Physical medium comprising color center for use in quantum system

Abstract

An apparatus comprising: a crystal; and a color center within the crystal, and the color center is adapted to receive a magnetic field such that a projection of the magnetic field on a color center axis of the color center causes a change in an electron spin resonance frequency of the color center, and an electromagnetic signal having a frequency substantially matched to the electron spin resonance frequency of the color center, the electron spin resonance frequency is changed by the projection of the magnetic field on the color center axis.

Description

Technical Field

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

[0002] Color centers are defects in diamond and other crystals that have a wide range of applications due to their physical properties, including quantum metrology and quantum computing. Such defects can 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 electromagnetic field can cause a change in the spin state of the color center. For example, the electromagnetic field can be generated by flowing an alternating current through a wire, inducing 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 metrology, thermal metrology, strain sensing), information processing, and communications. One of its most promising applications is quantum computing, where color centers have demonstrated multi-qubit gates, quantum entanglement, quantum key distribution, etc. For example, in quantum computing applications, a color center (or group of color centers) operating as (multiple) qubits can be activated in order to apply specific quantum computing operations (such as quantum state transformation or quantum state measurement).

[0005] For example, in quantum metrology applications, a color center (or group of color centers) operating as a (multiple) sensor can be activated to capture a sensor measurement 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, such as a magnetic field. If, instead of a selected group of color centers, all color centers / sensors are excited at the same time, 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 color centers. For example, in quantum metrology and quantum computing applications, it is useful to be able to individually control each sensor or qubit. As described above, color centers can be activated by applying an electromagnetic field at or sufficiently close to 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 transitions between electron spin states (typically at different energy levels) in a color center. In an array of multiple color centers, each color center typically has the same resonant frequency, resulting in difficulties in addressing individual color centers. The individual addressability of color centers can be achieved in a variety of ways, but not all of these ways are sufficiently scalable to practical deployment.

[0007] This summary is provided to introduce some concepts in a simplified form, which will be further described in the following detailed description. This summary is not intended to identify the 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 solve any or all of the disadvantages described herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] To assist in understanding the present disclosure and to show how embodiments may be implemented, reference is made to the accompanying drawings by way of example, 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] FIG3 a shows the splitting of the energy levels of a color center by an external magnetic field;

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

[0013] Figure 4 A schematic diagram of a nitrogen vacancy center in diamond is shown;

[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 example color center array having a wire pair configuration is shown;

[0017] Figure 8 shows an example color center array in which each color center is addressable by a pair of crossing wires; 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;

[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 said to be coupled to a conductor (or to a point of intersection between two crossing conductors), and the term includes situations where the color center is located sufficiently close to the conductor that it can be activated by activating the conductor (e.g., by generating a current in the conductor causing the conductor to emit an electromagnetic signal). For the avoidance of any doubt, this includes situations where the color center is separated from the conductor 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 conductor to which it is coupled. A device may refer to the crystal itself, or to a crystal in combination with one or more other elements (such as conductors). A device may be a complete device or other system, or merely a component (or collection of components) for such a system / device. A conductor refers to any structure capable of carrying an electrical signal that results in the emission of an electromagnetic signal, and includes external or internal conductors, conductors printed on or otherwise attached to a crystal, integrated conductors (e.g., graphene channels formed in a crystal), etc.

[0023] Color centers may be referred to as being "individually addressable" when they can be controlled with a degree of independence. This includes situations where any given color center can be activated without having any effect on the other(s) color centers (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 may be individually applied to any desired color center in a controllable manner (as opposed to situations where the desired operation may only be applied to all or a fixed subset of the color centers within the physical medium).

[0024] For some color centers, such as nitrogen-vacancy color centers, external magnetic fields are used to lift the degeneracy between their energy levels, as described in more detail later, allowing an oscillating 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. Nitrogen-vacancy centers are an example of this, where 3 A 2 The ground state m s =±1 spin projection state is degenerate in the external magnetic field.

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

[0026] In principle, any given color center can be addressed individually by activating its associated emitter. However, this requires that each color center has a separate, individually controllable emitter (e.g., wire). This limitation poses a challenge to scaling to larger numbers of color centers, since a large number of separate wires need to be created to generate 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 corresponding 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 microwave or radio frequency frequencies. Spins can be selected by applying a field whose frequency matches the energy difference (or splitting) between the nuclear energy levels. The splitting frequency can be found via a frequency scan, for example while the fluorescence emitted from the nucleus is observed. When the applied frequency matches the splitting frequency, a change in the emitted fluorescence can be observed, which change is generally referred to as resonance. According to the Zeeman effect, resonance is sensitive to an external magnetic field if the nucleus has non-zero angular momentum.

[0029] The following description considers color centers with various applications in quantum devices / systems (e.g., 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 experience electron spin energy level shifts based on an external magnetic field based on the electron gyromagnetic ratio (about 28 GHz / T), as described in further detail below, while nuclear-based systems typically experience shifts of less than three orders of magnitude, on the order of MHz / T. As a result, a larger magnetic field will be required to separate the resonances in the case of nuclear spins, which makes it impractical to apply a magnetic field gradient for individual addressing in a system with a high density of nuclear spins (as described in more detail below). Furthermore, the lower frequency of the electromagnetic signal directed to the nuclear spin system 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 a lower frequency system.

[0030] Despite decades of research on color centers, challenges remain when it comes to individually addressing them, a prerequisite for scaling up single color-center-based sensors and qubits to more complex sensor or qubit arrays, such as those used in imaging arrays or quantum computer chips.

[0031] The challenge with individual addressing is that color centers are most often addressed using structures that generate microwave fields that radiate over a large area. As a result, when addressing of a single color center is attempted, the rest of the color centers in its area are also driven (although not as strongly) by the same microwave field, which leads to decoherence and / or crosstalk between the color centers, both of which are undesirable for the application.

[0032] The solution is to exploit the intrinsic magnetic field dependence of the color center energy level transition frequencies (resonances) in combination with a multi-color center microwave irradiation geometry to individually address the color centers.

[0033] This article describes a quantum system that is able to address a single color center in an arrangement of multiple color centers by creating a magnetic field gradient so that the magnetic field applied to different color centers is different. This causes each color center to have a different electron spin resonance frequency so that an electromagnetic field applied to the array of color centers activates only those color centers with the resonant frequency of the electromagnetic field. This allows addressing of a single color center without activating nearby color centers. This enables the expansion of systems based on color sensors (such as multi-qubit arrays and color center-based sensors) to include more color centers, providing a basis for more complex components such as imaging arrays and quantum computer chips.

[0034] Specific geometries are also described that further reduce crosstalk between color centers by maximizing the electromagnetic field applied to the target color center to be addressed while minimizing the electromagnetic field applied outside the target color center.

[0035] 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, in particular an external static magnetic field, which is 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, while 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 mentioned elsewhere in the article.

[0036] Example embodiments will now be described.

[0037] 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, which are necessary for quantum control, occur only when 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 across 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, then a single color center can still be addressed even if it is placed in a multi-color center microwave radiation geometry.

[0038] 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 (e.g., carrying a 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 produce 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 the desired resonance shift (or shifts) in the color center (or centers).

[0039] The microwave radiation geometry used to activate a color center (or centers) having a specific resonant frequency (or multiple frequencies) can take many different forms, such as a single conductor or conductor loop carrying alternating current (AC), or even a multi-conductor color center surround geometry with parallel current flow, crossed conductor geometries, etc.

[0040] 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 also 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 and high temperature (HPHT) techniques. Color centers may also be placed at desired locations within diamond by implanting ions into the diamond (nitrogen ions for nitrogen vacancy centers and silicon for 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.

[0041] 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 is shown, such as diamond, having two color centers 104a, 104b. A typical 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, but each color center has an axis that is aligned with the nitrogen (or silicon, for example for 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 an electromagnetic signal applied 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 108 transmits microwave radiation, while 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.

[0042] There are a number of possible methods for generating the electromagnetic field used to activate the color centers. One example is by running an alternating current through a copper wire to generate an electromagnetic field of the desired frequency. Another possibility is to print a wire on top of (or inside) a diamond or other crystalline substrate (such as silicon carbide) using photolithography. A third possibility is to irradiate the diamond with high-intensity ultrashort laser pulses, resulting in graphitization of the diamond, where the graphite is conductive and can therefore act as a wire and carry the current used to generate the required electromagnetic field. The wire can therefore be inside or outside the crystal, and the term includes a variety of physical structures. In general, a wire refers to a carrier of an electrical signal that is capable of operating as an electromagnetic field transmitter.

[0043] 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 relative to spatial variation (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 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 field strengths applied to each color center are different enough so that the color centers have different resonant frequencies. The frequencies should be separated by some 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, the magnetic field generator causes a magnetic field B1 to be applied to color center 104a, which results in a resonant frequency F1, while a different magnetic field B2 is applied to color center 104b, causing the color center to have a resonant frequency 104b.

[0044] For clarity, the description refers to different magnetic fields (such as B1 and B2) at different locations. More precisely, in order to provide separate 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 axes parallel to each other, this can be achieved with magnetic fields having different amplitudes at these locations, and can also be achieved with magnetic fields having different orientations at these 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 can be zero or substantially zero.

[0045] Unless otherwise indicated or the context requires otherwise, 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.

[0046] 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.

[0047] 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 1 As shown, when a signal of frequency F is generated, where F is equal to the resonant frequency F1 of the color center 104a, the color center is activated while the other color center is not activated because the resonant frequency of the other color center is different from the frequency of the transmitted signal. Note that this description relates 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.

[0048] Selective activation of individual color centers allows such arrangements to be used, for example, in quantum computing applications, where each color center operates as a qubit, which allows arrays of multiple color centers to implement multi-qubit gates.

[0049] Figure 2A schematic block diagram of a quantum system is shown having a "classical" (non-quantum) computer processor 204 (or processors) coupled to a memory 202 (or memories) as well as a magnetic field generator 110 and an electromagnetic signal generator 108 to control the activation of color centers. For example, based on "classical" (non-quantum) computer program instructions 203 that can be stored in the memory 202, the classical processor 204 can be caused to implement a quantum computer program in the crystal 102. When these instructions 203 are executed, the processor 202 is configured to generate an electromagnetic signal of a specific frequency to enable the activation and control of a single color center, such as a qubit. 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 individually activated and controlled, as described above. This enables more complex operations to be performed, including quantum gates of multiple qubits. Thus, a program implemented on a quantum computer including a collection of qubits implemented by color centers may be implemented by executing conventional computer instructions on the computer processor 204 to control the electromagnetic signals required to activate the individual qubits according to the quantum program.

[0050] 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 Figure 1 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 L " At, and m s = +1 and m s = -1, respectively, with two up spins or two down spins, shown at the same energy level L on the left (±1) Note that since energy and frequency are directly related, the energy level L " and L (±1) is marked with frequency values. In the NV center, L " and L (±1) The frequency is split by 2.87 GHz, so the transition between the 0 state and the +1 or -1 state can be triggered by an applied microwave field of 2.87 GHz.

[0051] Figure 3A The right side of the figure 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 causes m s = +1 and m s = -1 energy level splitting, but does not affect m s =0 state energy level. As shown in Figure 3, m s = 0 is still at the same energy level L" = 0, because the 0 state is unaffected by the external magnetic field. However, the +1 and -1 states split, and the distance between the energy levels is proportional to the external magnetic field. This phenomenon is called 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 a new energy level L +1 The change in the frequency 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 higher the applied magnetic field, the larger the splitting between the +1 and -1 energy levels. In this case, for m s = 0 state and m s = The resonant frequency of the transition between the -1 state and m s = 0 state and m s = +1 states have different values ​​for the resonant frequencies. Any of these energy state pairs can be selected, for example, for use as a qubit. References herein to the resonant frequency of a color center can refer to the resonant frequency that matches any of these energy state pairs.

[0052] 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 of a color center can be measured, and such a curve 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 pairs of spin states that can undergo transitions, but this example only describes the resonant frequency for 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 light emission at the first frequency F " For nitrogen vacancies in diamond, this frequency is about 2.87 GHz. Figure 3BThe curve shown in rises sharply around this frequency. In order to address different color centers individually by ensuring that they are excited by different resonance frequencies, it is important that the resonance curves associated with different color centers do not overlap at a point where the frequency of the first color center may also excite the second color center, or 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. Although the FWHMΔv depends on factors such as the quality of the crystalline material and the power of the electromagnetic radiation, a typical 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: ΔF=F B3 +γB,

[0053] where F B" is the transition frequency for a given color center in zero external magnetic field, and γ is the electron gyromagnetic ratio. 1 ,B 2 In the case of , the transition frequency difference between the color centers is: γ(B 1 -B 2 ).

[0054] Setting the frequency to 200 KHz, it can be easily calculated that the magnetic field variation required to achieve individual addressing between each color center is approximately 7 μT.

[0055] 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 induces 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 different color centers caused by hyperfine splitting, the frequency difference between the different color centers can be set to about 6 MHz instead, which results in a required magnetic field difference of about 0.2 mT between each color center according to the above formula. Alternatively, nuclear polarization techniques can be used to deplete two of the three hyperfine 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 the wire in the examples described herein. This is in Figure 3B This is shown in the illustration of where with a given frequency F , The electromagnetic field actually spans a width Δv ,frequency range.

[0056] 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 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 the order of time t will result in a line width broadening of about Δf~1 / t. Typical examples of pulse widths targeting color centers can range from tens of nanoseconds to a few microseconds, which means that for smaller pulse widths, this effect may require a peak separation of the order of 10s MHz, while for longer pulse widths, peak separations of about 100kHz are required to ensure that the field pulse targeting a given color center does not overlap with the resonant frequency of another color center.

[0057] The determined magnetic field differences between each color center that needs to be individually addressed are 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 distance in the direction of the magnetic field gradient.

[0058] Figure 4 A schematic diagram of a nitrogen vacancy center in diamond is shown, one 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 where 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 produced using chemical vapor deposition and high pressure and high temperature techniques, as well as by implanting ions in diamond or by irradiating diamond via ultrashort laser pulses. The axis of the NV center is along the axis where the nitrogen atoms and vacancies are located. As described above, in order to control the color center, when the color center and the electromagnetic signal generator (such as 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 that activates the color center.

[0059] 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 location of the coordinates inside the diamond is not important. However, one of the four possible orientations may grow preferentially, so the best case can be considered to be one in which all NVs point to the same axis.

[0060] After all NV color centers are aligned to the axis of production, 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 diamond surface. {111} results in the axis of the color center being perpendicular to the diamond surface, while {100} will result in the color center having an orientation of 45 degrees relative to the top surface of the diamond. For diamond, the color center is aligned with one of three crystal planes or "facets": (111), (110), (100). Different facets can be used for different wire configurations (e.g., such as wires photolithographically printed onto the diamond surface) to ensure that the electromagnetic field is optimally applied relative to the axis of the color center. For wires generated inside the diamond, for example by ultrashort (femtosecond) laser irradiation rather than printed on the surface of the diamond, there is more flexibility because the wires can be placed in specific locations or along specific directions relative to the axis of the color center. This also allows 3D geometries of color centers controlled by wires at different depths within the crystal.

[0061] The spin state of the color center can be initialized by laser irradiation. For a nitrogen vacancy center, for example, the state of the color center can be initialized by an optical process that excites the spin state, which then 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, for example, m s = 0 state and m s = ±1 states. 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 is higher than m s =±1 state emits more photons (higher intensity).

[0062] 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 indicated by the set of arrows, a varying magnetic field is applied to the system, with a stronger magnetic field at the top of the array and a weaker magnetic field at the bottom, so that each color center along the vertical wire 500 experiences a different magnetic field. The component of the applied magnetic field parallel to the axis of the color center is the effective field that causes the energy level of the color center to shift, 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 strength 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 strength required to adjust the resonant frequency of a given color center by the amount required for individual addressing.

[0063] The external magnetic field is a static 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 of the same vertical height, that is, the magnetic field changes only along the vertical axis. The external magnetic field is a static field applied in a direction parallel to the color center 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 illustrate the gradient, with the highest magnetic field shown by the large arrow and the lowest magnetic field shown by the small arrow, the arrows indicating the direction of the external magnetic field.

[0064] 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 of each color center can be calculated based on the known magnetic field at the center according to the formula described above. A given color center 104 can then be addressed by running an alternating current along the conductor 500 so as to produce 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 addressed using one conductor per 'column' alone. Current can be run through adjacent conductors producing different frequencies so as to activate different color centers near the conductor. More than one color center in a given column can be addressed by multiplexing, i.e., generating multiple electromagnetic fields from the same conductor at the same time, each electromagnetic field 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 a wire addresses only those color centers that are closest to that wire, the wire and the color center are separated by a minimum distance from the wire and the color center of the next "column" so that the electromagnetic field is weak enough to not cause activation of color centers at adjacent wires. A threshold rate 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 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.

[0065] 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 the expansion of color centers to create larger quantum systems, such as quantum computers and quantum sensor arrays.

[0066] Figure 5 The exemplary color center array shown in generates a magnetic field that flows in a clockwise direction (when viewed in the direction of current flow). The magnetic field spreads radially outward from the wire 500, with the strength of the magnetic field being inversely proportional 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, presenting a problem when expanding to larger quantum systems requiring many quantum bits or quantum sensors.

[0067] However, certain wire configurations can be achieved that enhance the field experienced by color centers targeted by a given wire or set 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 can be combined. However, as Figure 6 As shown, the magnetic field pattern produced is independent of the frequency of the field. In fact, the amplitude and frequency of the fields produced by the different wires are the same.

[0068] A first wire configuration and the resulting magnetic field are shown in curve 600. In this configuration, the current flows in the positive direction (outward from the plane of the image), which, according to well-known electromagnetic principles, will result in a magnetic field pointing counterclockwise from the perspective shown in the figure in the case of a single wire. The direction of the current along the wire is also indicated by the set of arrows below the graph, where the downward arrow represents a positive current J. It should be noted that J is used in physics to represent current density, but in this article, the term "current" can refer to current or current density interchangeably. Current density and current are directly related to the cross-sectional area of ​​the current carrier (e.g., wire). Two wires running 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 field in the space between the two wires points in opposite directions, while the field in the area around the two wires points in the same direction. For this pair of wires, the total field is related to 1 / r 2 The field is proportional to 1 / r, rather than 1 / r for a single conductor, which reduces the effect of the pair in areas far from the conductors. Three pairs of parallel current-carrying conductors placed alongside each other produce an overall field that is weakest in the area between the two conductors of each pair and between the conductors of adjacent pairs because the fields cancel at these points due to the parallel currents.

[0069] The wire configuration shown in the middle diagram 602 provides a magnetic field further positioned to the target area while reducing the field outside those areas. In this configuration, the wire pair is arranged to have a first wire with a positive current and a second wire with a negative current. This also becomes an antiparallel arrangement because the current density vector is antiparallel, as shown by the arrow below the curve 602. As shown by the field lines, for this area arranged between the two wires, the magnetic field is the strongest, because for the first wire, the current flows 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 magnetic field between the two wires also points upward, thereby causing the field in the area between the two wires of the pair to be stronger. This arrangement can be applied to the color center in the area positioned between the wire pairs to maximize the field at the color center to achieve addressing, wherein the field strength outside the area is weaker. Compared with only a single wire pair, the field in the area between the adjacent pairs of wires is also increased to give a stronger overall field because the current for the two pairs of nearest wires is antiparallel.

[0070] A third possible configuration is shown in curve 604. In this case, the two wires of each pair are arranged to carry currents that are antiparallel relative to each other, but adjacent wires belonging to different pairs carry parallel currents. This results in the fields between the wires of the same pair being superimposed, because the antiparallel wires produce fields with the same direction in the region between the wires, and since the adjacent wires of the adjacent pairs have currents with the same direction and the fields between the two wires have opposite directions, i.e. at the midpoint between any two pairs of wires in this configuration, the magnetic fields between the wire pairs cancel each other out. This configuration provides the most effective localization of the field in the desired region while minimizing the field experienced between the wires, which reduces the risk of crosstalk and decoherence for the set of color centers in the region between each pair of antiparallel wires.

[0071] Reference numerals 612, 614, 616 and 618 represent first, second, third and fourth conductors (conductor 1 to conductor 4 shown in cross-section), respectively. For simplicity, the description relates 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 arranged substantially parallel to each other, with conductors 1 and 2 (612, 614) forming a first conductor pair and conductors 3 and 4 (616, 618) forming a second conductor pair. Generally, it is not required that these conductors are parallel. In order to achieve the above-mentioned beneficial effects, the conductors of a given conductor pair only need to be reasonably parallel to each other to generate a magnetic field of the desired form.

[0072] The localization effect is caused by a combination of constructive and destructive wave interference. Each conductor carrying an alternating current emits an oscillating electromagnetic field. Utilizing a pair of conductors carrying antiparallel currents of substantially equal amplitude, constructive interference between their corresponding magnetic fields occurs in the conductor pair local region, thereby strengthening the magnetic field. Outside the local region, destructive interference occurs (at least to a certain extent, the electromagnetic magnetic field "cancels"), reducing crosstalk and decoherence effects between color centers adjacent to (or otherwise coupled to) different conductor pairs. In this example, each conductor pair including a first conductor pair (612, 614) and a second conductor pair (616, 618) acts as a single signal carrier.

[0073] 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 with antiparallel currents, each current frequency is at or approximately at the resonant frequency of the color center, thereby resulting in a single localized electromagnetic activation signal at or approximately at the resonant frequency of the color center (and the magnetic field component of the signal along the axis of the color center thereby causing the desired energy transition in the color center).

[0074] 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 with 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.

[0075] Figure 7 An example wire configuration for a 2D array 104 suitable for addressing color centers 104 is shown, the configuration comprising a plurality of pairs of wires 500, each pair of wires being separated by a distance of 200 μm. Note that the required distance between wire pairs depends on the nature of the wires and the strength of the field generated. 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 In the configuration shown in , the color centers can be placed more closely together along the conductor pair, such as Figure 5 The single wire configuration shown is more likely to be achieved without causing crosstalk or decoherence.

[0076] 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 particular signal implemented within the conductor configuration.

[0077] Using specialized geometry allows certain electromagnetic fields to be applied, such as a circularly polarized field only at specific target points (or lines) rather than at larger volume areas. One example application where circular polarization is useful is the use of color centers for magnetometry, i.e., the detection and measurement of magnetic fields. In this case, the use of this specialized geometry allows only those color centers located at specific points (or lines) to experience the circularly polarized field and measure the magnetic field with optimal efficiency.

[0078] 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 a color center is placed adjacent to each intersection, such as directly below or above the intersection, where each color center can be addressed by a field generated at the intersection, as described below. Note that, as described below, the field generated at an intersection affects all color centers that are equidistant from the two wires crossing at the intersection. The term "adjacent" applies herein to a given intersection if the given intersection is positioned so that it is addressable by the field generated at the intersection, so "adjacent" in this article refers to color centers that are sufficiently close to the xy positioning of the intersection to be addressed by the field at the intersection, as well as to 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 in the addressed color center depends on the line width of the generated signal 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 produces an electromagnetic field of some amplitude, phase, and direction that interferes with the other. The electromagnetic fields from the two wires propagate outward with decreasing amplitude and a phase that oscillates with time (given by the frequency of the field). The direction of the electromagnetic field is given by the direction of propagation of the current inside the wire that generates the field.

[0079] The above description relates to addressing a color center by emitting a signal at the resonant frequency of that 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 a single color center without applying the same manipulation to other color centers along the same (multiple) wires. This allows direct addressing of a single color center arranged in a 2D array with crossed wires by generating a combination of signals at the different wires so that the desired field or combination of fields is produced only at the (multiple) intersections corresponding to the (multiple) color center to be addressed, for example by generating a combination of signals that generates circularly polarized fields only at the intersections.

[0080] At the interference point, if the fields have the same amplitude, phase difference and directions perpendicular to each other, 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 perpendicular to each other, but as one wire 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 tapers off so that the fields no longer have the same amplitude, and the direction of the field "rotates away" from the intersection direction as the effect from the further away wire becomes negligible, and so the resulting field is no longer circularly polarized.

[0081] The advantage 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 are needed than color centers to achieve individual addressing. The effect becomes more pronounced for larger systems. 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 a single color center arrangement 1002, a two color center arrangement 1004, a four color center arrangement 1006, and a six color center arrangement 1008. In order to address a single color center by the effect produced by the interaction field at the intersection, a crossover point is required, which requires two conductors 1012a, 1012b that are crossed (i.e., not parallel).

[0082] Similarly, for the dual color center arrangement 1004, three conductors are required to construct two intersections through which the two color centers can be individually addressed. 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 necessary.

[0083] For the four color center arrangement 1006, at least four conductors are required to create four intersections through which the four color centers can be individually addressed. Fig.10In the example shown, two conductors 1016a are arranged substantially parallel to each other, while the other two conductors 1016b are arranged in the same plane, and both conductors 1016b intersect with 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 conductors, each of which is positioned proximate to a different color center) is that a color center configured to be addressed by a particular conductor can also be addressed (albeit weakly) by a nearby conductor, thereby causing decoherence and crosstalk. For crossed conductors, as will be described in more detail below, the color center is addressed by the field effect generated by the two associated conductors (i.e., by controlling the timing, amplitude and / or phase of the field), which field effect is only localized at the intersection in the xy plane, and therefore the effects of decoherence and crosstalk are minimized.

[0084] 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 that are substantially parallel to each other, and three wires 1018b that are substantially parallel to each other and cross each of the two wires 1018a, as shown, all arranged in the same plane. For any system with more than 6 color centers, the color centers can be addressed by fewer wires than the number of color centers. This allows for the expansion of color center systems, such as for quantum computing applications, without the need for a proportionally expanded number of wires, thereby enabling systems with more color centers to be realized, where the number of wires is limited, such as by spatial constraints or the properties of the wires and / or the properties of the crystal material (in which they are implemented).

[0085] The activation of the color centers by crossing conductors is described below.

[0086] Figure 8 A schematic diagram of a color center array having wires 500 arranged in a crossed wire configuration is shown, wherein each color center array is positioned close to 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 electromagnetic field applied to the nitrogen vacancy color center typically varies from a few nanoseconds to a few microseconds. By controlling the properties of the field generated by the wires, including phase, pulse timing, and pulse duration, a specific effect can be produced at only one color center.

[0087] One way to produce a specific effect at only one 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 sequence of repeated π pulses, where a π pulse is a pulse of a specific duration that causes a change in the electron spin state. The π pulse is a well-known method for manipulating the electron spin state and will not be described in detail herein. In the XY8 pulse sequence, eight pulses are repeated at π times. . and π / Alternating between . and π / are all π pulses (and therefore have the same duration), they are out of phase with each other The sequence consists of the following pulses: π . -π / -π . -π / -π . -π / -π . -π / ,

[0088] There is a predefined duration time interval τ between each pair of pulses.

[0089] To use such a sequence to address only a single target color center, Figure 8 The crossed wire geometry shown in can be used to generate pulses with different phases on two wires that cross at a point close to where the target color center is located. All pulses have the same frequency, which should be the resonant frequency of the target color center. With the plane of the crossed wires as the xy plane, the color center is located at a position equidistant from the two wires, such as at corresponding (x, y) positions of the crossed wires at different heights, such as below the crossed 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 . 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 / signal, which has a phase difference with the first pulse A second pulse of phase is generated by conductor 500b so that the pulse arrives at the target color center just after time τ. The distance each given pulse must travel and the color center and the speed of the electromagnetic wave are known, which means that the required time when the pulse needs to be generated by the second conductor can be accurately determined. All other color centers along conductor 500b experience pulse π / , but the pulses arrive at the target color center 104 only at the times defined by the pulse sequence. This process is repeated for all pulses of the sequence, with the pulses being timed so that they arrive at the crossing point at regular time intervals τ.

[0090] The color center located at the intersection or at any point equidistant from the two wires along which the corresponding pulses are transmitted experiences the influence of the pulse sequence. Since the pulses have a short duration, the corresponding pulses arrive at 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.

[0091] Note that this method requires good control of the phase of the pulses generated by the respective wires to ensure that they are out of phase by the required amount to generate π . and π / pulse.

[0092] The XY-8 pulse is a phase sensitive pulse. This is because it contains both π_x and π_y pulses, which can be achieved by phase offsetting. A similar technique to that described above can be used to generate a circularly polarized field, with zero phase difference between the fields from the two wires, to instead generate linearly polarized microwaves at the intersection. The frequency of the field corresponds to some wavelength, which is about 10cm in the case of 3GHz. At non-equidistant points, or points that are not separated by an integer wavelength distance, the field will instead be elliptically polarized (or circularly polarized). In a typical realization of a quantum system of diamond color centers, this wavelength is much larger than the distance between any color center and the intersection. Color centers located adjacent to the intersection experience a linear polarization at π . and π / The correct phase difference between the pulses, while the other color centers will experience the elliptical field.

[0093] It should be noted that the above method is only an example, and there are other methods that can be used to control Figure 8 The spin state of a single color center is manipulated and controlled by the field generated by the crossed wire pair 500 in the crossed wire geometry. In the above example, the wire 500 is configured to generate an electromagnetic field whose phase differs only by a certain amount at the crossing point. This results in a circularly polarized microwave field only at these points, while outside these points the field is linearly or elliptically polarized. This can be used to control the spin state of the color center at the (x,y) location corresponding to the intersection point.

[0094] While circular or linear polarization is an example effect that can be produced at an intersection, the principle can be extended to other situations as well. For example, since the field orientation changes with movement away from the equidistant line, the intensity of the drive field for differently positioned color centers has an effect. The drive is greatest when the magnetic field generated by the wire is perpendicular to the color center axis, so this effect can be observed when the color center axis is not perpendicular to the plane of the cross-wire geometry. For example, timing between pulses can also be used. If the sequence requires that a pulse from wire 1 be implemented first, and then the sequence requires a pulse from wire 2 or a pulse that is very sensitive to timing, the wire divides the main substrate into parts that may or may not meet the correct conditions. Note that the latter case is for electromagnetic field pulses generated by the wires and not for continuous wave applications. The above-mentioned cross-wire geometry can also be used when continuous operation separated by specific time windows is required, where the electromagnetic pulses are timed at the two cross-wires so that continuous operation occurs only at the intersection.

[0095] 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 fully-regular 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 the highest efficiency, the color centers are placed at equidistant lines or multiples of the wavelength. However, as mentioned above, for microwaves, the wavelength is on the order of centimeters, making it impractical to target a high density of color centers. In this example application, the quantum gate will therefore be selectively applied to color centers placed at equidistant points between two wires.

[0096] 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 in the cross-wire configuration shown. 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 at the required timing to generate a field or pulse sequence that controls the spin state of only those color centers.

[0097] The crossed wire geometry can be used to achieve individual addressing of color centers in 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 sequence generated at a given frequency at the intersection is not only limited to color centers at the same (x, y) location as the intersection, but is also limited in the z direction to color centers that experience the external magnetic field so that their resonant frequencies match the frequency of the emitted pulses.

[0098] It should also be noted that although Figure 8 For simplicity, a single conductor 500a, 500b is shown, but Figure 8 The geometry of the embodiment can be matched by replacing each conductor 500a, 500b with a conductor pair. Figure 6 The invention is combined with a geometric structure in which 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 vertical direction). In this case, each color center is coupled to a unique pair of wire pairs (four wires in total, but each wire pair acts as a single signal carrier).

[0099] Wires 500a and 500b are shown as being substantially perpendicular to each other, but typically they are not parallel so that crossing each other (forming a crossover point) is sufficient. Wires 500a and 500b are substantially straight, but this is typically not required (in some cases, the curved wires may cross each other more than once and thus form more than one crossover point).

[0100] Fig. 9 An example 3D array is shown having color centers 104 arranged in a 3D array with a 2D cross-wire configuration layer above the array of color centers. For clarity, only one "face" of the configuration is shown in the zx plane to show the color centers in three dimensions. In reality, the array of color centers includes color centers at each 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 color centers at specific xy locations in the 2D grid. However, in 3D, these pulses will also address color centers at the same xy location but at different heights. However, as described above, external magnetic field gradients can be used to adjust the resonant frequency of the color centers along the z-axis. This is in Fig. 9 , as shown by arrows that increase in size as height decreases. The magnetic field separates the spin energy levels of the color centers so as to adjust the transition frequency to go from one spin state to another. The pulse sequence affects only the color centers that have a resonance frequency that matches the frequency of the pulse. This means that a pulse sequence generated at one of the intersections affects only the color center at the (x, y) position corresponding to the location of the intersection and at the z-location corresponding to the pulse frequency, making it possible to address a single color center within the 3D array in the same way without manipulating the spins of other surrounding color centers.

[0101] Figure 6Three 2D arrays of vertically stacked color centers (layers) are shown. In general, 3D geometries can have two or more layers. Color centers in different layers can be formed in different crystals, for example, using wires printed on the surface(s) of the crystal, or wires 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., as graphene channels passing through the crystal).

[0102] The term magnetic gradient is widely used to refer to 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 its respective axis), this will be sufficient to functionally isolate these color centers from each other. As already noted, the magnetic field can have a value of zero or close to zero at a color center or a subset of color centers (the key lies in the relative differences in the resonant frequencies between nearby color centers, and therefore the differences in the projections of the magnetic fields at those color centers).

[0103] Fig.11 A schematic diagram showing an example configuration of a color center, the color center comprising two layers, each layer having six color centers, having the color centers according to the above reference Fig.10 The six color center configuration 1008 described is arranged as a collection of intersecting wires in the plane of each layer. The top layer has three wires 1114a arranged substantially parallel to each other, and another two wires 1112a arranged substantially parallel to each other and each intersecting each of the wires 1114a to form a set of six intersections as shown. The six color centers are located 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 but not parallel to wire 1114b, so that the two wires 1112b each intersect with each of the wires 1114b to form six intersections.

[0104] As described above, sending pulses in a particular way along the crossing wires produces a localized effect confined to a point equidistant between the two wires, so that adjacent color centers of the same layer are not addressed by a given field or combination of fields induced 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 also addresses color centers at the same xy location (or equidistant from the two wires) in a different layer. As described above with reference to Fig. 9 As described above, 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 axis of different color centers cause the color centers to have different electron spin resonance frequencies. By generating a varying magnetic field, the magnetic field B1 is projected onto the color center of the top layer and the different magnetic fields B 2 The color center of the top layer (eg, color center 1104a) can be projected onto the color center of the bottom layer by the first frequency f 1 The color center of the bottom layer (e.g., color center 1104b) can be addressed by a frequency f 2 The second frequency f 2 Therefore, if the intersection point adjacent to the color center 1104a is addressed by the current I flowing along the two wires crossing at the intersection point 1 and I 2 At frequency f 1 If a field is generated (e.g. a pulse or a sequence of pulses as described above), it addresses only the color center 1104a, because the effect is localized only to this location in the xy plane due to the effect of the crossed wires as described above, and only to the color centers of the top layer, since only these can be addressed by a given frequency. The different color centers of the bottom layer can be addressed by generating a field with f 2 The field is activated simultaneously, which is composed of a frequency f 2 The current I 3 and I 0 Generated.

[0105] 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 simultaneously addressed by simultaneously generating electromagnetic field pulses of multiple frequencies to match the corresponding resonant frequencies of the color centers. Similarly, multiple color centers in the same xy plane can be addressed by generating pulses from multiple corresponding wire pairs at the timing required according to a given addressing method.

[0106] 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 local electromagnetic field is generated in a region adjacent to the conductor via constructive interference between the first electromagnetic field and the second electromagnetic field in the region and destructive electromagnetic fields between the first electromagnetic field and the second electromagnetic field outside the region.

[0107] One aspect of the present invention provides a quantum device, including: a group of crystal materials having a first color center at a first color center position and a second color center at a second color center position; a magnetic field generator configured to generate a magnetic field within the crystal material so that a first magnetic field projection on a first color center axis of the first color center is different from a second magnetic field projection on a second color center axis of the second color center, wherein the first color center has a first electron rotation resonance frequency depending on the first magnetic field projection, and the second color center has a second electron rotation resonance frequency depending on the second magnetic field projection; and an electromagnetic signal generator to generate an electromagnetic signal at the first color center position and the second color center position, the electromagnetic signal having a first frequency that substantially matches the first electron spin resonance frequency of the first color center but does not match the second electron spin resonance frequency of the second color center, thereby inducing an energy level transition in the first color center without inducing any energy level transition in the second color center.

[0108] According to one aspect disclosed herein, there is provided a device comprising: a crystal; and a color center within the crystal, and the color center is adapted to receive: a magnetic field such that a projection of the magnetic field on a color center axis of the color center causes a change in the electron spin resonance frequency of the color center, and an electromagnetic signal having a frequency substantially matching the electron spin resonance frequency of the color center, the electron spin resonance frequency being changed by the projection of the magnetic field on the color center axis.

[0109] According to another aspect, a device is provided, comprising: a crystal; and a color center within the crystal; wherein the color center is placed in a magnetic field so that a projection of the magnetic field on a color center axis of the color center causes a change in the electron spin resonance frequency of the color center; and the color center is placed in an electromagnetic field having a frequency that substantially matches the electron spin resonance frequency of the color center, which changes with the projection of the magnetic field on the color center axis.

[0110] In an embodiment, the device also includes a first color center, which is located at a first color center position in the crystal and has a first electron spin resonance frequency, which depends on a first projection of the magnetic field on the first color center axis of the first color center; and a second color center, which is located at a second color center position in the crystal and has a second electron spin resonance frequency different from the first electron spin resonance frequency, which depends on a second projection of the magnetic field on the second color center axis of the second color center.

[0111] In an embodiment, the apparatus further comprises a conductor coupled to the first color center and the second color center, wherein the conductor is configured to transmit an electromagnetic signal receivable by the first color center and the second color center.

[0112] In an embodiment, the device also includes an electromagnetic signal generator, which is configured to generate: a first electromagnetic signal, which is received by the first color center and the second color center and has a first frequency that substantially matches the first electron spin resonance frequency of the first color center, thereby causing a first energy level transition in the first color center, and a second electromagnetic signal, which is received by the first color center and the second color center and has a second frequency that substantially matches the second electron spin resonance frequency of the second color center, thereby causing a second energy level transition in the second color center.

[0113] In an embodiment, an electromagnetic signal generator includes at least one conductor, and a current source coupled to the at least one conductor and controllable to cause the conductor to emit a first electromagnetic signal having a first frequency and a second electromagnetic signal having a second frequency.

[0114] In an embodiment, the apparatus further comprises a magnetic field generator configured to generate a magnetic field.

[0115] In an embodiment, at least one color center is configured to provide at least one qubit.

[0116] In an embodiment, a first color center is configured to provide a first quantum bit, wherein the second color center is configured to provide a second quantum bit, wherein a first energy level transition in the first color center affects a first quantum bit transformation of the first quantum bit or a first quantum bit measurement of the first quantum bit, and wherein a second energy level transition in the second color center affects a second quantum bit transformation of the second quantum bit or a second quantum bit measurement of the second quantum bit.

[0117] In an embodiment, the crystal is configured to operate as a quantum sensor.

[0118] In an embodiment, the apparatus further comprises a plurality of conductive lines, and for each conductive line of the plurality of conductive lines, a plurality of color centers are coupled to the conductive line.

[0119] In an embodiment, the apparatus further comprises a mutually parallel pair of conductors coupled to the color center and configured to carry respective currents in antiparallel to generate an electromagnetic signal receivable by the color center.

[0120] In an embodiment, the apparatus further comprises: a first plurality of color centers located in a first plane; a first plurality of conductors, wherein each color center in the first plurality of color centers is coupled to a corresponding non-parallel pair of conductors in the first plurality of conductors; a second plurality of color centers located in a second plane substantially parallel to the first plane; and a second plurality of conductors, the second plurality of conductors being positioned in a second direction non-parallel to the first direction, wherein each color center in the second plurality of color centers is coupled to a corresponding non-parallel pair of conductors in the second plurality of conductors; The magnetic field generator is configured to generate a magnetic field having a magnetic field gradient perpendicular to the first plane and the second plane, so that the first plurality of color centers have an electron spin resonance frequency different from that of the second plurality of color centers.

[0121] According to another aspect disclosed herein, a quantum system is provided, comprising: a crystal; and a color center located within the crystal; a magnetic field generator; an electromagnetic signal generator; a memory containing computer-readable instructions; and a processor, the processor being coupled to the magnetic field generator, the electromagnetic signal generator, and 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: control the magnetic field generator to generate a magnetic field so that a projection of the magnetic field on a color center axis of the color center causes a change in an electron spin resonance frequency of the color center, and control the electromagnetic signal generator to generate an electromagnetic signal having a frequency substantially matching the electron spin resonance frequency of the color center, the electron spin resonance frequency being changed by the projection of the magnetic field on the color center axis.

[0122] In an embodiment, the quantum system further comprises: a first color center, the first color center being located at a first color center position within the crystal and having a first electron spin resonance frequency, the first electron spin resonance frequency depending on a first projection of a magnetic field on a first color center axis of the first color center; and a second color center, the second color center being located at a second color center position within the crystal and having a second electron spin resonance frequency different from the first electron spin resonance frequency, the second electron spin resonance frequency depending on a second projection of the magnetic field on a second color center axis of the second color center; wherein the computer readable instructions, when executed by the processor, are configured to cause the processor to control the electromagnetic signal generator to generate: a first electromagnetic signal, the first electromagnetic signal being received by the first color center and the second color center and having a first frequency substantially matching the first electron spin resonance frequency of the first color center, thereby inducing a first energy level transition in the first color center, and a second electromagnetic signal, the second electromagnetic signal being received by the first color center and the second color center and having a second frequency substantially matching the second electron spin resonance frequency of the second color center, thereby inducing a second energy level transition in the second color center.

[0123] In an embodiment, the first color center is configured to provide a first qubit and the second color center is configured to provide a second qubit; a. wherein the processor is configured to generate a first electromagnetic signal and a second electromagnetic signal based on quantum program instructions stored in the memory, wherein a first energy level transition in the first color center affects one of a first quantum bit transformation of the first quantum bit and a first quantum bit measurement of the first quantum bit as specified by the quantum program instructions, and wherein a second energy level transition in the second color center affects one of a second quantum bit transformation of the second quantum bit and a second quantum bit measurement of the second quantum bit as specified by the quantum program instructions.

[0124] According to another aspect disclosed herein, there is provided a method for addressing a color center in a crystal, the method comprising: generating a magnetic field so that a projection of the magnetic field on a color center axis of the color center causes a change in an electron spin resonance frequency of the color center; and generating an electromagnetic signal having a frequency substantially matching the electron spin resonance frequency of the color center, the electron spin resonance frequency being changed by the projection of the magnetic field on the color center axis.

[0125] In an embodiment, the method includes generating a first electromagnetic signal received by a first color center within a crystal and a second color center within the crystal, and the first electromagnetic signal has a first frequency that substantially matches a first electron spin resonance frequency of the first color center, thereby inducing a first energy level transition in the first color center; and generating a second electromagnetic signal received by the first color center and the second color center, and the second electromagnetic signal has a second frequency that substantially matches a second electron spin resonance frequency of the second color center, thereby inducing a second energy level transition in the second color center.

[0126] In an embodiment, a first color center provides a first quantum bit, wherein a second color center provides a second quantum bit, wherein a first energy level transition in the first color center affects a first quantum bit transformation of the first quantum bit or a first quantum bit measurement of the first quantum bit, and wherein a second energy level transition in the second color center affects a second quantum bit transformation of the second quantum bit or a second quantum bit measurement of the second quantum bit.

[0127] In an embodiment, the color center operates as a quantum sensor.

[0128] In an embodiment, the method is performed by a processor in response to computer readable instructions received from a memory coupled to the processor of the computer.

[0129] A "current source" may refer to an internal component of a device (such as a circuit or a group of circuits) that is coupled to (multiple) conductors and that is connectable to a power source (such as a battery or a group of batteries, a power outlet or power output, etc.) and that when connected to a power source can be controlled to provide current to a given conductor or conductors.

[0130] It should be understood that the computer processor or processor 204 can 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 multiple chips may include a circuit system (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 system, and a radio frequency circuit system, which can be configured to operate according to exemplary embodiments. In this regard, the exemplary embodiments can 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 can 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 the process according to the present invention. The carrier can 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 a process according to the 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. 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.

[0131] 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; as well as A color center is located within the crystal and is adapted to receive: a magnetic field such that a projection of the magnetic field on the color center axis of the color center causes a change in the electron spin resonance frequency of the color center, and An electromagnetic signal having a frequency substantially matched to the electron spin resonance frequency of the color center, the electron spin resonance frequency being altered by the projection of the magnetic field onto the color center axis.

2. The device according to claim 1, comprising: a first color center, the first color center being located at a first color center position in the crystal and having a first electron spin resonance frequency, the first electron spin resonance frequency being dependent on a first projection of the magnetic field on a first color center axis of the first color center; as well as A second color center is located at a second color center position in the crystal and has a second electron spin resonance frequency different from the first electron spin resonance frequency, the second electron spin resonance frequency being dependent on a second projection of the magnetic field on a second color center axis of the second color center.

3. The device according to claim 2, comprising: An electromagnetic signal generator configured to generate: a first electromagnetic signal received by the first color center and the second color center and having a first frequency substantially matching the first electron spin resonance frequency of the first color center, thereby inducing a first energy level transition in the first color center, and A second electromagnetic signal is received by the first color center and the second color center and has a second frequency substantially matching the second electron spin resonance frequency of the second color center to induce a second energy level transition in the second color center.

4. The device according to claim 3, wherein the electromagnetic signal generator comprises: At least one conductor, and A current source is coupled to the at least one conductive line and is controllable to cause the conductive line to emit the first electromagnetic signal having the first frequency and the second electromagnetic signal having the second frequency.

5. The device according to any one of the preceding claims, comprising: A magnetic field generator is configured to generate the magnetic field.

6. An apparatus according to any one of the preceding claims, wherein the at least one colour centre is configured to provide at least one qubit.

7. An apparatus according to claim 3 or any claim based on claim 3, wherein the first color center is configured to provide a first quantum bit, wherein the second color center is configured to provide a second quantum bit, wherein the first energy level transition in the first color center affects a first quantum bit transformation of the first quantum bit or a first quantum bit measurement of the first quantum bit, and wherein the second energy level transition in the second color center affects a second quantum bit transformation of the second quantum bit or a second quantum bit measurement of the second quantum bit.

8. The apparatus of any one of claims 1 to 6, wherein the crystal is configured to operate as a quantum sensor.

9. The device according to any one of the preceding claims, comprising: A pair of mutually parallel conductors are coupled to the color center and are configured to carry corresponding currents in antiparallel to generate the electromagnetic signal receivable by the color center.

10. The apparatus according to claim 5 or any claim dependent thereon, comprising: a first plurality of color centers located in a first plane; a first plurality of conductors, wherein each color center in the first plurality of color centers is coupled to a corresponding non-parallel pair of conductors in the first plurality of conductors; a second plurality of color centers located in a second plane substantially parallel to the first plane; as well as a second plurality of conductors, the second plurality of conductors being positioned in a second direction non-parallel to the first direction, wherein each color center in the second plurality of color centers is coupled to a corresponding non-parallel pair of conductors in the second plurality of conductors; The magnetic field generator is configured to generate a magnetic field having a magnetic field gradient perpendicular to the first plane and the second plane, so that the first plurality of color centers have an electron spin resonance frequency different from that of the second plurality of color centers.

11. A quantum system comprising: Crystals; as well as a color center located within the crystal; Magnetic field generator; Electromagnetic signal generator; a memory containing computer-readable instructions; as well as a processor coupled to the magnetic field generator, the electromagnetic signal generator, and 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: controlling the magnetic field generator to generate a magnetic field such that a projection of the magnetic field on a color center axis of the color center causes a change in the electron spin resonance frequency of the color center, and The electromagnetic signal generator is controlled to generate an electromagnetic signal having a frequency substantially matching the electron spin resonance frequency of the color center, the electron spin resonance frequency being changed by the projection of the magnetic field onto the color center axis.

12. The quantum system according to claim 11, comprising: a first color center, the first color center being located at a first color center position in the crystal and having a first electron spin resonance frequency, the first electron spin resonance frequency being dependent on a first projection of the magnetic field on a first color center axis of the first color center; as well as a second color center, the second color center being located at a second color center position in the crystal and having a second electron spin resonance frequency different from the first electron rotation resonance frequency, the second electron spin resonance frequency being dependent on a second projection of the magnetic field on a second color center axis of the second color center; wherein the computer readable instructions, when executed by the processor, are configured to cause the processor to control the electromagnetic signal generator to generate: a first electromagnetic signal received by the first color center and the second color center and having a first frequency substantially matching the first electron spin resonance frequency of the first color center, thereby inducing a first energy level transition in the first color center, and A second electromagnetic signal is received by the first color center and the second color center and has a second frequency substantially matching the second electron spin resonance frequency of the second color center to induce a second energy level transition in the second color center.

13. A method for addressing color centers in a crystal, the method comprising: generating a magnetic field such that a projection of the magnetic field on a color center axis of the color center causes a change in the electron spin resonance frequency of the color center; as well as An electromagnetic signal is generated having a frequency substantially matching the electron spin resonance frequency of the color center, the electron spin resonance frequency being altered by the projection of the magnetic field onto the color center axis.

14. The method according to claim 13, comprising: generating a first electromagnetic signal received by a first color center within the crystal and a second color center within the crystal, and wherein the first electromagnetic signal has a first frequency substantially matching the first electron spin resonance frequency of the first color center, thereby inducing a first energy level transition in the first color center; as well as A second electromagnetic signal is generated that is received by the first color center and the second color center and has a second frequency that substantially matches the second electron spin resonance frequency of the second color center, thereby inducing a second energy level transition in the second color center.

15. A method according to claim 13 or 14, executed by a computer processor in response to computer readable instructions received from a memory coupled to the processor.

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