Optical addressing method and apparatus

Abstract

The present application discloses a method and apparatus for optically addressing quantum bits, comprising: an optical addressing system including a source of electromagnetic radiation; at least one multi-frequency modulator configured to modulate electromagnetic radiation generated by the source of electromagnetic radiation to simultaneously generate at least two beams of electromagnetic radiation having different frequencies, each configured to at least partially cause one or more transitions between energy levels of a multi-level quantum object when applied to the multi-level quantum object; and a router configured to selectively direct the at least two beams of electromagnetic radiation to the multi-level quantum object.

Description

[Technical field]

[0001] Quantum computing platforms promise to provide solutions to many computationally intractable problems. In such computers, information is stored in quantum bits or "qubits", and the power of a quantum computer is increased in part by the number of qubits that can be controlled independently and simultaneously. In quantum computers composed of qubits such as trapped ions or neutral atoms, guided RF or microwave beams are typically used to implement the manipulation of qubits such as electron dots or superconducting rings, while light beams implement independent qubit operations. [Background technology]

[0002] In such quantum computers, each qubit control operation consists of a pulse of electromagnetic radiation with a particular frequency and intensity profile. Quantum computers therefore typically include a device that selectively generates such pulses for each qubit. This device typically includes a single control tone generator, such as an oscillator or modulator, that controls each qubit by switching its output tone between different qubits at the expense of simultaneous control, or an independent control tone generator for each qubit. Summary of the Invention [Problem to be solved by the invention]

[0003] Various embodiments disclosed herein relate to methods and apparatus for optically addressing quantum bits. In one or more aspects, the optical addressing system includes: a source of electromagnetic radiation; at least one multi-frequency modulator configured to modulate the electromagnetic radiation generated by the electromagnetic radiation source to simultaneously generate at least two electromagnetic radiation beams having different frequencies, each configured to at least partially cause one or more transitions between energy levels of the multi-level quantum object when applied to the multi-level quantum object; and a router configured to selectively direct the at least two electromagnetic radiation beams to the multi-level quantum object. In some embodiments, the multi-level quantum object can include neutral atoms, trapped ions, quantum dots, and superconducting rings. In certain embodiments, the at least one multi-frequency modulator can be further configured to generate electromagnetic radiation beams having a spectral distribution of frequencies for each of the at least two beams, such that one beam has a first spectral distribution and another beam has a second spectral distribution, and the first and second spectral distributions do not overlap. In some embodiments, the optical addressing system further includes at least one single frequency modulator configured to modulate the electromagnetic radiation generated by the electromagnetic radiation source to generate an electromagnetic radiation beam having a frequency that, in combination with a single beam of the at least two beams generated by the at least one multi-frequency modulator, satisfies a frequency resonance condition, and the combination induces one or more transitions between energy levels of the multi-level quantum object. In some of these embodiments, the beams of electromagnetic radiation generated by the multi-frequency and single frequency modulators are optical beams, the electromagnetic radiation source is an optical radiation source, and the router further includes a nonlinear optical medium that combines the optical beams. In certain embodiments, the nonlinear optical medium is periodically poled lithium niobate (PPLN).In some embodiments, the frequency resonance condition is that the sum of the frequency of the beam of electromagnetic radiation generated by the single frequency modulator and the frequency of a single beam of the at least two beams generated by the at least one multi-frequency modulator causes a transition, and the energy level is a ground state energy level and an excited state energy level of the multi-level quantum object. In some other embodiments, the frequency resonance condition is that the difference between the frequency of the beam of electromagnetic radiation generated by the single frequency modulator and the frequency of a single beam of the at least two beams generated by the at least one multi-frequency modulator causes a transition, and the energy level is a hyperfine energy level of the ground state and another hyperfine energy level of the multi-level quantum object.

[0004] In certain embodiments, the one or more transitions are k-photon transitions, where k is 2 or greater. In some embodiments, the router further comprises: m Let N be the beams of electromagnetic radiation generated by the modulators. m -choose-k unique combinations, each multi-level quantum object N q receiving k beams having frequencies that satisfy a frequency resonance condition for transitions between energy levels of a multilevel quantum object, each of the k beams being generated by a different modulator;

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[0005] In some embodiments, the router may be further configured to combine the beams in free space. In some other embodiments, the beams of electromagnetic radiation may be combined at a multi-level quantum object. In certain embodiments, the router may include at least one waveguide arranged to combine at least two electromagnetic radiation beams. In some embodiments, the router may include at least one photonic integrated circuit (PIC) configured to combine at least two electromagnetic radiation beams. In certain embodiments, the router may include a holographic addressing system. In some of these embodiments, the holographic addressing system may be a spatial light modulator (SLM). In other embodiments, the holographic addressing system may be a phase plate.

[0006] In certain embodiments, the router may further include a frequency division demultiplexer (demultiplexer) configured to separate the at least two beams of electromagnetic radiation. In some embodiments, the at least two beams of electromagnetic radiation generated by the at least one multi-frequency modulator may be optical beams, the source of electromagnetic radiation may be an optical radiation source, and the demultiplexer may be an optical demultiplexer.

[0007] In some embodiments, the optical radiation source may be a laser or a superluminescent diode. In certain embodiments, the optical radiation source and the at least one multi-frequency modulator may be integrated into a multi-frequency optical radiation source. In some embodiments, the at least one multi-frequency modulator may be an electro-optic modulator, an acousto-optic modulator, a microelectromechanical (MEM) modulator, or a variable gain amplifier. In certain embodiments, the optical demultiplexer may be at least one dispersive optical element. In some of these embodiments, the at least one dispersive optical element may be at least one optical grating, such as at least one reflective grating or a volume Bragg grating. In some other embodiments, the at least one dispersive optical element may be at least two dispersive optical elements, such as at least two etalons. In certain embodiments, the optical demultiplexer may be at least one dispersive optical fiber element, such as at least one fiber Bragg grating. In some embodiments, the optical demultiplexer may be a photonic integrated circuit (PIC). In some of these embodiments, the PIC may include a tree of unbalanced Mach-Zehnder interferometers, or an array of micro-ring resonators. In certain embodiments, the router may further include at least one optical waveguide, such as at least one fiber, or at least one optical integrated structure. In some embodiments, the router may further include a beam shaping device, such as a spatial light modulator (SLM), a phase plate, or an array of phase plates. In certain embodiments, the at least two electromagnetic radiation beams generated by the at least one multi-frequency modulator are RF or microwave beams, the source of electromagnetic radiation is an oscillator or a digital synthesizer, and the demultiplexer may be an electronic demultiplexer. In some of these embodiments, the router may further include at least one RF or microwave waveguide configured to direct the at least two beams of RF or microwave electromagnetic radiation to the multilevel quantum object. In certain embodiments, the at least one RF or microwave waveguide may be a coaxial cable or a stripline.In some embodiments, the electronic demultiplexer can be an assembly of electronic filters, an assembly of electronic mixers, or an assembly of electronic switches.

[0008] Optical addressing systems that include a smaller number of modulators than the number of qubits have many advantages, including reducing the complexity and cost of commercially useful quantum computing platforms.

[0009] The foregoing apparatus and method embodiments may be implemented by any suitable combination of the aspects, features, and operations described above or in more detail below. These and other aspects, embodiments, and features of the present teachings may be more fully understood from the following description taken in conjunction with the accompanying drawings. [Brief description of the drawings]

[0010] The foregoing will become apparent from the following more particular description of exemplary embodiments, as illustrated in the accompanying drawings, in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the embodiments.

[0011] [Figure 1A] FIG. 1A illustrates a schematic of a spectrally addressable optical addressing system according to one or more embodiments.

[0012] [Figure 1B] FIG. 1B illustrates a schematic diagram of another spectrally addressable optical addressing system in accordance with one or more embodiments.

[0013] [Figure 1C] FIG. 1C illustrates a schematic diagram of yet another spectrally-addressable optical addressing system according to one or more embodiments.

[0014] [Figure 2A-B]FIG. 2A illustrates non-overlapping control tones in the frequency domain (top) and spatial domain (bottom) in accordance with one or more embodiments.

[0015] FIG. 2B illustrates overlapping control tones in the frequency domain (top) and spatial domain (bottom) in accordance with one or more embodiments.

[0016] [Diagram 3] FIG. 3 illustrates a schematic diagram of a router including a fiber Bragg grating according to one or more embodiments.

[0017] [Figure 4] FIG. 4 illustrates a schematic of an optical addressing system including an etalon in accordance with one or more embodiments.

[0018] [Diagram 5] FIG. 5 illustrates a schematic of an optical addressing system including a micro-ring resonator according to one or more embodiments.

[0019] [Figure 6] FIG. 6 illustrates a schematic of an optical addressing system including a Mach-Zehnder interferometer in accordance with one or more embodiments.

[0020] [Figure 7A] FIG. 7A illustrates a schematic of an active matrix optical addressing system according to one or more embodiments.

[0021] [Figure 7B] FIG. 7B illustrates a schematic diagram of a two-photon level diagram according to one or more embodiments.

[0022] [Figure 8A] FIG. 8A illustrates a schematic diagram of another active matrix optical addressing system according to one or more embodiments.

[0023] [Figure 8B]FIG. 8B illustrates a schematic of an active matrix optical addressing system on a two-dimensional grid in accordance with one or more embodiments.

[0024] [Figure 9] FIG. 9 illustrates generally another active matrix optical addressing system on a two-dimensional grid in accordance with one or more embodiments.

[0025] [Figure 10A] FIG. 10A illustrates a schematic of a three-photon active matrix optical addressing system on a two-dimensional grid according to one or more embodiments.

[0026] [Figure 10B] FIG. 10B illustrates a schematic diagram of a three-photon level diagram in accordance with one or more embodiments.

[0027] [Figure 11] FIG. 11 illustrates a schematic of an optical addressing system including a nonlinear optical element according to one or more embodiments. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0028] As described above, some quantum computers control qubits using pulses of electromagnetic radiation generated by a control-tone generator for each qubit. However, the complexity and cost of integrating many such control-tone generators presents a formidable challenge in scaling up quantum computing platforms to commercially useful sizes with large numbers (e.g., 100 or more) of qubits.

[0029] It would therefore be desirable for an optical addressing system to include a smaller number of control tone generators than the number of qubits. The inventors have recognized and appreciated a technique suitable for controlling a large number of qubits (e.g., 100 or more) using a smaller number of modulators than the number of qubits. This technique may reduce the amount of hardware required to control a large number of qubits while reducing crosstalk between qubits, resulting in a more practically scalable system as the number of qubits increases.

[0030] Described herein is an arrangement of active control channels, also referred to as modulators, and passive devices, also referred to herein as routers, that provide control over many qubits independently and simultaneously, using a number of active control channels less than the number of qubits. In various embodiments, the qubits can include multilevel quantum states, a subset of which is used to store information. Control of the qubits encompasses causing transitions between qubit states. The control channels encompass modulated electromagnetic radiation sources, such as oscillators or lasers, that can modulate frequency and power, or devices that can modulate electromagnetic radiation generated elsewhere, such as voltage controlled amplifiers, phase shifters, electro-optic modulators, and acousto-optic modulators. Routing this electromagnetic radiation may encompass propagating the radiation through a waveguide, such as a coaxial cable, stripline, optical fiber, or integrated waveguide, or propagating radiation in different spatial modes through free space, such as a Gaussian beam, with a frequency-dependent distribution that depends on the modulator. Described herein are two types of implementations of modulators and routers, as well as combinations of modulators and routers. In both types of implementations, at least one multi-frequency modulator generates beams of electromagnetic radiation having different frequencies, also referred to herein as "control tones" or simply "tones" as described further below, to control separate quantum bits. These tones are then selectively routed to the quantum bits and / or they are combined with the outputs of other modulators in such a way as to selectively produce desired quantum bit responses.

[0031] The first type of implementation, collectively referred to herein as spectroscopic addressing implementations, uses at least one multi-frequency modulator coupled to a type of router called a frequency division demultiplexer ("demultiplexer"). The bandwidth B of the modulator m is the bandwidth required to control each qubit, B q Since the bandwidth of the modulator can be divided among multiple qubits, the control tones intended for each qubit differ in frequency by the spectral resolution of the demultiplexer, and are routed by the demultiplexer to separate waveguides or separate spatial modes (also referred to herein as beams) and thereby to the qubits. In this type of implementation, the number of qubits each modulator can control is limited by B m / B q This provides a multiplicative advantage.

[0032] The second type of implementation, collectively referred to herein as active-matrix implementations, exploits the nonlinear response of qubits to electromagnetic radiation of different frequencies. In some multilevel quantum objects, transitions between qubit states are induced by multiple photons only if the sum or difference of the energy of the multiple photons is approximately equal to the energy difference between the qubit states. Active-matrix implementations use a series of multi- and single-frequency modulators whose outputs are arranged such that each qubit only receives control tones generated by a unique subset of the modulators. These implementations scale superlinearly in the number of qubits, i.e., the number of qubits that can be controlled by N modulators is N k where k is an integer greater than 1 (e.g., k=2 or 3) and corresponds to the number of photons involved in a transition between qubit levels (e.g., a two-photon or three-photon transition).

[0033] In some embodiments, the two types of implementations can also be combined, thereby benefiting from the advantages of spectroscopic addressing devices in reducing the total number of control channels / modulators and reducing crosstalk between qubits, and the advantages of active matrix devices in super-linear scaling of the number of controllable qubits.

[0034] Implementing Spectroscopic Addressing According to one or more embodiments, as shown in Figures 1A-1C, a spectroscopic optical addressing system 100 includes a source 110 of electromagnetic radiation 115. The example of Figure 1A shows a system suitable for one-dimensional qubit addressing, while the examples of Figures 1B-1C show a system suitable for two-dimensional qubit addressing. However, the same components may be utilized in each system, and the following description of the components may apply to any of the embodiments of the system described herein.

[0035] 1A-1C each include one or more electromagnetic radiation sources 110. Examples of suitable electromagnetic radiation sources 110 include oscillators, lasers, incoherent sources such as superluminescent diodes, or other sources as further described below. Each optical addressing system 100 further includes one or more multi-frequency modulators 120 each configured to modulate the beam 115 generated by the radiation source 110 under the direction of the controller 105, thereby generating multiple electromagnetic radiation beams 125 having multiple frequencies. Examples of suitable multi-frequency modulators 120 include voltage variable amplifiers, such as variable gain amplifiers, voltage variable phase shifters, microelectromechanical (MEM) modulators, electro-optic or acousto-optic modulators that directly modulate radiation.

[0036] In FIG. 1A-1B, the bandwidth B m The multi-frequency modulator 120 having a frequency ν is configured to modulate an incident laser beam 115 having a modulation bandwidth B m (i.e., ν1, ν2, and ν3) m ​). The modulation frequencies v1, v2, and v3 are typically in the RF frequency range (20 kHz to 300 GHz), and therefore are also referred to herein as RF tones. As a result, the modulator 120 can generate three beams of electromagnetic radiation 125 having different frequencies v+v1, v+v2, and v+v3. These beams are also referred to herein as control tones. In at least some cases, the frequencies of the modulated electromagnetic radiation components 125 can be much higher than the RF frequency range. In some embodiments, the radiation source 110 and the multi-frequency modulator 120 can be provided as an integrated multi-frequency radiation source. The frequency v of the electromagnetic radiation depends on the particular control scheme of the particular multi-level qubit system, and therefore in some embodiments the frequency v can be in the ultraviolet-visible-infrared frequency range (e.g., in the range of about 300 nm to about 1.5 μm), or in other embodiments the frequency v can be in the microwave frequency range.

[0037] A variety of different types of routers are suitable for the optical addressing system 100. In the embodiment shown in FIGS. 1A-1B, the router 130 is a frequency division demultiplexer ("demultiplexer") 130, such as an optical demultiplexer 130 configured to separate the beam of electromagnetic radiation 125. The optical demultiplexer 130 shown in FIGS. 1A and 1B is a dispersive optical element 130, such as an optical grating 130 (e.g., a reflective grating), that spatially separates different control tones of the beam of electromagnetic radiation 125 into different spatial or guided modes 135, three such modes 135' (v+v1), 135" (v+v2), and 135"' (v+v3) shown in FIG. A variety of different types of dispersive elements are suitable for the dispersive element 130, such as a virtual image phase array (VIPA), a diffraction grating, an arrayed waveguide grating, a dispersive optical fiber element such as a fiber Bragg grating or a volume Bragg grating.

[0038] The router 130 includes optical elements or elements 140 that direct or otherwise deliver one or more beams 135 of spectrally separated electromagnetic radiation to target qubits 150 for individual addressing. The elements 140 may include any suitable free-space optics and / or waveguides. In the example of FIG. 2, in FIG. 1A, three qubits 150', 150'', and 150''' are shown to be addressed by beams 135', 135'', and 135'''', respectively. As a more formal explanation, consider the case where the optical modulator 120 is triggered by three RF tones V1cos(ν1t+φ1), V2cos(ν2t+φ2), and V3cos(ν3t+φ3) to modulate the amplitude of the incident laser beam 115. Then, the modulated laser field E(t) 125 is:

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[0039] The implementation of spectroscopic addressing can be extended to two-dimensional qubit addressing, as shown in Figure 1B, where only one row is labeled for clarity. When multiple modulated beams 125 are incident on a dispersive element 130 with their positions shifted (i.e., tilted) along the second dimension (i.e., the vertical or y-axis), a two-dimensional array of beams 135 is formed, whose amplitudes and phases are independently controllable, corresponding to a two-dimensional array of qubits 150.

[0040] In yet another embodiment, the implementation of spectroscopic addressing can be extended to two-dimensional qubit addressing by using a virtual image phased array (VIPA), as shown in FIG. 1C, where in this example, out of a group of eight fiber EOs, only three fiber electro-optic (EO) modulators 120 are labeled for clarity. Each of the multi-frequency modulators 120 is modulated at a frequency v 1~8 The router 130 is configured to modulate a beam 115 having a frequency v generated by the radiation source 110 with a frequency of v, thereby generating eight electromagnetic radiation beams 125 having eight different frequencies [(v+v1), (v+v2), (v+v3), (v+v4), (v+v5), (v+v6), (v+v7), (v+v8)]. The router 130 includes optical element 140 that directs a 1x8 fiber array 140' through lenses 140'' and 140''' to the VIPA 130 which separates the beam of electromagnetic radiation 125 into different spatial modes 135 that are focused by another cylindrical lens 140'''' and address a two-dimensional (8 x 8) array of qubits 150.

[0041] The number of active control channels 135 that the modulator 120 can generate is ultimately determined by the total bandwidth B m and qubit B q Ratio of the minimum required modulator bandwidth per m / B qIn some embodiments, the multi-frequency modulator 120 is configured to generate beams 135 of electromagnetic radiation having a spectral distribution of frequencies for each of the beams 135, such that one beam 135' has a first spectral distribution and another beam 135'' has a second spectral distribution, and the first and second spectral distributions do not overlap. In practice, however, the resolution of the router 130 reduces the maximum number of channels due to overlap of spatial modes at the positions of the qubits or the input to the fiber array. As shown in FIG. 2A, in some embodiments, spatial modes 135', 135'', and 135''' are separated far enough apart that their overlap is negligible (i.e., they do not overlap), while as shown in FIG. 2B, spatial modes 135 begin to overlap before the switching speed limit of modulator 120 (not shown) is reached (for clarity, only three spatial modes 135', 135'', and 135''' are labeled). Therefore, dispersive elements with high resolution are preferred for router 130 described herein.

[0042] In some embodiments, the router may comprise at least two dispersive optical elements, such as several narrowband frequency filters. Examples of suitable filters include fiber Bragg gratings, volume Bragg gratings, arrayed waveguide gratings, optical cavities (e.g., etalons), microring resonators, or arrays of unbalanced Mach-Zehnder interferometers. In one embodiment shown in FIG. 3, the router 330 includes a fiber Bragg grating 322. A plurality of tones 125 from the modulator 120 (not shown) are coupled into an optical fiber 321, each tone 125 resonantly reflects off a corresponding fiber Bragg grating 322', 322'', or 322''', and a resonant frequency beam 335', ​​335'', or 335''' is coupled out using a corresponding optical circulator 323', 323'', or 323'''.

[0043] In another embodiment shown in FIG. 4, the router 430 includes several narrowband optical cavities (e.g., etalons) 422. The modulated light 125 is reflected off an array of etalons, three etalons 422′, 422″, and 422′″ shown in FIG. 4, each passing an individual spectral tone 435′, 435″, or 435′″, and other frequency components are reflected. In this embodiment, the number of control channels, crosstalk, and switching speed are interrelated. Improved performance can be achieved by using multiple identical etalons in series (not shown) to filter individual spectral tones 435. Alternatively, in an embodiment shown in FIG. 5 using a photonic integrated circuit (PIC), the router 530 includes several micro-ring resonators 522, three micro-ring resonators 522′, 522″, and 522′″ shown in FIG. 5, instead of free-space etalons that filter individual control tones 535′, 535″, or 535′″ from the common beam 125.

[0044] In yet another embodiment using a photonic integrated circuit (PIC) as shown in FIG. 6, the router 630 includes an array of unbalanced Mach-Zehnder interferometers that filter individual control tones. In this embodiment, the two arms of the interferometer have a precisely designed path length difference L such that a subset of frequency components is demultiplexed at each layer of interferometers 622′, 622″, and 622′″. As an example, a grid of equally spaced control tones 635′, 635″, and 635′″, etc. is obtained by cascading multiple interferometer layers such that the path length difference ΔL is halved for each layer, shifting the center frequency of the interferometer filter function to select the frequency components. In another embodiment, the PIC can also implement a frequency filter based on optical dispersion through an arrayed waveguide grating (AWG). The AWG consists of an input waveguide containing radiation at multiple frequencies, which is diffracted and passes through a waveguide array. Radiation at different frequencies accumulates different phases in the waveguide array and is thus guided to different output waveguides. Yet another embodiment of the PIC uses a combination of in-plane diffraction and reflective interfaces within the PIC to create an echelle grating within the PIC. For example, a single input waveguide can direct multiple radiation frequencies into a blazed grating etched into the PIC, which distributes the individual frequencies to separate output waveguides.

[0045] Active matrix implementation Active matrix implementations utilize a combinatorial approach to increase the number of qubits that can be addressed with a given number of modulators. Simultaneity and specificity of addressing are achieved by ensuring that each qubit receives at least one unique combination of tones, which satisfies the resonance condition, and at least one of the tones in this unique combination is from a different modulator than the other tones.

[0046] An electromagnetic transition between two quantum states in a quantum m-level system is resonantly triggered only if the sum or difference of the energies of the incident photon fields reaches a certain resonance condition. For example, a transition is triggered by a single photon if the energy of the photon is equal to the energy difference ΔE between the quantum states. A two-photon transition is resonantly triggered if the sum of the energies of the two photons equals ΔE or if the difference in the energies of the photons equals ΔE. A three-photon transition is resonantly triggered if the sum of the three photon energies equals ΔE or if the sum of the two photon energies minus the other photon energy equals ΔE. If a quantum system is triggered by a photon whose energy does not reach a resonance condition, the transition is said to be non-resonantly triggered, and if the photon is sufficiently non-resonant, the change that the photon makes to the original quantum state is small. If the energy levels involved belong to a qubit, non-resonant actuation can lead to gate errors. In some embodiments, the energy levels are the ground and excited state energy levels of the qubit. In other embodiments, the energy levels are the hyperfine energy level of the ground state of the qubit and another hyperfine energy level.

[0047] Multiphoton transitions can be triggered between two quantum states singly or through an intermediate state of the same qubit. In general, the presence of an intermediate state greatly increases the rate at which transitions can be triggered. For example, for a two-photon transition between two states through a single intermediate state where both photons are equally off-resonant, the collective Rabi frequency can be expressed as Ω1Ω2 / Δ, where Ω1 and Ω2 are the resonant driving Rabi frequencies from each state to the intermediate state, and Δ is the general detuning from the intermediate state (provided Δ is much larger than the loss rate from the intermediate state). Equivalent expressions can be formulated for multiphoton transitions with a larger number of photons. Note that the value of Δ can be chosen freely so that there are many possible combinations of photon frequencies at which a two-photon transition can be resonantly triggered (though the two-photon Rabi frequency will necessarily vary).

[0048] According to one or more embodiments, as shown in FIG. 7A, the active matrix optical addressing system 700 includes one or more electromagnetic radiation sources 710. Examples of suitable electromagnetic radiation sources 710 include electronic oscillators, lasers, master-slave laser and amplifier systems, or incoherent sources such as superluminescent diodes. The source 710 may or may not be locked to an external reference frequency source through an injection locking subsystem or other frequency locking techniques. The power source 710 may operate with continuous wave (CW) power or as a pulsed oscillator. The optical addressing system 700 further includes one or more multi-frequency modulators 720 each configured to modulate the beam 715 of electromagnetic radiation generated by the radiation source 710, thereby generating multiple (725′, 725″, and 725′″ shown in FIG. 7A) electromagnetic radiation beams 725 having multiple frequencies. Examples of suitable multi-frequency modulators 720 include electrically driven optical frequency modulators based on electro-optic (e.g., Pockels, Kerr, or electrorotatory mechanisms), acousto-optic, stress-optic, optoelectronic semiconductor effects (e.g., plasma dispersion effect, quantum confined Stark effect or Franz-Keldysh effect, or other optical gain or loss modulation), or electrically driven microwave radiation modulators based on electron-induced dielectric constant changes in guiding or non-guiding (bulk) optical geometries, or varactors, or other diode-, MOSFET-, JFET-, and bipolar transistor-based devices such as mixers, parametric amplifiers, nonlinear transmission lines, variable gain amplifiers, etc. Alternatively, the modulator can be constructed from nonlinear optics or microwave electronics, where the modulation imprinted at one frequency using the modulator described above is transferred to the radiation of interest using a nonlinear medium, such as a nonlinear optical material (lithium niobate, potassium niobate, KTP, SiN, BBO, etc.), where the optical gain medium in such pumping effects acts as a nonlinearity, or in the microwave frequency range, discrete devices such as varactors or other diodes, MOSFETs, JFETs, and bipolar transistors, either alone or in combination, acting as an effective medium, or other nonlinear metamaterials.The modulators can be configured to modulate the amplitude, and / or phase, and / or polarization, and / or multiple guided mode states of the beam 715. The modulators 720 can be constructed in any one of a variety of topologies, including a single pass through a modulating structure, or a more complex structure such as an interferometer (e.g., Mach-Zehnder, Sagnac, Michelson, or Fizeau) coupled to a resonator that modulates inside or outside the resonator, or may be placed in the so-called "critical coupling" regime. The addressing system 700 further includes one or more single-frequency modulators 716, similar to the multi-frequency modulators described above, but each configured to modulate the beam of electromagnetic radiation 715 generated by the radiation source 710 to generate an electromagnetic radiation beam 717 having a desired single frequency. Alternatively, the optical addressing system 700 can further include one or more additional electromagnetic radiation sources to generate an electromagnetic radiation beam having a desired single frequency (not shown). The optical addressing system 700 further includes a router 740 configured to selectively direct the beam of electromagnetic radiation to the qubits 750. Router 740 includes a power splitter 741, for example made up of fiber splitter 741, and a power combiner 742, for example made up of fiber combiner 742, which directs a beam of electromagnetic radiation to quantum bits 750, as shown in FIG. 7A. Additional embodiments of elements 741 and 742 of router 740 are further described below. Any combination of elements 710, 720, 740, 741, and 742 can optionally be integrated into a monolithic assembly using an integrated photonics platform (e.g., using silicon photonics, indium phosphide photonics, silicon nitride photonics, lithium niobate integrated photonics, aluminum oxide photonics, aluminum nitride photonics, PLZT materials, or hybrid combinations thereof), integrated microwave electronics technology (e.g., using semiconductor, microstrip, stripline, or printed circuit board technology), or can be constructed from individual elements in a non-integrated manner.Alternatively, the functions of the radiation source 710 and the modulator 720 may be optionally combined into a single element, such as a current modulated laser diode or parametric oscillator driven by a modulated pump source. Alternatively, the "open loop" structure described above may be operated in a "closed loop", where one or more output radiation modes 725, or a portion of the energy of one or more radiation modes from the router 740, are redirected as full or partial inputs referring to or replacing the source 710.

[0049] Implementing N-choose-k Considering transitions caused by k different frequency photons (k is an integer equal to or greater than 2), it is possible to create combinations of the outputs of N modulators such that more than N qubits can be controlled simultaneously and independently. Although many qubits can be exposed to radiation from a particular modulator, tones from at least two modulators are required, since no single modulator can provide photons at all k relevant frequencies to cause a particular transition. Different modulators can provide the same combination of tones, and these tones can be switched on and off individually. Thus, N qubits can be controlled simultaneously for k photon transitions. m Maximum qubits N that can be addressed by a modulator q teeth,

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[0050] For example, consider a qubit triggered by a two-photon (i.e., k=2) transition from |g> to |e> via an optional intermediate state |i>, as shown in FIG. 7B. All different two-modulator combinations shown in FIG. 7A can simultaneously and independently trigger resonant two-photon transitions in different qubits. A suitable, but non-limiting recipe for selecting appropriate frequency tones is as follows: Let single frequency modulator 716 generate frequency v1. Let each of the remaining N-1 multi-frequency modulators 720 generate a frequency v1+v2=v res Let us generate a frequency ν2 such that res is the resonant frequency of the transition. Let us combine the outputs of these modulators 716 and 720 into unique N-1 combinations of the first and the remaining N-1 modulators as shown in FIG. 7A. By switching on and off the modulator 720 that generates a tone at v2 using controller 705, control of the N-1 qubits can be achieved. Now, multi-frequency modulator 720' also generates a tone v3, and v3+v4=v4, such that neither v1+v3 nor v2+v3 satisfy the resonant condition. res 7A. Let the remaining N-2 multi-frequency modulators 720 generate tone v4 such that neither v1+v4 nor v2+v4 satisfy the resonance condition. The outputs shall be coupled to a unique combination of modulator 720' shown in FIG. 7A and the remaining N-2 multi-frequency modulators 720'' and 720'''. This process repeats for the N m This is repeated until all modulators are used, as shown for =4. The number of addressable qubits is therefore (N-1)! for two-photon transitions (3!=6 qubits in the example shown in Figure 7A), or more generally N! / (k!(Nk)!) for k-photon transitions.

[0051] Various different configurations of devices that enable control of qubits are described herein. Apart from generating the control tones, the active matrix device must combine and transmit the tones from the various modulators to the qubits. If the qubit transitions are optical frequency transitions, a suitable device can use fiber optic elements. The output of each of the N modulators is split into N-1 channels by fiber splitters 741, and all N-choose-k combinations of these split outputs are created in fiber combiner 742. The combined control tones can be delivered to the qubits using a fiber array and an imaging system. An equivalent device replaces all or part of the fiber elements with photonic integrated circuit (PIC) elements. Another version of a suitable device for inducing two-photon transitions retains the fiber splitters but omits the fiber combiner and projects an array of beams onto the qubits from opposite sides (e.g., using two opposing fiber arrays), so that the control tones are combined at the qubits. Additionally, a third version of the active matrix device creates the array of beams without the use of the aforementioned fiber optic elements by employing an implementation of holographic addressing. In such devices, spatial light modulators or phase plates can be used to create arbitrary patterns of beams, with different patterns being created by different illumination angles. The system is configured so that overlapping beams from different combinations of modulators are imaged onto each qubit. This version of the active matrix device is dynamically reconfigurable, so it is not limited to addressing qubits arranged according to a specific geometry.

[0052] Grid Index Implementation In an embodiment where the qubits are located on a D-dimensional grid, for two-photon transitions, the qubits are located at the points of a two-dimensional (2D) grid in space, with rows and columns addressed by separate modulators. For three-photon transitions, the qubits can be located at the points of a 3D grid. In either case, the grid can be a logical index structure rather than a real-space arrangement. Thus, this implementation can be used for transitions caused by four or more photons, with the grid being a logical index structure that is mapped to a real-space structure of three dimensions or less. This combinatorial arrangement of modulators allows N modulators to cause k-photon transitions (N / k). k It becomes possible to control quantum bits.

[0053] Nine qubits (N q An optical addressing system 800 consisting of six modulators (N=6) on a two-dimensional (D=2) grid of three (N=9) modulators is shown in FIGS. 8A-8B. Three selectable electromagnetic radiation beams 825 are q (k-1) / D =9 1 / 2 =3) multi-frequency modulator 820, and three ([N q 1 / D x(k-1)]=9 1 / 2=3) The single frequency modulators each combine with a single one of the beams generated by the multi-frequency modulator 820 to generate a beam of electromagnetic radiation with a distinct frequency that satisfies the frequency resonance condition. The combination of the modulator outputs selected by the controller 805 can be done in a router 840 with fiber or integrated waveguide splitters 841 and combiners 842 by holographically multiplexing the control beams or by a combination of these two approaches. If the qubit transitions are RF or microwave transitions, each qubit can be coupled to k striplines. Alternatively, if the qubit transitions are optical transitions and the real space arrangement of qubits is a grid, the rows, columns, and sheets of a two- or three-dimensional grid can be illuminated by beams propagating along the grid dimensions. An embodiment of two-photon transitions and two-dimensional qubit arrays is shown in FIG. 8B.

[0054] Although the scale of the number of qubits to the number of modulators for the grid-indexed device is not as favorable as the N-choose-k device described above, each modulator requires a lower bandwidth because it must generate at most N / k tones instead of N-1 tones. Furthermore, multi-frequency modulators 820', 820'', and 820''' are only required along one dimension of the modulator arrangement. The other dimension can be driven by single-frequency modulators 816', 816'', and 816'''. By employing one of the frequency division demultiplexing devices described above, the single-frequency dimension of the modulator arrangement can be driven by a multi-tone modulator / demultiplexer (not shown), further reducing the total number of modulators.

[0055] Tagged implementations Another embodiment of the active matrix device involves providing the k-1 photons required for a k-photon transition in a static manner in at least one dimension, such that each quantum bit requires a kth photon of a different frequency to complete the transition. In effect, each quantum bit is "tagged" with a unique frequency. The quantum bits are also globally triggered by a separate modulator that generates all the control tones required to complete each quantum bit transition, one control tone corresponding to each quantum bit arranged on a k-dimensional grid, and the router is configured to provide a set of N m Let the beam of electromagnetic radiation generated by the modulators be (N m / k) kqubits. If the qubit transitions are optical transitions, then any of the above devices can be supplemented with modulators, delivery optics, and a beam that collectively illuminates all qubits to enable this tagged implementation for simultaneous and independent qubit addressing using k-photon transitions for at least two k's. An embodiment for k=2 using the level scheme shown in FIG. 7B is shown in FIG. 9 for six single-frequency modulators (Nm=6). Either the row single-frequency modulators 916', 916'', and 916''' or the column single-frequency modulators 917', 917'', and 917'''' can be statically turned on, and turning on one modulator in the other dimension and turning on one of the tones v2, v4, or v6 of the multi-frequency modulator 920 will address a particular qubit. Another embodiment of a tagged active matrix implementation with a three-photon transition between the ground state |g> and the excited state |e>, and two intermediate states |i1> and |i2>, is shown in Figures 10A and 10B. Here, the qubits are also arranged on a grid, and the row 1016 and column 1020 modulators generate static tones, so that each qubit is addressable by a unique combination of two tones ("tags"). The three-photon transition is completed for each qubit by a unique third tone, generated by a multi-frequency modulator corresponding to every qubit. Thus, active control of only a single multi-frequency modulator 1021 is required to simultaneously and independently control all qubits.

[0056] Addressing nonlinear optical elements In the above described embodiment, the control tone in the active matrix implementation induces multi-photon transitions in the qubits at the sum or difference frequency. In yet another embodiment, the nonlinear optical element physically generates new light waves at the sum or difference frequency of the incident light, which propagate and generate single or multi-photon transitions in the qubits. An arbitrary dimensional array of such nonlinear optical devices, as many as the number of qubits being addressed, can be seeded with an input laser beam in the above described active matrix implementation, thus similarly reducing the number of modulators used to address a given number of qubits.

[0057] As shown in FIG. 11, each nonlinear optical element 1145 in the array selectively generates a specific mixed product wavelength resulting from a combination selected by the controller 1105 of the beam 1117 from the single frequency modulator 1116 and the beam 1125 from the multi-frequency modulator 1120 split by the power splitter 1141 and combined by the power combiner 1142 in the router 1140. The sum or difference frequency generation process can be selectively resonated using phase matching and a resonator structure built around the nonlinear optical elements, similar to the transition of a qubit caused between energy levels. Optical downconverters, upshifters, or optical parametric amplifiers and oscillators can be created by passing two or more laser beams of frequency νi through optical nonlinear materials such as lithium niobate, lithium tantalate, BBO, potassium niobate, silicon nitride, aluminum nitride, or other nonlinear materials. These nonlinear materials can be periodically polarized to phase match a specific frequency conversion process to generate a new frequency ν'=Σ i m i ν i can be efficiently generated, where m i is a positive or negative integer. For example, two laser beams with a nominal wavelength of 1560 nm are 2 Optical nonlinearities can be exploited to efficiently double the frequency. Another example is the χ 3The use of nonlinearity to generate near-third harmonic light at an optical wavelength of about 420 nm from three different laser beams at wavelengths of about 1260 nm. In either or both of these examples, nonlinear processes can occur within the waveguide structure to improve optical conversion efficiency with limited optical power, and furthermore, cavity-like structures can enhance resonance. In one embodiment, the resonant structure is a waveguide ring lithographically defined in a silicon nitride photonic circuit.

[0058] equivalent Thus, although some exemplary embodiments have been described, it will be understood that various changes, modifications, and improvements will be readily made by those skilled in the art. Such changes, modifications, and improvements are intended to form part of this disclosure and are intended to be within the spirit and scope of this disclosure. Although some examples presented herein include specific combinations of functions or structural elements, it should be understood that these functions and elements may be combined in other ways in accordance with this disclosure to achieve the same or different purposes. In particular, acts, elements, and features described in connection with one embodiment are not intended to be excluded from similar or other roles in other embodiments. Furthermore, elements and components described herein may be further divided into additional components or combined together to form fewer components for performing the same functions.

[0059] The foregoing description of exemplary embodiments has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise form disclosed. Many modifications and variations are possible in light of this disclosure. It is intended that the scope of the disclosure be limited not by this detailed description, but by the appended claims. Future applications claiming priority to this application may claim the disclosed subject matter in a different manner, and may generally include any set of one or more limitations as variously disclosed or demonstrated herein.

Claims

1. 1. An optical addressing system comprising: Sources of electromagnetic radiation; at least one multi-frequency modulator configured to modulate electromagnetic radiation generated by an electromagnetic radiation source to simultaneously generate at least two beams of electromagnetic radiation having different frequencies, each configured to, when applied to a multi-level quantum object, at least partially cause one or more transitions between energy levels of the multi-level quantum object; a router configured to selectively direct at least two beams of electromagnetic radiation to a multi-level quantum object. The system comprising:

2. 2. The system of claim 1, wherein the at least one multi-frequency modulator is further configured to generate a beam of electromagnetic radiation having a spectral distribution of frequencies for each of the at least two beams of claim 1, such that one beam has a first spectral distribution and another beam has a second spectral distribution, the first and second spectral distributions being non-overlapping.

3. 13. The system of claim 1, further comprising at least one single frequency modulator configured to modulate the electromagnetic radiation generated by the source of electromagnetic radiation to generate an electromagnetic radiation beam having a frequency that, in combination with a single beam of the at least two beams generated by the at least one multi-frequency modulator, satisfies a frequency resonance condition, the combination causing one or more transitions between energy levels of the multi-level quantum object.

4. 4. The system of claim 3, wherein the beams of electromagnetic radiation generated by the multi-frequency and single-frequency modulators are optical beams, the source of electromagnetic radiation is an optical radiation source, and the router further comprises a nonlinear optical medium for combining the optical beams.

5. The system of claim 4 , wherein the nonlinear optical medium is periodically poled lithium niobate (PPLN).

6. 6. The system of claim 3, wherein the frequency resonance condition is that the sum of the frequency of the beam of electromagnetic radiation generated by the single frequency modulator and the frequency of a single beam of the at least two beams generated by the at least one multi-frequency modulator causes a transition, and the energy levels are ground state energy levels and excited state energy levels of the multi-level quantum object.

7. 6. The system of claim 3, wherein the frequency resonance condition is that a difference between the frequency of the beam of electromagnetic radiation generated by the single frequency modulator and the frequency of a single beam of the at least two beams generated by the at least one multi-frequency modulator causes a transition, and the energy level is a hyperfine energy level other than the hyperfine energy level of the ground state of the multi-level quantum object.

8. The system of claim 1 , wherein the one or more transitions are k-photon transitions, where k is 2 or greater.

9. The router further ｍ Let N be the beams of electromagnetic radiation generated by the modulators. ｍ -choose-k unique combinations, each multi-level quantum object N ｑ receiving k beams having frequencies that satisfy a frequency resonance condition for transitions between energy levels of a multi-level quantum object, each of the k beams being generated by a different modulator; [0010] The system of claim 8 ,

10. 10. The system of claim 9, wherein the frequency resonance condition is that the sum of the frequencies of the k beams causes a transition, and the energy levels are ground state energy levels and excited state energy levels of a multi-level quantum object.

11. 10. The system of claim 9, wherein the frequency resonance condition is that the difference between the frequencies of the k beams causes a transition, the energy level of which is a hyperfine energy level other than the hyperfine energy level of the ground state of the multi-level quantum object.

12. The router is ｍ The electromagnetic radiation beams generated by the modulators (N ｍ 10. The system of claim 9, further configured to selectively direct k unique combinations, wherein the multi-level quantum objects are arranged on a k-dimensional grid.

13. N ｑ The multi-level quantum objects are arranged on a D-dimensional grid, and the router further comprises: ｑ （ｋ－１）／Ｄ The selectable beams are N ｑ the system is further configured to selectively direct the multi-level quantum objects at [N ｑ １／Ｄ x(k−1)], each of which generates an electromagnetic radiation beam having a different frequency that satisfies a frequency resonance condition in combination with a single beam of the at least two beams generated by the at least one multi-frequency modulator.

14. The system of claim 3 , wherein the router is further configured to combine the beams in free space.

15. The system of claim 3 , wherein the beams of electromagnetic radiation are combined with multi-level quantum objects.

16. The system of claim 3 , wherein the router comprises at least one waveguide positioned to combine at least two beams of electromagnetic radiation.

17. The system of claim 3 , wherein the router comprises at least one photonic integrated circuit (PIC) configured to combine at least two beams of electromagnetic radiation.

18. The system of claim 3 , wherein the router comprises a holographic addressing system.

19. The system of claim 18 , wherein the holographic addressing system is a spatial light modulator (SLM).

20. The system of claim 18 , wherein the holographic addressing system is a phase plate.

21. The system of claim 1 , wherein the router further comprises a frequency division demultiplexer (demultiplexer) configured to separate the at least two beams of electromagnetic radiation.

22. 22. The system of claim 21, wherein the at least two beams of electromagnetic radiation generated by the at least one multi-frequency modulator are RF or microwave beams, the source of electromagnetic radiation is an oscillator or digital synthesizer, and the demultiplexer is an electronic demultiplexer.

23. 23. The system of claim 22, wherein the router further comprises at least one RF or microwave waveguide configured to direct at least two beams of RF or microwave electromagnetic radiation to the multi-level quantum object.

24. 24. The system of claim 23, wherein at least one RF or microwave waveguide is a coaxial cable or a stripline.

25. 23. The system of claim 22, wherein the electronic demultiplexer is an assembly of electronic filters.

26. 23. The system of claim 22, wherein the electronic demultiplexer is an assembly of electronic mixers.

27. 23. The system of claim 22, wherein the electronic demultiplexer is an assembly of electronic switches.

28. 22. The system of claim 21, wherein the at least two electromagnetic radiation beams generated by the at least one multi-frequency modulator are optical beams, the source of electromagnetic radiation is an optical radiation source, and the demultiplexer is a volume Bragg grating.

29. 22. The system of claim 21, wherein the at least two electromagnetic radiation beams generated by the at least one multi-frequency modulator are optical beams, the source of electromagnetic radiation is an optical radiation source, and the demultiplexer is an optical demultiplexer.

30. 30. The system of claim 29, wherein the light radiation source is a laser or a superluminescent diode.

31. 30. The system of claim 29, wherein the photo-radiation source and the at least one multi-frequency modulator are integrated into a multi-frequency photo-radiation source.

32. 30. The system of claim 29, wherein the at least one multi-frequency modulator is an electro-optic modulator, an acousto-optic modulator, a micro-electromechanical (MEM) modulator, or a variable gain amplifier.

33. 30. The system of claim 29, wherein the optical demultiplexer is at least one free space dispersive optical element.

34. 34. The system of claim 33, wherein the at least one dispersive optical element is at least one optical grating.

35. 35. The system of claim 34, wherein the at least one optical grating is at least one reflective grating.

36. 34. The system of claim 33, wherein the at least one dispersive optical element is at least two free space dispersive optical elements.

37. 37. The system of claim 36, wherein the at least two dispersive optical elements are at least two etalons.

38. 30. The system of claim 29, wherein the optical demultiplexer is at least one dispersive optical fiber element.

39. 40. The system of claim 38, wherein the at least one dispersive optical fiber element is at least one fiber Bragg grating.

40. 30. The system of claim 29, wherein the optical demultiplexer is a photonic integrated circuit (PIC).

41. 41. The system of claim 40, wherein the PIC comprises a tree of unbalanced Mach-Zehnder interferometers.

42. 41. The system of claim 40, wherein the PIC comprises an array of micro-ring resonators.

43. 30. The system of claim 29, wherein the router further comprises at least one optical waveguide.

44. 44. The system of claim 43, wherein the at least one optical waveguide is at least one fiber.

45. 44. The system of claim 43, wherein the at least one optical waveguide is at least one integrated optical structure.

46. 30. The system of claim 29, wherein the router further comprises a beam forming device.

47. 47. The system of claim 46, wherein the beam shaping device is a spatial light modulator (SLM), a phase plate, or an array of phase plates.

48. The system of claim 1 , wherein the multi-level quantum object is selected from the group consisting of neutral atoms, trapped ions, quantum dots, and superconducting rings.

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