JP2020096107A - Quantum bit and control method thereof - Google Patents

Abstract

To provide a quantum bit structure with a topological superconducting phase and its edge state by externally controlling the effective magnitude of spin-orbit interaction without the need for an external magnetic field.SOLUTION: A ferromagnetic semiconductor is formed on an s-wave superconductor in the shape of a nanowire, and an effective spin-orbit interaction is achieved by introducing a domain wall into the ferromagnetic semiconductor. A quantum bit is made up that induces a phase transition to topological superconducting phase by providing a gate in the ferromagnetic semiconductor with a superconducting component due to the superconducting proximity effect and controlling the chemical potential by a gate voltage to form a Majorana bound state at the gate edge. Further, a plurality of gates are provided, and voltage control of each gate is synchronized with domain wall movement of a wire-shaped ferromagnetic semiconductor due to pulse current application, thereby moving the quantum bit.SELECTED DRAWING: Figure 1

Description

The present invention relates to a qubit, and more particularly to a configuration of a stable qubit in a solid and a control method thereof.

A quantum computer, which is said to realize parallelism by using quantum mechanical superposition, has a "bit" in which a conventional computer can have only one state that represents some binary value such as "0 or 1" for information. Instead of handling in, information is handled by superposition state by "qubit".

Researches have been made on making qubits by various methods, and in solid-state calculation methods, methods using superconducting qubits and silicon qubits are mainly studied.

Carriers of qubits in solids include charges, electron spins, and nuclear spins. In order for these carriers to function as qubits, the coherence time needs to be kept longer. Therefore, attention has been paid to the removal of noise sources including the cryogenic environment at each element level and the configuration of the error correction circuit at the circuit level.

On the other hand, in a field called topological quantum computation (Non-Patent Document 1), a braid that is caused by a phase change caused by two-particle exchange of particles confined in a mathematical two-dimensional plane or quasiparticles A group is used as the basis of calculation (Patent Document 1). In order to realize the braid group, it is considered promising to induce a topological superconducting phase transition in a hybrid structure using superconductivity and to use the Majorana bound state formed at the edge of the topological superconducting region as a qubit. There is. The topological superconducting phase is obtained by forming a semiconductor wire having a strong spin-orbit interaction on an ordinary s-wave superconductor and applying an external magnetic field (Non-Patent Document 2).

Special table 2013-532373 gazette

Jason Alicea, Yuval Oreg, Gil Refael, Felix von Oppen, and Matthew P. A. Fisher, Non-Abelian statistics and topological quantum information processing in 1D wire networks, Nature Physics 7. 412 (2011). V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, L. P. Kouwenhoven, "Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices", SCIENCE VOL 336, 25 MAY 2012

The technique disclosed in Non-Patent Document 2 opens a superconducting gap by a superconducting proximity effect in a band structure of a semiconductor having a strong spin-orbit interaction, and further applies an external magnetic field to apply a band inversion effect to a band forming the superconducting gap. To realize a topological superconducting phase. When these conditions are expressed by the formulas at the center of the Brillouin region, that is, at k=0, they can be written as the following formula (1).

ここで、Bは外部磁場、Δはｓ波超伝導体の秩序変数、μはゲートにより変調するキャリア密度に対応した化学ポテンシャルの大きさを表す。しかし外部磁場の印加は局所的な制御には適さない。またスピン軌道相互作用の大きさは材料選択に依存し、外部からの制御は不可能である。

Here, B is the external magnetic field, Δ is the order variable of the s-wave superconductor, and μ is the magnitude of the chemical potential corresponding to the carrier density modulated by the gate. However, application of an external magnetic field is not suitable for local control. The magnitude of spin-orbit interaction depends on the material selection and cannot be controlled from the outside.

The present invention provides a configuration of a qubit with a topological superconducting phase and its end states by externally controlling the effective magnitude of spin-orbit interaction without the need for an external magnetic field, and further, the migration of the qubit A method of controlling an operation is provided.

In a preferred example of the qubit of the present invention, in a structure in which a ferromagnetic semiconductor is joined to an s-wave superconductor in a nanowire form, a gate structure is provided in the ferromagnetic semiconductor, and a domain wall is introduced into the ferromagnetic semiconductor immediately below the gate portion. Where J is the exchange interaction of the ferromagnetic semiconductor, M is the magnetization, Δ is the order variable of the s-wave superconductor, and μ is the chemical potential due to the applied voltage to the gate structure, By filling and cooling below the superconducting transition temperature of the s-wave superconductor, a Majorana bound state is formed in the portion of the ferromagnetic semiconductor corresponding to the edge of the gate structure.

Further, as another feature of the present invention, in the qubit, the s-wave superconductor is Al, and the ferromagnetic semiconductor is (Ga,Mn)As {Compound semiconductor GaAs in which Ga is replaced by 5% by Mn. } Consists of.

Further, in a preferable example of the method for controlling a qubit of the present invention, in a structure in which a ferromagnetic semiconductor is joined to an s-wave superconductor in a nanowire shape, the first and second gate structures are linearly connected to the ferromagnetic semiconductor. Power supply for moving the domain wall is arranged at both ends of the ferromagnetic semiconductor, the domain wall is introduced into the ferromagnetic semiconductor immediately below the first gate portion, and cooled to a temperature below the superconducting transition temperature of the s-wave superconductor. After that, the chemical potential μ due to the applied voltage to the first gate structure is expressed by Equation (2), where J is the exchange interaction of the ferromagnetic semiconductor, M is the magnetization, and Δ is the order variable of the s-wave superconductor. The movement of the domain wall from the first gate structure, which satisfies the relational expression and in which the domain wall is arranged, to the second gate structure in which the domain wall is arranged, and the applied voltage to the first gate structure is applied to the second gate structure. It is characterized in that a current is supplied to the ferromagnetic semiconductor in a direction opposite to the moving direction of the domain wall in synchronization with the switching to apply.

The present invention enables local control of qubit generation in topological quantum computation. It also allows local control of qubit movement.

It is a schematic diagram which shows the structural example of the quantum bit of this invention. It is a schematic diagram which shows the example of the movement operation of the qubit of this invention. It is a figure showing the magnitude|size of the standardized magnetization in case the domain wall width is 20, 100, 200 atoms in a simulation result. It is a figure showing the magnitude of effective spin orbit interaction corresponding to the simulation result in each domain wall width of FIG. It is a figure which shows the local density of states distribution of Majorana bound state formed in the edge part of a topological superconducting region. It is a figure which shows the local spin density distribution corresponding to the Majorana bound state formed in the edge part of the topological superconducting region of FIG.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a schematic diagram showing a configuration example of a quantum bit of this embodiment.
The qubit of the present embodiment has a topological superconductivity with respect to the s-wave superconductor 10, the ferromagnetic semiconductor 20, and the ferromagnetic semiconductor 20. {Normal superconductivity means that when a substance is cooled above a critical temperature. Phenomenon that occurs when electrical resistance becomes zero. In the superconducting state, electricity flows through a material without losing energy. In topological superconductivity, a superconducting gap peculiar to the superconducting state is opened inside a substance, whereas a topologically protected metal state appears on the surface or edge. } Is provided for controlling the carrier density. The ferromagnetic semiconductor 20 has a pseudo one-dimensional shape (nanowire shape) formed by stacking atomic layers on the s-wave superconductor 10 by vapor deposition, and has a domain wall 21 introduced therein.

In order to induce topological superconductivity in the ferromagnetic semiconductor 20, the thickness of the ferromagnetic semiconductor 20 (thickness in the Z-axis direction) is preferably within 5 atomic layers. When the thickness is 5 atomic layers or more, the region in which topological superconductivity is induced is expressed as the interface between the s-wave superconductor 10 and the ferromagnetic semiconductor 20. In order to generate topological superconductivity, the setting of the chemical potential μ by the gate 30 needs to satisfy the relational expression of Expression (2).

ここでＪ・Ｍは強磁性半導体２０における交換相互作用Ｊと磁化Ｍの積、Δはｓ波超伝導体１０における秩序変数の大きさを表す。

Here, J·M is the product of the exchange interaction J and the magnetization M in the ferromagnetic semiconductor 20, and Δ is the magnitude of the order variable in the s-wave superconductor 10.

Under this setting, the gate 30 is cooled below the superconducting transition temperature of the s-wave superconductor 10 and the chemical potential is controlled by the gate voltage to induce a phase transition to the topological superconducting phase. At this time, it should be noted that it is desirable that the spin-orbit interaction {interaction between electron spin and electron orbital angular momentum} in the s-wave superconductor 10 or the ferromagnetic semiconductor 20 is relatively large. If the magnitude of the spin-orbit interaction is not sufficient for the topological superconducting transition, the spin-orbit interaction can be enhanced by introducing the domain wall 21 into the ferromagnetic semiconductor 20.

As Example 1, Al is used for the s-wave superconductor 10 and (Ga,Mn)As is used for the ferromagnetic semiconductor 20. The (Ga,Mn)As used in this example is a standard compound semiconductor GaAs in which Ga is replaced with 5% of Mn, and the ferromagnetic transition temperature of bulk (Ga,Mn)As is 95K. The material of the gate 30 is a metal having crystal growth matching the material of the ferromagnetic semiconductor 20, and 32 is an insulator.

A gate structure 30 is provided on (Ga,Mn)As, which is a p-type semiconductor, the carrier density is controlled, and the superconducting transition temperature of Al is cooled to 0.5K, which is 1.2K (Kelvin) or lower, to generate topological superconductivity. Check if Based on the above materials, the above parameters are estimated to be J·M=0.1 eV and Δ=0.02 eV. Therefore, |μ|> 0.1 eV is desirable for producing topological superconductivity. In this embodiment, μ=-0.1 eV was applied to the gate structure 30 (41).

The generation of topological superconductivity is confirmed by the ferromagnetic semiconductor 20 corresponding to the edge of the gate structure 30.
It is the same value as the confirmation of the Majorana bound state in the part of, and it was confirmed by measuring the local spin density using a spin polarized STM (Scanning Tunnel Microscope). The zero-energy bound states in the superconducting gap can be detected by the spin-polarized STM energy and spin decomposition.

Here, the Majorana bound state is a state in which Majorana particles are bound to the potential. The Majorana particle is a particle that was theoretically proposed by E. Majorana in 1937, and it has the characteristic that the particle becomes its own antiparticle, and its application to a quantum computer has been proposed. .. Majorana particles, which are predicted to appear in topological superconductivity, are different from ordinary electrons in that they exist without charge and have spin.

In addition, the spin-polarized STM (Scanning Tunnel Microscope) is a metal needle (probe) with a sharp tip that traces the surface of a substance so that it scans from the tip atom of the probe to the measurement surface. By observing the presence or absence of the tunnel current, it is possible to detect the atomic level energy and spin state of the measurement surface.

In this example, first, generation of topological superconductivity was confirmed without introducing a domain wall into (Ga,Mn)As of the ferromagnetic semiconductor 20. In this case, the local spin density derived from the Majorana bound state is not formed in the portion of the ferromagnetic semiconductor 20 corresponding to the end of the gate structure 30, and the topological superstructure may be caused only by the carrier density modulation effect of the gate structure 30. It was confirmed that no conduction was generated.

Next, the domain wall 21 is introduced into (Ga,Mn)As of the ferromagnetic semiconductor 20 by applying an external magnetic field generated by passing a current through the ferromagnetic semiconductor 20 from the end. After the introduction of the domain wall 21 is confirmed, the external magnetic field is removed. After the domain wall is introduced into (Ga,Mn)As, the carrier density is controlled by the gate structure 30 and cooled to 0.5 K as in the above procedure. It was confirmed that due to the effect of introducing the domain wall, a local spin density was formed in the portion of the ferromagnetic semiconductor 20 corresponding to the end of the gate structure 30, and a Majorana bound state existed. The existence of the Majorana bound state means that (Ga,Mn)As is transformed into topological superconductivity.

FIG. 2 is a schematic diagram illustrating an example of the qubit transfer operation described in the first embodiment. As shown in FIG. 2, a power supply 40 used to move the domain wall 21 and a plurality of gate structures 30 and 31 are provided. The length of each gate (length in the X-axis direction) is 1 μm. Μ=-0.1 eV is applied to the gate structure 30, and the region of the ferromagnetic semiconductor 20 corresponding to directly under the gate structure 30 is set as a topological superconducting phase. On the other hand, the gate structure 31 is set to μ=0 eV, which is a normal superconductivity. After introducing the domain wall 21 into the ferromagnetic semiconductor 20 (Ga,Mn)As, the power supply 40 supplies a current of 100 nA to the ferromagnetic semiconductor 20. The domain wall 21 of the ferromagnetic semiconductor 20 moves in the direction opposite to the current. In synchronization with this, μ=−0.1 eV is applied to the gate structure 31 (42), and the gate structure 30 is set to μ=0 eV (41). After conducting the current for 100 ms, the measurement by the spin polarization STM shows that the ferromagnetic semiconductor 20 corresponding to the end of the gate structure 31 changes from the part of the ferromagnetic semiconductor 20 corresponding to the end of the gate structure 30 as the domain wall 21 moves. It was confirmed that the local spin density moved to the part. Further, by reversing the polarity of the current 40, the local spin density, that is, the portion of the ferromagnetic semiconductor 20 corresponding to the end of the gate structure 31 in the Majorana bound state to the ferromagnetic semiconductor 20 corresponding to the end of the gate structure 30. It was confirmed to move to the part.

In the schematic diagram of the configuration example of the qubit shown in FIG. 1, an example in which Al is used for the s-wave superconductor 10 and (In,Fe)Sb is used for the ferromagnetic semiconductor 20 is shown. (In,Fe)Sb used in this example is a standard compound semiconductor InSb with In replaced by 15% by In, and the ferromagnetic transition temperature of bulk (In,Fe)Sb is 290K. The experiment was performed in substantially the same manner as in Example 1 above, but since (In,Fe)Sb is an n-type semiconductor, μ=+0.1 eV was applied to the gate structure 30 (41). Similarly to the first embodiment, in (In,Fe)Sb, topological superconductivity is not generated only by the effect of modulating the carrier density by the gate structure 30, and the ferromagnetic semiconductor corresponding to the end of the gate structure 30 after the domain wall 21 is introduced. It was confirmed that local spin densities were formed at 20 and Majorana bound states existed.

In the schematic diagram of the configuration example of the qubit shown in FIG. 1, it is assumed that the materials of the s-wave superconductor 10 and the ferromagnetic semiconductor 20 are the same as in Example 1, and the one-dimensional tight binding model is used to calculate the topological A simulation was conducted to induce conduction.

The one-dimensional tight binding model is composed of a one-dimensional array of 500 lattice points (simple one-dimensional chain), and the atoms that compose each lattice point are the characteristics of (Ga,Mn)As (the band structure of a compound semiconductor is modeled. It is expressed as one kind of appearance that is expressed as a parameter. The range of the 100th to 400th lattice points corresponds to the gate, and the energy is changed. The center of the domain wall was fixed to the 250th lattice point, and the simulation was performed under the respective conditions when the domain wall width was 20, 100, and 200 atoms.

Fig. 3 shows the normalized magnitude of magnetization when the domain wall width is 20 atoms (51), 100 atoms (52), and 200 atoms (53) (with the domain wall as the boundary, the magnetization directions on both sides are opposite. Normalize to be +1 and -1 at both ends of the domain wall.). The domain wall center is fixed at the 250th lattice point.

FIG. 4 shows the magnitude of the effective spin-orbit interaction corresponding to the simulation result for each domain wall width in FIG. It can be seen that the smaller the domain wall width, the larger the absolute value of the effective spin-orbit interaction.

Figure 5 shows a superconducting gap (in the superconducting state, two electrons are paired (Cooper pair). It is the effective attractive force that acts between the electrons that stabilizes the electron pairs, so finite energy is required to destroy the electron pairs. At energies below this stabilizing energy, it is not possible to excite the individual electrons that do not form a pair, so a gap is created in the low-energy excitation spectrum of the electrons. This gap is called a superconducting gap. } Shows the local density of states of the bound state formed in the. The range of the 100-400th lattice point is the topological superconducting region, and the domain wall width is 100 atoms. A localized state with a width of about 100 atoms appears at the edge of the topological superconducting region. (It should be noted that there is a state in which the local density of states in the bound state is localized in a width of about 100 atoms symmetrically near the 400th lattice point near the other end of the topological superconducting region. In this figure, it is omitted because it is difficult to see the whole. Only the state localized at a width of about 100 atoms near the 100th lattice point is shown.)
It is assumed that a peak of density of states [number/eV] appears near the 100th lattice point (edge of the region corresponding to the gate), and Majorana particles are present.

FIG. 6 shows local spin densities corresponding to the simulation results of obtaining the local density of states in the bound state shown in FIG. (Note that the local spin density peaks also appear symmetrically near the 400th lattice point, which is the other end of the topological superconducting region, but are omitted in this figure for the same reason as in FIG. Only the state localized in the width of about 100 atoms near the 100th lattice point is shown.)
It is assumed that a local spin density peak appears near the 100th lattice point (at the edge of the region corresponding to the gate), and there are Majorana particles that have only spin but no charge.

10 s-wave superconductor 20 Ferromagnetic semiconductor 21 Domain wall portions 30 and 31 in ferromagnetic semiconductor Gate structure 32 Insulator 40 Power supplies 41 and 42 for driving domain wall 41 Applied voltage to gate structure 51 Simulation result with domain wall width of 20 atoms 52 Simulation result for domain wall width of 100 atoms 53 Simulation result for domain wall width of 200 atoms

Claims (10)

In a structure in which a ferromagnetic semiconductor is joined to an s-wave superconductor in the form of nanowires,
A gate structure is provided on the ferromagnetic semiconductor, and a domain wall is introduced into the ferromagnetic semiconductor directly below the gate portion.
When the exchange interaction of the ferromagnetic semiconductor is J, the magnetization is M, the order variable of the s-wave superconductor is Δ, and the chemical potential due to the applied voltage to the gate structure is μ, the relational expression of the formula (1) is satisfied,

A qubit characterized by forming a Majorana bound state in a portion of a ferromagnetic semiconductor corresponding to an end of a gate structure by cooling to a temperature below the superconducting transition temperature of an s-wave superconductor. 2. The quantum according to claim 1, wherein the s-wave superconductor is Al, and the ferromagnetic semiconductor is (Ga,Mn)As {compound semiconductor GaAs in which Ga is replaced by 5% by Mn}. bit. 2. The quantum according to claim 1, wherein the s-wave superconductor is Al, and the ferromagnetic semiconductor is (In,Fe)Sb {compound semiconductor InSb in which In is replaced by 15% by Fe}. bit. In the qubit according to claim 1,
A qubit, wherein a plurality of gate structures are linearly arranged in the ferromagnetic semiconductor, and a power supply for moving a domain wall is arranged at both ends of the ferromagnetic semiconductor. In the qubit according to claim 4,
A qubit characterized in that a domain wall is arranged in a ferromagnetic semiconductor immediately below a gate portion where a chemical potential μ due to an applied voltage to the gate structure satisfies the relational expression (1). In the qubit according to claim 5,
The movement of the domain wall from the first gate structure in which the domain wall is arranged to the second gate structure in which the domain wall is arranged is switched so that the voltage applied to the first gate structure is applied to the second gate structure. A qubit characterized in that a current is supplied to the ferromagnetic semiconductor in a direction opposite to the moving direction of the domain wall in synchronism with the above. The ferromagnetic semiconductor bonded to the s-wave superconductor in the form of nanowires,
The atomic layer is laminated on the s-wave superconductor by vapor deposition to form a quasi-one-dimensional shape, and the thickness thereof is within 5 atomic layers. Qubit. In a structure in which a ferromagnetic semiconductor is joined to an s-wave superconductor in the form of nanowires,
First and second gate structures are linearly provided on the ferromagnetic semiconductor, and a power supply for moving a domain wall is arranged at both ends of the ferromagnetic semiconductor,
A domain wall is introduced into the ferromagnetic semiconductor immediately below the first gate section,
After cooling below the superconducting transition temperature of the s-wave superconductor,
The chemical potential μ due to the applied voltage to the first gate structure is expressed by the relational expression (1) where J is the exchange interaction of the ferromagnetic semiconductor, M is the magnetization, and Δ is the order variable of the s-wave superconductor. The filling,
Switching the movement of the domain wall from the first gate structure in which the domain wall is arranged to the second gate structure in which the domain wall is arranged is switched so that the voltage applied to the first gate structure is applied to the second gate structure. A method of controlling a qubit, characterized in that a current is supplied to the ferromagnetic semiconductor in a direction opposite to a moving direction of a domain wall in synchronism with the above. 9. The quantum according to claim 8, wherein the s-wave superconductor is Al, and the ferromagnetic semiconductor is (Ga,Mn)As {compound semiconductor GaAs in which Ga is replaced by 5% by Mn}. Bit control method. 9. The quantum according to claim 8, wherein the s-wave superconductor is Al, and the ferromagnetic semiconductor is (In,Fe)Sb (compound semiconductor InSb in which In is replaced by 15% by Fe). Bit control method.

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