Quantum bit fabrication methods, equipment, and quantum computers

Abstract

This disclosure relates to the field of computer technology, and particularly to a method, apparatus, and quantum computer for fabricating qubits. The method for fabricating qubits includes: forming a two-dimensional nanostructure comprising a strongly spin-orbit coupled material, wherein multiple boundaries of the two-dimensional nanostructure are coupled in close proximity to a superconducting material; introducing disorder at a designated boundary among the multiple boundaries; generating zero-energy quasi-particles at a designated location on the two-dimensional nanostructure by applying a designated magnetic field to the designated boundary; and generating qubits based on the zero-energy quasi-particles.

Description

Technical Field

[0001] This disclosure relates to the field of computer technology, and in particular to a method, apparatus, and quantum computer for preparing qubits. Background Technology

[0002] With the continuous iteration and evolution of quantum computing technology, the related theories and hardware architectures are developing rapidly. Quantum computing systems are gradually moving from laboratory prototypes to practical applications, and the demand for the preparation of qubits is constantly increasing.

[0003] Topological qubits are a type of qubit protected by a topological structure. Quantum information in topological qubits is stored non-locally, resulting in stronger anti-interference capabilities and intrinsic fault tolerance.

[0004] However, in related technologies, the methods for preparing topological qubits mainly focus on one-dimensional nanowire structures, which have certain structural limitations. Summary of the Invention

[0005] In view of this, this disclosure provides a method, apparatus, and quantum computer for preparing qubits. By introducing disorder at a specified boundary of a two-dimensional system, the parameter requirements for generating zero-energy quasi-particles can be reduced, thereby enabling the generation of zero-energy quasi-particles in a two-dimensional system and further enabling the generation of topological qubits.

[0006] According to one aspect of this disclosure, a method for fabricating a quantum bit is provided, comprising: forming a two-dimensional nanostructure comprising a strongly spin-orbit coupled material, wherein a plurality of boundaries of the two-dimensional nanostructure are coupled in close proximity to a superconducting material; introducing disorder at a designated boundary among the plurality of boundaries; generating zero-energy quasi-particles at a designated location in the two-dimensional nanostructure by applying a designated magnetic field to the designated boundary; and generating a quantum bit based on the zero-energy quasi-particles.

[0007] In some embodiments, after the specified magnetic field is applied, the specified boundary is in a first boundary state, and the other boundaries among the plurality of boundaries are in a second boundary state.

[0008] In some embodiments, the first boundary state includes an Anderson localized state, and the second boundary state includes a topological superconducting state.

[0009] In some embodiments: the disorder includes disorder caused by defects in the specified boundary, the defects including at least one of point defects, line defects, surface defects, and volume defects; the critical disorder intensity is determined based on the superconducting band gap of the superconducting material and the strength of the specified magnetic field.

[0010] In some embodiments, the critical disorder intensity is positively correlated with the superconducting band gap and negatively correlated with the intensity of the specified magnetic field.

[0011] In some embodiments, introducing disorder at a designated boundary among the plurality of boundaries includes introducing the disorder by doping at the designated boundary.

[0012] In some embodiments, introducing the disorder by doping the designated boundary includes: doping the designated boundary; or doping the plurality of boundaries, wherein the doping concentration of the designated boundary is different from the doping concentration of the other boundaries among the plurality of boundaries.

[0013] In some embodiments, the strong spin-orbit coupling material comprises a topological insulator material, and the introduction of disorder by doping at the designated boundary includes: doping with magnetic impurities when the topological insulator material comprises a II-VI material quantum well; or doping with non-magnetic impurities when the topological insulator material comprises a III-V material quantum well.

[0014] In some embodiments: the doping method includes at least one of growth stage doping, surface adsorption doping, ion beam doping, plasma doping, and diffusion doping; and / or the doping distribution includes at least one of continuous band distribution, lattice distribution, cluster distribution, and gradient distribution.

[0015] In some embodiments, introducing disorder into a designated boundary among the plurality of boundaries includes introducing the disorder by changing the shape of the designated boundary to a rough boundary.

[0016] In some embodiments, the manner of altering the shape of the specified boundary includes at least one of electron beam exposure, ion etching, and plasma processing; and / or the rough boundary includes at least one of serrated boundary, stepped boundary, random concave-convex boundary, and corner passivation boundary.

[0017] In some embodiments, generating a qubit based on the zero-energy quasi-particles includes generating a qubit using four of the zero-energy quasi-particles, wherein the overall parity of the four zero-energy quasi-particles is conserved.

[0018] In some embodiments, the zero-energy quasi-particle includes Majorana zero-energy modes.

[0019] According to a second aspect of this disclosure, a device is provided, comprising: a two-dimensional nanostructure, wherein the two-dimensional nanostructure includes a plurality of boundaries, wherein the disorder of a specified boundary among the plurality of boundaries differs from the disorder of other boundaries among the plurality of boundaries, the material of the two-dimensional nanostructure includes a strongly spin-orbit coupled material; and a superconducting material, which is coupled in close proximity to the plurality of boundaries of the two-dimensional nanostructure.

[0020] According to a third aspect of this disclosure, a quantum computer is provided, comprising: a device according to any embodiment of this disclosure; and an electromagnet configured to apply a magnetic field to a designated boundary of a two-dimensional nanostructure in the device to generate zero-energy quasi-particles at a designated location on the two-dimensional nanostructure. Attached Figure Description

[0021] The accompanying drawings, which form part of this specification, illustrate embodiments of this disclosure and, together with the specification, serve to explain the principles of this disclosure.

[0022] This disclosure will become clearer with reference to the accompanying drawings and the following detailed description, wherein: Figure 1 A flowchart illustrating a preparation method according to some embodiments of the present disclosure is shown; Figure 2 A schematic diagram of a two-dimensional nanostructure according to some embodiments of the present disclosure is shown; Figure 3 A schematic diagram showing the wave function distribution of the two states with the lowest energy according to some embodiments of the present disclosure is provided. Figure 4 This diagram illustrates the wave function distribution at the boundary of the two lowest-energy states according to some embodiments of the present disclosure; Figure 5 This diagram illustrates the energy distribution according to some embodiments of the present disclosure; Figure 6 This diagram illustrates a comparison of low-energy states according to some embodiments of the present disclosure; Figure 7 A schematic diagram illustrating the inverse participation rate according to some embodiments of the present disclosure is shown; Figure 8 A schematic diagram illustrating the relationship between energy ratio and disorder intensity according to some embodiments of the present disclosure; Figure 9 A schematic diagram illustrating the relationship between the inverse participation rate and the disorder strength according to some embodiments of the present disclosure; Figure 10 A block diagram of a device according to some embodiments of the present disclosure is shown; Figure 11 A block diagram of a quantum computer according to some embodiments of the present disclosure is shown.

[0023] It should be understood that the dimensions of the various parts shown in the accompanying drawings are not drawn to actual scale. Furthermore, the same or similar reference numerals denote the same or similar components. Detailed Implementation

[0024] Various embodiments of the present disclosure will now be described in detail with reference to the accompanying drawings. The descriptions of the embodiments are merely illustrative and are in no way intended to limit the scope of the disclosure or its application or use. The present disclosure may be implemented in many different forms and is not limited to the embodiments described herein. These embodiments are provided to make the disclosure thorough and complete, and to fully express the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specifically stated, the relative arrangement of components and steps set forth in these embodiments should be interpreted as merely illustrative and not as limiting.

[0025] The terms “first,” “second,” and similar words used in this disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different parts. Words such as “including” mean that the element preceding the word covers the element listed after the word, and do not exclude the possibility of covering other elements as well.

[0026] It should also be understood that any component, data or structure mentioned in the embodiments of this disclosure can generally be understood as one or more unless expressly defined or given to the contrary in the context.

[0027] All terms used in this disclosure (including technical or scientific terms) have the same meaning as understood by one of ordinary skill in the art to which this disclosure pertains, unless otherwise specifically defined. It should also be understood that terms defined in a general dictionary, such as a dictionary, should be interpreted as having a meaning consistent with their meaning in the context of the relevant art, and not as having an idealized or highly formalized meaning, unless expressly defined herein.

[0028] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0029] In related technologies, the methods for preparing topological qubits mainly focus on one-dimensional nanowire structures, which have certain structural limitations. Therefore, it is very important to find new material structures that may realize topological qubits.

[0030] One theoretical approach to realizing topological qubits in a two-dimensional system is to use a topological insulator material to create a topological Majorana fermion mode at the vertices of the insulator, thereby fabricating a topological qubit. However, this theoretical method has certain limitations on material parameters, such as requiring a high magnetic field, making it difficult to achieve the corresponding parameters in experimental systems.

[0031] In view of this, this disclosure proposes a method, apparatus, and quantum computer for preparing qubits. By introducing disorder at a specified boundary of a two-dimensional system, the parameter requirements for generating zero-energy quasi-particles can be reduced, thereby enabling the generation of zero-energy quasi-particles in a two-dimensional system and further realizing the generation of topological qubits.

[0032] First, combined Figure 1 The method for preparing qubits in this disclosure is described. Figure 1 A flowchart illustrating a preparation method according to some embodiments of the present disclosure is shown.

[0033] like Figure 1 As shown, the method for preparing a quantum bit may include: step S1, forming a two-dimensional nanostructure, the two-dimensional nanostructure including a strongly spin-orbit coupled material, and multiple boundaries of the two-dimensional nanostructure being coupled in close proximity to a superconducting material; step S2, introducing disorder at a designated boundary among the multiple boundaries; step S3, generating zero-energy quasi-particles at a designated position in the two-dimensional nanostructure by applying a designated magnetic field to the designated boundary; and step S4, generating a quantum bit based on the zero-energy quasi-particles.

[0034] In step S1, a two-dimensional nanostructure can be formed first, serving as the basic material for preparing zero-energy quasi-particles. This two-dimensional nanostructure is, for example, an ultrathin layered structure with a thickness on the nanometer scale and a planar lateral dimension significantly larger than its thickness.

[0035] The effect of the above structure on thickness is negligible compared to its effect on length. In other words, the above structure can be considered a two-dimensional structure. For example, the above system can be represented by a two-dimensional Hamiltonian.

[0036] In some embodiments, the strong spin-orbit coupling material may include a topological insulator material. A topological insulator material is, for example, a bulk insulating material with conductive states at its boundaries protected by time-reversal symmetry.

[0037] Topological insulator materials can include, for example, two-dimensional quantum spin Hall insulators. Due to the special band structure of the quantum spin Hall system, when the interior of a two-dimensional quantum spin Hall material is in an insulating state, its boundaries have gapless boundary states, thus classifying it as a topological insulator material.

[0038] Furthermore, because the boundary states of a two-dimensional quantum spin Hall insulator are protected by the bulk topology, they cannot open the bandgap through symmetry-compliant interactions under weak perturbations. In other words, low-energy weak perturbations do not violate the system's time-reversal symmetry, and the boundary topological states always maintain a bandgap-free characteristic.

[0039] Therefore, when measuring the transport properties of the aforementioned materials, quantized behavior can be obtained. For example, the direction of electron motion at the boundary can correspond one-to-one with the electron's spin; for instance, an electron with spin up can move in one direction, while an electron with spin down can move in the opposite direction.

[0040] Optional two-dimensional quantum spin Hall material types may include, for example, quantum well types and van der Waals material types.

[0041] Quantum well-type quantum spin Hall insulators can refer, for example, to quantum spin Hall insulators generated through semiconductor heterojunction quantum wells. Specifically, semiconductor heterojunction quantum wells are, for example, double heterojunction sandwich structures formed by epitaxial growth and stacking of two or more semiconductor materials with different band gaps. These structures can be classified into type I single quantum wells and type II gap-broken quantum wells.

[0042] In a type I single quantum well, a layer formed of a narrow bandgap semiconductor material can be used as a well layer, and two layers formed of a wide bandgap semiconductor material can be used as barrier layers to sandwich the well layer, thereby forming a quantum well structure.

[0043] The thickness of the aforementioned well layer can be close to the de Broglie wavelength of electrons or holes in semiconductor materials, thereby restricting the movement of charge carriers through the quantum confinement effect and realizing a quantum well with quantized energy levels.

[0044] The material of the aforementioned type I single quantum well can be, for example, mercury telluride (HgTe) or cadmium telluride (CdTe). HgTe has a narrower band gap and can be used as the material of the well layer, while CdTe has a wider band gap and can be used as the material of the barrier layer.

[0045] It should be understood that the above-mentioned materials are merely exemplary. The material of a type I single quantum well can also be mercury telluride / mercury cadmium telluride, wherein mercury cadmium telluride is, for example, a mixed crystal composed of tellurium (Te), cadmium (Cd), and mercury (Hg).

[0046] For quantum spin Hall platforms formed by type I single quantum wells, the processes of epitaxial growth, gate voltage modulation, and integration with superconducting electrodes are relatively mature, making them suitable for realizing regular devices and subsequent boundary engineering.

[0047] In a type II quantum well with a gap, two narrow-bandgap semiconductor materials with different band gaps can be used to form an electron trap layer and a hole trap layer respectively and directly bonded together. Then, two barrier layers formed by a wide-bandgap semiconductor material sandwich this coupled double-layer structure, thereby forming a type II quantum well structure with spatial separation of electrons and holes.

[0048] The thickness of the aforementioned electron trap layer and hole trap layer can be similar to the de Broglie wavelengths of electrons and holes in the corresponding semiconductor materials, respectively. Thus, through the quantum confinement effect, the movement of electrons and holes can be constrained, thereby realizing a type II quantum trap where electrons and holes are spatially separated and both have quantized energy levels.

[0049] The materials for the aforementioned type II gap-broken quantum wells can be, for example, indium arsenide (InAs), gallium antimonide (GaSb), or aluminum antimonide (AlSb). InAs can be used as the material for the electron trap layer, GaSb can be used as the material for the hole trap layer, and AlSb, with its wider band gap, can be used as the material for the barrier layer.

[0050] For a quantum spin Hall platform formed by a type II gapped quantum well, the Fermi level can be finely tuned by the upper and lower gates of the quantum well because the system has an electron-hole inversion band structure.

[0051] A quantum spin Hall system of van der Waals material type is, for example, a quantum spin Hall insulator that is bound together by weak van der Waals forces between layers, such as a van der Waals monolayer two-dimensional material formed by mechanical exfoliation or van der Waals epitaxy.

[0052] The aforementioned materials can be prepared by using a monolayer distorted octahedral phase (1T') transition metal dichalcogenide (TMD), such as 1T'-tungsten ditelluride (WTe2) or 1T'-tungsten diselenide (WSe2).

[0053] The aforementioned van der Waals system possesses quantum spin Hall edge conductivity and can maintain edge transport quantization at high temperatures. Furthermore, this van der Waals topological insulator can form a clean interface when stacked with van der Waals superconductors such as niobium diselenide (NbSe2), facilitating subsequent measurements using scanning tunneling microscopy (STM) or scanning tunneling spectroscopy (STS).

[0054] The materials used in this invention have been described above through various examples. It should be understood that these materials are merely illustrative, and the proposed quantum bit fabrication method can also be implemented using other materials with similar properties.

[0055] In some embodiments, the two-dimensional nanostructure described in step S1 can be formed on a substrate in the form of one or more layers.

[0056] After forming a two-dimensional nanostructure, multiple boundaries of the nanostructure can be further coupled to the superconducting material in close proximity.

[0057] Near-neighbor coupling can be achieved by the close contact between the boundary of a nanostructure and a superconductor. Through the superconducting nearest-neighbor effect, superconducting pairing correlation is introduced into the topological boundary of the nanostructure, realizing the quantum coherent coupling of their electronic states.

[0058] The aforementioned proximity coupling effect can occur, for example, when the superconducting material and the nanostructure boundary are in direct contact or when the distance between the superconducting material and the nanostructure boundary is less than the superconducting coherence length of the superconducting material.

[0059] Specifically, due to the presence of Cooper pairs inside superconducting materials, when the superconducting material approaches the topological boundary of the nanostructure, the Cooper pairs tunnel into the topological boundary. Under the combined effect of strong spin-orbit coupling, this can be equivalent to generating a topological superconducting state.

[0060] In the topological superconducting state, electrons are simultaneously constrained by superconducting pairing and topological symmetry, resulting in a superconducting energy gap at the boundary. In other words, electron excitation requires a certain energy threshold; below this threshold, electrons cannot move freely within the boundary.

[0061] The aforementioned superconducting materials can be, for example, S-wave superconducting materials. S-wave superconducting materials can be, for example, superconducting materials where the relative orbital angular momentum of Cooper pairs is equal to zero. Near-neighbor coupling using S-wave superconducting materials exhibits better uniformity and higher process tolerance.

[0062] The above text elaborates on how the two-dimensional nanostructure is formed in step S1. It should be understood that the above-described formation process of the two-dimensional nanostructure is merely exemplary and not limiting. Two-dimensional nanostructures with the above properties can also be generated in other ways to subsequently generate zero-energy quasi-particles.

[0063] In some embodiments, zero-energy quasiparticles may include Majorana zero modes. Majorana zero modes are, for example, quasiparticles generated by low-energy excitations specific to topological superconductors. These quasiparticles are themselves equivalent to their antiparticles and are therefore self-conjugated fermions. Furthermore, the energy of these quasiparticles approaches zero, for example, and may be localized at the boundaries of topological superconductivity.

[0064] Next, we will continue to introduce how to introduce disorder at the specified boundary of the above structure in step S2.

[0065] The aforementioned disorder can be, for example, the inhomogeneity of atomic arrangement, composition, or interfaces within a material. By introducing controllable disorder at specified boundaries of a two-dimensional structure, the topological state of the boundaries can be further altered, so that zero-energy quasi-particles, such as Majorana zero modes, can be generated in the system through the topological state relationships between the boundaries.

[0066] In some embodiments, the disorder may include disorder caused by defects in the specified boundary, the defects including at least one of point defects, line defects, surface defects, and volume defects.

[0067] In other words, the controllable disorder within the specified boundaries can be achieved by introducing specific defects. Based on the dimension corresponding to the defect, defects can be categorized as point defects, line defects, surface defects, and volume defects, for example.

[0068] Point defects can include single-point defects such as atomic vacancies, interstitial atoms, substitutional impurities, and antisite defects. Line defects can include one-dimensional extended defects such as dislocations and missing atomic chains. Planar defects can include two-dimensional planar defects such as stacking faults, grain boundaries, phase boundaries, and interface defect layers. Volume defects can include three-dimensional structural defects such as surface steps, pits, protrusions, holes, and edge serrations.

[0069] The critical disorder intensity mentioned above can be determined, for example, based on the superconducting band gap of the superconducting material and the strength of the specified magnetic field.

[0070] The intensity of disorder can characterize, for example, the magnitude of random potential fluctuations caused by lattice defects. Taking disorder caused by substitutional impurities as an example, the intensity of disorder is related to the concentration of impurities. The higher the concentration of impurities, the stronger the random potential fluctuations in the lattice, and the higher the intensity of disorder.

[0071] To alter the boundary states at a specified boundary, the time-reversal symmetry in the topological superconducting state can be disrupted by using disorder and a magnetic field, resulting in effects such as localization at the boundary. For this effect to occur, the intensity of the disorder needs to exceed a certain threshold, known as the critical disorder intensity. The critical disorder intensity can be determined jointly by the superconducting bandgap of the superconducting material and the strength of the specified magnetic field.

[0072] For example, the critical disorder intensity can be positively correlated with the superconducting bandgap and negatively correlated with the intensity of the specified magnetic field. When the introduced disorder intensity is greater than the critical disorder intensity, the disorder and the specified magnetic field can disrupt the generation of the topological superconducting state, thus enabling the subsequent generation of zero-energy quasi-particles.

[0073] The types of defects have been introduced above. Below, we will use two implementation methods as examples to further illustrate how to controllably introduce disorder at specified boundaries, i.e., introducing one or more of the defects mentioned above.

[0074] A first way to introduce disorder can be, for example, doping. In some embodiments, introducing disorder at a designated boundary among the plurality of boundaries includes introducing the disorder by doping at the designated boundary.

[0075] During doping, based on the doping concentration, disorder can be introduced, for example, through defects such as substitutional impurities, interstitial atoms, dislocations, and grain boundaries. In other words, the disorder introduced by doping can include at least one of point defects, line defects, and surface defects.

[0076] Disorder caused by doping can be understood as the artificial introduction of randomly or quasi-randomly distributed impurities, vacancies, adsorbed atoms, substitutional atoms, interstitial atoms, or changes in the local chemical environment at a specified boundary of a sample, in order to alter the local chemical potential, local transition intensity, local spin-orbit coupling, or local exchange field at the boundary.

[0077] In the above embodiments, doping can be performed only on the specified boundaries. For example, boundary selective doping can be used on the specified boundaries, that is, the disorder is introduced only in the narrow strip one-dimensional structure at the specified boundaries, while the bulk region of the two-dimensional nanostructure and the remaining boundaries remain relatively clean regions.

[0078] Furthermore, in the above embodiments, multiple boundaries of the two-dimensional nanostructure can also be doped, wherein the doping concentration of the specified boundary is different from the doping concentration of other boundaries among the multiple boundaries. By using different doping doses for different boundaries, the topological states between the doped boundaries can also be different, thereby facilitating the subsequent generation of Majorana zero modes.

[0079] The impurities in the above doping process can be classified into non-magnetic impurities and magnetic impurities. Non-magnetic impurities include, for example, boron, phosphorus, zinc, aluminum, nitrogen, sulfur, and molybdenum. Magnetic impurities include, for example, manganese, chromium, vanadium, iron, cobalt, and nickel.

[0080] The disorder caused by non-magnetic impurities can manifest as random fluctuations in local chemical potential and transition intensity. Its advantages are that it has a weaker direct impact on the superconductivity of the nearest neighbor and a wider process window, making it suitable for realizing boundary states dominated by "random chemical potential".

[0081] In addition to introducing random potentials, the disorder caused by magnetic impurities also provides local exchange fields or equivalent local magnetic fields. This has the advantage of more easily disrupting time reversal and enhancing boundary scattering, thus facilitating the preparation of Majorana zero modes. To avoid weakening the induced superconducting gap or introducing additional trivial bound states, low-concentration, low-coverage magnetic impurities can be introduced through tunable dosing processes.

[0082] Both types of impurities can be used to introduce disorder at specified boundaries. To improve the doping effect, impurities that can form a statistically significant one-dimensional random potential at specified boundaries without completely destroying the superconducting nearest-neighbor coupling effect can be selected for doping.

[0083] As described above, the strongly spin-orbit coupled two-dimensional nanostructures in the embodiments of this disclosure may include topological insulator materials, such as quantum spin Hall insulators. For topological insulator materials employing different systems, different types of impurities can be used for doping.

[0084] For example, when the topological insulator material includes a II-VI material quantum well, it can be doped with magnetic impurities.

[0085] Taking a two-dimensional quantum spin Hall system as an example, the II-VI material quantum well can be the HgTe / CdTe quantum well mentioned above. For HgTe / CdTe quantum wells, doping can be performed using magnetic equivalent substitution atoms such as manganese (Mn), thereby maintaining the inverted band structure of the quantum well during the doping process. This is suitable for constructing boundary disorder caused by the mixing of local exchange fields and random potentials.

[0086] For example, when the topological insulator material includes a III-V material quantum well, it can be doped with non-magnetic impurities.

[0087] Continuing with the example of a two-dimensional quantum spin Hall system, the III-V material quantum well can be the InAs / GaSb / AlSb quantum well mentioned above. For the InAs / GaSb system, it can be diluted and doped with non-magnetic impurities such as silicon (Si), thereby further suppressing the residual bulk conductivity in the topological insulator and retaining edge transport, which is suitable for constructing boundary disorder caused by random chemical potential.

[0088] The previous section introduced examples of impurity types during doping. Below, we will continue to introduce the doping methods available during doping.

[0089] In some embodiments, the doping method includes at least one of growth stage doping, surface adsorption doping, ion beam doping, plasma doping, and diffusion doping.

[0090] Growth stage doping, for example, involves substitutional doping or delta (δ) doping during molecular beam epitaxy (MBE) or other epitaxial growth processes that form two-dimensional nanostructures. The doped layer is arranged in the form of narrow strips at a location close to the specified boundary projection region.

[0091] In the case of a two-dimensional nanostructure containing multiple quantum wells, a narrow strip region covering the boundaries of multiple quantum wells can be selected for doping, thereby achieving doping at a specified boundary.

[0092] Surface adsorption doping, for example, involves low-coverage vapor deposition on the exposed boundary regions of a two-dimensional nanostructure after patterning, so that magnetic or non-magnetic atoms are preferentially adsorbed at the structural edges, steps, and defect sites of the specified boundaries.

[0093] Ion beam doping involves masking non-target areas using photoresist, hard metal masks, or hexagonal boron nitride (hBN) protective layers, exposing only the designated boundaries to be doped, and utilizing He... + Ne + Ar + Plasma beams bombard exposed areas to create vacancies, inversions, and edge defects, thereby forming a random potential at a specified boundary.

[0094] Plasma doping, for example, involves using a mixed plasma of argon, oxygen, and hydrogen to briefly treat the target boundary, thereby introducing lattice defects, achieving localized oxidation, or completing surface functionalization modification, thus achieving disorder at the specified boundary.

[0095] Diffusion doping can be contact layer diffusion or interface diffusion. For example, it can be achieved by depositing metal, magnetic insulating layer or other two-dimensional material at the structural boundary, and then driving a small number of interface atoms to diffuse into the boundary region of the specified boundary through a controlled annealing process, thereby forming a random potential at the boundary.

[0096] It should be understood that the above methods are merely exemplary, and other methods can also be used to dope two-dimensional nanostructures. Furthermore, the above doping methods can be used individually or in combination.

[0097] For a given type of two-dimensional nanostructure, doping can also be performed using corresponding doping methods to improve the doping effect.

[0098] For example, for quantum spin Hall insulators in single-layer or few-layer van der Waals systems, since the surface of such materials is exposed and defects are easily written locally, doping can be carried out by means of surface adsorption doping, ion beam doping, plasma doping, controlled oxidation or controlled vacancies, etc., to improve the doping effect and at the same time facilitate subsequent measurement with STM.

[0099] As a concrete example of doping, to achieve boundary doping while avoiding simultaneous destruction of the bulk region, doping can be performed by opening windows at designated boundaries after encapsulating or covering the entire two-dimensional nanostructure with a mask. Alternatively, the two-dimensional nanostructure can be etched first to expose the device's sidewalls, and then directional deposition or ion implantation can be performed on the sidewalls of the designated boundaries to achieve doping. Or, after patterning the two-dimensional nanostructure multiple times, different dosages can be applied to different boundaries of the device to achieve different topological states at the device boundaries.

[0100] In the doped region of the specified boundary, the distribution of dopant may include at least one of continuous band distribution, lattice distribution, cluster distribution, and gradient distribution.

[0101] The previous section elaborated on introducing disorder through doping. Below, we will introduce another method for introducing disorder.

[0102] In some embodiments, introducing disorder into a specified boundary among the plurality of boundaries may include introducing the disorder by changing the shape of the specified boundary to a rough boundary.

[0103] In addition to introducing doping disorder by doping at a specified boundary, geometric disorder can also be introduced by changing the local geometric properties at the boundary.

[0104] The rough boundary in the above embodiments may include at least one of the following: a serrated boundary, a stepped boundary, a random concave-convex boundary, and a corner blunting boundary.

[0105] A serrated boundary represents, for example, randomly misaligned atomic rows along the boundary, or missing edges, with the scale of the missing edges being close to the lattice constant. A stepped boundary represents a boundary composed of alternating straight segments of varying lengths and single or multiple layers of steps. A random concave-convex boundary represents a boundary with random undulations along the normal direction, resulting in a rough edge. A corner-blunted boundary represents a boundary where the endpoints are no longer ideal corners, but rather rounded, notched, or multi-stepped corners.

[0106] The defects introduced by the aforementioned morphological changes can be transformed into stochastic potentials, such as stochastic chemical potentials, stochastic mass terms, or stochastic transition terms, in an effective model with a specified boundary. For the one-dimensional boundary states, geometric disorder, similar to doping disorder, can also serve as a source of change in the boundary states.

[0107] Two-dimensional nanostructures can have one or more shape changes at a specified boundary. In other words, the shape change at the specified boundary is not limited to any particular aggregate morphology, but can include, for example, arbitrary micro- and nanostructure irregularities that can form random scattering and localization near the specified boundary.

[0108] In the above embodiments, the method of changing the shape of the specified boundary may include at least one of electron beam exposure, ion etching, and plasma processing.

[0109] Two-dimensional nanostructures may develop structural defects such as edge jaggedness, steps, notches, protrusions, missing atomic chains, dislocations, grain boundaries, and random width fluctuations during etching, transfer, peeling, annealing, or oxidation processes. These defects will lead to changes in the boundary morphology.

[0110] Specifically, the aforementioned disorder can be controllably introduced at a specified boundary through one or more of the processes described above. For example, ion etching can be used to directly sputter using a focused ion beam with uneven dosage, thereby forming an edge notch at the specified boundary. Another example is the formation of a photomask with rough edges using electron beam exposure, followed by ion etching to replicate the rough edges onto a two-dimensional nanostructure.

[0111] Furthermore, after introducing the aforementioned geometric defects, the defects can be amplified by processes such as plasma etching, air exposure, or heat treatment to induce edge oxidation or surface functionalization, thereby further increasing the disorder strength.

[0112] The foregoing section described two methods for introducing disorder at a specified boundary. It should be understood that the aforementioned defects and methods of introducing defects are merely exemplary and not restrictive. For example, the defects introduced at a specified boundary in the embodiments of this disclosure may also include boundary nanopores or defect clusters, i.e., discrete vacancy clusters or micropores formed within a range of several nanometers from the boundary in a two-dimensional nanostructure.

[0113] Furthermore, the two methods of introducing disorder mentioned above are not mutually exclusive; disorder can be introduced at a specified boundary by combining the two methods.

[0114] For example, in two-dimensional transition metal chalcogenides, plasma treatment not only leads to doping, oxidation, and defects, but also morphological changes. In other words, plasma treatment can simultaneously introduce doping disorder and geometric disorder.

[0115] The preceding text elaborated on how to introduce disorder at the specified boundary in step S2. By introducing controllable disorder, the parameter requirements for changing the boundary state at the specified boundary can be reduced, thereby facilitating the subsequent generation of zero-energy quasi-particles and realizing the generation of topological qubits.

[0116] Below, we will combine Figure 2 Next, we will introduce how to generate zero-energy quasi-particles by applying a magnetic field to the above structure in step S3.

[0117] In some embodiments, after the specified magnetic field is applied, the specified boundary is in a first boundary state, and the other boundaries among the plurality of boundaries are in a second boundary state.

[0118] In other words, when the boundary states of a specified boundary are different from those of other boundaries in the structure, zero-energy quasi-particles, such as Majorana zero modes, can be generated at the vertices where the specified boundary intersects with other boundaries.

[0119] Figure 2 A schematic diagram of a two-dimensional nanostructure according to some embodiments of the present disclosure is shown. Figure 2In the example shown, the two-dimensional nanostructure 21 is a rectangular two-dimensional quantum spin Hall insulator material, wherein all four sides 211 to 214 of the two-dimensional nanostructure 21 are coupled in close proximity to the superconductor. The aforementioned two-dimensional nanostructure 21 can, for example, be formed on a substrate.

[0120] Below, we will first introduce how to generate Majorana zero modes in a structure without introducing disorder.

[0121] As mentioned earlier, the quantum spin Hall insulator boundary coupled to the superconductor is in a topological superconducting state. In other words, before the magnetic field is applied, all four sides of the two-dimensional nanostructure 21 are in a topological superconducting state.

[0122] By applying a magnetic field, for example, edges 211 and 213 in the two-dimensional nanostructure 21 can be transformed into topologically trivial states, such that the boundary states of edges 211 and 213 are different from those of edges 212 and 214, so as to generate Majorana zero modes at intersections 221 to 224.

[0123] Specifically, the Hamiltonian of the two-dimensional quantum spin Hall system of the two-dimensional nanostructure 21 after applying a magnetic field can be expressed as: .

[0124] In the above formula, and It is a spin-orbit coupling term. For kinetic energy, For superconducting pairing, For the Seman field item.

[0125] Specifically, σ represents the orbital degrees of freedom of the electron. When the electron has two possible orbits in two-dimensional space, σ can correspond to three Pauli matrices. .

[0126] Characterizes the ground-state exchange operator. For example, for a bipolar lattice space, It can enable electrons to switch between two sublattices.

[0127] Characterizing the ground-state exchange operator with phase. For example, for a bipolar lattice space, It can characterize the switching transitions of electrons with virtual phases between two sublattices.

[0128] Characterize the ground state labeling operator. and and different, The operations corresponding to operators do not swap the ground states of electrons, but rather label the ground states, for example, by assigning opposite eigenweights to the two ground states. For example, in a bipolar lattice space, It can be used to distinguish the types of sublattices in which electrons reside.

[0129] The σ mentioned above is merely an example; for instance, when electrons have more orbital degrees of freedom, other matrices can also be used to characterize the orbital degrees of freedom of electrons.

[0130] Similar to σ, s and τ can guarantee the spin degree of freedom of the electron and the particle / hole degree of freedom, respectively.

[0131] For example, if an electron can have two spins, its spin degree of freedom is 2. s can correspond to three Pauli matrices. . and Similarly, it can characterize the switching of electron spin states. and Similarly, it can characterize the phase switching of the electron spin state. and Similarly, it can characterize the labeling of electronic spin states.

[0132] For example, the particle-hole mixing transformation of electrons can include two operations: generating electrons and generating holes. Generating a hole is equivalent to removing an electron, and the particle / hole degree of freedom of an electron can be 2. τ can correspond to three Pauli matrices. . and Similarly, it can characterize the switching of particle-hole mixing operations, such as switching from adding an electron to removing an electron. and Similarly, it can characterize the phase switching of particle-hole mixing operations. and Similarly, it can characterize the labeling of particle-hole mixing operations.

[0133] Based on the aforementioned degrees of freedom, the spin-orbit coupling term can be determined by considering the interaction between the electron's orbital angular momentum and spin during the electron's opposite transitions in the x-direction or y-direction.

[0134] For example, in a two-dimensional structure, to distinguish different transition types, the x and y directions mentioned above can be defined as the directions of paired straight sublattices on the same horizontal line and the directions of staggered oblique sublattices. In other words, for a bi-sublattice space, the direction of the horizontal straight line arrangement of the lattice can be defined as the x-direction. Electron transitions in the x-direction are straight-line transitions, and no additional phase is generated during the transition. Furthermore, the direction of the staggered arrangement of the crystal lattice can be defined as the y-direction. Electron transitions in the y-direction are diagonal transitions, which will result in an additional virtual phase during the transition. .

[0135] For the two-dimensional nanostructure 21 described above, edges 211 and 213 can be, for example, edges along the x-direction, and edges 212 and 214 can be, for example, edges along the y-direction.

[0136] Based on the above directions, consider an electron with planar momentum k, where momentum k has two components. and .

[0137] For electron transitions along the x-direction and along the -x-direction, i.e., corresponding to The transition. Since the above transition is a linear transition, there are no mirror-image pairing paths inside the lattice. Therefore, during the round-trip transition, due to the error distortion within the lattice, an angular momentum component in the z-direction will be generated. After Fourier transform, we can obtain... .in, This represents the amplitude of the spin-orbit coupling strength. It is the momentum function in Fourier space that represents the above process, used to characterize the strength of spin-orbit coupling corresponding to different planar momentum k.

[0138] Similarly, for electron transitions along the y-direction and along the -y-direction, i.e., corresponding to... The transition is a second-nearest neighbor oblique transition. Since the aforementioned transition is a second-nearest neighbor oblique transition, mirror-image paired paths exist within the lattice. Therefore, during the round-trip transition, the angular momentum generated by the two parallel transition channels corresponding to the paired paths will cancel each other out. Ultimately, only the orbital phase change needs to be considered. After a Fourier transform, we can obtain... .

[0139] The above section introduced the origin of the spin-orbit coupling term in the Hamiltonian of a two-dimensional quantum spin Hall system. The following section will introduce the other terms.

[0140] For a twin lattice space, the kinetic energy term middle, It is the energy required for a particle to transition as momentum k changes, and μ is the chemical potential of the material. The difference between these potential energies can characterize the kinetic energy of the electron.

[0141] Superconducting pairing middle, It could be the superconducting pairing strength. As mentioned earlier, Switching between corresponding particle-hole mixing operations allows coupling to form between electron generation and hole generation. Through... and The product of these can characterize the interactions of electron pairing, Cooper pair creation, and annihilation in a superconducting system.

[0142] Seman Field In this context, 'h' can characterize the applied magnetic field. Specifically, it can be the product of the magnetic field and the Landé factor of the material, i.e., the g factor representing the ratio between the electron spin magnetic moment and the spin angular momentum. By multiplying the applied magnetic field by the Pauli matrix corresponding to the spin, the coupling effect between the magnetic field and the electron spin magnetic moment can be characterized.

[0143] The Hamiltonian of a two-dimensional quantum spin Hall system has been introduced above. Based on this Hamiltonian, to obtain the behavior at the boundary, a low-energy efficient model of the boundary of a two-dimensional quantum spin Hall insulator can be considered. For example, to simplify the problem, a model with zero chemical potential and a magnetic field having only the x-direction quantity h can be considered. x In this case, by projecting the Hamiltonian onto the boundary, we can obtain the effective Hamiltonians for the x and y boundaries: .

[0144] As can be seen from the two boundary states, the y-boundaries of the aforementioned two-dimensional nanostructure 21, namely edges 212 and 214, are always in a topologically superconducting state, while the x-boundaries, namely edges 211 and 213, exhibit a phase transition from the topologically superconducting state to a trivial bandgap state. The critical point of this phase transition is... That is, the effect of an external magnetic field will disrupt the superconducting pairing phenomenon, resulting in the boundary exhibiting a topologically trivial state.

[0145] Furthermore, when the chemical potential is not zero, the influence of the kinetic energy term needs to be considered, and the critical point of the phase transition is... .

[0146] It is evident that, in the aforementioned system without introducing disorder, a sufficiently strong magnetic field is required to generate Majorana zero modes. For example, considering the Landé factor of materials, a magnetic field of 40 Tesla is typically needed to achieve this, a parameter that cannot be realized experimentally.

[0147] The effects of disorder introduced in the embodiments of this disclosure on the boundary will be described below. The aforementioned disorder induces a transition of the specified boundary from a topological superconducting state to a localized state.

[0148] In some embodiments of this disclosure, the first boundary state of the designated boundary includes an Anderson localized state, and the second boundary state of the other boundaries includes a topological superconducting state.

[0149] In other words, unlike systems that do not introduce disorder, where the boundary states are transformed from topological superconducting states to trivial gapped states, the system proposed in this disclosure can transform the boundary states into Anderson localized states by introducing disorder. Anderson localized states refer to boundary states where the electron wavefunction exponent is confined to a local region due to disorder effects, resulting in suppressed band diffusion and transport insulation.

[0150] Specifically, taking the two-dimensional quantum spin Hall system mentioned above as an example, consider the random chemical potential caused by disorder at the boundary. The corresponding boundary low-energy effective Hamiltonian is: .

[0151] In the above formula, and Corresponding to fermions propagating in the +x direction, The representative produces fermions. It represents the annihilation of fermions. and Corresponding to fermions propagating in the -x direction, The representative produces fermions. It represents the annihilation of fermions. The actual Fermi velocity of a fermion is represented by, for example, the velocity obtained after external field correction based on the original Fermi velocity. This represents the superconducting pairing gap in the aforementioned system. Chemical potential representing the boundary Represents a perturbation of the local chemical potential. It is the conjugate of the perturbation.

[0152] Since the superconducting pairing strength caused by the proximity effect is often weak, it can be assumed that the superconducting pairing gap Δ in the above system is much smaller than 1. Furthermore, a finitely large specified magnetic field h can exist along a specified boundary in the system. x It is used to disrupt the time-reversal symmetry topology protection of the system.

[0153] By solving the Hamiltonian above, the Lyapunov exponents of the corresponding transition matrix can be obtained: .

[0154] In the above formula, w refers to the disorder intensity, which is obtained through... definition. It is the original Fermi velocity. It is the static chemical potential at the boundary, that is, the boundary chemical potential before the introduction of disorder.

[0155] For the aforementioned exponent, when γ=0, a phase transition from a topological superconducting state to an Anderson localized state will occur at the corresponding boundary. It can be seen that the critical disorder intensity corresponding to the phase transition... for: .

[0156] In other words, given the superconducting pairing strength and the specified magnetic field to be applied When the disorder intensity is greater than the critical value When the disorder intensity is less than the critical value, the corresponding boundary will be in an Anderson localized state. Conversely, when the disorder intensity is less than the critical value... At that time, the corresponding boundary will be in a topological superconducting state.

[0157] The above process can also be understood as follows: when the localization length required for Anderson localization is less than the superconducting coherence length required to establish an effective superconducting phase, the localized state is established within a shorter scale, thus disrupting the generation of the superconducting state, and the boundary is in the localized state. However, if the localization length is greater than the superconducting coherence length, the superconducting state is established before sufficient localization, and the boundary is in the superconducting state.

[0158] refer to Figure 2 The quantum spin Hall system shown can, for example, introduce disorder and apply a magnetic field to edges 211 and 213. When two edges of the system are in Anderson localized states, four Majorana zero modes will exist at the four vertices since the other two edges are still in topological superconducting states.

[0159] For the aforementioned quantum spin Hall system, numerical simulations can be performed by introducing random chemical potentials at specified boundaries. Figure 3 A schematic diagram showing the wave function distribution of the two states with the lowest energy according to some embodiments of the present disclosure is provided. Figure 3 (a) in the figure shows the wave function density distribution of the lowest energy state in the numerical simulation. Figure 3 (b) in the figure shows the wave function density distribution of the second-lowest energy state in the numerical simulation.

[0160] from Figure 3 It can be seen that the wave functions of the two lowest-energy states are mainly distributed at the four vertices 311 to 314, corresponding to the four Majorana fermion modes locally located at the vertices. Furthermore, Figure 4 A schematic diagram showing the wave function distribution at the boundary of the two states with the lowest energy according to some embodiments of the present disclosure is illustrated.

[0161] Figure 4 (a) in the figure shows the x-boundary, for example Figure 3 The wave function density distribution of the lowest energy state is shown for edges 321 and 323. Figure 4 (b) in the diagram shows the boundary at the y-axis, for example... Figure 2 The wave function density distribution of the lowest energy state is shown for edges 322 and 324. Figure 4(c) in the figure shows the wave function density distribution of the second lowest energy state at the x boundary. Figure 4 (d) in the figure shows the wave function density distribution of the second lowest energy state at the y boundary.

[0162] It can be seen that in the example structure above, the wave function distributions of the two edges 322 and 324 on the y-boundary are mainly concentrated at both ends, and decrease exponentially inwards. Similarly, on the two edges 321 and 323 on the x-boundary, although the distribution of the wave function exhibits random fluctuations due to the presence of stochastic chemical potential, it still gradually decreases exponentially inwards overall. It is evident that the density peaks of the wave function on all four edges are located at the vertices, for example... Figure 3 311 to 314. The above simulation results further show that the Majorana zero mode generated in the embodiments of this disclosure is localized at the four vertices of the structure.

[0163] also, Figure 5 A schematic diagram of energy distribution according to some embodiments of the present disclosure is shown. Figure 5 As can be seen, the energy distribution exhibits a sharp peak near zero energy, corresponding to two zero energy states, namely the Majorana modes at the four vertices of the structure.

[0164] Figure 6 A schematic diagram showing a low-energy state comparison according to some embodiments of the present disclosure is provided. Figure 6 This diagram illustrates the distribution of energy ratios between the two lowest-energy states E0 and E1 and the next excited state E2 in the above embodiments, where the horizontal axis represents the logarithm of the ratio and the vertical axis represents the number of ratios. From Figure 6 As can be seen from this, the ratio of the lowest energy state E0 to the next excited state E2 is, as follows: Figure 6 As shown in the gray area, it is concentrated in The ratio of the next lowest energy state E1 to the next excited state E2, as shown in the figure. Figure 6 The diagonal area shown in the image is concentrated in... The above results indicate that the energy ratio between the low-energy state and the excited state is much less than one, further suggesting that the two lowest-energy states are Majorana zero modes.

[0165] Figure 7 A schematic diagram of the inverse participation ratio according to some embodiments of the present disclosure is shown. The inverse participation ratio (IPR) is a physical quantity characterizing the spatial locality of a wave function. Figure 7 For example, it is shown that Figure 3 The boundary inverse participation rate of the structure. The first x-boundary can correspond to edge 311, the first y-boundary can correspond to edge 312, the second x-boundary can correspond to edge 313, and the second y-boundary can correspond to edge 314. For example... Figure 7As shown, the excitation positive states (e.g., E2, E3, etc.) of the x-edge after introducing disorder have a high inverse participation rate, indicating that the x-edge is in an Anderson local state.

[0166] The numerical simulation results above demonstrate that, by introducing disorder at specified boundaries, the embodiments of this disclosure can generate Majorana zero-energy modes at the vertices of a two-dimensional system. More specifically, Figure 8 A schematic diagram illustrating the relationship between energy ratio and disorder intensity according to some embodiments of the present disclosure.

[0167] Figure 8 (a) shows the relationship between the ratio of the lowest energy state E0 to the next excited state E2 and the disorder intensity for different system sizes L. Figure 8 (b) shows the relationship between the ratio of the second lowest energy state E1 and the next excited state E2 and the disorder intensity for different system sizes L.

[0168] from Figure 8 It can be seen that the results for different system sizes intersect at the phase transition point. To the left of the intersection point, the larger the system size, the larger the ratio, indicating that the ratio of the energies of the two lowest-energy states to the energy of the next state gradually increases with the increase of the system size. To the right of the intersection point, the ratio decreases with the increase of the system size, indicating that as the system size approaches infinity, the ratio also approaches zero, corresponding to the Majorana zero-energy modes localized at the four vertices. Using the data collapse method, the corresponding phase transition point can be fitted as follows: ≈0.3.

[0169] also, Figure 9 A schematic diagram illustrating the relationship between the inverse participation rate and the disorder strength according to some embodiments of the present disclosure is shown. When the system is in a local state, the inverse participation rate does not change with the system size and is a constant. Figure 9 This shows the relationship between the inverse participation rate and the disorder intensity when the critical disorder intensity is 0.3. From... Figure 9 It can be seen that the inverse participation rate is basically the same for different system sizes. In other words, by fitting the ratio between the inverse participation rate and the power of the system size, it can be determined that the corresponding phase transition point is also the critical disorder intensity. ≈0.3.

[0170] It is evident that consistent phase transition points can be obtained through different types of simulations, corresponding to the transition of the quantum spin Hall system boundary from a topological superconducting state to an Anderson localized state. Therefore, when the degree of disorder is sufficient, the system boundary will be in an Anderson localized state, resulting in Majorana zero modes localized at the four vertices.

[0171] In the above embodiments, the realization of the Anderson localized state and the generation of the Majorana zero mode do not require the strength of the specified magnetic field itself, but only that the specified magnetic field be non-zero to break the time reversal symmetry. In other words, the critical disorder intensity required to generate the Majorana zero mode can be determined based on the specified magnetic field strength that can be applied during the experiment, and corresponding boundary doping or boundary morphology changes can be performed.

[0172] It is evident that by introducing disorder at a specified boundary of a two-dimensional system, the parameter requirements for generating zero-energy quasiparticles can be reduced, thereby enabling the generation of zero-energy quasiparticles in a two-dimensional system.

[0173] In some embodiments, the generated Majorana zero mode can also be measured and verified by at least one of the following methods: STM measurement, STS measurement, cryogenic transport / tunneling spectroscopy measurement, Josephson microwave measurement, and quantum dot / quantum capacitor readout measurement.

[0174] In STM or STS measurements, for example, conductivity-voltage spectrum measurements can be performed at the four vertices, the middle of the boundary, and the bulk region of the device under low temperature and non-zero external magnetic field conditions to determine the distribution of the zero bias signal, thereby verifying the existence of the Majorana zero mode.

[0175] Cryogenic transport / tunneling spectroscopy measurements can be performed by placing metal probes or grids near the apex of the sample, defining a tunneling barrier, measuring local differential conductance and nonlocal conductance, and verifying the existence of Majorana zero modes through local resonance.

[0176] Josephson microwave measurements, for example, can verify the existence of Majorana zero modes by current-relationships after introducing a Josephson junction at a corner boundary.

[0177] Quantum dot / quantum capacitance readout measurements, for example, can couple quantum dots or superconducting islands near the apex and read out the total parity change via radio frequency reflection measurement, quantum capacitance measurement, or dispersion readout, thereby verifying the existence of Majorana zero modes.

[0178] The process of generating zero-energy quasi-particles in the embodiments of this disclosure has been described in detail above. Below, we will return to... Figure 1 Next, we will introduce how to prepare qubits based on the generated zero-energy quasi-particles in step S4.

[0179] In some embodiments, generating a qubit based on the zero-energy quasi-particle may include generating a qubit using four of the zero-energy quasi-particles, wherein the overall parity of the four zero-energy quasi-particles is conserved.

[0180] Taking a two-dimensional quantum spin Hall system as an example, it can be achieved by generating four Majorana zero modes at the four vertices. Define a qubit and make the parity of its four zero-energy modes equal. It remains unchanged.

[0181] The Pauli operators X, Y, and Z corresponding to the aforementioned qubits each correspond to the product of two Majorana fermions. , and .

[0182] By using gates that allow tunable electronic transitions and connecting one of the quantum dots to a quantum capacitance readout device based on radio frequency reflection measurements, the total parity of all Majorana fermions traversed by a specified closed loop can be measured using the quantum capacitance in that closed loop, thereby enabling topological quantum computing.

[0183] The above text describes the quantum bit preparation method proposed in the embodiments of this disclosure. By introducing disorder at a specified boundary of a two-dimensional system, the parameter requirements for generating zero-energy quasi-particles can be reduced, thereby enabling the generation of zero-energy quasi-particles in a two-dimensional system and further realizing the generation of topological quantum bits.

[0184] Below, we will combine Figure 10 An apparatus proposed in this disclosure is described, which can be used to generate zero-energy quasi-particles, thereby further preparing qubits. Figure 10 A block diagram of a device according to some embodiments of the present disclosure is shown.

[0185] like Figure 10 As shown, device 10 may include a two-dimensional nanostructure 101, wherein the two-dimensional nanostructure includes multiple boundaries, and the disorder of a specified boundary among the multiple boundaries is different from the disorder of other boundaries among the multiple boundaries. The material of the two-dimensional nanostructure includes a strongly spin-orbit coupled material; and a superconducting material 102, which is coupled in close proximity to the multiple boundaries of the two-dimensional nanostructure.

[0186] The near-neighbor coupling between the superconducting material 102 and the two-dimensional nanostructure 101 has been described above and will not be repeated here.

[0187] In the aforementioned two-dimensional nanostructure, the degree of disorder at a designated boundary differs from that at other boundaries. For example, the disorder intensity of the designated boundary can be higher than that of other boundaries, such as exceeding the critical disorder intensity, while the disorder intensity of other boundaries can be lower than the critical disorder intensity. Thus, when a magnetic field is applied to the designated boundary of the device, the boundary state of the designated boundary can become an Anderson localized state, while the boundary states of other boundaries remain topologically superconducting states. This generates zero-energy quasi-particles, such as Majorana zero modes, at the vertices of the two-dimensional nanostructure.

[0188] The aforementioned device can reduce the parameter requirements for generating zero-energy quasi-particles by introducing disorder at a specified boundary of a two-dimensional system, thereby enabling the generation of zero-energy quasi-particles in a two-dimensional system.

[0189] Figure 11 A block diagram of a quantum computer according to some embodiments of the present disclosure is shown.

[0190] like Figure 11 As shown, the quantum computer 11 may include: a device 10; and an electromagnet 111 configured to apply a magnetic field to a designated boundary of a two-dimensional nanostructure in the device to generate zero-energy quasi-particles at a designated location in the two-dimensional nanostructure.

[0191] In other words, the aforementioned quantum computer can be implemented using the device 10 described above. By applying a magnetic field to a designated boundary in the device 10 using an electromagnet 111, Majorana zero modes can be generated, for example, at the vertices of a two-dimensional nanostructure, thereby further preparing qubits for topological quantum computing.

[0192] Various embodiments of this disclosure have now been described in detail. To avoid obscuring the concept of this disclosure, some details known in the art have not been described. Those skilled in the art will fully understand how to implement the technical solutions disclosed herein based on the above description.

[0193] While specific embodiments of this disclosure have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of this disclosure. Those skilled in the art should understand that modifications can be made to the above embodiments or equivalent substitutions can be made to some technical features without departing from the scope and spirit of this disclosure. The scope of this disclosure is defined by the appended claims.

Claims

1. A method for preparing a quantum bit, comprising: A two-dimensional nanostructure is formed, the two-dimensional nanostructure comprising a strongly spin-orbit coupled material, and multiple boundaries of the two-dimensional nanostructure being coupled in close proximity to a superconducting material; A specified boundary among the plurality of boundaries introduces disorder; By applying a specified magnetic field to the specified boundary, zero-energy quasi-particles are generated at specified locations in the two-dimensional nanostructure. Quantum bits are generated based on the zero-energy quasi-particles.

2. The preparation method according to claim 1, wherein, After the specified magnetic field is applied, the specified boundary is in a first boundary state, and the other boundaries among the plurality of boundaries are in a second boundary state.

3. The preparation method according to claim 2, wherein: The first boundary state includes the Anderson local state; The second boundary state includes the topological superconducting state.

4. The preparation method according to claim 1, wherein: The disorder includes disorder caused by defects in the specified boundary, and the defects include at least one of point defects, line defects, surface defects, and volume defects; The critical disorder intensity is determined based on the superconducting band gap of the superconducting material and the strength of the specified magnetic field.

5. The preparation method according to claim 4, wherein, The critical disorder intensity is positively correlated with the superconducting gap and negatively correlated with the intensity of the specified magnetic field.

6. The preparation method according to claim 1, wherein, The introduction of disorder at a specified boundary among the plurality of boundaries includes: The disorder is introduced by doping at the specified boundary.

7. The preparation method according to claim 6, wherein, Introducing the disorder by doping at the specified boundary includes: Doping is performed on the specified boundary; or The plurality of boundaries are doped, wherein the doping concentration of the specified boundary is different from the doping concentration of the other boundaries among the plurality of boundaries.

8. The preparation method according to claim 6, wherein, The strong spin-orbit coupling material includes a topological insulator material, and the disorder is introduced by doping at the designated boundary, comprising: In the case where the topological insulator material includes a II-VI material quantum well, doping is performed by magnetic impurities; or In the case where the topological insulator material includes a III-V material quantum well, it is doped with non-magnetic impurities.

9. The preparation method according to claim 6, wherein: The doping method includes at least one of the following: growth stage doping, surface adsorption doping, ion beam doping, plasma doping, and diffusion doping; and / or The doping distribution includes at least one of continuous band distribution, lattice distribution, cluster distribution, and gradient distribution.

10. The preparation method according to claim 1, wherein, The introduction of disorder at a specified boundary among the plurality of boundaries includes: The disorder is introduced by changing the shape of the specified boundary to a rough boundary.

11. The preparation method according to claim 10, wherein: The morphology of the specified boundary can be altered by at least one of electron beam lithography, ion etching, and plasma processing; and / or The rough boundary includes at least one of the following: serrated boundary, stepped boundary, random concave-convex boundary, and corner blunting boundary.

12. The preparation method according to claim 1, wherein, Generating qubits based on the zero-energy quasi-particle includes: A qubit is generated using four zero-energy quasi-particles, and the overall parity of the four zero-energy quasi-particles is conserved.

13. The preparation method according to claim 1, wherein, The zero-energy quasi-particles include Majorana zero-energy modes.

14. An apparatus comprising: A two-dimensional nanostructure, wherein the two-dimensional nanostructure includes multiple boundaries, wherein the disorder degree of a specified boundary among the multiple boundaries differs from the disorder degree of other boundaries among the multiple boundaries, and the material of the two-dimensional nanostructure includes a strongly spin-orbit coupled material; and A superconducting material is coupled in close proximity to the multiple boundaries of the two-dimensional nanostructure.

15. A quantum computer, comprising: The device according to claim 14; An electromagnet is configured to apply a magnetic field to a designated boundary of a two-dimensional nanostructure in the device to generate zero-energy quasi-particles at a designated location on the two-dimensional nanostructure.

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