Method for shifting defect centers in a substrate for quantum applications in a defined direction

Abstract

Method (20) for displacing defect centers (6) in a substrate for quantum applications in a defined direction, the method comprising the following steps - in particular providing a substrate, in particular diamond, which comprises defect centers (6) in a bulk substrate structure, in particular a massive diamond crystal lattice (50), - detecting the position of at least one defect center (6) in the bulk substrate structure, in particular the massive diamond crystal lattice (50), and - Displacing (61) the at least one defect center (6) in the volume substrate structure, in particular the massive diamond crystal lattice (50), in particular in a location-specific manner, in a defined direction.

Description

[0001] The invention relates to a method for shifting defect centers in a substrate, in particular diamond, for quantum applications in a defined direction.

[0002] The invention relates to a method for training a machine learning model. The invention relates to a method for the automated spatial structuring of defect centers in a substrate, in particular a diamond crystal lattice. The invention relates to a system configured and structured to perform at least one of the respective methods. The invention relates to a computer program product. The invention relates to a device, in particular a diamond crystal. The invention relates to a method configured to manufacture a device.

[0003] Defect centers in certain substrates, such as diamond, are promising structures for the study of quantum properties and represent a promising tool for quantum computing, such as the creation of qubit calculations. Alternatively, or additionally, they can function as measurement tools for optically detecting magnetic resonances to study biological materials and their respective properties, and they provide powerful quantum sensors for investigating magnetic phenomena at the nanoscale, from biological processes to novel magnetic materials. Their implementation is difficult and requires precise control, especially in terms of enabling coupling between defect centers, which is suitable for the creation of corresponding quantum gates, quantum communication networks, or the like.

[0004] Scanning tunneling microscopy has been used in combination with atomic force microscopy to resolve atom positions, modify the surface, and manipulate surface atoms with its sharp atomic tip. However, this requires cryogenic temperatures and conductive surfaces, and the tip must be positioned closer to the surface. This increases the complexity of the respective techniques but still leaves much to be desired in terms of control.

[0005] One object of the invention is to improve the control of the production of corresponding modifications. One object of the invention is to reduce the complexity of the required structure and the method to be carried out.

[0006] The object of the invention is achieved by a method for displacing defect centers in a substrate for quantum applications in a defined direction according to claim 1 and / or claim 2. The object of the invention is achieved by a method for training a machine learning model according to claim 15. The object of the invention is achieved by a method for the automated spatial structuring of defect centers in a substrate (a structure), in particular a diamond crystal lattice, according to claim 16. The object of the invention is achieved by a system according to claim 18. The object of the invention is achieved by a computer program product according to claim 19. The object of the invention is achieved by a device, in particular a diamond crystal, according to claim 20. The object of the invention is achieved by a manufacturing method according to claim 21.

[0007] Advantageous embodiments of the invention are the subject of the dependent claims, the description, and the figures. Features, feature combinations, technical effects, and advantages described in connection with the method for manipulating defect centers also apply to the method for training a machine learning model and the method for the automated spatial structuring of defect centers in a substrate structure, in particular a diamond crystal lattice, as well as to a manufacturing method. Features, feature combinations, technical effects, and advantages described in connection with one of the methods also apply with regard to the system, the computer program product, or the device, in particular the diamond crystal. This also applies vice versa, so that with regard to the disclosure of the individual aspects of the invention, reciprocal reference is always made.can be, in particular regardless of the category described and / or claimed.

[0008] According to one aspect, the object is achieved by a method having the features of claim 1.

[0009] The method can be configured to displace defect centers in a substrate for quantum applications in a defined direction as an exemplary form of manipulation. The method can comprise a step of providing a substrate, in particular a diamond, wherein the substrate, in particular the diamond, comprises defect centers in a bulk substrate structure, in particular in a massive diamond crystal lattice. The method can comprise a step of detecting the position of at least one defect center in the bulk substrate structure, in particular in the massive diamond crystal lattice. The method can comprise a step of displacing the at least one defect center in the bulk substrate structure, in particular in the massive diamond crystal lattice. The displacing of the at least one defect center in the bulk substrate structure, in particular the massive diamond crystal lattice, can be carried out in a particularly location-specific manner.The displacement can be performed in a defined direction. This allows for increased precision in the manipulation of defect centers in substrates, especially diamonds, which can be used as solid-state qubits for quantum information processing.

[0010] The provision of a substrate, in particular diamond, can be understood as the prefabrication of the substrate, in particular diamond, which is partially doped with defect centers located at several randomly spaced and positioned structural sites of the substrate, in particular lattice sites. In the case of nitrogen vacancy centers (NV centers), these can be implanted into the substrate structure, in particular the diamond lattice, using two methods: ion implantation and electron irradiation. Both methods are particularly stochastic, meaning that the formation of NV centers is probabilistic and therefore cannot be reliably used to generate a network of coupled spins. Nevertheless, these methods make it possible to provide a suitable substrate, in particular in the form of diamond.

[0011] Alternatively or additionally, the term "providing a substrate" may refer to any handling of a substrate, such as diamond, doped with corresponding defect centers, at least one of which is to be moved during the process described elsewhere herein. Therefore, any use or handling of a corresponding substrate may be considered providing the substrate.

[0012] The manufacture of a device comprising a substrate, which comprises at least one defect center, in particular having a plurality of defect centers, is understood here in particular to mean the completion of a substrate in which at least one defect center is positioned at an intended structural position (lattice position), which differs in particular from the initial defect center position when the substrate, in particular the diamond, is provided for the method to begin the displacement of at least one defect center. Positioning, displacement, and corresponding further steps apply analogously to the case where multiple defect centers are placed within the structure of the substrate, in particular the diamond crystal lattice.

[0013] A defect center in the bulk substrate structure, in particular the bulk diamond crystal lattice, may be a configuration in which the structure of the substrate, in particular the diamond crystal lattice, deviates from the standard structural configuration of the substrate; in the case of diamond, the carbon configuration deviates from that of a standard and average diamond crystal lattice, in particular as described elsewhere herein.

[0014] Displacing the at least one defect center in the bulk substrate structure, in particular the massive diamond crystal lattice, is understood to mean, in particular, changing the position of the defect center from the initial position of the defect center when the substrate, in particular diamond, is provided for carrying out the respective method.

[0015] Displacing the at least one defect center in a (precisely) defined direction refers, in particular, to the ability of the method to initiate and execute a displacement that is not merely determined by a statistical displacement of the defect center in a stochastic manner. The respective manipulation of the defect center can therefore have a preferred displacement direction in which the respective defect center moves upon appropriate execution of the method steps.

[0016] According to embodiments also set forth in more detail elsewhere herein, the directional manipulation and controlled positioning of defect centers, such as vacancy color centers, as solid-state qubits in diamonds may be based on the use of a focused, atom-sized vortex electron beam formed by a holographic aperture in an aberration-corrected scanning transmission electron microscope (AC-STEM) to fabricate a scalable multi-qubit quantum processor enabling quantum information processing applications, such as quantum sensing and quantum information processing, in particular quantum computing. Furthermore, the respective method could enable the fabrication of test and research devices to investigate the respective behavior of these qubit structures and qubit networks.

[0017] This and similar embodiments offer an advanced technique for directing individual vacancy centers in diamonds in a desired direction, e.g., by using the electron vortex beam at the atomic level within AC-STEM. Starting with accelerating voltages in the range of 60 to 160 keV, which are well below the threshold energy for the displacement of carbon atoms in diamonds, and by selecting the focused atom-sized vortex beam on the desired atom, the atom can be excited by the transfer of orbital angular momentum and then migrate to the next lattice site in the selected direction.

[0018] In embodiments of the method, defect centers, such as nitrogen vacancy centers, within the substrate, such as a diamond lattice, can be identified using monochromatic energy-resolution loss spectroscopy with high-energy electrons, as detailed elsewhere herein. If the position of the irradiated atom does not change after a certain time or electron dose, the method and / or its individual steps can be repeated until the desired result is achieved.

[0019] The term "bulk substrate structure" refers in particular to the volume of the substrate and not to its surface. The respective defect center is therefore located at least in the second layer below the surface, and more particularly in the third layer or even the fourth layer, or even further below the surface of the substrate structure. Furthermore, the structure of the substrate can preferably comprise at least one defect center in a core region (not necessarily the central atom, but somewhere in a central region or central volume between the surfaces of the diamond).

[0020] If the substrate is diamond, the term "massive diamond crystal lattice" refers in particular to the mass of the diamond and not to its surface. The respective defect center is therefore located at least in the second layer below the surface, and more particularly in the third layer or even the fourth layer, or even further below the surface of the diamond crystal lattice. Furthermore, the diamond crystal lattice can preferably comprise at least one defect center in a core region (not necessarily the central atom, but somewhere in a central region or volume between the surfaces of the diamond).

[0021] The displacement of at least one defect center can be performed in a location-specific manner. Thus, not all respective defect centers need to be moved simultaneously or even quasi-simultaneously; instead, individual defect centers can be selected and each one can be displaced individually. This makes it possible to determine a respective displacement strategy for how individual defect centers, in particular at least one, can be moved in order to achieve a specific desired configuration of the relative positions of the defect centers to one another or to achieve a specific desired configuration of at least one defect center with respect to the substrate, in particular diamond.

[0022] In embodiments, site specificity may refer to the possibility of different defect centers being displaced while others remain unaffected. In these embodiments, it may be possible to influence, and in particular, displace, a subset of defect centers, as described elsewhere herein.

[0023] Embodiments may provide a groundbreaking solution for the precise alignment of defect centers in substrates such as diamonds, which can serve as solid-state qubits in quantum information processing and quantum computing. Defect creation techniques, including doping, implantation, and irradiation, can result in defects being arranged randomly and uncontrollably. The method for manipulating defect centers described herein can prevent the use of high-energy beams, which can cause stochastic and random defect displacement. The method can provide an approach for the directed and controlled displacement of defects and enables the manipulation of one, two, or a specific number of, for example, spins, to bring them closer together or apart for interaction purposes.In particular, the manipulation can be site-specific; more particularly, the manipulation can enable a displacement in a defined direction. Therefore, the method can provide a displacement that is not primarily based on a stochastic "random walk" through a substrate structure such as a diamond crystal lattice or similar, but rather on the determination of a principal probability of a direction. The movement of the defect center could be based on the movement of the specific atoms during electron irradiation. Atomic dynamics or atom migration may be possible if the atoms are briefly displaced and, in the meantime, exchange their position with neighboring atoms. The neighboring atom can be located on any side; therefore, according to some embodiments, the vortex beam can provide a direction by selecting a specific location.This can be achieved by using an atom-sized vortex electron beam containing orbital angular momentum. The generation of this electron beam can be based on aberration-corrected scanning transmission electron microscopy (AC-STEM). The described method enables the manipulation of individual, multiple, and composite impurities such as nitrogen, silicon, tin, or others within the substrate structure, particularly the diamond crystal lattice. It enables controlled movement across atomic lattice sites and thus precise manipulation of solid-state qubits. This potentially overcomes the limitations posed by the random positioning of qubits at the atomic scale, which can lead to decoupled qubits and hinder the scaling of spin qubits or the achievement of large-scale entanglement, which is particularly useful for quantum computing.With precision in the angstrom range and control over distances in the tens of micrometers, the described methods, devices, and systems significantly improve the connectivity between spin systems. This could facilitate the controlled creation of large, interacting spin qubits in solid-state environments, such as NV defects in diamond. The method is broadly applicable to various defects in solid-state contexts and could lead to the creation of coupled qubits, which are essential for scalable quantum communication, information processing, quantum computing, and sensing applications.

[0024] The creation of NV centers (nitrogen vacancy centers) in diamonds through ion implantation and electron irradiation is particularly stochastic, meaning the formation of NV centers is probabilistic. This process, or comparable other processes, can be defined as the provision of defect centers for a particular substrate. By shifting the defect centers, a network of, for example, coupled spins can be reliably created, for example, for quantum applications. Furthermore, more than three defect centers can be created with distances of 10 nanometers or less from each other. For a scalable quantum processor based on magnetically coupled spin qubits, such as NV centers, precise positioning can be achieved. Ideally, these defect centers, such as NV centers, can be placed at a distance of 5±2 to 15±3 nanometers from each other.Vortex electron beams, which carry orbital angular momentum with a defined direction when interacting with defect centers, can make it possible to transfer a force with a specific direction to the defect center. This makes it possible to displace the defect center, particularly in a defined direction and, moreover, in a location-specific manner.

[0025] According to a further, particularly independent, aspect, a method for relocating defect centers in a substrate for quantum applications—as an exemplary form of manipulation—can be provided. The method can comprise the step of relocating a group of defect centers. The relocation can take place simultaneously, in particular in a group-specific manner, in particular in a defined direction. This may make it possible to relocate several defect centers simultaneously. This can increase the speed of application of the method and boost manufacturing throughput. It may be possible to relocate a certain number of defect centers in a coarse relocation step, in particular in a group-specific manner, i.e., to address a defined group of defect centers, and later to proceed to a location-specific fine relocation of individual defect centers.This allows the precision and spatial specificity of the method to be combined with increased speed. Furthermore, it enables the scaling of the respective quantum qubit devices, particularly for implementing and / or investigating quantum qubit networks.

[0026] The described method enables the directed manipulation and control of the positioning of defect centers, for example, vacancy color centers as solid-state qubits in diamonds, using a (focused) vortex electron beam (at atomic scale). This beam can be formed, for example, by a holographic aperture in an aberration-corrected scanning transmission electron microscope (AC-STEM). This could enable the fabrication of a scalable multi-qubit quantum processor, enabling quantum information processing applications such as quantum sensing and quantum information processing, especially quantum computing.

[0027] The described methods make it possible to direct individual defect centers, such as vacancy centers, in a substrate, e.g., diamond, in a desired and precisely defined direction using vortex electron beams at the atomic level in the AC-STEM. Alternatively or additionally, the described methods make it possible to direct subgroups of defect centers in a defined direction. The method can be initiated, in particular, with accelerating voltages in the range of 60 to 160 keV, i.e., well below the threshold energy for the displacement of carbon atoms in diamond. By selecting the focused atom-sized electron beam onto the desired atom, this atom can be excited by the transfer of orbital angular momentum and then migrate in a selected direction to the next lattice site.The methods described herein can also be used to identify defect centers in a substrate, particularly nitrogen vacancy centers in a diamond crystal lattice, for example, by using monochromatic energy-loss spectroscopy with high-energy electrons. Provided the position of an irradiated atom remains unchanged after a certain time or electron dose, the method steps can be repeated until the desired result is achieved. Furthermore, it is possible to simultaneously move a volume distribution of defect centers, particularly as a subset of defect centers that exhibit the same or a similar (desired) displacement direction.

[0028] The vortex electron beam can be applied to a displacement zone such that at least a specific area or volume of the substrate overlaps with an electron beam having a defined expansion distribution. This expansion distribution can be donut-shaped, or a petal-shaped distribution, particularly with two, three, four, or more petals. These petals can be distributed point-symmetrically around the z-axis of the beam propagation. Other expansion distributions can be crescent-shaped, particularly with a single crescent shape, with two opposing crescent shapes, or other combinations of crescent shapes. Other expansion distributions can comprise a disk shape, particularly with zones of reduced or no electron density. These can be referred to as holes in the disks.The disks can have at least one hole, in particular two holes, and in particular three or more holes. The expansion distribution can be designed to interact with a selected subset of defect centers. The electrons in the electron beam provide the orbital angular momentum in these zones and can therefore transmit a force to displace the respective defect centers in the selected subset.

[0029] According to one aspect, the method may comprise the step of specifically providing a substrate, in particular diamond, having defect centers in a bulk substrate structure, in particular a massive diamond crystal lattice. The method may comprise the step of detecting the position of at least a first subgroup of the defect centers in the bulk substrate structure, in particular the diamond crystal lattice. The method may comprise the step of displacing a second subgroup, which is at least partially a subgroup of the first subgroup of defect centers in the bulk substrate structure, in particular the massive diamond crystal lattice.

[0030] The terms “provision of a substrate”, “substrate”, “defect centers”, “massive structure” and “massive diamond crystal lattice” are to be understood in particular as defined elsewhere herein.

[0031] A first subgroup of defect centers may refer to a group of defect centers whose position is detected and / or monitored, in particular selected from all defect centers in the bulk substrate structure. A respective first subgroup may therefore be a subgroup of the group of all defect centers in the respective provided substrate.

[0032] The second subgroup may at least partially be a subgroup of the first subgroup of defect centers in the bulk substrate structure, in particular the massive diamond crystal lattice. The second subgroup of defect centers may refer to the defect centers actually being displaced together, in particular simultaneously. The second subgroup may overlap with the first subgroup, but need not be identical to the respective first subgroup. In embodiments, the respective second subgroup may also be different from the first subgroup. In these embodiments, the respective first subgroup may function as an indicator of respective lattice sites of interest relative to which respective defect centers of the second subgroup may be displaced.

[0033] According to one aspect, a step for checking or monitoring the position of the displaced defect center can be provided. This enables a position determination, in particular in real time—so-called monitoring—or a determination of an initial, intermediate, or final position of at least one defect center in the substrate structure, in particular the diamond crystal lattice—so-called verification. This makes it possible to determine whether the displacement is proceeding as intended or whether a respective desired configuration has been achieved.

[0034] According to one aspect, the method may comprise the step of directing a scanning transmission vortex electron beam (at atomic scale), in particular using aberration-corrected scanning transmission electron microscopy, to displace the at least one defect center in the bulk substrate structure, in particular the massive diamond crystal lattice, in particular in a defined direction.

[0035] Additionally or alternatively, the method may comprise the step of directing a vortex electron beam (at the atomic level), in particular using aberration-corrected scanning transmission electron microscopy, to simultaneously displace, in particular in a defined direction, the group of defect centers, which in particular is at least the second subgroup of defect centers, in the bulk substrate structure, in particular the bulk diamond crystal lattice. Using the aberration-corrected scanning transmission electron microscopy (AC-STEM) technique, the method can distinguish and position defect centers, in particular atomic impurities such as nitrogen, silicon, tin, and others, as described elsewhere herein, within the substrate structure, in particular the diamond crystal lattice.The method described herein relates in particular to the manipulation and controlled positioning of defect centers, such as vacancy color centers, as solid-state qubits in substrates, in particular diamonds (in particular in a single diamond), using a focused, aberration-corrected scanning transmission electron microscope (AC-STEM) to fabricate a scalable multi-qubit quantum processor enabling quantum information processing applications, such as quantum sensing and quantum information processing, in particular quantum computing. Building on these core concepts, this method specifically represents an advanced technique for relocating individual vacancy centers in substrates, in particular diamonds, using electron beam techniques at the atomic level within AC-STEM.

[0036] Using aberration-corrected scanning transmission electron microscopy, or AC-STEM for short, it is possible to manipulate and control the position of individual defect centers, thus shifting them within the substrate structure, particularly the diamond crystal lattice. This movement is also referred to as a displacement, as the respective defect centers exchange places with certain neighboring atoms, particularly carbon atoms in the diamond crystal lattice. Through several displacement steps, a net migration of the defect center occurs within the substrate structure, particularly within the diamond crystal lattice.

[0037] For this purpose, an atom-sized scanning transmission electron beam can be provided, which can provide the correct amount of energy to enable the position change and has the appropriate orbital angular momentum in the region and / or volume where the defect center is located in the substrate to displace it in a defined direction. Furthermore, the atom-sized scanning transmission electron beam may not provide enough energy to eject an atom or defect center from the respective irradiation site.

[0038] According to one aspect, the diameter of a directed (scanning transmission) atom-sized vortex electron beam can be in the range of 0.5 to 2 angstroms, in particular from 0.5 to 1 angstrom, further in particular from 0.5 to 0.8 angstroms. The angstrom-sized electron beam can provide the correct energy to move the defect center, in particular in the form of an atom (point defect), across lattice sites in a controlled manner. Alternatively or additionally, the diameter of a directed (scanning transmission) atom-sized vortex electron beam can be in the range of 1 to 200 angstroms, in particular from 10 to 150 angstroms, further in particular from 50 to 100 angstroms. This beam enables the movement of a group, in particular a second subgroup, of defect centers.As described elsewhere herein, the vortex electron beam may cover an expansion distribution that may be designed to overlap with a (first) subset of defect centers intended for displacement in a defined direction having at least one component parallel to the orbital angular momentum of the vortex electron beam.

[0039] In particular, the diameter may refer to the definition of an electron beam in which only 3% or less of the respective electron density (power density) lies outside the respective beam diameter. The same may apply to expansion distributions.

[0040] According to one aspect, an acceleration voltage for accelerating electrons in the directed (scanning transmission) vortex electron beam (at atomic scale) can be set below the impact damage to the substrate structure, in particular the diamond crystal lattice. In particular, the acceleration voltage can be set between 60 and 160 keV, especially for diamond. This prevents certain atoms from being ejected from the substrate, in particular the lattice; instead, they are displaced. In particular, starting with acceleration voltages set between 60 and 160 keV and in particular by focusing the vortex electron beam on the desired defect center, in particular the atomic defect, can ensure that the atom forming the atomic defect can be excited and then migrate to the next lattice site and is not ejected.

[0041] Alternatively or additionally, a convergence angle can be greater than 15 mrad, in particular greater than 20 mrad, and furthermore, in particular greater than 32 mrad. When a conical, convergent electron beam illuminates a sample, the half-angle of the cone can be referred to as the "convergence angle." Therefore, the respective vortex electron beam can be precisely defined to determine the respective displacement direction.

[0042] Impact damage refers to radiation damage caused by the collision of electrons in the beam with an atomic nucleus. The speed of the respective electrons, and thus the potential energy they can transfer to the respective nuclei, may be below the energy required to cause impact damage. The accelerating voltages can be adjusted to avoid damage to the defect centers, especially the NV centers, by setting the accelerating voltage below the impact damage of the substrate, especially the diamond. This can be between 60 and 160 keV.

[0043] In particular, the bond strength of the respective bond in the substrate structure, especially the diamond crystal lattice structure, can be adjusted to enable the respective bond to exchange the position of the respective binding partners, resulting in a shift of the defect center.

[0044] In embodiments, the direct exchange energy for Al is between 13 and 16 eV, for Si the binding energy is between 14 and 18 eV, and for P between 16 and 17.5 eV (at theta, the angle of incidence of 0°). The upper value may represent the knockout value. The values ​​are determined for a graphene substrate. The binding energies for different defect centers may vary. The threshold energy for displacement (the minimum energy required to remove an atom from the transferred energy of the electron beam) may also vary depending on the surrounding atom (defect centers).

[0045] The elastic frontal collision can be determined based on the following formula ET=(4mi∗mc)Ei / (mi+mc)2 where E T the transferred energy is E i the initial energy of the particle with mass m i to particles with mass m c is.

[0046] According to one aspect, the directed (scanning transmission) vortex electron beam (at atomic scale) can be directed at the defect center to be displaced. Alternatively or additionally, the directed (scanning transmission) vortex electron beam (at atomic scale) can be directed at the subgroup of defect centers to be displaced. This transfers the energy to the defect center and not necessarily to the specific atom with which the defect center can exchange position in the substrate structure, in particular the diamond crystal lattice. Furthermore, an entire (second) subgroup can be addressed for simultaneous displacement in a specific, defined direction.

[0047] The motion can be initiated by directing a (scanning transmission) vortex electron beam (atom-sized) directly onto a defect center or onto a subset of defect centers as an extensional distribution. This can lead to an elastic collision that overcomes the bond strength between the defect center and the carbon atom that may exchange places with the defect center. If the vortex electron beam has a precisely defined orbital angular momentum, the direction of displacement can be predetermined. In other embodiments, the respective carbon atom, which may exchange places with the defect center, can be directly impacted by the (scanning transmission) electron beam (atom-sized).

[0048] According to one aspect, the method may comprise a step of dark-field imaging with ongoing electron spectral analysis, which identifies at least one defect center or the first subgroup of defect centers in the bulk substrate structure, in particular the bulk diamond crystal lattice. This makes it possible to identify defect centers, in particular nitrogen vacancy centers. For validation, a concentrated beam can be focused on desired defect centers, e.g., nitrogen vacancy centers, while subsequent spin spectroscopy (e.g., ODMR) and imaging examinations can confirm the displacement of the defect center, in particular the displacement of the atom. In embodiments, it may also be possible to determine the displacement of the defect centers. This makes it possible to check or monitor the respective progress of a displacement strategy, in particular a predetermined one.

[0049] Dark field imaging with continuous electron spectral analysis is a special technique that excludes from the analysis the initial main electron beam directed at the substrate structure, in particular the diamond crystal lattice, but can focus on the scattered electrons that have interacted with the respective substrate structure, in particular the diamond crystal lattice, as provided or modified by a directed atomic-sized electron beam, as described elsewhere herein.

[0050] AC-STEM can provide structural insights into crystalline materials such as diamonds. The technology can provide mapping of defect centers, particularly specific point defects such as nitrogen vacancy centers, offering the respective advantages described elsewhere herein and in emerging fields such as quantum computing. In the proposed AC-STEM method, the electron beam grid scans the desired surface or volume pixel by pixel, and after the (vortex) electron beam interaction with the sample, scattered electrons can be collected with an annular angular dark-field detector. Since the intensity of atoms is approximately proportional to Z2, where Z is the atomic number, the elements can be directly distinguished at the atomic level based on image contrast.

[0051] As a first step, defect centers, such as nitrogen vacancy centers, can be located in the substrate, particularly in diamond, using a combination of dark-field imaging, in situ electron and optical spectral spectroscopy techniques (e.g., EELS, ODMR), as described elsewhere herein. An image of the desired area can be acquired using the scattered defect centers, particularly the nitrogen vacancy centers, as a reference point. A focused beam can be directed directly at individual defect centers, such as nitrogen vacancy centers, to irradiate them for a certain time, and then another spin spectroscopy measurement can be performed to confirm the motion. Furthermore, the image can also be acquired to observe successful manipulation.

[0052] According to one aspect, a step of confirming and / or monitoring the displacement of at least one defect center may be performed using at least one of spin spectroscopy, imaging studies, or ODMR. This allows the displacement to be verified and monitored and provides feedback loop control.

[0053] According to one aspect, at least one step for mapping, evaluating, and / or evaluating at least the chemical composition or the electronic structure can be provided. In particular, at least one of the methods energy-dispersive X-ray spectroscopy (EDX), electron energy loss spectroscopy (EELS), or four-dimensional STEM (4D-STEM) can be used. Alternatively or additionally, cathodoluminescence techniques can be used.

[0054] Particularly in embodiments where nitrogen vacancies are used as defect centers, the following may apply. Nitrogen atoms (N) are located immediately adjacent to carbon atoms (C) in the periodic table, which can make it extremely difficult to distinguish nitrogen atoms from carbon atoms in the bulk diamond crystal lattice structure using atomic-scale dark-field imaging. Furthermore, it can be used to identify other heavier, impurity-based vacancy centers (e.g., Si, Sn) in diamond. Therefore, chemical composition can be provided by energy-dispersive spectroscopy and electron energy loss spectroscopy simultaneously with atomic-scale imaging, allowing the edge fine structures of the vacancy centers to be precisely identified at the atomic level.However, this may also apply analogously to embodiments in which other types of defect centers can be used to improve their detection and position verification.

[0055] According to one aspect, at least one of spin spectroscopy, imaging studies, or ODMR can be used to confirm or monitor the displacement of the defect center(s). This makes it possible to locate and track the respective defect centers, particularly before, during, and after the displacement.

[0056] A mapping step enables the provision of an overall map of the positions in the substrate structure, in particular the diamond crystal lattice structure. A step of assessing and / or evaluating at least the chemical composition or the electronic structure can provide the respective information about the environment in the substrate structure, in particular the diamond crystal lattice structure, the atomic bond structure, and the respective strengths therein. In this way, it might be possible to determine required or desired vortex electron beam acceleration voltages that are to be adjusted or predicted.

[0057] ODMR refers to a technique called optically sensed magnetic resonance (ODMR), which allows the electron spin state of a substrate defect center, such as a crystal defect in diamond, to be optically pumped for spin initialization and readout. It can be used for nitrogen vacancy (NV) color centers in diamond, for example, to measure the modulus and orientation of an external magnetic field using a confocal microscope setup. ODMR of NVs can find applications in magnetometry, sensing, biomedical imaging, quantum information, and fundamental physics research. Here, ODMR enables the implementation of an additional feedback dimension.

[0058] According to one aspect, the method may comprise the step of using at least one sub-sampling window to manipulate the defect center and / or defect centers, in particular the second subgroup. Alternatively or additionally, it may be used to monitor the change in the bulk substrate structure, in particular the solid diamond lattice structure, in real time.

[0059] The term "subsampling" can refer to a limited portion of a sampling frame during imaging, sensing, or measurement. Using a small subsampling window as an (alternative) approach allows for manipulating defect centers, especially NV centers, and also monitoring structural changes in real time. Defect centers (e.g., NV qubits) in a lattice can be brought closer together (parallel) or moved farther apart at once by defining a raster scanning path or sampling window using an AC-STEM. A subsampling window can be provided that falls within the respective sampling window. The subsampling window can be used for spin spectroscopy or imaging studies. Information about the electron beam colliding with the defect center can be combined with information from additional sensing, imaging, or spectroscopy techniques.According to one aspect, the method may comprise the step of providing a map of the defect centers to determine potential qubit coupling via the controlled positioning of the defect centers as potential qubits and relocating individual defect centers accordingly. Additionally or alternatively, defect centers may be moved and the qubit coupling monitored to improve the coupling between at least two defect centers. This specifically addresses the drawback of qubit connectivity and allows qubit coupling to be engineered via the controlled positioning of the qubits, enabling potential applications in the fabrication of quantum sensing devices. Using a method step described elsewhere herein, an atom-sized electron beam can bring qubits closer together, but can also move them apart in a controlled manner at the atomic level within the diamond crystal lattice.Additionally or alternatively, defect centers can be moved and qubit coupling monitored to improve the coupling between at least two defect centers.

[0060] As described elsewhere herein, a map of the defect centers can provide information on the spatial structure, electronic structure, and potential qubits to determine the potential qubit coupling in the substrate structure, in particular the diamond crystal lattice, upon relocating certain defect centers. The current position of the defect centers can be displayed on the map. Alternatively or additionally, the map can provide information about a substrate structure, in particular the diamond crystal lattice, that can be realized by the method described elsewhere herein, in particular by relocating at least one defect center, in particular by relocating several defect centers, in particular in a location-specific manner. This allows a relocation strategy to be defined.

[0061] In one embodiment, the focus is not on moving the qubits, but on establishing the coupling between them and also on the possibility of determining the improvement in a kind of feedback loop, even based on the application of a machine learning model, as described elsewhere herein. The detection of a change in movement can be fed back to the machine learning model to determine a corresponding approximation to a desired state, especially if the coupling corresponds to a specific desired state or structure.

[0062] According to one aspect, the method (or certain steps thereof) can be repeated until a displacement of the defect center and / or the defect centers is detected. Alternatively or additionally, the method (or certain steps thereof) can be repeated until the group of defect centers has reached a desired configuration. If the substrate structure sites, in particular the lattice sites, remain unchanged, the respective method steps can be repeated until the defect center(s), in particular the NV centers, are moved in a location-specific and / or group-specific manner.

[0063] According to one aspect, the defect center may be at least one of the following: an atomic point defect, an atomic point defect, in particular with P1 as the substitution configuration, a silicon atom impurity, a nitrogen atom impurity, a tin atom impurity, a phosphorus atom impurity, a bismuth atom impurity, a vacancy center, a nitrogen vacancy center, a silicon vacancy center, a tin vacancy center, a phosphorus vacancy center, a bismuth vacancy center, a germanium vacancy center, or a higher coordinated defect. Alternatively or additionally, the substrate may comprise at least one of diamond, silicon, silicon carbide, or a wide bandgap semiconductor. In other words, the substrate may be a crystal structure or matrix made of the respective atoms.

[0064] A method step can be provided to use a (focused) vortex electron beam (at atomic scale) in STEM to manipulate other solid-state qubits such as silicon (Si), phosphorus (P), and tin (Sn) within a substrate structure, in particular the diamond lattice. Si and C can exchange their places within a substrate structure, in particular the diamond crystal lattice, by irradiation with vortex electron beams. This also applies in particular to heavier elements such as bismuth atoms. It enables the positioning and nanofabrication of a substrate structure, in particular the diamond host lattice, with different solid-state qubits (e.g., Si in SiC).

[0065] A "point defect" is specifically an atomic-scale imperfection in an otherwise perfect crystal. It can thus be contrasted with an "extended defect," which affects a large portion of the crystal and is important for determining its mechanical properties.

[0066] The term atomic point defect refers, in particular, to defects that occur only at or around a single lattice point, particularly when an atom is placed at a different position than the expected atom in the lattice structure. In particular, they are not spatially extended in any dimension. However, these defects usually involve at most a few additional or missing atoms.

[0067] An atomic point defect with P1 as the substitution configuration refers to a P1 center, which is a spin-1 / 2 substitution nitrogen impurity in a diamond lattice, which can also exhibit long coherence and relaxation times, although it may not be optically active.

[0068] In crystallography, a vacancy or vacancy defect is a type of point defect in a crystal in which an atom is missing from one of the lattice sites.

[0069] A nitrogen vacancy center (analogous to other atom-type vacancy defects) is specifically defined as the combination of a nitrogen atom incorporated into the diamond lattice structure alongside a vacancy. This defect center can provide particularly unique quantum mechanical properties that are of interest for a wide range of applications, from sensing to qubit-based computations.

[0070] Nitrogen vacancy centers (NV centers) in diamond could provide a leading platform for applications in solid-state quantum technology if their position is controlled as described elsewhere herein. They exhibit unprecedented coherence times, optical interaction, and robustness to quantum states even at room temperature. An NV center is a point defect comprising a substitutional nitrogen atom adjacent to a lattice vacancy in the diamond's carbon matrix. These NV centers can be optically active, fluorescent atomic defects. This enables localization based on optical confocal microscopy. NV centers can exhibit coherence times exceeding 2 milliseconds at room temperature and even longer, on the order of several seconds, under cryogenic conditions (4 Kelvin).These coherence times enable the realization of quantum operations and improved sensitivity for quantum sensing applications. These properties of NV quantum systems could make them attractive qubits for quantum computing and quantum information processing in general. The potential of NV centers for quantum applications is further enhanced by their ability to emit photons with high quantum yield, optical spin polarization, and optically resolved detection of the 0, +1, -1 spin sublevels. Optically sensed magnetic resonance (ODMR) techniques, which can be used on NV centers, can detect magnetic fields as low as a few nT (nanotesla).This degree of sensitivity, coupled with the spatial resolution afforded by the nanoscale of NV centers, could provide a powerful quantum sensor for studying nanoscale magnetic phenomena ranging from biological processes to novel magnetic materials. Furthermore, the zero-phonon line (ZPL) for these NV centers in particular is located at approximately 637 nm, enabling efficient collection and integration with various optical systems for quantum communication and long-range entanglement between qubits. These properties enable NV centers to act as nodes in quantum networks or as quantum repeaters in long-distance quantum communication.NV centers in diamonds may also be potential qubits for quantum computing applications, particularly due to their unique properties that enable laser-assisted optical initialization and optical readout at room temperature. One of the greatest strengths of NV centers is their long coherence times, with T2 times often exceeding 2 milliseconds under ambient conditions, making them one of the few candidates for solid-state qubits operable at room temperature. Furthermore, the two-level system of the NV defect can be coherently manipulated by microwave radiation at Rabi frequencies typically up to 10–100 MHz, enabling efficient quantum gate operations. In the search for scalable quantum computing, NV centers offer the possibility of interacting with nearby nuclear spins, thus providing a potential opportunity for multi-qubit interactions.The most abundant nuclear spin in diamonds that can interact with the NV center is the carbon-13 isotope (C13), which can occur in nature at an abundance of about 1.1%. These nuclear spins can serve as additional quantum memories or quantum registers, expanding the computational capacity of the NV-based quantum system.

[0071] The coupling between defect centers can be determined using ODMR at approximately 10 kHz. This can provide feedback from the system as to whether the defect center is moving in the right or wrong direction.

[0072] In embodiments, 2D materials such as graphene, hexagonal boron nitride (H-BN) ribbon, and transition metal dichalcogenides can be used as substrates for placing and relocating defect centers. Furthermore, bulk substrate structures made of H-BN ribbon and transition metal dichalcogenides can be provided.

[0073] The process (or certain steps thereof) can be repeated until a shift of the defect center is detected, as described elsewhere herein. Alternatively or additionally, the process (or individual process steps) can be repeated until the group of defect centers has reached a desired configuration. This allows for real-time monitoring of the change in the bulk substrate structure, in particular the bulk diamond lattice structure.

[0074] According to one aspect, at least one intermediate step for displacement can be planned. Alternatively or additionally, at least one parameter setting is planned for at least one intermediate step. The planning can, in particular, also comprise a calculation. This represents a special possibility for manipulating qubits within the substrate structure, in particular the diamond crystal lattice, for one or more intermediate steps, calculated optimistically. Furthermore, it also provides the flexibility to change and optimize the parameter settings for the intermediate steps, which can further demonstrate the deterministic control of the (focused) vortex electron beam manipulation at the atomic level.

[0075] Intermediate steps are understood to mean, in particular, the individual displacement steps that the respective defect center must perform in order to move it from a respective starting position via intermediate positions to a final position.

[0076] Parameter settings can be any device parameters that allow for the displacement of at least one defect center. It can also refer to any parameter setting that allows for the detection, validation, and / or monitoring of the defect centers and their respective positions within the substrate structure, in particular the diamond crystal lattice. The parameters can also refer to the positioning and configuration of a holographic aperture, as described elsewhere herein. Alternatively or additionally, the parameters can refer to an additional magnetic field applied to the cavity of the electron microscope to modulate the vortex electron beam.

[0077] Planning can be understood as the determination of a respective displacement strategy. Therefore, a calculation to determine parameters and intermediate steps can be performed based on specific physical models of a substrate structure, in particular a diamond crystal lattice, in particular based on a digital twin of the substrate structure, in particular the diamond crystal lattice, to be created. The digital twin or a specific model can be referred to as a predefined structure.

[0078] According to one aspect, the step of placing suitable defect centers as qubits for quantum communication can be provided in an arranged array. Alternatively or additionally, the step of placing suitable defect centers as qubits for quantum communication can be provided in an ordered, corral nanostructure within the bulk substrate structure, in particular the massive diamond crystal lattice. This allows the controlled production of a large number of qubits suitable for quantum communication to be implemented by placing them in an arranged array and / or by corral nanostructures within the substrate structure, in particular the diamond crystal lattice.To further improve the manufacturing process, in-situ, feedback-controlled manipulation can be combined with a predefined structure, allowing an imaging detector to read the real-time signal from qubits. For example, changing the position of the defect center can provide the signal from the substrate, especially diamond. When the beam is positioned over a defect center such as the N-center, it can display a higher signal due to the Z-contrast imaging principle.

[0079] An arranged array is understood in particular to mean the placement of defect centers in a sorted and in particular linked chain or sorted and linked substructure in the substrate structure, in particular the diamond crystal lattice.

[0080] The arranged corral nanostructures are structured defect center patterns that link these defect centers together, for example, via quantum mechanical effects (spin-spin coupling or other effects), to realize quantum mechanical structures for specific applications. These applications can include sensing applications, qubit-based quantum computations, etc. Some of these applications are described elsewhere herein.

[0081] According to one aspect, in-situ, feedback-controlled manipulation can be combined with a predefined structure in one step. This can be used for real-time monitoring of qubit signals. In particular, this represents a method step for manipulating the complex and / or composite defect centers in the substrate structures, in particular the diamond crystal lattices (diamond atom lattices), e.g., using a (focused) vortex electron beam in STEM. Defect centers, in particular NV centers, can encompass many configurations in diamonds. Their (optimal) interactions within a lattice can be quite complex. Therefore, the inter-interactions of qubits, in particular spin qubits, can be measured, and the best possible final configurations suitable for the performance of scalable qubits in the solid state can be selected.These (optimal) interactions and the respective positions for implementing these interactions can be the predefined structure of the diamond crystal lattice—a model or digital twin that could enable the determination of a displacement strategy. The in-situ, feedback-controlled manipulation in combination with a predefined structure can be based on such a model or digital twin as a predefined structure to implement a comparison between calculated data and measurements, thus determining whether the respective diamond crystal lattice structure realized by a displacement strategy—e.g., during intermediate steps—reaches or approaches the predefined structure. For this purpose, real-time monitoring of the qubit signals can be implemented.This makes it possible to determine whether certain defect centers can fulfill their intended function, particularly in a combined and linked manner.

[0082] According to one aspect, in a repositioning step, the relative positions of the complex and / or composite defect centers in the bulk substrate structure, in particular the diamond crystal lattice, can be optimized. This allows the feedback loop to be implemented in a real physical structure of a substrate structure, in particular the diamond crystal lattice. The repositioning of the relative positions of the complex and / or composite defect centers in the bulk substrate structure, in particular in the bulk diamond crystal lattice, can be optimized such that their respective functions and / or their respective interconnections can reach a predicted, calculated, or modeled level.

[0083] According to one aspect, temperature effects on defect centers can be investigated in a range from room temperature to 1500°C. Alternatively or additionally, at least one of heating, cooling, or tempering can be applied for analysis. Considering the role of temperature in the thermal displacement of defect centers, particularly NV centers, for the individual qubits in substrates, particularly diamonds, can improve the respective structural design. For example, a very high temperature can graphitize the diamond surface, disperse the vacancy centers (as a type of defect center, potentially also applicable to other defect centers), and reduce the hydrocarbon impurities that are very common in the carbon family of materials.Therefore, investigating the influence of temperatures in the range from RT to 1500 °C on the fabricated qubits using in-situ methods can provide relevant insights into the material behavior.

[0084] At least one repair step can be implemented. This repair step can be performed after examining the respective temperature or temperature range. In the repair step, at least one potentially displaced defect core can be shifted as described elsewhere herein to achieve a structure that is identical or similar to the structure before the temperature disturbance.

[0085] Room temperature is understood to mean in particular the temperature range between 20 °C and 22 °C, in particular explicitly 21 °C.

[0086] According to one aspect, at least one defect center can be relocated to a site-specific marker of the structure of the substrate, in particular the diamond crystal lattice. The site-specific marker can, in particular, be a C13 isotope. This makes it possible, on the one hand, to identify specific defect centers and their respective positions via a site-specific marker in the lattice, not only via the respective defect centers themselves, but also via an independent pathway. On the other hand, it makes it possible to establish links between the defect centers and the site-specific markers for quantum applications. This can provide a method step of embodiments for bringing the electron spins close to the isotopic C13 nuclear spins in a controlled manner by manipulating them with vortex electron beams (e-beams) at the atomic level.In a first step, the existence of nuclear spins can be confirmed by spectral imaging using electron energy loss spectroscopy and an optically detected magnetic resonance technique (electron-nuclear double resonance). Subsequently, using a focused e-beam, the defect centers, especially NV centers, can be positioned in their vicinity, enabling a potential application of this method, for example, in a quantum register.

[0087] The positioning relative to C13 isotopes can also be determined using ODMR, allowing one to determine whether a defect center is moving away from or toward a C13 isotope. Therefore, it is possible to implement a feedback loop to repeatedly apply the movement of at least one defect center to bring it closer to at least one C13 isotope in the crystal lattice.

[0088] A site-specific marking of the substrate structure, in particular the diamond crystal lattice, can be any potentially identifiable marking that allows tracking and / or identification within the lattice. Furthermore, the respective position can be tracked. In some embodiments, the marking can also be moved, particularly after its position has been determined. Alternatively or additionally, the site-specific marking can have quantum mechanical properties that are advantageous for the intended application, as described by way of example elsewhere herein.

[0089] The most abundant nuclear spin in diamonds that can interact with defect centers, particularly in the form of a NV center, is the carbon-13 isotope (C13), which occurs at approximately 1.1% in nature. These nuclear spins can serve as additional quantum memories or quantum registers, which can expand the computational capacity of the defect-center-based quantum system, especially the NV-based quantum system. Nevertheless, the entanglement of separate defect centers, especially separate NV centers, is a step toward the implementation of scalable quantum computing. Because the method described here and elsewhere does not rely purely on the stochastic nature of defect center formation, especially NV center formation, both the precision and efficiency of defect center formation are increased and the control is improved, enabling the creation of quantum computing functions and the formation of qubit networks.

[0090] According to one aspect, a holographic aperture in the aberration-corrected scanning transmission electron microscope can form a particularly focused vortex electron beam (at the size of an atom). Additionally or alternatively, the particularly focused vortex electron beam (at the size of an atom) can be formed by applying an additional magnetic field to an electron beam in the aberration-corrected scanning transmission electron microscope. This makes it possible to move a subgroup of defect centers simultaneously, in particular in a location-specific manner, in a defined direction. Additionally or alternatively, it may be possible to move a subgroup of defect centers in a specific region of the substrate structure, in particular a diamond crystal lattice, in a defined direction.

[0091] Electron holography can be based on the introduction of a spatial and / or phase interference pattern of an electron beam, thereby distributing the electron density over an extensional distribution. The extensional distribution can be formed and / or positioned to match the respective distribution of at least one subset of defect centers.

[0092] The controlled fabrication of vacancy centers in diamond at the atomic scale may pose a major challenge for expanding the field of quantum computing. The proposed method enables the construction of qubit connectivity by manipulating defect centers, such as the vacancy centers described in detail elsewhere herein as solid-state qubits in substrates such as diamond, by precisely directing a vortex electron beam (at atomic scale) that can be formed by a holographic aperture in a scanning transmission electron microscope, particularly with a diameter in the range of 1 to 2 Ångströms.The potentially transferred orbital angular momentum from the vortex electron beam to the selected defect center, particularly the vacancy center, within the substrate structure, particularly the diamond lattice, could make it possible to control the motion in a fixed and selected direction, which may enable potential applications in quantum information processing. Unlike scanning tunneling microscopy combined with atomic force microscopy, the described method may not be limited to uses for modifying the surface and manipulating only the surface atoms using their sharp atomic tips. In particular, aberration-corrected scanning transmission electron microscopy (AC-STEM) can be a highly advanced technique providing atomic-scale imaging, spectroscopy, and material modification capabilities.

[0093] Improvements could be achieved through efficient design of the aberration corrector and beam shaping, enabling direct visualization of individual atoms at the atomic level, analysis of structural quality, and identification of individual material defects. In particular, when combined with energy-dispersive spectroscopy (EDX), four-dimensional STEM (4D-STEM), in situ heating / cooling / biasing, electron energy loss spectroscopy (EELS), and cathodoluminescence techniques, AC-STEM (or any specific combination thereof) can reveal fine chemical composition and material interfaces, map electric charge and fields, analyze detailed morphological structures at the atomic scale, assess electron-photon interactions with matter, and investigate in situ atomic-scale atomic dynamics and ferroelectric phenomena.In addition to these advanced techniques, atom-sized vortex electron beams with selected orbital angular momentum can be used in applications ranging from magnetic field detection to mapping of biological samples to edge contrast enhancement.

[0094] Unlike the "image" of an electron beam in classical physics, an electron beam in the quantum framework can carry orbital angular momentum. Therefore, electrons can exhibit fascinating behavior in which they can manifest a wave-like rotation around their propagation direction. This phenomenon may be a manifestation of the quantum mechanical property called "vortex electron beams," which carry orbital angular momentum. Various methods can be implemented to generate the electron vortex beam, only a few of which are listed here as examples. Vortex electron beams can be generated by using at least one of the following: phase plates, holographic fork shutters, holographic spiral shutters, manipulation of aberration functions, and use of the magnetic field, the latter of which is also described elsewhere herein.Furthermore, by using the electron energy loss magnetic chiral dichroism (EMCD) technique in STEM, an atom-sized vortex electron beam with selected orbital angular momentum can be generated.

[0095] The manipulation of the foreign atoms with a focused electron beam in the Ångström range as a "probe beam" in an aberration-corrected STEM, where incident electrons can interact with the atomic nuclei and scattered electrons can transfer energy and momentum to the individually targeted foreign atom, so that the foreign atom is not ejected but can be excited to move to the next "neighboring" lattice site, offers the potential for atomically precise manipulation. Using this mechanism, electron beam manipulation of various foreign atoms can be implemented in bulk silicon [18,19], graphene, and carbon nanotubes. An aberration-corrected scanning transmission electron microscopy (AC-STEM) technique can further be used to analyze the substrate surface, particularly the surface of the diamond crystal.It can be used, particularly in ultrahigh vacuum, to indirectly move defect centers, especially vacancy centers, in the substrate, especially the diamond crystal. The described method can prevent the expulsion of the foreign atom and / or double lattice site jumps and / or triple lattice site jumps, particularly caused by continuous electron irradiation of the neighboring atoms and directly of the foreign atoms. This stochastic process could result in the control of the manipulation being limited in its directionality. The manipulation of defect centers in the substrate can be implemented both clockwise and counterclockwise (relative to a plane that is particularly perpendicular to the beam propagation direction) using a vortex electron beam with appropriate orbital angular momentum.

[0096] The described method can use a vortex electron beam (at atomic scale) with selected orbital angular momentum, particularly in STEM, to direct individual defect centers, such as vacancy centers, in a substrate, such as diamond, in a precisely defined direction. In particular, the described method involves freestanding diamond samples into which the impurities (e.g., N, Si, Sn) can be carefully and controlledly implanted. These dopants can form atomic point defects (e.g., P1, substitution configuration). Furthermore, it can be annealed at high temperatures to form vacancy centers and higher-coordinate defects. The samples can be annealed in ultrahigh vacuum to avoid impurities that can be problematic during electron beam manipulation (at the atomic scale).

[0097] In view of the above, in one embodiment of the method (and a system as described elsewhere herein), orbital angular momentum can be provided to steer individual nitrogen vacancy centers in diamonds in a precisely defined direction using an atomic-sized vortex electron beam in an aberration-corrected STEM. A focused spiral vortex electron beam can be formed through a holographic fork aperture and placed directly onto individual nitrogen vacancy centers to irradiate them for a specific time. The (vortex) electron beam can form a rapidly spinning vortex that can interact with atoms, and by imparting orbital angular momentum to the atoms, it steers them in a highly controlled manner.To mitigate the removal of vacancy centers and avoid unwanted damage to the diamond, the selected accelerating voltages can range from 60 to 200 keV and include convergence angles of over 32 mrad, which can correspond to a beam size of 1 to 2 angstroms in diameter.

[0098] In a first step, nitrogen vacancy centers in diamond can be localized using a combination of atomic-scale dark-field imaging, high-resolution monochromatic electron energy-loss spectroscopy, and / or optical spectral and spin spectroscopy (e.g., EELS, ODMR). An image can be acquired, and a region of interest containing the scattered nitrogen vacancy centers can be selected as a reference point. The individually selected vortex electron beam, carrying orbital angular momentum, can be transmitted with different vortex states to effect directional manipulation toward the vacancy center and prevent the irradiated atom from jumping to the random neighboring carbon atoms in the diamond. Therefore, the directional movement of the vacancy center can be a defined path, which can be controlled due to the calibrated orbital angular momentum transfer direction.Furthermore, if the lattice sites remain unchanged when observed by imaging or spectroscopy, the manipulation process can be repeated until the NV centers can be moved and stopped once the vacancy center can be moved to the desired distance and direction.

[0099] According to another embodiment of the method, an approach for overcoming the limitations of qubit connectivity is presented. This embodiment is particularly characterized by a unique method for constructing a qubit coupling by precisely controlling the placement of the qubits. This could not only solve the challenge of qubit connectivity but also pave the way for consistent, large-scale production of scalable quantum sensing devices. The method can begin with doping, in particular during growth and / or through ion implantation, followed in particular by annealing, which can lead to a random distribution of vacancy centers. A phase-singular, atom-sized spiral vortex electron beam can be used.This beam may have a zero-intensity center and a non-zero intensity in its spiral profile, resulting in, in particular, varying local electron densities and corresponding angular momenta. This method (and the respective system described elsewhere herein) is used exclusively to move multiple randomly distributed qubits closer together toward the center or along a spiral path within the vortex beam region. As explained with regard to the other embodiment, this can be achieved by manipulating them using orbital angular momentum transfer in scanning transmission electron microscopy (STEM). By continuously irradiating electrons with a vortex electron beam, the orbital angular momentum can be transferred, effectively rearranging the position of the vacancy centers as desired.Using a uniform electron beam, multiple defect centers can be manipulated simultaneously along a precisely defined path, allowing the user to multiplex the process (and respective process steps) and generate many coupled spins from two to many thousands.

[0100] This method (and a respective system as described elsewhere herein) can be used to fabricate scalable quantum computers and quantum sensors that harness quantum phenomena. This embodiment allows for addressing qubit connectivity by irradiating a large area with a vortex electron beam. Multiple defect centers can be manipulated simultaneously.

[0101] The respective embodiments described above can be modified by using different types of defect centers, in particular with different dopants, as described elsewhere herein. Alternatively or additionally, the embodiment can be modified such that other substrates can be used, as described elsewhere herein.

[0102] In embodiments of the method, arbitrary vortex electron beams in the desired shape can be generated by a holographic, nanostructured aperture, which can in particular be formed by a gradient in the orbital angular momentum, in particular via an automated process that enables the simultaneous manipulation of multiple vacancy centers in diamonds and the control of the beam shapes and the profile of defect centers in STEM.

[0103] Alternatively or additionally, at least one magnetic field can be applied to the cavity of the electron microscope, within which the electron beam can propagate. This additional magnetic field can enhance a vortex electron beam. A magnetic field parallel to the propagation of the electron beam can create the respective shapes of the expansion distribution described elsewhere herein (petals, donuts, rings, disks, etc.).

[0104] The respective embodiment enables the generation of any desired vortex electron beams in at least one desired shape through a holographic, nanostructured aperture, which can create a gradient in orbital angular momentum via an automated process. This enables the simultaneous manipulation of multiple vacancy centers in diamonds and allows for the control of the beam shapes and the profile of the defect centers in the STEM. In other words, the beam shape can be controlled automatically before the beam can coordinately scan the sample or pattern, in particular the group of defect centers that are to be shifted in a defined direction.

[0105] According to an independent aspect, a method for training a machine learning model with a series of spatially placed defect centers in a bulk structure of a substrate, in particular a bulk diamond crystal lattice, can be provided. The automation of a defect center process step, such as the manipulation of vacancy centers with an atom-sized focused electron probe in STEM, can be provided. The process can be combined with machine learning to automatically detect the pristine lattice and other vacancy centers in real time. Subsequently, the control of the e-beam can be automated to controllably place the defect centers, in particular the vacancy centers, at the atomic level, thereby enabling the fabrication of high-precision devices that enable a direct correlation between atomic structure and quantum properties.

[0106] A machine learning model can be a machine-readable program routine configured to be executed on a computer machine, in particular on a control unit, in particular stored on a storage device, and which enables the determination of a respective displacement strategy. The machine learning model can be an artificial neural network that can be provided with a series of images, spectra, or other data of spatially placed defect centers in a bulk substrate structure, in particular a solid diamond crystal lattice. These spatially placed defect centers can be any final configurations for specific applications, intermediate configurations, in particular those representing specific intermediate steps, or initial configurations (initial configurations) of defect centers, their respective distributions, spatial positions, or information and measurement data derived therefrom.Thus, the machine learning model (supervised or unsupervised) learns certain types of configurations and can also be trained using pathfinding algorithms in machine learning models to determine a respective displacement strategy when starting from a certain configuration to reach a final configuration and thus provide a predefined structure of a substrate structure, in particular the diamond crystal lattice.

[0107] A deep learning-based fully convolutional neural network (FCNN) can be applied as a machine learning model in a supervised approach. Local atomic coordinates can be used to identify and classify defect centers based on atomic-resolution images in the substrate, especially diamond. More specifically, this can be achieved by applying Laplacian-of-Gaussian blob detection techniques to the FCNN output. Positioning is determined based on Gaussian blob detection, which allows for the classification of structural information based on its atomic coordinates (bond length, chemical species, and bond angle).

[0108] An encoder-decoder type can be used as an FCNN. The input can consist of convolved layers with filters, and the features can then be mapped in reverse (pixel-based classification) (upsampling). The FCNN can consist of three convolved layers, especially with different kernels (e.g., 3x3). One layer can serve as encoding, one as filtering, and one as decoding. The first layer can be the input layer, and the last layer can be the output layer.

[0109] Simulated images with different defect centers and other defect types in a substrate, especially diamond, can be used to train the model. All operations and calculations can be performed in a real spatial coordinate system rather than a Fourier transform space. Blending the experimental images with different resolutions (which can be further segmented into different pixel sizes, e.g., 256 x 256 pixels) can also be used. Images can be fed to the trained FCNN model, which outputs a probability map. They can then be thresholded to generate binary images with small blobs corresponding to the atomic lattice sites in the substrate, especially diamond. Finally, Laplacian-of-Gaussian blob detection techniques can be used to calculate the atomic coordinates.

[0110] In another embodiment, deep convolutional neural networks (DCNNs) can be used. They provide fast and robust atom identification without noise and distortion and are particularly suitable for single-image acquisitions.

[0111] Deep convolutional neural networks (DCNNs) can automatically determine the Bravais lattice symmetry present in atomically resolved images. DCNNs can be trained to identify the Bravais lattice class based on a two-dimensional fast Fourier transform of the input image. Therefore, Fourier transform images can be used. The internal processing can be the same as that of an FCNN.

[0112] Different types of algorithms within CNNs can be performed on the convolutional and deconvolutional layers of networks. One example is a ResUNet architecture. The concatenation of the convolutional layer with the corresponding deconvolutional layer can represent a U-Net scheme.

[0113] Other image denoising architectures can also be used, such as Grouped Residual Dense Network (GRDN), Multi-resolution U-Net (MR-UNET) or Concatenated Grouped Residual Dense Network (CGRDN).

[0114] Alternatively or additionally, Generative Adversarial Networks (GANs) can be used. They provide an unsupervised generative attention network with adaptive layer instance normalization for image-to-image translation (U-GAT-IT), particularly for the noise amplification model (U-GAT-IT). They can process uniform simulated images and, in particular, use them as a training set for the defect identification model (U Net). This not only allows for accurate description of experimental images but also increases the diversity of the training set through random assembly, thus meeting the demand for a large amount of training data.

[0115] According to one aspect, a vortex electron beam shape can be defined based on the defect center distribution provided to the trained machine learning model. Therefore, the respective parameters for generating a respective and desired vortex electron beam, which can enable the displacement of at least one defect center, in particular a group of defect centers, can be defined by the subsequently trained machine learning model. The machine learning model can be provided with corresponding parameter settings, originally existing distribution information of respective defect centers, and with corresponding resulting distribution information after applying the respective parameters to generate a vortex electron beam. The respective machine learning model can be as described elsewhere herein.

[0116] According to an independent aspect, a method for the automated spatial structuring of defect centers in a substrate, in particular a diamond crystal lattice, can be provided. The method can comprise the step of providing a defect center distribution for a machine learning model.

[0117] In particular, the machine learning model can be trained according to a training method as described elsewhere herein. The machine learning model can provide an output for relocating individual defect centers. The method can include the step of relocating at least one defect center. This provides a method for fabricating atomic-scale qubits in substrates, particularly diamonds, for scalable quantum communication, information processing, and sensing applications.

[0118] A method for the automated spatial structuring of defect centers in a substrate structure, in particular a diamond crystal lattice, can provide an automated or semi-automated approach for realizing a final configuration intended for a future application, as described elsewhere herein. It can provide an output for the displacement of individual defect centers and thus lay the foundation for a displacement strategy. In particular, the method can be capable of performing at least one intermediate step of displacing at least one defect center on the way to implementing or following a displacement strategy.Alternatively or additionally, the method may provide at least one parameter suitable for implementing a vortex electron beam with a desired angular momentum to enable the displacement of at least one defect center, in particular the displacement of a group of defect centers, for example, to enable the realization of qubit connectivity. Additionally or alternatively, the respective method may comprise a step, wherein the parameters for manipulating the electron beam to implement different types of shapes and / or angular momenta may be provided in a series of intermediate steps to enable semi-automated or fully automated displacement in at least two intermediate steps of the method.Alternatively and / or additionally, in particular between different (intermediate) process steps, switching can take place between individual excitation for the fine displacement of individual defect centers and group excitation for the coarser displacement of a group of defect centers in a defined direction.

[0119] According to an independent aspect, a system may be configured and structured to perform a method as described elsewhere herein. The system may comprise a displacement device configured and positioned to displace defect centers in a substrate, in particular a diamond crystal lattice. The system may comprise at least one detector configured and positioned to determine the initial position of the defect center. Alternatively or additionally, the detector may be configured and positioned to monitor the displacement of at least one defect center in the bulk substrate structure, in particular the solid diamond crystal lattice. The system may comprise a control unit configured to determine a displacement strategy and to control the displacement device to follow the displacement strategy.The methods and apparatus may be capable of generating a large, scalable network of precisely positioned, dipole-dipole coupled spin qubits. This groundbreaking technology offers a viable path to the realization of scalable quantum processors. The system may include a holographic aperture for modulating and generating a vortex electron beam. The system may include a magnetic field generator for generating a magnetic field for the formation of a cortex electron beam, in particular based on predictions of an expansion distribution.

[0120] The control unit may be independent of the machine and may include a storage unit or provide a link to a storage unit for accessing at least one machine-readable computer program product, as described elsewhere herein, to perform a respective method, as described elsewhere herein. The storage unit may also be provided as part of a computer network, an internet network, or a similar network structure.

[0121] The “optics”, micro-optics, microelectronic components and other parts of the system can be configured and placed so that the defect center can be moved to the “intended location”.

[0122] The displacement device may be any type of device or apparatus capable of performing one or at least one of the methods or method steps described elsewhere herein. Therefore, the respective features, advantages, and properties described in conjunction with one of the methods may also apply to the displacement device.

[0123] In particular, the displacement device is configured and positioned so that it can be controlled by a control unit, wherein it is configured and positioned so that the displacement device can follow the displacement strategy and at least perform the task of displacing at least one defect center, as described elsewhere herein.

[0124] The detector may be configured and positioned to determine at least one of an initial position of at least one defect center, an intermediate position of the at least one defect center, or the final position of the at least one defect center.

[0125] The control unit may be a computing machine configured to determine a displacement strategy and / or configured to apply a displacement strategy, in particular by analyzing the data measured by at least one detector and / or by controlling at least one displacement device.

[0126] Therefore, the respective system and / or its individual components can be described by the respective features, combinations of features, technical effects and / or advantages as described with respect to one of the methods, device, system or apparatus, in particular the diamond crystal, in particular independently of the respective category (method, apparatus, system, use) with which they are described and / or independently of a particular combination of individual components or aspects thereof.

[0127] According to an independent aspect, a computer program product may be configured to perform a method as described elsewhere herein when the computer program product is executed on a control unit, in particular in a system as described elsewhere herein.

[0128] The computer program product may be any type of machine-readable code that can transmit the respective information and instructions to a control unit when executed thereon, in particular can be read from a storage device, in order to carry out at least one of the methods or method steps described elsewhere herein. Therefore, the respective computer program product and / or its individual components can be described by the respective features, combinations of features, technical effects and / or advantages as described with respect to one of the methods, device, system or apparatus, in particular the diamond crystal, in particular regardless of the respective category (method, apparatus, system, use) with which they are described and / or regardless of a specific combination of individual components or aspects thereof.

[0129] According to an independent aspect, a device, in particular a diamond crystal, can comprise a substrate structure, in particular a diamond crystal lattice. The substrate structure, in particular the diamond crystal lattice, can comprise a qubit network of suitable defect centers arranged in spatial proximity such that they form the qubit network. The qubit network comprises in particular at least two suitable defect centers. The qubit network comprises in particular at least four suitable defect centers, in particular at least five suitable defect centers, furthermore in particular at least six suitable defect centers, furthermore in particular up to an integer n of suitable defect centers. The integer n can in particular be between 10 and 1000 defect centers, furthermore in particular between 20 and 900 defect centers, furthermore in particular between 100 and 800 defect centers.Alternatively, the integer number n of suitable defect centers may be, in particular, between 1000 and 1000 000 defect centers, furthermore, in particular, between 1500 and 900 000 defect centers, furthermore, in particular, between 2000 and 800 000 defect centers.

[0130] A device, in particular a diamond crystal, may comprise a substrate structure, in particular a diamond crystal lattice, comprising the respective defect centers as described elsewhere herein.

[0131] The method described elsewhere herein can provide a substrate, in particular a diamond, with at least three defect centers with distances between them of 10 nanometers or less. For a scalable quantum processor based on magnetically coupled spin qubits, such as NV centers, precise positioning can be provided based on the respective methods described elsewhere herein. These NV centers can be spaced from each other by a distance of 1 to 19 nm, in particular between 3 to 9 nm, and further in particular between 3.5 to 4.5 nm. In other embodiments, the NV centers can be spaced from each other by a distance of between 5±2 and 15±3 nanometers.Achieving this level of precision and efficiency closes a significant bottleneck in the development of scalable quantum processors using defect-based spin qubits in substrates, especially diamonds (and other materials, especially provided in the form of 2D materials).

[0132] The respective product of one of the methods - the substrate, in particular the diamond crystal - can be described by the respective features, combinations of features, technical effects and / or advantages as described with respect to one of the methods, the device or the system, in particular independently of the respective category (method, device, system, use) with which they are described and / or independently of a particular combination of individual components or aspects thereof.

[0133] An integer number n of suitable defect centers may refer to embodiments in which no physical-technical limitation may be provided for the respective number of defect centers that may be suitable defect centers for the respective applications described elsewhere herein.

[0134] According to an independent aspect, a method for manufacturing a device comprising a substrate may be configured as described elsewhere herein. The method may include a method for manipulating defect centers as described elsewhere herein. Regarding the advantages, features, and applications, reference is made to the further aspects of the device and / or method. These may specify the manufacturing method, particularly regardless of the category—method, use, device, or system.

[0135] An embodiment of the invention is shown in the drawings and will be explained in more detail below. They show: Fig. Figure 1 is a schematic representation of an embodiment of AC-STEM with electron spectroscopy-based feedback control for precisely moving and positioning the defect center qubits; Fig. Figure 2 is a schematic diagram of an embodiment of AC-STEM with optically acquired magnetic resonance spin resonance-based feedback control for precisely moving and positioning the defect center qubits; Fig. 3 a subset of defect centers in a lattice that are moved in a defined direction in a location-specific manner by using AC-STEM with an atom-sized vortex electron beam modulated by a holographic aperture; and Fig. 4 an embodiment of a training method.

[0136] The figures contain partially simplified, schematic representations. In some cases, identical reference symbols are used for similar, but possibly not identical, elements. Different views of the same elements may be scaled differently. Directional references such as "left," "right," "top," and "bottom" are to be understood relative to the respective figure and may vary in individual representations compared to the object depicted.

[0137] The figures contain partially simplified, schematic representations. In some cases, identical reference symbols are used for similar, but possibly not identical, elements. Different views of the same elements may be scaled differently. Directional references such as "left," "right," "top," and "bottom" are to be understood relative to the respective figure and may vary in individual representations compared to the object depicted.

[0138] Fig. Figure 1 shows a schematic representation of an embodiment of an aberration-corrected scanning transmission electron microscopy system (AC-STEM) 10 with an electron spectroscopy-based control 21, 23 of the feedback 5 for precisely moving and positioning the individual defect centers 6 as qubits. The AC-STEM 10 enables the manipulation and control 21, 23 and positioning of individual defect centers 6, in particular as vacancy color centers as solid-state qubits in a diamond crystal lattice 50 (see Fig. 3A to 5B for details) using a focused, aberration-corrected, scanning transmission electron microscopy-derived vortex electron beam (E-beam) 51 to fabricate a scalable multi-qubit quantum processor enabling quantum information processing applications such as quantum sensing and quantum information processing, in particular quantum computing.

[0139] The controlled creation of vacancy centers on an atomic scale in a substrate such as diamond is a major challenge for advancing the field of quantum computing. Therefore, a method is described for constructing qubit connectivity by manipulating defect centers 6 in a substrate, here a diamond crystal lattice 50. The vacancy centers can be placed as solid-state qubits in diamond by precisely directing an atom-sized vortex electron beam 51 formed by a holographic aperture 68 in a scanning transmission electron microscope. According to one embodiment, the diameter of the vortex electron beam 51 can be between 1 and 2 Ångstroms.The transferred orbital angular momentum from the vortex electron beam 51 to the selected vacancy center within the diamond lattice 50 can control the motion in a fixed and selected direction 66, which may enable potential applications in quantum information processing. Aberration-corrected scanning transmission electron microscopy (AC-STEM) can provide atomic-scale imaging, spectroscopy, and material modification.

[0140] Progress could result from the efficient design of the aberration corrector 69 and the beam shaping, which allows direct visualization of individual atoms 52, 53, 54 (see Fig. 3) at the atomic level, enabling structural quality analysis and the identification of individual defect centers 6 in materials. Combined with energy-dispersive spectroscopy (EDX), four-dimensional STEM (4D-STEM), in-situ heating and / or cooling and / or biasing, electron energy loss spectroscopy (EELS), and cathodoluminescence techniques, AC-STEM can visualize fine chemical composition and material interfaces, map electric charge and fields, analyze detailed morphological structures at the atomic level, evaluate electron-photon interactions with matter, and investigate in-situ atomic-level atomic dynamics and ferroelectric phenomena. In addition to these advanced techniques, atom-sized vortex electron beams 51 with selected orbital angular momentum provide a means for detecting magnetic field mapping, biological samples, and enhancing edge contrast.

[0141] The AC-STEM 10 enables the displacement of individual defect centers 6, in particular individual vacancy centers, in diamond crystal lattices 50 using techniques with a vortex electron beam (e-beam) 51 at the atomic level within the AC-STEM 10. The vortex e-beam 51 can be derived with accelerating voltages between 60 and 160 keV. By focusing the vortex e-beam 51 on the desired individual defect center 6, in particular a defect atom, the individual defect center 6, in particular the defect atom, can be excited. The individual defect center 6, in particular the defect atom, may then not be ejected but migrate to the next lattice site. The manufacturing process 20 can identify individual defect centers 6, e.g., nitrogen vacancy centers, by integrating dark-field imaging with ongoing electron spectral analyses.The E-beam 51 is, in particular, a vortex electron beam 51 that is guided through a monochromator 71 and a magnetic field generator 81. The magnetic field generator 81, in combination with a holographic aperture 67, enables the formation of a vortex electron beam 51 to displace several defect centers 6 simultaneously, as shown in FIG. Fig. 3. Here, the magnetic field generator 81 is shown schematically and by way of example and provides a magnetic field based on the e-beam 51 itself. The vortex electron beam 51 can pass through lenses 72 for focusing and an aberration corrector 69 for compensating the aberration of the lenses 72.

[0142] In the quantum framework, electrons exhibit fascinating behavior in which they can manifest a wave-like rotation around their propagation direction. Vortex electron beams 51 can thus carry orbital angular momentum. Various techniques can be used to generate the electron vortex beam 51, such as phase plates, holographic fork shutters, holographic spiral shutters, manipulation of aberration functions, and / or the use of a magnetic field (provided by the electron beam itself, by the lenses 72 of the electron microscope, or an additional magnetic field generator 81). Atom-sized vortex electron beams 51 with selected orbital angular momentum can be used for the electron energy loss magnetic chiral dichroism (EMCD) technique in STEM.

[0143] For manipulating the foreign atoms (defect centers 6) using an Ångström-sized focused electron probe in an aberration-corrected STEM, where incident electrons interact with the atomic nuclei and scattered electrons transfer energy and momentum to the individually targeted foreign atom, such that the foreign atom is not ejected but excited to move to the nearest neighboring lattice sites, can provide atomically precise manipulation. Using this mechanism, in some embodiments, electron beam manipulation of various foreign atoms in bulk silicon, graphene, and carbon nanotubes can be implemented. Using aberration-corrected scanning transmission electron microscopy (AC-STEM), the surface of (nano)diamonds can be analyzed and can be used to indirectly move the vacancy centers in nanodiamonds in ultrahigh vacuum.However, due to the continued electron irradiation of the neighboring atoms and directly onto the foreign atoms, the foreign atoms could be knocked out or double or triple lattice jumps could occur. This stochastic process limits the directionality of the manipulation. Therefore, a direction of lattice jumps can be defined by manipulating both clockwise and counterclockwise using a vortex electron beam 51 with the respective orbital angular momentum. This allows a preferred direction 66 to be defined, and respective vortex electron beams 51 can be provided to initiate and execute lattice jumps in the desired direction 66.

[0144] In the proposed method 20, an atom-sized vortex electron beam 51 may have a selected orbital angular momentum in STEM to direct individual vacancy centers as defect centers 66 in a substrate such as diamond in a well-defined direction 66 (see Fig. 3). The process 20 may involve freestanding diamond samples, where the impurities (e.g., N, Si, Sn) may have been carefully and controlledly implanted. These dopants form atomic point defects (e.g., P1, substitution configuration). Furthermore, it may be annealed at high temperatures to form vacancy centers and higher coordinate defects. The samples may be annealed in an ultrahigh vacuum to avoid impurities that can be problematic during electron beam manipulation 51 at the atomic scale. This preparation of doped substrates may be referred to as staging. Alternatively or additionally, any handling step may be referred to as staging.

[0145] In view of the above, in one embodiment of the method 20 and apparatus, orbital angular momentum can be provided by an atom-sized vortex electron beam 51 that can direct individual nitrogen vacancy centers in diamonds in a precisely defined direction 66. The atom-sized vortex e-beam 51 can be generated by aberration-corrected STEM. A focused spiral vortex electron beam 51, which can be formed by a holographic fork aperture 68, can be placed directly onto individual nitrogen vacancy centers to irradiate them for a specific time. The electron beam 51 can form a rapidly spinning vortex that can interact with the atoms 52, 53 and, by imparting orbital angular momentum to the atoms 52, 53, can thereby be directed in a very controlled manner, as in Fig. 3. By setting acceleration voltages in the rangeFrom 60 to 200 keV, the removal of vacancy centers can be mitigated and unwanted damage in the diamond can be avoided. Convergence angles above 32 mrad can correspond to beam sizes of 1-2 angstroms in diameter. In a first step, nitrogen vacancy centers in the diamond can be located using a combination of atomic-scale dark-field imaging, high-resolution monochromatic electron energy loss spectroscopy, and optical spectral and spin spectroscopy (e.g., EELS, ODMR). A monochromator 71 can be placed to provide the means for high-resolution monochromatic electron energy loss spectroscopy. Consequently, an image can be acquired and a region of interest (extension distribution) defined with the scattered nitrogen vacancy centers as a reference point. In embodiments, it is possible to select a first subset of defect centers 6 for displacement.This can be, at least in part, a subset of initially determined (imaged) defect centers 6. The individually selected vortex electron beam 51 can carry orbital angular momentum and transfer it with different vortex states (also called orders 51a, 51b, 51c), whereby a directional manipulation of the defect centers 6, in particular vacancy centers, can be manifested. This can, for example, prevent the irradiated atoms from jumping to the random (neighboring) carbon atoms 51 in diamonds. Therefore, the directional movement 66 of the vacancy center can be controlled along a defined path based on the calibrated transfer direction of the orbital angular momentum (see ). Fig. 3). If the lattice positions remain unchanged during imaging or spectroscopic observation, the manipulation process can be repeated until the defect centers 6, especially the NV centers, are moved. This process can be stopped once the defect centers 6, especially the NV centers, have moved to the desired distance and direction.

[0146] An annular dark-field detector 7 can be provided to detect individual defect centers 6 based on electrons from the (vortex) e-beam 51 that are scattered by individual defect centers 6. Alternatively or additionally, electron energy loss spectroscopy (EESL) 8 can be implemented to also determine the chemical structure of the respective individual defect center 6. From this, a STEM image direct electron signal 4 can be obtained to determine the position of individual defect centers 6 and their respective bonding and chemical nature.

[0147] After identifying an individual defect center 6 of interest, e.g., because it could act as a qubit, the desired defect center 6 is selected 1. The energy of the e-beam 51 is tuned to the correct e-beam energy 2, and the e-beam 51 is focused on the individual defect center 6 (in particular, its atom as the defect atom).

[0148] The method 20 for producing a diamond crystal lattice 50 with individual defect centers 6 may include at least one step for checking 21 whether a displacement of the respective defect center has occurred. For this purpose, in the Fig. In the embodiment shown in Figure 1, annular dark-field spectroscopy can be combined with EESL 8 to obtain a STEM image direct electron signal 4, which can be compared with an expected signal to verify whether a shift has occurred. If this is not the case, the E-beam 51 can be repositioned 22 on the individual defect center 6 of interest. In a second control step 23, an attempt is made to obtain verification of the shift. If a successful shift cannot be verified, the method or method step of repositioning 22 the E-beam 51 on the individual defect center 6 of interest can be repeated, in particular until the respective shift has occurred.

[0149] If it can be verified that the displacement has occurred (in particular directly after the first control step 21 or after one of the subsequent control steps 23), the E-beam 51 can be moved 24 to the next single defect center 6 of interest. The method steps described above can be repeated.

[0150] The method can be carried out using the respective feedback 5 as described above and repeated until no more individual defect centers 6 need to be moved. An intermediate step can be the movement of a specific individual defect center 6. After the intermediate step, the specific individual defect center 6 can be placed in an intermediate position, but not in the final position intended based on a specific displacement strategy. Several intermediate steps may be required until the individual defect centers 6 reach a final position. The method 20 described above can therefore be carried out for each of the intermediate steps for each and every one of the defect centers 6 to be displaced to their final position, in particular independently of one another and in particular location-specifically.Furthermore, the respective individual defect centers 6 may be embedded in the interior of the diamond crystal lattice 50 and do not necessarily have to be located in the surface region or in the surface volume (e.g., down to the third layer of carbon atoms 52 in the diamond crystal lattice 50).

[0151] In particular, if the step of checking 25 whether all defect centers 6 have been moved to achieve their final configuration reveals that a respective translation step is necessary, the method 20 can return to selecting the desired defect center 6 as an individual qubit to be relocated. The method can therefore be based on feedback 5 and iteratively achieve the respective final configuration. It may even be possible to execute multiple paths along the translation strategy, e.g., if certain intermediate steps can be exchanged to avoid impact damage or other damage over time.

[0152] Fig. Figure 2 shows a schematic representation of an embodiment of AC-STEM 10 with optically acquired magnetic resonance ODMR 15. This allows for the implementation of a spin resonance-based control 21, 23 of the feedback 5 to precisely move and position the individual defect centers 6 as qubits. The respective AC-STEM 10 differs from the one shown in Fig. 1 embodiment shown in that for validation a concentrated E-beam focused on the desired nitrogen vacancy centers as in relation to Fig. 1, followed by spin spectroscopy, such as optically detected magnetic resonance (ODMR) 15. Alternatively or additionally, further imaging studies can confirm the displacement of the individual defect centers 6, in particular of the defect atom and / or the vacancy and / or both. For this purpose, steps 21, 23, 25 for checking whether the position of the individual defect center 6 is moved, as described in connection with Fig. 1 explained in detail. As with regard to Fig. 1 above, the E-beam 51 is a vortex electron beam 51 due to interaction with a holographic aperture 68. In the embodiment shown, a magnetic field generator 81 may be provided, although not shown here.

[0153] Spin spectroscopy can also be based on a laser 11 irradiating the individual defect center 6 (in particular, by illuminating at least one sub-scanning window of the E-beam 51 scanning the diamond crystal lattice 50). Single photons can be emitted as fluorescence photons 12 if the defect center is active, as may be the case with certain NV centers. These fluorescence photons 12 can be detected by a single-photon detector 13 and converted into an electronic signal that can be analyzed in the ODMR electronics 14. This allows the feedback 5 to be based on the respective ODMR information.

[0154] Consequently, in the Fig. 1 and Fig. 2, an image of the desired region with the scattered individual defect centers 6, in particular the nitrogen vacancy centers, can be obtained as a reference point. A focused beam can be placed directly onto individual defect centers 6, such as nitrogen vacancy centers, to irradiate them for a specific time, e.g., followed by a spin spectroscopy measurement to confirm the movement, wherein the image can be recorded to observe and verify successful manipulation. If it is verified by the control 21, 23 of the lattice sites that the lattice sites are unchanged, the respective steps of the method 20 can be repeated until the individual defect centers 6, in particular the NV centers, are moved, which is verified accordingly.The use of a small subsampling window as an alternative approach can be used alternatively or additionally to manipulate the respective individual defect centers, especially the NV centers, and also to monitor the change of the structure in real time.

[0155] In summary and in other words, the embodiments in Fig. 1 and Fig. 2 introduces a unique technical approach to performing a process 20 for fabricating a diamond crystal lattice 50. It utilizes an Ångström-sized vortex e-beam 51 within the aberration-corrected scanning tunneling electron microscope (AC-STEM) system 10. Because electrons from the vortex e-beam 51 can collide with atomic nuclei, their scattered counterparts can transfer energy and momentum directly to the targeted foreign atoms. Instead of ejecting these atoms, the process can excite them, causing a shift to neighboring lattice sites and enabling manipulation with unprecedented atomic precision. This method can effectively manipulate foreign atoms in materials such as silicon, graphene, and carbon nanotubes.The method 20 enables the performance of precise placement in 3D macrocrystals such as diamond and enables operation independent of a diffusion-based process of e-beam-induced NV center migration through vacancy-induced motions. Rather, individual defect centers can be targeted in a particularly location-specific manner with a vortex e-beam 51 to perform individual displacements. These displacements can be intermediate steps in a displacement strategy. The method 20 enables the repositioning of individual vacancy centers in diamond using the manipulation of vortex e-beams 51 at the atomic level within an AC-STEM 10. To ensure the safety and integrity of the process, the accelerating voltages are carefully selected between 60 and 160 keV and, in particular, kept below the threshold for impact damage in diamonds.The procedure can begin with the identification of defect centers 6, such as nitrogen vacancy centers, using combined dark-field imaging and electron and optical in-situ spectral techniques. An image of the desired region with recognizable defect centers, such as nitrogen vacancy centers, can then be used as a reference. As part of the validation process, a concentrated beam can be used to directly irradiate specific defect centers 6, such as nitrogen vacancy centers. Subsequent spin spectroscopy measurements and imaging techniques can confirm the motion. If the atoms remain stationary, the process can be repeated until the desired motion can be achieved and verified. As an additional level of precision, a minimized subsampling window can be used to both maneuver the defect centers 6, especially NV centers, and continuously monitor structural changes.This could revolutionize the way atomic structures are manipulated by combining the power and precision of an AC-STEM 10 with careful safety measures and validation techniques, allowing individual atoms to be moved with unprecedented accuracy. The method 20 enables the implementation of a scalable qubit fabrication technology, particularly for spin defects in solids. The immediate application could be the construction of a scalable quantum computer, but many other applications in quantum technologies can be realized with the method 20, for example, by forming a large-scale entangled network of solid-state qubits (more than 5, even up to 10, 20, or 100, or even more possible).

[0156] Fig. 3 shows a subgroup of defect centers 6 in a diamond crystal lattice 50, which are moved in a defined direction 66 in a location-specific manner by using AC-STEM with an atom-sized vortex electron beam 51 modulated by a holographic aperture 68. Fig. Figure 3 shows a precision movement 61 based on an individual precision displacement of a subgroup of defect centers 6. Orders 51a, 51b, and 51c of the vortex e-beam 51 interact with individual defect centers 6, which comprise nitrogen 53 and vacancy centers 54 in the lattice 50 of carbon 52. The respective defect centers 6 form part of a subgroup 80 to be displaced in a defined direction 66. The defect centers are displaced in a defined direction 66 after interaction with orders 51a, 51b, and 51c of the vortex e-beam 51.

[0157] The Fig. The embodiment shown in Figure 3 illustrates one example of an approach to overcoming the limitations of qubit connectivity. It features a unique method 20, 100 for constructing a qubit coupling by precisely controlling the placement of the qubits. This approach not only addresses the challenge of qubit connectivity but also enables consistent, large-scale production of scalable quantum sensing devices. The method 20, 100 may begin with doping during growth or ion implantation (also referred to as provisioning), followed by annealing, which may result in a random distribution of defect centers 6, particularly vacancy centers.A phase-singular, atom-sized, spiral vortex electron beam 51 may be used, which in particular has a zero-intensity center and a non-zero intensity in its spiral profile, thereby generating varying local electron densities and corresponding angular momenta. Methods 20, 100 (see . Fig. 1, Fig. 2, Fig. 4) and devices (see Fig. 1, Fig. 2) can move multiple randomly distributed qubits closer together toward the center or along a spiral path within the region of the vortex electron beam 51 (also referred to as exposure distribution). As explained with respect to other embodiments, this is achieved by manipulating them using orbital angular momentum transfer in scanning transmission electron microscopy (STEM). By continuously irradiating electrons with a vortex electron beam 51, the orbital angular momentum can be transferred, effectively rearranging the position of the vacancy centers as desired. Using a uniform electron beam 51, multiple defect centers 6 can be manipulated simultaneously along a precisely defined path, allowing the user to multiplex the process and create many coupled spins, from two to many thousands.The corresponding methods and devices enable the production of scalable quantum computers and quantum sensors that can utilize and apply quantum phenomena.

[0158] Fig. 4 shows an embodiment of a training method 100. The method 100 is shown as circular. Thus, in particular, a machine learning model can be retrained and it can also enable the application of the newly trained machine learning model in a STEM step for relocating defect centers 6 in a diamond crystal lattice 50, as shown in Fig. 3. The method may comprise a step of image acquisition 4, 110, as already described with respect to Fig. 1 and Fig.2. Based on processing 130 of the images and alignment, at least one defect center 6 can be selected 120, and a vortex e-beam 51 can be positioned such that the respective defect centers 6 can be displaced in a defined direction 66. The image can be filtered 140 and used to train the respective machine learning model. Based on the trained machine learning model, a particularly spiral-shaped vortex electron beam 51 can be controlled 150 to perform STEM 160.

[0159] The embodiments described herein employ an angstrom-sized vortex electron beam 51, particularly in a spiral shape, formed by a holographic aperture 68 within the aberration-corrected scanning tunneling electron microscope (AC-STEM) frame. As with conventional electron beam-matter interactions, electrons collide with atomic nuclei 52, 53, transferring energy and momentum directly to the targeted foreign atoms to their scattered counterparts. If the threshold energy for displacement of the target atom is lower than the transferred energy from the vortex electron beam 51, then these atoms are not ejected by the process but are excited, causing them to be pushed to neighboring lattice sites and enabling manipulation with unprecedented atomic precision. However, the controlled directional motion can still be a stochastic process.Furthermore, the simultaneous movement of multiple impurities is limited. However, by selecting the transferred orbital angular momentum from a focused, atom-sized vortex spiral beam 51 formed by the holographic apertures 68, these limitations can be overcome by moving the desired atom in the selected direction 66 to the nearest lattice site. This method 20, 100 enables effective manipulation of defect centers 6 in a substrate.

[0160] The described methods 20, 100 enable the repositioning of individual defect centers 6 in a substrate, particularly vacancy centers in diamonds, by manipulating eddy e-beams 51 at the atomic level within STEM. Acceleration voltages are specifically chosen between 60 and 160 keV. This allows the transferred energy to be kept below the threshold for impact damage when diamond is used as a substrate. This improves the safety and integrity of the methods 20, 100. The procedure may begin with the identification of nitrogen vacancy centers using combined dark-field imaging and electron and optical in-situ spectral techniques, as described elsewhere herein. An image of the desired region, particularly with recognizable nitrogen vacancy centers, may be taken as a reference.As part of the validation process, a concentrated vortex electron beam can directly irradiate 51 specific nitrogen vacancy centers. Subsequent spin spectroscopy can make measurements, and imaging techniques can confirm the motion. If the atoms remain stationary, the procedure can be repeated until the desired motion is achieved. As an additional level of precision, a minimized subsampling window can be used to both maneuver the NV centers and continuously monitor structural changes.

[0161] The respective images and the respective measurement parameters can be used and fed into a machine learning model for training. The trained machine learning model can be used to determine whether a respective displacement occurs in the correct or incorrect direction. Alternatively or additionally, the machine learning model can enable the implementation of a pathfinding algorithm that can adjust the respective settings of the vortex electron beam to enable a desired displacement of one or more defect centers 6.

[0162] The embodiments can harness the power and precision of AC-STEM, coupled with careful safety measures and validation techniques. Thus, individual atoms can be moved with high precision. These methods enable the provision of scalable qubit manufacturing technology, particularly for spin defects in solids. The immediate application is the construction of a scalable quantum computer. This innovative method for forming a large-scale entangled network of solid-state qubits can be used to realize many other applications in quantum technology.

[0163] In particular, the terms "may" or "can" refer to optional features of the invention. Consequently, there are also further aspects and / or embodiments of the invention which additionally or alternatively comprise the respective feature(s). All features in feature combinations are also disclosed independently thereof and can also be taken from the feature combinations disclosed herein and used in combination with other features to concretize the subject matter of any claim, whereby any structural and / or functional relationship that may exist between the features is dissolved. Terms such as "first", "second", "third" can be used to refer to a list of elements, but do not necessarily describe these features or elements according to their importance, order of occurrence, or structural order.Therefore, these elements or characteristics may indicate the different aspects in any other order, unless explicitly stated otherwise. List of reference symbols 1 Selecting the desired defect center as a qubit 2 Tuning to the correct e-beam energy 3 Focusing the e-beam on the defect center (in particular on one atom of it as the effect atom) 4 STEM image direct electron signal 5 Feedback 6 individual defect center as QuBit 7 ring-shaped dark field detector 8 Electron Energy Loss Spectroscopy (EELS) 9 spin resonance spectroscopy, e.g. B. DEER, ENDOR 10 aberration-corrected scanning transmission electron microscopy system (AC-STEM) 11 lasers 12 fluorescence photons 13 Single photon detector 14 ODMR electronics 15 optically acquired magnetic resonance (ODMR) 20 Methods for producing a diamond with defect centers 21 Check whether the position of the defect center has moved 22 Repositioning the electron beam 23 Check whether the position of the defect center has moved as desired 24 Moving the e-beam as a qubit to the new defect center 25 Check whether all defect centers have been moved 48 Raster scan path 50 diamond crystal lattices 51 Electron beam (E-beam) 51a, 51b, 51c Orders of the electron beam from the holographic aperture 52 carbon atoms (C) 53 nitrogen atoms (N) 54 blank spaces 55 shifted defect center after interaction with e-beam 56 Relocation of the first defect center 57 Relocation of the second defect center 58 Relocation of the third defect center 59 Relocation of the fourth defect center 60 Maintaining the final configuration 61 Precise movement based on individual precision displacement of a subset of defect centers 63 Initial configuration 64 Final configuration 65 Relocation of defect centers to achieve the final configuration based on raster scanning 66 defined direction 67 C13 atoms 68 holographic aperture 69 Aberration corrector 71 Monochromator 72 lens 80 subgroup 81 Magnetic field generator 100 procedures 110 Image capture 120 Selecting the defect center and placing the E-beam 130 Processing the image and aligning 140 Filtering the image and using it for training 150 Controlling the spiral vortex electron beam 160 STEM. X x-coordinate Y y-coordinate Z z-coordinate

Claims

[1] Method (20) for relocating defect centers (6) in a substrate for quantum applications in a defined direction, the method comprising the following steps - in particular providing a substrate, especially diamond, comprising defect centers (6) in a bulk substrate structure, in particular a massive diamond crystal lattice (50), - Determining the position of at least one defect center (6) in the bulk substrate structure, in particular the massive diamond crystal lattice (50), and - Displacement (61) of the at least one defect center (6) in the bulk substrate structure, in particular of the massive diamond crystal lattice (50), in particular in a site-specific manner, in a defined direction. [2] Method (20) for relocating defect centers (6) in a substrate for quantum applications in a defined direction, in particular according to claim 1, wherein the method comprises the following steps - Displacement (61) of a group of defect centers (6) in the bulk substrate structure, in particular of the massive diamond crystal lattice (50), simultaneously, in particular group-specifically, in particular in a defined direction. [3] Method (20) according to one of claims 1 or 2, characterized by at least one of the following steps: - providing a substrate, in particular diamond, which contains defect centers (6) in a bulk substrate structure, in particular a massive diamond crystal lattice (50); - Determining the position of at least one first subgroup of the defect centers (6) in the bulk substrate structure, in particular the massive diamond crystal lattice (50); - Relocation of a second subgroup, which is at least partially a subgroup of the first subgroup of defect centers (6), in the bulk substrate structure, in particular the massive diamond crystal lattice (50); or - Checking or monitoring the position of the displaced defect center (55) or the positions of the displaced defect centers (55). [4] Method (20) according to any one of the preceding claims, characterized by at least one of the following steps - Directing a vortex electron beam (51) (at the atomic level), in particular using aberration-corrected scanning transmission electron microscopy (10), to displace the at least one defect center (6) in the bulk substrate structure, in particular the massive diamond crystal lattice (50), in a defined direction (61); or - Directing a vortex electron beam (51) (at the atomic level), in particular using aberration-corrected scanning transmission electron microscopy (10), to simultaneously displace the group of defect centers (6), which in particular is at least the second subgroup of defect centers (6), in the bulk substrate structure, in particular the massive diamond crystal lattice (50), in a defined direction (61). [5] Method (20) according to claim 4, wherein a diameter of a directed vortex electron beam (51) of atomic size is in the range of 0.5 to 3 Ångstroms, in particular in the range of 0.5 to 2 Ångstroms, and furthermore in particular in the range of 0.5 to 0.8 Ångstroms; and / or wherein a diameter of a directed scanning transmission vortex electron beam (51) (of atomic size) is in the range of 1 to 200 Ångstroms, in particular in the range of 10 to 150 Ångstroms, and furthermore in particular in the range of 50 to 100 Ångstroms. [6] Method (20) according to one of the preceding claims, wherein an accelerating voltage for accelerating electrons in the directed vortex electron beam (51) (at atomic size) is set below the impact damage of the structure of the substrate, in particular the diamond crystal lattice (50), in particular wherein the accelerating voltage is set between 60 and 160 keV, in particular for diamond; and / or wherein a convergence angle is higher than 15 mrad, in particular higher than 20 mrad, and furthermore in particular higher than 32 mrad. [7] Method (20) according to one of the preceding claims, wherein the directed vortex electron beam (51) (atomic size) is directed at the defect center (6) to be relocated and / or at the group of defect centers to be relocated. [8] Method (20) according to any of the preceding claims, characterized by at least one of the following steps - Darkfield imaging with ongoing electron spectral analysis, which identifies at least one defect center (6) in the massive diamond crystal lattice (50) or the group, in particular the at least first subgroup, of defect centers (6); - Confirming or monitoring the displacement (61) of at least one defect center (6), in particular by applying at least one of the following methods: spin spectroscopy, imaging studies or ODMR; - Mapping, assessing and / or evaluating at least the chemical composition and / or electronic structure, in particular using at least one of energy-dispersive X-ray spectroscopy (EDX), electron energy loss spectroscopy (EELS) (8) or four-dimensional STEM (4D-STEM); - Using at least one subsampling window to manipulate the at least one defect center (6) and / or the defect centers (6); and / or to monitor the change in the bulk substrate structure, in particular the structure of the massive diamond crystal lattice (50), in real time; - Providing a map of defect centers to determine a potential qubit coupling by controlled positioning of the defect centers (6) as potential qubits and accordingly relocating individual defect centers (6) or a group of defect centers; or - Moving individual defect centers or a group of defect centers and monitoring the qubit coupling to improve the coupling between at least two defect centers, in particular to improve the coupling of a qubit network; [9] Method (20) according to any of the preceding claims, wherein the method (20) is repeated until a displacement (61) of the at least one defect center (6) is detected; or wherein the method is repeated until the group of defect centers (6) has reached a desired configuration. [10] Method (20) according to any one of the preceding claims, wherein the defect center (6) is at least one of the following: an atomic point defect, an atomic point defect with P1 as the substitution configuration, a silicon atom impurity, a nitrogen atom impurity, a tin atom impurity, a phosphorus atom impurity, a bismuth atom impurity, a vacancy center, a nitrogen vacancy center, a silicon vacancy center, a tin vacancy center, a phosphorus vacancy center, a bismuth vacancy center, a germanium vacancy center or a higher coordinated defect; and / or wherein the substrate comprises at least one of diamond, silicon, silicon carbide or a wide bandgap semiconductor. [11] Method (20) according to one of the preceding claims, wherein at least one intermediate step for relocation is planned, in particular calculated, and / or wherein at least one parameter setting for at least one intermediate step is planned, in particular calculated. [12] Method (20) according to one of the preceding claims, comprising the step of placing suitable defect centers (6) as qubits for quantum communication in an ordered array and / or a corral nanostructure within the bulk substrate structure, in particular the massive diamond crystal lattice. [13] Method (20) according to any of the preceding claims, characterized by at least one of the following steps - a manipulation controlled by in-situ feedback (5) in combination with a predefined structure used for real-time monitoring of qubit signals; - Repositioning the relative positions of the complex and / or composite defect centers in the bulk substrate structure, in particular the diamond crystal lattice (50), in particular optimizing these; - Investigating temperature effects on defect centers (6) in a range from room temperature to 1500 °C; - Applying at least one of heating, cooling or pre-stressing for analysis; or - Relocation of at least one defect center (6) to a site-specific marker of the substrate structure, in particular of the diamond crystal lattice (50), especially a C13 isotope. [14] Method according to one of the preceding claims, wherein a vortex electron beam (atomic size), in particular a focused one, is formed by a holographic aperture in the aberration-corrected scanning transmission electron microscope; and / or wherein the vortex electron beam (atomic size), in particular a focused one, is formed by applying an additional magnetic field to an electron beam in the aberration-corrected scanning transmission electron microscope. [15] Method for training a machine learning model with a series of images of spatially placed defect centers (6) in a bulk substrate structure, in particular a massive diamond crystal lattice (50). [16] Method for automated spatial structuring of defect centers (6) in a substrate, in particular a diamond crystal lattice (50), in particular a method (20) according to any one of claims 1 to 13, comprising the following steps: - Providing a distribution of defect centers (6) for a machine learning model, wherein the machine learning model is trained in particular according to a method according to claim 15, wherein the machine learning model provides an output for the displacement of individual defect centers (6), - Relocation of at least one defect center (6). [17] Method according to claim 16, wherein the shape of a vortex electron beam is defined based on the defect center distribution provided to the trained machine learning model. [18] System (10) configured and structured to carry out a method according to any of the preceding claims, wherein the system (10) comprises: - a displacement device configured and positioned to relocate defect centers (6) in a substrate, in particular a diamond crystal lattice (50); - at least one detector (7, 13) configured and positioned to determine the initial position of the defect center (6) and / or configured and positioned to monitor the displacement of at least one defect center (6) in the bulk substrate structure, in particular the massive diamond crystal lattice (50), - a control unit configured to determine a displacement strategy and to control the displacement device to follow the displacement strategy. [19] Computer program product configured to perform a method (20) according to any one of claims 1 to 13 when executed on a control unit in a system (10) according to claim 18. [20] Device, in particular diamond crystal, comprising a substrate structure, in particular a diamond crystal lattice (50), comprising a qubit network of suitable defect centers arranged in close proximity to each other to form the qubit network, wherein the qubit network comprises in particular at least two suitable defect centers (6), in particular at least four suitable defect centers (6), in particular at least five suitable defect centers (6), furthermore in particular at least six suitable defect centers (6), furthermore in particular up to an integer n suitable defect centers (6), wherein n is in particular between 10 and 1000 defect centers (6), furthermore in particular between 20 and 900 defect centers (6), furthermore in particular between 100 and 800 defect centers (6);and / or comprising up to an integer n of suitable defect centers (6), wherein n is in particular between 1000 and 1,000,000 defect centers (6), furthermore in particular between 1500 and 900,000 defect centers (6), furthermore in particular between 2000 and 800,000 defect centers (6). [21] Method configured to manufacture a device comprising a substrate, in particular according to claim 20, comprising at least one method according to any one of claims 1 to 17.

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