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

Abstract

Method of automated spatial patterning of defect centers (6) in a substrate, particularly a diamond crystal lattice (50), comprising the following steps: - providing a defect center (6) distribution to a machine-learning model, the machine-learning model being particularly trained to determine an output for displacement of at least one defect center (6) based on the provided defect center (6) distribution, the machine learning model providing an output for displacement of individual defect centers (6), - particularly providing a substrate, particularly diamond, comprising defect centers (6) in a bulk structure of the substrate, particularly a bulk diamond crystal lattice (50), - detecting the position of at least one defect center (6) in the bulk structure of the substrate, particularly the bulk diamond crystal lattice (50), and - displacing (61) the at least one defect center (6) in the bulk structure of the substrate, particularly the bulk diamond crystal lattice (50), particularly site-specific, in a defined direction.

Description

[0001] Method for displacing defect centers in a substrate for quantum applications in a defined direction

[0002] DESCRIPTION

[0003] The invention refers to a method for displacing defect centers in a substrate, particularly diamond, for quantum applications in a defined direction. The invention refers to a method of training a machine-learning model. The invention refers to a method of automated spatial patterning of defect centers in a substrate, particularly a diamond crystal lattice. The invention refers to a system configured and structured to perform at least one of the respective methods. The invention refers to a computer program product. The invention refers to a device, particularly a diamond crystal. The invention refers to a method configured to manufacture a device.

[0004] Defect centers in certain substrates such as diamond are promising structures for studying quantum properties and they provide a promising tool for quantum computing, such as establishing qubit calculations. Alternatively or additionally, they may function as sensing tools for optically detecting magnetic resonances, to study biological materials and their respective properties provide powerful quantum sensors for studying magnetic phenomena at the nanoscale, ranging from biological processes to novel magnetic materials. Their implementation is difficult and has to be controlled precisely, particularly in a sense that allows coupling between defect centers suitable for establishing respective quantum gates, quantum communication networks or the like.

[0005] Scanning tunneling microscopy in combination with atomic force microscopy has been used to resolve atomic positions, modify the surface and manipulate the surface atoms using their atomic sharp tip, however, it requires cryo-temperatures, conductive surfaces, and tip needs to be closer to the surface. This increases the complexity of the respective methods but still lacks behind on the desirable control.

[0006] Prior art document 1 describes that atomic engineering is envisioned to involve selectively inducing the desired dynamics of single atoms and combining these steps for larger-scale assemblies. It focuses on the first part by surveying the single-step dynamics of graphene dopants, primarily phosphorus, caused by electron irradiation both in experiment and simulation, and develop a theory for describing the probabilities of competing configurational outcomes depending on the postcollision momentum vector of the primary knock-on atom. The predicted branching ratio of configurational transformations agrees well with atomically resolved experiments.

[0007] Prior art document 1 : "Engineering single-atom dynamics with electron irradiation", Cong Su, Mukesh Tripathi, Qing-Bo Yan, Zegao Wang, Zihan Zhang, Christoph Hofer, Haozhe Wang, Leonardo Basile, Gang Su, Mingdong Dong, Jannik C. Meyer, Jani Kotakoski, Jing Kong, Juan-Carlos Idrobo, Toma Susi, Ju Li, Su et aL, Sci. Adv. 2019; 5:eaav2252.

[0008] Prior art document 2 describes the direct manipulation of individual atoms in materials using scanning probe microscopy having been a seminal achievement of nanotechnology. Recent advances in imaging resolution and sample stability have made scanning transmission electron microscopy a promising alternative for singleatom manipulation of covalently bound materials. Pioneering experiments using an atomically focused electron beam have demonstrated the directed movement of silicon atoms over a handful of sites within the graphene lattice. It is achieved a much greater degree of control, allowing to precisely move silicon impurities along an extended path, circulating a single hexagon, or back and forth between the two graphene sublattices. Even with manual operation, the manipulation rate is already comparable to the state-of-the-art in any atomically precise technique. It is further exploring the influence of electron energy on the manipulation rate, supported by improved theoretical modeling taking into account the vibrations of atoms near the impurities, and implement feedback to detect manipulation events in real time. In addition to atomic-level engineering of its structure and properties, graphene also provides an excellent platform for refining the accuracy of quantitative models and for the development of automated manipulation.

[0009] Prior art document 2: "Electron-Beam Manipulation of Silicon Dopants in Graphene" Mukesh Tripathi, Andreas Mittelberger, Nicholas A. Pike, Clemens Mangier, Jannik C. Meyer, Matthieu J. Verstraete, Jani Kotakoski, and Toma Susi, DOI: 10.1021 / acs.nanolett.8b02406 Nano Lett. 2018, 18, 5319-5323 Prior art document 3 describes that the recent predictions and subsequent creation of electron vortex beams in a number of laboratories occurred after almost 20 years having elapsed since the recognition of the physical significance und potential for applications of the orbital angular momentum carried by optical vortex beams. A rapid growth in interest in electron vortex beams followed, with swift theoretical and experimental developments. Much of the rapid progress can be attributed in part to the clear similarities between electron optics and photonics arising from the functional equivalence between the Helmholtz equations governing the free-space propagation of optical beams and the time-independent Schrodinger equation governing freely propagating electron vortex beams. There are, however, key differences in the properties, of the two kinds of vortex beams. The review is primarily concerned with the electron type, with specific emphasis on the distinguishing vortex features: notably the spin, electric charge, current and magnetic moment, the spatial distribution, and the associated electric and magnetic fields. The physical consequences and potential applications of such properties are pointed out and analyzed, including nanoparticle manipulation and the mechanism of orbital angular momentum transfer in the electron vortex interaction with matter.

[0010] Prior art document 3: "Electron vortices: Beams with orbital angular momentum", S. M. Lloyd, M. Babiker, G. Thirunavukkarasu, and J. Yuan, DOI.

[0011] 10.1103 / RevModPhys.89.035004

[0012] Prior art document 4 discusses the possibility of realizing quantum computation on the basis of a cluster of single interacting nuclear spins in solids. This idea seems to be feasible because of the combination of two techniques Single Molecule Spectroscopy and Optically Detected Electron Nuclear Double Resonance. Compared to the well-known bulk Nuclear Magnetic Resonance (NMR), the proposed method of quantum computation has the advantage that quantum computation is performed with pure spin states and the quantum processor is more easily scalable. At the same time, the advantages of NMR quantum computation are kept: long coherence time and easy construction of quantum gates. As a specific system to implement the above idea, it is discussed the13C-nuclear spins in the nearest vicinity of a single nitrogen-vacancy (NV) defect center in diamond, which can be optically detected using the technique of scanning confocal microscopy. Owing to the hyperfine coupling of the ground state electron paramagnetic spin S = 1 of the center to13C nuclear spins in a diamond lattice, the states of nuclear spins in the vicinity of the defect-center can be addressed individually. Preliminary consideration shows that it should be possible to address up to 12 individual13C nuclear spins. The dephasing time of the nuclear spin states at low temperatures allows realization up to 105gates.

[0013] Prior art document 4: "Quantum Computation Using the13C Nuclear Spins Near the Single NV Defect Center in Diamond', J. Wrachtrup, S. Ya. Kilin, and A. P.

[0014] Nizovtsev, Optics and Spectroscopy, Vol. 91 , No. 3, 2001 , pp. 429-437. From Optika i Spektroskopiya, Vol. 91 , No. 3, 2001 , pp. 459-466.

[0015] Prior art document 5, DE 10 2022 107 528 A1 , describes a method for creating a quantum data token based on a system with a plurality of qubits, characterized in that a number (N) of qubits is combined into an ensemble and forms an information unit, wherein the ensemble is brought together into a predetermined quantum state and wherein the number (N) of qubits in an ensemble is chosen in such a way that a quantum state of a subensemble that has at most half of the qubits of one of the ensembles cannot be determined due to quantum projection noise.

[0016] Prior art document 6 describes that in recent years, machine and quantum learning have gained considerable momentum sustained by growth in computational power and data availability and have shown exceptional aptness for solving recognition- and classification-type problems, as well as problems that require complex, strategic planning. In this work, it is discussed and analyzed the role machine and quantum learning are playing in the development of diamond-based quantum technologies. This matters as diamond and its optically addressable spin defects are becoming prime hardware candidates for solid state-based applications in quantum information, computing and metrology. Through a selected number of demonstrations, it is shown that machine and quantum learning are leading to both practical and fundamental improvements in measurement speed and accuracy. This is crucial for quantum applications, especially for those where coherence time and signal-to-noise ratio are scarce resources. Some of the most prominent machine and quantum learning approaches are summarized that have been conducive to the presented advances and discuss their potential, as well as their limits, for proposed and future quantum applications. Prior art document 6: "Machine and quantum learning for diamond-based quantum applications", Dylan G Stone and Carlo Bradac, Mater. Quantum TechnoL 3 (2023) 012001.

[0017] It is an object of the invention to improve the control of manufacturing respective modifications. It is an object of the invention to reduce the complexity of the required setup and the method to be performed.

[0018] The object of the invention is solved by a method of automated spatial patterning of defect centers in a substrate (structure), particularly a diamond crystal lattice, according to claim 1 . The object of the invention is solved by a method for displacing defect centers in a substrate for quantum applications in a defined direction according to claim 2. The object of the invention is solved by a method of training a machine-learning model according to claim 16. The object of the invention is solved by a system according to claim 17. The object of the invention is solved by a computer program product according to claim 18. The object of the invention is solved by a device, particularly a diamond crystal, according to claim 19. The object of the invention is solved by a method of manufacturing according to claim 20.

[0019] 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 applies to the method of training a machine learning model as well as the method of automated spatial patterning of defect centers in a substrate structure, particularly a diamond crystal lattice, as well as to a method of manufacture. Features, feature combinations, technical effects and advantages described in connection with any of the methods apply with respect to any of the system, the computer program product or the device, particularly the diamond crystal. This also applies the other way around, so that with regard to the disclosure of the individual aspects of the invention, reciprocal reference is or can always be made, particularly independent of the category described and / or claimed.

[0020] According to one aspect, the object is solved by a method with the features of claim 1.

[0021] The method can be configured for displacing - as exemplary form of manipulating - defect centers in a substrate for quantum applications in a defined direction. The method may comprise a step of providing a substrate, particularly diamond, wherein the substrate, particularly diamond, comprises defect centers in a bulk structure of the substrate, particularly in a bulk diamond crystal lattice. The method may comprise a step of detecting the position of at least one defect center in the bulk structure of the substrate, particularly the bulk diamond crystal lattice. The method may comprise a step of displacing the at least one defect center in the bulk structure of the substrate, particularly the bulk diamond crystal lattice. The displacing of the at least one defect center in the bulk structure of the substrate, particularly the bulk diamond crystal lattice, can be particularly site-specific. The displacing may be in a defined direction. This allows to increase the precision of manipulating defect centers in substrates, particularly diamonds, which can be used as solid-state qubits for quantum information processing.

[0022] The method may comprise the steps of (i) detecting or obtaining data on the positions of defect centers in the bulk diamond substrate; (ii) inputting said data into a trained machine-learning model configured to determine a displacement strategy; and (iii) controlling a displacement apparatus to relocate at least one defect center within the bulk diamond lattice according to the output of the machine-learning model, thereby achieving a, particularly site-specific, rearrangement of defect centers, particularly in a (well-)defined direction.

[0023] The method may be a method of automated spatial patterning of defect centers in a substrate, particularly a diamond crystal lattice. The method may comprise the step of providing a defect center distribution to a machine-learning model. The machinelearning model can particularly be trained to determine an output for displacement of at least one defect center based on the provided defect center distribution. The machine learning model may provide an output for displacement of individual defect centers. The method can be configured for displacing - as exemplary form of manipulating - defect centers in a substrate for quantum applications in a defined direction. The method may comprise a step of providing a substrate, particularly diamond, wherein the substrate, particularly diamond, comprises defect centers in a bulk structure of the substrate, particularly in a bulk diamond crystal lattice. The method may comprise a step of detecting the position of at least one defect center in the bulk structure of the substrate, particularly the bulk diamond crystal lattice. The method may comprise a step of displacing the at least one defect center in the bulk structure of the substrate, particularly the bulk diamond crystal lattice. The displacing of the at least one defect center in the bulk structure of the substrate, particularly the bulk diamond crystal lattice, can be particularly site-specific. The displacing may be in a defined direction. This allows to increase the precision of manipulating defect centers in substrates, particularly diamonds, which can be used as solid-state qubits for quantum information processing.

[0024] Providing a substrate, particularly diamond, can refer to pre-manufacturing of the substrate, particularly the diamond, that is partially doped with defect centers that are located at several randomly spaced and positioned structure sites of the substrate, particularly lattice sites. In case of Nitrogen-Vacancy (NV) centers, they can be implanted into the substrate structure, particularly the diamond lattice, by two methods - ion implantation and electron irradiation. Both methods are particularly stochastic, meaning the formation of NV centers is probabilistic, and hence cannot be reliably used for creating a network of coupled spins. Nevertheless, these methods allow to provide a respective substrate, particularly in form of diamond.

[0025] Alternatively or additionally, the expression of ..providing a substrate" may refer to any handling of a substrate, such as a diamond, doped with respective defect centers whereof at least one shall be moved during the method described herein elsewhere. Therefore, any use or handling of a respective substrate may be considered as providing the substrate.

[0026] Manufacturing a substrate-comprising device comprising at least one defect center, particularly with a plurality of defect centers, particularly refers to a substrate being completed here with at least one defect center being positioned at an intended structure (lattice) position, particularly different from the initial defect center position when the substrate, particularly the diamond, is provided for the method to begin displacing at least one defect center. Positioning, displacing and respective further steps apply analogously to the case where several defect centers are placed inside the structure of the substrate, particularly the diamond crystal lattice.

[0027] A defect center in the bulk structure of the substrate, particularly the bulk diamond crystal lattice, may be a configuration in which the structure of the substrate, particularly the diamond crystal lattice, deviates from the standard structural configuration of the substrate, in case of diamond the carbon configuration deviates from that of a standard and average diamond crystal lattice, particularly as described elsewhere herein.

[0028] Displacing the at least one defect center in the bulk structure of the substrate, particularly the bulk diamond crystal lattice, refers particularly to altering the position of the defect center from the initial position of the defect center when the substrate, particularly diamond, is provided to perform the respective method.

[0029] Displacing the at least one defect center in a (well-)defined direction particularly refers to the method’s capability to initiate and perform displacement that is not merely governed by a statistical displacement of the defect center in a stochastic fashion. Therefore, the respective manipulation of the defect center can have a preferred direction of displacement into which the respective defect center will move in case the method steps are performed accordingly.

[0030] According to embodiments, also laid out in further 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 using a focused atomic-sized vortex electron-beam formed through a holographic aperture in an aberration-corrected scanning transmission electron microscope (AC-STEM) for fabricating a scalable multi-qubit quantum processor which enables quantum information processing applications such as quantum sensing and quantum information processing especially quantum computation. Furthermore, the respective method may allow to manufacture test and research devices to study the respective behavior of those qubit structures and qubit networks.

[0031] This and comparable embodiments provide an advanced technique to direct individual vacancy centers in diamonds in a desired direction e.g., using the atomic- level electron vortex beam within AC-STEM. Starting with acceleration voltages ranging from 60 to 160 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV) well below the displacement threshold energy of carbon atoms in diamond, and by selecting the focused atomic-sized vortex beam to the desired atom the atom can be excited via transferred orbital angular momentum and then migrate to the next lattice site in the chosen direction. In embodiments of the method defect centers such as nitrogen vacancy centers within the substrate such as a diamond lattice may be identified by using the monochromatic high-energy electron energy resolution loss spectroscopy as laid out in detail elsewhere herein. If the position of irradiated atom is not changed after a particular time or electron dose, the method and / or it’s particular steps can be repeated until achieving the desired outcome.

[0032] The term “bulk structure of the substrate” particularly refers to the bulk of the substrate, not to the surface. The respective defect center is thus placed at least in the second layer underneath the surface, further particularly in the third layer or even the fourth layer or even further below the surface of the substrate structure. Further preferably the structure of the substrate may comprise at least one defect center in a core region (not necessarily the central atom, but somewhere in a middle region or middle volume between the surfaces of the diamond).

[0033] In case the substrate is diamond, the term “bulk diamond crystal lattice” particularly refers to the bulk of the diamond, not to the surface. The respective defect center is thus placed at least in the second layer underneath the surface, further particularly in the third layer or even the fourth layer or even further below the surface of the diamond crystal lattice. Further preferably the diamond crystal lattice may comprise at least one defect center in a core region (not necessarily the central atom, but somewhere in a middle region or middle volume between the surfaces of the diamond).

[0034] The displacing of the at least one defect center may be site-specific. Thus, not all the respective defect centers are to be moved simultaneously or even quasi- simultaneously, but individual defect center can be chosen and each and every single one of them may be displaced individually. Thus, it is possible to determine a respective displacement strategy on how to move individual defect centers around, particularly at least one, to reach a certain desired configuration of relative defect center positions to each other or to reach a certain desired configuration of at least one defect center with respect to the substrate, particularly diamond.

[0035] In embodiments the site-specificity may refer to the possibility that different defect centers may be displaced while others remain unaffected. In those embodiments it may be possible to impact and particularly displace a subgroup of defect centers as described elsewhere herein.

[0036] Embodiments can provide a breakthrough solution for precisely aligning defect centers in substrates such as diamonds, which may serve as solid-state qubits in quantum information processing and quantum computing. Defect creation techniques, comprising doping, implantation, and irradiation, can result in defects being positioned randomly and uncontrollably. The method described herein for manipulating defect centers can prevent the use of energetic beams that may cause stochastic and random defect displacement. The method can provide an approach for directed and controlled displacement of defects, enabling the manipulation of one, two, or any specific number of e.g., spins to be brought closer or moved apart for interaction purposes. In particular, the manipulation may be site-specific, but further in particular, the manipulation may allow displacement in a defined direction.

[0037] Therefore, the method may provide a displacement not mainly based on a stochastic “random walk” through a substrate structure such as a diamond crystal lattice or others, but to determine a main likelihood of a direction. The movement of the defect center may be based on the movement of the specific atoms upon electron irradiation. Atomic dynamics or walk can be possible if the atoms are momentarily displaced and if they switch position with neighboring atoms in the meantime. The neighboring atom can be any sides; hence the vortex-beam according to some embodiments, can provide a direction by selecting a particular site. This can be achieved through the use of an atomic-sized vortex electron-beam, comprising an orbital angular momentum. Generating this electron beam can be based on using aberration-corrected scanning transmission electron microscopy (AC-STEM). The described method allows the manipulation of single, multiple, and compound impurities, such as nitrogen, silicon, and tin, or others, within the substrate structure, particularly the diamond crystal lattice. It allows for controlled movement across atomic lattice sites, thus enabling precise manipulation of solid-state qubits. Thus, it may overcome the limitations posed by the random positioning of atomic-scale qubits, which can result in uncoupled qubits and which can hinder the scaling of spin qubits or achieving large-scale entanglement that is particularly useful for quantum computation. With angstrom-level precision and control over distances spanning tens of micrometers, the described methods, devices and systems significantly advance the connectivity between spin systems. This may facilitate the controlled creation of large-scale interacting spin qubits in solid-state environments, such as NV defects in diamonds. The method can be broadly applicable to various defects in solid-state contexts and may lead to the production of coupled qubits essential for scalable quantum communication, information processing, quantum computing, and sensing applications.

[0038] Creating NV (Nitrogen-Vacancy) centers in diamonds by ion implantation and electron irradiation, are particularly stochastic, meaning the formation of NV centers is probabilistic. This methods or comparable other methods may be defined as a providing of a respective substrate with defect centers. Displacing the defect centers allows to reliably create a network of e.g., coupled spins for example for quantum applications. Furthermore, more than three defect centers with distances between them of 10 nanometers or less can be created. 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 within 5±2 to 15±3 nanometers of each other. Vortex electron beams carrying an orbital angular momentum with defined direction when interacting with defect centers may allow to transfer a force with a respective direction to the defect center. This allows to displace the defect center particularly in a defined direction, further particular site specific.

[0039] According to another, particularly independent, aspect a method for displacing - as exemplary form of manipulating - defect centers in a substrate for quantum applications may be provided. The method can comprise the step of displacing a group of defect centers. The displacing may be performed simultaneously, particularly group-specific, particularly in a defined direction. This may allow to displace several defect centers simultaneously. Thus, the speed of the application of the method may be increased and the manufacturing throughput may be increased. It may be possible to displace a certain number of defect centers in a coarse step of displacement, particularly group-specific meaning that a defined group of defect centers can be addressed, and later-on turn to a site-specific fine displacement of individual defect centers. Thus, the precision and site-specificity of the method may be combined with higher speed. Furthermore, it allows to scale the respective quantum qubit devices to particularly implement and / or study quantum qubit networks.

[0040] This described method allows the directional manipulation and control of positioning of defect centers, for example vacancy color centers as solid-state qubits in diamonds, using a (focused atomic-sized) vortex electron-beam. This beam may be - as matter of example - be formed through a holographic aperture in an aberration- corrected scanning transmission electron microscope (AC-STEM). It may allow fabricating a scalable multi-qubit quantum processor which enables quantum information processing applications such as quantum sensing and quantum information processing especially quantum computation.

[0041] The described methods allow to direct individual defect centers e.g., vacancy centers in a substrate e.g., diamonds in a desired and well-defined direction using atomic- level vortex electron beam within AC-STEM. Alternatively or additional the described methods allow to direct subgroups of defect centers in a defined direction. The method may in particular be starting with acceleration voltages ranging from 60 to 160 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV) well, particularly below the displacement threshold energy of carbon atoms in diamond. By selecting the focused atomic-sized electron beam to the desired atom the atom can be excited via transferred orbital angular momentum and then migrate to the next lattice site in a chosen direction. The methods described herein can also identify defect centers in a substrate, particularly such as nitrogen-vacancy centers within a diamond crystal lattice, by using the monochromatic high-energy electron energy resolution loss spectroscopy for example. If a position of an irradiated atom is not changed after a particular time or electron dose, the method steps can be repeated until achieving the desired outcome. Furthermore, it is possible to move a bulk distribution of defect centers simultaneously, particularly as a subgroup of defect centers sharing a same or similar direction of (desired) displacement.

[0042] The vortex electron beam may be applied to a displacement zone such that at least one particular area or volume of the substrate overlaps with an electron beam having a defined expansion distribution. This expansion distribution may be of the form of a donut, of a petal distribution with particularly two, three, four or even more petals. These petals may be distributed point-symmetrically around the z-axis of beam propagation. Other expansion distributions may be crescent shaped, particularly with a single crescent shape, with two opposing crescent shapes or other combinations of crescent shapes. Other expansion distributions may comprise a disk shape, particularly with zones of diminished electron density or no electron density at all. Those may be referred to as holes in the disks. The disks may comprise at least one hole, particularly two holes, further particularly three holes, or even more holes. The expansion distribution may be designed to interact with a chosen subgroup of defect centers. The electrons in the electron beam provide the orbital angular momentum in these zones and therefore may transfer a force to displace the respective defect centers in the chosen subgroup.

[0043] According to an aspect, the method can comprise the step of particularly providing a substrate, particularly diamond, comprising defect centers in a bulk structure of the substrate, particularly a bulk diamond crystal lattice. The method can comprise the step of detecting the position of at least a first subgroup of the defect centers in the bulk structure of the substrate, particularly the bulk diamond crystal lattice. The method can comprise the step of displacing a second subgroup being at least partially a subgroup of the first subgroup of the defect centers in the bulk structure of the substrate, particularly the bulk diamond crystal lattice.

[0044] The terms of “providing a substrate”, “substrate”, “defect centers”, “bulk structure” and “bulk diamond crystal lattice” are particularly to be understood as defined elsewhere herein.

[0045] A first subgroup of defect centers may refer to a group of defect centers whos position is detected and / or monitored, particularly selected from all of the defect centers in the bulk structure of the substrate. Therefore, a respective first subgroup may be a subgroup of the group of all defect centers in the respective substrate provided.

[0046] The second subgroup may be at least partially a subgroup of the first subgroup of the defect centers in the bulk structure of the substrate, particularly the bulk diamond crystal lattice. The second subgroup of the defect centers may refer to the defect centers being actually displaced in concert, particularly simultaneously. The second subgroup can overlap with the first subgroup, but may also not be identical with the respective first subgroup. In embodiments the respective second subgroup may also be distinct from the first subgroup. In these embodiments the respective first subgroup may function as an indicator for respective lattice sites of interest where respective second subgroup defect centers may be displaced relative to.

[0047] According to an aspect, a step of verifying or monitoring the position of the displaced defect center may be provided. This allows to determine the position, particularly in real time - referred to as monitoring - or to determine an initial, interim or final position of at least one defect center in the substrate structure, particularly the diamond crystal lattice - referred to as verifying. This allows to determine if the displacement progresses as intended or if a respective desired configuration has been achieved.

[0048] According to an aspect, the method can comprise the step of directing an (atomicsized) scanning transmission vortex electron beam, particularly using aberration- corrected scanning transmission electron microscopy to displace the at least one defect center in the bulk structure of the substrate, particularly the bulk diamond crystal lattice, particularly in a defined direction. Additionally or alternatively, the method can comprise the step of directing an (atomic-level) vortex electron beam, particularly using aberration-corrected scanning transmission electron microscopy to displace the group of defect centers, particularly being at least the second subgroup of defect centers, in the bulk structure of the substrate, particularly the bulk diamond crystal lattice, simultaneously, particularly in a defined direction. Utilizing the aberration-corrected scanning transmission electron microscopy (AC-STEM) technique, the method can differentiate and position defect centers, particularly atomic impurities like nitrogen, silicon, tin and others, as described elsewhere herein within the substrate structure, particularly the diamond crystal lattice. The method described herein particularly relates to the manipulations and controlled positioning of defect centers such as vacancy color centers as solid-state qubits in the substrates, particularly diamonds (particularly in a single diamond), using a focused aberration- corrected scanning transmission electron microscope (AC-STEM) for fabricating a scalable multi-qubit quantum processor which enables quantum information processing applications such as quantum sensing and quantum information processing especially quantum computation. Building on this core concepts, this method particularly presents an advanced technique to shift individual vacancy centers in substrates, particularly diamonds, using atomic-level electron beam techniques within AC-STEM.

[0049] Aberration-corrected scanning transmission electron microscopy or in short AC- STEM allows to manipulate and control the position of the respective individual defect centers and therefore allows to move those in the substrate structure, particularly the diamond crystal lattice. The moving is also referred to as displacement as the respective defect centers change place with certain neighboring atoms, particularly carbon atoms in the diamond crystal lattice. Multiple steps of displacement result in a net migration of the defect center in the substrate structure, particularly the diamond crystal lattice.

[0050] To do so, an atomic-sized scanning transmission vortex electron beam may be provided that can provide the correct amount of energy to allow the position change and which comprises the respective orbital angular momentum in the area and / or volume where the defect center is located in the substrate to displace it in a defined direction. Additionally, the atomic-sized scanning transmission electron beam may not provide enough energy to eject an atom or a defect center from the respective irradiation site.

[0051] According to an aspect, a diameter of a directed atomic-sized (scanning transmission) vortex electron beam can range from 0.5 to 2 Angstrom, particularly from 0.5 to 1 Angstrom, further particularly from 0.5 to 0.8 Angstrom. The Angstromsized electron beam can provide the correct energy to move the defect center, particularly in form of an atom (point defect), across lattice sites in a controlled way. Alternatively or additionally, the diameter of a directed (atomic-sized) (scanning transmission) vortex electron beam can range from 1 to 200 Angstrom, particularly from 10 to 150 Angstrom, further particularly from 50 to 100 Angstrom. This beam allows to move a group, particularly a second subgroup, of defect centers. As described elsewhere herein the vortex electron beam may be covering an expansion distribution that may be designed to overlap with a (first) subgroup of defect centers intended for displacement in a defined direction having at least a component parallel to the orbital angular momentum of the vortex electron beam. The diameter may particularly refer to the definition of an electron beam where only 3% or less of the respective electrons’ (power) density is outside the respective beam diameter. The same may hold true for expansion distributions.

[0052] According to an aspect, an acceleration voltage for accelerating electrons in the directed (atomic-sized) (scanning transmission) vortex electron beam can be set below the knock-on damage of the substrate structure, particularly the diamond crystal lattice. Particularly the acceleration voltage can be set between 60 to 160 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV), particularly for diamond. This prevents particular atoms from being ejected from the substrate, particularly the lattice, but being displaced instead. Particularly starting with acceleration voltages set between 60 to 160 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV), and particularly by focusing the vortex electron beam to the desired defect center, particularly the atomic defect, it may be ensured that the atom forming the atomic defect can be excited and can then migrate to the next lattice site rather than getting ejected.

[0053] Alternatively or additionally, a convergence angle can be higher than 15 mrad, particularly higher than 20 mrad, further particularly higher than 32 mrad. When a cone shaped, convergent electron beam illuminates a specimen, the semi-angle of the cone can be termed "convergence angle." Therefore, the respective vortex electron beam may be well defined to determine the respective displacement direction.

[0054] Radiation damage resulting from the collision of beam electrons with an atomic nucleus is referred to as Knock-on damage. The respective electrons’ velocity and therefore the potential energy they may transfer to the respective nuclei may be below the energy that is necessary to cause the Knock-on damage. The acceleration voltages can be set to avoid damage to the defect centers, particularly the NV centers, in that the acceleration voltage is adjusted below the knock-on damage of the substrate, particularly the diamond. This may be ranging from 60 to 160 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV). In particular, the bond strength of the respective bond in the substrate structure, particularly the diamond crystal lattice structure, may be matched to allow the respective bond to swap the position of the respective bonding partners resulting in displacement of the defect center.

[0055] In embodiments the energy of direct exchange of Al ranges between 13 and 16 eV, for Si the binding energy ranges between 14 and 18 eV and it ranges for P between 16 and 17.5 eV (at Theta, the angle of incidence of 0°). The upper value may represent the value of knock out. The values are determined for a graphene substrate. The binding energies for different defect centers may vary. Also the displacement threshold energy (which is minimum energy required to remove an atom from the transferred energy of electron beam) may change due to the surrounding atom (defect centers).

[0056] The head on elastic collision may be determined based on the formula

[0057] ET = (4rrii * mc) Ei / (mi + mc)2wherein ET is the transferred energy, Ei is the initial energy of the particle with mass mi to particle with mass mc.

[0058] According to an aspect, the directed (atomic-sized) (scanning transmission) vortex electron beam can be directed to the defect center to be displaced. Alternatively or additionally, the directed (atomic-sized) (scanning transmission) vortex electron beam can be directed to the subgroup of defect centers to be displaced. This allows to transfer the energy to the defect center, not necessarily to the respective atom with which the defect center can swap the position in the substrate structure, particularly the diamond crystal lattice. Furthermore, a whole (second) subgroup may be addressed for simultaneous displacement in a particular defined direction.

[0059] The movement may be initiated by directing an (atomic-sized) (scanning transmission) vortex electron beam onto a defect center directly or a subgroup of defect centers as an expansion distribution. This may result in an elastic collision that overcomes the bond strength between the defect center and the carbon atom which may be swapping places with the defect center. In case of the vortex electron beam having a well definable orbital angular momentum, the direction of displacement can be predetermined. In other embodiments, the respective carbon atom which may be swapping places with the defect center may be directly hit by the (atomic-sized) (scanning transmission) electron beam.

[0060] According to an aspect, the method may comprise a step of dark field imaging with on-the-fly electron spectral analysis identifying at least one defect center or the first subgroup of defect centers in the bulk substrate structure, particularly the bulk diamond crystal lattice. This allows to identify defect centers, particularly nitrogenvacancy centers. For validation, a concentrated beam can be focused in on desired defect centers e.g., nitrogen-vacancy centers, while subsequent spin spectroscopy (e.g ODMR) and imaging studies may confirm the defect center’s displacement, particularly of the atom’s displacement. In embodiments it may also be possible to determine the defect centers’ displacement. Therefore, it is possible to allow verifying or monitoring the respective progress made on a displacement strategy, particularly laid out in advance.

[0061] Dark field imaging with on-the-fly electron spectral analysis is a particular technique which excludes the initial main electron beam directed to the substrate structure, particularly the diamond crystal lattice, from analysis but can focus on the scattered electrons that interacted with the respective substrate structure, particularly the diamond crystal lattice, as provided or as altered by a directed atomic-sized electron beam as described elsewhere herein.

[0062] AC-STEM can offer structural insights for crystalline materials, like diamonds. The technology can provide mapping of defect centers, particularly of specific point defects e.g., such as nitrogen vacancy centers, which provide the respective advantages as described elsewhere herein and in the emerging fields like quantum computing. In the proposed AC-STEM method, the electron-beam raster scans the desired surface or volume pixel by pixel, and after (vortex) electron beam interaction with the specimen, scattered electrons can be collected with an annular angular dark field detector. Since the intensity of the atoms is approximately proportional to Z2, where Z is the atomic number, the elements can be distinguished directly from the atomic scale imaging contrast.

[0063] As a first step, defect centers such as nitrogen-vacancy centers can be located in the substrate, particularly the diamond, combined via dark field imaging, in-situ electron, and optical spectral spectroscopic (e.g. EELS, ODMR) techniques as described elsewhere herein. An image can be acquired from the desired area with the scattered defect centers, particularly the nitrogen vacancy centers, as a reference point. A focused beam can be placed directly on individual defect centers such as nitrogenvacancy centers to irradiate it for a certain amount of time and then another spin spectroscopy measurement can be performed to confirm the movement.

[0064] Furthermore, the image can also be captured to observe the successful manipulation.

[0065] According to an aspect, a step of confirming and / or monitoring the displacement of at least one defect center can be performed by at least one of spin spectroscopy, imaging studies or ODMR. This allows to verify and monitor the displacement and to provide a feedback loop control.

[0066] According to an aspect, at least one step of mapping, assessing and / or evaluating at least one of the chemical composition or the electronic structure can be provided. Therein, particularly at least one of energy-dispersive X-ray spectroscopy (EDX) or electron energy loss spectroscopy (EELS) or four-dimensional STEM (4D-STEM) can be applied. Alternatively or additionally, cathodoluminescence techniques may be used.

[0067] Particularly in embodiments wherein nitrogen-vacancies are used as defect centers the following may apply. Nitrogen (N) atoms are very next to the carbon (C) atoms in the periodic table, hence differentiating the nitrogen atoms from carbon with atomic- scale dark field imaging can be extremely difficult in bulk diamond crystal lattice structure. Moreover, it can be used to identify other heavier impurity-based vacancy centers (e.g., Si, Sn) in diamond. Therefore, the chemical composition through energy dispersive spectroscopy and electron energy loss spectroscopy can be provided simultaneously with atomic-scale imaging which can be used to identify edge fine structures of the vacancy centers precisely at the atomic level.

[0068] Nevertheless, this can also apply analogously to embodiments where other types of defect centers can be used to improve their detection and position verification.

[0069] According to an aspect, in a step at least one of spin spectroscopy, imaging studies or ODMR can confirm or can monitor the defect center’s or the defect centers’ displacement. This allows to find and track the respective defect centers, particularly before, during and after displacement. A step of mapping allows to provide an overall map of the positions in the substrate structure, particularly the diamond crystal lattice structure. A step of assessing and / or of evaluating at least one of the chemical composition or the electronic structure may provide the respective information about the environment in the substrate structure, particularly the diamond crystal lattice structure, the atomic binding structure and respective strength’ therein. This way it may be possible to determine necessary or desired vortex electron beam acceleration voltages to be adapted or to be predicted.

[0070] ODMR may refer to a technique called optically detected magnetic resonance (ODMR) by which the electron spin state of a substrate defect center such as a crystal defect in diamond can be optically pumped for spin initialization and readout. It may be utilized for nitrogen-vacancy (NV) color centers in diamond e.g., to measure the modulus and orientation of an external magnetic field using a confocal microscopy setup. ODMR of NV can have applications in magnetometry, sensing, biomedical imaging, quantum information and for the fundamental study of physics. Here, ODMR allows to implement another dimension of feedback.

[0071] According to an aspect, the method may comprise the step of using at least one subscan window to manipulate the defect center and / or the defect centers, particularly of the second subgroup. Alternatively or additionally, it can be used to monitor the change in the bulk substrate structure, particularly the bulk diamond lattice structure, in real time.

[0072] The term “sub scan” may refer to a limited part of a scanning frame in the imaging or sensing or measuring. Using a small sub-scan window as an (alternative) approach allows to manipulate the defect centers, particularly the NV centers, and also to monitor the change in the structure in real time. Defect centers (e.g., NV qubits) in a lattice can be brought closer together all-at-once (parallel) or moved further apart by defining a raster scanning path or scanning window using an AC-STEM. A sub-scan window can be provided that falls into the respective scanning window. The sub-scan window can be used for spin spectroscopy or imaging studies. Therein, information of the electron beam colliding with the defect center can be fused with information from the additional sensing, imaging or spectroscopy methods. According to an 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 to displace individual defect centers accordingly. Additionally or alternatively, defect centers can be moved and the qubit coupling can be monitored to improve the coupling between at least two defect centers. This particularly addresses the qubit connectivity drawback and allows to engineer the qubit coupling via the controlled positioning of the qubits which will enable the potential applications in the fabrication of quantum sensing devices. Using a method step as described elsewhere herein, an atomic sized electron beam can bring qubits closer together but can also move them apart from each other within the diamond crystal lattice at the atomic level in a controlled way. Alternatively or additionally, defect centers can be moved and the qubit coupling can be monitored to improve the coupling between at least two defect centers

[0073] As described elsewhere herein, a map of the defect centers can provide spatial, electronical structure and potential qubit information to determine potential qubit coupling in the substrate structure, particularly the diamond crystal lattice, when displacing particular defect centers. The map can show the current position of the defect centers. Alternatively or additionally, the map can provide the information of a substrate structure, particularly the diamond crystal lattice, that can be realized by the method described elsewhere herein, particularly by displacement of at least one defect center, particularly by displacement of several defect centers, particularly site specific. This allows to define a displacement strategy.

[0074] In an embodiment, moving the qubits may not be the main focus, but to establish the coupling between them and to also allow to determine the improvement in a type of feedback loop, even based on machine learning model application as described elsewhere herein. The detection of change of the movement may be fed back to the machine learning model to determine a respective approach to a desired state, particularly where the coupling corresponds to a particular desired state or structure.

[0075] According to an aspect, the method (or particular steps thereof) can be repeated until displacement of the defect center and / or the defect centers is detected. Alternatively or additionally, the method (or particular steps thereof) can be repeated until the group of defect centers reached a desired configuration. If the substrate structure sites, particular the lattice sites, are particularly unchanged then the respective method steps may be repeated until the defect center / defect centers, particularly the NV centers, are moved, particularly site-specific and / or group-specific.

[0076] According to an aspect, the defect center can be at least one of an atomic point defect, an atomic point defect, particularly with P1 as substitutional configuration, a silicon atomic impurity, a nitrogen atomic impurity, a tin atomic impurity, a phosphorous atomic impurity, a bismuth atomic impurity, a vacancy center, a nitrogen-vacancy center, a silicon-vacancy center, a tin-vacancy center, a phosphor- vacancy center, a bismuth-vacancy center, 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 high-band gap semiconductor. In other words, the substrate may be a crystal structure or matrix made from the respective atoms.

[0077] A method step can be provided to employ a (focused atomic-sized) vortex electron beam in STEM to manipulate other solid-state qubits such as silicon (Si), phosphorous (P), and tin (Sn) within a substrate structure, particularly the diamond lattice. Si and C can switch their places in a substrate structure, particularly the diamond crystal lattice, upon vortex electron-beam irradiation. This particularly applies to heavier elements such as bismuth atoms as well. It allows positioning and nanofabricating a substrate structure, particularly the diamond host lattice, with various solid-state qubits (e.g, Si in SiC).

[0078] A “point defect” is particularly an atomic-scale imperfection in an otherwise perfect crystal. It thus may be contrasted with an “extended defect” which involves a large portion of the crystal and which is important in determining its mechanical properties.

[0079] The term atomic point defect particularly refers to defects that occur only at or around a single lattice point, particularly by placing an atom at a position different to the expected atom in the lattice structure. They are particularly not extended in space in any dimension. However, these defects typically involve at most a few extra or missing atoms.

[0080] An atomic point defect with P1 as substitutional configuration, refers to a P1 center being a spin-1 / 2 substitutional nitrogen impurity in a diamond lattice that may also exhibit long coherence and relaxation times, even though it may not optically active. A vacancy or vacancy defect in crystallography particularly refers to a type of point defect in a crystal where an atom is missing from one of the lattice sites.

[0081] A nitrogen-vacancy center (analogously for other atom -type- vacancy defects) is particularly a combination of a nitrogen atom being incorporated into the diamond lattice structure next to a vacancy. This defect center can provide particularly unique quantum mechanical properties to be of interest for a broad range of applications from sensing to qubit-based calculations.

[0082] Nitrogen-vacancy (NV) centers in diamond may provide a leading platform for solid- state quantum technology applications, if their position is controlled as described elsewhere herein. They provide unparalleled coherence times, optical interaction and quantum state robustness even at room temperature. An NV center is a point-defect that comprises 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 allows localization based on optical confocal microscopy. NV centers can demonstrate 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 realization of quantum operations and enhanced sensitivity for quantum sensing applications. These properties of NV quantum systems may render them attractive qubits for quantum computation and in general quantum information processing. The potential of NV centers for quantum applications is further bolstered by their capability to emit photons with a high quantum yield, optical spin polarization and optically resolved detection of spin sub-levels 0, +1 , -1. The optically detected magnetic resonance (ODMR) techniques that can be employed with NV centers can detect magnetic fields as low as a few nT (nanotesla). This level of sensitivity, coupled with the spatial resolution granted by the nanoscale nature of NV centers, may provide a powerful quantum sensor for studying magnetic phenomena at the nanoscale, ranging from biological processes to novel magnetic materials. Additionally, the zero-phonon line (ZPL) for these NV centers particularly lies around 637 nm, facilitating efficient collection and integration with various optical systems for quantum communications and long-distance entanglement among qubits. These features allow the NV centers to act as nodes in quantum networks or quantum repeaters in long-distance quantum communication. NV centers in diamond can also be potential qubits for quantum computing applications, especially because of their unique properties that allow for laser-assisted optical initialization and optical readout at room temperature. One of the major 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 solid-state qubit candidates operable at room temperature. Furthermore, the two- level system of the NV defect can be coherently manipulated using microwave radiation with Rabi frequencies typically reaching up to 10 - 100 MHz, which allows for efficient quantum gate operations. In the quest for scalable quantum computing, NV centers provide an ability to interact with nearby nuclear spins, offering a potential avenue for multi-qubit interactions. In diamond, the most common nuclear spin that may interact with the NV center is the carbon-13 isotope (C13), which can have a natural abundance of about 1 .1%. These nuclear spins can serve as auxiliary quantum memories or quantum registers, which can extend the computational capacity of the NV-based quantum system.

[0083] Coupling between defect centers can be determined using ODMR at around 10 kHz. This may provide a feedback from the system if the defect center is moving in the right or wrong direction.

[0084] In embodiments 2D materials like graphene, hexagonal boron nitride (H-BN) band and transition metal dichalcogenides may be used as substrates for placing and dislocating defect centers. Also, bulk substrate structures of H-BN band and transition metal dichalcogenides may be provided.

[0085] The method (or particular steps thereof) can be repeated until displacement of the defect center is detected as described elsewhere herein. Alternatively or additionally, the method can be repeated (or particular method steps) until the group of defect centers reached a desired configuration. It allows to monitor the change in the bulk substrate structure, particularly the bulk diamond lattice structure, in real time to do so.

[0086] According to an aspect, at least one intermediate step for displacement can be planned. Alternatively or additionally, at least one parameter setting for at least one intermediate step is planned. Planning can be particularly comprising calculating. This presents a particular way to manipulate qubits within the substrate structure, particularly the diamond crystal lattice, for optimistically calculated one or more intermediate steps. In addition, it also can provide the flexibility to modify and optimize the parameter settings for the intermediate steps which further may show the deterministic control of (focused) vortex electron beam manipulation at the atomic scale.

[0087] Intermediate steps are particularly the individual steps of displacement the respective defect center has to do in the attempt to move it from a respective initial position to a final position via interim positions.

[0088] Parameter settings can be any of the device’s parameters that allow the displacement of at least one defect center. It may also refer to any parameter setting that allows to detect, to validate and / or to monitor the defect centers and their respective position within the substrate structure, particularly the diamond crystal lattice. The parameters may also refer to the positioning and configuration of a holographic aperture as it is described elsewhere herein. Alternatively or additionally, the parameters may refer to an additional magnetic field applied to the cavity of the electron microscope to modulate the vortex electron beam.

[0089] Planning can refer to determining a respective displacement strategy. Therefore, calculating can be performed to determine parameters and intermediate steps based on particular physical models of a substrate structure, particularly a diamond crystal lattice, particularly based on a digital twin of the substrate structure, particularly the diamond crystal lattice, that shall be established. The digital twin or any particular model can be referred to as a predefined structure.

[0090] According to an aspect, the step of placing suitable defect centers as qubits for quantum communication in an arranged array can be provided. Alternatively or additionally, the step of placing suitable defect centers as qubits for quantum communication in an arranged corral nanostructure within the bulk structure of the substrate, particularly the bulk diamond crystal lattice, can be provided. This can implement fabricating a large number of suitable qubits for quantum communication in a controlled way via placing them in an arranged array and / or corral nanostructures within the substrate structure, particularly the diamond crystal lattice. To further improve the fabrication process, particularly additionally, an in-situ feedback-controlled manipulation can be combined with a predefined structure, which will enable an imaging detector to read the real-time signal of qubits. As an example, if the vacancy center position is changed, then it can provide the signal from the substrate, particularly the diamond, and if the beam is on top of a defect center such as the N center then it can indicate a higher signal due to the Z-contrast imaging principle.

[0091] An arranged array particularly refers to the placement of defect centers in a sorted and particularly linked chain or sorted and linked substructure in the substrate structure, particularly the diamond crystal lattice.

[0092] Arranged corral nanostructures are structured defect center patterns that link these defect centers e.g., via quantum mechanical effects (spin-spin coupling or other effects) to realize quantum mechanical structures for certain applications. Those applications may be sensing applications, qubit-based quantum calculations, etc. Some of these applications are described elsewhere herein.

[0093] According to an aspect, in a step an in-situ feedback-controlled manipulation can be combined with a predefined structure. It can be used for real-time qubit signal monitoring. This particularly presents a method step to manipulate the complex and / or compound defect centers in the substrate structures, particularly the diamond crystal lattices (diamond atomic lattice), e.g., using a (focused) vortex electron beam in STEM. Defect centers, particularly NV centers, can comprise many configurations in diamonds. Their (optimal) interactions within a lattice can be quite complex.

[0094] Hence, measuring the intermediate interactions of qubits, particularly spin qubits, and choose the best possible final configurations suitable for the performance of scalable qubits in solid-state can be realized. These (optimal) interactions and the respective positions to implement these interactions can be the predefined structure of the diamond crystal lattice - a model or digital twin that may allow to determine a displacement strategy. The in-situ feedback-controlled manipulation combined with a predefined structure can be based on such a model or digital twin as predefined structure to implement a comparison between calculated data and measurements to determine if the respective diamond crystal lattice structure realized by a displacement strategy - e.g., during intermediate steps - reaches or approaches the predefined structure. To do so, real-time qubit signal monitoring can be implemented. This may allow to determine if particular defect centers can perform their intended task, particularly in a combined and linked fashion. According to an aspect, in a step of re-positioning the relative positions of the complex and / or compound defect centers in the bulk structure of the substrate, particularly the diamond crystal lattice, can be optimized. This allows to implement the feedback loop in a real physical structure of a substrate structure, particularly the diamond crystal lattice. The re-positioning of the relative positions of the complex and / or compound defect centers in the bulk substrate structure, particularly the bulk diamond crystal lattice, can be optimized such that their respective functions and / or their respective links can reach a predicted, calculated or modeled level.

[0095] According to an aspect, temperature effects on defect centers can be probed in a range from room temperature up to 1500°C. Alternative or additionally, at least one of heating, cooling or biasing can be applied for analysis. Addressing the role of the temperature of thermal displacement of defect centers, particularly NV centers, for the individual qubits in substrates, particularly diamonds, can improve the respective structural design. As an example, a very high temperature can graphitize the diamond surface, diffuse the vacancy centers (as type of defect centers, may apply also for other defect centers), and may reduce the hydrocarbon contaminations which are very prone to the carbon family of materials. Hence, probing the influence of temperatures ranging from RT to 1500°C on the fabricated qubits using in-situ methods can provide respective insights on material behavior.

[0096] At least one step of repair can be implemented. This step of repair can be performed after probing the respective temperature or temperature range. In the step of repair at least one defect center that may be dislocated can be displaced as described elsewhere herein, to reach a structure identical or similar to the structure as it occurred before the temperature disturbance.

[0097] Room temperature refers particularly to the temperature range between 20°C and 22°C, particularly to explicitly 21 °C.

[0098] According to an aspect, at least one defect center can be dislocated to a site-specific marker of the structure of the substrate, particularly the diamond crystal lattice. The site-specific marker can particularly be a C13-isotope. This allows on the one hand to identify certain defect centers and their respective position also via a site-specific marker in the lattice, not only via the respective defect centers themselves, but also via an independent route. On the other hand, it allows to establish links between the defect centers and the site-specific marker for quantum applications. This can provide a method step of embodiments to bring the electron spins close to the isotopic C13 nuclear spins in a controlled way at the atomic level via vortex electron beam (e-beam) manipulation. As a first step, electron energy loss spectroscopy spectral imaging and optically detected magnetic resonance technique (electron- nuclear double resonance) can confirm the presence of nuclear spins. Then, a focused e-beam can be used to place the defect centers, particularly NV centers, near it, which will enable its potential application e.g., in a quantum register.

[0099] The positioning relative to C13-isotopes can also be determined by ODMR and it is thus possible to determine if a defect center is moving away or towards a C13- isotope. Therefore, it is possible to implement a feedback loop to apply repetitively the moving of at least one defect center to move it closer to at least one C13-isotope in the crystal lattice.

[0100] A site-specific marker of the substrate structure, particularly the diamond crystal lattice, may be any potentially identifiable marker that allows to be tracked and / or to be identified in the lattice. Furthermore, the respective position can be traced. In some embodiments, the marker can be displaced as well, particularly after its position is determined. Alternatively or additionally the site-specific marker may exhibit quantum mechanical properties that are beneficial for the intended application as they are described exemplarily elsewhere herein.

[0101] In diamond, the most common nuclear spin that can interact with defect centers, particularly in form of an NV center, is the carbon-13 (C13) isotope, which has a natural abundance of about 1 .1%. These nuclear spins can serve as auxiliary quantum memories or quantum registers, which can extend the computational capacity of the defect center-based quantum system, particularly the NV-based quantum system. Nevertheless, the entanglement of separate defect centers, particularly separate NV centers, are a step towards implementing scalable quantum computing. As the method described here and elsewhere herein does not rely purely on a stochastic nature of defect center formation, particularly NV center creation, both precision and efficiency of defect center formation are increased, and the control is improved that allows to establish quantum computing capabilities and the formation of qubit networks. According to an aspect, a, particularly focused, (atomic-sized) vortex electron-beam may be formed through a holographic aperture in the aberration-corrected scanning transmission electron microscope. Additionally or alternatively the, particularly focused, (atomic-sized) vortex electron-beam can be formed by applying an additional magnetic field to an electron beam in the aberration-corrected scanning transmission electron microscope. This allows to move a subgroup of defect centers simultaneously, particularly site-specific, in a defined direction. Additionally or alternatively, it may allow to move a subgroup of defect centers in a certain region of the substrate structure, particularly a diamond crystal lattice, in a defined direction.

[0102] Electron holography can be based on introducing a spatial and / or a phase interference pattern of an electron beam distributing the electron density over an expansion distribution. The expansion distribution may be formed and / or placed such that it matches the respective distribution of at least a subgroup of defect centers.

[0103] The Controlled atomic-scale fabrication of vacancy centers in the diamond can be a major challenge for extending the quantum computing field. The proposed method allows to engineer qubit connectivity via manipulating defect centers such as the vacancy centers described in detail elsewhere herein as solid-state qubits in substrates such as diamonds by precisely directing an (atomic-sized) vortex electron beam which may be formed through a holographic aperture in a scanning transmission electron microscope, particularly with a diameter ranging from 1 to 2 Angstrom. The potentially transferred orbital angular momentum from the vortex electron beam to the selected defect center, particularly vacancy center, within the substrate structure, particularly the diamond lattice, may allow to control the movement in a fixed and selected direction, which can enable potential applications in quantum information processing. Different from scanning tunneling microscopy in combination with atomic force microscopy the described method may not be limited to uses to modify the surface and manipulate only the surface atoms using their atomic sharp tip. Particularly Aberration-Corrected Scanning Transmission Electron Microscopy (AC-STEM) can be a sophisticated technique providing atomic-scale imaging, spectroscopy, and materials modification capabilities.

[0104] Improvements may come from the efficient design in the aberration-corrector and beam shaping enabling direct visualization of individual atoms at atomic level, structural quality analysis, and identification of single defects in materials. Particularly when combined with energy-dispersive spectroscopy (EDX), four-dimensional STEM (4D-STEM), in-situ heating / cooling / biasing, and electron energy loss spectroscopy (EELS), and cathodoluminescence techniques, AC-STEM (or any particular combination thereof) can reveal the fine chemical composition, materials interfaces, map electric charge and field, analyzing the detailed morphological structures at the atomic scale, evaluating the electron-photon interaction with the matter, and allows studying the in-situ atomic dynamics at atomic-scale and ferroelectric phenomena. Apart from these sophisticated methods, atomic-sized vortex electron beam with selected orbital angular momentum can be used in applications ranging from detecting the magnetic field, mapping biological samples and edge contrast enhancements.

[0105] Different from the electron beam “picture” in classical physics, an electron beam can carry orbital angular momentum in the quantum framework. Therefore, electrons may exhibit an intriguing behavior where they can manifest a wave-like rotation around their direction of propagation. This phenomenon can be a manifestation of the quantum mechanical property called “vortex electron beams” which carry orbital angular momentum. To generate the electron vortex beam, various methods can be implemented where just a few a listed here as matter of example. Vortex electron beams may be generated using at least one selected from a phase plate, holographic fork apertures, holographic spiral apertures, manipulating the aberration functions and using the magnetic field, the latter as described elsewhere herein as well. Furthermore, atomic-sized vortex electron beam with selected orbital angular momentum can be achieved using electron energy-loss magnetic chiral dichroism (EMCD) technique in STEM.

[0106] To manipulate the impurity atoms using a focused Angstrom-sized electron “probe” beam in aberration-corrected STEM, where impinging electrons may interact with the atomic nuclei and where scattered electrons may transfer the energy and momentum to the individually targeted impurity atom such that the impurity atom cannot be ejected but can be excited so that it moves to a next “neighboring” lattice site, unfolding a potential for atomically precise manipulation. Using this mechanism, electron-beam manipulation of various impurity atoms in bulk Silicon [18,19], graphene and carbon nanotubes can be implemented. 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 to indirectly move the defect centers, particularly the vacancy centers, in the substrate, particularly the diamond crystal, particularly in ultra-high vacuum. The described method may avoid knock-out of the impurity atom and / or of double lattice site jumps and / or triple lattice site jumps particularly caused by continued electron irradiation to the neighboring atoms, and directly to impurity atoms. This stochastic process could render the control of manipulation limited in directionality. The manipulation defect centers in the substrate can be implemented in both clockwise and anticlockwise direction (respective to a plane particularly perpendicular to the direction of beam propagation) using a vortex electron beam with respective orbital angular momentum.

[0107] The described method can employ an (atomic-sized) vortex electron beam 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 well-defined direction. The described method particularly comprises free-standing diamond samples, which can have been carefully implanted with the impurities (e.g., N, Si, Sn) in a controlled way. These dopants can form atomic point defects (e.g., P1 , substitutional configuration). Furthermore, it can be annealed at high temperatures to form vacancy centers and higher coordinated defects. The samples can be annealed in an ultra-high vacuum to avoid contamination which can be problematic for (atomic- scale) electron-beam manipulation.

[0108] In light of the above, in one exemplary embodiment of the method (and of a system as described elsewhere herein) orbital angular momentum can be provided to direct individual Nitrogen vacancy centers in diamonds in a well-defined direction using an atomic sized vortex electron beam in aberration-corrected STEM. A focused spiral vortex electron beam can be formed through a holographic fork aperture, can be placed directly on individual nitrogen-vacancy centers to irradiate it for a certain amount of time. The (vortex) electron beam can form a swirling vortex that can interact with atoms and by imparting orbital angular momentum to the atoms, it directs them in a highly controlled manner. To mitigate the removing of the vacancy centers and to avoid unwanted damage in the diamond, select acceleration voltages can range from 60 to 200 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV) and can comprise convergence angles higher than 32 mrad which can correspond to a beam size from 1 to 2 Angstrom in diameter.

[0109] A respective angle of rotation can be implemented such that the angle of the diamond crystal lattice 50 with respect to the (former) incident plane changes. Thus, the incident plane can be changed to allow dislocation also in a third direction / dimension. The movement of defect centers may thus cover the full three- dimensional space of the substrate, particularly the diamond crystal lattice 50. It may not be locked to a two-dimensional plane of the diamond crystal lattice.

[0110] As a first step, nitrogen-vacancy centers can be located in the diamond combined via atomic scale dark field imaging, high resolution monochromated electron energy loss spectroscopy and / or optical spectral and spin spectroscopic (e.g. EELS, ODMR) techniques. An image can be acquired, and a region of interest area can be selected with the scattered nitrogen vacancy centers as a reference point. The individually selected vortex electron beam carrying orbital angular momentum can transfer with different vortex states to manifest the directional manipulation to the vacancy center and it can avoid the jump of irradiated atom to the random carbon neighboring atoms in diamond. Hence, 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. If the lattice sites are unchanged when seen by imaging or spectroscopy then further the manipulation process can be repeated until the NV centers can have been moved and stopped once the vacancy center can have been moved to the desired distance and direction.

[0111] According to another embodiment of the method, it particularly introduces an approach to overcome the limitations of qubit connectivity. The embodiment particularly features a unique method for engineering qubit coupling by precisely controlling the placement of qubits. This may not only address the qubit connectivity challenge but also paves the way for consistent, large-scale production of scalable quantum sensing devices. The method can begin with doping, particularly during growth and / or by ion implantation, particularly followed by annealing, which may result in a random distribution of vacancy centers. A phase singular spiral atomicsized vortex electron beam can be used. This beam can have a zero-intensity center and non-zero intensity in its spiral profile, particularly creating varying local electron densities and corresponding angular momentum. This method (and the respective system described elsewhere herein) is uniquely employed to move multiple randomly distributed qubits closer together towards the center or along a spiral path within the vortex beam area. As explained with respect to the other embodiment this can be achieved by manipulating them through orbital angular momentum transfer in Scanning Transmission Electron Microscopy (STEM). Continuous electron irradiation with a vortex swirl electron beam can transfer orbital angular momentum, which effectively can rearrange the position of the vacancy centers as desired. Multiple defect centers can be manipulated simultaneously in a well-defined path using an uniform electron beam which allows the user to multiplex the method (and respective method steps) and to produce many coupled spins from two to many thousands.

[0112] This method (and a respective system as described elsewhere herein) can be used for producing scalable quantum computers and quantum sensors that take advantage of quantum phenomenon. This embodiment allows to address qubit connectivity by exposing a large area with a vortex electron beam. Multiple defects centers can be manipulated simultaneously.

[0113] The respective embodiments described above can be modified using different types of defect centers, particularly with different dopants, as described elsewhere herein. Alternatively or additionally, the embodiment can be modified in that other substrates may be used as described elsewhere herein.

[0114] In embodiments of the method arbitrary vortex electron beams can be generated into desired shape through a holographic nanopatterned aperture which can be formed particularly by a gradient in the orbital angular momentum, particularly via an automated process enabling the manipulation of multiple vacancy centers in diamond at a same time and to control the beam-shapes and profile of defect centers in the STEM.

[0115] Alternatively or additionally, at least one magnetic field may be applied to the cavity of the electron microscope where the electron beam may propagate. This additional magnetic field may enforce a vortex electron beam. A magnetic field parallel to the propagation of the electron beam may provide the respective shapes of the expansion distribution described elsewhere herein (petals, donuts, rings, disks, etc.). The respective embodiment allows to generate the arbitrary vortex electron beams into at least one desired shape through a holographic nanopatterned aperture which can form a gradient in the orbital angular momentum via an automated process enabling the manipulation of multiple vacancy centers in diamond at a same time and to control the beam-shapes and profile of defect centers in the STEM. In other words, the beam shape can be controlled using automation before the beam can scan the specimen and / or the sample, particularly the group of defect centers to be displaced in a defined direction in a coordinated manner.

[0116] According to an independent aspect, a method of training a machine-learning model with a series of spatially placed defect centers in a bulk structure of a substrate, particularly a bulk diamond crystal lattice, can be provided. Automation of a method step of defect centers such as vacancy center manipulation with a focused atomicsized electron probe in the 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. Then, the control of the e-beam can be automated to place the defect centers, particularly the vacancy centers, in a controlled way at the atomic level, which will enable high-precision devices to be fabricated, allowing for direct correlation between atomic structure and quantum properties.

[0117] A method of training a machine-learning model to predict control parameters for defect center displacement may be provided: The method may comprise the step of providing the model with a series of training inputs in the form of images and / or data representing different spatial configurations of defect centers in a bulk diamond crystal. The method may comprise the step of providing corresponding desired outputs for each training input, the outputs including displacement instructions and / or target positions for the defect centers. The method may comprise the step of optimizing the model’s parameters (through supervised learning and / or reinforcement learning) such that the model learns to output correct displacement instructions to achieve a desired spatial arrangement of defect centers.

[0118] A machine-learning model may be a machine-readable program routine that is configured to run on a computer machine, particularly on a control unit, particularly stored on a storing device, and which allows to determine a respective displacement strategy. The machine learning model may be an artificial neural network that may be provided with a series of images, spectra or other data of spatially-placed defect centers in a bulk substrate structure, particularly a bulk diamond crystal lattice. These spatially-placed defect centers may be any of final configurations for certain applications, interim configurations, particularly representing certain intermediate steps or starting (initial) configurations of defect centers, their respective distributions, spatial positions or derived information and measurement data. Thus, the machinelearning model learns (supervised or unsupervised) certain types of configurations and may also be trained using path-finding algorithms in machine learning models to determine a respective displacement strategy when starting from a certain configuration to reach a final configuration and therefore to provide a predefined structure of a substrate structure, particularly the diamond crystal lattice.

[0119] As a machine learning model a deep learning based fully convoluted neural network (FCNN) may be applied in a supervised approach. To identify and classify the defect centers from the atomic resolution images in the substrate, particularly diamond, the local atomic coordinates may be used. More specifically it can be done by applying Laplacian of Gaussian blob detection techniques to the output of FCNN data.

[0120] Therein, the position is determined based on the Gaussian blob detection. It allows to classify the structural information based on their atomic coordinates (bond length, chemical species, and bond angle).

[0121] As an FCNN, an Encoder-decoder type may be used. The input may consist of convoluted layers with filters and then map (up sampling) the features in reverse way (pixel based classification). The FCNN may consist of 3 convoluted layers, particularly with different kernels (e.g. 3*3). Therein, one layer may be encoding, one layer may be filtering and one layer may be decoding. The first layer may already be the input layer, the last layer may be the output layer.

[0122] Training of model may use simulated images with various defect centers, and other defect types in a substrate, particularly diamond. All operations and calculations may be performed in a real space coordinate system, not a fourier transform space. Also, mixing the experimental images with different resolutions (which can be further segmented into different pixel sizes, e.g. 256*256 pixels) may be used. Images can be fed to the trained FCNN model that outputs a map of probabilities, then can be thresholded to produce binary images with small blobs which correspond to the atomic lattice sites in the substrate, particularly diamond. Finally, Laplacian of Gaussian blob detection techniques can calculate the atom coordinates.

[0123] In a different embodiment deep convoluted neural networks (DCNN) may be used. They provide fast and robust atom identification against both noise and distortion, particularly suitable for single-shot images.

[0124] Deep convolutional neural networks (DCNN) can automatically determine the Bravais lattice symmetry present in atomically-resolved images. DCNN can be trained to identify the Bravais lattice class given a 2D fast Fourier transform of the input image. Therefore, fourier-transform images may be used. Internal processing can be the same as with an FCNN.

[0125] Different ways within CNN may be performed to convolution or deconvolution layers of networks. As an example a ReslINet architecture may be used. Therein, concatenating the convolution layer with corresponding deconvolution layer can represent a U-Net scheme.

[0126] Other different image denoising architectures may be used such as Grouped Residual Dense Network (GRDN), Multi-resolution U-Net (MR-UNET), Concatenated Grouped Residual Dense Network (CGRDN).

[0127] Alternatively or additionally, Generative Adversarial Networks (GAN) may be used. They provide an unsupervised generative attentional network with adaptive layer instance normalization for image-to-image translation (U-GAT-IT), particularly for the noise augment model (U-GAT-IT). Therein unit simulated images may be processed and particularly used as the training set for the defect identification model (U Net). This allows not only to accurately describe experimental images but also to increase the diversity of the training set through random assembly, meeting the demand for a large quantity of training data.

[0128] According to an 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 may allow to displace at least one defect center, particularly a group of defect centers, may be defined by the later trained machine learning model. The machine learning model can be provided with respective parameter settings, originally present distribution information of respective defect centers and with respective resulting distribution information after applying the respective parameters to generate a vortex electron beam. The respective machine learning model may be as described elsewhere herein.

[0129] According to an aspect, the machine-learning model can be trained on simulation data obtained by a molecular dynamics or machine-learning interatomic potential to predict the outcome of electron-beam interactions with the lattice.

[0130] According to an independent aspect, a method of automated spatial patterning of defect centers in a substrate, particularly a diamond crystal lattice, can be provided. The method can comprise the step of providing a defect center distribution to a machine-learning model. The machine-learning model can particularly be trained according to a method of training as described elsewhere herein. The machine learning model can provide an output for displacement of individual defect centers. The method can comprise the step of displacing at least one defect center. This provides an atomic-scale qubit fabrication method in substrates, particularly diamonds, for scalable quantum communication and information processing and sensing applications.

[0131] A method of automated spatial patterning of defect centers in a substrate structure, particularly a diamond crystal lattice, may provide an automated or semi-automated approach to realize a final configuration that is intended to determine a future application as described elsewhere herein. It may provide an output for displacement of individual defect centers and may therefore lay ground for a displacement strategy. In particular, the method may be capable to perform at least one intermediate step of displacing at least one defect center on the way of performing or following a displacement strategy. Alternatively or additionally, the method may provide at least one parameter suitable to implement a vortex electron beam with a desired angular momentum to allow for displacing at least one defect center, particularly for displacing a group of defect centers, to allow qubit connectivity for example to be realized. Additionally or alternatively, the respective method may comprise a step wherein the parameters for manipulation of the electron beam to implement different types of shapes and / or angular momenta in a series of intermediate steps may be provided to allow for semiautomated or fully automated displacement in at least two intermediate steps of the method. Alternatively and / or additionally, switching between single site excitation for fine displacement of individual defect centers and group excitation for courser displacement of a group of defect centers in a defined direction can be implemented, particularly between different (intermediate) method steps.

[0132] In more general terms, one can describe the respective machine-learning method as follows: In a step there is a feature identification and / or lattice site assignment with respective features, for example in a feature map, also called a mask. This can be done by a first machine learning model, particularly designed for picture segmentation. In a subsequent step, a respective feature segmentation map I mask may be fed to a second machine-learning model that allows to set parameters of the system such as irradiation angle, angle of the diamond relative to the incident beam, energy of irradiation, spot size (FWHM), irradiation time, pulse sequence frequency, and / or others based on a respective input image and an image of the desired outcome (a final state of positions for the defect centers in the respective lattice). As described elsewhere herein, both the respective machine-learning models can be trained. The second machine-learning model may implement a reinforcement learning (RL), while the first machine-learning model may be the eyes of the second machine-learning model as it provides an image segmentation technique.

[0133] According to an aspect, the machine-learning model can be implemented as part of a control unit that particularly uses reinforcement learning with feedback from a detector to iteratively adjust the displacement strategy in real time.

[0134] According to an independent aspect, a system can be configured and structured to perform a method as described elsewhere herein. The system may comprise a displacement apparatus configured and positioned to dislocate defect centers in a substrate, particularly 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 structure of the substrate, particularly the bulk diamond crystal lattice. The system may comprise a control unit configured to determine a displacement strategy and to control the displacement apparatus to follow the displacement strategy. The methods and the device can be capable of producing a large, scalable network of precisely positioned, dipole-dipole coupled spin qubits. This breakthrough technology offers a viable pathway for the realization of scalable quantum processors. The system may comprise a holographic aperture to modulate and generate a vortex electron beam. The system may comprise a magnetic field generator to generate a magnetic field for cortex electron beam formation, particularly based on predictions of an expansion distribution.

[0135] The control unit can be independent of the machine and may comprise a storage unit or may provide a link to a storage unit to access 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 any comparable network structure.

[0136] The „optics“ micro-optics, micro-electronic components and other parts of the system may be configured and placed such that the defect center can be moved to the ..intended spot".

[0137] The displacement apparatus may be any type of apparatus or device capable to perform any - or at least one - of the methods or method steps described elsewhere herein. Therefore, the respective features, advantages and characteristics described in concatenation with any of the methods may also apply to the displacement apparatus. The displacement apparatus is particularly configured and position such that it can be controlled by a control unit, being configured and positioned such that the displacement apparatus may follow the displacement strategy and perform at least the task of displacing at least one defect center as described elsewhere herein.

[0138] The detector may be configured and placed to determine at least one of an initial position of at least one defect center, an interim position of the at least one defect center or the final position of the at least one defect center.

[0139] The control unit may be a computer-machine configured to determine a displacement strategy and / or configured to apply a displacement strategy, particularly by analyzing the data measured by at least one detector and / or by controlling at least one displacement apparatus.

[0140] Therefore, the respective system and / or its individual components may be described by the respective features, feature combinations, technical effects and / or advantages as described with respect to any of the methods, the apparatus, the system or the device, particularly the diamond crystal, particularly independent of the respective category (method, device, system, use) it is described with and / or independent of any particular combination of individual components or aspects thereof.

[0141] According to an independent aspect, a computer program product can be configured to perform a method as described elsewhere herein, when the computer program product is run on a control unit, particularly in a system as described elsewhere herein.

[0142] The computer program product may be any type of machine-readable code that can transfer the respective information and instructions to a control unit when run thereon, particularly read from a storage device to perform at least one of the methods or method steps described elsewhere herein. Therefore, the respective computer program product may be described by the respective features, feature combinations, technical effects and / or advantages as described with respect to any of the methods, the apparatus, the system or the device, particularly the diamond crystal, particularly independent of the respective category (method, device, system, use) it is described with and / or independent of any particular combination of individual components or aspects thereof.

[0143] According to an independent aspect, a device, particularly a diamond crystal can comprise a substrate structure, particularly a diamond crystal lattice. The substrate structure, particularly the diamond crystal lattice, can comprise a qubit network of suitable defect centers placed in spatial proximity such that they form the qubit network. The qubit network particularly comprises at least two suitably defect centers. The qubit network particularly comprises at least four suitable defect centers, particularly comprises at least five suitable defect centers, further particularly comprises at least six suitable defect centers, further particularly comprises up to an integer n of suitable defect centers. The integer n may particularly be between 10 and 1000 defect centers, further particularly between 20 and 900 defect centers, further particularly between 100 and 800 defect centers. Alternatively, the integer n of suitable defect centers may particularly be between 1000 and 1 000 000 defect centers, further particularly between 1500 and 900 000 defect centers, further particularly between 2000 and 800 000 defect centers. A device, particularly a diamond crystal, can comprise a substrate structure, particularly a diamond crystal lattice, comprising the respective defect centers as described elsewhere herein.

[0144] The method described elsewhere herein can provide a substrate, particularly 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 method described elsewhere herein. These NV centers can be within 1 to 19 nm, particularly between 3 to 9 nm, further particular between 3.5 to 4.5 nm of each other. In other embodiments, the NV centers can between 5±2 to 15±3 nanometers of each other. 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, particularly diamonds (and other materials, particularly provided as 2D materials as well).

[0145] The respective product of any of the methods - the substrate, particularly the diamond crystal - may be described by the respective features, feature combinations, technical effects and / or advantages as described with respect to any of the methods, the apparatus or the system, particularly independent of the respective category (method, device, system, use) it is described with and / or independent of any particular combination of individual components or aspects thereof.

[0146] An integer n of suitable defect centers can refer to embodiments wherein no physical - technical limitation may be provided for the respective number of defect centers which can be suitable defect centers for the respective applications described elsewhere herein.

[0147] According to an independent aspect a method may be configured to manufacture a device comprising a substrate as described elsewhere herein. The method may comprise a method for manipulating defect centers as described elsewhere herein. It is referred to the other aspects of the device and / or the method for advantages, features and applications. Those may specify the method of manufacturing, particularly independent of the category - method, use, device, system. An embodiment of the invention is shown in the drawings and is explained in more detail below. It is shown in:

[0148] Fig. 1 a schematic representation of an embodiment of AC-STEM with electron spectroscopy-based feedback control to precisely move and position the defect center qubits;

[0149] Fig. 2 a schematic representation of an embodiment of AC-STEM with Optically Detected Magnetic Resonance - spin resonance-based feedback control to precisely move and position the defect center qubits;

[0150] Fig. 3 a subgroup of defect centers in a lattice moved site-specific in a defined direction by using AC-STEM with an atomic sized vortex electron beam modulated by a holographic aperture;

[0151] Fig. 4 an embodiment of a training method; and

[0152] Fig. 5 a schematic representation of a machine-learning guided workflow for NV center engineering in diamond using STEM.

[0153] Some of the figures contain simplified, schematic representations. In some cases, identical reference signs are used for the same, but possibly not identical, elements. Different views of the same elements might be scaled differently. Directions such as "left", "right", "up" and "down" are to be understood in relation to the respective figure and may vary in the individual representations compared to the object depicted.

[0154] Some of the figures contain simplified, schematic representations. In some cases, identical reference signs are used for the same, but possibly not identical, elements. Different views of the same elements might be scaled differently. Directions such as "left", "right", "up" and "down" are to be understood in relation to the respective figure and may vary in the individual representations compared to the object depicted.

[0155] Fig. 1 shows a schematic representation of an embodiment of an aberration- corrected scanning transmission electron microscopy system (AC-STEM) 10 with electron spectroscopy-based feedback 5 control 21 , 23 to precisely move and position the individual defect center 6 as qubits. The AC-STEM 10 allows manipulating and controlling 21 , 23 and positioning of individually defect centers 6, particularly as vacancy color centers as solid-state qubits in a diamond crystal lattice 50 (see Figs. 3A to 5B for details) using a focused aberration-corrected scanning transmission electron microscopy derived vortex electron beam (e-beam) 51 for fabricating a scalable multi-qubit quantum processor which enables quantum information processing applications such as quantum sensing and quantum information processing especially quantum computation.

[0156] The controlled atomic-scale fabrication of vacancy centers in a substrate such as diamond is a major challenge for extending the quantum computing field. Therefore, a method is described to engineer qubit connectivity via manipulating defect centers 6 in a substrate, here a diamond crystal lattice 50. The vacancy centers may be placed as solid-state qubits in diamonds by precisely directing an atomic-sized vortex electron beam 51 which is formed through a holographic aperture 68 in a scanning transmission electron microscope, wherein the vortex electron beam’s 51 diameter may range from 1 to 2 Angstrom according to one embodiment. The transferred orbital angular momentum from the vortex electron beam 51 to the selected vacancy center within diamond crystal lattice 50 can control the movement in a fixed and selected direction 66, which can enable potential applications in quantum information processing. Aberration-Corrected Scanning Transmission Electron Microscopy (AC- STEM) can provide atomic-scale imaging, spectroscopy, and materials modification capabilities.

[0157] Advancements may come from the efficient design in the aberration-corrector 69 and beam shaping enabling direct visualization of individual atoms 52, 53, 54 (see Fig. 3) at atomic level, structural quality analysis, and identification of single 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, and electron energy loss spectroscopy (EELS), and cathodoluminescence techniques, AC-STEM can reveal the fine chemical composition, materials interfaces, map electric charge and field, analyzing the detailed morphological structures at the atomic scale, evaluating the electron-photon interaction with the matter, and studying the in-situ atomic dynamics at atomic-scale and ferroelectric phenomena. Apart from these sophisticated techniques, atomic-sized vortex electron beam 51 with selected orbital angular momentum provide means for detecting the magnetic field mapping, biological samples and edge contrast enhancements. The AC-STEM 10 allows to shift individual defect centers 6, particularly individual vacancy centers, in diamond crystal lattices 50 using atomic-level vortex electron beam (e-beam) 51 techniques within the AC-STEM 10. The vortex e-beam 51 may be derived with acceleration voltages set between 60 to 160 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV). Focusing the vortex e-beam 51 to the desired individual defect center 6, particularly a defect atom, the individual defect center 6, particularly the defect atom, can be excited. The individual defect center 6, particularly the defect atom, may then migrate to the next lattice site rather than getting ejected. The method of manufacturing 20 can identify individual defect centers 6 e.g., nitrogen-vacancy centers, by integrating dark field imaging with on- the-fly electron spectral analyses. The e-beam 51 is particularly a vortex electron beam 51 guided through a monochromator 71 and a magnetic field generator 81 .

[0158] The magnetic field generator 81 in combination with a holographic aperture 67 allows the formation of a vortex electron beam 51 to simultaneously displace several defect centers 6 as shown in Fig. 3. Here, the magnetic field generator 81 is shown schematically and exemplarily and provides a magnetic field based on the e-beam 51 itself. The vortex electron beam 51 can pass lenses 72 for focusing and an aberration corrector 69 for compensating aberration from the lenses 72.

[0159] In the quantum framework, electrons exhibit an intriguing behavior where they can manifest a wave-like rotation around their direction of propagation. Vortex electron beams 51 can thus carry orbital angular momentum. To generate the electron vortex beam 51 , various methods can be used such as phase plates, holographic fork apertures, holographic spiral apertures, manipulating the aberration functions and I or using a magnetic field (provided by the electron beam itself, by the lenses 72 of the electron microscope or an additional magnetic field generator 81 ). Atomic-sized vortex electron beams 51 with selected orbital angular momentum can be used for electron energy-loss magnetic chiral dichroism (EMCD) technique in STEM.

[0160] To manipulate the impurity atoms (defect centers 6) using a focused Angstrom-sized electron probe in aberration-corrected STEM, where impinging electrons interact with the atomic nuclei and scattered electrons transfer the energy and momentum to the individually targeted impurity atom such that the impurity atom is not ejected but excited so that it moves to next neighboring lattice sites, can provide for atomically precise manipulation. Using this mechanism, electron-beam manipulation of various impurity atoms in bulk silicon, graphene and carbon nanotubes can be implemented in some embodiments. The aberration-corrected scanning transmission electron microscopy (AC-STEM) technique can analyze the (nano-)diamond surface and can be used to indirectly move the vacancy centers in nanodiamonds in ultra-high vacuum. However, due to continued electron irradiation to the neighboring atoms, and to the directly to impurity atoms, it could knock-out the impurity atom or could lead to double or triple lattice site jumps. This stochastic process makes the control of manipulation limited in directionality. Therefore, manipulation in both clockwise and anticlockwise direction using a vortex electron beam 51 with the respective orbital angular momentum can define a direction of lattice site jumps. This allows to define a preferred direction 66 and to provide the respective vortex electron beams 51 to initiate and proceed with lattice site jumps in the desired direction 66.

[0161] In the proposed method 20 an atomic-sized vortex electron beam 51 can have a selected orbital angular momentum in STEM to direct individual vacancy centers as defect centers 66 in a substrate such as diamonds in a well-defined direction 66 (see Fig. 3). The method 20 can comprise free-standing diamond samples, wherein the impurities (e.g., N, Si, Sn) can have been implanted in a controlled way, carefully. These dopants form atomic point defects (e.g., P1 , substitutional configuration). Furthermore, it can be annealed at high temperatures to form vacancy centers and higher coordinated defects. The samples can be annealed in an ultra-high vacuum to avoid contamination which can be problematic for atomic-scale electron-beam manipulation 51 . This manufacturing of doped substrates can be referred to as providing. Alternatively or additionally, any step of handling may be referred to as providing.

[0162] In the light of above, in an exemplary embodiment of the method 20 and the device an orbital angular momentum can be provided by an atomic-sized vortex electron beam 51 which may direct individual Nitrogen vacancy centers in diamonds in a well- defined direction 66. The atomic-sized vortex e-beam 51 can be generated by aberration-corrected STEM. A focused spiral vortex electron beam 51 which can be formed thorough a holographic fork aperture 68, can be placed directly on individual nitrogen-vacancy centers to irradiate it for a certain amount of time. The electron beam 51 can form a swirling vortex that can interact with atoms 52, 53 and by imparting orbital angular momentum to the atoms 52, 53. This may direct them in a highly controlled manner as shown in Fig. 3. Setting acceleration voltages ranging from 60 to 200 keV may mitigate the removing of vacancy centers and to avoid unwanted damage in the diamond. Convergence angles higher than 32 mrad may correspond to beam sizes from 1 -2 Angstrom in diameter. As a first step, nitrogenvacancy centers can be located in the diamond combined via atomicscale dark field imaging, high resolution monochromated electron energy loss spectroscopy and optical spectral and spin spectroscopic (e.g. EELS, ODMR) techniques. A monochromator 71 may be placed to provide the means for high resolution monochromated electron energy loss spectroscopy. Consequently, an image can be acquired, and a region of interest area (expansion distribution) can be defined with the scattered nitrogen vacancy centers as a reference point. In embodiments it is possible to select a first subgroup of defect centers 6 for displacement. It may be at least partially a subgroup of initially determined (imaged) defect centers 6. The individually selected vortex electron beam 51 may carry an orbital angular momentum and can transfer it with different vortex states (also named orders 51 a, 51 b, 51c) which can manifest the directional manipulation to the defect centers 6, particularly vacancy centers. It may avoid the jump of irradiated atoms to the random carbon (neighboring) atoms 51 in diamond for example. Hence, directional movement 66 of the vacancy center in a defined path can be controlled due to the calibrated orbital angular momentum transfer direction (see Fig. 3). If the lattice sites remain unchanged when seen by imaging or spectroscopy then further the manipulation process can be repeated until the defect centers 6, particularly the NV centers, are moved. It may be stopped once the defect centers 6, particularly the NV centers have moved to the desired distance and direction.

[0163] An annular dark field detector 7 may be provided to detect individual defect centers 6 based on electrons from the (vortex) e-beam 51 being scattered on individual defect centers 6. Alternatively or additionally, electron energy loss spectroscopy (EESL) 8 may be implemented to determine also the chemical structure of the respective individual defect center 6. A STEM image direct electron signal 4 may be obtained therefrom, to determine the position of individual defect centers 6 and their respective bonding and chemical nature. After identifying an individual defect center 6 of interest e.g., as it may function as a qubit, the desired defect center 6 is selected 1 . The energy of the e-beam 51 is tuned 2 to the correct e-beam energy and the e-beam 51 is focused on the individual defect center 6 (particularly the atom thereof as defect atom).

[0164] The method 20 of manufacturing a diamond crystal lattice 50 with individual defect centers 6 can comprise at least one step of controlling 21 if a displacement of the respective defect center took place. To do so, in the embodiment as shown in Fig. 1 annular dark field spectroscopy may be combined with EESL 8 to obtain a STEM image direct electron signal 4 which may be compared with an expected signal to verify if a displacement occurred. In case it did not, the e-beam 51 can be placed again 22 on the individual defect center 6 of interest. In a second step of controlling 23 a verification of the displacement is tried to be obtained. IN case a successful displacement cannot be verified the method or the method step of placing the e- beam 51 again 22 on the individual defect center 6 of interest may be repeated, particularly until the respective displacement occurred.

[0165] In case the displacement can be verified to have occurred (particularly directly after the first step of controlling 21 or after any of the subsequent steps of controlling 23) the e-beam 51 can be moved 24 to the next individual defect center 6 of interest. There, the method steps as described above can be repeated.

[0166] The method may run and be repeated using the respective feedback 5 as described above, until no more individual defect centers 6 have to be moved. Moving a particular individual defect center 6 may be an intermediate step. After the intermediate step the particular individual defect center 6 may be placed at an interim position, but not at the final position intended based on a particular displacement strategy. It may take several intermediate steps for the individual defect center 6 to reach a final position. Therefore, the method 20 described above may be performed for each of the intermediate steps for each and every single one of the individual defect centers 6 to be displaced to their final positions, particularly independent from each other and particularly site-specific. Furthermore, the respective individual defect centers 6 can be embedded inside the diamond crystal lattice 50 and may not necessarily be placed in the surface area or surface volume (e.g., down to the third layer of carbon atoms 52 in the diamond crystal lattice 50). Particularly, as long as the step of controlling 25 if all defect centers 6 have been moved to reach their final configuration reveals that a respective step of displacement is necessary, the method 20 may return to selecting the desired defect center 6 as individual qubit to be displaced. The method therefore can be feedback 5 based an can iteratively reach the respective final configuration. It may even be possible to run down several paths along the displacement strategy e.g., in case certain intermediate steps can be exchanged to avoid knock-on damage over time or other types of damages.

[0167] Fig. 2 shows a schematic representation of an embodiment of AC-STEM 10 with Optically Detected Magnetic Resonance ODMR 15. This allows to implement a spin resonance-based feedback 5 control 21 , 23 to precisely move and position the individual defect center 6 as qubits. The respective AC-STEM 10 differs from the embodiment shown in Fig. 1 in that for validation, a concentrated e-beam focused in on desired nitrogen-vacancy centers as described with respect to Fig. 1 is subsequently 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 center 6, particularly the defect atom and / or the vacancy and / or both. To do so, steps of controlling 21 , 23, 25 if the position of the individual defect center 6 is moved can be performed as explained in great detail with respect to Fig. 1 . As described with respect 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, even if not shown here.

[0168] The spin spectroscopy may also be based on a laser 11 irradiating the individual defect center 6 (particularly by illuminating at least a sub-scan window of the e-beam 51 scanning the diamond crystal lattice 50). Single photons may be emitted as fluorescence photons 12 in case the defect center is active as it can be the case for certain NV-centers. These fluorescence photons 12 may be detected by a single photon detector 13 and being converted to an electronic signal which may be analyzed in the ODMR electronics 14. This allows to base the feedback 5 on the respective ODMR information. Consequently, in the embodiments as shown in Fig. 1 and 2 an image can be acquired from the desired area with the scattered individual defect centers 6, particularly the nitrogen vacancy centers, as a reference point. A focused beam can be placed directly on individual defect centers 6 such as nitrogen-vacancy centers to irradiate it for a certain amount of time followed e.g., by a spin spectroscopy measurement to confirm the movement, wherein the image can be captured to observe and to verify the successful manipulation. If the controlling 21 , 23 of the lattice sites verifies that the lattice sites are unchanged then the respective steps of method 20 can be repeated until the individual defect centers 6, particularly the NV centers, are moved which is verified accordingly. Using a small sub-scan window as an alternative approach can alternatively or additionally be used to manipulate the respective individual defect centers, particularly the NV centers, and also to monitor the change in the structure in real time.

[0169] As a summary and in other words, the embodiments in Figs. 1 and 2 introduce a unique technical approach for performing a method 20 of manufacturing a diamond crystal lattice 50. Therein, an Angstrom-sized vortex e-beam 51 is applied within the aberration corrected scanning tunneling electron microscope system (AC-STEM) 10. As electrons from the vortex e-beam 51 may collide with atomic nuclei, their scattered counterparts may transfer energy and momentum directly to targeted impurity atoms. Instead of ejecting these atoms, the process can excite them, prompting a shift to adjacent lattice sites and enabling unparalleled atomic precision in manipulation. This methodology can effectively manipulate impurity atoms in materials like silicon, graphene, and carbon nanotubes. The method 20 allows to perform respective precision placement in 3D macrocrystals such as diamond and allows to operate independent of a diffusion-based process of e-beam-induced NV center migration through vacancy-mediated movements. Instead, individual defect centers can particularly site-specifically be targeted with an vortex e-beam 51 to individually perform displacements. These displacements can be intermediate steps in a displacement strategy. The method 20 allows to reposition individual vacancy centers in diamonds using atomic-level vortex e-beam 51 manipulation within an AC- STEM 10. To ensure the safety and integrity of the process, acceleration voltages are carefully selected between 60 to 160 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV), particularly kept below the knock-on damage threshold for diamonds. The procedure can commence with the identification of defect centers 6 such as nitrogen-vacancy centers using combined dark field imaging and in-situ electron and optical spectral techniques. An image of the desired region, with discernible defect centers such as nitrogen vacancy centers, can then be taken for reference. As part of the validation process, a concentrated beam can directly irradiate specific defect centers 6 such as nitrogen-vacancy centers. Subsequent spin spectroscopy measures and imaging can confirm the movement. If atoms remain stationary, the procedure can be iterated until the desired movement can be achieved and verified. As an added layer of precision, a minimized sub-scan window can be employed to both maneuver the defect centers 6, particularly NV centers, and to continually monitor structural alterations. This can revolutionize the way atomic structures are manipulated in that the power and precision of an AC-STEM 10 is coupled with meticulous safety measures and validation techniques, such that individual atoms can be shifted with unparalleled accuracy. The method 20 allows to implement scalable qubit fabrication technology, particularly in spin defects in solids. The immediate application can be the construction of a scalable quantum computer but many more applications in quantum technologies can be realized using method 20 e.g., 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).

[0170] Fig. 3 shows a subgroup of defect centers 6 in a diamond crystal lattice 50 moved site-specific in a defined direction 66 by using AC-STEM with an atomic sized vortex electron beam 51 modulated by a holographic aperture 68. Fig. 3 shows a precise movement 61 based on individual precision displacing of a subgroup of defect centers6. Orders 51a, 51 b, 51 c from the vortex e-beam 51 interact with individual defect centers 6 comprising nitrogen 53 - vacancy 54 centers in the carbon 52 lattice 50. 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 the orders 51 a, 51 b, 51 c of the vortex e-beam 51 .

[0171] The embodiment shown in Fig. 3 shows an exemplary embodiment for an approach to overcome the limitations of qubit connectivity. It features a unique method 20, 100 for engineering qubit coupling by precisely controlling the placement of qubits. This approach not only addresses the qubit connectivity challenge but also allows for 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 providing), followed by annealing, which may result in a random distribution of defect centers 6, particularly vacancy centers. A phase singular spiral atomic-sized vortex electron beam 51 may be used, particularly having a zero-intensity center and nonzero intensity in its spiral profile, creating varying local electron densities and corresponding angular momentum. The methods 20, 100 (see Figs. 1 , 2, 4) and devices (see Figs. 1 , 2) can move multiple randomly distributed qubits closer together towards the center or along a spiral path within the vortex electron beam’s 51 area (also referred to as exposition distribution). As explained with reference to other embodiments this is achieved by manipulating them through orbital angular momentum transfer in Scanning Transmission Electron Microscopy (STEM). Continuous electron irradiation with a vortex swirl electron beam 51 may transfer orbital angular momentum, which effectively rearranges the position of the vacancy centers as desired. Multiple defects centers 6 manipulated simultaneously in a well- defined path using an uniform electron beam 51 allows the user to multiplex the process and produce many coupled spins from two to many thousands. The respective methods and devices allow producing scalable quantum computers and quantum sensors that take advantage of quantum phenomenon and which may apply those.

[0172] Fig. 4 shows an exemplary embodiment of a training method 100. Therein, the method 100 is shown to be circular. Thus it may particularly retrain a machine learning model and it may also allow to apply the retrained machine learning model in a step of STEM of displacing 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 Figs. 1 and 2. Based on an processing 130 of the images and aligning at least one defect center 6 may be selected 120 and a vortex e- beam 51 may be placed such that the respective defect centers 6 can be displaced in a defined direction 66. The image may be filtered 140 and used for training the respective machine learning model. Based on the trained machine learning model a, particularly spiraling, vortex electron beam 51 can be controlled 150 to perform a STEM 160. The embodiments described herein employ an Angstrom-sized vortex electron beam 51 , particularly in spiral shape formed through a holographic aperture 68 within the aberration corrected scanning tunneling electron microscope (AC-STEM) framework. As the traditional electron beam-matter interaction, electrons collide with atomic nuclei 52, 53, their scattered counterparts transfer energy and momentum directly to targeted impurity atoms. If the displacement threshold energy of the target atom is lower than the transferred energy from vortex electron beam 51 , then instead of ejecting these atoms, the process excites them, prompting a shift to adjacent lattice sites and enabling unparalleled atomic precision in manipulation. However, the controlled directional movement can still be a stochastic process. It further limits the movement of multiple impurities at the same time. However, by selecting the transferred orbital angular momentum from a focused atomic-sized vortex spiral beam 51 which is formed through the holographic apertures 68, these limitations can be overcome by moving to the desired atom to the next lattice site in chosen direction 66. This method 20, 100 allows effective manipulation of defect centers 6 in a substrate.

[0173] The described methods 20, 100 allow to reposition individual defect centers 6 in a substrate, particularly vacancy centers in diamonds, using atomic-level vortex e- beam 51 manipulation within STEM. Acceleration voltages are particularly selected between 60 to 160 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV). This may keep the transferred energy below the knock-on damage threshold in case of diamonds as a substrate. This improves the safety and integrity of the methods 20, 100. The procedure may commence with the identification of nitrogen-vacancy centers using combined dark field imaging and in-situ electron and optical spectral techniques as described elsewhere herein. An image of the desired region, particularly with discernible nitrogen vacancy centers, may be taken for reference. As part of the validation process, a concentrated vortex electron beam 51 may directly irradiate specific nitrogen-vacancy centers. Subsequent spin spectroscopy can measure and imaging can confirm the movement. If atoms remain stationary, the procedure can be iterated until the desired movement is achieved. As an added layer of precision, a minimized sub-scan window can be employed to both maneuver the NV centers and to continually monitor structural alterations. The respective images and the respective measurement parameters may be used and fed into a machine learning model for training. The trained machine learning model may be used to determine if a respective displacement is going in the right or wrong direction. Alternatively or additionally, the machine learning model may allow to implement a path finding algorithm that may realize the respective settings of the vortex electron beam to provide for a desired displacement of one or several defect centers 6.

[0174] The embodiments may harness the power and precision of AC-STEM, coupled with meticulous safety measures and validation techniques. Thus, individual atoms can be shifted with high accuracy. These methods allow to provide scalable qubit fabrication technology, especially in spin defects in solids. The immediate application being construction of a scalable quantum computer. Many more applications in quantum technologies can be realized using this innovative method to form a large-scale entangled network of solid-state qubits.

[0175] Fig. 5 shows a schematic representation of a machine-learning workflow 200 for NV center engineering in a substrate such as a diamond crystal lattice 50 using STEM (see Fig. 1 and 2).

[0176] In the following for matter of simplicity the vortex electron beam is referenced as electron beam or even simpler as e-beam. The vorticity of the e-beam and / or parameters rendering an electron beam into a vortex e-beam may be parameters that can be set by the machine-learning approach as described in the following and elsewhere herein.

[0177] The method 200 may comprise at least one of the following steps. It may be applied to other substrates than diamond crystal lattices 50, particularly those described elsewhere herein, even though the following may focus on diamond crystal lattices 50. The same may hold for the type of defects. Other defects may be manipulated than NV-centers, particularly those that are described elsewhere herein.

[0178] A step of STEM image acquisition 210 may comprise capturing high-resolution images of a diamond crystal lattice 50 using high-angle annular dark-field (HAADF)- STEM.

[0179] A step of simulation and dataset preparation 220 may comprise generating synthetic STEM images with NV centers and defects. A step of neural network training 230 may comprise training convolutional neural network(s), for example a U-Net, to detect atomic defects from (simulated) data. A step of real-time defect detection 240 may comprise applying a model to experimental data for NV localization.

[0180] A step of feedback and beam steering 250 may comprise guiding a STEM beam to induce and / or dislocate vacancies near nitrogen atoms. Dislocation may allow to move the respective defect center through the substrate as described elsewhere herein.

[0181] A step of validation and post irradiation analysis 260 may comprise re-imaging to confirm NV formation and / or dislocation and comparing the image with a model output.

[0182] A step of dynamic tracking and reinforcement learning (RL) control 270 may comprise using time series data and RL to automate manipulation.

[0183] The steps may be performed in the particular order shown in Fig. 7. They may also be performed in another order and / or steps may also be skipped when performing the method 100. Particularly the training of the machine-learning models such as neural networks may be performed only once and / or independent from inference, particularly with the steps linked particularly to training the machine-learning models being performed only when the machine-learning model is indeed trained. Thereafter, only the steps of inference may be performed, particularly in a repetitive order (in a loop) to dislocate the respective defect center(s) and to bring them into a final configuration. For matters of simplicity in the following a certain order is described as matter of example only.

[0184] Stepwise Workflow Overview

[0185] In the following a stepwise workflow overview over the machine-learning workflow 100 for NV center engineering in a substrate is given.

[0186] Step 1 :

[0187] In a particularly first step, STEM Image Acquisition high-angle annular dark-field (HAADF) STEM can be employed to capture high-resolution images of the diamond crystal lattice 50. These images can highlight atomic columns with intensity proportional to the atomic number (Z), particularly enabling distinction between nitrogen 53 dopants and carbon atoms 52 in case of NV centers in diamond crystal lattices 50.

[0188] To do so Aberration-corrected STEM (e.g. Nion UltraSTEM) can be used as instrumentation. It may be set at 60 keV to 100 keV, particularly 80 keV - 90 keV. It may output a real-time image stream of color centers, atomic lattice and impurities in the diamond crystal lattice 50.

[0189] As an example HAADF image, one can use a simulated image which shows the top view of diamond lattice, with an NV center. To train the model, the image can be sliced into many and fed into the model.

[0190] Step 2:

[0191] Particularly in a second step, a simulation and dataset preparation allow to create synthetic STEM images to serve as the initial training dataset. These simulations can use DFT-relaxed atomic models and electron scattering simulations to replicate expected NV and other defect signatures.

[0192] As tools multi-slice image simulation (e.g., QSTEM, abTEM) can be utilized. It may be connected to augmentation techniques such as noise addition, contrast variation, rotation, and defocus.

[0193] Step 3:

[0194] Particularly in a third step, neural network (NN) training can be performed. In one embodiment supervised learning for defect detection can be performed. A convolutional neural network (CNN), particularly a U-Net architecture, can be trained using labeled synthetic images (of the images generated in the previous, particularly second, step). The model can perform semantic segmentation to identify atomic columns, vacancies (single, double, complex), and substitutional atoms in the substrate such as a diamond crystal lattice 50.

[0195] As input, one or both of simulated and real images may be used. The (CNN) model may be at least one of a U-Net, a ResNet and / or a transformer-based segmentation.

[0196] As output, a pixel-wise classification of atomic structures may be generated. It may comprise a mask of atomic position that additionally may also highlight the class of atoms that are present in the mask for example carbon 52, nitrogen 53, a vacancy, a C13 atom, etc. This may not be limited to the respective diamond crystal lattice 50 as described here, but may also be transferred to other aspects with different substrates and / or defects.

[0197] In an embodiment, a U-Net architecture can be used. It may be composed of standard encoder-decoder building blocks for segmentation. Specifically, the U-Net components can be:

[0198] Encoder:

[0199] The Encoder may implement a down-sampling path and may be a sequence of convolutional layers performing down-sampling operations. Each stage of the encoder can apply convolution filters (e.g., 3x3 kernels) to extract features and then can reduce the spatial dimension (using pooling or strided convolutions). This path progressively can capture higher-level features of the image while reducing resolution.

[0200] Bottleneck layer:

[0201] The Bottleneck layer can be an intermediate layer at the "bottom" (most resolution reduced state of the image) of the U-Net (after several downsampling steps). This layer can have the most compressed representation of the image. It may be referred to as a “filtering” layer. It can further process the features before expansion (up- sampling). One may think of it as a bridge between encoder and decoder, comprising convolutions that operate on the deepest level features.

[0202] Decoder:

[0203] The Decoder can represent an up-sampling path. It may perform a sequence of up- sampling operations and can comprise convolutional layers that reconstruct the image segmentation. Each stage of the decoder can take the lower-resolution feature maps and can up-sample them (for example, via transpose convolution or interpolation and convolution) to a higher resolution. After up-sampling, a convolution can refine the features. The decoder essentially reverses what the encoder did, step by step, predicting a segmentation mask as it goes to the original image size. This mask may hold a lattice structure, but also the respective type of atoms at the respective lattice site position. Skip connections:

[0204] - Skip connections can represent lateral connections between corresponding encoder and decoder layers. In U-Net, for every encoder block (down-sampling stage), one can pass its output feature map directly to the matching decoder block (concatenating the feature maps). These skip connections can be building blocks that provide the decoder with high-resolution details from the encoder. This helps the network accurately localize features (like individual atoms) despite the encoder’s down-sampling.

[0205] Input and output layers:

[0206] The U-Net can have a defined input layer which takes in the raw image (for instance, a 256x256 STEM image patch). The output layer can be the final convolution that produces a segmentation map - also referred to as the segmentation mask. For a binary segmentation (defect vs background), the output layer might have one channel (plus a sigmoid activation) giving a mask of defect probabilities. If multiple classes (say, distinguish different defect types), the output could have multiple channels (with softmax). In the embodiment described here, the output can highlight atomic structures such as vacancies and impurity positions in the diamond crystal lattice 50 (as well as positions of the diamond crystal lattice 50). The U-Net used can be described as an encoder-decoder CNN “without residuals” - meaning that residual connections inside the blocks were not used, but only the standard skip connections between encoder and decoder. One simplified description can be given such that a fully convolutional network with three convolutional layers can be used: one acting as encoder, one as an intermediate filter, and one as decoder. In practice, a full U-Net can comprise more layers. Each convolution layer could be followed by a non-linear activation (like ReLU). In the encoder part, a down-sampling can be performed. In the decoder part, an up-sampling can precede the convolution. All these building blocks can come together to enable the U-Net to take an input image and output a pixel-wise classification with high precision.

[0207] The input to the U-Net can be fed into the very start of the encoder. In other words, the raw data (in this case, a STEM image of the diamond crystal lattice 50 with a defect center) can enter the network at the input layer, which then (immediately) can pass it through the first convolutional layer of the encoder. The model’s input can comprise images (both or one of simulated and real). So, the input can be linked to the U-Net’s first convolution block (the first encoding layer).

[0208] The output can be produced at the final layer of the decoder, which can provide the segmentation result. This output can be a pixel-wise classification of the image. For example, each pixel might be labeled as “background”, “carbon atom” 52, “nitrogen atom” 53, or “vacancy” 54 depending on what the U-Net has detected at that location. In simpler terms, the output can be the (segmentation) mask and / or annotated image that can highlight the defect centers. This can emerge from the last network layer (particularly a 1 x1 convolution that maps the final feature map to class labels).

[0209] In the context of the overall system (during inference), the U-Net’s input is particularly coming from the electron microscope’s imaging stream (or a dataset of images during training), and its output (the defect mask I segmentation mask I mask) is fed into an reinforcement learning (RL) controller as described elsewhere herein. The output particularly links to an RL loop by serving as the state representation, as described elsewhere herein. So, particularly, the U-Net’s output goes to a software interface where an agent (of the RL controller) reads it to decide on the next action. The input and output are thus the interface points: input linking the physical experiment (or simulated data) into the ML model, and output linking the ML model’s prediction into the decision-making algorithm.

[0210] The (segmentation) mask can highlight the NV center distinctly. In an examplary embodiment, the overlay mask on a STEM image might show all detected atomic sites or defects in one color. However, since the NV center is a specific combination (a nitrogen next to a vacancy), it can be marked different from a normal (C12) carbon atom. Particularly, a solution is to have the U-Net (or subsequent processing) differentiate the NV center. This can be done by assigning separate classes or markers in the segmentation output.

[0211] The U-Net can be trained for multi-class segmentation, not just a binary mask. In a respective embodiment, different features in the training data can be labeled: for instance, nitrogen impurity atoms 53 might be one class, vacancies 54 another, and regular lattice atoms another. The model, when predicting, could then output a mask with different labels. By identifying a nitrogen 53 and an adjacent vacancy 54, one can infer the presence of an NV center. In fact, one of the stated functionalities of the system is to “Identify N-V pairs” specifically. So, the pipeline can account for distinguishing an NV center from other defects. The mask can be directly the output (or visualization of the output) of the U-Net. In practice, the U-Net’s output could have the NV center labeled different from other atoms (of the lattice) or impurities or defects. For example, the nitrogen atom 53 might be highlighted in one color and the vacancy 54 in another; seeing them adjacent tells one that it is an NV center. One could also have a post-processing step that scans the U-Net’s defect mask and tags the specific nitrogen vacancy pair as “NV” for display. In summary, the U-Net can provide detailed info on all atoms and defects, and from this highlighting the NV center (and their respective position in the lattice) is possible. The mask can be linked to the U-Net in that it is the U-Net’s detection output being overlaid on an image generated by STEM (or simulated STEM image for training). To make the NV stand out, it can be ensured that the U-Net knows about the different atom types. By training it appropriately (the network sees examples of NV centers and other atoms), it can segment the image such that the NV center is distinguishable. The NV-center could be shown differently from other atoms and can such be identified by a user, but also fully automized by an appropriate machine - learning model. The U-Net-based segmentation can be the tool that enables that differentiation by labeling the constituent parts of the NV (the N and the vacancy) which may then be interpreted as an NV center in the visual mask.

[0212] The U-Net may be trained. In training backpropagation can happen "behind the scenes" to adjust the network’s weights. The training may be based on STEM images and / or simulated STEM images, such as HAADF, showing different positions of defect centers in a substrate such as NV-centers in diamond. Alternatively or additionally, C13 atoms may be placed (in the lattice) additionally. The respective U- Net may be trained with these images to allow identification of these atoms and to give out a respective mask as described elsewhere herein.

[0213] Defect center such as NV-center detection can be implemented using supervised training using a binary cross entropy, a dice loss and / or a focal loss. It allows to segment the defect centers such as NV-centers vs. background in STEM images. The atom position estimation can be implemented using supervised training using a mean square error (MSE) and / or Huber loss as loss I gain functions to allow regressing atomic coordinates.

[0214] Step 4:

[0215] Particularly in a third step, real-time defect detection in experimental images can be performed. Once trained, the network can be applied to incoming experimental HAADF-STEM data. The (previous) steps of training may not be performed during the inference, but the inference steps may run isolated from training. The model can locate nitrogen atoms 53 and nearby vacancies 54 to identify NV centers, potential NV formation sites or sites where the NV center may be dislocated to or must not be dislocated to.

[0216] A visualization may be performed. It may be performed in that an overlay of a mask on original STEM images is generated. An overlay mask can be applied to the simulated and experimental images to detect the lattice sites.

[0217] An uncertainty estimation can be performed. Confidence maps via Bayesian networks or ensemble learning can be implemented.

[0218] This allows the following functionality. Atomic sites for color centers, defects and / or vacancies can be labeled. N-V pairs can be identified as NV centers. It further allows to quantify confidence and / or uncertainty in the predictions. There may be a cutoff hreshold for an uncertainty that may be too high, to act on it. This uncertainty may be set between 20% and 50% certainty - respective uncertainty between 80% and 50% - , particularly between 30% and 40% certainty - respective uncertainty between 70% and 60%.

[0219] Step 5:

[0220] Particularly in a 5th step, feedback and beam steering may be performed as part of an inference. Examples of respective beam steering is shown in Fig. 3. A feedback system can use ML predictions to guide the electron beam. It can target atomic sites for vacancy creation or modification using calibrated irradiation. A control loop can be implemented, for example based on Python-based scripting (e.g. Nion Swift) or custom interfaces. The goal may be to position the e-beam to create or modify NV structures with minimal collateral damage.

[0221] In this particular step, the system may perform an action that may lead to an alteration of the respective configuration of the lattice. It may be for example that a dislocation of a defect center such as an NV center can have taken place within the substrate such as a diamond defect center. The respective result has to be validated and analysed, though.

[0222] Step 6:

[0223] Particularly in a 6th step, validation and post-irradiation analysis can be performed. Post-manipulation STEM imaging can confirm whether the desired NV center was formed and / or dislocated (in the previous, particularly the 5th step). The ML model can be reused to re-evaluate the region, validate success, and update training datasets if desired. Therefore, the respective steps of inference may run in a loop until a final desired configuration of the respective positioning of defects such as NV centers can be confirmed.

[0224] The analysis particularly comprises before-and-after (manipulation) defect maps. This way it is possible to directly determine the respective impact of the previous manipulation step.

[0225] An error handling can be implemented such as a re-attempt manipulation if the defect, such as the NV center, is not detected and / or if it is not detected at a respective final, desired position.

[0226] An HAADF image (simulated HAADF image during training) can show the pre- and post-manipulation process of the defect center such as an NV center in a substrate such as a diamond crystal lattice 50, and a re-attempt can be performed in case the manipulation has not been successfully done. The image may be fed to a first machine-learning model such as the U-Net, to allow determining the respective (alteration in) position of the defect center that should have been dislocated in a respective direction of the substrate. The resulting image may be fed to a next step, particularly a 7th step. Steps 5 to 7 may run in particular in a loop during inference of the method. Step 7:

[0227] Particularly as a 7th step, dynamic tracking and reinforcement learning (RL) can be implemented.

[0228] Dynamic processes, such as atomic migration, manipulation or NV hopping, can be tracked using time-resolved STEM sequences. Reinforcement learning (RL) agents can learn optimal manipulation policies.

[0229] The RL Algorithm can comprise at least one of Soft Actor-Critic (SAC) or Proximal Policy Optimization (PPO), Recurrent Neural Networks (RNNs) or Temporal CNNs for tracking the respective evolution over time.

[0230] As a reward function minimizing the deviation of the current NV position from target NV position can be used.

[0231] The environment can be the real-time feedback from STEM and a defect classifier.

[0232] This workflow presents a machine learning pipeline for automated detection, tracking, and manipulation of NV centers in diamond using STEM. The integration of physics- informed simulation, U-Net-based segmentation, feedback beam control, and reinforcement learning particularly forms a robust and adaptive system for atomic- scale engineering of color centers in diamond.

[0233] Reinforcement learning (RL) can be implemented. The beam-control task can be formulated as a reinforcement learning problem and a deep RL approach can be used to train (and / or infer) an agent. Particularly, the agent can be implemented with neural networks and can be trained (and / or inferred) using state-of-the-art algorithms like Soft Actor-Critic (SAC) or Proximal Policy Optimization (PPO). These algorithms enable the agent to learn a policy for manipulating defect centers through trial and error.

[0234] The RL agent’s policy can be represented by a neural network that observes the current state of the system (e.g. the configuration of defects) and can output an action (how to steer the electron beam). Over many simulated episodes, the agent can improve this policy by maximizing cumulative rewards. The training particularly involves backpropagating reward feedback into the network parameters, gradually teaching the agent which beam movements can lead to successful NV-center creation and / or dislocation, particularly in a desired I defined direction.

[0235] To handle the sequential nature of atomic manipulations, the RL implementation can incorporate temporal modeling. Particularly, the agent’s network can include recurrent layers or temporal convolution layers so it can account for the history of states and actions. This allows the agent to learn from time-resolved sequences (e.g. a moving or “hopping” defect) and develop an optimal strategy for beam steering.

[0236] At least one of a reward, an agent or an environment can be implemented for RL.

[0237] Environment:

[0238] The environment can be the physical scenario of the substrate under the electron beam, simulated for training purposes and informed by real experiment data. The state of the environment can be derived from the real-time STEM imaging and the defect detection model - essentially the positions of atoms and defects as identified by the U-Net can serve as the state input. In simulation, the environment updates the defect configuration based on the agent’s actions (e.g. moving an atom creates a new arrangement), mimicking the real diamond lattice 50 response.

[0239] Agent:

[0240] The agent can be the RL controller (a neural network) that takes the state and decides on an action. In embodiments herein, the agent’s action space could be, for example, directing the electron beam to a certain lattice position or applying a pulse of a given energy. The agent can use a learned policy (parameterized by the neural network) to choose these actions. The agent can be implemented by using an actorcritic neural network architecture (as implied by using SAC / PPO), meaning the agent can have a policy network that outputs actions. It particularly learns with the help of a value / Q-network that critiques those actions during training. The agent’s goal can be to maximize the total reward over an episode (an episode might be the process of creating and / or dislocating one defect such as an NV center).

[0241] Rewards:

[0242] We design a reward function that incentivizes the agent to achieve the desired defect configuration. A primary component of the reward is based on how close the result is to creating a correct NV center at the target location. For example, the reward can be sparse (a big positive reward only when the NV center is successfully created and / or dislocated) or shaped to guide the agent (small rewards for intermediate steps that move the defect closer to the target). In an implementation, a reward can be such that it “minimizes deviation from the target NV position,” meaning the closer the impurity-vacancy pair is to the desired site, the higher the reward. One may also include an entropy-based term in the reward (particularly in algorithms like SAC) to encourage exploration. Negative rewards (penalties) can be given for undesired outcomes like causing lattice damage or ejection of the respective defect center or locking it in a position where it cannot be manipulated anymore in case this is not a desired configuration.

[0243] The RL model (and control strategy) is particularly not limited to just the direction of dislocation (movement of the defect). In addition to choosing a direction to nudge an atom or vacancy, the method allows considering several beam parameters that can affect the outcome:

[0244] Angle of incidence:

[0245] The electron beam in the setup system as shown and described in Figs. 1 and 2 is particularly directed straight (0° incidence) for maximum energy transfer to the lattice. Normal incidence can be primarily used in simulations, but the angle could be a parameter - in principle, tilting the beam can change how momentum is delivered to an atom. Furthermore, the respective orientation of the diamond can be tweaked to allow the movement of the respective defect center such as the NV center to move also in the third dimension. If the apparatus allows, the model could explore slight beam tilts to direct forces in different orientations, particularly in a two-dimensional plane of the diamond, although a STEM particularly has a fixed column direction, and one could move the sample stage to change angle. Therefore, a respective angle of rotation can be implemented such that the angle of the diamond with respect to the former incident plane changes. Thus, the incident plane can be changed to allow dislocation also in a third direction. The movement of defect centers may thus cover the full three-dimensional space of the substrate, particularly the lattice.

[0246] Beam power (energy): The beam’s acceleration voltage (and beam current) can be accounted for rather than keeping it fixed. In fact, the method explicitly sets the beam energy in a specific range ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV) to ensure atoms can be displaced (also called dislocated) rather than knocked out (the latter would be (highly) penalized by the machine learning method). The power (electron beam dose) delivered can be crucial: a higher beam energy or longer dwell time can increase the chance to overcome the atomic bonding and cause a displacement. The proposed machine-learning model will use a beam energy high enough to induce the atomic shift but below the threshold that would sputter atoms (to avoid creating a new vacancy by outright ejection). This parameter can be tuned as part of the strategy.

[0247] Other parameters:

[0248] Additional parameters can comprise the beam size (spot size), frame size, and / or dwell time. We can use an atomic-sized focused probe (on the order of ~1 A diameter (FWHM)) so that the energy can be delivered very locally. The dwell time (how long the beam stays on one spot) or number of pulses can be adjusted - a longer exposure could increase the probability of a successful hop, but also risks damage, so the model could learn an optimal timing. The scanning pattern or sequence of irradiation points is another factor (for instance, whether to approach the target site from a certain direction). Environmental conditions like substrate temperature could also play a role (higher temperature might aid atom mobility), though those are particularly fixed during operation. All these parameters can be incorporated into the model’s observations or action space. In summary, the control model is multi-parametric: it doesn’t particularly rely solely on move direction, but can comprise at least one of beam angle, energy, focus, timing, diamond orientation etc., as variables to optimize the defect manipulation process.

[0249] The RL model may comprise a (specific) RL model architecture:

[0250] The RL model can use a deep neural network architecture particularly following an actor-critic design. The “actor” network can represent the policy (mapping states to actions), and the “critic” network can represent the value function (estimating how good a state or state-action is). In practical terms, one might have one network for the policy and another for the Q-function, or a single network with two heads (one outputting the action probabilities and one outputting the state value) depending on the algorithm. For instance, with Soft Actor-Critic one can use separate function approximators for the policy (actor) and for the Q-value estimators (critics).

[0251] State input:

[0252] The input to the RL network can be a representation of the current state of the environment. Rather than raw image pixels, one can use the processed output of a neural network defect detection, particularly a CNN defect detection, further particularly the U-Net defect detection as as the state feed. This could be a set of features such as coordinates of the nitrogen 53 and vacancies 54 or an overlay mask indicating defect locations. It can be ensured that the state vector includes everything the agent may need in the particular implementation (e.g., the relative position of an impurity and a vacancy 54, so the agent knows where the NV center is or needs to be).

[0253] Neural network layers:

[0254] The architecture can then process this state input through several layers. Often there can be an encoder part of the network (e.g., fully connected layers or convolutional layers if an image / mask are inputted) to extract a latent feature representation. Because the respective problem described herein can be time-dependent, one can incorporate either a recurrent layer (RNN) or a temporal convolution in the network to handle sequence information. For example, a Long Short Term Memomry (LSTM) layer could take in the sequence of recent states so that the agent remembers the trajectory of a moving atom. This can help the agent to predict the outcome of actions over time (important for tracking defect motion).

[0255] Policy output (actor):

[0256] The actor network can output the action the agent could take. In a case the action might be continuous (e.g., a 2D vector for beam shift direction or an (x, y) target coordinate, plus perhaps a parameter like beam pulse duration). If using SAC / PPO, the actor could output parameters of a probability distribution (mean and variance for a Gaussian over actions) from which the actual beam command can be sampled. The architecture can be designed such that this output layer can adjust to the required action format (discrete moves vs continuous offsets, etc.). Value / Q output (critic):

[0257] The critic network (which can share some layers with the actor or be separate) can take the state (and in some cases the action as well) and can output a value: either V(s) or Q(s,a) depending on formulation. For SAC, typically two Q-networks can be used for stability. For PPO, a single value head can predict V(s). The critic’s architecture can be similar to the actor’s encoder part, ensuring it can have the same view of the state.

[0258] In summary, the RL model architecture can be a deep neural network that can ingests the defect state (informed by the "previous" neural network, particularly a CNN, further particularly a U-Net), possibly uses recurrent units for temporal context, and particularly having separate outputs for the policy and value estimates. This enables the agent to learn an optimal policy for beam control. The algorithms like SAC and PPO can represent the use of an actor-critic setup with function approximators; for example, Recurrent Neural Networks (RNNs) or Temporal CNNs for tracking can be integrated to handle dynamic sequences, and the policy can be learned to maximize rewards (minimize distance to target NV) as evaluated by the critic.

[0259] The RL may comprise a Q-function, a value function and a policy.

[0260] Policy:

[0261] In reinforcement learning, the ‘policy’ can be the strategy that the agent follows to choose actions. Formally, a policy IT can be a mapping from states of the environment to the probabilities of taking each possible action. It can define the agent’s behavior at a given time. Herein, the policy could tell the agent how to adjust the electron beam when the defects are in a certain configuration. The agent’s goal is to learn an ‘optimal policy’ that maximizes the expected reward (e.g., always move the electron beam in a way that creates and / or displaces the NV center most efficiently).

[0262] Q-function (state-action value function):

[0263] The Q-function, usually denoted Q(s,a), can give the expected cumulative reward (often called return) if the agent is in state ‘s’, takes an action ‘a’, and then continues following a certain policy. In other words, it evaluates how good a particular action is in a given state. A higher Q-value means that action ‘a’ in state ‘s’ can be predicted to lead to a higher total reward. In an algorithm like Q-learning or in the critic of an actor-critic, the Q-function is what the agent can learn to understand which actions are beneficial. For example, Q(s,a) could tell the merit of aiming the beam at a particular spot (action) when the defects are in configuration ‘s’, in terms of eventually achieving and / or displacing the NV center, particularly in a defined direction.

[0264] Value function (state value function):

[0265] The value function, denoted V(s), can give the expected cumulative reward from state ‘s’ if the agent follows the policy thereafter. This is essentially the usefulness of being in state ‘s’. If V(s) is high, it means that state is favorable because from that state the agent can achieve a lot of reward (i.e., it’s close to the goal under an optimal policy). In a scenario, a state where the impurity and vacancy are adjacent (forming an NV) would have a high value, whereas a state where they are far apart might have a lower value. The same may hold true for an NV center or other desired defect being in closer proximity to the respective final position it is desired to displace the NV center to. The value function can relate to the Q-function by V(s) = max_a Q(s,a) for the optimal policy (or VATT(S) can be the expected value following policy IT).

[0266] In summary, the policy can be the agent’s decision-making rule (what action to take in each state), the Q-function can tell how good an action-choice can be in a state (state-action pair evaluation), and the value function can tell how good it can be to be in a state overall. The RL implementation can use these concepts: the agent’s neural network can encode a policy, and the learning algorithm (like SAC) can use Q- functions (critics) and value functions internally to guide the policy toward maximizing rewards.

[0267] The U-Net for atom detection can be linked with the RL.

[0268] The U-Net for atom / defect detection can be integrated as the perception component of the RL system. It can process the microscope’s STEM images and can produce a segmentation identifying key features: atomic columns, vacancies 54, and impurity atoms (like N 53). Particularly, the U-Net can observe the environment and can yield the state information needed for decision-making. The output of the U-Net (for example, a mask or a set of coordinates indicating where the nitrogen 53 and vacancies 54 are) can be used as the state input to the RL agent. Instead of the RL agent trying to interpret raw images, it gets a high-level representation: e.g., “Nitrogen at position (x,y), vacancy at (x',y')”. This way, the agent particularly knows the defect configuration. For instance, once trained, the network can locate nitrogen 53 and nearby vacancies 54 in an image to identify an NV center or a potential site, and that information could feed into the agent.

[0269] After the RL agent particularly takes an action (such as moving the beam to a new position), the environment (substrate) particularly changes - perhaps the impurity atom moved. A new STEM image can be acquired in real time and fed through the U- Net again. The U-Net updates the segmentation mask to reflect the new positions of atoms / defects. This updated state is passed to the agent for the next decision. In this way, the U-Net and RL can form a closed feedback loop: the U-Net can continuously interpret the experimental data into state information, and the RL agent can use that to decide on the next beam action. In summary, the U-Net serves as the eyes of the RL agent. It links to the RL by converting raw images into a concise state (defect locations, types, etc.) that the agent can use. The phrase “real-time feedback from STEM and defect classifier” as used elsewhere herein particularly refers to exactly this connection - the defect classifier (U-Net) provides feedback to the RL agent about the result of its actions. Without the U-Net, the agent could not reliably know what happened after it moved the beam; with the U-Net, the agent can have a quantitative observation of the environment to inform its learning and actions.

[0270] Beam control can be realized using RL.

[0271] RL can use sparse reward, shaped reward and / or entropy reward as loss I gain functions to learn to steer the e-beam to dislocate NV centers.

[0272] Uncertainty estimation can be implemented using a probabilistic approach. Negative log likelihood and / or Monte Carlo Dropout can be used as loss I gain functions. It allows to estimate confidence in predictions.

[0273] In more general terms, one can describe the respective machine-learning method as follows: In a step there is a feature identification and / or lattice site assignment with respective features, for example in a feature map, also called a mask. This can be done by a first machine learning model, particularly designed for picture segmentation. In a subsequent step, a respective feature segmentation map / mask may be fed to a second machine-learning model that allows to set parameters of the system such as irradiation angle, angle of the diamond relative to the incident beam, energy of irradiation, spot size (FWHM), irradiation time, pulse sequence frequency, and / or others based on a respective input image and an image of the desired outcome (a final state of positions for the defect centers in the respective lattice).

[0274] 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 have the respective feature or features. All features in feature combinations are also disclosed independently thereof and may also be singled out from the combinations of features disclosed herein and used in combination with other features to specify the subject-matter of the any of the claims, dissolving any structural and / or functional relationship that may exist between the features. Terms like “first”, “second”, “third” may be used to refer to a list of elements but does not necessarily describe these features or elements according to their importance, their order of appearance or order of structure. Therefore, these elements or features may specify the different aspects in any other particular order, unless explicitly expressed otherwise.

[0275] LIST OF REFERENCE SIGNS

[0276] 1 selecting the desired defect center as qubit

[0277] 2 tune to the correct e-beam energy

[0278] 3 focus the e-beam on the defect center (particularly the an atom thereof as defect atom)

[0279] 4 STEM image direct electron signal

[0280] 5 Feedback

[0281] 6 individual defect center as qubit

[0282] 7 annular dark field detector

[0283] 8 electron energy loss spectroscopy (EELS)

[0284] 9 spin resonance spectroscopy e.g., DEER, ENDOR

[0285] 10 aberration-corrected scanning transmission electron microscopy system (AC-STEM)

[0286] 11 Laser fluorescence photon single photon detector

[0287] ODMR electronics optically detected magnetic resonance (ODMR) method of manufacturing a diamond with defect centers controlling if position of defect center moved placing of electron beam again controlling if position of defect center moved as desired moving e-beam to new defect center as qubit controlling if all defect centers have been moved raster scanning path diamond crystal lattice electron beam (e-beam) a, 51 b, 51 c orders of electron beam from holographic aperture carbon atom (C) nitrogen atom (N) vacancy displaced defect center after interaction with e-beam displacing first defect center displacing second defect center displacing third defect center displacing fourth defect center obtaining final configuration precise movement based on individual precision displacing of a subgroup of defect centers initial configuration final configuration raster scanning-based displacing defect centers to reach final configuration defined direction

[0288] C13 (scientifically written also as13C) atom holographic aperture aberration-corrector 71 monochromator

[0289] 72 lens

[0290] 80 subgroup

[0291] 81 magentic field generator

[0292] 100 method

[0293] 110 image acquisition

[0294] 120 selecting defect center and placing e-beam

[0295] 130 processing image and aligning

[0296] 140 filtering image and using it for training

[0297] 150 controlling spiraling vortex electron beam

[0298] 160 STEM

[0299] 200 machine-learning workflow for NV center engineering in diamond using STEM

[0300] 210 STEM image acquisition: capturing high-resolution images of diamond lattice using HAADF-STEM

[0301] 220 simulation and dataset preparation: Generating synthetic STEM images with NV centers and defects

[0302] 230 neural network training: train convolutional neural network(s), for example a U-Net, to detect atomic defects from (simulated) data

[0303] 240 real-time defect detection: apply model to experimental data for NV localization

[0304] 250 feedback and beam steering: guiding STEM beam to induce vacancies near nitrogen atoms

[0305] 260 validation and post irradiation analysis: re-imaging to confirm NV formation, comparing with model output

[0306] 270 dynamic tracking and reinforcement learning (RL) control: using time series data and RL to automate manipulation

[0307] X x-coordinate

[0308] Y y-coordinate

[0309] Z z-coordinate

Claims

CLAIMS1 . Method of automated spatial patterning of defect centers (6) in a substrate, particularly a diamond crystal lattice (50), comprising the following steps:- providing a defect center (6) distribution to a machine-learning model, the machine-learning model being particularly trained to determine an output for displacement of at least one defect center (6) based on the provided defect center (6) distribution, the machine learning model providing an output for displacement of individual defect centers (6),- particularly providing a substrate, particularly diamond, comprising defect centers (6) in a bulk structure of the substrate, particularly a bulk diamond crystal lattice (50),- detecting the position of at least one defect center (6) in the bulk structure of the substrate, particularly the bulk diamond crystal lattice (50), and- displacing (61 ) the at least one defect center (6) in the bulk structure of the substrate, particularly the bulk diamond crystal lattice (50), particularly sitespecific, in a defined direction.

2. Method (20) for displacing defect centers (6) in a substrate for quantum applications in a defined direction, particularly according to claim 1 , the method comprising the step of- displacing (61 ) a group of defect centers (6), in the bulk structure of the substrate, particularly the bulk diamond crystal lattice (50), simultaneously, particularly group-specific, particularly in a defined direction.

3. Method (20) according any of the claims 1 or 2, characterized by at least one of the steps of - providing a substrate, particularly diamond, comprising defect centers (6) in a bulk structure of the substrate, particularly a bulk diamond crystal lattice (50);-detecting the position of at least a first subgroup of the defect centers (6) in the bulk structure of the substrate, particularly the bulk diamond crystal lattice- displacing a second subgroup being at least partially a subgroup of the first subgroup of the defect centers (6) in the bulk structure of the substrate, particularly the bulk diamond crystal lattice (50); or- verifying or monitoring the position of the displaced defect center (55) or the positions of the displaced defect centers (55).

4. Method (20) according to one of the preceding claims, characterized by at least one of the following steps of- directing an (atomic-level) vortex electron beam (51 ), particularly using aberration- corrected scanning transmission electron microscopy (10), to displace (61 ) the at least one defect center (6) in the bulk structure of the substrate, particularly the bulk diamond crystal lattice (50), in a defined direction; or- directing an (atomic-level) vortex electron beam (51 ), particularly using aberration- corrected scanning transmission electron microscopy (10), to displace (61 ) the group of defect centers (6), particularly being at least the second subgroup of defect centers (6), in the bulk structure of the substrate, particularly the bulk diamond crystal lattice (50), simultaneously, particularly in a defined direction.

5. Method (20) according to claim 4, wherein a diameter of a directed atomic-sized vortex electron beam (51 ) ranges from 0.5 to 3 Angstrom, particularly from 0.5 to 2 Angstrom, further particularly from 0.5 to 0.8 Angstrom; and / or wherein a diameter of a directed (atomic-sized) scanning transmission vortex electron beam (51 ) ranges from 1 to 200 Angstrom, particularly from 10 to 150 Angstrom, further particularly from 50 to 100 Angstrom.

6. Method (20) according to any of the preceding claims, wherein an acceleration voltage for accelerating electrons in the directed (atomic-sized) vortex electron beam (51 ) is set below the knock-on damage of the structure of the substrate, particularly the diamond crystal lattice (50), particularly the acceleration voltage is set between 60 to 160 keV ((about) 60 keV to 160 keV, particularly 70 keV to 150 keV, further particularly 80 keV to 140 keV, further particularly 90 keV to 130 keV), particularly for diamond; and / or wherein a convergence angle is higher than 15 mrad, particularly higher than 20 mrad, further particularly higher than 32 mrad.

7. Method (20) according to any of the preceding claims, wherein the directed(atomic-sized) vortex electron beam (51 ) is directed to the defect center (6) to be displaced and / or to the group of defect centers to be displaced.

8. Method (20) according to any of the preceding claims, characterized by at least one of the following steps of- dark field imaging with on-the-fly electron spectral analysis identifying at least one defect center (6) in the bulk diamond crystal lattice (50) or the group, particularly the at least first subgroup, of defect centers (6);- confirming or monitoring the displacement (61 ) of at least one defect center (6), particularly by applying at least one of spin spectroscopy, imaging studies or ODMR;- mapping, assessing and / or evaluating at least one of the chemical composition or the electronic structure, particularly by at least one of energy-dispersive X-ray spectroscopy (EDX), electron energy loss spectroscopy (EELS) (8) or fourdimensional STEM (4D-STEM);- using at least one sub-scan 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 structure of the substrate, particularly the bulk diamond crystal lattice’s (50) structure, in real time;- providing a map of defect centers to determine potential qubit coupling via the controlled positioning of the defect centers (6) as potential qubits and displacing individual defect centers (6) or a group of defect centers accordingly; 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, particularly improving the coupling of a qubit network;9. Method (20) according to any of the preceding claims, wherein the method (20) is repeated until 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) reached a desired configuration.

10. Method (20) according to any of the preceding claims, wherein the defect center (6) is at least one of an atomic point defect, an atomic point defect with P1 substitutional configuration, a silicon atomic impurity, a nitrogen atomic impurity, a tin atomic impurity, a phosphorous atomic impurity, a bismuth atomic impurity, a vacancy center, a nitrogen-vacancy center, a silicon-vacancy center, a tin- vacancy center, a phosphor-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 high- band gap semiconductor.11 . Method (20) according to any of the preceding claims, wherein at least one intermediate step for displacement is planned, particularly calculated, and / or wherein at least one parameter setting for at least one intermediate step is planned, particularly calculated.

12. Method (20) according to any of the preceding claims, comprising the step of placing suitable defect centers (6) as qubits for quantum communication in an arranged array and / or a corral nanostructure within the bulk structure of the substrate, particularly the bulk diamond crystal lattice.

13. Method (20) according to any of the preceding claims, characterized by at least one of a step of- an in-situ feedback (5)-controlled manipulation combined with a predefined structure being used for real-time qubit signal monitoring;- re-positioning the relative positions of the complex and / or compound defect centers in the bulk substrate structure, particularly the diamond crystal lattice (50), particularly being optimized; .- probing temperature effects on defect centers (6) in a range from room temperature up to 1500°C;- applying at least one of heating, cooling or biasing for analysis; or- dislocating at least one defect center (6) to a site-specific marker of the substrate structure, particularly the diamond crystal lattice (50), particularly a C13-isotope.

14. Method according to any of the preceding claims, wherein a, particularly focused, (atomic-sized) vortex electron-beam is formed through a holographic aperture in the aberration-corrected scanning transmission electron microscope; and / or wherein the, particularly focused, (atomic-sized) vortex electron-beam is formed by applying an additional magnetic field to an electron beam in the aberration- corrected scanning transmission electron microscope.

15. Method according to at least one of the preceding claims, wherein a vortex electron beam shape is defined based on the defect center distribution provided to the machine learning model, particularly the trained machine learning model.

16. Method of training a machine-learning model with a series of images of spatially placed defect centers (6) in a bulk structure of a substrate, particularly a bulk diamond crystal lattice (50).

17. System (10) configured and structured to perform a method according to any of the preceding claims, the system (10) comprising:- a displacement apparatus configured and positioned to displace defect centers (6) in a substrate, particularly 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 structure of the substrate, particularly the bulk diamond crystal lattice (50),- a control unit configured to determine a displacement strategy and to control the displacement apparatus to follow the displacement strategy.

18. Computer program product configured to perform a method (20) according to any of the claims 1 to 16, when run on a control unit in a system (10) according to claim 17.

19. Device, particularly a diamond crystal, comprising a substrate structure, particularly a diamond crystal lattice (50), comprising a qubit network of suitable defect centers placed in spatial proximity such that they form the qubit network, the qubit network particularly comprising at least two suitably defect centers (6), particularly comprising at least four suitable defect centers (6), particularlycomprising at least five suitable defect centers (6), further particularly comprising at least six suitable defect centers (6), further particularly comprising up to an integer n of suitable defect centers (6), wherein n is particularly between 10 and 1000 defect centers (6), further particularly between 20 and 900 defect centers (6), further particularly between 100 and 800 defect centers (6); and / or comprising up to an integer n of suitable defect centers (6), wherein n is particularly between 1000 and 1 000 000 defect centers (6), further particularly between 1500 and 900 000 defect centers (6), further particularly between 2000 and 800 000 defect centers (6).

20. Method configured to manufacture a device comprising a substrate, particularly according to claim 19, comprising at least a method according to any of the claims 1 to 16.

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