 20 to 5 GHz or more and 40 GHz or less is r and capacitance C r Various combinations of L and L are possible based on equation (8). Among these combinations, we select L that can make the nonlinear coefficient K in equation (7) 1 MHz or more and 10 MHz or less. r and C. r By using this combination, it is possible to realize a nonlinear oscillator having the appropriate nonlinearity required for a quantum computer.

[0050] For example, if the oscillation frequency f0 is 10 GHz and the critical current value I C 0.83μA, capacitance C r 0.57pF, inductance L r If we select 225 pH, the nonlinear coefficient K is calculated to be 4.2 MHz. In other words, in this case, it is possible to realize the moderate nonlinearity required for a quantum computer.

[0051] In this way, the inductance value of the linear inductor 130 is set to a value equal to the equivalent inductance L J , the oscillation frequency f0, and the critical current value IC and capacitance C r The inductance of the linear inductor 130 is preset based on the above. That is, the inductance of the linear inductor 130 is designed to be a predetermined value, not a stray inductance. In other words, the linear inductor 130 is an inductor that exists as a non-stray component. The linear inductor 130 may be implemented as, for example, a meander wiring or a coil, but the implementation method is not limited to these.

[0052] Fig. 3 is a schematic diagram showing a configuration for controlling and reading out the oscillator 20 of this embodiment. As will be described later, the configuration shown in Fig. 3 is used, for example, as a quantum bit circuit for a quantum computer.

[0053] In the configuration shown in FIG. 3, a control unit 50 and a readout unit 51 are added to the configuration shown in FIG. 2. The control unit 50 is a circuit connected to the magnetic field generating unit 200 of the oscillator 20, and supplies the magnetic field generating unit 200 with a direct current for controlling the oscillation frequency of the oscillator 20 and an alternating current for oscillating the oscillator 20. The readout unit 51 is a circuit connected to the resonator 300 via a capacitor 52, and reads out the internal state of the oscillator 20, i.e., the oscillation state. In the configuration shown in FIG. 3, the readout unit 51 is connected to a shunt circuit (a series circuit consisting of a capacitor 120 and a linear inductor 130 that shunts the loop circuit 110) via the capacitor 52.

[0054] <Third embodiment> Next, a third embodiment will be described. In the second embodiment, the capacitor and the linear inductor used in the shunt are connected in series, but in the third embodiment, the capacitor and the linear inductor used in the shunt are connected in parallel.

[0055] FIG. 4 is a schematic diagram showing the configuration of a superconducting nonlinear oscillator (Josephson parametric oscillator) according to the third embodiment. As shown in FIG. 4, the oscillator 30 has a resonator 400 and a magnetic field generating unit 200. The resonator 400 includes a loop circuit 110, a capacitor 120, and a linear inductor 130. The loop circuit 110 includes a first superconducting line 101 connecting the first Josephson junction 103 and the second Josephson junction 104, and a second superconducting line 102 connecting the first Josephson junction 103 and the second Josephson junction 104. In other words, the resonator 400 includes a loop circuit 110 in which the first superconducting line 101 and the second superconducting line 102 are connected by the first Josephson junction 103 and the second Josephson junction 104, a capacitor 120, and a linear inductor 130.

[0056] In the resonator 400, the loop circuit 110 is shunted by a circuit in which the capacitor 120 and the linear inductor 130 are connected in parallel. That is, the first portion 105 of the first superconducting line 101 and the second portion 106 of the second superconducting line 102 are shunted by the capacitor 120 and the linear inductor 130 connected in parallel. In other words, the resonator 400 is shunted by the capacitor 120 and the linear inductor 130 to which the input and output ends of the DC-SQUID are connected in parallel. That is, it can be said that a loop circuit in which the loop circuit 110 is incorporated on the line of the loop is configured by connecting the parallel circuit consisting of the capacitor 120 and the linear inductor 130 to the loop circuit 110 in a ring shape. Note that, as shown in FIG. 4, one end of the loop circuit may be grounded.

[0057] The magnetic field generating unit 200 and the resonator 400 are magnetically coupled via mutual inductance. In other words, the magnetic field generating unit 200 and the resonator 400 are inductively coupled. Even in the configuration of FIG. 4, parametric oscillation is realized by generating an AC magnetic field. That is, when an AC magnetic field twice the resonant frequency of the resonator 400 is applied to the loop circuit 110 by passing an AC current through the magnetic field generating unit 200, the oscillator 30 oscillates at the resonant frequency (i.e., an oscillation frequency 0.5 times the frequency of the AC magnetic field). The frequency of the AC magnetic field is equal to the frequency of the AC current. Also, in this embodiment, as can be seen from equation (4) and equation (11) described later, the oscillation frequency can be controlled by the magnitude of the current passed through the magnetic field generating unit 200. Although the magnetic field generating unit 200 is represented by one wire in FIG. 4, it may be configured by two wires, with a DC current passed through one wire and an AC current passed through the other wire.

[0058] The Hamiltonian H of the oscillator 30 shown in FIG. 4 (the Hamiltonian H of the resonator 400) is expressed by the following equation (9).

[0059]

number

[0060] In equation (9), L r is the inductance of the linear inductor 130 in FIG. 4. Also, f0 is the oscillation frequency of the oscillator 30. In the Hamiltonian H of the equation (9), the second term, i.e., (a † +a) 4 The term is a nonlinear term. Therefore, the nonlinear coefficient K of the oscillator 30 of this embodiment is expressed by the following formula (10).

[0061]

number

[0062] In equation (10), L r=∞, the nonlinear coefficient K is expressed by the same formula as formula (5). This corresponds to the fact that removing the linear inductor 130 from the oscillator 30 of this embodiment results in the nonlinear oscillator shown in FIG. 1. In other words, the oscillator 30 of this embodiment is an oscillator in which the linear inductor 130 is inserted into the nonlinear oscillator of FIG. 1. As can be seen from formula (10), the inductance L of the linear inductor 130 r The smaller the nonlinear coefficient K, the smaller the capacitance C of the capacitor 120 used in the shunt. r Therefore, it is possible to reduce the nonlinear coefficient K to a suitable value required for a quantum computer without increasing the loss of the nonlinear oscillator.

[0063] The oscillation frequency f0 of the oscillator 30 of the present embodiment shown in FIG.

[0064]

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[0065] In this embodiment, the oscillation frequency f0 of the oscillator 30 is preferably 5 GHz or more and 40 GHz or less. C The value of is preferably 10 nA or more and 0.1 mA or less.

[0066] Critical current I of Josephson junctions C If the current is 10 nA or more and 0.1 mA or less, the equivalent inductance L J From equation (4), it is 1.85 pH or more and 18.5 nH or less. In addition, the calculation was performed by setting the value of Φ in equation (4) to 0.3Φ0. When the equivalent inductance is 1.85 pH or more and 18.5 nH or less, the inductance L that can set the oscillation frequency f0 of the oscillator 30 to 5 GHz or more and 40 GHz or less isr and capacitance C r Various combinations of L and L are possible based on equation (11). Among these combinations, we select L that can make the nonlinear coefficient K in equation (10) 1 MHz or more and 10 MHz or less. r and C. r By using this combination, it is possible to realize a nonlinear oscillator having the appropriate nonlinearity required for a quantum computer.

[0067] For example, if the oscillation frequency f0 is 10 GHz and the critical current value I C 0.83μA, capacitance C r 0.57pF, inductance L r If we select 30 pH, the nonlinear coefficient K is calculated to be 4.0 MHz. In other words, in this case, it is possible to realize the moderate nonlinearity required for a quantum computer.

[0068] In this way, the inductance value of the linear inductor 130 is set to a value equal to the equivalent inductance L J , the oscillation frequency f0, and the critical current value I C and capacitance C r That is, the inductance of the linear inductor 130 is not a stray inductance, but is designed to have a predetermined value. In other words, the linear inductor 130 is an inductor that exists as a non-stray component.

[0069] Fig. 5 shows a configuration for controlling and reading out the oscillator 30 of this embodiment. As will be described later, the configuration shown in Fig. 5 is used, for example, as a quantum bit circuit for a quantum computer.

[0070] In the configuration shown in Fig. 5, a control unit 50 and a readout unit 51 are added to the configuration shown in Fig. 4, similarly to the configuration shown in Fig. 3. Note that in the configuration shown in Fig. 5, the readout unit 51 is connected to a shunt circuit (a parallel circuit consisting of a capacitor 120 and a linear inductor 130 that shunts the loop circuit 110) via a capacitor 52.

[0071] <Fourth embodiment> Next, an embodiment will be described in which the oscillator 20 and the oscillator 30 shown in the second or third embodiment are used as a quantum bit circuit for a quantum computer. The quantum computer here is a quantum annealing type computer that calculates a solution to any problem that can be mapped to an Ising model. As described above, the oscillator 20 and the oscillator 30 undergo parametric oscillation when an AC magnetic field having a frequency twice the resonant frequency is applied to the loop circuit 110. At this time, the oscillation state can be either a first oscillation state or a second oscillation state that differ from each other in phase by π. The first oscillation state and the second oscillation state correspond to the 0 and 1 of the quantum bit.

[0072] Fig. 6 is a schematic diagram showing the configuration of a quantum computer using the oscillator shown in the second or third embodiment. The configuration shown in Fig. 6 is a quantum computer configuration using a distributed constant type superconducting parametric oscillator described in Non-Patent Document 1, in which the above-mentioned oscillator 20 or oscillator 30 is applied instead of the distributed constant type superconducting parametric oscillator. More specifically, the configuration shown in Fig. 6 is, for example, a configuration described in Fig. 4 of Non-Patent Document 1, in which the above-mentioned oscillator 20 or oscillator 30 is applied instead of the distributed constant type superconducting parametric oscillator. In Fig. 6, oscillator 40 represents oscillator 20 or oscillator 30.

[0073] In the quantum computer 60 shown in FIG. 6, four oscillators 40 are connected to one coupling circuit 41. More specifically, when the oscillator 40 is the oscillator 20, the coupling circuit 41 is connected to a shunt circuit of the oscillator 20 (a series circuit consisting of a capacitor 120 and a linear inductor 130 that shunts the loop circuit 110). Similarly, when the oscillator 40 is the oscillator 30, the coupling circuit 41 is connected to a shunt circuit of the oscillator 30 (a parallel circuit consisting of a capacitor 120 and a linear inductor 130 that shunts the loop circuit 110). As shown in FIG. 3 or FIG. 5, a control unit 50 and a readout unit 51 are connected to each oscillator 40. That is, the control unit 50 is connected to the magnetic field generating unit 200 of the oscillator 40. In addition, the readout unit 51 is connected to the shunt circuit of the oscillator 40 via a capacitor 52. The coupling circuit 41 is a circuit that couples four oscillators 40, and is composed of one Josephson junction 410 and four capacitors 411. More specifically, the coupling circuit 41 couples a ring-shaped circuit having a capacitor 120 and a loop circuit 110 in each oscillator. The coupling circuit 41 couples a first set of oscillators consisting of two oscillators 40 out of the four oscillators 40, and a second set of oscillators consisting of the other two oscillators 40, via the Josephson junction 410. Here, each of the first set of oscillators is connected to a superconductor 412_1 via a capacitor 411. Also, each of the second set of oscillators is connected to a superconductor 412_2 via a capacitor 411. Here, the superconductor 412_1 is a wiring connected to one terminal of the Josephson junction 410, and the superconductor 412_2 is a wiring connected to the other terminal of the Josephson junction 410. In other words, it can be said that the superconductor 412_1 and the superconductor 412_2 are joined by a Josephson junction 410. That is, the first oscillator 40 of the first oscillator group is connected to one terminal of the Josephson junction 410 via a first capacitor 411. Also, the second oscillator 40 of the first oscillator group is connected to one terminal of the Josephson junction 410 via a second capacitor 411. Similarly, the third oscillator 40 of the second oscillator group is connected to the other terminal of the Josephson junction 410 via a third capacitor 411. Also, the fourth oscillator 40 of the second oscillator group is connected to the other terminal of the Josephson junction 410 via a fourth capacitor 411.

[0074] The control unit 50 uses alternating currents of different frequencies for the four oscillators 40. When the magnetic field generating unit 200 is configured with two wires, one of which is used for direct current and the other for alternating current, the wire for alternating current may be a wire shared by the multiple oscillators 40. That is, the wire for alternating current may be provided so as to run around the multiple oscillators 40. In this case, multiple control units 50 are connected to the shared wire for alternating current in order to control the multiple oscillators 40, and alternating currents of different frequencies are superimposed by these control units 50. In the configuration shown in Fig. 6, the control units 50 may be provided in a distributed manner to control each oscillator 40, or a plurality of control units 50 may be provided in one location. In addition, although four readout units 51 are used in the configuration shown in Fig. 6, one readout unit 51 may read out the four oscillators 40. In this case, the readout unit 51 provided in common to the plurality of oscillators 40 distinguishes between the oscillators 40 and reads out the oscillators 40 according to the difference in the frequency used by each oscillator 40.

[0075] In the configuration shown in FIG. 6, the quantum computer has four oscillators 40. However, by arranging and connecting a plurality of unit structures using the configuration shown in FIG. 6 as a unit structure, a quantum computer integrating any number of oscillators 40 can be realized. An example of the configuration is shown in FIG. 7. FIG. 7 is a schematic diagram showing the configuration of a quantum computer 61 integrating oscillators 40. In the configuration shown in FIG. 7, each coupling circuit 41 is connected to four oscillators 40 as shown in FIG. 6. Then, each oscillator 40 is connected to one to four coupling circuits 41, and the oscillator 40 is shared and arranged by a plurality of unit structures, thereby arranging the unit structures shown in FIG. 6. In the quantum computer 61, at least one oscillator 40 is connected to a plurality of coupling circuits 41. In particular, in the example shown in FIG. 7, at least one oscillator 40 is connected to four coupling circuits 41. The quantum computer 61 can also be described as follows. The quantum computer 61 has a plurality of oscillators 40, and each oscillator 40 is connected to one to four coupling circuits 41. The number of coupling circuits 41 to which each oscillator 40 is connected corresponds to how many unit structures the oscillator 40 is shared among. Thus, in the example shown in FIG. 7, the quantum computer 61 has a plurality of unit structures, and the oscillator 40 is shared among the plurality of unit structures. In the example shown in FIG. 7, 13 superconducting nonlinear oscillators are integrated, but any number of oscillators 40 can be integrated in a similar manner.

[0076] 7, the control unit 50 and the readout unit 51 are omitted for ease of understanding of the drawing, but in reality, the control unit 50 and the readout unit 51 are used to control and read out the oscillator 40. The operating principle and control method of the quantum computer are described in Non-Patent Document 1, and the operating principle and control method described in Non-Patent Document 1 are also applied to the quantum computers shown in FIGS. According to this embodiment, it is possible to realize a quantum computer that has both appropriate nonlinearity and low loss, and that has a reduced circuit area. The superconducting nonlinear oscillator according to the present disclosure can be applied not only to quantum annealing circuits but also to gate-type quantum computing circuits. In addition, in the fourth embodiment, as a preferred embodiment, the oscillator 20 and the oscillator 30 shown in the second or third embodiment are used as a quantum bit circuit for a quantum computer, but the oscillator 10 shown in the first embodiment may also be used.

[0077] The present invention is not limited to the above-described embodiment, and can be modified as appropriate without departing from the spirit and scope of the present invention.

[0078] Although the present invention has been described above with reference to the embodiment, the present invention is not limited to the above. Various modifications that can be understood by those skilled in the art can be made to the configuration and details of the present invention within the scope of the invention.

[0079] This application claims priority based on Japanese Patent Application No. 2019-133814, filed on July 19, 2019, the disclosure of which is incorporated herein in its entirety. [Explanation of symbols]

[0080] 10 Oscillators 20 Oscillators 30 Oscillators 40 Oscillator 41 Combined circuit 50 Control section 51 Readout section 52 Capacitor 60 Quantum Computer 61 Quantum computer 100 resonators 101 The first superconducting line 102 Second Superconducting Line 103 The first Josephson junction 104 Second Josephson Junction 105 First Part 106 Second Part 110 Loop Circuit 120 Capacitor 130 Linear Inductor 200 Magnetic field generating unit 300 resonator 400 resonator 410 Josephson Junction 411 Capacitor 412_1 Superconductor 412_2 Superconductors

Claims

1. 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; a capacitor having a capacitance of 1 pF or less; having the capacitor and the loop circuit are connected in a ring shape, It is a lumped constant circuit. resonator.

2. The nonlinear coefficient of the resonator is 1 MHz or more and 10 MHz or less. The resonator according to claim 1 .

3. Further, the linear inductor The circuit including the capacitor and the linear inductor is connected in a circular manner to the loop circuit.

3. The resonator according to claim 1 or 2.

4. 1. An oscillator comprising: A resonator according to any one of claims 1 to 3; A magnetic field generating unit that applies a magnetic field to the loop circuit; having A control unit that supplies a current for controlling the oscillator to the magnetic field generating unit is connected to the magnetic field generating unit. Oscillator.

5. A plurality of oscillators, each including a resonator according to any one of claims 1 to 3; at least one combining circuit for combining the plurality of oscillators; A quantum computer having the above structure.

6. The coupling circuit includes a Josephson junction. The quantum computer according to claim 5 .

7. The coupling circuit includes a capacitor coupled to the oscillator.

7. The quantum computer according to claim 5 or 6.

8. the oscillator includes a magnetic field generating unit that applies a magnetic field to the loop circuit, A control unit that supplies a current for controlling the oscillator to the magnetic field generating unit is connected to the magnetic field generating unit.

8. A quantum computer according to any one of claims 5 to 7.

9. At least one of the plurality of oscillators is connected to a plurality of the coupling circuits.

9. A quantum computer according to any one of claims 5 to 8.

10. The plurality of oscillators is four oscillators, At least one of the four oscillators is connected to the four coupling circuits.

10. The quantum computer of claim 9.

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