Method and device for providing anyons, and use of the device

Abstract

The present invention relates to a method and apparatus (100) for providing anyons that can be used for topological quantum computing. The method comprises the following steps: providing a magnetic material (10) comprising at least one magnetic texture (15); providing a superconductor (30) comprising at least one vortex (35); generating at least one magnetic texture-vortex pair (50a, 50b) by coupling the magnetic material (10) to the superconductor (30), wherein each magnetic texture-vortex pair (50a, 50b) combines anyons located at the vortex (35) of the corresponding magnetic texture-vortex pair (50a, 50b) in the superconductor (30).

Description

Technical Field

[0001] The present invention relates to a method and apparatus for providing anyons that can be used for topological quantum computing. In addition, the invention relates to the use of the apparatus. Background Art

[0002] One of the major challenges of the next generation is to realize quantum technologies and introduce quantum computing into commercial applications. For example, the European Union (EU) has launched the European Flagship program as a large-scale, long-term research initiative with an estimated budget of 1 billion euros focusing on four application areas: quantum communication, quantum simulation, quantum computing and quantum metrology and sensing. Storing and processing information based on so-called qubits rather than classical binary logic units (bits) allows solving computational problems that are practically infeasible on classical computers. Although quantum computing is currently a research field in its infancy, the economic benefits of realizing quantum computers are enormous, and therefore any invention that brings this field forward can be considered a major achievement. For example, there is currently a fiercely competitive race between academic and industrial research centers working on several different physical platforms, such as superconducting qubits, ion traps, nitrogen vacancy centers and quantum dots, to name just a few.

[0003] A very promising area in the field of quantum computing is topological quantum computing, which circumvents instabilities by exploiting topological properties. Here, logical subspaces are constructed from topological excitations of the underlying material (called anyons), and computational gates are performed by their controlled exchange (i.e., braiding).

[0004] A topological quantum computer is a quantum computer that uses two-dimensional quasiparticles called anyons, whose world lines are woven around each other to form a braid in three-dimensional space-time (i.e., one time plus two spatial dimensions). These braids form the logic gates that make up the computer. The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is more stable. Small cumulative perturbations may cause the quantum state to be decomposed and introduce errors in the calculation, but such small perturbations will not change the topological properties of the braid. Anyons are quasiparticles in two-dimensional space. Anyons are neither fermions nor bosons, and like fermions, they cannot occupy the same state. Therefore, the world lines of two anyons cannot intersect or merge, which allows their paths to form a stable braid in space-time. When anyons are woven, the transformation of the quantum state of the system depends only on the topological class of the anyon's trajectory (which is classified according to the braiding group). Therefore, small errors in the trajectory will not destroy the quantum information stored in the system state.

[0005] The main challenge in today's topological quantum computing is to develop robust, stable, and efficient techniques for performing anyon weaving. Several different techniques have been proposed, but none have yet been implemented. Moreover, previously proposed techniques have practical drawbacks. The best-known proposal is the T-junction approach, in which a T-shaped semiconductor wire is placed on a superconductor and the braiding is accomplished by exchanging states at the edges, as described by J. Alicea et al. in “Non-Abelian statistics and topology quantum information processing in 1D wire networks,” Nat. Phys., vol. 7, pp. 412-417, May 2011, D. Aasen et al.: “Milestones toward Majorana-based quantum computing,” Phys. Rev. X, vol. 6, pp. 031016, August 2016, and B. Bauer et al.: “Dynamics of Majorana-based qubits operated with an array of tunable gates,” SciPost Phys. Phys., vol. 5, p. 004, July 2018. A problem with this technique is that it requires time-dependent tuning of the local chemical potential, which can be performed using gate voltages but is difficult to perform experimentally. Furthermore, it is a one-dimensional system. However, braiding in two dimensions is preferable because anyons are a concept of a two-dimensional system.

[0006] Topological quantum computing has also been theoretically studied in atomic lattice systems, such as in A. Bühler et al., “Majorana modes and p-wave superfluids for fermionic atoms in optical lattices,” Nature Communications, vol. 5, p. 4504, December 2014, and B. Paredes et al., “1 / 2-Anyons in Small Atomic Bose-Einstein Condensate,” Phys. Rev. Lett., vol. 87, p. 010402, June 2001. In such systems, it has been proposed to use lasers to perform the weaving of anyons. Although truly two-dimensional, a robust toolbox for performing computations is still lacking.

[0007] Furthermore, there is a large uncertainty as to whether the zero-energy patterns experimentally discovered so far in several condensed matter systems are true anyons. The only way to be sure whether the found patterns are anyons is to weave them. Summary of the Invention

[0008] The present invention therefore aims to overcome the aforementioned drawbacks. In particular, it aims to provide a platform in which such patterns can be generated so that they can be unambiguously identified as anyons and used for topological quantum computing and quantum memory. Furthermore, it aims to provide methods and devices that can weave arbitrary quasiparticles using currently available technologies, thereby providing central building blocks for realizing topological quantum computers. These problems are solved by the features defined in the independent claims. Preferred embodiments are defined in the dependent claims.

[0009] According to one aspect of the present invention, a method for providing, and in particular manipulating and / or weaving, at least one anyon capable of being used for topological quantum computing is provided. The method comprises the following steps:

[0010] - providing a magnetic material comprising at least one magnetic texture;

[0011] - providing a superconductor comprising at least one eddy current; and

[0012] - generating at least one magnetic texture-vortex pair by coupling a magnetic material to a superconductor, wherein each magnetic texture-vortex pair incorporates anyons localized at vortices of a corresponding magnetic texture-vortex pair in the superconductor.

[0013] Preferably, more than one anyon is provided by the method, in particular at least two anyons. Thus, the magnetic material comprises at least two magnetic textures, the superconductor comprises at least two vortices, and at least two magnetic texture-vortex pairs are generated by coupling the magnetic material to the superconductor.

[0014] The magnetic material may be provided as a thin magnetic layer. It may comprise or be, for example, a ferromagnetic, antiferromagnetic or ferrimagnetic material. Possible magnetic materials include any material in which a magnetic texture, in particular a skyrmion, can be generated, such as MnSi, FeCoSi. In particular, a layered system suitable for breaking the inversion symmetry to allow magnetic texture or skyrmions, such as CoFeB, FeGe or Fe / Ir, may be used as the magnetic material. Depending on the interface interactions, Co or Permalloy may also be used. The size of the magnetic material is selected so that it allows the inclusion of at least one skyrmion. The size of the skyrmion is on the order of a typical helical length scale, which is typically in the range of 1 nm to 5 μm. For example, an overview of known skyrmion-forming materials is given in Table 1 of K. Everschor-Sitte et al.: “Perspective: Magnetic Skyrmions—Overview of recent progress in an active research field,” Journal of Applied Physics 124, 240901 (2018), https: / / doi.org / 10.1063 / 1.5048972, which is incorporated herein by reference in its entirety. The thickness of the magnetic layer can be on the order of 1 nm to 100 nm.

[0015] A superconductor (particularly a type II superconductor) may be provided as the superconducting layer. For example, Nb, cuprate-based type II superconductors such as YBCO, NbSe2, covalent superconductors such as boron-doped diamond or silicon carbide, or carbon-based compounds such as C 60 Cs2Rb or C 60 Rb x ) can be used as a superconductor. The size of the superconductor can be a size that can accommodate at least one eddy current. In particular, the size of the superconductor can be larger or on the order of magnitude of the size of the magnetic material.

[0016] The magnetic texture may generally comprise any magnetic structure or spin structure. Preferably, the magnetic texture is a magnetic local structure, in particular a local spin structure or spin texture. Preferably, the magnetic texture is a topological magnetic texture, and in particular a topological magnetic local structure. In this respect it is noted that topology is a well-known mathematical concept which represents a system for which two structures are equivalent when a continuous mapping from one structure to the other exists. In physics, this concept translates into a finite energy barrier separating two topologically different configurations.

[0017] The magnetic texture can be a skyrmion, an antiskyrmion, a skyrmionium, a biskyrmion, and / or any other spin texture suitable for incorporation into a superconducting vortex. In K. Everschor-Sitte et al., “Perspective: Magnetic skyrmions—Overview of recent progress in an active research field,” J. Appl. Phys. 124, 240901 (2018), https: / / doi.org / 10.1063 / 1.5048972 (see in particular the Figure 1An overview of variations in (topological) magnetic texture, including information on how such magnetic texture is generated, annihilated, and moved in magnetic materials, is given in Sections 4 and 5 (hereinafter referred to as "Sections 4.A and 4.B"), which are incorporated herein by reference in their entirety. In particular, as described herein (particularly Section IV.A therein), skyrmions can be generated by magnetic fields, thermal excitation, spin torque, and / or electric fields. Thus, in a preferred embodiment, the step of providing a magnetic material comprising a magnetic texture comprises generating a magnetic texture in the magnetic material by a magnetic field, an electric field, an electromagnetic field, thermal excitation, and / or spin torque. In addition, the most recent paper on the production of ferrimagnetic skyrmions is Woo et al., “Deterministic creation and deletion of a single magnetic skyrmion observed by direct time-resolved X-ray microscopy,” Nature Electronics, vol. 1, pp. 288–296, May 2018, https: / / www.nature.com / articles / s41928-018-0070-8. Since how to generate magnetic texture in magnetic materials is generally well known, it will not be described in more detail in this article.

[0018] Providing a magnetic material that includes or forms a magnetic texture particularly means preparing and manipulating the magnetic material such that the magnetic texture is present in the magnetic material. Correspondingly, providing a superconductor that includes or forms eddy currents particularly means preparing and manipulating the superconductor such that superconducting eddy currents or magnetic flux quanta (such as Abrikosov eddy currents) are present in the superconductor.

[0019] By coupling a magnetic material to a superconductor, at least one magnetic texture-vortex pair is generated or formed, i.e., a pair consisting of a magnetic texture included in the magnetic material and an eddy current included in the superconductor. In other words, in the magnetic texture-vortex pair, the magnetic texture of the magnetic material is coupled or combined with the eddy current of the superconductor. The magnetic texture-vortex pair, also known as a spin texture-vortex pair, can be considered a quasiparticle.

[0020] In the context of this specification, the term "coupled" particularly means that the magnetic material and the superconductor are arranged and / or in proximity to one another such that a so-called "proximity effect" occurs. Due to the proximity effect, the properties of the magnetic material are introduced into the superconductor, and vice versa. In other words, magnetic texture-eddy current pairs are generated due to the attractive interaction between the magnetic texture of the magnetic material and the eddy currents of the superconductor. For further general information on proximity effects in superconductor-ferromagnet heterostructures, refer to A.I. Buzdin: “Proximity effects in superconductor-ferromagnet heterostructures,” Rev. Mod. Phys., vol. 77, no. 3, pp. 935-976, September 2005, American Physical Society, DOI: 10.1103 / RevModPhys.77.935, https: / / link.aps.org / doi / 10.1103 / RevModPhys.77.935, which is incorporated herein by reference in its entirety.

[0021] In G. Yang et al., “Majorana bound states in magnetic skyrmions,” Phys. Rev. B, vol. 93, No. 22, pp. 1–8, 2016, K. Poyhonen et al., “Skyrmion-induced bound states in a p-wave superconductor,” Phys. Rev. B, vol. 94, No. 21, pp. 1–9, 2016, and U. et al.: "Stabilization and control of Majorana bound states with elongated skyrmions", Phys. Rev. B, vol. 97, p. 115136, March 2018, have proposed that Majorana modes appear at the junctions of magnetic (higher-order) skyrmions with superconductors, without coupling them to vortices. However, it has been found in the present invention that these Majorana modes have major disadvantages with regard to their usability for quantum computing. First, it has been found in the present invention that in such systems Majorana modes are only weakly bound to skyrmions via the exchange field. Furthermore, it has been found in the present invention that additional Majorana modes appear at the boundaries of skyrmions, which hinders the controlled weaving of Majorana modes.

[0022] According to the present invention, anyons are bound to magnetic texture-vortex pairs and localized at the vortices of the magnetic texture-vortex pairs. That is, the anyons are completely localized in the superconductor. In particular, it has been found in the present invention that in a device or system according to the present invention, when there are at least two magnetic texture-vortex pairs, anyons bound to the magnetic texture-vortex pairs are all localized within the corresponding magnetic texture-vortex pairs. In particular, each magnetic texture-vortex pair is bound to exactly one (i.e., only one) anyon. Therefore, according to the present invention, a device or system is provided in which anyons are localized only to quasiparticles (i.e., magnetic texture-vortex pairs). This advantageously allows anyons to be individually addressed.

[0023] The method according to the invention and the corresponding device or system allow for the first weaving of anyons by known experimental techniques (referred to herein as the "spintronics toolbox"). In particular, the magnetic texture-vortex pairs generated according to the invention are controllable by the evolving spintronics toolbox. This therefore decisively eases the manipulation of anyons and ultimately eases access to topological quantum information processing. Furthermore, weaving can advantageously be performed in real two-dimensional systems and requires little error correction. Furthermore, the proposed method and device according to the invention allow for scalability, which addresses another major challenge to quantum computing settings in the current trend.

[0024] In a preferred embodiment, the magnetic texture comprises or is a skyrmion. Additionally or alternatively, the magnetic texture-vortex pair comprises or is a skyrmion-vortex pair. Additionally or alternatively, the anyon comprises or is a Majorana zero mode. A skyrmion is a vortex-shaped magnetic texture with a unique topological structure. In particular, a skyrmion is any spin structure in which the central magnetization is opposite to the direction of its boundary and it can be mapped onto a sphere once. In this sense, a radially symmetric skyrmion can be characterized by two quantities, namely its radial profile and its torsion angle.

[0025] In another preferred embodiment, the superconductor is a type II superconductor and operates in the Shubnikov phase. This can be achieved by applying a magnetic field between the two critical magnetic fields BC1 and BC2 of the superconductor at a temperature below the Curie temperature. In particular, an Abrikosov vortex lattice can be formed in the superconductor.

[0026] In another preferred embodiment, coupling the magnetic material to the superconductor comprises arranging the magnetic material and the superconductor to form a heterostructure based on the magnetic material and the superconductor. In particular, the magnetic material can be arranged directly on the superconductor. In particular, by arranging the magnetic material on the superconductor, an attractive interaction occurs between the magnetic texture (e.g. skyrmions) in the magnetic layer and the eddy currents in the superconductor. Due to this attractive interaction, magnetic texture-eddy current pairs are generated. Alternatively, the magnetic material and the superconductor can be separated by a thin insulating layer in which the magnetic texture is moved by an electric current (see below). The thickness d of the insulating layer is selected such that the attractive interaction between the magnetic texture in the magnetic layer and the eddy currents in the superconductor still exists and is sufficient to generate magnetic texture-eddy current pairs. In other words, the thickness d of the insulating layer is selected such that the current in the superconductor can be neglected, while the heterostructure still experiences a significant exchange field coupling the magnetic texture and the eddy currents. This is possible because the exchange field and the current have different orders of magnitude as a function of the layer thickness d. When the exchange field is proportional to d 2 When the current is proportional to d 4 For example, the thickness d of the insulating layer may be in the range of a few angstroms (eg, 0.2 nm to 5 nm).

[0027] In another preferred embodiment, the method further comprises the step of moving at least two magnetic texture-vortex pairs by means of spintronics so that anyons bound to (and positioned with) the moved magnetic texture-vortex pairs are woven. By weaving two magnetic texture-vortex pairs, a computational gate, i.e., a quantum bit, can be provided. Preferably, two adjacent magnetic texture-vortex pairs are moved. In particular, exactly two magnetic texture-vortex pairs are moved. Spintronics technology particularly comprises applying a magnetic field gradient to a magnetic material, applying an electric field to a magnetic material, inducing a spin torque in a magnetic material, inducing magnetic oscillators in a magnetic material, generating a temperature gradient in a magnetic material, and / or generating thermal fluctuations in a magnetic material. By using this recognized "spintronics technology," anyons (particularly Majorana zero modes) can be manipulated in two-dimensional superconductors. The so-called spintronics toolbox is well known and is processed every day in laboratories around the world. Regarding the “spintronics toolbox”, reference is made to K. Everschor-Sitte et al., “Perspective: Magnetic skyrmions—Overview of recent progress in an active research field,” Journal of Applied Physics, Vol. 124, 240901 (2018), https: / / doi.org / 10.1063 / 1.5048972, in particular Section IV thereof, which has been cited above and is incorporated herein by reference in its entirety. For example, spin torque is the torque induced by an electric current to manipulate magnetic texture. The main examples are STT (spin transfer torque) and SOT (spin orbit torque), which are being experimented on by several groups worldwide. Moving magnetic texture—vortex pairs—by electric fields can be performed, for example, by means of a scanning tunneling microscope (STM) tip. An alternative to a specific approach involving spin texturing involving magnons is to use a temperature gradient. Here, thermal spin currents can transfer angular momentum, and additional entropic effects can also lead to motion of the spin structure. Moreover, even without any external actuators, magnetic textures or skyrmions can randomly change their positions due to very weak thermal fluctuations in the pinned sample at higher temperatures.

[0028] In another preferred embodiment, the two magnetic texture-vortex pairs are woven by moving them with at least one scanning tunneling microscope (STM) tip and / or by applying an electric current (including current pulses) in the magnetic material. Due to their topological structure, the skyrmions experience the Magnus effect, which is similar to the rotation of a ball during a curved shot, and thus move along the applied current.

[0029] In another preferred embodiment, the method includes a step of reading out information by fusing two anyons. In particular, the information read out is logical information in the form of quantum bits. Two anyons, i.e., an anyon pair (e.g., two Majoranas), form a fermionic state that is either occupied or unoccupied by electrons. By moving the two anyons relative to each other and then fusing these anyons, electrons may or may not be generated. Therefore, the readout step preferably includes electron detection and / or current measurement.

[0030] In another preferred embodiment, providing the magnetic material includes constructing the magnetic material to form a grid of magnetic material. The grid can be constructed or formed using standard manufacturing techniques such as optical and / or electron beam lithography. Thus, the provided magnetic material is formed into a grid. The grid of magnetic material preferably includes a plurality of electrodes. A voltage can be applied to the electrodes so that an electric current can be induced into the magnetic material or the grid of magnetic material. The electrodes are used to move the magnetic texture-eddy current pairs by the electric current. The electrodes can be manufactured using standard manufacturing techniques (such as optical and / or electron beam lithography and vacuum deposition). In particular, the geometry of the grid is configured so that the magnetic texture-eddy current pairs can move around each other within the grid, in particular within a predetermined path of the grid. Preferably, the geometry of the grid is configured so that the magnetic texture-eddy current pairs can move independently within the grid or along a predetermined path of the grid. In other words, the grid preferably includes or defines one or more (predetermined) paths along which at least one texture-eddy current pair can be moved, for example, by an electric current. In particular, the grid includes or defines a plurality of such paths. The number of paths can depend on the number of magnetic textures present in the magnetic material. The grid can include gaps with rectangular or triangular cross-sections. The number of gaps can depend on the number of magnetic textures present in the magnetic material, and therefore on the number of magnetic texture-vortex pairs. In particular, the more magnetic texture and / or magnetic texture-vortex pairs are generated, the more gaps must be present in the grid. Since the magnetic material is constructed or formed into a grid, the magnetic texture-vortex pairs can be controlled and / or moved, thereby allowing the controlled weaving of anyons.

[0031] In particular, the method comprises the steps of moving two magnetic texture-vortex pairs, and therefore two anyons, by applying voltages to at least some of the electrodes of the grid such that the two anyons move towards each other, thereby weaving the anyons.

[0032] According to another aspect of the present invention, there is provided an apparatus for providing anyons, and in particular for manipulating and weaving anyons. The apparatus comprises:

[0033] - a magnetic material comprising at least one magnetic texture in the operating mode of the device;

[0034] - a superconductor which, in the operating mode of the device, contains at least one eddy current;

[0035] wherein the magnetic material and the superconductor are arranged to be coupled to each other such that in an operating mode of the device at least one magnetic texture-vortex pair is generated, wherein each magnetic texture-vortex pair incorporates anyons located at the vortices of the corresponding magnetic texture-vortex pair in the superconductor.

[0036] In particular, the device provides more than one anyon, in particular at least two anyons. Thus, the magnetic material comprises at least two magnetic textures, the superconductor comprises at least two eddies, and at least two magnetic texture-eddy pairs are generated by coupling the magnetic material to the superconductor.

[0037] The operating mode is a mode in which the device is operated to provide at least one anyon. In particular, operating the device in the operating mode means satisfying any conditions necessary to generate at least one magnetic texture in the magnetic material and at least one eddy current in the superconductor, such as temperature, magnetic field, electric field, etc. For example, to generate at least one eddy current in the superconductor, the superconductor can be operated in the Shubnikov phase, which is achieved by applying a magnetic field between two critical magnetic fields BC1 and BC2 of the superconductor at a temperature below the Curie temperature of the superconductor. In addition, to generate at least one magnetic texture in the magnetic material, any available technique can be used, such as generating magnetic texture by magnetic and / or electric fields, generating magnetic texture by thermal excitation and / or generating magnetic texture by spin torque, see above.

[0038] In a preferred embodiment, the magnetic material and the superconductor, in particular a type II superconductor, are arranged to form a heterostructure.

[0039] In another preferred embodiment, the device comprises an insulating layer arranged between the magnetic material and the superconductor.

[0040] In another preferred embodiment, the magnetic material is configured to form a grid of magnetic material, wherein the grid preferably has a rectangular or square geometry. Alternatively, the grid has a triangular geometry or shape, i.e., a geometry having a triangular structure or lattice. In particular, the grid has a plurality of gaps, wherein each of the plurality of gaps preferably has a rectangular cross-section and / or a square cross-section or a triangular cross-section. With these geometries, anyons can be woven by moving anyons within the grid or along a predefined path of the grid. Thus, due to the grid, magnetic textures and thus magnetic texture-eddy current pairs can be manipulated, moved and / or woven in a controlled manner.

[0041] In another preferred embodiment, the grid of magnetic material includes a plurality of electrodes to which a voltage can be applied. The electrodes are used to move the magnetic texture-eddy current pairs by the current. The number of electrodes can be proportional to the number of anyons in the device or system.

[0042] In another preferred embodiment, the grid of magnetic material forms a plurality of (predetermined) paths along which the magnetic texture is able to move. Due to their function, the paths or channels can also be referred to as current paths. The magnetic texture (in particular skyrmions) can be moved along these paths by applying a current flowing through the paths via electrodes. Thus, in this embodiment, the movement of the magnetic texture is current-driven. Preferably, each of the paths has two end portions. Furthermore, each of the end portions preferably comprises an electrode. Thus, the number of (current) paths formed by the grid is half the number of electrodes.

[0043] In another preferred embodiment, the device comprises an operating unit configured to place the magnetic material and / or the superconductor in an operating mode. In other words, the operating unit is configured to generate at least one magnetic texture in the magnetic material and / or generate at least one eddy current in the superconductor. Thus, the operating unit is configured to operate the device in an operating mode in which at least one magnetic texture-eddy current pair (and thereby anyons) is formed or generated. The operating unit may comprise any unit necessary to generate at least one magnetic texture in the magnetic material and at least one eddy current in the superconductor. More specifically, the operating unit may comprise a magnetic texture generating unit and / or an eddy current generating unit. The magnetic texture generating unit is configured to generate at least one magnetic texture in the magnetic material, and the eddy current generating unit is configured to generate at least one eddy current in the superconductor. Preferably, the operating unit, and in particular the magnetic texture generating unit, includes at least one of the following units: a magnetic field unit for generating a magnetic field in the magnetic material; a magnetic field gradient unit for generating a magnetic field gradient in the magnetic material; an electric field unit for generating an electric field in the magnetic material; a spin torque generating unit for generating a spin torque in the magnetic material; a magnon generating unit for generating magnons in the magnetic material; a temperature gradient generating unit for generating a temperature gradient in the magnetic material; and a thermal fluctuation generating unit for generating thermal fluctuations in the magnetic material. Further preferably, the operating unit, and in particular the eddy current generating unit, includes a magnetic field unit for applying a magnetic field to the superconductor and a cooling unit for cooling the superconductor to below its Curie temperature. In addition, the operating unit may include a control unit for controlling any other units included in the operating unit. The control may be performed based on predetermined or adjustable parameters, wherein the parameters depend on the magnetic material and / or superconductor of the device.

[0044] Furthermore, another aspect of the present invention is the use of the device according to the invention for topological quantum computing and / or quantum memory.

[0045] Any quantum circuit can be simulated to arbitrary precision using a combination of CNOT gates and single-qubit rotations. Two anyons or Majoranas correspond to one qubit. "Real computation" can be performed with as few as two qubits, or four anyons or Majoranas. With four anyons, the minimum computational basis for all required quantum gates can be realized. Thus, in particular by providing four anyons or Majoranas, the device according to the invention can be used for topological quantum computing, the general principles of which are described, for example, in DAIvanov et al., “Non-Abelian Statistics of Half-Quantum Vortices in p-Wave Superconductors”, Physical Review Letters (Phys. Rev. Lett.), Vol. 86, No. 2, pp. 268-271, January 2001, American Physical Society, DOI: 10.1103 / PhysRevlett.86.268, https: / / journals.aps.org / prl / abstract / 10.1103 / PhysRevlett.86.268.

[0046] Furthermore, the method and apparatus according to the invention are inherently scalable, since the qubit density can be increased simply by adding more magnetic texture-vortex pairs. The fundamental limit is simply given by the repulsive length scale of the pairs, which is of the order of 10 micrometers for the systems studied so far. Since one qubit can be represented by four magnetic texture-vortex pairs, this allows for approximately 10 5 qubits / cm 2 This leads to a significant reduction in the complexity of quantum error correction, saving material and energy resources, on the long-explored path to topological quantum computing.

[0047] The present invention enables high computational power, i.e., a qubit density at least a thousand times higher (10 5 qubits / cm 2 This compares to the 100 qubits / cm typically achievable in conventional superconducting qubit systems. 2, because more error correction is required here). Therefore, the present invention enables miniaturized topological quantum computing. In particular, a device size 1000 times smaller than previously proposed systems with the same qubit density is possible. In addition, with the present invention, topological quantum computing is possible, with which problems that cannot be solved by current classical computers can be solved. For example, more chemical, pharmaceutical or medical problems can be calculated. In addition, neural network systems can be accelerated and better pattern recognition is possible. In addition, improvements in the fields of material development and coding can be achieved.

[0048] In a preferred embodiment, the use of the device comprises:

[0049] - operating the device to provide at least two anyons; and

[0050] - providing at least one qubit by braiding at least one pair of at least two anyons.

[0051] In another preferred embodiment, the use of the device further comprises reading out information by fusing at least one of the anyon pairs.

[0052] For the further independent aspects mentioned above, and in particular for the preferred embodiments of these aspects, the explanations given above or below regarding the embodiments of the first aspect also apply. In particular, for an independent aspect of the present invention and for the preferred embodiments of this aspect, the explanations given above and below regarding the embodiments of the corresponding other aspects also apply.

[0053] The various embodiments for solving the problem are described below in an exemplary manner with reference to the accompanying drawings. In this case, the various embodiments described partially have features that are not absolutely necessary for realizing the claimed subject matter, but provide desired properties in specific applications. In this regard, embodiments that do not have all the features of the embodiments described below are also intended to be considered to be disclosed in the manner of the technical teachings described below. In addition, in order to avoid unnecessary repetitions, specific features are mentioned only for each embodiment in the embodiments described below. It is to be noted that the various embodiments are therefore not only intended to be considered as themselves, but also to be considered in conjunction with each other. Based on this joint consideration, those skilled in the art will recognize that the various embodiments can also be modified by including single or multiple features of other embodiments. It is to be noted that the systematic combination of the various embodiments with the single or multiple features described with respect to other embodiments may be desirable and advantageous, and is therefore intended to be considered and is also considered to be included in the specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The above and other objects, features, and advantages of the present invention will become more apparent upon reading the following description of preferred embodiments and the accompanying drawings. Other features and advantages of the subject matter described herein will be apparent from the description, drawings, and claims. It should be understood that even if embodiments are described separately, their individual features and functions may be combined without affecting additional embodiments. The present disclosure is illustrated by way of example and is not limited by the accompanying drawings.

[0055] Preferred embodiments of the present invention are exemplarily described with reference to the following drawings:

[0056] Figure 1 shows a schematic representation of an apparatus according to an example of the present invention in an exploded view;

[0057] Figure 2a shows the simulated probability density of Majorana zero modes in a system with one skyrmion-vortex pair;

[0058] Figure 2b shows the simulated probability density of Majorana zero modes in a system with two skyrmion-vortex pairs;

[0059] Figure 3 shows a schematic representation of an apparatus according to another example of the present invention, wherein the magnetic texture-vortex current pair moves together with the STM tip;

[0060] Figure 4a-4c shows a schematic representation of a device according to another example of the present invention, wherein two magnetic textures and therefore two magnetic texture-eddy current pairs move with an electric current;

[0061] Figure 5 shows a schematic representation of an apparatus according to another example of the present invention;

[0062] Figure 6a-6d shows a schematic representation of a device according to another example of the present invention, wherein two magnetic textures and therefore two magnetic texture-eddy current pairs move with an electric current;

[0063] Figure 7 A schematic representation of an apparatus according to another example of the present invention is shown. DETAILED DESCRIPTION

[0064] The following detailed description relates to exemplary embodiments of the present invention. Other embodiments of the present invention are also possible within the scope of the invention as defined by the appended claims. For example, in the following description, the magnetic texture is considered to be skyrmions, although other magnetic textures such as anti-skyrmions or skyrmions are also possible. The same reference numerals are used for the same or similar elements throughout the drawings.

[0065] Figure 1 A schematic representation of an exploded view of a device 100 according to an example of the present invention is shown. The device 100 includes a magnetic material 10 and a superconductor 30. The magnetic material 10 contains skyrmions 15, while the superconductor 30 contains vortices 35. The magnetic material 10 is arranged on top of the superconductor 30, thereby forming a heterostructure. In the device 100 or heterostructure 100 comprising coupled superconducting and magnetic layers, anyons carrying superconducting vortices 35 can be controlled by magnetic skyrmions 15. Thus, anyons can be woven and topological quantum computing can be performed using spintronics techniques.

[0066] In particular, the magnetic material 10 forming the skyrmions 15 is coupled to a type II superconductor 30. As a result, certain topological quasiparticles are formed, so-called skyrmion-vortex pairs. In the present invention, it has been found that these skyrmion-vortex pairs combine with Majorana modes, which can be used for weaving. The advantage of skyrmion-vortex pairs is that the localization of the Majorana modes occurs entirely at the vortices 35 in the superconductor 30, and the skyrmions 15 even enhance this effect, without obtaining additional Majorana modes at the boundaries. Previously, it has been proposed that Majorana modes appear at the junction of magnetic (higher-order) skyrmions with the superconductor (without coupling them to the vortices). However, these Majorana modes have major disadvantages in terms of their usability for quantum computing. First, in such a system, Majorana modes are only weakly coupled to the skyrmions via the exchange field. In addition, additional Majorana modes appear at the boundaries of the skyrmions, which hinders weaving.

[0067] exist Figure 1 In the device 100 shown, skyrmion-vortex pairs can be generated and eliminated in a controlled manner. To this end, a superconductor 30 can be manipulated to form an Abrikosov vortex lattice, and magnetic skyrmions can be written into the magnetic material 10 using standard devices. Skyrmion-vortex pairs form due to the attractive interaction between skyrmions and vortices. Skyrmion-vortex pairs can also be eliminated by annihilating skyrmions in the magnet. Note that skyrmions can also be written and eliminated using a scanning tunneling microscope.

[0068] By self-consistently solving the Bogoliubov de-Gennes equation, we have found that in certain parameter regimes, superconducting ferromagnetic heterostructures form Majorana modes, which are a type of anyon. In a system with only one skyrmion-vortex pair, two Majorana zero modes can be found, one of which is localized inside the skyrmion-vortex pair and one at the edge of the sample. Figure 2a This situation is shown in Figure 2aFigure 2 shows the simulated probability density of Majorana zero modes in a system with one skyrmion-vortex pair. L represents the dimensions (length and width) of the sample. The Majorana modes at the edge are scaled by a factor of three for clarity.

[0069] When there are two skyrmion-vortex pairs, two Majorana modes are localized within each of the two pairs, e.g. Figure 2b As shown, Figure 2b Shown is the simulated probability density of Majorana zero modes in a system with two skyrmion-vortex pairs. This setup, in which Majorana modes are localized only to quasiparticles, allows for individual addressing of Majorana modes.

[0070] Skyrmion-vortex pairs are strongly bound: for example, theoretical estimates for a monolayer of the superconductor NbSe2 suggest that proximity-induced exchange fields of the order of 2.3 meV in the superconductor give rise to binding exceeding the temperature scale typical of these experimental systems (3 K). Therefore, the entire spintronic toolbox can be used to move skyrmions, and hence anyon-bearing skyrmion-vortex pairs.

[0071] like Figure 3 Shown is the controlled form of moving magnetic textures via scanning tunneling microscopy (STM). Figure 3 A schematic representation of an apparatus 100 according to another example of the present invention is shown. In this example, a magnetic material 10 is separated from a superconductor 30 by an insulator 20. A first skyrmion-vortex pair 50a and a second skyrmion-vortex pair 50b are each moved by an STM tip. Thus, anyons bound to the skyrmion-vortex pairs 50a and 50b can move relative to each other and thus be woven together. In other words, the skyrmion-vortex pairs 50a and 50b are dragged with the STM tip so as to follow the circular motion until both pairs 50a and 50b are replaced. This is a good setup for a proof of principle, but is very impractical for scalability.

[0072] Figure 4a-4c Shown is a schematic representation of an apparatus 100 according to another example of the present invention, which may be used for scalability. Figure 4a-4cThe device 100 further comprises a magnetic material 10 and a superconductor 30. The magnetic material 10 is formed into a grid of magnetic material and is arranged on top of the superconductor 30. The grid of magnetic material comprises a plurality of gaps 17, i.e. areas where no magnetic material is present. The magnetic material 10 is separated from the superconductor by a thin insulating layer 20 and an electric current is used to move the skyrmions and therefore the skyrmion-eddy current pairs 50a and 50b. The function of the insulating layer 20 is to protect the superconductor 30 from the effects of the electric current applied to the magnetic material 10. The thickness d of the insulating layer needs to be chosen so that the current in the superconductor 30 is negligible while it still experiences a significant exchange field coupling the skyrmions and eddy currents. This is possible because the exchange field and the current magnitude are different functions of the insulating layer thickness d. When the exchange field is proportional to d 2 When the current is proportional to d 4 To weave Majorana, two skyrmion-vortex pairs 50a, 50b can be moved with counter-propagating currents. This drive needs to be slow enough to ensure that i) the skyrmion-vortex pairs 50 do not dynamically unbind, and more importantly ii) the superconducting state remains in its (quasi-) zero-energy excitation region. Criterion ii) has proven to be the most stringent and leads to estimates of possible skyrmion velocities of the order of 40 m / s.

[0073] like Figure 4a-4c As shown in FIG, the grid of magnetic material 10 has a rectangular geometry and comprises a plurality of electrodes 13 labeled A, B, C, ... to P. Figure 4a , a voltage is applied between electrodes O and F. This induces a current that drives or moves the first skyrmion-eddy current pair 50a along a first predetermined current path, which is arranged between electrodes O and F, toward electrode F. Simultaneously, an opposite voltage is applied between electrodes N and G, thereby inducing a current that drives or moves the second skyrmion-eddy current pair 50b along a second predetermined current path, which is arranged between electrodes G and N, toward electrode N. Subsequently, as Figure 4b As shown, a voltage is applied between electrodes C and J. This induces a current that drives or moves the first skyrmion-eddy current pair 50a along a predetermined current path disposed between electrodes C and J, toward electrode J. Simultaneously, an opposite voltage is applied between electrodes B and K, thereby inducing a current that drives or moves the second skyrmion-eddy current pair 50b along a predetermined current path disposed between electrodes B and K, toward electrode B. Thus, according to Figure 4a-4c The procedure shown weaves the Majorana bound to the skyrmion-vortex pair 50a and 50b by exchanging their positions. Figure 4a-4c , the skyrmion-eddy current pairs move from the negative voltage electrode to the positive voltage electrode.

[0074] Figure 5 A schematic top view of a device 100 according to another example of the present invention is shown. Figure 4a-4c The example shown in FIG and illustrates its scalability to provide more qubits. In the example shown, a grid of magnetic material 10 is arranged on top of a superconductor 30, wherein the grid has square gaps 17.

[0075] Figure 6a-6d A schematic representation of an apparatus according to another example of the present invention is shown, wherein two anyons and therefore two anyon-eddy current pairs 50a and 50b are moved by an electric current. Figure 4a-4c The device 100 has a grid of magnetic material of rectangular geometry, Figure 6a-6d The device 100 has a grid 10 of magnetic material 10 with a triangular geometry.

[0076] like Figure 4a-4c As shown in FIG, the magnetic material 10 is passed through a thin insulating layer ( Figure 6a-6d ) is separated from the superconductor 30, and an electric current is used to move the skyrmions, and thus the skyrmion-vortex pairs 50a and 50b. Figure 6a-6d In FIG, the electrodes 13 are labeled Q, R, S, T, U, and V. To weave Majorana, the skyrmion-vortex pairs 50a and 50b are moved as follows: Figure 6a , a voltage is applied between electrodes V and S. This induces a current that drives or moves the first skyrmion-eddy current pair 50a along a predetermined current path arranged between electrodes V and S, toward electrode S. Subsequently, as Figure 6b As shown, a voltage is applied between electrodes T and Q. This induces a current that drives or moves the second skyrmion-eddy current pair 50b along a predetermined current path arranged between electrodes T and Q, toward electrode Q. Subsequently, as Figure 6c As shown, a voltage is applied between electrodes R and U. This induces a current that drives or moves the first skyrmion-eddy current pair 50a along a predetermined current path arranged between the electrodes R and U, towards the electrode U. Thus, by Figure 6a-6d The Majorana particles bound to the skyrmion-vortex pairs 50a and 50b have been woven by replacing their positions. Figure 6a-6c , the skyrmion-eddy current pairs move from the electrode with negative voltage to the electrode with positive voltage.

[0077] Figure 7 A schematic top view of a device 100 according to another example of the present invention is shown. Figure 6a-6dThe example shown in FIG. 1 and its scalability to provide more qubits is shown. In the example shown, a grid of magnetic material 10 is arranged on top of a superconductor 30, wherein the grid has triangular gaps. Figure 7 The dashed line in represents one of the predetermined current paths P. This path has two end portions, wherein each end portion comprises an electrode 13 .

[0078] The ability to weave anyons, as the core of any topological quantum gate, opens the path to fully fledged topological quantum computers. To verify the functionality of any gate, the system must be read out. This can be accomplished by fusing two anyons. A possible approach to fusing anyons bound to a skyrmion-vortex pair is to pin one skyrmion and move the other skyrmion into it. By fusing anyons, the logical information stored in the system's state can be accessed.

[0079] In summary, with the present invention, an experimentally achievable platform is provided to generate, manipulate and read out anyons, especially those of the simplest non-Abelian class, namely Majorana zero-energy modes, in a more practical way than any other theoretical proposal made before. In particular, a direct device is provided to perform a smoking gun experiment for weaving, which has not been observed so far and is a key missing component in the field of topological quantum computing. The present invention not only allows the generation, weaving and fusion of anyons, but also provides the possibility of expanding the number of qubits, thereby paving the way for topological quantum computing and solving several challenges. More specifically, the present invention enables the weaving of arbitrary quasiparticles with the help of currently available technology, thereby demonstrating and providing a central building block for the realization of a topological quantum computer.

[0080] Reference Signs List

[0081] 10 Magnetic material (magnetic layer)

[0082] 13 electrodes

[0083] 15 Magnetic texture (skyrmions)

[0084] 17 Gaps in Magnetic Materials

[0085] 20 Insulator (insulating layer)

[0086] 30 Superconductor (superconducting layer)

[0087] 35 Superconducting vortex

[0088] 40 Scanning Tunneling Microscope (STM) Tip

[0089] 50 Magnetic texture-eddy current pairs (skyrmion-eddy current pairs)

[0090] 50a The first magnetic texture-vortex pair (the first skyrmion-vortex pair)

[0091] 50b The second magnetic texture-vortex pair (the second skyrmion-vortex pair)

[0092] 100 Devices (Magnet-Superconductor Heterostructures)

[0093] P-path

Claims

1. A method for providing at least one anyon capable of being used for topological quantum computing, comprising the following steps: - providing a magnetic material (10) comprising at least one magnetic texture (15); - providing a superconductor (30) comprising at least one eddy current (35); and - generating at least one magnetic texture-vortex pair (50a, 50b) by coupling the magnetic material (10) to the superconductor (30), wherein each magnetic texture-vortex pair (50a, 50b) combines anyons located at the vortex (35) of the corresponding magnetic texture-vortex pair (50a, 50b) in the superconductor (30), wherein the magnetic material (10) is configured to form a grid of magnetic material, and wherein the grid of magnetic material forms a plurality of paths in which the magnetic texture (15) can move.

2. The method according to claim 1, wherein The at least one magnetic texture (15) comprises skyrmions, and / or The at least one magnetic texture-vortex pair (50a, 50b) comprises a skyrmion-vortex pair, and / or The anyons are Majorana zero modes.

3. A method according to any one of the preceding claims, wherein Connecting the magnetic material (10) to the superconductor (30) includes arranging the magnetic material (10) and the superconductor (30) so as to form a heterostructure (100) based on the magnetic material (10) and the superconductor (30).

4. The method according to claim 1, further comprising the steps of: - moving at least two magnetic texture-vortex pairs (50a, 50b) by means of a spintronics technique to weave anyons coupled to the moved magnetic texture-vortex pairs (50a, 50b), wherein the spintronics technique in particular comprises applying a magnetic field gradient to the magnetic material (10), applying an electric field to the magnetic material (10), inducing a spin torque in the magnetic material (10), inducing magnons in the magnetic material (10), generating a temperature gradient in the magnetic material (10) and / or generating a thermal fluctuation in the magnetic material (10).

5. The method according to claim 1, wherein The two magnetic texture-vortex pairs (50a, 50b) are woven by moving the two magnetic texture-vortex pairs (50a, 50b) by means of at least one scanning tunneling microscope tip (40) and / or by applying an electric current in the magnetic material (10).

6. The method according to claim 1, further comprising the steps of: - reading out information by fusing two anyons, wherein fusing the two anyons comprises pinning a first anyon of the two anyons and moving a second anyon of the two anyons into the first anyon of the two anyons.

7. The method according to claim 1, wherein Providing a magnetic material (10) includes structuring the magnetic material (10) to form a grid of magnetic material, wherein the grid of magnetic material includes a plurality of electrodes (13) and / or wherein the grid of magnetic material includes gaps (17) having a rectangular cross-section or a triangular cross-section.

8. A device (100) for providing at least one anyon, comprising: - a magnetic material (10) comprising at least one magnetic texture (15) in the operating mode of the device (100); - a superconductor (30) containing at least one eddy current (35) in an operating mode of the device (100); wherein the magnetic material (10) and the superconductor (30) are arranged to be coupled to each other such that in the operating mode of the device (100) at least one magnetic texture-vortex pair (50a, 50b) is generated, wherein each magnetic texture-vortex pair (50a, 50b) combines anyons located at the vortex (35) of the corresponding magnetic texture-vortex pair (50a, 50b) in the superconductor (30), wherein the magnetic material (10) is configured to form a grid of magnetic material, and wherein the grid of magnetic material forms a plurality of paths in which the magnetic texture (15) can move.

9. The device (100) according to claim 8, wherein The magnetic material (10) and the superconductor (30) form a heterostructure, and / or wherein an insulating layer (20) is arranged between the magnetic material (10) and the superconductor (30).

10. The device (100) according to claim 8 or 9, wherein: The grid has a rectangular or triangular geometry, and / or The grid comprises gaps (17) having a rectangular or triangular cross-section, and / or The grid comprises a plurality of electrodes (13) to which a voltage can be applied.

11. The device (100) according to claim 8, wherein Each of the plurality of paths has two end portions, and wherein each of the end portions includes an electrode (13).

12. The apparatus (100) according to claim 8, further comprising an operating unit configured to operate the magnetic material (10) and the superconductor (30) in the operating mode.

13. Use of the device (100) according to claim 8, wherein the use is for topological quantum computing and / or quantum memory.

14. Use of the device (100) according to claim 13, wherein: At least one qubit is provided by weaving at least one pair of anyons.

15. Use of the device (100) according to claim 14, further comprising: - reading out information by fusing anyons of at least one of the anyon pairs, wherein fusing two anyons comprises pinning a first anyon of the two anyons and moving a second anyon of the two anyons into the first anyon of the two anyons.

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