Physical medium comprising color center for use in quantum system

Abstract

An apparatus comprising: a crystal; at least three first conductive lines arranged substantially parallel to each other; at least two second conductive lines arranged substantially parallel to each other, each second conductive line being arranged so as not to be parallel to each first conductive line such that each second conductive line intersects each first conductive line forming at least six intersection points; and at least six color centers, each color center being positioned within the crystal and adjacent to a different one of the at least six cross points.

Description

Technical Field

[0001] The present disclosure relates generally to color centers, and to devices, systems, and other physical media that contain the same, as well as practical applications thereof (e.g., in quantum computers, quantum sensors, or other quantum devices or quantum systems). Background Art

[0002] Color centers are defects in diamond and other crystalline solids that have a wide range of applications due to their physical properties, including quantum metrology and quantum computing. Such defects may be naturally occurring or artificially created.

[0003] The color center can be activated by applying an electromagnetic field in a specific orientation relative to the axis of the color center. The field can cause a change in the spin state of the color center. The electromagnetic field can be generated, for example, by flowing an alternating current along a wire, causing an oscillating magnetic field around the wire.

[0004] Color centers have been shown to be important physical systems for various quantum technologies, including quantum metrology (e.g., magnetic measurement, thermal measurement, strain sensing), information processing, and communication. One of its most promising applications is quantum computing, where color centers have demonstrated multi-qubit gates, quantum entanglement, quantum key distribution, etc.

[0005] For example, in quantum computing applications, a color center (or a group of color centers) operating as (multiple) qubits can be activated to apply a specific quantum computing operation (such as a quantum state transformation or a quantum state measurement). In quantum metrology applications, a color center (or a group of color centers) operating as (multiple) sensors can be activated to capture sensor measurements at a specific moment. In quantum metrology applications, different groups of color centers operating as sensors can be selected to construct a 2D / 3D image of the measured quantity (e.g., magnetic field). If all color centers / sensors are activated at the same time instead of the selected multiple groups, only the average value of the measured quantity can be obtained. Summary of the invention

[0006] One technical challenge addressed herein is the scalability of devices containing color centers, such as quantum imaging arrays (e.g., with color centers operating as sensors) or quantum computer chips (e.g., with color centers operating as qubits). For example, one challenge in scaling quantum systems based on color centers is maintaining the ability to individually address the color centers. For example, in quantum metrology and quantum computing applications, it is useful to be able to independently control each sensor or qubit. In an array of multiple color centers, difficulties may arise in addressing individual color centers. For example, when color centers are activated via currents in a wired network, crosstalk / decoherence effects between nearby color centers may limit individual addressability. Individual addressability of color centers can be achieved in a variety of ways, not all of which are sufficiently scalable for practical deployment. For example, one possibility is to increase the physical spacing between color centers to prevent crosstalk and / or decoherence effects between color centers, which may otherwise occur when a signal intended to activate one color center inadvertently activates another nearby color center (which may in turn lead to, for example, computational or sensing errors). One or more examples herein utilize a "crosshatch" wire geometry that provides individual addressability within a 2D or 3D array of color centers. In at least some examples, scalability is achieved using a crosshatch geometry that requires fewer wires than there are individual color centers. A color center located near the intersection between two crosshatch wires can be activated via simultaneous current in the two crosshatch wires.

[0007] This summary is provided to introduce a selection of concepts in simplified form, which will be further described in the following detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. The claimed subject matter is not limited to implementations that address any or all of the disadvantages described herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] To aid understanding of the present disclosure and to show how the embodiments may be effected, reference is made by way of example to the accompanying drawings, in which:

[0009] Figure 1 is a schematic block diagram of a quantum system including two color centers;

[0010] Figure 2 is a schematic block diagram illustrating control of a quantum system by a computer system;

[0011] Figure 3a shows the splitting of the energy states of a color center by an external magnetic field;

[0012] FIG3 b shows a graph of the resonant frequency for different applied magnetic fields;

[0013] Figure 4 Schematic diagram showing nitrogen vacancy centers in diamond;

[0014] Figure 5 Schematic diagram showing an exemplary 2D configuration of a color center in a crystalline material;

[0015] Figure 6 A schematic diagram showing magnetic fields generated by a plurality of alternative conductor pair configurations;

[0016] Figure 7 An exemplary color center array having a wire pair configuration is shown;

[0017] Figure 8 An exemplary array of color centers is shown, wherein each color center is addressable by a pair of crossing conductive lines; and

[0018] Fig. 9 An example 3D color center array with magnetic field gradient and crossed wire configuration is shown.

[0019] Fig.10 shows a set of example cross-wire configurations for addressing different numbers of color centers; and

[0020] Fig.11 An example 3D color center array with multiple layers of color centers addressable by crossing conductive lines is shown. DETAILED DESCRIPTION

[0021] Example embodiments are described below. First, some relevant context for the described embodiments is provided.

[0022] A color center may be referred to as being coupled to a wire (or coupled to a point of intersection between two crossing wires), and this term includes the case where the color center is close enough to the wire that it can be activated by activating the wire (causing the wire to emit an electromagnetic signal, such as by inducing a current in the wire). For the avoidance of any doubt, this includes the case where the color center is separated from the wire by a sufficiently small vacuum or air gap. A color center may be "addressable" in that the color center may be activated by activating the wire to which it is coupled. A device may refer to a crystal by itself or to a crystal in combination with one or more other elements (such as wires). A device may be a complete device or other system, or simply a component (or collection of components) used in such a system / device. A wire refers to any structure capable of carrying an electrical signal that results in the emission of an electromagnetic signal, and includes external or internal wires, wires printed on or otherwise attached to a crystal, integral wires (e.g., graphene channels formed in a crystal), etc.

[0023] Color centers are said to be "individually addressable" when they can be controlled with some degree of independence. This includes the case where any given color center can be activated without any effect on other(s) color center(s) (complete independence), but the term is not limited in this respect. For example, an electromagnetic field may be generated that causes a desired operation to be applied to any given color center and also has some different secondary effect on one or more other color centers; such an arrangement may still provide individual addressability (although not complete independence) because the desired operation can be individually applied in a controllable manner to any desired color center (as opposed to the case where it is only possible to apply the desired operation to, for example, all color centers within a physical medium or to a fixed subset of color centers).

[0024] For some color centers, such as nitrogen-vacancy color centers, an external magnetic field is used to lift the degeneracy between their energy levels and thus allow an electromagnetic field of a given frequency to address the color center by changing its spin state, but other types of color centers may be addressable in the absence of any external magnetic field. An example of this is a nitrogen-vacancy center, where 3 A2 ground state m s = ±1 spin projection states are degenerate in the external magnetic field.

[0025] In a system with multiple color centers, each center is positioned proximate to a different corresponding electromagnetic field emitter, such as a current carrying wire, in order to address only one color center at a given time.

[0026] In principle, any given color center can be individually addressed by activating its associated emitter. However, this requires a separate and individually controllable emitter (e.g., wire) for each color center. This limitation leads to challenges for scaling to a larger number of color centers, as a large number of individual wires need to be created for generating the field for each center.

[0027] Furthermore, since electromagnetic fields radiate outward from the wires that generate them, there is a risk of activating other centers, leading to decoherence and / or crosstalk between the color centers. To reduce this "crosstalk" effect, the color centers and their respective wires can be placed further away from each other. However, this imposes a limit on the density of color centers within the material, which also affects the scaling of quantum systems to many color centers.

[0028] Individual nuclear spins can be addressed by different microwaves or radio frequencies. Spins can be selected by applying a field whose frequency matches the energy difference (or splitting) between the energy levels of the nucleus. The splitting frequency can be found by frequency scanning while, for example, observing the fluorescence emitted from the nucleus. When the applied frequency matches the longitudinal cutting frequency, a change in the emitted fluorescence can be observed, which change is usually called resonance. According to the Zeeman effect, a resonance is sensitive to an external magnetic field if it has a non-zero angular momentum.

[0029] The following description considers color centers with various applications in quantum devices / systems (e.g., as qubits, quantum sensors, etc.). Some existing quantum systems use different physical states as qubits or quantum sensors, such as ion traps and nuclear spin states as alternatives to color centers. However, ion traps require surface electrodes for stability, and both ion traps and nuclear spin states are driven by electromagnetic field frequencies much lower than the electron spin states of the color center (usually in the kHz-MHz range), especially for the resonant frequency of nitrogen vacancy color centers (usually GHz). Electronic-based systems rely on external magnetic fields based on the electron gyromagnetic ratio (about 28 GHz / T) to experience shifts in their electron spin energy levels, as described in further detail below, while nuclear-based systems experience shifts of typically three orders of magnitude smaller, on the order of MHz / T. Therefore, a larger magnetic field will be required to separate the resonances in the nuclear spin shells, which makes it impractical to apply magnetic field gradients (as described in more detail below) for individual addressing in systems with high density nuclear spins. Furthermore, the lower frequency of the electromagnetic signal used for nuclear spin systems limits the rate at which the spins can be addressed, which in turn limits the maximum achievable information throughput. The higher frequency used to address the color centers means that a greater number of addressing operations can be performed per second compared to lower frequency systems.

[0030] Despite decades of research on color centers, they remain challenging when it comes to individual addressing, a prerequisite for scaling single color center-based sensors and qubits to more complex sensor or qubit arrays, which could be used, for example, in imaging arrays or quantum computer chips.

[0031] The challenge with individual addressing is that color centers are most often addressed using a microwave field generating structure that radiates in a wide area. Thus, when addressing of an individual color center is attempted, the rest of the color centers in its area are also driven by the same microwave field (although not as strongly), which results in decoherence and / or crosstalk between color centers, both of which are undesirable for the application.

[0032] Herein, example wire geometries are described that allow individual addressability within a 2D array of color centers, where the number of wires is less than the number of color centers in the 2D array, and where there is relatively small spacing between the color centers.

[0033] The described geometry can optionally be combined with an additional solution incorporating a multiple color center microwave radiation geometry to exploit the inherent magnetic field dependence of the color center energy level transition frequencies (resonances) to address them individually. In combination with any of the described wire geometries, this significantly increases scalability (e.g., allowing closer spacing of color centers, and further, allowing multiple color centers to be addressed via the same wire).

[0034] Thus, a quantum system is described herein that is capable of addressing individual color centers in an arrangement of multiple color centers by creating a magnetic field gradient such that the magnetic fields applied to different color centers are different. This causes each color center to have a different electron spin resonance frequency, such that an electromagnetic field applied to the array of color centers activates only those color centers having the resonance frequency of the electromagnetic field. This allows individual color centers to be addressed without activating nearby color centers.

[0035] Also described are optional wire pair geometries in which color centers coupled to a wire pair can be activated via antiparallel currents through the wire pair. The wire pair geometry can reduce crosstalk / decoherence effects even at relatively short distances, allowing for reduced physical spacing between color centers and thus improving scalability. The wire pairs can be arranged in a cross-section geometry to provide 2D (or 3D) addressability, with relatively small color center spacing having fewer crosstalk / decoherence events.

[0036] In another example or examples, individual addressability can be extended to 3D arrays of color centers. In such an arrangement, horizontal 2D arrays of color centers are "stacked" vertically, with each 2D array being addressed using a corresponding network of wires in a cross-section geometry to provide individual addressability within the 2D array. A magnetic field gradient in the vertical direction (z) provides individual addressability in the z direction by functionally isolating each 2D array of color centers from its vertically adjacent (multiple) arrays (because the magnetic field gradient causes the color centers in the vertically adjacent arrays to have different activation / resonance frequencies). It should be understood that the terms horizontal and vertical are completely arbitrary labels used for simplicity. Equivalently, each 2D array of color centers can be said to be substantially parallel to a plane (xy), and the 2D arrays of color centers can be said to be adjacent to each other in a direction (z) perpendicular to that plane.

[0037] As described above, color centers can be activated by applying an electromagnetic field at or near the resonant frequency of the color center, where the resonant frequency is the frequency of transitions between states or energy levels of the color center. The term "electron spin resonance frequency" generally refers to the frequency that causes a color center to transition between electron spin states (usually at different energy levels). Each color center can have the same intrinsic resonance frequency or similar intrinsic resonance frequencies, increasing the risk that a signal intended for one color center inadvertently activates another color center.

[0038] Note that the electromagnetic field used to activate the color center is an oscillating electromagnetic field that oscillates at a specific frequency that matches the resonant frequency of the target color center. Other fields are also described herein, particularly external static magnetic fields, which are applied to shift the energy levels and therefore the resonant frequency of the color center. It should be noted that the component of the external magnetic field parallel to the axis of the color center is the effective magnetic field that causes the energy level shift of the color center, and the component of the oscillating electromagnetic field perpendicular to the axis of the color center is the effective field for addressing the color center. It will be clear from the context which fields are referenced elsewhere in the specification.

[0039] Example embodiments will now be described.

[0040] When an external magnetic field is applied to the color center, its resonance is shifted in energy by a factor proportional to the projection of the magnetic field along the color center axis multiplied by the electron gyromagnetic ratio and a factor related to the color center spin. Transitions between color center energy levels necessary for quantum control occur only if the frequency of the externally applied microwave field matches the transition energy frequency of the color center under the applied magnetic field. By applying a magnetic field gradient over the color center array, each color center resonance can be shifted at a different frequency. If the frequency shift is sufficient to separate the color center resonances by a factor equal to or greater than half of their full width at half maximum, individual color centers can be addressed even if they are placed in a multi-color center microwave radiation geometry.

[0041] The application of the magnetic field can be achieved in a variety of ways depending on the color center array. For example, a single wire loop or a system of wire loops that carries non-alternating direct current (DC) to provide a static magnetic field can be used to generate the magnetic field, or a Halbach array can be used to generate a uniform high-intensity magnetic field over one area and a low magnetic field intensity over another area. In general, the magnetic field generator can take any form that can induce a desired resonance shift (or multiple resonance shifts) in the color center (or multiple color centers).

[0042] The microwave radiation geometry used to excite a color center (or multiple color centers) with a specific resonant frequency (or multiple resonant frequencies) can take many different forms, such as a single conductor or conductor loop carrying alternating current (AC), or even a conductor-numbered geometry surrounding the color center with parallel current flow, crossed conductor geometry, etc.

[0043] The following examples consider quantum systems that include multiple color centers. Specific examples involve nitrogen vacancy (NV) centers in diamond, but other types of color centers may be used, such as silicon vacancies in diamond. For example, color centers may be present in other crystalline materials such as silicon carbide. Color centers may occur naturally in diamond and other materials, but may also be created by chemical vapor deposition (CVD) and high pressure, high temperature (HPHT) techniques. Color centers may also be placed at desired locations within diamond by implanting ions within the diamond (nitrogen ions are implanted into nitrogen vacancy centers and silicon is implanted into silicon vacancy centers), or by irradiating the diamond with ultrashort (femtosecond to picosecond) laser pulses. This description may refer to color centers as qubits, but it should be understood that the description is equally applicable to applications of color centers other than quantum computing, such as quantum sensor applications.

[0044] Figure 1 A schematic block diagram of a quantum system 100 of at least two color centers is shown, wherein the system has a mechanism for individually addressing each color center. A crystalline material 102, such as diamond, is shown having two color centers 104a, 104b. A common color center in diamond is a nitrogen vacancy center, which includes a pair of nitrogen atoms and a lattice vacancy in the crystal. Although in Figure 1 106. The color centers are shown as circles in FIG. 106, but each color center has an axis which is the axis that aligns the nitrogen (or silicon, such as a silicon vacancy center) atom and the vacancy. The color centers are located along line 106. As described above, the color centers are addressed by applying an electromagnetic signal to the color center at the resonant frequency of the color center. The signal is applied perpendicular to the axis of the color center. Figure 1 An electromagnetic signal transmitter 108 is shown generating an electromagnetic signal at a frequency F. For NV centers, the resonant frequency is in the microwave range and the electromagnetic signal transmitter 08 transmits microwave radiation, other frequency ranges may be suitable for other types of color centers. The electromagnetic signal transmitter 108 may, for example, take the form of a wire (or wires) coupled to a controllable current source.

[0045] There are several possible ways to generate the electromagnetic field for activating the color centers. One example is by flowing an alternating current in a copper wire to generate an electromagnetic field of the desired frequency. Another possibility is to print conductive wires on top of (or inside) diamond or other crystalline substrates (such as silicon carbide) using photolithography. A third possibility is to irradiate the diamond with high-intensity ultrashort laser pulses, which results in graphitization of the diamond, where the graphite is conductive and can therefore act as a conductor and carry the current used to generate the desired electromagnetic field. The conductor can therefore be inside or outside the crystal, and the term includes a variety of physical structures. In general, a conductor refers to a carrier of an electrical signal that is capable of operating as an electromagnetic field transmitter.

[0046] In order to individually address each color center, a magnetic field generator 110 (external to the crystal 102) is used to generate a magnetic field that is applied to the color centers 104a, 104b. The term "magnetic field" gradient is associated with spatial variations (i.e., a magnetic field whose amplitude and / or orientation varies with position). The magnetic field may or may not be time-varying. As described in more detail with reference to FIG3, application of a magnetic field along the axis of the color center causes a splitting of the energy levels of the color center, which changes the associated resonant frequency (or multiple resonant frequencies) of the color center. The extent of the energy level splitting depends on the magnetic field generated, such that higher magnetic field strengths produce greater splitting between energy levels. The magnetic field generator 110 is therefore configured to generate a varying magnetic field such that the strength of the field applied to each color center is sufficiently different so that the color center has different resonant frequencies. The frequencies should be separated by a certain minimum amount to ensure that there is no overlap between the color centers, which depends on the material 102 and the color centers used, as described below. As Figure 1 As shown, a magnetic field generator causes a magnetic field B1 to be applied to color center 104a, which results in a resonant frequency F1, and another different magnetic field B2 is applied to color center 104b, causing the color center to have a resonant frequency 104b.

[0047] The present description relates to different magnetic fields (such as B1 and B2) at different locations of conscious interest. More precisely, in order to provide individual addressability, the projections of the magnetic field on the axis of the color center at those locations can be different (for example, if the color centers have mutually parallel axes, this can be achieved not only with magnetic fields that are different in amplitude at those locations, but also with magnetic fields that are differently oriented at those locations). Reference may be made herein to different magnetic field projections at different locations, and it should be understood that one of those magnetic field projections may be zero or substantially zero.

[0048] Unless otherwise stated or required by context, the term "resonance frequency" in the following description refers to the electron spin resonance frequency, where the resonance occurs between the energy levels of the electron spin states of the color center. As mentioned above, the magnetic field can be applied along the axis of the color center. However, this is generally not necessary; a magnetic field that is not parallel to the color center axis will still be able to excite the color center if the projection of the magnetic field on the color center axis has sufficient amplitude.

[0049] There are many possible ways to generate a varying magnetic field, for example by generating current within an arrangement of wire loops (coils), or using a Halbach array in a more complex configuration to produce a high intensity magnetic field in one area and a low intensity magnetic field in another area.

[0050] The quantum system 100 is operable to address individual color centers 104a, 104b by controlling the frequency of the field generated by the electromagnetic signal generator 108. Figure 1As shown, when a signal of frequency F is generated, where F is equal to the resonant frequency of F1 to the color center 104a, the color center is activated while the other color center is not activated because its resonant frequency is different from the frequency of the transmitted signal. Note that this description refers to a single resonant frequency associated with a color center. In reality, a color center can have multiple resonant frequencies associated with transitions between different pairs of energy levels, but for ease of understanding, the description focuses on one transition and one resonant frequency for each color center.

[0051] Selective activation of individual color centers allows the use of such arrangements, for example for quantum computing applications, where each color center acts as a qubit, allowing arrays of multiple color centers to implement multi-qubit gates.

[0052] Figure 2 A schematic block diagram of a quantum system having a "conventional" (non-quantum) computer processor 204 (or processors) coupled to a memory 202 (or memories) and a magnetic field generator 110 and an electromagnetic signal generator 108 for controlling the activation of color centers is shown. For example, the conventional processor 204 can be caused to implement a quantum computer program in the crystal 102 based on "conventional" (non-quantum) computer program instructions 203 that can be stored in the memory 202. When these instructions 203 are executed, the processor 202 is configured to generate electromagnetic signals of specific frequencies to enable activation and control of individual color centers, such as qubits. Multiple electromagnetic signal generators can be implemented, and in this case, the processor is configured to generate a corresponding signal at each electromagnetic signal generator 108, which allows multiple color centers 104a, 104b to be independently activated and controlled, as described above. This enables more complex operations to be performed, including quantum gates involving multiple qubits. Thus, a program implemented on a quantum computer comprising a collection of qubits implemented by colour centres may be effected by executing conventional computer instructions on computer processor 204 to control the electromagnetic signals required to activate individual qubits according to the quantum program.

[0053] Figure 3A is a schematic diagram showing the energy level splitting of a color center in the presence of an external magnetic field. Figure 3A The left side of shows an example energy level structure for a color center, such as the ground state of a nitrogen vacancy center. This contains three spin states: m s = 0, with antiparallel spin at the first energy level L0, m s = +1 and m s = -1, respectively, with two upward spins or two downward spins, with the same energy level L on the left ±1 Note that since energy and frequency are directly related, the levels L0 and L ±1 Labeled by frequency value. In NV center, L0 and L ±1The frequency is split at 2.87 GHz, so the transition between the 0 state and the +1 or -1 state can be triggered by an applied microwave field at 2.87 GHz.

[0054] Figure 3A The right side of the diagram shows the energy level structure of the color center in the presence of an external magnetic field B. The magnetic field in the direction of the color center axis induces energy levels m s = -1 and m s = +1, but does not affect m s =0 state. As shown in Figure 3, m s = 0 are at the same L0 energy level, since the 0 state is not affected by the external magnetic field. However, the +1 and -1 states split, with the distance between the energy levels being proportional to the external magnetic field. This phenomenon is known as the Zeeman effect, which affects the resonant frequency of spin states with non-zero angular momentum. Then, m s =-1 state is at the new energy level L -1 , and m s = +1 state has energy level L +1 The frequency change of the energy levels in response to a magnetic field depends directly on the magnetic field B. In the presence of an external magnetic field, the splitting between the +1 and -1 energy levels is 2γB, where γ is the electron gyromagnetic ratio, a known constant with a value of approximately 28 GHz / T. The stronger the applied magnetic field, the larger the splitting between the +1 and -1 energy levels. In this case, m s = 0 state and m s = -1 state has a resonant frequency with m s = 0 state and m s = +1 states. Any of these pairs of states may be selected, for example for use as a qubit. References herein to the resonant frequency of a color center may refer to a resonant frequency that matches any of these pairs of states.

[0055] Figure 3B An example graph of the resonant frequency of a color center in the presence of different external magnetic fields is shown. The resonant frequency for a color center can be measured, and such a graph can be generated by measuring the luminescence intensity of the color center for electromagnetic radiation of different frequencies, where the luminescence intensity has a sharp peak at the transition frequency of the spin state pair. As mentioned above, there are multiple possible spin state pairs for which transitions can occur, but this example only describes the resonant frequency of one such pair, for example m s = 0 state and m s = +1 state. Figure 3B As shown, in the absence of an external magnetic field, the luminescence has a resonance at a first frequency F0. For nitrogen vacancies in diamond, this frequency is about 2.87 GHz. Figure 3BThe curve shown in increases sharply around this frequency. In order to address different color centers individually by ensuring that they are activated by different resonance frequencies, it is important that the resonance curves associated with different color centers do not overlap with points where the resonance frequency of the first color center may also activate the second color center, and vice versa. The width of each curve can be characterized by a metric called the full width at half maximum (FWHM), where this has been measured for different color centers for electromagnetic radiation applied under different conditions. The FWHMΔv depends on factors such as the quality of the crystalline material and the power of the electromagnetic radiation, however a common value for nitrogen vacancy centers in high quality diamond is 100 kHz. In order to ensure separation between different color centers, a magnetic field difference resulting in at least 200 kHz (2Δv) is sufficient. The transition frequency for a color center for a given external magnetic field B is given by the following formula:

[0056] ΔF=F B3 +γB,

[0057] where F B0 is the transition frequency for a given color center in zero external magnetic field, and γ is the electron gyromagnetic ratio. Therefore, the difference in transition frequency between color centers in the presence of different external magnetic fields B1, B2 is:

[0058] γ(B1-B2).

[0059] Setting this frequency to 200 KHz, the magnetic field variation required between each colour centre to enable individual addressing can be easily calculated to be approximately 7 μT.

[0060] However, in Figure 3B In an effect not shown in , the resonant frequency of the color center is also affected by the nuclear spin state, which causes an effect called hyperfine splitting, resulting in three peaks instead of one for a given color center at a given external magnetic field. These effects have been observed and are well known from experiments. 14 For nitrogen vacancy centers of N atoms, a hyperfine splitting of about 2 MHz can be observed. To avoid any overlap between the energy levels of the different color centers caused by the superfine splitting, the frequency difference between the different color centers can instead be set to about 6 MHz, which, according to the above equation, results in a required magnetic field difference of about 0.2 mT between each color center. Alternatively, nuclear polarization techniques can be used to deplete two of the three ultrafine splitting resonances. The applied electromagnetic field also has an associated width, which for a continuous field depends on the line width of the electromagnetic field source, such as a wire in the examples described herein. This is in Figure 3B The illustration shows that with a given frequency F E The electromagnetic field actually spans a region with a width Δv E frequency range.

[0061] The electromagnetic field used to address the color centers can be applied as a continuous field or in the form of pulses (i.e., fields of short duration). Different applications require different types of fields to be applied. In the case of DC metrology, the above considerations are sufficient to determine the separation of the color center resonances. However, for applications using pulsed electromagnetic fields, such as pulsed metrology and pulsed qubit control, the width of the applied magnetic field should also be considered. For example, a pulse with a pulse width of time t will produce a broadened linewidth of about Δf~1 / t. Common examples of pulse widths for color centers can be in the range of tens of nanoseconds to a few microseconds, which means that for smaller pulse widths of MHz or for longer pulse widths of 100kHz, the effect can result in a peak separation of 10s in order to ensure that a field pulse targeting the resonant frequency of a given color center does not overlap with the resonant frequency of another color center.

[0062] The determined magnetic field difference between each color center that needs to be individually addressed is used to configure a magnetic field generator, such as one or more coils carrying current, to generate a magnetic field gradient that varies along the array of color centers at a rate of at least ΔB / center. The density of color centers in a given crystalline material can be used to determine the minimum change in magnetic field with a distance in the direction of the magnetic field gradient.

[0063] Figure 4 A schematic diagram of a nitrogen vacancy center in diamond is shown, which is an example of a color center that can be activated and controlled according to the above methods. Diamond includes carbon atoms having a diamond cubic crystal structure. In diamond, natural defects occur where the lattice structure becomes irregular, or one or more atoms are added to or replace carbon atoms in the lattice. The nitrogen vacancy center consists of a nitrogen atom 400 that replaces one of the carbon atoms 402 in the crystal structure and a lattice vacancy 404 (an atom that does not exist within the crystal structure). As shown in FIG. Figure 4 As shown, the additional electron 406 is located at the vacancy site. As described above, NV centers occur naturally, but can also be created using chemical vapor deposition and high pressure and high temperature techniques, as well as by implanting ions in diamond or irradiating diamond with ultrashort laser pulses. The axis of the NV center is the axis along which the nitrogen atoms and vacancies are located. As described above, for control of the color center, when the color center and the electromagnetic signal generator (e.g., a wire) are arranged so that the electromagnetic field is perpendicular to the axis of the color center, this allows the field to optimally drive the color center because the component of the field perpendicular to the axis of the color center is the effective field to activate the color center.

[0064] The color centers in the diamond lattice are not randomly oriented, their orientation is constrained due to the structure of the diamond. Due to the crystal structure of diamond, four different orientations of, for example, NV color centers can be encountered in diamond. These four orientations are repeated throughout the sample, so the position in terms of coordinates within the diamond is not critical. However, it is possible to preferentially grow one of the four possible orientations, so one can consider the best case scenario, where all color centers will point along the same axis.

[0065] After all the color centers are aligned along the axis, the diamond can be cut along different planes, typically {100}, {110} or {111}. If the diamond is cut along the {110} plane set, it is possible to have color centers oriented parallel to the surface of the diamond. {111} results in color centers with their axes perpendicular to the diamond surface and {100} will result in color centers oriented 45 degrees relative to the top surface of the diamond. For diamond, the color centers are aligned with one of three crystal planes or "cuts": (111), (110), (100). Different cuts can be used for different wire configurations (e.g., the wires are lithographically printed onto the diamond) to ensure that the electromagnetic field is optimally applied relative to the axis of the color center. For wires created inside the diamond, such as by ultrashort (femtosecond) laser irradiation, rather than printed on the surface of the diamond, the wires can be placed at specific locations and along specific directions relative to the color center axis, so there is greater flexibility. This also allows 3D geometry of color centers controlled by wires at different depths within the crystal.

[0066] The spin state of the color center can be initialized by laser irradiation. For nitrogen vacancy centers, for example, the state of the color center can be initialized by an optical process that excites the spin state, which later decays to the ground state m s =0. Figure 4 Also shown is a microwave signal for controlling an NV center by changing the center's electron spin state, where the microwave signal has a similar frequency to, for example, m s = 0 state and m s = The frequency of transitions between the +1 state and the ground state is the same as the frequency of transitions between the ground state and the ground state. The spin state of the NV center can be "read out" by measuring the photoluminescence intensity of the center, which depends on its spin state, where the ground state emission ratio is m s = ±1 state more photons (higher intensity).

[0067] Figure 5An example arrangement of color centers in a 2D array is shown, where multiple color centers are positioned along a set of vertical wires 500. As shown by the set of arrows, a varying magnetic field is applied to the system, with a larger magnetic field at the top of the array and a smaller magnetic field at the bottom, so that each color center along the vertical wires 500 experiences a different magnetic field. The component of the magnetic field applied parallel to the axis of the color center is the effective field to shift the energy level of the color center, so the required magnetic field determined for each color center of a given configuration should be applied parallel to the axis of the color center, or the magnetic field should be adjusted to ensure that the component of the external magnetic field parallel to the axis of the color center is the determined magnetic field required to adjust the resonant frequency of the given color center by the desired amount.

[0068] The external magnetic field is a static magnetic field applied in a direction parallel to the axis of the color center. As mentioned above for the specific example of NV centers in diamond, the magnetic field gradient required to ensure independent addressing of the color center can be calculated based on the transition frequency of the spin state of a given color center. Figure 5 In the example shown, the magnetic field gradient is implemented so that the magnetic field is the same at all points along the same vertical height, that is, the magnetic field varies only along the vertical axis. This can be achieved using a wire loop or a wire loop system carrying a current (such as a Helmholtz coil). For example, a Halbach array can be used to generate a magnetic field with high intensity in one area and a magnetic field with low intensity in another area. Figure 5 The magnetic field in is shown by arrows, which gradually decrease in size to show the gradient, with the highest magnetic field shown by the large arrow and the smallest magnetic field shown by the small arrow, the arrow indicating the direction of the external magnetic field.

[0069] Since each color center along a given conductor 500 experiences a different magnetic field, the resonant frequency of each color center 104 along each conductor 500 is different. The resonant frequency for each color center can be calculated based on the known magnetic field at the center according to the aforementioned formula. A given color center 104 can then be addressed by flowing an alternating current along the conductor 500 so as to create an electromagnetic field having the same frequency as the resonant frequency of that color center 104, while other color centers are not affected by this field due to the separation of resonances by the magnetic field gradient. In this way, a complete array of color centers can be individually addressed using one conductor per "column". Current can be run through adjacent conductors that produce different frequencies in order to activate different color centers that are located close to the conductor. More than one color center in a given column can be addressed by multiplexing, i.e., multiple electromagnetic fields are generated simultaneously from the same conductor, each having a different frequency corresponding to the multiple corresponding frequencies of the color centers to be addressed. The strength of the electromagnetic field is strongest near the conductor and decreases with distance from the conductor. To ensure that the field generated by one wire addresses only those color centers that are closest to that wire, the wire and color centers are separated by a minimum distance from the wires and color centers of the next "column" so that the electromagnetic field is weak enough that it does not cause activation of color centers at adjacent wires. A threshold ratio can be set below which activation of other color centers will be acceptable. For example, it can be determined that if an operation can tolerate a 1% error and it requires 100 operations to be completed using the electromagnetic field, the amplitude of the other color centers should be less than 1 / 10000 of the amplitude of the field of the target color center.

[0070] We will now describe certain configurations of wires designed to reduce crosstalk between color centers by confining the fields generated by the wires to only those intended to excite local color centers. For these configurations, denser arrangements of color centers are possible, enabling scaling of color centers to create larger quantum systems, such as quantum computers and quantum sensor arrays.

[0071] Figure 5 The exemplary color center array shown in generates a magnetic field as follows: a magnetic field that flows in a clockwise direction when viewed in the direction of current flow. The magnetic field extends radially outward from the wire 500, with the strength of the magnetic field inversely related to the distance from the wire 500. Therefore, the strongest field for a given wire 500 is experienced by the color center adjacent to the wire. However, there are still some fields at the next wire, which can cause crosstalk or decoherence between color centers, which is a problem for quantum computers and quantum sensors. One way to reduce this effect is to separate the wires and their corresponding color centers by a minimum distance so that the electromagnetic fields from adjacent wires are weak enough not to affect the addressing of the color centers. However, this limits the number of color centers that can be used in a given surface area of ​​the crystal, exposing problems when scaling to larger quantum systems that require many qubits or quantum sensors.

[0072] However, certain wire configurations can be achieved that enhance the field experienced by color centers targeted by a given wire or group of wires, while reducing the field experienced by other color centers. Figure 6 Three example wire configurations are shown that use wire pairs to generate different magnetic fields, some of which are particularly suitable for individually addressing color centers in an array. Note that in the following description and Figure 6 , the field is shown as a static field generated by a constant DC current along the wire 500 in a given direction. This is to illustrate the principle of how magnetic fields of equal amplitude generated by current carrying wires in different directions combine. However, as Figure 6 The resulting magnetic field pattern shown is independent of the frequency of the field. In fact, the amplitude and frequency of the fields generated by the different wires are the same.

[0073] A first wire configuration and the resulting magnetic field are shown in graph 600. In this configuration, according to well-known electromagnetic principles, the current flows in the positive direction (outward from the plane of the image), which will result in a magnetic field pointing counterclockwise from the perspective shown in the graph in the case of individual wires. The direction of the current along the wire is also indicated by a set of arrows below the graph, where the downward arrow represents a positive current J. Note that J is used in physics to represent current density, however the term "current" refers to current or current density interchangeably in this article. Current density and current are directly related to the cross-sectional area of ​​the current carrier (e.g., wire). Two wires that both flow current in the same direction are placed side by side with each other, and the counterclockwise magnetic field cancels in the area between the two wires and combines in the area outside the two wires because the magnetic field in the space between the two wires points in opposite directions, while the magnetic field in the area around the two wires points in the same direction. For this pair of wires, the total field is 1 / r for a single wire. 2 Rather than scaling with 1 / r, this reduces the effect of that pair in areas far from the wire. Three pairs of parallel current-carrying wires placed alongside each other have the weakest overall fields in the area between the two wires of each pair and between the wires of adjacent pairs, as the fields cancel at these points due to the parallel currents.

[0074] The wire configuration shown in the middle graph 602 provides a magnetic field that is further localized to the target area while reducing the field outside those areas. In this configuration, the wire pair is arranged with a first wire having a positive current and a second wire having a negative current. This is also called an antiparallel arrangement because the current density vectors are antiparallel, as shown by the arrows below the graph 602. The electric field lines are shown in the figure, and the magnetic field is the strongest for this arrangement in the area between the two wires, because for the first wire flowing current in the positive direction, the field points counterclockwise, so that the field in the area between the two wires points upward, and for the second wire of the pair, the current flows in the negative direction, so that the magnetic field is clockwise, and the field between the two wires of the pair also points upward, resulting in a stronger field in the area between the two wires of the pair. This arrangement can be applied to the color center positioned in the area between the pair, so as to maximize the field at the color center to enable addressing, where the field outside the area is not too intense. Compared with only a single wire pair, the field in the area between the wires of the adjacent pairs is also increased to give a stronger overall field because the currents of the nearest wires of the two pairs are antiparallel.

[0075] A third possible configuration is shown in graph 604. In this case, the two conductors of each pair are arranged to carry currents that are antiparallel with respect to each other but adjacent conductors belonging to different pairs carry parallel currents. This causes the fields between the conductors of the same pair to be increased, because antiparallel conductors produce fields with the same direction in the region between the conductors, while the fields between pairs are cancelled because adjacent conductors of adjacent pairs have the same current direction and these fields have opposite directions between the two conductors (i.e., at the midpoint between any two pairs of conductors in the configuration). This configuration provides the most efficient localization of the field to the desired area while minimizing the field experienced between the conductors, which reduces the risk of crosstalk and decoherence for a set of color centers placed in the region between the two antiparallel conductors of each pair.

[0076] Reference numerals 612, 614, 616 and 618 represent the first, second, third and fourth conductors (conductor 1 to conductor 4 shown in cross section), respectively. For simplicity, the description refers to the same conductors 612, 614, 616, 618 for each configuration 600, 602, 604. The geometric arrangement of conductors 1 to 4 is the same between these configurations 600, 602, 604; in this example, conductors 1 to 4 are substantially parallel to each other, wherein conductors 1 and conductor 2 (612, 614) form a first conductor pair, and conductors 3 and conductors 4 (616, 618) form a second conductor pair. Generally speaking, the conductors do not need to be parallel. In order to achieve the above-mentioned beneficial effects, the conductors of a given conductor pair only need to be reasonably sufficiently parallel to each other to generate a magnetic field of the desired form.

[0077] The localized effect is caused by a combination of constructive and destructive wave interference. Each conductor carrying an alternating current emits an oscillating electromagnetic field. With a pair of conductors carrying antiparallel currents of substantially equal magnitude, constructive interference between their respective magnetic fields occurs in a local region of the conductor pair, reinforcing the magnetic field. Outside the local region, destructive interference occurs (at least to some extent, together with the electromagnetic field "cancellation"), reducing crosstalk and decoherence effects between color centers located close to (or otherwise coupled to) different conductor pairs. In this example, each conductor pair acts as a single signal carrier, and each conductor includes a first conductor pair (612, 614) and a second conductor pair (616, 618).

[0078] In the second arrangement 602 and the third arrangement 604, in order to address the color center coupled to a given wire pair, both wires of the given wire pair are activated using antiparallel currents at the resonant frequency of the color center or at a resonant frequency close to the color center, resulting in the following signal: an electromagnetic activation signal localized at the resonant frequency of the color center or at a resonant frequency close to the color center (and its magnetic field component along the axis of the color center thereby causes the desired energy transition in the color center).

[0079] In the third configuration 604, the second conductor 614 of the first conductor pair (612, 614) is adjacent to the third conductor 616 of the second conductor pair (616, 618) because no other conductors are located in the region between the second and third conductors, and these conductor pairs are supplied with currents flowing antiparallel with respect to each other and antiparallel to the current in the other conductor of their respective conductor pairs (the first conductor 612 and the fourth conductor 618, respectively). This results in a set of (+J, -J, +J, -J) currents (where J can be positive or negative) through the four conductors, achieving maximum localization.

[0080] Figure 7 An example wire configuration suitable for addressing a 2D array of color centers 104 is shown, comprising a plurality of pairs of wires 500, each pair being separated by a distance of 200 μm. Note that the required distance between wire pairs depends on the characteristics of the wires and the strength of the generated field. However, as described above, the wire pair configuration causes the field outside the wire pair to decrease more rapidly than the field of a single wire, particularly for antiparallel wire pairs, thereby reducing crosstalk between color centers. Thus, for Figure 7 The configuration shown in Figure 5 Color centers can be placed in more tightly packed rows along a conductor pair than is possible with the single conductor configuration shown without causing crosstalk or decoherence.

[0081] In addition to reducing crosstalk between conductors / color centers, certain conductor configurations can also be used to achieve individual addressing of color centers by controlling the electromagnetic signals used to activate the color centers so that only one color center is addressed by a specific signal implemented within the conductor configuration.

[0082] The use of specialized geometry allows for the application of specific electromagnetic fields, such as circularly polarized fields only at specific target points (or lines) rather than larger volume areas. One example application in which circular polarization is useful is the use of color centers for magnetometry, i.e., the detection and measurement of magnetic fields. The use of such specialized geometry allows only those color centers placed at specific points (or lines) to experience circularly polarized fields and measure the magnetic field with optimal efficiency in that case.

[0083] One example configuration is an array of crossing wires, including a grid of vertical and horizontal wires, with an array of points where two wires cross. The system is arranged so that color centers are placed adjacent to each intersection point, such as directly below or above the intersection point, with each color center being addressable by a field generated at that intersection point, as described below. Note that, as described below, the field generated at an intersection point affects all color centers that are equidistant from the two wires crossing at that intersection point. If a given intersection point is positioned so that it is addressable by a field generated at that intersection point, then the term "adjacent" is applied herein to that given intersection point, so "adjacent" herein refers to color centers that are close enough to the xy position of the intersection point to be addressable by the field at the intersection point, as well as color centers at those points along the line that are equidistant from the two wires. Note that the spatial accuracy of the signal generated by the wire when addressing the color center depends on the line width of the signal generated and the frequency of the color center being addressed. In later references to Fig. 9 In the 3D configuration described, multiple color centers are placed along the z-axis at the same (x,y) coordinates as a given intersection point, where the field generated at that point is used to address any (or all) of those color centers. Each of the two wires generates an electromagnetic field of a certain amplitude, phase and direction that interferes with each other. The electromagnetic field from the two wires propagates outward with an amplitude and oscillating phase (given by the frequency of the field) that decreases with time. The direction of the electromagnetic field is given by the direction of propagation of the current inside the wire that generates the field.

[0084] The above description relates to addressing a color center by emitting a signal at the resonant frequency of the color center, where the color center has a different resonant frequency due to the application of a magnetic field gradient. However, a crossed wire configuration allows more complex manipulation of individual color centers without applying the same manipulation to other color centers along the same (multiple) wires. This allows direct addressing of individual color centers arranged in a 2D array with crossed wires by generating a combination of signals at different wires so that the desired field or combination of fields is produced only at the (multiple) intersections corresponding to the (multiple) color centers to be addressed, for example by generating a combination of signals that generates circularly polarized fields only at the intersections.

[0085] At the interference point, if the fields have the same amplitude and phase difference and mutually perpendicular directions, then the resulting field will be circularly polarized. The crossed wire geometry is such that every point of equal distance between the wires satisfies this condition. For example, below the intersection between two wires, the fields point perpendicularly to each other, but as one field moves laterally away from the intersection (parallel to one of the wires), the field from one wire has the same amplitude, but the field from the other wire decreases, so the fields no longer have the same amplitude, and the direction of the field "rotates away" from the intersection direction because the effect from the distant wire becomes negligible, and so the resulting field is no longer circularly polarized.

[0086] The benefit of addressing individual color centers by crossing wires is that for a system with a two-dimensional grid of six or more color centers, fewer wires than color centers are needed to achieve individual addressing. For larger systems, the effect becomes more pronounced. For example, an array of one million color centers arranged in a 1000x1000 configuration can be addressed by a grid of 2000 wires. Fig.10 This effect is shown for one color center arrangement 1002, two color center arrangement 1004, four color center arrangement 1006 and six color center arrangement 1008. In order to address a single color center by the effect of interacting fields at the intersection, a crossover point is required, which requires two conductors 1012a, 1012b that are crossed (i.e. not parallel).

[0087] Similarly, for the two color center arrangement 1004, three conductors are required to construct two intersections by which the two color centers can be addressed separately. Two substantially parallel conductors 1014b are crossed by a single non-parallel conductor 1014a, forming two intersections adjacent to the two color centers. Although conductor 1014a is shown as being perpendicular to conductor 1014b, this is not required.

[0088] For the four color center arrangement 1006, at least four conductors are required to create four cross points, and the four color centers can be addressed individually through the four cross points. Fig.10 In the example shown, two conductors 1016a are substantially parallel to each other, while the other two conductors 1016b are in the same plane that each crosses the two conductors 1016a. For the case of four color centers, the same number of conductors is required for the configuration in which the color centers are each addressed by a single conductor. However, as discussed above, a potential problem with addressing color centers by individual conductors (e.g., a set of parallel lines that are each positioned proximate to a different color center) is that a color center configured to be addressed by a particular conductor may also be addressed (although less efficiently) by a nearby conductor, thereby causing decoherence and crosstalk. For crossed conductors, as will be described in more detail below, the color centers are addressed by a field effect that is localized only to the intersection in the xy plane by controlling the timing, amplitude and / or phase of the field generated by the two associated conductors, and thus the effects of decoherence and crosstalk are minimized.

[0089] For the six color center arrangement 1008, to construct six separate intersections for the six color centers to be individually addressed, only five wires are required, two wires 1018a are substantially parallel to each other, and three wires 1018b are substantially parallel to each other and each wire crosses wire 1018a, as shown, all of the wires are located in the same plane. For any system with a number of color centers greater than 6, the color centers can be addressed by fewer wires than the number of color centers. This allows for scale-up of systems of color centers, such as for quantum computing applications, without requiring the number of wires to be scaled up, enabling systems with more color centers to be realized, where the number of wires is limited, for example, by the spatial constraints or properties of the wires and / or crystal materials in which they are realized.

[0090] The activation of the color centers by crossing conductors is described below.

[0091] Figure 8 A schematic diagram of a color center array having wires 500 arranged in a crossed wire configuration is shown, where each color center 104 is located near the intersection of two wires. Thus, each color center 104 is associated with a different combination of two wires (or a different combination of two wire pairs, see below). Note that the microwave field generated by the wires as described herein can be applied as a "pulse", i.e., an electromagnetic signal of very short duration. For applications such as quantum computing and metrology, the duration of the applied electromagnetic field typically varies from a few nanoseconds to a few microseconds for nitrogen vacancy color centers. By controlling the characteristics of the field generated by the wires, including phase, pulse timing, and pulse duration, it is possible to produce a specific effect at only one color center.

[0092] One way to create a specific effect at a color center is to time the pulse sequence generated by the wires configured so that only the target color center experiences the specific pulse sequence. Pulse sequences are used in quantum systems to manipulate electron spin states and prevent decoherence. An example pulse sequence is called an XY8 pulse sequence, which includes a repeating sequence of π pulses, where a π pulse is a pulse of a specific duration that causes a change in the electron spin state. π pulses are a well-known method of manipulating electron spin states and will not be described in detail herein. In the XY8 pulse sequence, eight pulses are repeated at π times. x and π y and are π pulses (and therefore have the same duration) that are out of phase with each other The sequence consists of the following pulses:

[0093] π x -π y -π x -π y -π x -π y -πx -π y ,

[0094] There is a predefined duration gap τ between each pair of pulses.

[0095] To address only a single target color center using such a sequence, one can use Figure 8 The cross-wire geometry shown in is used to generate pulses with different phases of two wires that cross at the point closest to the target color center being located. All pulses have the same frequency, which should be the resonant frequency of the target color center. With the plane of the cross-wires as the xy plane, the color center is located at positions equidistant from the two wires, such as at different heights at the corresponding (x, y) positions of the cross-wires, such as below the cross-wire array. Figure 8 The wires marked 500a and 500b in FIG. 1 cross only at the upper left color center 104. If the first x If a pulse is generated by wire 500b, the pulse is emitted to all color centers located along the length of the wire, and more weakly to color centers at other wires. However, in order to generate π at the target color center after time τ y The signal generated by the conductor 500b has a phase difference with the first pulse The second pulse is generated by the second wire so that it arrives at the target color center exactly after time τ. The distance each given pulse needs to travel and the speed of the color center and the electromagnetic wave are known, which means that the required time when the pulse needs to be generated by the second wire can be determined accurately. All other color centers along wire 500b experience pulse π y , but the pulses arrive at the target color center 104 only at the times defined by the pulse sequence. This is repeated for all pulses of the sequence, where the pulses are timed so that they arrive at the crossing point at regular time intervals τ.

[0096] A color center located at the intersection or at any point equidistant from the two wires along which the corresponding pulses are transmitted is affected by the pulse sequence. Since the pulses have such a short duration, the corresponding pulses arrive at the other color centers at different times, so that only the target color center receives the above-mentioned XY8 pulse sequence, and therefore only the spin state of the target color center is controlled according to the spin sequence.

[0097] Note that this method requires good control of the phase of the pulses generated by the respective wires to ensure that the phases differ by the required amount to produce π x and π y pulse.

[0098] The XY-8 pulse is a phase-sensitive pulse. This is because it contains π x and π ypulses, which can be achieved by phase shifting. A circularly polarized field can be generated using a similar technique to that described above, with zero phase difference between the fields from the two wires, instead of generating linearly polarized microwaves at the intersection. The frequency of the field corresponds to some wavelength, which is about 10 cm in the case of 3 GHz. At non-equidistant points, or at points that are not spaced apart by integer wavelength distances, the field will be elliptically (or circularly) polarized. In a typical realization of a quantum system of color centers in diamond, this wavelength is much higher than the distance between any color center and the intersection. A color center located adjacent to a intersection experiences a wavelength in π x and π y The correct phase difference between the pulses, while the other color centers will experience the elliptical field.

[0099] Note that the above method is only an example, and there are Figure 8 Other methods of manipulating and controlling the spin states of individual color centers by the fields generated by the crossed wire pairs 500 in the crossed wire geometry. In the above example, the wires 500 are configured to generate electromagnetic fields that differ in phase by exactly 1 / 200 Å only at the crossing points. This results in a circularly polarized microwave field being generated only at these points, while outside these points the field is linear or elliptical. This can be used to control the spin state of the color center at the (x, y) position corresponding to the intersection point.

[0100] While circular or linear polarization is one example effect that can be produced at a crossover point, the principle can be extended to other situations as well. For example, since the field orientation changes with movement away from the equidistant lines, it has an effect on the strength of the drive field for differently positioned color centers. The drive is greatest when the magnetic field produced by the wire is perpendicular to the color center axis, so the effect can be observed in cases where the color center axis is not perpendicular to the plane of the crossover wire geometry. For example, the timing between pulses can also be used. If the sequence requires that a pulse from wire 1 be achieved first, then a pulse from wire 2, or the pulses are very sensitive to timing, the wires divide the main substrate into parts that may or may not meet the appropriate conditions. Note that the latter case applies to electromagnetic field pulses produced by the wires, not to continuous wave applications. The above-described crossover wire geometry can also be used when it is necessary to separate continuous operations in specific time windows, where the electromagnetic pulses are timed at the two crossover wires so that continuous operations only occur at the crossover point.

[0101] Both quantum metrology and quantum computing have applications that utilize similar pulses (such as the pulse train described above). Crossed wire geometry is useful for producing these effects for individual color centers for both quantum computing and quantum metrology. An example quantum computing application is a full quantum gate, in which polarization effects can be produced at the intersection due to the phase relationship between the electromagnetic fields generated by the wires. In order to achieve this with maximum efficiency, the color centers are placed at equidistant lines or at multiples of the wavelength. However, as described above, for microwaves, the wavelength is in the centimeter range, making this wavelength impractical for a high density of color centers. In this example application, the gate will therefore be selectively applied to the color centers placed at equidistant points between the two wires.

[0102] Other methods can be used to control Figure 8 The spin state is controlled by one or more of the phase, timing, and duration of the electromagnetic field generated by the wires 500 of the crossed wire configuration shown in . Multiple color centers can be addressed simultaneously by selecting wire pairs that cross at the locations of the target color centers and generating pulses from these wires with the desired timing to generate a field or pulse sequence that controls the spin state of only those color centers.

[0103] The crossed wire geometry can be used to achieve individual addressing of color centers within the 2D xy plane. Note that this 2D addressability can be achieved without the use of magnetic field gradients. This can be extended to three dimensions by introducing a magnetic field gradient ΔB as described above to control the resonant frequencies of color centers located at different heights along the z dimension, so that the pulse train generated at a given frequency at the intersection is not only limited to the color centers at the same (x, y) location as the intersection, but is also limited in the z direction to the color centers that experience the external magnetic field so that their resonant frequencies match the frequency of the transmitted pulses.

[0104] It should also be noted that although Figure 8 For simplicity, a single conductor 500a, 500b is shown, but Figure 8 The geometry can be matched by replacing each conductor 500a, 500b with a conductor pair. Figure 6 A geometric combination of antiparallel currents (e.g., pulsed currents) are selectively generated to achieve addressability with reduced crosstalk / decoherence in 2D (without magnetic field gradient) or 3D (with magnetic field gradient in the perpendicular direction). In this case, each color center is coupled to a unique pair of wires in the wire pairs (four wires in total, but each wire pair acts as a single signal carrier).

[0105] Wire 500a and wire 500b are shown as being substantially perpendicular to each other, but generally speaking, it is sufficient that they are not parallel so that they can cross each other (forming a crossover point). Then, wire 500a and wire 500b are substantially straight, but this is generally not required (in some cases, the curved wires can cross each other more than once and thus form more than one crossover point).

[0106] Fig. 9 An example 3D array is shown having color centers 104 arranged in a 3D array, with a 2D cross-wire configuration layered above the array of color centers. For clarity, only one "face" of the configuration is shown in the zx plane to illustrate the color centers in three dimensions. In reality, the array of color centers includes a color center at every location of the 3D grid. As described above, various methods can be used to generate electromagnetic field pulses from the configured cross-wires 500 in order to address a color center at a specific xy location in the 2D grid. However, in 3D, these pulses will also address the color center at the same xy location but at a different height. However, as described above, an external magnetic field gradient can be used to adjust the resonant frequency of the color center along the z-axis. This is in Fig. 9 , which is shown by arrows that decrease in size with height. The magnetic field separates the spin energy levels of the color centers so as to adjust the transition frequency to change from one spin state to another. The pulse sequence only affects the color centers that have a resonant frequency that matches the frequency of the pulse. This means that a pulse sequence generated at one of the intersections only affects the color center at the (x, y) position corresponding to the position of the intersection and at the z position corresponding to the frequency of the pulse, making it possible to address individual color centers within the 3D array in the same way without having to manipulate the spins of other surrounding color centers.

[0107] Figure 6 Three 2D arrays of vertically stacked color centers (layers) are shown. In general, 3D geometries can have two or more layers. The color centers in different layers can be formed in different crystals, for example, with wires printed on the surface(s) of the crystal, or formed on the surface of the crystal (e.g., graphene channels created on the surface). It is also possible to have multiple layers of color centers in the same crystal, with wires formed in the crystal itself (e.g., like graphene channels running through the crystal).

[0108] The term magnetic gradient is used broadly to denote any spatially varying magnetic field. The magnetic field can have many possible spatial configurations. In general, if the magnetic field at a given color center in a given layer is different from the magnetic field at its closest color center in an adjacent array (or more precisely, the projection of the magnetic field on their respective axes), this will be sufficient to functionally isolate these color centers from each other. As already noted, the magnetic field may have a value of zero, or approximately at one color center or a subset of color centers (what is important is the relative difference in the resonant frequencies between nearby color centers, and therefore the difference in the projection of the magnetic field at those color centers).

[0109] Fig.11 A schematic diagram showing an example configuration of a color center, the color center shown includes two layers, each layer having six color centers, wherein the set of crossing wires is based on the above reference Fig.10 The six color center configurations 1008 described are in the plane of each layer. The top layer has three wires 1114a that are substantially parallel to each other, and two other wires 1112a that are substantially parallel to each other and each cross each of the wires 1114a to form a set of six intersections as shown. The six color centers are positioned adjacent to each of the intersections. Similarly, the bottom layer has a set of three wires 1114b that are all substantially parallel to each other and another set of two wires 1112b that are parallel to each other and not parallel to the wire 1114b so that they each cross each of the wires 1114b to form six intersections.

[0110] As described above, sending pulses in a particular way along the crossing wires has the effect of being localized to points equidistant between the two wires, so that adjacent color centers of the same layer are not addressed by a given field or the combination of fields caused by a selected pair of wires. However, in a 3D configuration as shown, there is a risk that the field generated at a given crossing point addresses color centers at the same xy position (or otherwise equidistant between the two wires) in different layers. As described above with reference to Fig. 9 As described, this effect can be counteracted by generating an external magnetic field that varies along the z direction, as shown. As described above, different external magnetic fields projected onto the color center axes of different color centers cause the color centers to have different electron spin resonance frequencies. By generating a varying magnetic field such that a magnetic field B1 is projected onto the color centers of the top layer and a different magnetic field B2 is projected onto the color centers of the bottom layer, the color centers of the top layer (e.g., color center 1104a) are addressable by a field of a first frequency f1, and the color centers of the bottom layer (e.g., color center 1104b) are addressable by a field of a second frequency f2 having a frequency f2. Therefore, if an intersection adjacent to color center 1104a is generated with a field at frequency f1 (e.g., a pulse or pulse sequence as described above) along the two wires that cross at the intersection, it only addresses color center 1104a because the effect is only localized to that location in the xy plane due to the effect of the crossing wires as described above, and is only localized to the color centers of the top layer because only those color centers can be addressed by a given frequency. Different color centers of the bottom layer can be simultaneously activated by generating a field with a frequency f2, the field being generated at this frequency by the currents I3 and I4.

[0111] Note that "individually addressing" does not necessarily mean that only one color center is addressed at a given time. As described above, multiple color centers at different z locations can be addressed simultaneously by simultaneously generating electromagnetic field pulses of multiple frequencies to match the respective resonant frequencies of the color centers. Similarly, multiple color centers in the same xy plane can be addressed by generating pulses from multiple corresponding pairs of conductors at the timing required according to a given addressing method.

[0112] The first alternating current can cause the first conductor to emit a first electromagnetic field, and the second alternating current can cause the second conductor to emit a second electromagnetic field. A localized electromagnetic field can be created in the region via constructive interference between the first and second electromagnetic fields in the region adjacent to the conductor and destructive electromagnetic field interference between the first and second electromagnetic fields outside the region.

[0113] According to one aspect disclosed herein, there is provided a device comprising: a crystal; at least three first conductors, which are substantially parallel to each other; at least two second conductors, which are substantially parallel to each other, each second conductor being non-parallel to each first conductor, so that each second conductor crosses each first conductor to form at least six intersections; and at least six color centers, each color center being positioned within the crystal and adjacent to a different one of the at least six intersections.

[0114] According to another aspect, a device is provided, comprising: a crystal; at least three first conductors arranged substantially parallel to each other; at least two second conductors arranged substantially parallel to each other, each second conductor being arranged non-parallel to each first conductor so that each second conductor crosses each first conductor to form at least six intersections; and at least six color centers, each color center being positioned within the crystal and adjacent to a different one of the at least six intersections.

[0115] In an embodiment, the device includes a current source coupled to each first conductor and each second conductor and controllable to generate a simultaneous current in any first conductor of the at least three first conductors and any second conductor of the at least two second conductors, such that the simultaneous current activates the color center adjacent to the intersection between the first conductor and the second conductor.

[0116] In an embodiment, the current source can be controlled to generate: a first current pulse in any first conductor of the at least three first conductors; and a second current pulse in any second conductor of the at least two second conductors, the second current pulse being timed so as to coincide with the first current pulse at the intersection between the first conductor and the second conductor.

[0117] In an embodiment, the first conductor and the second conductor are substantially in a first plane, wherein each color center is adapted to receive a magnetic field, the device comprising:

[0118] At least six other color centers are located in a second plane substantially parallel to the first plane, each of the other color centers being positioned adjacent to a different intersection of the at least six intersections and being adapted to receive the magnetic field such that a first projection of the magnetic field on the color center axis of each color center is different from a second projection of the magnetic field on the color center axis of the other color center that is closest thereto.

[0119] In an embodiment, the at least three first conductors are basically in a first plane, wherein each color center is suitable for receiving a magnetic field, and the device includes: at least three third conductors, which are basically parallel to each other in a second plane, and the second plane is basically parallel to the first plane and adjacent to the first plane in a direction perpendicular to the first plane; at least two fourth conductors, which are basically parallel to each other, and each fourth conductor is not parallel to each third conductor, so that each fourth conductor crosses each third conductor to form at least six other intersections; and at least six other color centers, each other color center is positioned adjacent to a different other intersection among the at least six other intersections, and is suitable for receiving the magnetic field, so that a first projection of the magnetic field on the color center axis of each color center is different from a second projection of the magnetic field on the color center axis of the other color center closest to it.

[0120] In an embodiment, the apparatus comprises a magnetic field generator and is configured to generate a magnetic field.

[0121] In an embodiment, the device includes: a current source coupled to each first wire and each second wire, the current source controllable to generate a simultaneous alternating current at a first frequency in any first wire of the at least three first wires and any second wire of the at least two second wires, so that the first simultaneous current activates the color center at the intersection of the first wire and the second wire, the first frequency substantially matches a first electron spin resonance frequency of the color center adjacent to the intersection, the first electron spin resonance frequency being caused by the first projection of the magnetic field on the color center axis of the color center, wherein the first frequency is different from a second electron spin resonance frequency of the other color center adjacent to the intersection of the first wire and the second wire, and the simultaneous alternating current therefore does not activate the other color center.

[0122] In an embodiment, the device includes: a current source, coupled to each first wire, each second wire, each third wire and each fourth wire, and controllable to: generate a first simultaneous alternating current at a first frequency in any first wire among the at least three first wires and any second wire among the at least two second wires, so that the first simultaneous current excites the color center at the intersection of the first wire and the second wire, the first frequency substantially matches a first electron spin resonance frequency of the color center adjacent to the intersection, the first electron spin resonance frequency being caused by the first projection of the magnetic field on the color center axis of the color center, and generate a second simultaneous alternating current at a second frequency in any third wire among the at least three third wires and any fourth wire among the at least two fourth wires, so that the second simultaneous current excites the other color center adjacent to the other intersection of the third wire and the fourth wire, the second frequency substantially matches a second electron spin resonance frequency of the other color center adjacent to the other intersection.

[0123] In an embodiment, the device includes another crystal, wherein the at least six other color centers are located in the other crystal, and each first wire, each second wire, each third wire and each fourth wire are outside the crystal and the other crystal or formed on the surface of the crystal or the other crystal.

[0124] In an embodiment, the at least six other color centers are located in the crystal, and each first conductive line, each second conductive line, each third conductive line, and each fourth conductive line are formed in the crystal.

[0125] In an embodiment, the apparatus comprises: for each first conductive line, a further first conductive line located adjacent to the first conductive line, the first conductive line and the further first conductive line being adapted to receive respective first currents flowing substantially antiparallel to each other; and

[0126] For each second conductive line, a further second conductive line is located adjacent to the second conductive line, the second conductive line and the further second conductive line being adapted to receive second respective currents flowing substantially antiparallel to each other.

[0127] In an embodiment, the apparatus comprises a current source coupled to each first conductive line, each other first conductive line, each second conductive line and each other second conductive line and controllable to generate a respective first current and a respective second current.

[0128] In an embodiment, the current source may be controlled to generate:

[0129] a first alternating current in any first conductor of the at least three first conductors;

[0130] A second alternating current in any second conductor of the at least two second conductors, wherein the phase of the current is controlled such that a circularly polarized electromagnetic field is generated at the intersection between the first conductor and the second conductor.

[0131] In an embodiment, at least six color centers are each configured to provide a qubit.

[0132] In an embodiment, at least six color centers are each configured to operate as a quantum sensor.

[0133] According to another aspect disclosed herein, a quantum system is provided, comprising: a crystal; at least three first wires, which are substantially parallel to each other; at least two second wires, which are substantially parallel to each other, each second wire being non-parallel to each first wire, so that each second wire crosses each first wire to form at least six intersections; and at least six color centers, each color center being positioned within the crystal and adjacent to a different intersection among the at least six intersections; a current source, coupled to each first wire and each second wire; and a memory, containing computer-readable instructions; and a processor, coupled to the memory, wherein the processor is configured to execute the computer-readable instructions, which are configured to, when executed by the processor, cause the processor to: control the current source to generate a simultaneous current in any first wire of the at least three wires and any second wire of the at least two second wires, so that the simultaneous current activates the color center adjacent to the intersection between the first wire and the second wire.

[0134] In an embodiment, the at least three first wires are substantially in a first plane, and the quantum system further comprises: a magnetic field generator; and at least three third wires, which are substantially parallel to each other in a second plane, the second plane being substantially parallel to the first plane and adjacent to the first plane in a direction perpendicular to the first plane; at least two fourth wires, which are substantially parallel to each other, each fourth wire being non-parallel to each third wire, so that each fourth wire intersects with each third wire to form at least six other intersections; and at least six other color centers, each other color center being positioned adjacent to a different other intersection of the at least six other intersections, wherein the computer readable instructions are configured to, when executed by the processor, cause the processor to control the magnetic field generator to generate a magnetic field, so that a first projection of the magnetic field on the color center axis of each color center is different from a second projection of the magnetic field on the color center axis of the other color center closest thereto.

[0135] According to another aspect disclosed herein, a method for addressing a color center in a crystal is provided, the method comprising: generating a first current in a first conductor among at least three first conductors that are substantially parallel to each other; and generating a second current in a second conductor among at least two second conductors that are substantially parallel to each other, each second conductor being non-parallel to each first conductor, so that each second conductor intersects with each first conductor to form at least six intersections, wherein the first current and the second current are simultaneous, so that the simultaneous current activates the color center adjacent to the intersection between the first conductor and the second conductor.

[0136] A "current source" may refer to an internal component of a device (such as a circuit or group of circuits) that is coupled to (multiple) conductors and is connectable to a power source (such as a battery or a group of batteries, a power socket or outlet, etc.) and that when connected to the power source can be controlled to provide current to a given conductor or conductors.

[0137] It should be understood that the computer processor or processor 204 may actually be provided by a single chip or integrated circuit or multiple chips or integrated circuits, optionally provided as a chipset, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), a graphics processing unit (GPU), etc. The chip or chip may include circuits (and possible firmware) for embodying at least one or more of a data processor or processor, a digital signal processor or processor, a baseband circuit, and a radio frequency circuit, which can be configured to operate according to exemplary embodiments. In this regard, the exemplary embodiments may be implemented at least in part by computer software stored in a non-transitory memory and executable by a processor, or by hardware or by a combination of tangibly stored software and hardware (and tangibly stored firmware). Some aspects of the embodiments described herein with reference to the accompanying drawings include computer processes executed in a processing system or processor. Some aspects also extend to computer programs suitable for putting the present invention into practice, especially computer programs on or in a carrier. The program may be in the form of non-transitory source code, object code, code intermediate source and object code, such as in a partially compiled form, or in any other non-transitory form suitable for use in the implementation of a process according to the present invention. The carrier may be any entity or device capable of carrying a program. For example, the carrier may include a storage medium such as a solid state drive (SSD) or other semiconductor-based RAM; a ROM such as a CD ROM or a semiconductor ROM; a magnetic recording medium such as a floppy disk or a hard disk; a typical optical memory device; and the like. Reference is made herein to a data storage device for storing data. This may be provided by a single device or by a plurality of devices. Suitable devices include, for example, a hard disk and a non-volatile semiconductor memory (e.g., a solid state drive or an SSD). Although at least some aspects of the embodiments described herein with reference to the accompanying drawings include computer processes executed in a processing system or a processor, the invention also extends to a computer program suitable for putting the invention into practice, in particular a computer program on or in a carrier. The program may be in the form of a non-transitory source code, an object code, a code intermediate source and object code, such as in a partially compiled form, or in any other non-transitory form suitable for use in the implementation of the process according to the invention. The carrier may be any entity or device capable of carrying the program. For example, the carrier may include a storage medium such as a solid state drive (SSD) or other semiconductor-based RAM; a ROM such as a CD ROM or a semiconductor ROM; a magnetic recording medium such as a floppy disk or a hard disk; a typical optical memory device; and the like. The examples described herein are to be understood as illustrative examples of embodiments of the invention. Further embodiments and examples are contemplated.Any feature described with respect to any one example or embodiment may be used alone or in combination with other features.In addition, any feature described with respect to any one example or embodiment may also be used in combination with one or more features of any other example or embodiment in the example or embodiment or any combination of any other example or embodiment. In addition, equivalents and modifications not described herein may also be used within the scope of the present invention, which are defined in the claims.

[0138] It should be understood that the above embodiments are disclosed only as examples. Once given the disclosure herein, other variations or uses may become apparent to those skilled in the art. The scope of the present disclosure is not limited by the above embodiments, but only by the appended claims.

Claims

1. A device comprising: Crystals; At least three first conductive wires are substantially parallel to each other; At least two second conductors are substantially parallel to each other, and each second conductor is not parallel to each first conductor, so that each second conductor crosses each first conductor to form at least six intersections; as well as At least six color centers are each positioned within the crystal and adjacent to a different one of the at least six intersections.

2. The device according to claim 1, comprising: A current source is coupled to each first conductor and each second conductor and is controllable to generate a simultaneous current in any first conductor of the at least three first conductors and any second conductor of the at least two second conductors, so that the simultaneous current activates the color center adjacent to the intersection between the first conductor and the second conductor.

3. The apparatus of claim 2, wherein the current source is controllable to generate: a first current pulse in any first conductor of the at least three first conductors; and A second current pulse in any second conductor of the at least two second conductors, the second current pulse being timed to coincide with the first current pulse at the intersection between the first conductor and the second conductor.

4. The device according to claim 1, 2 or 3, wherein the first conductor and the second conductor are substantially in a first plane, wherein each color center is adapted to receive a magnetic field, the device comprising: At least six other color centers in a second plane substantially parallel to the first plane, each other color center being positioned adjacent to a different intersection of the at least six intersections and being adapted to receive the magnetic field such that a first projection of the magnetic field on the color center axis of each color center is different from a second projection of the magnetic field on the color center axis of the other color center closest thereto.

5. The device according to claim 1, 2 or 3, wherein the at least three first conductors are substantially in a first plane, wherein each color center is adapted to receive a magnetic field, the device comprising: at least three third conductive lines, which are substantially parallel to each other in a second plane, wherein the second plane is substantially parallel to the first plane and is adjacent to the first plane in a direction perpendicular to the first plane; at least two fourth conductors, which are substantially parallel to each other, and each fourth conductor is not parallel to each third conductor, so that each fourth conductor crosses each third conductor to form at least six other intersections; as well as At least six other color centers, each other color center is positioned adjacent to a different other intersection point among the at least six other intersection points and is suitable for receiving the magnetic field so that a first projection of the magnetic field on the color center axis of each color center is different from a second projection of the magnetic field on the color center axis of the other color center closest to it.

6. The device according to claim 4 or 5, comprising: The magnetic field generator is configured to generate the magnetic field.

7. The device according to claim 6, when referring to claim 4, comprising: a current source coupled to each first conductor and each second conductor, the current source controllable to generate simultaneous alternating currents at a first frequency in any first conductor of the at least three first conductors and any second conductor of the at least two second conductors, such that the first simultaneous currents excite the color center at the intersection of the first conductor and the second conductor, the first frequency substantially matching a first electron spin resonance frequency of the color center adjacent to the intersection, the first electron spin resonance frequency being caused by the first projection of the magnetic field on the color center axis of the color center, Wherein the first frequency is different from a second electron spin resonance frequency of the other color center adjacent to the intersection of the first conductor and the second conductor, the simultaneous alternating current therefore does not excite the other color center.

8. The device according to claim 6, when referring to claim 5, comprising: a current source coupled to each first conductor, each second conductor, each third conductor, and each fourth conductor, and controllable to: generating a first simultaneous alternating current at a first frequency in any first conductor of the at least three first conductors and in any second conductor of the at least two second conductors such that the first simultaneous current excites the color center at the intersection of the first conductor and the second conductor, the first frequency substantially matching a first electron spin resonance frequency of the color center adjacent to the intersection, the first electron spin resonance frequency being caused by the first projection of the magnetic field onto the color center axis of the color center, and A second simultaneous alternating current is generated at a second frequency in any third conductor of the at least three third conductors and in any fourth conductor of the at least two fourth conductors, such that the second simultaneous current activates the other color centers adjacent to the other intersections of the third conductors and the fourth conductors, and the second frequency substantially matches a second electron spin resonance frequency of the other color centers adjacent to the other intersections.

9. The device according to any one of the preceding claims, comprising: For each first conductive line, another first conductive line is located adjacent to the first conductive line, the first conductive line and the other first conductive line being adapted to receive respective first currents flowing substantially antiparallel to each other; as well as For each second conductive line, a further second conductive line is located adjacent to the second conductive line, the second conductive line and the further second conductive line being adapted to receive second respective currents flowing substantially antiparallel to each other.

10. The device according to claim 9, comprising: A current source is coupled to each first conductive line, each other first conductive line, each second conductive line and each other second conductive line and is controllable to generate a respective first current and a respective second current.

11. An apparatus according to claim 2 or any claim dependent thereon, wherein the current source is controllable to generate: a first alternating current in any first conductor of the at least three first conductors; A second alternating current in any second conductor of the at least two second conductors, wherein the phase of the current is controlled such that a circularly polarized electromagnetic field is generated at the intersection point between the first conductor and the second conductor.

12. The apparatus of any preceding claim, wherein the at least six colour centres are each configured to provide a qubit.

13. A quantum system comprising: Crystals; At least three first conductive wires are substantially parallel to each other; At least two second conductors are substantially parallel to each other, and each second conductor is not parallel to each first conductor, so that each second conductor crosses each first conductor to form at least six intersections; as well as at least six color centers, each color center being positioned within the crystal and adjacent to a different one of the at least six intersections; a current source coupled to each first conductor and each second conductor; as well as a memory containing computer-readable instructions; as well as a processor coupled to the memory, wherein the processor is configured to execute the computer-readable instructions, which, when executed by the processor, are configured to cause the processor to: The current sources are controlled to generate simultaneous currents in any first conductive line of the at least three conductive lines and any second conductive line of the at least two second conductive lines such that the simultaneous currents activate the color center adjacent to the intersection between the first conductive line and the second conductive line.

14. The quantum system according to claim 13, wherein the at least three first wires are substantially in a first plane, the quantum system further comprising: Magnetic field generator; as well as at least three third conductive lines, which are substantially parallel to each other in a second plane, wherein the second plane is substantially parallel to the first plane and is adjacent to the first plane in a direction perpendicular to the first plane; at least two fourth conductors, which are substantially parallel to each other, and each fourth conductor is not parallel to each third conductor, so that each fourth conductor crosses each third conductor to form at least six other intersections; as well as at least six other color centers, each other color center being located adjacent to a different other intersection point of the at least six other intersection points, The computer-readable instructions are configured to, when executed by the processor, cause the processor to control the magnetic field generator to generate a magnetic field such that a first projection of the magnetic field on the color center axis of each color center is different from a second projection of the magnetic field on the color center axis of the other color center closest thereto.

15. A method of addressing a color center in a crystal, the method comprising: generating a first current in a first conductive line among at least three first conductive lines that are substantially parallel to each other; as well as A second current is generated in a second conductor among at least two second conductors that are substantially parallel to each other, each second conductor being non-parallel to each first conductor so that each second conductor crosses each first conductor to form at least six intersection points, wherein the first current and the second current are simultaneous so that the simultaneous current activates the color center adjacent to the intersection point between the first conductor and the second conductor.

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