JP2019219667A - Resonator and quantum computer - Google Patents

Abstract

To increase the success probability of quantum gate operation.SOLUTION: A resonator according to one embodiment comprises a spherical mirror attached to a birefringent crystal that includes a physical system within and a plane mirror attached to a birefringent crystal facing the spherical mirror, and has a resonator mode that combines with the physical system. The birefringent crystal has a first refractive index to a light polarized to a first direction parallel to the direction of polarization in the resonator mode on the optical axis of the resonator and a second refractive index to a light polarized to a second direction parallel to the optical axis and different from the first refractive index, and the equation lA/L=ωπn/λ is satisfied, where l represents the resonator length of the resonator, ω represents the mode west radius of the resonator mode, L represents the total loss per reciprocation of the resonator, A represents the loss per reciprocation of the resonator independent of the resonator length, nrepresents a second refractive index, and λ represents the wavelength of light of the resonator mode.SELECTED DRAWING: Figure 1

Description

  An embodiment of the present invention relates to a resonator coupled to a physical system and a quantum computer using the resonator.

  In recent years, quantum computers using coupling between a resonator and a physical system arranged in the resonator have been actively studied. In such a quantum computer, a physical system coupled to a common resonator mode of the resonator is used as a qubit. Quantum computers perform calculations by introducing interactions between qubits by resonating the qubits into a common resonator mode, and manipulating the qubits with light in that state. In quantum computers, it is required to increase the probability of successful operation of a qubit by light called quantum gate operation.

JP-A-8-148739

T. Pellizzari et al., Phys. Rev. Lett. 75, 3788 (1995) H. Goto et al, Opt. Exp. 21 20 24 332 (2013)

  The problem to be solved by the present invention is to provide a resonator and a quantum computer that can increase the probability of successful quantum gate operation.

A resonator according to one embodiment includes a spherical mirror mounted on a birefringent crystal including a physical system therein, and a plane mirror mounted on the birefringent crystal facing the spherical mirror. The resonator has a resonator mode coupled to the physical system. The birefringent crystal has a first refractive index for light polarized in a first direction parallel to a polarization direction of the resonator mode on the optical axis of the resonator, and is different from the first refractive index. And a second refractive index for light polarized in a second direction parallel to the optical axis. The resonator length of the resonator is l, the mode waist radius of the resonator mode is ω, the total loss per round trip of the resonator is L, the loss per round trip of the resonator independent of the resonator length Is represented by A, the second refractive index is represented by n _z , and the wavelength of light in the resonator mode is represented by λ, the following expression is satisfied.

FIG. 2 is a cross-sectional view illustrating the resonator according to the first embodiment. FIG. 2 is a perspective view showing the resonator according to the first embodiment. The figure which shows a refractive index ellipsoid. FIG. 3 is a diagram illustrating a range of design parameters of the resonator according to the first embodiment. FIG. 3 is a diagram illustrating a range of design parameters of the resonator according to the first embodiment. FIG. 9 is a block diagram illustrating a quantum computer according to a second embodiment. (A) and (b) are a top view and a front view showing an example of the resonator concerning a 2nd embodiment. (A) and (b) are the top view and the front view which show other examples of the resonator concerning a 2nd embodiment. (A) and (b) are the top view and the front view which show other examples of the resonator concerning a 2nd embodiment. FIG. 11 is a top view showing another example of the resonator according to the second embodiment. (A) and (b) are the top view and the front view which show other examples of the resonator concerning a 2nd embodiment. FIG. 9 is a schematic diagram illustrating a relationship between a change direction of operation light and a wavefront in a resonator mode according to the second embodiment. FIG. 9 is a schematic diagram illustrating a relationship between a change direction of operation light and a wavefront in a resonator mode according to the second embodiment. FIG. 4 is a diagram for explaining direction dependency of scattered light intensity. (A) And (b) is a figure for explaining the direction of the crystal axis of the solid medium in the resonator concerning Example 3. (A) And (b) is a figure for demonstrating the size of the mode which arises in the solid medium shown in FIG. FIG. 13 is a diagram illustrating a quantum computer according to a comparative example related to the third embodiment. FIG. 13 is a perspective view showing a resonator according to a third embodiment. FIG. 9 is a diagram illustrating a quantum computer according to a third embodiment.

  Hereinafter, various embodiments will be described with reference to the drawings. In the following embodiments, the same components are denoted by the same reference numerals, and redundant description will be omitted as appropriate.

[First Embodiment]
2. Description of the Related Art A quantum computer is known which includes a monolithic resonator in which mirrors are attached to a birefringent crystal face to face, and uses the coupling between a resonator and a physical system included in the birefringent crystal. In such a resonator, it is desired that the resonator mode and the physical system are efficiently coupled. This can be achieved by reducing the resonator loss and reducing the resonator relaxation rate (the rate at which energy in the resonator mode is lost per unit time). The resonator loss includes a loss caused by coupling between modes (hereinafter, referred to as a mode coupling loss). In the present embodiment, a method for reducing the mode coupling loss will be described. By using a resonator in which a resonator mode and a physical system are efficiently coupled to a quantum computer, it is possible to improve the probability of successful operation of a quantum gate such as a quantum gate based on an adiabatic passage.

  1 and 2 are a sectional view and a perspective view schematically showing a resonator 10 according to the first embodiment. The resonator 10 is mounted on a surface 15 of the birefringent crystal 11 facing the spherical mirror 12 and a spherical mirror 12 mounted on the surface 14 of the birefringent crystal 11 as shown in FIGS. And a plane mirror 13. R shown in FIG. 2 represents the radius of curvature of the spherical mirror 12.

The birefringent crystal 11 includes a physical system (for example, an atom or an ion) that is coupled to a common resonator mode of the resonator 10. In the present embodiment, the direction parallel to the optical axis of the resonator 10 is defined as the z-axis direction, and the polarization direction of the common resonator mode on the optical axis of the resonator 10 is defined as the x-axis direction. Here, the polarization direction indicates the direction of the electric field vector of light. In birefringent crystal 11, the refractive indices n _x to light (light electric field vector is oriented in the x-axis direction) polarized in the x axis direction is different from the refractive index n _z for light polarized in the z-axis direction. In this resonator 10, a mode waist is formed on the plane mirror 13. The mode waist refers to a place where the spot size of the resonator mode becomes the smallest.

  In the present embodiment, conditions (resonator length and mode waist radius) of a resonator that can suppress mode coupling loss generated in the resonator 10 are provided. First, the mode coupling loss in the birefringent crystal is formulated. For that purpose, (1) the refractive index of the birefringent crystal with respect to the wave number vector is obtained, (2) the electric field distribution of the resonator mode is obtained, (3) the spot size of the resonator mode and the radius of curvature of the wavefront are obtained, and (4) 2.) Find the spatial distribution of the refractive index of the birefringent crystal, and find the mode coupling constant for the resonator length and mode waist radius, and the figure of merit of the arithmetic element. Subsequently, from the mode coupling loss formulated by such a procedure, (5) conditions for suppressing the mode coupling loss and obtaining high operation element performance are obtained.

(1) Refractive index distribution (wave number distribution)
Since the refractive index in a birefringent crystal varies depending on the polarization direction, the refractive index also varies depending on the wave vector. Therefore, the refractive index when an arbitrary wave number vector is given is formulated. The index ellipsoid 30 of the coordinate system shown in FIG. 3 is represented by the following equation.

  Using this θ, the distance r from the origin of the cut ellipse is expressed by the following equation.

(2) Formulation of the electric field distribution in the resonator mode Using the relationship between the refractive index and the wave number formulated in this way, the electric field distribution in the resonator mode is integrated as follows (Fresnel-Kirchhoff diffraction integral). Is represented by

To perform this integration, to expand the coefficients of z exponent until secondary k _x and k _y. Direction of the wave vector in the vicinity of the optical axis of the resonator modes for near the z-axis direction, k _x and k _y is smaller than the wave number, such approximation is reasonable. electric field distribution of the resonator mode and developed up to the second order of k _x and k _y are as follows.

(3) Formulation of spot size and radius of curvature of wavefront The spot size of the mode and the radius of curvature of the wavefront at each point on the z-axis (optical axis) are obtained from the electric field distribution of the resonator mode. Mode j of x ² and y ² sections and the spot size ω _jx, ω _jy and wavefront radii of curvature R _jx, the relationship between the R _jy is expressed by the following equation.

Therefore, the spot size and the radius of curvature of the wavefront are expressed by the following equations.

(4) Refractive index distribution (spatial distribution), mode coupling constant, and figure of merit of arithmetic element A resonator made of a medium having birefringence has a refractive index distribution in the medium corresponding to the resonator mode. . When such a refractive index distribution exists, the spatial mode (transverse mode) of each polarized light is coupled to each other. Therefore, a coupling constant and a mode coupling loss when the fundamental mode is coupled with an infinite number of higher-order modes are obtained. Further, a performance index of a quantum operation device using such a resonator is formulated. Here, the coupling constant of the mode coupling is proportional to a value obtained by integrating a value obtained by multiplying the refractive index distribution _ni (x, y, z) by the electric field intensity E (x, y, z) over the entire space. At this time, since it is assumed that there are an infinite number of higher-order modes coupled to the fundamental mode, the effective coupling constant representing the sum of couplings of all higher-order modes does not depend on the type or number of coupled higher-order modes. Further, the refractive index distributions in the x and y axis directions are represented by the same function having a different width for each z due to the nature of the Gaussian beam. Therefore, by determining the refractive index distribution n _si (z) on the spot size of each z, the coupling constant can be determined as in the following equation.

Spatial distribution of the refractive index at each position can be determined from k _y / k _z and k _x / k _z wave vectors. The k _y / k _z on the spot size of each z and tangent slope of the curve connecting the spot size of each z in the plane of x = 0, the spot of each z in the plane of k _x / k _z a y = 0 The slope of the tangent to the curve connecting the sizes. This is obtained by differentiating ω _1x (z) with z. From such a k obtained by _y / k _z and k _x / k _z, the following equation can be obtained a spatial distribution of the refractive index on the spot.

Coupling between modes occurs due to such a refractive index distribution. The coupling constant is obtained as in the following equation.

Here, assuming that f (l) is the sum of the loss per resonator length other than the mode coupling loss and the transmittance of the mirror, the loss per resonator length of the resonator is expressed by the following equation.

Here, L ₀ is a coefficient obtained by recalculating all proportional coefficients relating to inter-mode coupling. Using this, the cavity relaxation rates κ ₁ and κ ₂ for each polarization mode are represented by the following equations.

The performance index n _ai that determines the performance of the resonator as an arithmetic element can be expressed by the following equation.

The figure of merit indicates that the smaller the value is, the higher the performance of the arithmetic element is. The figure of merit n _ai is expressed by the following equation using the above κ ₁ and κ ₂ .

Here, c _i is a constant obtained by recalculating the coefficients of γ and g for ω ² and the coefficient of κ _i .

(5) Conditions under Which Loss can be Suppressed and High Arithmetic Element Performance Can be Obtained From the equation of the performance index n _ai of the resonator thus determined, conditions for suppressing loss and improving the performance as an arithmetic element are examined. First, a condition for obtaining the optimum operation element performance when the loss other than the mode coupling loss does not depend on the resonator length (f (l) = AL ₀ ) is examined. In this case, n _ai is represented by the following equation.

By differentiating these equations, the optimum resonator length l is expressed by the following equation.

Further, as apparent from FIG. 4, the range of up to 2 times the half of the cavity length l optimum cavity length _{l 0 (0.5l 0 ≦ l ≦} 2l 0), the change in performance index n _a small That is, the loss due to inter-mode coupling is effectively suppressed. Therefore, the resonator may be designed so that 0.5l ₀ ≦ l ≦ 2l ₀ is satisfied.

In addition, when the loss other than the mode coupling loss is proportional to the resonator length (f (l) = BlL ₀ ), conditions for obtaining the optimum operation element performance are examined. In this case, n _ai is represented by the following equation.

By differentiating this equation, the optimum resonator length is expressed by the following equation.

Furthermore, even ranges of up to two times half the cavity length l optimum cavity length _{l 0 (0.5l 0 ≦ l ≦} 2l 0), losses due to inter-modal coupling is effectively suppressed. Therefore, the resonator may be designed so that 0.5l ₀ ≦ l ≦ 2l ₀ is satisfied.

  Such a condition can be obtained by a method similar to the above method even when the loss other than the mode coupling loss is represented by a more general function. The example shown here is merely an example. By formulating the mode coupling loss for the various resonators using the analysis method described above, the loss of the resonator mode of the resonator attached to the birefringent crystal can be obtained. Can be obtained.

(Example 1)
In the first embodiment, an example of the resonator in the case where the loss other than the mode coupling loss does not depend on the resonator length will be described.

As shown in FIG. 1, the resonator according to the first embodiment includes a Y ₂ SiO ₅ crystal (Pr: YSO) doped with Pr ³⁺ ions as a birefringent crystal 11 and a surface 14 of the Y ₂ SiO ₅ crystal. Is a monolithic Fabry-Perot resonator including a spherical mirror 12 disposed on a surface mirror 13 disposed on a surface 15 of a Y ₂ SiO ₅ crystal. The spherical mirror 12 and the plane mirror 13 are arranged such that the b axis of the crystal axes (b axis, D ₁ axis, D ₂ axis) of the Y ₂ SiO ₅ crystal is in the optical axis (z axis) direction of the resonator. is, the polarization direction of the resonator mode at the optical axis (x-axis direction) is used such that D ₂ axially. When the wavelength of the light with 606 nm, the refractive index of the polarization of the D ₂ axis direction is about 1.81, the refractive index of the b-axis direction of the polarized light is about 1.79. The spherical mirror 12 is manufactured by polishing the surface 14 of the Y ₂ SiO ₅ crystal so that the radius of curvature is R = 2.000 mm, and forming a dielectric multilayer film on the polished surface 14. The Y ₂ SiO ₅ crystal is processed so that the resonator length becomes 0.173 mm. The plane mirror 13 is manufactured by forming a dielectric multilayer film on the surface 15 that has been planarly polished. Thereby, the mode waist radius becomes 5 μm.

The resonator processed in this manner has the above-described mode when, for example, there is a loss of about AL ₀ = 0.01% on the spherical mirror 12 and the loss BlL ₀ in the birefringent crystal is negligible. The condition for suppressing the coupling loss is satisfied. Also, such machined resonators has, for example, a BLL ₀ = about 0.01% loss in the birefringent crystal, and, even when the loss AL ₀ in on the spherical mirror 12 is only negligibly Satisfy the condition for suppressing the mode coupling loss described above. Therefore, according to the resonator according to the first embodiment, mode coupling loss can be suppressed.

(Example 2)
Example 2 In Example 2, a quantum computer using the resonator according to the first embodiment will be described.
FIG. 6 schematically illustrates a quantum computer according to the second embodiment. The quantum computer shown in FIG. 6 includes the resonator 10 shown in FIG. The resonator 10 includes a Pr ³⁺ : Y ₂ SiO ₅ crystal as a birefringent crystal 11. The resonator 10 is installed in the cryostat 68 and kept at a low temperature (for example, at 4K).

  The quantum computer includes a light source device that generates operation light for operating a physical system that carries a qubit, and irradiates the operation light with the physical system. The light source device includes a semiconductor laser 60, a beam splitter 61, a mirror 62, acousto-optic devices 63 and 64, mirrors 65 and 66, a lens 67, and a control device 69. The laser light output from the semiconductor laser 60 is split into two by a beam splitter 61. One of the split laser beams enters the acousto-optic device 63, and the other is reflected by the mirror 62 and enters the acousto-optic device 64. The acousto-optic devices 63 and 64 modulate the frequency and intensity of the laser light according to the control signal generated by the control device 69. The laser light modulated by the acousto-optic element 63 is guided by mirrors 65 and 66 and a lens 67 so as to irradiate the resonator 10. The laser light modulated by the acousto-optic element 63 is guided by the lens 67 so as to irradiate the resonator 10. A quantum computer can execute a quantum gate by selectively operating two qubits by irradiation of these two laser beams.

  The quantum computer according to the second embodiment performs a quantum gate operation using a resonator in which the resonator mode of the resonator and the physical system included in the birefringent crystal arranged in the resonator are efficiently coupled. Thereby, the probability of success of the quantum gate operation can be improved.

[Second embodiment]
When a quantum gate operation error occurs from a specific cause in a quantum computer that operates the physical system that carries the qubit with light and introduces interaction between the physical systems by resonating the physical system with a common resonator mode In addition, a method for suppressing the influence of the error on information processing is known. Here, the error of the quantum gate operation corresponds to the fact that the actual quantum state of the qubit after the quantum gate operation is different from the quantum state of the qubit expected after the quantum gate operation. For example, a conditional quantum gate that changes the quantum state of another qubit according to the quantum state of another qubit, or a quantum gate called a two-qubit gate is executed by a method called an adiabatic passage by operating light, In doing so, either the photon is lost by spontaneous emission from the physical system that carries the qubit, or the photon in the cavity mode necessary to introduce an interaction between the physical systems that carry the qubit is lost. Errors may occur. The photons lost in this way are called lost photons. In these cases, a quantum computer is configured to detect a lost photon while performing a quantum gate operation for error correction, and the quantum computer employs an information processing result when no lost photon is detected. Thereby, the influence of the error on the information processing can be suppressed efficiently.

  However, if the qubit is in a solid medium, the operation light is scattered in the solid medium or at the interface between the outside and the solid medium, and scattered light stronger than the lost photons reaches the photodetector, and the scattered light due to the operation light Differentiation from lost photons becomes difficult. Therefore, a lost photon cannot be correctly detected. Therefore, even if the lost photons are not actually lost, the information processing result may be discarded due to the scattered light, that is, the quantum gate operation may be considered to have failed .

  In the second embodiment, when a physical system in a solid medium is used as a qubit, a method for correctly detecting a lost photon without being affected by scattering of operation light for operating the qubit. I will provide a.

  FIGS. 7A and 7B are a top view and a front view schematically showing an example of a resonator 70 used in the quantum computer according to the second embodiment. As shown in FIGS. 7A and 7B, the resonator 70 is attached to the solid medium 71, the spherical mirror 72 attached to the solid medium 71, and the solid medium 71 facing the spherical mirror 72. Spherical mirror 73. The solid medium 71 includes a physical system that resonates in a common resonator mode of the resonator 70 therein. The solid medium 71 has regions having different thicknesses in the traveling direction of the operation light for operating the physical system that carries the qubit. Hereinafter, unless otherwise specified, the thickness refers to the thickness in the traveling direction of the operation light. In FIG. 7A, the operation light travels from the entrance surface 77 to the exit surface 78. Specifically, the solid medium 71 includes a thin region 74, a thick region 76 adjacent to the spherical mirrors 72 and 73, and a tapered region 75 between the region 74 and the region 76. And The physical system located in the region 74 is used as a qubit, and a part of the region 74 is irradiated with operation light. Hereinafter, the region 74 is referred to as an irradiation region. The operation light is emitted, for example, from a light source device as shown in FIG.

  The physical system that carries the qubit resonates in a common resonator mode and interacts with the two-qubit gate via the photons present in that resonator mode. The solid medium 71 is partially thinned in such a range that the influence of the resonator mode on the photon lifetime does not hinder the implementation of the two-qubit gate.

  The total amount of the scattered light generated by the operation light inside the solid medium 71 is determined when the solid medium 71 is a general uniform transparent medium and the total amount of the scattered light is a small portion (for example, 10% or less) of the incident light. Is substantially proportional to the optical path length of the operation light inside the solid medium 71. The solid medium 71 can be such a transparent medium. The solid medium 71 is formed such that the irradiation region 74 is thinner than the neighboring regions 75 and 76 so that the optical path length of the operation light inside the solid medium 71 is short. Thereby, generation of scattered light can be reduced.

  FIGS. 8A and 8B are a top view and a front view schematically showing another example of a resonator 80 used in the quantum computer according to the second embodiment. As shown in FIGS. 8A and 8B, the resonator 80 is attached to a solid medium 81, a spherical mirror 82 attached to the solid medium 81, and a solid medium 81 opposed to the spherical mirror 82. A flat mirror 83. The solid medium 81 includes therein a physical system that resonates in a common resonator mode of the resonator 80. The solid medium 81 includes an irradiation region 84 having a small thickness adjacent to the plane mirror 83, a region 86 having a large thickness adjacent to the spherical mirror 82, and a region 85 expanding in a taper shape between the irradiation region 84 and the region 86. And

  FIGS. 9A and 9B are a top view and a front view schematically showing another example of a resonator 90 used in the quantum computer according to the second embodiment. The resonator 90 shown in FIGS. 9A and 9B is a toroidal or disk resonator having a resonator mode called a whispering gallery mode. The resonator 90 includes a disk-shaped solid medium 91. The solid medium 91 is connected to a tapered optical fiber (not shown) for inputting and outputting light. The solid medium 91 includes therein a physical system that resonates in a common resonator mode of the resonator 90. This resonator mode exists inside the solid medium 91 along the outer periphery of the solid medium 91. The solid medium 91 includes an irradiation region 94 having a small thickness along the outer circumference, and a region 95 having a large thickness located inside the irradiation region 94.

  FIG. 10 is a top view schematically showing another example of the resonator 100 used in the quantum computer according to the second embodiment. As shown in FIG. 10, the resonator 100 includes a solid medium 101 and spherical mirrors 102, 103, and 104 attached to the solid medium 101. The solid medium 101 includes therein a physical system that resonates in a common resonator mode of the resonator 100. This resonator mode exists between the spherical mirror 102 and the spherical mirror 103, between the spherical mirror 103 and the spherical mirror 104, and between the spherical mirror 102 and the spherical mirror 104. The irradiation area 105 of the solid medium 101 is formed thinner than other nearby areas.

  The resonator 80 shown in FIGS. 8A and 8B, the resonator 90 shown in FIGS. 9A and 9B, and the resonator 100 shown in FIG. ) And (b) have a shape in which the optical path length of the operation light inside the solid medium is shortened, thereby reducing the generation of scattered light. Can be.

  Additional scattered light may be generated as described below. For example, in the resonator 70 shown in FIG. 7, the operation light enters the solid medium 71 through the incident surface 77, passes through the solid medium 71, and is emitted out of the solid medium 71 through the emission surface 78. At this time, part of the operation light is reflected by the emission surface 78 and passes through the solid medium 71 again. In this case, further scattered light is generated inside the solid medium 71 by the reflected light from the emission surface 78. When the reflected light reaches the incident surface 77, most of the reflected light is emitted to the outside of the solid medium 71 through the incident surface 77, but a part of the reflected light is reflected by the incident surface 77 and Pass again. Further scattered light is generated inside the solid medium 71 by the reflected light from the incident surface 77. Further, the operation light emitted from the emission surface 78 may re-enter the solid medium 71, for example, being reflected by some object. Further scattered light is generated inside the solid medium 71 due to the operation light reentering the solid medium 71. A mechanism for preventing the generation of further scattered light as described above will be described.

  FIGS. 11A and 11B are a top view and a front view schematically showing another example of the resonator 110 used in the quantum computer according to the second embodiment. As shown in FIGS. 11A and 11B, the resonator 110 includes a solid medium 71, spherical mirrors 72 and 73 attached to the solid medium 71 so as to face each other, and an incident surface 77 of an irradiation area 74. , An anti-reflection coating 112 applied to the emission surface 78 of the irradiation area 74, and an optical trap 113 provided to face the anti-reflection coating 112. The optical trap 113 is provided before the antireflection coating 112 in the traveling direction of the operation light. Note that the solid medium 71 is not limited to the example in which the irradiation area 74 as shown in FIG. 11A has a thinner shape than the neighboring areas 75 and 76. For example, as in the resonator 10 shown in FIG. The irradiation region 74 may have the same thickness as the other regions 75 and 76.

  The anti-reflection coatings 111 and 112 prevent internal reflection. Specifically, the anti-reflection coating 112 prevents the operation light traveling in the solid medium 71 from being reflected on the emission surface 78. By providing the anti-reflection coating 112, the operation light reflected on the emission surface 78 is reduced. The anti-reflection coating 111 prevents the operation light, which is reflected on the emission surface 78 and travels in the solid medium 71, from being reflected on the incident surface 77. By providing the anti-reflection coating 111, the operation light reflected on the incident surface 77 is reduced.

  In the example shown in FIGS. 11A and 11B, the anti-reflection coating is applied to both the entrance surface 77 and the exit surface 78. It is not limited to. For example, the anti-reflection coating may be applied to only one of the entrance surface 77 and the exit surface 78. Preferably, the exit surface 78 is provided with an anti-reflective coating. Further, the anti-reflection coating may be applied to portions other than the entrance surface 77 and the exit surface 78.

  The optical trap 113 traps (traps) operation light transmitted through the solid medium 71. The provision of the optical trap 113 prevents the operation light transmitted through the solid medium 71 from being incident on the solid medium 71 again. Note that a light absorber may be used instead of the light trap 113.

  Note that the antireflection coating and the optical trap or light absorber include the resonator 80 shown in FIGS. 8A and 8B, the resonator 90 shown in FIGS. 9A and 9B, and the resonator 80 shown in FIGS. Can be applied to other resonators such as the resonator 100 shown in FIG.

  As described above, the anti-reflection coatings 111 and 112 and the optical trap 113 prevent the operation light from being multiple-reflected in the solid medium 71 to generate scattered light, and once out of the solid medium 71. This prevents the operation light from returning to the solid medium 71 again to generate scattered light, and prevents the operation light that has exited the solid medium 71 from reaching any scatterer and generating scattered light. As a result, it is possible to prevent the scattered light from reaching the photodetector that detects the lost photons. Furthermore, when the scattered light generated in the solid medium 71 reaches the entrance surface 77 or the exit surface 78, it can be prevented from being reflected by the entrance surface 77 or the exit surface 78 and returning to the solid medium 71 again. .

  In the present embodiment, the polarization direction of the operation light can be set to a direction that intersects (for example, is orthogonal to) the wavefront of the resonator mode. The polarization direction refers to the direction of the electric field vector of light. FIGS. 12A and 12B show the polarization direction of the operation light in the Fabry-Perot resonator 70 shown in FIGS. 7A and 7B set to a direction orthogonal to the wavefront of the resonator mode. It shows the situation. FIGS. 13 (a) and 13 (b) show that, in a resonator 130 such as the resonator 90 shown in FIGS. 9 (a) and 9 (b), the polarization direction of the operation light is in a direction orthogonal to the wavefront of the resonator mode. This shows how it is set. In the solid medium 131 of the resonator 130, the irradiation region has the same thickness as the region in the vicinity. When the polarization direction of the operation light is set to a direction orthogonal to the wavefront in the resonator mode, scattered light is less likely to be generated in a direction orthogonal to the wavefront in the resonator mode. The reason will be described later.

  It is assumed that lost photons are mainly lost from an input / output unit between light in the resonator mode and light outside the resonator. For example, in the case of a Fabry-Perot resonator, lost photons are lost from mirrors (for example, the spherical mirror 72 or the spherical mirror 73) constituting the resonator. In the case of a toroidal or disk resonator, lost photons are lost through the tapered optical fibers for input and output. In these cases, since the spatial mode (location and traveling direction) outside the resonator mode of the lost photons exiting the solid medium from the resonator mode is clear, the photodetector is adjusted to the spatial mode. Alternatively, it is considered that a photon detector is installed, that is, it is installed near a mirror constituting the resonator or at an end face of the tapered optical fiber for input / output. At that time, by setting the polarization direction of the operation light to a direction orthogonal to the wavefront of the resonator mode, the possibility that photons that are not lost photons, that is, scattered light generated by the operation light, reach the photodetector is greatly increased. Can be reduced.

Next, the reason why the polarization direction of the operation light is set to a direction orthogonal to the wavefront of the resonator mode, so that scattered light is less likely to be generated in the direction orthogonal to the wavefront of the resonator mode will be described.
When the scatterer is irradiated with light and generates scattered light, the intensity distribution of the scattered light largely depends on the traveling direction of the irradiated light and its polarization direction. The dependency will be described with reference to FIG. As shown in FIG. 14, it is assumed that irradiation light traveling in the z-axis direction has an electric field vector oscillating in the y-axis direction. When scattered light is generated by scattered irradiation light by the scatterer, the direction of the dipole moment induced by the scatterer is also in the y-axis direction. Electromagnetic waves emitted from this dipole moment are scattered light, and the intensity in the far field is strong in scattered light traveling in the z-axis and x-axis directions, and weak in scattered light traveling in the y-axis direction. Become. Assuming that the angle between the y-axis direction and the direction from the scatterer to the observation point where the intensity of the scattered light is observed is θ, the intensity (power) per unit solid angle is proportional to sin ² θ. Therefore, by setting the polarization direction of the operation light to a direction orthogonal to the wavefront of the resonator mode, scattered light is less likely to be generated in the direction orthogonal to the wavefront of the resonator mode.

  As described above, when the antireflection coating is provided on the irradiation area, the scattered light generated in the solid medium comes out of the solid medium without being reflected at the interface between the solid medium and the outside. In addition, when the polarization direction of the operation light is set to a direction orthogonal to the wavefront of the resonator mode, the direction in which the scattered light exiting the solid medium becomes stronger depends on the wavefront of the resonator mode including the operation light irradiation spot of the solid medium. Is limited to the in-plane direction. For this reason, by providing an anti-reflection coating on the irradiation area and setting the polarization direction of the operation light to a direction orthogonal to the wavefront of the resonator mode, the loss photons are reduced to the light in the resonator mode and the light outside the resonator. If the operating light is lost from other than the input / output unit between the two, for example, if it is lost due to spontaneous emission from the physical system that carries the scattered light or the qubit in the resonator mode, the operating light is scattered by the solid medium. The effect of the scattered light generated can be avoided, and the arrangement of the photodetector for detecting the lost photons more accurately can be selected.

  As described above, according to the present embodiment, (1) the irradiation region of the solid medium is formed thinner than other nearby regions, (2) the antireflection coating and the light trap or light absorber are provided, and (3) setting the polarization direction of the operation light in a direction that intersects the wavefront of the resonator mode, by employing at least one of the above, the influence of the scattering of the operation light for operating the qubit. Can correctly detect a lost photon without using the same.

(Example 3)
In the quantum computer according to the third embodiment, the quantum state of the nuclear spin of Pr ³⁺ ions in the Y ₂ SiO ₅ crystal is used as the qubit.
The solid medium 151 including the qubit shown in FIGS. 15A and 15B is prepared as follows. A 3 mm cube of Pr ³⁺ : Y ₂ SiO ₅ crystal in which 10 ^-6 % of the Y ³⁺ ions in the Y ₂ SiO ₅ crystal were replaced with Pr ³⁺ ions was prepared, and one of the cubes was formed. The surface is machined into a spherical surface with a radius of curvature of 3.3 mm that is in contact with the center of the surface. At this time, the direction of the crystal axis of the Pr ³⁺ : Y ₂ SiO ₅ crystal is set as follows. The crystal is oriented in a direction perpendicular to a straight line connecting the center of the spherical surface (referred to as point O) and the center of the plane facing the spherical surface (referred to as point B), and perpendicular to any of the four planes contacting the spherical surface. Set the B axis. The D2 axis is not parallel or orthogonal to the straight line connecting the points O and B.

As shown in FIG. 16, when the dielectric multilayer mirrors 162 and 163 are formed on the spherical surface of the solid medium 151 and a plane facing the spherical surface, a resonator mode occurs in the solid medium 151. The point of intersection of the straight line connecting points O and B and the spherical surface formed on the crystal is referred to as point A. Of TEM ₀₀ mode occurring along a straight line AB connecting the point A and point B, ³ H ₄ of Pr ³⁺ ions - the ¹ D ₂ transition resonator mode 494.7THz vicinity of the resonance, physical responsible for qubit It is used to introduce an interaction between systems (between Pr ³⁺ ions). This resonator mode has a mode waist at point B where the thickness of the mode is minimum, and the mode waist radius (mode radius) is about 10 μm. In the vicinity of the mode waist, the wavefront of the mode is substantially flat. At the point A, the mode radius becomes the maximum of 33 μm.

The magnitude of the interaction (coupling constant) between the resonator mode and the Pr ³⁺ ion becomes stronger as it approaches the straight line AB and as the mode radius becomes smaller. Therefore, ions near point B are used as qubits. In the case of the present embodiment, the end face of the solid medium 151 and the dielectric multilayer mirror 163 are located at the position of the mode waist. In order to prevent the operation light from being scattered by the end face of the solid medium 151 or the dielectric multilayer mirror 163, the ion at the point C moved in the direction of the point A by about 500 μm from the point B is used as the qubit. In the case of the present embodiment, the mode waist radius 10 μm is sufficiently larger than the wavelength of the resonator mode (approximately 606 nm corresponding to 494.7 THz), so that the mode spread angle in the direction of the point A is small. Almost the same coupling constant is obtained. Therefore, the operation light used for the operation of the qubit is condensed to about 10 μm at the point C and irradiated, and the ions existing there are used as the qubit.

  The surface of the solid medium 151 facing the spherical surface may also be processed into a spherical surface to generate a mode waist inside the solid medium 151. For example, as a solid medium, the length (resonator length) between the point A and the point B of the solid medium 151 of the present embodiment is 6 mm, and the plane on the point B side is also located at the center of the plane. If the spheres are processed so as to be in contact with each other, and the radii of curvature of both spheres are set to 3.3 mm, a mode waist is generated at the midpoint of the line connecting the points A and B. In that case, the midpoint is irradiated with operating light, and the ions present there are used as qubits.

When the solid medium 151 is a single crystal that is substantially transparent to the operation light and the polishing accuracy of the surface on which the mirror is manufactured is sufficiently high, the interaction between the solid medium 151 and Pr ³⁺ ions carrying qubits from the solid medium 151 of this embodiment. It is considered that the main process of losing the photons required in the process is a process in which the photons exit the solid medium 151 through the mirror 162 or 163. In order to detect the lost photons lost in such a process, a pinhole 171 having a radius of 100 μm and a photodetector 173 are provided near point A and a 30 μm radius near point B is detected as shown in FIG. A pinhole 172 and a photodetector 174 are provided.

In this state, first, about 100 μW of operating light whose electric field vector is orthogonal to the straight line AB and whose electric field vector is parallel to the plane of incidence is irradiated, and the sum of the light intensities detected by the two photodetectors 173 and 174 is obtained. record the to it as I _1.

Next, a mirror of a 100 μm × 3 mm rectangle (the long side is parallel to the incident surface) sharing the center with the center of the square surface facing the spherical surface of the solid medium 151 is left, and both sides of the rectangle are left. A resonator having a structure (shown in FIG. 18) in which a square pillar is cut out so as to go to the side is prepared. As shown in FIG. 19, a pinhole 171 having a radius of 100 μm and a photodetector 173 are provided near point A as shown in FIG. Then, a 30 μm pinhole 172 and a photodetector 174 are set near point B. In the same manner as described above, by irradiating the operating light point C, record the total detected light intensity by the photodetector 173 and 174, to do it and I _2.

The ratio of I ₁ to I _{2 is} as follows, mainly due to the difference in the optical path length that the operation light travels through the solid medium 151 while generating scattered light.

Here, S is the opening area of the pinhole 171 near the point A. In the case where the resonator shown in FIG. 18 is used, the photons of the scattered light reaching the photodetectors 173 and 174 are reduced to about 1/30. That is, in the quantum computer (FIG. 19) according to the present embodiment, the operation light is scattered by the solid medium by using the solid medium 151 in which the thickness of the solid medium in the irradiation area is smaller than the thickness of other parts near the irradiation area. The effect of the resulting scattered light on accurate detection of lost photons can be reduced.

(Example 4)
The quantum computer according to the fourth embodiment differs from the quantum computer according to the third embodiment in that an anti-reflection coating is applied to the operation light incidence surface and the operation light emission surface of the solid medium 151. Due to this coating, the operation light is reflected on the emission surface and reenters the solid medium 151 to generate scattered light, or is repeatedly reflected between the emission surface and the incidence surface to generate scattered light in the solid medium. Also, the probability that the scattered light generated in the solid medium 151 reaches the exit surface or the entrance surface, is reflected, and returns to the solid medium 151 again is reduced. Therefore, according to the present embodiment, the number of photons of the scattered light reaching the photodetector can be further reduced as compared with the case of the third embodiment.

  Further, in the present embodiment, an optical trap for receiving the operation light emitted from the emission surface is provided. This reduces the effect that the operation light emitted from the emission surface hits an object or is scattered by air or fine particles in the air, reaches the photodetector, and hinders accurate detection of lost photons. The effect of the installation of the optical trap is also effective in the third embodiment and a fifth embodiment to be described later.

  As described above, in the quantum computer according to the present embodiment, the anti-reflection coating is provided on the operation light incidence surface and the operation light emission surface of the solid material, and the light trap or the light absorber is provided at the end of the emission surface, so that the operation can be performed. It is possible to reduce the influence of scattered light generated by light being scattered by a solid medium or a substance outside the solid medium preventing accurate detection of lost photons.

(Example 5)
In the fifth embodiment, in the quantum computer similar to the fourth embodiment, the polarization direction of the operation light is set so as to match the direction of the straight line AB, that is, orthogonal to the wavefront of the resonator mode at the point C. . In this case, the angle between the traveling direction of the scattered light reaching the photodetector and the polarization direction of the operation light is represented by θ ₁ for the detector 173 on the point A side, and θ ₂ for the detector 174 on the point B side. Then

Becomes In the polarization of the operation light in Examples 3 and 4,

It is.

The intensity of the scattered light generated by the operation light is proportional to sin ² θ, where θ is the angle between the polarization direction of the operation light and the direction from the scatterer to the observation point where the intensity of the scattered light is observed. Therefore, by setting the polarization direction of the operation light as in the present embodiment, the photons of the scattered light reaching the photodetector can be further reduced to about 1/100 to 1/1000 as compared with the third embodiment. Can be.

The scattering generated by the operation light inside the solid medium 151 in this embodiment is considered to be the degree of scattering of light having a wavelength of 700 nm by the quartz of the optical fiber. Optical fiber quartz has a scattering loss of about 3 dB / km. Therefore, the total scattered light intensity when the incident light intensity I _in has proceeded to lkm solid medium 151 medium (scattering loss)

Becomes In this embodiment, since the thickness of the solid medium 151 in the traveling direction of the operation light in the irradiation region is 100 μm, the total scattered light generated by the operation light of 100 μW is:

Becomes Among these, the intensity I of the scattered light reaching the two photodetectors 173 and 174 is, if the polarization direction of the operation light is orthogonal to the straight line AB,

, And when the polarization direction of the operation light as in this embodiment is parallel to the line AB is the intensity of scattered light reaching the two optical detectors 173, 174 thereof 1 / 100-1 / 1000 10 ^- It can be less than ¹⁵ W.

For example, when a two-qubit gate is executed in 100 μs, the energy of one photon of a lost photon is about 4 × 10 ⁻¹⁹ J. Therefore, the detection of the lost photon in such a quantum gate requires one time per gate. It is necessary to accurately detect light of 4 × 10 ⁻¹⁹ J / 100 μs = 4 × 10 ⁻¹⁵ W, which is the loss photon intensity when one photon is lost. In the present embodiment, the intensity of the photons of the scattered light generated by the operation light reaching the photodetector can be suppressed to 10 ^-15 W or less, and the loss photons can be accurately detected.

  In the above-described third, fourth, and fifth embodiments, a case is considered in which scattered light is generated by strong operation light, and multiple scattering in which the generated scattered light is further scattered in a solid medium is negligibly small. Even if multiple scattering is considered, the technique described in the second embodiment is effective. The technique described in the second embodiment is effective even when the scattering at the interface between the solid medium and the outside is taken into consideration in the above Examples 3, 4 and 5.

(Note)
Hereinafter, preferable aspects of the second embodiment will be additionally described.

[1] The quantum computer according to the first aspect,
A resonator having a solid medium including a physical system that carries a qubit, and a resonator having a resonator mode that resonates with the physical system,
In a state where the physical systems are coupled to each other by the resonator mode, a light source unit that irradiates the physical system with operation light having a polarization direction crossing the wavefront of the resonator mode,
A detector for detecting photons lost from the physical system or photons lost from the resonator mode,
Is provided.

  [2]: In the quantum computer according to [1], the solid medium includes a first region in which the physical system is arranged and a second region different from the first region, and the first region Is thinner in the traveling direction of the operation light than the second region.

  [3]: In the quantum computer according to [1] or [2], the first surface of the solid medium on which the operation light enters is provided with a first antireflection coating, and the operation light is emitted. A second surface of the solid medium to be coated with a second anti-reflection coating, and further comprising a light trap or light absorber disposed opposite the second anti-reflection coating.

[4]: The quantum computer according to the second aspect,
A resonator including a first region in which a physical system that carries a qubit is arranged and a solid medium including a second region different from the first region, and having a resonator mode that resonates with the physical system, A resonator in which the first region has a thickness smaller than that of the second region in a traveling direction of operation light for operating the physical system;
In a state where the physical system is coupled by the resonator mode, a light source unit that irradiates the physical system with operation light for operating the physical system,
A detector for detecting photons lost from the physical system or photons lost from the resonator mode,
Is provided.

  [5]: In the quantum computer according to [4], the first surface of the solid medium on which the operation light enters is provided with a first antireflection coating, and the solid medium from which the operation light exits Has a second anti-reflection coating on the second surface thereof, and further includes a light trap or light absorber disposed opposite to the second anti-reflection coating.

[6]: The quantum computer according to the third aspect,
A resonator comprising a solid medium including a physical system that carries a qubit, and having a resonator mode that resonates with the physical system, wherein the operation light for operating the physical system is incident on the first of the resonators. A resonator having an anti-reflection coating applied to a surface thereof, and a second anti-reflection coating applied to a second surface of the resonator from which the operation light is emitted;
A light trap or light absorber disposed opposite the second anti-reflection coating;
In a state where the physical system is coupled by the resonator mode, a light source unit that irradiates the physical system with the operation light,
A detector for detecting photons lost from the physical system or photons lost from the resonator mode,
Is provided.

[7] The quantum calculation method according to the fourth aspect,
Providing a resonator having a resonator mode that resonates with the physical system, comprising a solid medium including a physical system that carries the qubit,
In a state where the physical systems are coupled to each other by the resonator mode, irradiating the physical system with operation light having a polarization direction crossing the wavefront of the resonator mode,
Detecting photons lost from the physical system or photons lost from the resonator mode;
Is provided.

  [8]: In the quantum calculation method according to [7], the solid medium includes a first region in which the physical system is arranged, and a second region different from the first region, wherein the first region is different from the first region. The region has a smaller thickness in the traveling direction of the operation light than the second region.

  [9]: The quantum calculation method according to [7] or [8], wherein a first antireflection coating is applied to a first surface of the solid medium on which the operation light is incident, and the operation light is A second surface of the solid medium that emits is provided with a second anti-reflection coating, and the method further includes providing an optical trap or a light absorber disposed opposite to the second anti-reflection coating. .

[10]: The quantum calculation method according to the fifth aspect,
A resonator including a first region in which a physical system that carries a qubit is arranged and a solid medium including a second region different from the first region, and having a resonator mode that resonates with the physical system, Preparing a resonator, wherein the first region has a thickness smaller than that of the second region in a traveling direction of operation light for operating the physical system;
In a state where the physical system is coupled by the resonator mode, irradiating the physical system with operation light for operating the physical system,
Detecting photons lost from the physical system or photons lost from the resonator mode;
Is provided.

  [11]: In the quantum calculation method according to [10], a first surface of the solid medium on which the operation light enters is provided with a first antireflection coating, and the solid from which the operation light exits is provided. A second surface of the medium is provided with a second anti-reflective coating, and the method further comprises providing a light trap or light absorber disposed opposite the second anti-reflective coating.

[12]: The quantum calculation method according to the sixth aspect,
A resonator comprising a solid medium including a physical system that carries a qubit, and having a resonator mode that resonates with the physical system, wherein the operation light for operating the physical system is incident on the first of the resonators. Preparing a resonator, wherein an anti-reflection coating is applied to a surface, and a second anti-reflection coating is applied to a second surface of the resonator from which the operation light is emitted;
Providing a light trap or light absorber disposed opposite the second anti-reflective coating;
Irradiating the operation light to the physical system while the physical system is coupled by the resonator mode;
Detecting photons lost from the physical system or photons lost from the resonator mode;
Is provided.

  While some embodiments of the invention have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. These new embodiments can be implemented in other various forms, and various omissions, replacements, and changes can be made without departing from the spirit of the invention. These embodiments and their modifications are included in the scope and gist of the invention, and are also included in the invention described in the claims and their equivalents.

  Reference Signs List 10 resonator, 11 birefringent crystal, 12 spherical mirror, 13 plane mirror, 30 index ellipsoid, 60 semiconductor laser, 61 beam splitter, 62 mirror, 63 acousto-optic element, 64 Acousto-optical element, 65, 66 mirror, 67 lens, 68 cryostat, 69 control device, 70 resonator, 71 solid medium, 72, 73 spherical mirror, 74 irradiation area, 77 incident surface, 78: outgoing surface, 80: resonator, 81: solid medium, 82: spherical mirror, 83: plane mirror, 84: irradiation area, 90: resonator, 91: solid medium, 94: irradiation area, 100: resonator DESCRIPTION OF SYMBOLS 101 ... Solid medium, 102, 103, 104 ... Spherical mirror, 105 ... Irradiation area, 110 ... Resonator, 111, 112 ... Antireflection coating, 113 ... Optical trap, 130 ... Resonator, 31 ... solid medium, 151 ... solid medium, 162, 163 ... dielectric multilayer film mirror 171 and 172 ... pinhole, 173, 174 ... photodetector.

Claims (12)

A resonator including a solid medium including a physical system and having a resonator mode that resonates with the physical system,
When the physical system is coupled by the resonator mode, a light source unit that irradiates the physical system with operation light having a polarization direction crossing the wavefront of the resonator mode,
A detector for detecting photons from the physical system or the resonator mode,
Quantum computer with.   The solid medium includes a first region in which the physical system is disposed and a second region different from the first region, and the first region has a thickness in the traveling direction of the operation light that is equal to the thickness of the second region. 2. The quantum computer according to claim 1, wherein the quantum computer is thinner than the second region. A resonator comprising a solid medium including a first region in which a physical system is arranged and a second region different from the first region, and having a resonator mode that resonates with the physical system, A region having a thickness smaller in a traveling direction of operation light for operating the physical system than the second region, a resonator;
When the physical system is coupled by the resonator mode, a light source unit that irradiates the physical system with the operation light,
A detector for detecting photons from the physical system or the resonator mode,
Quantum computer with. A first anti-reflection coating applied to a first surface of the solid medium on which the operation light is incident;
A second antireflection coating applied to a second surface of the solid medium from which the operation light is emitted;
A light trap or light absorber disposed opposite the second anti-reflection coating;
The quantum computer according to any one of claims 1 to 3, further comprising: A resonator including a solid medium including a physical system and having a resonator mode that resonates with the physical system, wherein an anti-reflection is applied to a first surface of the resonator on which operation light for operating the physical system is incident. A resonator, wherein a second anti-reflection coating is applied to a second surface of the resonator from which the operation light is emitted, and
A light trap or light absorber disposed opposite the second anti-reflection coating;
When the physical system is coupled by the resonator mode, a light source unit that irradiates the physical system with the operation light,
A detector for detecting photons from the physical system or the resonator mode,
Quantum computer with.   The quantum computer according to claim 1, wherein the physical system is used as a qubit.   The quantum computer according to claim 1, wherein the photon is a photon lost from the physical system or a photon lost from the resonator mode. Including a solid medium including a physical system, preparing a resonator having a resonator mode that resonates with the physical system,
When the physical system is coupled by the resonator mode, irradiating the physical system with operation light having a polarization direction crossing the wavefront of the resonator mode,
Detecting photons from the physical system or the resonator mode;
A quantum computation method comprising:   The solid medium includes a first region in which the physical system is disposed and a second region different from the first region, and the first region has a thickness in the traveling direction of the operation light that is equal to the thickness of the second region. The quantum calculation method according to claim 8, wherein the quantum calculation method is thinner than the second region. A resonator comprising a solid medium including a first region in which a physical system is arranged and a second region different from the first region, and having a resonator mode that resonates with the physical system, Preparing a resonator in which the region has a thickness smaller than that of the second region in a traveling direction of operation light for operating the physical system;
Irradiating the physical system with the operation light when the physical system is coupled by the resonator mode;
Detecting photons from the physical system or the resonator mode;
A quantum computation method comprising:   A first antireflection coating is applied to a first surface of the solid medium on which the operation light is incident, and a second antireflection coating is applied to a second surface of the solid medium from which the operation light is emitted. The quantum calculation method according to any one of claims 8 to 10, further comprising preparing an optical trap or a light absorber disposed opposite to the second anti-reflection coating. A resonator including a solid medium including a physical system and having a resonator mode that resonates with the physical system, wherein an anti-reflection is applied to a first surface of the resonator on which operation light for operating the physical system is incident. Providing a resonator, wherein the resonator is coated, and a second antireflection coating is applied to a second surface of the resonator from which the operation light is emitted;
Providing a light trap or light absorber disposed opposite the second anti-reflective coating;
Irradiating the physical system with the operation light when the physical system is coupled by the resonator mode;
Detecting photons from the physical system or the resonator mode;
A quantum computation method comprising: