JP2015207032A - Arithmetic device and arithmetic method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To realize an arithmetic device that is easy to downsize and integrate, and does not require the detailed adjustment of an optical system.SOLUTION: The arithmetic device comprises: parametric mechanical resonators 1-1 to 1-3 that are coupled with each other; oscillators 2-1 to 2-3 for parametrically exciting the drive parts of the parametric mechanical resonators 1-1 to 1-3 at the same time and capable of individually controlling the amplitude and phase of the excitation for each of the parametric mechanical resonators 1-1 to 1-3; lock-in amplifiers 3-1 to 3-3 for individually detecting the vibration phases of the parametric mechanical resonators 1-1 to 1-3; and an arithmetic processing unit 4 which, assuming that the vibration phases of the parametric mechanical resonators 1-1 to 1-3 correspond to an ising spin state, assigns a value representing this ising spin state to a prescribed expression and obtains a problem solution.

Description

  The present invention relates to a calculation device and a calculation method for obtaining a solution to a problem for a set of input numerical values.

In recent years, a method for solving a category problem called NP difficulty or NP complete using a dynamic system called an Ising model has been proposed. A general-purpose logic operation device has been used for the purpose of finding a solution to a problem for binary information given so far. However, a problem in a category called NP difficult or NP-complete is a general-purpose logic when the number of bits is N. Since it is a problem that cannot be solved in N polynomial times in an arithmetic device, calculation over a very long time is required as the number of bits increases. On the other hand, the Ising model is a dynamic system in which the energy of the system is given by the following equation using a binary variable σ _i = ± 1 called Ising spin.

It has been proved that many problems called NP difficulty or NP perfect can be solved by obtaining a set of σ _i giving the energy minimum value of this system.
For example, consider a partitioning problem which is an example of a problem known to be NP-complete. The division problem is to divide a given N integers a ₁ ,..., A _N into two sets, and the sum of the numbers in each set is equal to the sum of the numbers in the other set. It is a problem to determine whether or not it can be done. As can be easily understood, this problem can be solved by examining whether the minimum energy is zero in the following Ising model.

That is, for a set of sigma _i as the equation (2) is 0, sigma a set providing a _i = 1, if classify a _i to a set giving a sigma _i = -1, the a _i in each set The sum is equal in the two sets. As described above, it has been proved that many problems called NP difficulty or NP complete result in the problem of obtaining the energy minimum value of the Ising model. That is, the Ising model is an arithmetic unit using an actual physical system, that is, It has been pointed out that by implementing it as an Ising machine, it is possible to perform operations at a much higher speed than general-purpose logic operation devices.

One example is given in Non-Patent Document 1. In the example of Non-Patent Document 1, two phase states (0 and π) of an optical parametric oscillator correspond to two Ising spin states, σ _i = + 1, −1, N oscillators are prepared, To form an interaction J _ij .
Another example is given in Non-Patent Document 2. In the example of Non-Patent Document 2, the implementation of an Ising machine is proposed by making two Ising spin states correspond to two circularly polarized states of slave laser emission excited by a master laser.

Z. Wang, A. Marandi, K Wen, R. L. Byer, Y. Yamamaoto, “A Coherent Ising Machine Based on Degenerate Optical Parametric Oscillators”, arXiv: 1311.2696v1, 2013 S. Utsunomiya, K. Takata, Y. Yamamoto, “Mapping of Ising models onto injection-locked laser systems”, Optics Express, Vol. 19, pp. 18091-18108, 2011

Thus, although it has been shown that an Ising machine can be implemented by an optical system including a laser, the examples of Non-Patent Document 1 and Non-Patent Document 2 require a laser and an optical system corresponding to N degrees of freedom, There has been a problem that it is unsuitable for miniaturization and integration, which are the greatest features of logic operation devices using conventional semiconductor integrated circuits. As is clear from the above example, the magnitude of the interaction J _ij between different Ising spins needs to be adjusted depending on the problem to be solved. Adjustment is required, and there is a problem that the convenience in adapting to a plurality of different problems is low.

  The present invention has been made to solve the above problems, and an object of the present invention is to provide an arithmetic device and an arithmetic method that are easy to downsize and integrate and do not require detailed adjustment of an optical system.

The present invention is an arithmetic unit that obtains a solution to a problem by using an Ising machine in which a plurality of mechanical resonators including a vibrating portion disposed with a space between the substrate and a substrate are coupled. A plurality of mechanical resonators, vibration units of the plurality of mechanical resonators simultaneously parametrically excited, excitation means capable of individually controlling the excitation amplitude and excitation phase for each mechanical resonator, and the plurality of mechanical resonators It is assumed that the vibration phase of each of the plurality of mechanical resonators corresponds to the Ising spin state, and a value representing the Ising spin state is substituted into a predetermined equation to solve the problem. Arithmetic processing means for obtaining
Further, in one configuration example of the arithmetic device according to the present invention, the arithmetic processing means corresponds to the Ising spin state corresponding to the most frequently occurring vibration phase set among the vibration phase sets of the plurality of mechanical resonators. It is regarded that a solution to the problem is obtained by substituting a value representing this Ising spin state into a predetermined equation.

Further, in one configuration example of the arithmetic device according to the present invention, a space is further provided between the substrate on which the plurality of mechanical resonators are formed, and vibration portions of adjacent mechanical resonators are coupled to each other. A plurality of mechanical resonators coupled to each other by causing mechanical vibrations to propagate between adjacent mechanical resonators by coupling means corresponding to mechanical vibrations of the mechanical resonators; It is a feature.
Also, one configuration example of the arithmetic device of the present invention is characterized in that a piezoelectric material is used as a material constituting the vibration part of the plurality of mechanical resonators.
Further, one configuration example of the arithmetic device of the present invention further includes a coupling wiring for electrically coupling the vibration parts of adjacent mechanical resonators, and is generated by a piezoelectric effect corresponding to the mechanical vibration of the mechanical resonators. The plurality of mechanical resonators are coupled by mutually applying the applied voltages to the adjacent mechanical resonators via the coupling wiring.
Further, in one configuration example of the arithmetic device according to the present invention, the excitation means uses any one of a force due to a piezoelectric effect, a thermal stress due to light irradiation, an electrostatic force, or a Lorentz force. The detecting means converts the mechanical vibration of the plurality of mechanical resonators into an electrical signal using any one of a piezoelectric effect, a thermal stress effect by light irradiation, an electrostatic effect, and a magnetic interaction; The present invention is characterized in that vibration phases of a plurality of mechanical resonators are detected.
Further, in one configuration example of the arithmetic device according to the present invention, the problem is whether or not N (N is an integer of 2 or more) integers can be divided into two sets having the same sum of numbers in the set. It is a division problem.

  Further, the present invention is an arithmetic method for obtaining a solution of a problem using an Ising machine in which a plurality of mechanical resonators each having a vibration part disposed with a space between the substrate and a substrate are coupled. A plurality of mechanical resonators are simultaneously parametrically excited, an excitation step for individually controlling an excitation amplitude and an excitation phase for each mechanical resonator, a detection step for individually detecting a vibration phase of the plurality of mechanical resonators, And an arithmetic processing step for obtaining a solution to the problem by substituting a value representing the Ising spin state into a predetermined equation. It is.

  According to the present invention, a plurality of mechanical resonators are coupled to each other, the vibration parts of the plurality of mechanical resonators are simultaneously parametrically excited, and the vibration phases of the plurality of mechanical resonators are individually detected. The problem phase can be obtained by substituting the value representing the Ising spin state into a predetermined equation. As a result, according to the present invention, it is possible to realize an arithmetic device that is easy to downsize and integrate and does not require detailed adjustment of the optical system. In the present invention, the problem can be set by individually controlling the excitation amplitude and the excitation phase for each mechanical resonator.

It is a perspective view which shows the structure of a parametric mechanical resonator. It is a block diagram which shows the structure of the arithmetic unit which concerns on the 1st Embodiment of this invention. It is a block diagram which shows the structure of the arithmetic unit which concerns on the 2nd Embodiment of this invention. It is a block diagram which shows the structure of the arithmetic unit which concerns on the 3rd Embodiment of this invention.

[Principle of the Invention]
In the present invention, an Ising machine that is excellent in miniaturization and can easily control the interaction between spins by making two vibration states in a parametric mechanical resonator manufactured by microfabrication technology correspond to Ising spins. provide.
Parametric mechanical resonators already have many examples of implementation, and an element that can be integrated by actually applying a microfabrication technique has been realized. One example is disclosed in International Publication WO2009 / 041362, which is produced using a compound semiconductor heterostructure. This parametric mechanical resonator is shown in FIG.

The parametric mechanical resonator shown in FIG. 1 has a sacrificial layer 121 made of single-crystal Al _0.7 Ga _0.3 As and an insulation made of single-crystal insulating GaAs on a substrate 101 made of GaAs having a plane orientation of (001). A laminated structure including a layer 102, a conductive layer 103 made of single-crystal conductive GaAs doped with silicon, and a piezoelectric layer 104 made of single-crystal insulating AlGaAs is formed.

The piezoelectric layer 104 is made of, for example, Al _0.3 Ga _0.7 As. Further, in the present parametric mechanical resonator, the support portion 105, the support portion 106, and the beam 107 supported at both ends by the support portions 105 and 106 are formed by the above-described laminated structure. The lower surface of the beam 107 is separated from the surface of the substrate 101, and a space is formed between the opposed surfaces of the beam 107 and the substrate 101. Such a structure of the beam 107 can be formed by selectively etching the sacrificial layer 121 around and directly below the beam 107.

  An excitation electrode 108 is formed on one support portion 105, and a vibration detection electrode 110 is formed on the other support portion 106. The electrodes 108 and 110 are made of a metal material that forms a Schottky junction with the piezoelectric layer 104 made of a semiconductor. For example, the electrodes 108 and 110 are made of a laminated structure of a Ti layer and an Au layer formed thereon. The

  A common electrode 109 is formed on the conductive layer 103 exposed by removing a part of the piezoelectric layer 104 of the support portion 105. The common electrode 109 is made of a metal material that is ohmically connected to the conductive layer 103, and is made of, for example, an AuGeNi alloy. The excitation electrode 108 is connected to a wiring 111 to which an AC signal for parametric excitation or the like is supplied, the common electrode 109 is connected to a ground wiring 112, and the vibration detection electrode 110 is a vibration of the beam 107. The vibration detection wiring 113 to which a signal generated by the above is output is connected. In this logic element, the conductive layer 103 functions as a common electrode facing the excitation electrode 108 and the detection electrode 110 with the piezoelectric layer 104 interposed therebetween.

Here, the resonance angular frequency of the elastic beam 107 is ω ₀ . Here, when the ground wiring 112 is connected to the ground and a voltage is applied to the excitation electrode 108 through the parametric excitation wiring 111, the beam 107 is proportional to the applied voltage due to the piezoelectric effect of the piezoelectric layer 104. Subjected to strain in the extending direction. This distortion changes the resonance frequency of the beam 107. Thus, when applying an AC voltage of an angular frequency 2 [omega ₀ to the excitation electrode 108, the beam 107 is periodically subject to a distortion at the angular frequency 2 [omega _0, the resonance frequency of the beam 107 is modulated at the angular frequency 2 [omega _0, the beam 107 is the angular Parametrically excited at a frequency ω ₀ .
The motion of this parametric mechanical resonator is described by the following Hamiltonian H:

  Here, q is the displacement of the parametric mechanical resonator, p is the momentum conjugate to the displacement q, Γ is the strength of the parametric excitation, and β is the strength of the non-linearity of the parametric mechanical resonator. A time-dependent canonical transformation generator F is defined as follows.

  By using the canonical transformation generator F, the variables Q and P are defined as follows.

  That is, by using q and p defined as in the equations (7) and (8) and the effective Hamiltonian H ′ derived as in the equation (9) by the generator F, the rotational coordinate approximation is used. System can be described.

  This Hamiltonian H 'has two local minima, which correspond to steady vibrations. The variables P and Q giving this vibration state and the effective Hamiltonian H 'are given by the following equations.

  These parametric mechanical resonators are then linearly coupled. The Hamiltonian of the system is given by

Here, H _{int i, j} gives the linear coupling of the i-th and j-th two parametric mechanical resonators, and c _ij represents the strength of the linear coupling. As in the case of the single resonator, when the effective Hamiltonian H ′ in the rotating coordinate system when two parametric mechanical resonators are linearly coupled is obtained, the following equation is obtained.

That is, in addition to the effective Hamiltonian H ′ _0i in the case of a single resonator, an effective Hamiltonian H _{int i, j} resulting from the interaction of two parametric mechanical resonators is added. Now, assuming that the contribution of H _{int i, j} is sufficiently small compared to H ′ _0i , the minimum value of the effective Hamiltonian H ′ is all the formulas (10) under the condition that the effective Hamiltonian H ′ _0i is minimum. It can be obtained approximately by the condition that it holds for a parametric mechanical resonator. That is, the motion of the parametric mechanical resonator that gives the minimum value of the effective Hamiltonian H ′ is given by:

From the result of the equation (17), the effective energy for the vibration state of {σ _i } = {σ ₁ , σ ₂ ,..., Σ _N } is given by the following equation.

The energy shown in Expression (18) is the same as that of the Ising model energy (Expression (1)) except for a constant, and the coupling coefficient J _ij is given by the following expression.

From this, it is possible not only to construct an Ising machine by linearly coupling two or more parametric mechanical resonators, but also by controlling the excitation phase Δ _{i of} each parametric mechanical resonator and the intensity Γ _{i of the} parametric excitation. It can be seen that the magnitude of coupling between Ising spins can also be changed.

For the sake of simplicity, the implementation of only the second term of the Ising model (Equation (1)) has been described here, but the document “I. Mahboob, C. Froitier, H. Yamaguchi,“ A symmetry-breaking electromechanical detector ” , Applied Physics Letters, 96, 213103, 2010 ”, an energy difference is given to two phase states by simultaneously applying a voltage having an angular frequency ω ₀ , and an Ising model (Formula (1)) It is also possible to construct the first term. Thus, by linearly coupling N (N is an integer of 2 or more) parametric mechanical resonators, an Ising machine that can be integrated and can externally control the magnitude of coupling between Ising spins can be constructed. .

[First Embodiment]
Hereinafter, embodiments of the present invention will be described with reference to the drawings. Here, as a simplest example, a result of solving a division problem for three integers a _i = {1, 2, 3} using three parametric mechanical resonators is shown. The answer to this problem is to split it into {1,2} and {3}. That is, {σ ₁ , σ ₂ , σ ₃ } = {+ 1, + 1, −1} or {−1, −1, + 1} gives zero energy. The corresponding Ising Hamiltonian H is given by:
H = (σ ₁ + 2σ ₂ + 3σ ₃ ) ² = 14 + 2 (2σ ₁ σ ₂ + 6σ ₂ σ ₃ + 3σ ₃ σ ₁ )
... (20)

It is clear that H = 0 when {σ ₁ , σ ₂ , σ ₃ } = {+ 1, + 1, −1} or {−1, −1, + 1}. Of the three parametric mechanical resonators, the i-th and j-th two parametric mechanical resonators have linear coupling strengths c _ij (i and j are any one of 1 to 3 and i ≠ j) are all equal. In this case, the following equation is established from the equation (19).
Γ ₁ cos (Δ ₂ −Δ ₁ ): Γ ₂ cos (Δ ₃ −Δ ₂ ): Γ ₃ cos (Δ ₁ −Δ ₃ )
= 2: 6: 3 (21)

Therefore, in the simplest case, the Ising Hamiltonian (Expression (20)) corresponding to the division problem of the present embodiment can be realized by removing the constants as follows.
Δ ₁ = Δ ₂ = Δ ₃ , Γ ₁ : Γ ₂ : Γ ₃ = 2: 6: 3 (22)

That is, when the excitation phases of the three parametric mechanical resonators are the same, and the excitation intensity of the three parametric mechanical resonators is selected to be 2: 6: 3, excitation is performed with a pair of phases (σ ₁ , σ ₂ most frequently appearing). , Σ ₃ ) is substituted into equation (20), and whether or not the value of the Ising Hamiltonian H at that time is 0 is determined to determine whether or not division is possible.

  FIG. 2 is a block diagram illustrating a configuration of the arithmetic device according to the present embodiment. The arithmetic device of the present embodiment includes N parametric mechanical resonators 1-1 to 1-3 (N is an integer equal to or larger than 2 and N = 3 in the present embodiment), and parametric mechanical resonator 1-1. Oscillators 2-1 to 2-3 (excitation means) for applying an alternating voltage for excitation to 1-3, and lock-in amplifiers for detecting the vibration amplitude and vibration phase of the parametric mechanical resonators 1-1 to 1-3 The vibration phases of 3-1 to 3-3 (detection means) and the parametric mechanical resonators 1-1 to 1-3 are regarded as corresponding to the Ising spin state. The arithmetic processing unit 4 that obtains a solution by substituting, the coupling wiring 5-12 that electrically couples the vibrating parts of the parametric mechanical resonators 1-1 and 1-2, and the parametric mechanical resonator 1-2 , 1-3 to electrically couple the vibrating parts And if wiring 5-23, and a bond wire 5-13 Metropolitan electrically coupling the vibrating portions of the parametric mechanical resonator 1-1 and 1-3.

The example of FIG. 2 is a combination of three parametric mechanical resonators 1-1 to 1-3 similar to those in FIG. 1, and the parametric mechanical resonators 1-1 to 1-3 are manufactured in the same manner as in FIG. GaAs / AlGaAs parametric mechanical resonator. Parametric mechanical resonators 1-1 to 1-3 include beams 10-1 to 10-3 (vibrating portions) similar to the beam 107 in FIG. 1, electrodes 11-1 to 11-3, and electrodes 12-1, respectively. To 12-3 and electrodes 13-1 to 13-3. The electrodes 11-1 to 11-3, 12-1 to 12-3, 13-1 to 13-3 are applied with an AC voltage V _i cos (2ω ₀ t + 2Δ _i ) (i = 1 to 3) for parametric excitation. 1 is a Schottky electrode for detecting vibration and coupling between resonators, and corresponds to the electrodes 108 and 110 in FIG. In FIG. 2, for simplicity, the electrode corresponding to the common electrode 109 and the support portion are omitted.

The oscillators 2-1 to 2-3 generate AC voltages V _i cos (2ω ₀ t + 2Δ _i ) (i = 1 to 3), respectively, and apply them to the electrodes 11-1 to 11-3. The amplitude V _i and phase Δ _i of these AC voltages can be individually adjusted for each oscillator. At the same time, each of the oscillators 2-1 to 2-3 inputs an AC voltage having an angular frequency of ω ₀ as a reference signal to the lock-in amplifiers 3-1 to 3-3. The electrodes 11-1 to 11-3 are also connected to the inputs of the lock-in amplifiers 3-1 to 3-3.

As described with reference to FIG. 1, when an AC voltage having an angular frequency of 2ω ₀ is applied to the electrodes 11-1 to 11-3, the resonance frequency of the beams 10-1 to 10-3 serving as the vibration part is modulated at the angular frequency of 2ω _0. The beams 10-1 to 10-3 are excited parametrically at an angular frequency ω ₀ . The vibration of the angular frequency ω ₀ is output to the electrodes 11-1 to 11-3 in the form of a voltage signal due to the piezoelectric effect. The lock-in amplifiers 3-1 to 3-3 are based on the reference signals from the oscillators 2-1 to 2-3, and the amplitude of the voltage signal having the angular frequency ω ₀ output from the electrodes 11-1 to 11-3. Detect the phase. Thus, by detecting the amplitude and phase of the voltage signals output from the electrodes 11-1 to 11-3, the machine having the angular frequency ω ₀ caused by the parametric excitation of the parametric mechanical resonators 1-1 to 1-3 is detected. The amplitude and phase of vibration can be detected.

  The coupling wires 5-12, 5-23, and 5-13 are formed by Au Schottky gates, and electrically couple two adjacent parametric mechanical resonators. The coupling wiring 5-12 is connected to the electrode 12-1 of the parametric mechanical resonator 1-1 and the electrode 12-2 of the parametric mechanical resonator 1-2, and the coupling wiring 5-23 is connected to the parametric mechanical resonator. The electrode 13-2 of the 1-2 and the electrode 13-3 of the parametric mechanical resonator 1-3 are connected, and the coupling wiring 5-13 is connected to the electrode 13-1 of the parametric mechanical resonator 1-1 and the parametric mechanical resonance. It is connected to the electrode 12-3 of the device 1-3.

Wirings 5-12, 5-23, and 5-13 are formed for each of the three combinations of the three parametric mechanical resonators 1-1 to 1-3, and piezoelectrically by the displacement of the one parametric mechanical resonator. The generated voltage is propagated to the adjacent parametric mechanical resonator, and an external force is applied to the parametric mechanical resonator by the piezoelectric effect. If the resistances of the wirings 5-12, 5-23, and 5-13 are sufficiently small, the force is generated in proportion to the displacement at the same time as the variation of the resonator occurs. Therefore, the linear coupling H _{int i, j} Can be realized.

Now, the coupling strength between the parametric mechanical resonators 1-1 and 1-2, the coupling strength between the parametric mechanical resonators 1-2 and 1-3, and the coupling strength between the parametric mechanical resonators 1-1 and 1-3. Assuming that all are equal, c ₁₂ = c ₂₃ = c ₃₁ , and therefore, the amplitude V _i of the AC voltage for parametric excitation applied to the electrodes 11-1 to 11-3 is set to V ₁ according to the equation (15): If V ₂ : V ₃ = 2: 6: 3 is set, the coupling corresponding to the equation (21) can be realized. At this time, it is needless to say that the phases Δ _{1 to} Δ ₃ of the AC voltage for parametric excitation must all be equal.

Table 1 shows the vibration phases (φ ₁ , φ) of the parametric mechanical resonators 1-1 to 1-3 when the parametric excitation is performed many times using the AC voltage having such a voltage amplitude ratio and phase. ₂ , φ ₃ ) is 0 or π, detected by the lock-in amplifiers 3-1 to 3-3, and the statistics are obtained.

As can be seen from the results of Table 1, the vibration phases (φ ₁ , φ ₂ , φ ₃ ) of the parametric mechanical resonators 1-1 to 1-3 are (0, 0, π) or (π, π, 0). It can be seen that the case is most likely to oscillate. Phase 0 corresponds to the Ising spin state σ _i = + 1, and phase π corresponds to the Ising spin state σ _i = −1. Therefore, the state where the vibration phases (φ ₁ , φ ₂ , φ ₃ ) of the parametric mechanical resonators 1-1 to 1-3 are (0, 0, π) or (π, π, 0) is {σ ₁ , This corresponds to a spin state of σ ₂ , σ ₃ } = {+ 1, + 1, −1} or {−1, −1, + 1}.

The arithmetic processing unit 4 recognizes the vibration phase pair (0, 0, π) or (π, π, 0) that appears most frequently from the detection results of the lock-in amplifiers 3-1 to 3-3, and the vibration phase. Set (0, 0, π) to {σ ₁ , σ ₂ , σ ₃ } = {+ 1, +1, -1} spin state, and set the vibration phase (π, π, 0) to {σ ₁ , σ ₂ , σ ₃ } = {− 1, −1, +1}, and {σ ₁ , σ ₂ , σ ₃ } = {+ 1, +1, −1} or {σ ₁ , σ ₂ , σ ₃ } = {− 1, −1, + 1} is substituted into the equation (20), and it is checked whether or not the value of the Ising Hamiltonian H at that time is 0.

When the value of the Ising Hamiltonian H is 0, the arithmetic processing unit 4 determines that the three integers a _i = {1, 2, 3} can be divided into two sets having the same sum of numbers in the set. If the value of the Ising Hamiltonian H is not 0, it is determined that the division is impossible. In this example, it is determined that division is possible when H = 0. In this way, the solution of the division problem for a _i = {1, 2, 3} can be obtained.

  Such an arithmetic processing unit 4 can be realized by a computer having a CPU (Central Processing Unit), a storage device, and an interface, and a program for controlling these hardware resources. The CPU executes arithmetic processing according to a program stored in the storage device.

  As described above, according to the present embodiment, it is possible to realize an arithmetic device that is easy to downsize and integrate and does not require detailed adjustment of the optical system. In this embodiment, the problem can be set by individually controlling the excitation amplitude and the excitation phase for each parametric mechanical resonator.

[Second Embodiment]
Next, a second embodiment of the present invention will be described. FIG. 3 is a block diagram showing the configuration of the arithmetic unit according to the present embodiment, and the same components as those in FIG. In the first embodiment, three mechanically independent parametric mechanical resonators are electrically coupled. However, in the present embodiment, the three parametric mechanical resonators 1a-1 to 1a-3 are mechanically connected. It is a combination. For simplicity, the oscillators 2-1 to 2-3, the lock-in amplifiers 3-1 to 3-3, and the arithmetic processing unit 4 in FIG. 2 are omitted.

  Parametric mechanical resonators 1a-1 to 1a-3 include beams 10-1 to 10-3, Schottky electrodes 11-1 to 11-3, and support portions 14-1 to 14-3, 15-1 to 15-1, respectively. 15-3. Also in FIG. 3, an electrode corresponding to the common electrode 109 in FIG. 1 is omitted. In the region 7 in FIG. 3, the heterostructure (102 to 104, 121 in FIG. 1) is removed by mesa etching to the depth of the sacrificial layer (121 in FIG. 1) to expose the substrate (101 in FIG. 1). It is an area.

  On the other hand, the beams 10-1 to 10-3 composed of the insulating layer (102 in FIG. 1), the conductive layer (103 in FIG. 1), and the piezoelectric layer (104 in FIG. 1) are directly below the sacrificial layer by etching. The sacrificial layer is completely removed, and a mechanical vibration corresponding to the AC voltage applied from the electrodes 11-1 to 11-3 is possible by arranging a space between the sacrificial layer and the substrate. It has become. Both ends of the beams 10-1 to 10-3 are supported by support portions 14-1 to 14-3, 15-1 to 15-3 (see FIG. 1) composed of a sacrifice layer, an insulating layer, a conductive layer, and a piezoelectric layer. 105, 106).

  The coupling portions 6-12, 6-23, and 6-13 include an insulating layer (102 in FIG. 1), a conductive layer (103 in FIG. 1), and a piezoelectric layer (104 in FIG. 1). The coupling unit 6-12 mechanically couples one end of the beam 10-1 of the parametric mechanical resonator 1a-1 and one end of the beam 10-2 of the parametric mechanical resonator 1a-2, and the coupling unit 6-23 The other end of the beam 10-2 of the parametric mechanical resonator 1a-2 and the one end of the beam 10-3 of the parametric mechanical resonator 1a-3 are mechanically coupled, and the coupling portion 6-13 includes a parametric mechanical resonator. The other end of the beam 10-1 of 1a-1 and the other end of the beam 10-3 of the parametric mechanical resonator 1a-3 are mechanically coupled.

  The coupling portions 6-12, 6-23, and 6-13 are partially removed from the sacrificial layer by selective side etching of the sacrificial layer, and are disposed with a space between the substrate and the sacrificial layer. It is formed so as to project like a bowl. With such a structure, the coupling portions 6-12, 6-23, and 6-13 can propagate the mechanical vibration generated in one parametric mechanical resonator to another parametric mechanical resonator.

For example, when the beam 10-1 of the parametric mechanical resonator 1a-1 is displaced, the coupling portion 6-12 is similarly displaced, and this displacement causes a force in the same direction to the beam 10-2 of the parametric mechanical resonator 1a-2. It comes to work. Since this force is proportional to the displacement difference between the parametric mechanical resonator 1a-1 and the parametric mechanical resonator 1a-2, the linear combination H _{int 1,2} in the equations (11) to (13) can be realized. Similarly, linear couplings are also formed between the parametric mechanical resonator 1a-1 and the parametric mechanical resonator 1a-3, and between the parametric mechanical resonator 1a-2 and the parametric mechanical resonator 1a-3. All the interactions in (11) to (13) can be realized.

Therefore, as in the first embodiment, if an AC voltage having an angular frequency of 2ω ₀ with an amplitude ratio of V ₁ : V ₂ : V ₃ = 2: 6: 3 is applied to the electrodes 11-1 to 11-3. , An Ising machine corresponding to equation (20) can be realized.
The operations of the oscillators 2-1 to 2-3, the lock-in amplifiers 3-1 to 3-3, and the arithmetic processing unit 4 are as described in the first embodiment.

[Third Embodiment]
Next, a third embodiment of the present invention will be described. FIG. 4 is a block diagram showing the configuration of the arithmetic unit according to the present embodiment. The same components as those in FIG. The present embodiment shows an example in which an Ising machine including four elements is implemented using membrane-type parametric mechanical resonators 1b-1 to 1b-4 as parametric mechanical resonators. In FIG. 4, the oscillator, the lock-in amplifier, and the arithmetic processing unit are omitted for simplification.

  The parametric mechanical resonators 1b-1 to 1b-4 include the vibration units 16-1 to 16-4, the Schottky electrodes 11-1 to 11-4, 12-1 to 12-4, and 13-1 to 13-, respectively. 4, 17-1 to 17-4. The manufacturing method of such membrane-type parametric mechanical resonators 1b-1 to 1b-4 is as disclosed in, for example, Japanese Patent Application Laid-Open No. 2010-232983, and a through-hole is formed in a thin film having a sacrificial layer. From there, it can be fabricated by performing isotropic sacrificial layer etching.

  The vibrating parts 16-1 to 16-4 are arranged such that at least a part of the sacrificial layer immediately below is removed by selective etching of the sacrificial layer, and a space is provided between the vibrating parts 16-1 to 16-4. Such membrane-type vibrating parts 16-1 to 16-4 are described in documents “D. Hatanaka, I. Mahboob, H. Okamoto, K. Onomitsu, H. Yamaguchi,“ An electromechanical membrane resonator ”, Applied Physics Letters. , 101, 063102, 2012 ”, electrical drive and vibration detection are possible in the same manner as the beams 10-1 to 10-3, 107 of the double-supported beam structure.

The electrodes 11-1 to 11-4, 12-1 to 12-4, 13-1 to 13-4, and 17-1 to 17-4 are used for application of AC voltage for parametric excitation, vibration detection, and between resonators. This is a Schottky electrode for coupling.
Coupling wires 5-12, 5-13, 5-14, 5-23, 5-24, and 5-34 are formed of Au Schottky gates, and electrically couple two adjacent parametric mechanical resonators together. To do.

  The coupling wiring 5-12 is connected to the electrode 12-1 of the parametric mechanical resonator 1b-1 and the electrode 12-2 of the parametric mechanical resonator 1b-2, and the coupling wiring 5-13 is connected to the parametric mechanical resonator. The connection wiring 5-14 is connected to the electrode 13-1 of the parametric mechanical resonator 1b-1 and the electrode 17-1 of the parametric mechanical resonator 1b-1, and is connected to the electrode 12-1 of the parametric mechanical resonator 1b-3. The coupling wiring 5-23 is connected to the electrode 13-2 of the parametric mechanical resonator 1b-2 and the electrode 13-3 of the parametric mechanical resonator 1b-3. The coupling wiring 5-24 is connected to the electrode 17-2 of the parametric mechanical resonator 1b-2 and the electrode 12-4 of the parametric mechanical resonator 1b-4, and the coupling wiring 5-3. Is connected to the electrode 17-4 parametric mechanical resonator 1b-3 of the electrode 17-3 and the parametric mechanical resonator 1b-4. Note that an insulating layer 18 is formed between the coupling wires 5-14 and the coupling wires 5-23 so as not to be in electrical contact with each other.

  In the structure of the present embodiment, it is possible to couple parametric mechanical resonators in various directions in the plane by the isotropic shape of the membrane type parametric mechanical resonator. It can be said that the structure is more suitable for the configuration.

  In the first and second embodiments, the case where there are three parametric mechanical resonators and the case where there are four parametric mechanical resonators in the third embodiment has been described. However, as many electrodes and coupling portions as necessary are formed. Thus, it goes without saying that a similar Ising machine can be formed for any number of parametric mechanical resonators.

  In the first to third embodiments, the parametric mechanical resonator that causes frequency modulation by the piezoelectric effect is used. However, any kind of parametric mechanical resonator such as an electrostatic interaction or light irradiation is used. On the other hand, it goes without saying that an Ising machine can be formed by similarly introducing linear coupling between resonators.

  In the first to third embodiments, a GaAs / AlGaAs heterostructure material is used as a material constituting the beam and the vibration part. However, any solid material that can be frequency-modulated by applying a voltage is used. It can be used as a material for beams and vibrating parts. In the first to third embodiments, the piezoelectric effect is used as a mechanism for parametric excitation and signal detection, but an electrostatic effect and Lorentz force (magnetic interaction) can also be used.

  In the first to third embodiments, an example in which vibration modes are electrically mixed has been described. However, for example, when thermal stress is used, the same effect can be obtained by irradiating light. Needless to say, the present invention is not limited to this, and any method that can control the frequency of two mechanical resonances from the outside can be used.

  Further, in the first to third embodiments, the case where the resonance frequencies of the plurality of parametric mechanical resonators all coincide with each other is shown, but even when the resonance frequencies are different, the literature “Hajime Okamoto, Adrien Gourgout, Difference frequency and sum frequency as shown in Chia-Yuan Chang, Koji Onomitsu, Imran Mahboob, Edward Yi Chang, Hiroshi Yamaguchi, “Coherent phonon manipulation in coupled mechanical resonators”, Nature Physics, 9, 598, 2013. It is also possible to use parametric coupling, which provides coupling between different resonators by providing

  The present invention can be applied to a technique for obtaining a solution to a problem for a set of input numerical values.

  DESCRIPTION OF SYMBOLS 1, 1a, 1b ... Parametric mechanical resonator, 2 ... Oscillator, 3 ... Lock-in amplifier, 4 ... Operation processing part, 5 ... Coupling wiring, 6 ... Coupling part, 10 ... Beam, 11-13, 17 ... Electrode, Reference numerals 14 and 15 are support parts, 16 are vibration parts, and 18 are insulating layers.

Claims (8)

An arithmetic device that obtains a solution to a problem by using an Ising machine in which a plurality of mechanical resonators including a vibrating portion arranged with a space between the substrate and a substrate are coupled,
A plurality of mechanical resonators coupled together;
Excitation means capable of simultaneously parametrically exciting the vibration parts of the plurality of mechanical resonators, and individually controlling the excitation amplitude and the excitation phase for each mechanical resonator;
Detecting means for individually detecting vibration phases of the plurality of mechanical resonators;
Computation processing means that regards the vibration phases of the plurality of mechanical resonators as corresponding to the Ising spin state, and substitutes a value representing the Ising spin state into a predetermined equation to obtain a solution to the problem, Arithmetic unit to do. The arithmetic unit according to claim 1,
The arithmetic processing means regards a set of vibration phases that appears most frequently among a set of vibration phases of the plurality of mechanical resonators as corresponding to the Ising spin state, and sets a value representing the Ising spin state to a predetermined formula An arithmetic unit characterized by substituting into and obtaining a solution to the problem. In the arithmetic unit according to claim 1 or 2,
And a coupling means that is arranged with a space between the substrate on which the plurality of mechanical resonators are formed, and couples the vibrating portions of the adjacent mechanical resonators,
An arithmetic unit characterized in that the plurality of mechanical resonators are coupled by mutually propagating mechanical vibrations between adjacent mechanical resonators by deformation of the coupling means according to mechanical vibrations of the mechanical resonators. . In the arithmetic unit according to claim 1 or 2,
A computing device using a piezoelectric material as a material constituting a vibration part of the plurality of mechanical resonators. The arithmetic unit according to claim 4, wherein
Furthermore, a wiring for electrically coupling the vibration parts of adjacent mechanical resonators is provided,
Coupling the plurality of mechanical resonators by mutually applying a voltage generated by a piezoelectric effect corresponding to the mechanical vibration of the mechanical resonators between adjacent mechanical resonators via the coupling wiring; Arithmetic unit characterized. In the arithmetic unit according to claim 1 or 2,
The excitation means excites the vibration parts of the plurality of mechanical resonators using any one of a force due to a piezoelectric effect, a thermal stress due to light irradiation, an electrostatic force, or a Lorentz force,
The detecting means converts a mechanical vibration of the plurality of mechanical resonators into an electric signal using any one of a piezoelectric effect, a thermal stress effect by light irradiation, an electrostatic effect, and a magnetic interaction, and the plurality of mechanical resonances. An arithmetic device characterized by detecting a vibration phase of a vessel. The arithmetic device according to any one of claims 1 to 6,
The arithmetic apparatus according to claim 1, wherein the problem is a division problem that determines whether N (N is an integer of 2 or more) integers can be divided into two sets in which the sum of the numbers in the set is equal to each other. An arithmetic method for obtaining a solution to a problem by using an Ising machine in which a plurality of mechanical resonators including a vibrating portion arranged with a space between the substrate and a substrate are coupled,
An excitation step of simultaneously parametrically exciting the plurality of mechanical resonators and individually controlling an excitation amplitude and an excitation phase for each mechanical resonator;
A detection step of individually detecting vibration phases of the plurality of mechanical resonators;
An operation processing step that regards vibration phases of the plurality of mechanical resonators as corresponding to the Ising spin state, and substitutes a value representing the Ising spin state into a predetermined equation to obtain a solution to the problem. Calculation method to be performed.

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