JP2017053989A - Quantum computer and quantum calculation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To increase the number of available quantum bits.SOLUTION: A quantum computer comprises a plurality of physical systems and a light source unit. The plurality of physical systems disposed in a resonator, have three or more levels including two levels to be used for quantum bits, and have a transition that is combined with a common resonator mode of the resonator. The resonator mode has intensity distribution having a plurality of maximum values on a plane perpendicular to a progress direction of the resonator mode. The plurality of physical systems are arranged at a plurality of positions where the intensity of the resonator mode is half the maximum intensity of the resonator mode on the plane or greater. The light source unit generates a plurality of beams to irradiate the plurality of physical systems.SELECTED DRAWING: Figure 9

Description

  Embodiments described herein relate generally to a quantum computer that utilizes coupling between a resonator and a physical system.

  Quantum computers that perform operations using quantum mechanical superposition are actively studied. As one of quantum calculation methods, a method is known in which a physical system used for a qubit coupled to a resonator is irradiated with operation light and a quantum gate based on an adiabatic passage is executed. In order to perform practical calculations, a large number of qubits are required.

JP 2001-209083 A

T. Pellizzari et al., Phys. Rev. Lett. 75, 3788 (1995)

  The problem to be solved by the present invention is to increase the number of available qubits.

  A quantum computer according to an embodiment includes a plurality of physical systems and a light source unit. The plurality of physical systems are arranged in the resonator, have three or more levels including two levels used for qubits, and have transitions coupled to a common resonator mode of the resonator. The resonator mode has an intensity distribution having a plurality of local maximum values in a plane perpendicular to the traveling direction of the resonator mode, and the plurality of physical systems have the resonator mode intensity in the plane. The plurality of physical light source units disposed at a plurality of positions that are equal to or greater than half the maximum intensity of the mode generate a plurality of light beams that irradiate the plurality of physical systems.

Schematic which shows the optical resonator which concerns on embodiment. The figure which shows the basic mode of a Hermitian Gaussian beam. The figure which shows the higher-order mode (l = m = 10) of the Hermitian Gaussian beam which concerns on embodiment. The figure explaining the area | region where the qubit which concerns on embodiment is arrange | positioned. Schematic which shows three physical systems used for the qubit which concerns on embodiment. The figure which shows the pulse waveform used for the adiabatic passage through the resonator based on embodiment. The block diagram which shows the quantum computer which concerns on 1st Example. It shows the energy levels of ^{Pr 3+} ions in _Y 2 SiO ₅ crystal according to the first embodiment. The figure which shows arrangement | positioning of the qubit which concerns on 2nd Example. The figure which shows arrangement | positioning of the qubit which concerns on 3rd Example.

  Hereinafter, various embodiments will be described with reference to the drawings. Embodiments relate to a quantum computer that uses qubits coupled to a resonator by distinguishing them at their positions.

  In the quantum computer according to one embodiment, a plurality of qubits are arranged in a plane perpendicular to the traveling direction of the resonator mode, and are distinguished by a position in the plane perpendicular to the traveling direction of the resonator mode. Further, the qubits may be distributed in a direction parallel to the traveling direction of the resonator mode. In this case, a distinction is also made in the position in the direction parallel to the traveling direction of the resonator mode. In the quantum computer according to the present embodiment, for example, a higher-order mode of a Hermitian Gaussian beam is used as the resonator mode.

  In the quantum computer disclosed in the related technology T. Pellizzari et al., Phys. Rev. Lett. 75, 3788 (1995), the qubits are arranged in a direction parallel to the traveling direction of the resonator mode, It is distinguished by a position in a direction parallel to the traveling direction of the resonator mode. In the quantum computer according to the related art, the lowest order mode of the Hermitian Gaussian beam called the fundamental mode is used as the resonator mode.

  First, the Hermitian Gaussian beam will be described, and problems of the quantum computer according to the related art will be described. Subsequently, the quantum computer according to the present embodiment that uses the higher-order mode of the Hermitian Gaussian beam as the resonator mode will be described.

  FIG. 1 schematically shows a Fabry-Perot type optical resonator 10 in which a plane mirror 11 and a spherical mirror 12 are installed facing each other. When a laser beam coupled to a specific resonator mode of the resonator 10 is generated by adjusting the frequency and the beam pattern and is incident on the resonator 10 through the plane mirror 11 or the spherical mirror 12, the resonator mode corresponds to the resonator mode. Light having a specific frequency and spatial mode is excited inside the resonator 10. It is known that the spatial mode of the resonator mode is classified by the Hermitian Gaussian beam expressed by the following equation (1).

Here, the z coordinate is taken in the traveling direction of the resonator mode, the x and y coordinates are taken to be perpendicular to each other on a plane perpendicular to z, and the intensity of the resonator mode on the plane mirror 11 is maximized. The origin is taken. ω (z) is the beam spot size of the resonator mode at the z position, k is the wave number of the beam, E ₀ is a constant, H ₁ and H _m are Hermitian polynomials, and l and m are integers of 0 or more. A spatial pattern on the xy plane at an arbitrary position z is determined corresponding to l and m. When l = m = 0, the spatial pattern is a circular pattern as shown in FIG. The circle shown in FIG. 2 represents a region whose intensity is a predetermined value or more. A resonator mode in which l = m = 0 is called a fundamental mode. The resonator mode used in the quantum computer according to the related art corresponds to the case of l = m = 0. As l and m increase, the modes spread while being split. For example, when l = m = 10, the spatial pattern is as shown in FIG. A resonator mode in which at least one of l and m is 1 or more is called a high-order mode. Each circle shown in FIG. 3 represents a region whose intensity is a predetermined value or more. The intensity takes a maximum value at the center of the circle, and decreases as the distance from the center increases. In the present embodiment, the qubit is arranged in a region where the intensity of the resonator mode is equal to or more than half the maximum intensity of the resonator mode in the xy plane. FIG. 4 shows the intensity distribution at y = 0 in the resonator mode when l = 4 and m = 0. In FIG. 4, a region where the intensity is equal to or greater than half the maximum intensity is indicated by a double arrow. When representing the intensity at the x-y plane I (x, y, z) _{and, I (x, y, z} ) = | E lm (x, y, z) | ^2.

  In a quantum computer according to related technology, quantum bits are arranged at spatially separated positions on the z-axis and used for quantum computation by being coupled with a fundamental mode of a resonator. By manipulating the operation light to each qubit, the qubit can be executed by manipulating the qubit by the method of the adiabatic passage through the resonator.

As a specific example, as shown in FIG. 5, a case is assumed in which three four-level systems X ₁ , X ₂ , and X ₃ arranged in a resonator are used as qubits. Each four-level system X _i (i = 1, 2, 3) has four states. These four states are displayed as | 0> _i , | 1> _i , | 2> _i , | e> _{i in} ascending order of energy. The states | 0> _i and | 1> _i are used for qubits. That is, a qubit is expressed by a superposition state of states | 0> _i and | 1> _i . In addition, the state | 2> _i is used to assist the gate operation. | 2> _i- | e> _i transition (transition between state | 2> _i and state | e> _i ) is coupled to a common resonator mode with a coupling constant g.

In system shown in FIG. _{5, | 1> 1 - |} e> operation light _{L 1} that resonates with ₁ irradiates the four-level system _{X 1, | 1> 2 -} | e> 2 resonance in manipulating light L ₂ was irradiated to the four-level system _{X 2,} Rabi frequency Omega ₁ of the irradiation light _L 1, _{L 2,} Ω ₂ controls the irradiation light _L 1, _{L 2} to indicate that time change as shown in FIG. 6 Accordingly, the four-level systems X ₁ , X ₂ , and X ₃ can be operated from the state | 1> ₁ | 2> ₂ | 1> ₃ to the state | 2> ₁ | 1> ₂ | 1> ₃ . . Such an operation can be efficiently executed when the resonator coupling constant g is larger than the resonator relaxation rate κ and the energy relaxation rate γ of each four-level system.

  The four-level system is an example of a physical system that can be used as a qubit. A physical system having three or more levels and having a transition coupled to a common resonator mode can be used as a qubit.

  In the quantum computer according to the related art, the number of usable qubits is limited by the arrangement interval of the qubits in the traveling direction of the resonator mode and the spatial resolution of the operation light. In order to realize a quantum computer using more qubits, it is desirable that qubits can be executed by arranging qubits not only on the z axis but also at different positions on the xy plane. In the fundamental mode, the resonator mode is strongly localized on the z-axis, and in the xy plane, as the distance from the z-axis is increased, the intensity of the resonator mode becomes weaker and the coupling constant becomes smaller. Therefore, when quantum bits are arranged at different positions on the xy plane and coupled to the fundamental mode, the quantum gate cannot be executed with high efficiency.

  Therefore, this embodiment uses a higher-order mode of the Hermitian Gaussian beam as the resonator mode. In the higher-order mode, maximum values of intensity appear at a plurality of locations in the xy plane, resulting in a mode that is spatially broader than the basic mode. For example, when a higher-order mode of l = m = 10 as shown in FIG. 3 is used, there are 121 maximum values of intensity in the xy plane. The length of each side of the quadrilateral obtained by connecting the points located at the four corners among the points where the intensity becomes the maximum value is more than four times longer than the mode waist of the fundamental mode of the same resonator. Compared to the case where the fundamental mode is used by arranging the qubit near the position where the intensity becomes the maximum value and irradiating the operation light, the qubit is distinguished in the xy plane and used in the quantum computer. Becomes easier. In one embodiment, l and m satisfy ω (z) / d−1 <l + m <ω (z) / d. Here, d is the beam radius of the irradiation light.

The qubit is preferably arranged at a position where the intensity of the resonator mode is large. For example, the number of qubits (physical systems) is N (N is an integer of 2 or more), and M positions (M is an integer of N or more) on the xy plane where the intensity of the resonator mode is a maximum value. Are P ₁ , P ₂ ,..., P _{M in} descending order of intensity, and the N qubits have positions P ₁ , P ₂ ,..., P _N or positions P ₁ , P _{2 ,.} Arranged in the vicinity.

  The embodiments described here are merely examples. As the resonator mode, a higher-order resonator mode in an arbitrary resonator having a plurality of intensity maximum values in the xy plane can be used. The same effect can be obtained by irradiating the operation light to the qubit coupled to the resonator mode with a larger coupling constant so that the influence on the qubit that is not intended to be manipulated becomes smaller. Further, the present embodiment is combined with a method for distinguishing qubits in the z direction and / or a method for distinguishing qubits in the frequency domain as disclosed in Japanese Patent Laid-Open No. 2001-209083 as in the related art. As a result, more qubits can be used.

Examples will be described below.
(First embodiment)
FIG. 7 schematically shows a quantum computer 700 according to the first embodiment. In the quantum computer 700 shown in FIG. 7, a plane mirror 704 and a spherical mirror 705 made of a dielectric multilayer film are arranged on the side surface of a Y ₂ SiO ₅ crystal (Pr: YSO) 703 doped with Pr ³⁺ ions. . The plane mirror 704 and the spherical mirror 705 form a resonator. Pr: YSO 703 is installed in the cryostat 707 and kept at a low temperature (for example, at 4K).

In the first embodiment, Pr ³⁺ ions doped in a Y ₂ SiO ₅ crystal are used as a specific physical system that can be regarded as a four-level system X _i . FIG. 8 shows the energy levels of Pr ³⁺ ions in the Y ₂ SiO ₅ crystal. FIG. 8 shows three states (states in which the nuclear spins are −1/2, −3/2, and −5/2) of the hyperfine structure level of the ground state ³ H ₄ and an excited state ¹ D _2. 3 states (states in which nuclear spins are +1/2, +3/2, and +5/2) are shown. The wavelength corresponding to the transition frequency between the excited state ¹ D ₂ and the ground state ³ H ₄ is about 606 nm. Nuclear spins -1 / 2 ground state ³ H _4, -3 / 2, -5 / 2 state state | 0>, | 1>, | correspond to 2>, the excited state ¹ D ₂ Ultra The state where the nuclear spin is +5/2 among the fine structure levels corresponds to the state | e>. In this case, the | 0>-| e> transition, | 1>-| e> transition, | 2>-| e> transition can be optically transitioned, and | 0>-| 1> transition, | 0 The>-| 2> transition and the | 1>-| 2> transition are optically forbidden transitions.

In the first embodiment, as shown in FIG. 9, a mode corresponding to l = m = 1 in the Hermitian Gaussian beam expressed by the equation (1) is used as the resonator mode 706 of the resonator. Four Pr ³⁺ ions 901 to 904 coupled to the resonator mode 706 are used for the qubit. The Pr ³⁺ ions 901 to 904 are arranged at four points where the intensity of the resonator mode 706 has maximum values.

  Referring to FIG. 7 again, the quantum computer 700 includes a light source unit 701 and a control device 702 that controls the light source unit 701. The light source unit 701 includes an argon ion laser 711, a ring dye laser 712, beam splitters 713 to 715, acoustooptic devices 716 to 719, and mirrors 720 to 724.

  The light source unit 701 uses a ring dye laser 712 excited by an argon ion laser 711 as a light source. The laser light emitted from the ring dye laser 712 is divided into four laser lights by three beam splitters 713, 714, 715, and these four laser lights are transmitted to four acoustooptic elements 716, 717, 718, 719. Each is guided. Specifically, the beam splitter 713 splits the laser beam emitted from the ring dye laser 712 into two laser beams, one of the two laser beams is incident on the acousto-optic element 716 and the other is the beam splitter 714. Is incident on. The beam splitter 714 divides the incident laser light into two laser lights, one of the two laser lights is incident on the acousto-optic element 717 and the other is incident on the beam splitter 715. The beam splitter 715 splits the incident laser light into two laser lights, one of the two laser lights is incident on the acoustooptic element 718 and the other is reflected by the mirror 724 and incident on the acoustooptic element 719. Laser light incident on the acousto-optic elements 716 to 719 is referred to as laser light 751 to 754.

  The acoustooptic elements 716 to 719 modulate the frequencies of the laser beams 751 to 754 in accordance with the control signal generated by the control device 702. Specifically, the acoustooptic device 716 modulates the frequency of the laser beam 751 so that the laser beam 751 resonates with the | 1>-| e> transition of the ion 901, and the acoustooptic device 717 receives the laser beam 752. The frequency of the laser light 752 is modulated so as to resonate with the | 1> − | e> transition of the ion 902, and the acoustooptic device 718 causes the laser light 753 to resonate with the | 1> − | e> transition of the ion 903. Then, the acoustooptic device 719 modulates the frequency of the laser beam 754 so that the laser beam 754 resonates with the | 1> − | e> transition of the ion 904. The modulated laser beam 751 is guided to the ions 901 by the mirror 720. The modulated laser light 752 is guided to the ions 902 by the mirror 721. The modulated laser beam 753 is guided to the ions 903 by the mirror 722. The modulated laser beam 754 is guided to the ions 904 by the mirror 723.

In such a system, the remaining two laser beams are converted so that the two laser beams corresponding to the qubit (Pr ³⁺ ion) to be operated out of the laser beams 751 to 754 have a waveform as shown in FIG. By modulating with the acousto-optic elements 716 to 719 so that the intensity becomes zero, an adiabatic passage through a resonator can be executed between desired qubits. A similar device can be arranged for ions distributed in the traveling direction (z direction) of the resonator, and a quantum computer using a larger number of qubits than the case where the resonator mode 706 is the fundamental mode can be provided. realizable.

(Second embodiment)
The quantum computer according to the second embodiment has the same structure as the quantum computer 700 according to the first embodiment. In the second embodiment, the beam spot size of the resonator mode 706 at z = 10 μm is set to ω = 5 μm, the beam radii of the laser beams 751 to 754 are set to d = 2 μm, and the resonator mode 706 is set to l = m = 1. Use the matching mode. This design satisfies ω (z) / d−1 <l + m <ω (z) / d. Among Pr ³⁺ ions distributed at z = 10 μm, four Pr ³⁺ ions 901 to 904 coupled with the resonator mode in the arrangement as shown in FIG. 9 are used, and Pr ³⁺ ions distributed at z = 10 μm are used. It is possible to realize a quantum computer in which the resonator mode and the qubit are coupled with the highest coupling constant among the four qubit quantum computers.

(Third embodiment)
The quantum computer according to the third embodiment has the same structure as that of the quantum computer 700 according to the first embodiment. In the third embodiment, a resonator mode corresponding to l = 0 and m = 5 is used. In this resonator mode, the intensity distribution has six local maximum values as shown in FIG. The four Pr ³⁺ ions 1001 to 1004 are arranged at four places where the strength is higher. As a result, a quantum computer that can execute the quantum gate most efficiently among the quantum computers using four qubits using this resonator mode can be realized.

(Fourth embodiment)
The quantum computer according to the fourth embodiment has the same structure as that of the quantum computer 700 according to the first embodiment, and has the same qubit arrangement as that of the second embodiment. In the fourth embodiment, as shown in FIG. 9, the distance between the ions 901 and 903, the distance between the ions 901 and 904, the distance between the ions 902 and 903, and the ions 902 And the distance between the ions 904 are equal. The optical path of the laser beam 751 is designed so that the angle formed by the laser beam 751 and the straight line connecting the ions 901 and 903 and the angle formed by the laser beam 751 and the straight line connecting the ions 901 and 904 are both 45 degrees. The optical path of the laser beam 752 is designed so that the angle formed by the laser beam 752 and the straight line connecting the ions 902 and 903 and the angle formed by the laser beam 752 and the straight line connecting the ions 902 and 904 are both 45 degrees. The optical path of the laser beam 753 is set so that the angle formed by the laser beam 753 and the straight line connecting the ions 903 and 901 and the angle formed by the laser beam 753 and the straight line connecting the ions 903 and 902 are both 45 degrees. The angle formed between the straight line connecting the ion 904 and the ion 901 and the laser beam 754, and the ion 904 As angle formed linearly and the laser beam 754 connecting the ions 902 are both 45 degrees, to design the optical path of the laser beam 754. As a result, the influence of the laser beams 751 to 754 on the qubit that is not intended to be manipulated can be minimized, and a highly efficient quantum computer can be realized.

  Although several embodiments of the present invention have been described, these embodiments are presented by way of example and are not intended to limit the scope of the invention. These novel embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the scope of the invention. These embodiments and modifications thereof are included in the scope and gist of the invention, and are included in the invention described in the claims and the equivalents thereof.

DESCRIPTION OF SYMBOLS 10 ... Resonator, 11 ... Plane mirror, 12 ... Spherical mirror, 700 ... Quantum computer, 701 ... Light source part, 702 ... Control device, 703 ... Pr: YSO, 704 ... Plane mirror, 705 ... Spherical mirror, 706 ... Resonator Mode, 707 ... Cryostat, 711 ... Argon ion laser, 712 ... Ring dye laser, 713-715 ... Beam splitter, 716-719 ... Acousto-optic element, 720-724 ... Mirror, 901-904 ... Pr3 ⁺ ion, 1001-1004 ... Pr ³⁺ ion.

Claims (7)

A plurality of physical systems having three or more levels, including two levels used for qubits, arranged in a resonator and having transitions coupled to a common resonator mode of the resonator; The resonator mode has an intensity distribution having a plurality of local maximum values in a plane perpendicular to the traveling direction of the resonator mode, and the plurality of physical systems have the resonance mode intensity in the plane A plurality of physical systems arranged at a plurality of positions that are at least half the maximum intensity of the vessel mode, and
A light source unit for generating a plurality of light beams for irradiating the plurality of physical systems;
A quantum computer comprising: The resonator mode is in the plane
X and y represent coordinates in two directions perpendicular to each other in the plane, z represents the coordinates in the traveling direction, and ω (z) represents the resonator mode at the coordinate z. 2. The quantum computer according to claim 1, wherein the quantum computer represents a beam spot size, H ₁ and H _m represent Hermitian polynomials, l and m are integers of 0 or more, and at least one of l and m is 1 or more.   The quantum computer according to claim 2, wherein l and m satisfy ω (z) / d−1 <l + m <ω (z) / d, where d is a beam radius of the light beam. The number of the plurality of physical systems is N (N is an integer equal to or greater than 2), and the M points (M is an integer equal to or greater than N) on the plane where the intensity of the resonator mode has a maximum value is large. order _{P 1, P 2, ...,} when the _{P M,} the plurality of physical systems each point _{P 1, P 2, ...,} located in the region corresponding to the _{P N,} quantum computer according to claim 1 . The plurality of physical systems include four physical systems, and the light source unit generates first to fourth light beams that irradiate the four physical systems,
M (M is an integer of 4 or more) P ₁ points in order intensity is _large, P 2 on the plane intensity of the resonator mode becomes a maximum value, _..., when the P _M, the four The physical system is located at points P ₁ , P ₂ , P ₃ , P ₄ , respectively, and the optical paths of the first to fourth light beams form an angle of 45 degrees with the x-axis and the y-axis. Quantum computer.   2. The quantum according to claim 1, wherein each of the plurality of light rays passes through only one corresponding region among a plurality of regions on the plane that are equal to or greater than a half value of the maximum intensity of the resonator mode in the plane. calculator. A plurality of physical systems having three or more levels, including two levels used for qubits, arranged in a resonator and having transitions coupled to a common resonator mode of the resonator; The resonator mode has an intensity distribution having a plurality of local maximum values in a plane perpendicular to the traveling direction of the resonator mode, and the plurality of physical systems have the resonance mode intensity in the plane Preparing a plurality of physical systems arranged at a plurality of positions that are at least half the maximum intensity of the vessel mode;
Generating a plurality of light rays for irradiating the plurality of physical systems;
A quantum computation method comprising: