Parallel sideband cooling of multiple trapped ion motion modes by deflectors.

Abstract

Aspects of the present disclosure generally relate to parallel sideband cooling of multiple trapped ion motional modes using deflectors (e.g., acousto-optic deflectors or AODs) in quantum information processing (QIP) systems. Methods and systems are described for identifying a first group of ions (e.g., a middle portion of the ion chain) and a second group of ions (e.g., an outer portion of the ion chain) for an ion chain. The methods and systems include providing sideband cooling by applying a first pair of light beams to the first group of ions using a first pair of AODs and applying a second pair of light beams to the second group of ions using a second pair of AODs. For each AOD, an acousto-optic modulator (AOM) may be positioned upstream to provide frequency modulation to match the frequency difference to the correct detuning as part of the sideband cooling operation.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of priority to U.S. Provisional Application No. 63 / 286,865, filed on December 7, 2021, entitled “Parallel Sideband Cooling of Multiple Trapped-Ion Motional Modes with AODs,” and U.S. Non-Provisional Application No. 18 / 062,404, filed on December 6, 2022, entitled “Parallel Sideband Cooling of Multiple Trapped-Ion Motional Modes with Deflectors,” all of which are incorporated by reference herein for all purposes.

[0002] Aspects of the present disclosure generally relate to systems and methods for implementing, operating and / or using quantum information processing (QIP) systems. [Background technology]

[0003] Captured (or trapped) atoms are one of the primary implementations of quantum information processing and quantum computation. Atom-based qubits can be used as quantum memories or as quantum gates in quantum computers and quantum simulators, and can act as nodes in quantum communication networks. Qubits based on trapped atomic ions have a rare combination of properties. For example, qubits based on trapped atomic ions have exceptional coherence properties, can be created and measured with nearly 100% efficiency, and can be easily entangled with each other by modulating the Coulomb interaction with a suitable external control field, such as an optical or microwave field. These properties make atom-based qubits attractive for extended quantum operations, such as quantum computing and quantum simulation. Summary of the Invention [Problem to be solved by the invention]

[0004] It is therefore important to develop new techniques to improve the design, fabrication, implementation, control and / or functionality of various QIP systems used as quantum computers and quantum simulators, particularly those that involve operations based on atom-based qubits.

[0005] The following presents a simplified summary of one or more aspects in order to provide a basic understanding of such aspects. This summary is not an exhaustive overview of all contemplated aspects, nor is it intended to identify key or critical elements of all aspects or to delineate the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form as a prelude to the more detailed description that is presented later. [Means for solving the problem]

[0006] This disclosure describes various aspects of parallel sideband cooling of multiple trapped ion motional modes using deflectors (e.g., acousto-optic deflectors or AODs) in quantum information processing (QIP) systems. A method for sideband cooling of an ion chain includes identifying a first group of ions in the ion chain and a second group of ions in the ion chain, where the ions in the first group of ions are different from the ions in the second group of ions. The method further includes providing sideband cooling of the ion chain by applying a first pair of light beams to the first group of ions using a first pair of deflectors (e.g., AODs) and applying a second pair of light beams to the second group of ions using a second pair of deflectors (e.g., AODs).

[0007] A QIP system configured for sideband cooling of an ion chain comprises an ion trap configured to hold a chain of ions, where ions in the ion chain are part of a first population of ions or a second population of ions, the ions of the first population of ions being different from the ions of the second population of ions, the QIP system further comprises a first pair of deflectors (e.g., AODs) configured to apply a first pair of light beams to the first population of ions, and a second pair of deflectors (e.g., AODs) configured to apply a second pair of light beams to the second population of ions.

[0008] In this disclosure, the term quantum computer may be used interchangeably with the term QIP system to mean a system or device capable of performing quantum operations and quantum algorithms.

[0009] To the accomplishment of the foregoing and related ends, the one or more aspects comprise the features hereinafter fully described and particularly pointed out in the claims. The following description and the annexed drawings set forth in detail certain illustrative features of the one or more aspects. These features are indicative, however, of but a few of the various ways in which the principles of the various aspects may be employed and the description is intended to include all such aspects and their equivalents. [Brief description of the drawings]

[0010] The disclosed aspects are described below in conjunction with the accompanying drawings, which are provided to illustrate, and not to limit, the disclosed aspects, in which like designations refer to like elements and in which: [Figure 1] FIG. 1 is a diagram illustrating linear crystals or chains of atomic ions according to an embodiment of the present disclosure. [Diagram 2] FIG. 2 is a diagram illustrating an example of a quantum information processing (QIP) system according to an embodiment of the present disclosure. [Diagram 3] FIG. 3 is a diagram illustrating an example of a computing device according to an aspect of the present disclosure. [Figure 4]FIG. 4 is a diagram illustrating an example of a counter-propagating beam scanning system according to an embodiment of the present disclosure. [Figure 5A] FIG. 5A illustrates an example of a deflector-based Raman optical system according to an embodiment of the present disclosure. [Figure 5B] FIG. 5B illustrates an example of a deflector-based Raman optical system according to an embodiment of the present disclosure. [Figure 6] FIG. 6 illustrates an example of a technique for localized mode cooling according to an embodiment of the present disclosure. [Figure 7A] FIG. 7A illustrates an example of a technique for using deflectors for local mode cooling according to an embodiment of the present disclosure. [Figure 7B] FIG. 7B illustrates an example of a technique for using deflectors for local mode cooling according to an embodiment of the present disclosure. [Figure 8] FIG. 8 illustrates an example of how a deflector may be used for sideband cooling operation according to an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] The detailed description set forth below with respect to the accompanying drawings is intended as a description of various configurations or embodiments, and is not intended to represent the only configurations or embodiments in which the concepts described herein may be practiced. The detailed description includes specific details for the purpose of providing a thorough understanding of the various concepts. However, it will be apparent to those skilled in the art that these concepts may be practiced without these specific details. In some instances, one or more well-known structures and components are shown in block diagram form to avoid obscuring such concepts.

[0012] Optical Raman transitions are commonly used as a means by which trapped ions (see, for example, Figure 1) in linear chains are cooled to the ground state of their motional mode through a process known as sideband cooling (SBC). This is a critical step in the initialization of a trapped ion quantum computer, and the performance of this stage can directly affect the quality of the computation.

[0013] In trapped ion chains with only a few ions, SBC can be performed in a simple sequential manner, where each mode of the ion chain is cooled in turn. The technique does not depend on the details of the Raman light beam geometry and can be performed with fewer light beams than there are ions in the chain, for example with just a single pair of globally addressing light beams.

[0014] For long trapped ion chains (i.e. many ions arranged in a straight line), SBC becomes more complex. Since many modes of motion exist in long chains, sequential cooling takes a long time, and all ion traps have a so-called heating rate that is essentially in competition with the cooling provided by SBC. This heating rate limits the performance of the SBC and, if it is higher than the SBC rate, the cooling fails completely. Furthermore, longer trapped ion chains involve more complex mode structures, details of the light beam shape and the mode contribution of the trapped ions.

[0015] Several techniques have been proposed to efficiently perform SBC of long ion chains using a set of fully connected Raman light beams (e.g., one for each ion), known as "local mode cooling". This technique relies on the fact that it is possible to have as many simultaneous Raman light beams as there are ions in the chain, and that the light frequencies of each light beam can be chosen to be different. This allows one to tune which frequency of light hits which ion, enhancing the effect of the light cooling force on the ion chain and efficiently utilizing the available refractive power. However, limiting the configuration of a trapped ion quantum computer to a set of fully connected Raman light beams for the benefits of SBC may affect other, arguably important, features of the quantum computer, such as high-fidelity gates. Thus, although the technique is highly efficient, other concerns may arise in the performance of the overall system.

[0016] The present disclosure proposes the use of a technique that combines the use of an acousto-optic modulator (AOM) and a deflector (e.g., AOD) that has the capability of providing efficient parallel-mode sideband cooling of long ion chains without the penalty of having a fully connected set of Raman light beams.

[0017] Solutions to the above-mentioned problems are described in more detail in connection with Figures 1-7B, which provide background on QIP systems or quantum computers, and more specifically, atom-based QIP systems or quantum computers.

[0018] FIG. 1 illustrates a diagram 100 in which a number of atomic ions 106 (e.g., atomic ions 106a, 106b, ..., 106c, 106d) are trapped in a linear crystal or chain 110 using a trap (not shown, but the trap may be located in a vacuum chamber, as shown in FIG. 2). The trap may be referred to as an ion trap. The illustrated ion trap may be constructed or fabricated on a semiconductor substrate, a dielectric substrate, a glass die or a wafer (also referred to as a glass substrate). The ions 106 may be provided to the trap as atomic species for ionization and trapping in the chain 110. Some or all of the ions 106 may be configured to operate as quantum bits in a QIP system. Additionally, a quantum processor (sometimes simply referred to as a processor) may be part of a quantum computer or QIP system that includes the chain 110 and may perform quantum operations using the ions 106 in the chain 110.

[0019] In the example shown in Figure 1, the trap includes electrodes for trapping or confining a number of ions in chains 110 that are laser cooled to a nearly stationary state. The number of trapped ions is configurable, and more or fewer ions may be trapped. The ions may be, for example, ytterbium ions (e.g., 171 Yb + ions). The ions can be 171 Yb +The ions are illuminated with laser (optical) radiation tuned to the resonance of the ions, and the fluorescence of the ions is imaged on a camera or other type of detection device (e.g., photomultiplier tube or PMT). In this example, the ions may be separated from each other by as much as a few microns (μm), and the separation may vary depending on the architectural configuration. The separation of the ions is determined by a balance between external confinement forces and Coulomb repulsion, and does not have to be uniform. Furthermore, in addition to ytterbium ions, barium ions, neutral atoms, Rydberg atoms, or different types of atom-based qubit technologies may also be used. Furthermore, ions of the same species, different species, and / or ions of different isotopes may also be used. The trap may be a linear RF power trap, but other types of confinement devices may be used, including optical confinement. Thus, the confinement device may hold, for example, ions, neutral atoms, or Rydberg atoms based on various technologies, and an ion trap is one example of such a confinement device. The ion trap may be, for example, a surface trap.

[0020] 2 is a block diagram illustrating an example of a QIP system 200. QIP system 200 may also be referred to as a quantum computing system, a quantum computer, a computing device, a trapped ion system, etc. QIP system 200 may be part of a hybrid computing system in which QIP system 200 is used to perform quantum computations and operations, and the hybrid computing system also includes a classical computer for performing classical computations and operations. In such a hybrid system, quantum and classical computations and operations may interact.

[0021] Shown in FIG. 2 is a general controller 205 configured to perform various control operations of the QIP system 200. These control operations may be operator initiated, automated, or a combination of both. Instructions for at least some of the control operations may be stored in a memory (not shown) in the general controller 205 and updated over time via a communication interface (not shown). Although the general controller 205 is shown separate from the QIP system 200, it may be integrated with or be part of the QIP system 200. The general controller 205 may include an automation and calibration controller 280 configured to perform various calibration, inspection, and automation operations associated with the QIP system 200. These calibration, inspection, and automation operations may include, for example, all or a portion of the algorithms component 210, all or a portion of the optics and capture controller 220, and / or all or a portion of the chamber 250.

[0022] The QIP system 200 may include the algorithm component 210 described above, which may operate with other parts of the QIP system 200 to execute or implement a quantum algorithm, quantum application, or quantum operation. The algorithm component 210 may be used to execute or implement a combination stack or sequence of single qubit operations and / or multi-qubit operations (e.g., two qubit operations) as well as extended quantum computations. The algorithm component 210 may include software tools (e.g., compilers) that enable such performance or implementation. In this manner, the algorithm component 210 may provide directs, directly or indirectly, to various components of the QIP system 200 (e.g., the optical and capture controller 220) to enable the performance or implementation of a quantum algorithm, quantum application, or quantum operation. The algorithm component 210 may receive information resulting from the execution or implementation of a quantum algorithm, quantum application, or quantum operation, process the information, and / or forward the information to other components of the QIP system 200 or to another device (e.g., an external device connected to the QIP system 200) for further processing.

[0023] The QIP system 200 may include the aforementioned optics and trap controller 220, which controls various aspects of the trap 270 in the chamber 250, including generating signals to control the trap 270. The optics and trap controller 220 may also control the operation of the laser, optical system, and optical components used to provide a light beam that interacts with the atoms or ions in the trap. An optical system including multiple components may be referred to as an optical assembly. The light beam is used to set up the ions, run or implement a quantum algorithm, quantum application, or quantum operation on the ions, and read the results from the ions. Controlling the operation of the laser, optical system, and optical components may include dynamically changing the operating parameters and / or configuration, including controlling positioning using motorized mounts or holders. When used to confine or trap ions, the trap 270 may be referred to as an ion trap. However, the trap 270 may also be used to trap neutral atoms, Rydberg atoms, and different types of atom-based qubits. The laser, optical system, and optical components may be at least partially located within the optics and trap controller 220, the imaging system 230, and / or the chamber 250.

[0024] QIP system 200 may include an imaging system 230. Imaging system 230 may include a high resolution imager (e.g., a CCD camera) or other type of detection device (e.g., a PMT) for monitoring ions while they are being delivered to trap 270 and / or after they are delivered to trap 270. In some embodiments, imaging system 230 may be implemented separately from optics and trap controller 220, although the use of fluorescence to detect, identify, and label ions using image processing algorithms may need to be coordinated with optics and trap controller 220.

[0025] In addition to the above-mentioned components, QIP system 200 may include a source 260 that provides atomic species (e.g., a plume or flux of neutral atoms) to a chamber 250 having a trap 270. Where atomic ions are the basis of quantum operations, the trap 270 confines the atomic species once ionized (e.g., photoionized). The trap 270 may be part of the processor or processing portion of the QIP system 200. That is, the trap 270 may be considered to be at the core of the processing operations of the QIP system 200, as it holds the atomic-based quantum bits that are used to perform or implement quantum operations or quantum simulations. At least a portion of the source 260 may be implemented separately from the chamber 250.

[0026] It should be understood that the various components of the QIP system 200 depicted in Figure 2 are depicted at a high level for ease of understanding. Such components may include one or more subcomponents, the details of which are provided below as necessary to better understand certain aspects of the present disclosure.

[0027] Aspects of the present disclosure may be implemented, at least in part, using optical components within QIP system 200, including those that are part of and controlled by optics and capture controller 220, imaging system 230, and / or chamber 250.

[0028] An example of a computer system or device 300 is shown in FIG. 3. The computer device 300 may represent, for example, a single computing device, multiple computing devices, or a distributed computing system. The computer device 300 may be configured to perform a quantum computer (e.g., a QIP system), a classical computer, or a combination of quantum and classical computer functions (sometimes referred to as hybrid functions or operations). For example, the computer device 300 may be used to process information using quantum algorithms, classical computer data processing operations, or a combination of both. In some cases, the results of one set of operations (e.g., a quantum algorithm) are shared with another set of operations (e.g., classical computer data processing). A typical example of a computer device 300 implemented as a QIP system capable of performing quantum computation and quantum simulation is, for example, the QIP system 200 shown in FIG. 2.

[0029] The computing device 300 may include a processor 310 for performing processing functions related to one or more features described herein. The processor 310 may include a single or multiple processor sets or one or more multi-core processors. Additionally, the processor 310 may be implemented as an integrated and / or distributed processing system. The processor 310 may include one or more central processing units (CPUs) 310a, one or more graphics processing units (GPUs) 310b, one or more quantum processing units (QPUs) 310c, one or more intelligent processing units (IPUs) 310d (e.g., artificial intelligence or AI processors), or a combination of some or all of these types of processors. In one aspect, the processor 310 may refer to the overall processor of the computing device 300 and may include additional processors 310 that perform more specific functions (e.g., including functions to control the operation of the computing device 300). Quantum operations may be performed by the QPU 310c. Some or all of the QPUs 310c may use atom-based qubits, although it is also possible that different QPUs are based on different qubit technologies.

[0030] The computing device 300 may include a memory 320 for storing instructions executable by the processor 310 to perform operations. The memory 320 may store data for processing by the processor 310 and / or data resulting from processing by the processor 310. In some embodiments, for example, the memory 320 may correspond to a computer-readable storage medium that stores code or instructions for performing one or more functions or operations. As with the processor 310, the memory 320 may refer to the overall memory of the computing device 300 and may include additional memory 320 that stores instructions and / or data for more specific functions.

[0031] It should be understood that the processor 310 and memory 320 may be used in connection with different operations, including, but not limited to, operation, calculation, simulation, control, calibration, system management and other operations of the computing device 300, including any of the methods or processes described herein.

[0032] Additionally, the computing device 300 may include a communications component 330 for utilizing hardware, software, and services to establish and maintain communications with one or more parties. The communications component 330 may be used to communicate between components on the computing device 300 as well as between the computing device 300 and external devices, such as devices located on opposite sides of a communications network and / or connected serially or locally to the computing device 300. For example, the communications component 330 may include one or more buses and may further include transmit chain and receive chain components associated with transmitters and receivers, respectively, operable to connect and function with external devices. The communications component 330 may be used to receive updated information regarding the operation or functionality of the computing device 300.

[0033] Additionally, computing device 300 may include data storage 340, which may be any suitable combination of hardware and / or software, providing mass storage of information, databases, and programs employed in connection with the operation of computing device 300 and / or any method or process described herein. For example, data storage 340 may be a data repository for operating system 360 (e.g., a classical OS, a quantum OS, or both). In one embodiment, data storage 340 may include memory 320. In one embodiment, processor 310 executes operating system 360 and / or applications or programs, and memory 320 or data store 340 may store them.

[0034] Computing device 300 may also include a user interface component 350 configured to receive input from a user of computing device 300 and further configured to generate output for presentation to the user or for provision (directly or indirectly) to another system. User interface component 350 may include one or more input devices, including, but not limited to, a keyboard, a number pad, a mouse, a touch-sensitive display, a digitizer, navigation keys, function keys, a microphone, a voice recognition component, other mechanisms capable of receiving input from a user, or any combination thereof. Additionally, user interface component 350 may include one or more output devices, including, but not limited to, a display, a speaker, a haptic feedback mechanism, a printer, other mechanisms capable of presenting output to a user, or any combination thereof. In one embodiment, user interface component 350 may send and / or receive messages corresponding to operations of operating system 360. If computing device 300 is implemented as part of a cloud-based infrastructure solution, user interface component 350 may be used to enable a user of the cloud-based infrastructure solution to interact with computing device 300 remotely.

[0035] Methods and systems for parallel sideband cooling of multiple trapped ion motional modes using a deflector (e.g., an acousto-optic deflector or AOD) are described in more detail below in connection with the systems described in Figures 1-3.

[0036] Figure 4 is a diagram 400 illustrating an example of a counter-propagating optical beam scanning system that uses deflectors (e.g., AODs) for optical beam steering. The general optical concept here is that in a system that is symmetric in each propagation direction (double individual), the position-dependent frequency of the AODs cancels out and Df remains constant. In this example, a pair of optical beams can be directed at different ions in an ion chain, and each ion can be used to implement a single qubit gate.

[0037] Diagram 400 shows a left system including an optical beam source 405a, a deflector 410a, and a set of optical components 440a with imaging optical components 425a, 430a, 435a. Diagram 400 also shows a right system including an optical beam source 405b, a deflector 410b, and a set of optical components 440b with imaging optical components 425b, 430b, 435b. Deflectors 410a, 410b may be implemented with AODs to steer (based on control signals) the optical beam from the left system and the optical beam from the right system onto an ion plane 450 having a plurality of ions (e.g., ions 106 in chain 110). Thus, the left and right systems and their AODs may be used as counter-propagating beam scanning or beam steering systems, where the optical projection action translates the frequency input to each AOD to a specific location (i.e., a specific ion position) in the ion plane 450. However, the left and right systems do not need to have a non-zero angle between them.

[0038] In diagram 400, different light beams from the AODs represent different frequencies from the AODs (e.g., dashed lines are low frequencies and solid lines are high frequencies). As shown, AODs 410a, 410b are generating symmetric high frequency tones (solid lines) that are projected or imaged onto the same ion at the bottom of the chain at ion plane 450. For example, light beam 420a and light beam 420b are imaged onto the same ion at the bottom of the chain from opposite directions. A low frequency tone (dashed line) can be turned on to address another ion at the top of the chain at ion plane 450. For example, light beam 415a and light beam 415b are imaged together onto the same ion at the top of the chain from opposite directions.

[0039] For ion manipulation, only the frequency difference (Df) is important, so if the applied frequency of the higher (or lower) tone from the left system matches the applied frequency of the tone from the right system, the frequency difference will be zero, effectively removing the frequency dependence of the AOD on beam position.

[0040] As an example, an ion chain having 32 ions with 3 mm spacing between ions (see, e.g., FIG. 1) may typically use an individual addressing laser waist (i.e., optical beams waist) of 1 micron (mm). To accommodate each ion in the entire chain, the AOD optical beam scanning system requires a minimum of N=32 resolvable spots (one for each ion in the example) and a field of view (FOV) of 93 mm. The number of resolvable spots is calculated by the formula:

number

[0041] Commercially available AODs typically have an angular range of 3 degrees and an aperture of over 1 mm. This allows, for example, for an input light beam of 1 mm diameter, at a laser wavelength of 532 nm, ±1.5 degrees, to obtain approximately 100 resolvable spots. Each resolvable spot corresponds to one of several corresponding angles at which the AOD can steer or deflect the input light beam. The AOD can support a continuous range of angles at which the light beam can be steered. Thus, a specific angle from that range can be used to achieve a specific resolvable spot that matches the position or location of a specific ion in the chain. For comparison, a MEMS with a 250 mm diameter beam and ±6 degrees at a wavelength of 532 nm allows approximately 100 resolvable spots. The FOV can be evaluated by calculating the effective focal length (EFL) of the optical projection system. This EFL converts the Gaussian waist at the AOD, here 0.5 mm, to the Gaussian waist at the ion, here 1 mm. The formula for calculating the EFL is:

number

number

[0042] Diagram 460 of FIG. 4B shows an example of calculating EFL and FOV. In this example, w AOD = w0, w ion= w1, the input light beam 465 to the AOD 470 has a Gaussian waist w0, and the light beams 480a, 480b imaged onto the ions by the optical component 475 have a Gaussian waist w1. In this example, f is the focal length between the AOD 470 and the optical component 475, and also the focal length between the optical component 475 and the plane of the ions.

[0043] AODs can also be used to overcome the power limitations of MEMS devices: the AOD in the above example can handle roughly 10W of optical power, whereas an equivalent MEMS mirror can handle roughly 100mW of optical power. This impacts gate speed and therefore fidelity and errors, so higher power handling is preferred.

[0044] 5A is a diagram 500 illustrating an example of a diagram of a deflector-based Raman optical system according to an embodiment of the present disclosure. In this example, four deflectors (e.g., AODs) are used to generate two pairs of Raman light beams. By having two pairs of light beams, a two-qubit gate can be implemented in this system.

[0045] Diagram 500 shows a first combination of AODs consisting of AOD 510a and AOD 510b, and a second combination of AODs consisting of AOD 510c and AOD 510d. In the AOD device, the frequency of the steered light beam (e.g., by Bragg diffraction) is Doppler shifted based on the frequency of the acoustic wave used in the deflector. The frequency into AOD 510a can be expressed as f1L+df1Lm, and the output frequency can be expressed as f1L+df1Lm+df1Ld1. The frequency into AOD 510b can be expressed as f1R+df1Rm, and the output frequency can be expressed as f1R+df1Rm+df1Rd1. The frequency into AOD 510c can be expressed as f2L+df2Lm, and the output frequency can be expressed as f2L+df2Lm+df2Ld2. The frequency to AOD 510d can be expressed as f2R+df2Rm, and the output frequency can be expressed as f2R+df2Rm+df2Rd2.

[0046] Changing the frequency sent to the AOD in the form of a control signal (e.g., df1Ld1 for AOD 510a) changes the beam deflection angle, and subsequent imaging optics convert the angular deflection into a beam translation along the ion chain axis. Due to the ideal symmetry of the optical arrangement, and because Raman transitions depend only on the frequency difference between the two beams of a pair (e.g., between the dashed and solid lines), the system can take advantage of "individual-individual" addressability (and the associated low crosstalk) while limiting the complexity of frequency shifts: e.g., df1Ld1=df1Rd1; df2Ld2=df1Rd2. Small left-right asymmetries in the optical system require small deviations from these equations. To compensate for the frequency offset seen by the qubits, a small correction can be made via the upstream modulation AOM that shifts the frequencies df1Lm, df1Rm, df2Lm, df2Rm, restoring the above equations, e.g., modifying them to: df1Ld1+df1Lm=df1Rd1+df1Rm; df2Ld2+df2Lm=df1Rd2+df2Rm. In one example, diagram 580 in FIG. 5B shows upstream AOMs 585a, 585b, 585c, 585d providing frequency modulation to AODs 510a, 510b, 510c, 510d, respectively.

[0047] Multiple AODs can be combined to increase the number of individual manipulations of light beams to drive a two-qubit gate, as shown in diagram 500. To accommodate multiple chains, upstream combining optics and final projection optics can be accommodated, and the two AODs described in connection with diagram 400 can be replicated to provide scalability.

[0048] In the example depicted in FIG. 500, a left system is shown including a light beam source 505a, a deflector or AOD 510a, a set of optical components with imaging optical components 525a, 530a, 535a, and a beam splitter 540a. FIG. 500 also shows a right system including a light beam source 505b, a deflector of AOD 510b, a set of optical components with imaging optical components 525b, 530b, 535b, and a beam splitter 540b. FIG. 500 also shows a bottom system including a light beam source 505c, a deflector or AOD 510c, a set of optical components with imaging optical components 525c, 530c, as well as a beam splitter 540a and optical component 535a shared with the left system. Diagram 500 also shows another bottom system including a light beam source 505d, a deflector or AOD 510d, a set of optical components with imaging optical components 525d, 530d, and a beam splitter 540a and optical component 535b shared with the right system. The AODs are configured (based on control signals) to steer the light beams from the left system, the right system, and the bottom system onto an ion plane 550 having a number of ions (e.g., ions 106 in the chain 110). Thus, the left system, the right system, and the bottom system and their AODs may be used as counter-propagating beam scanning or beam steering systems, where the light projection action translates the frequency input to each AOD to a specific location (i.e., a specific ion position) in the ion plane 550.

[0049] AODs also have a unique advantage over other beam scanning systems such as MEMS or EODs in that they can drive multiple tones, and therefore multiple beams, simultaneously, resulting in parallel or global operation. For example, such an approach can be used to generate multiple beams by transmitting multiple RF tones. Any nonlinearity will cause tone mixing, which will result in extra beams. It is possible to avoid this by using tone phase control or an arbitrary waveform generator (AWG). This kind of phase control can be used to implement gating and can be used for sideband cooling.

[0050] Scanning systems may have other general advantages, and are a different modality than the fixed imaging systems commonly used in most ion trap quantum computers. For example, scanning systems such as AODs and MEMS can accommodate non-uniform ions or arbitrarily spaced ions. If a multi-channel AOM is only using two channels, the other channels are turned off (wasted power). A two-channel AOD system uses 100% power. Furthermore, multi-channel AOM systems are discrete, and deviations can lead to ion beam overlap errors and cause infidelity. AOD systems can be calibrated to eliminate this error.

[0051] It will be understood that the aspects of the system described above in connection with Figures 4, 5A and 5B may be implemented at least in part using the optics and capture controller 220, imaging system 230 and / or chamber 250 of the QIP system 200 described above in connection with Figure 2.

[0052] In order to initialize an ion trap quantum computer or QIP system, cooling of the ground state must be performed. This is usually done with sideband cooling. The local mode cooling technique is described in relation to diagram 600 of FIG. 6. In this case, a chain 110 of N ions 106 (e.g., circles hatched with diagonal cross-lines) is addressed with a chain 610 of N Raman light beams 615 (e.g., white elliptical cross-sections of the light beams) with (N+1) / 2 different frequencies applied as shown (e.g., symmetrical about the center of the chain 610). It is possible to apply so many tones because each Raman light beam 615 of the chain 610 has its own frequency modulation (e.g., separate channels of a multi-channel AOM) that is re-imaged onto the ions. Therefore, there is no positional dependence of the light beam with respect to the ions based on the frequency of the light beam. It should be understood that although an elliptical light beam can be used, other shapes of light beams can also be used, such as circular light beams.

[0053] It will be understood from diagram 600 that the chain 610 of N Raman light beams 615 is intended to illustrate the case where light beams are applied or imaged to each ion 106 from two different directions, with the light beams having ideal or matching elliptical cross sections and frequencies at each ion (and therefore appearing as a single elliptical cross section).

[0054] In AOD-based Raman systems such as those described above in connection with Figures 4, 5A and 5B, this is not necessarily the case. For example, in the AOD-based Raman system shown in diagram 500 of Figure 5A, each of the AODs may have a single AOM upstream that can control the Raman light beam frequency in a manner that is independent of the light beam position. In this example, there are a total of four AOMs upstream (see, for example, diagram 580 and AOMs 585a-585d of Figure 5B), which indicates that there is at least one AOM for each AOD. More AOMs and more AODs may be added to the configurations of diagrams 500 and 580 of Figures 5A and 5B, respectively, but it should be understood that such additions will come at the expense of cost and complexity. However, in this example, there is a single AOM upstream to modulate each laser beam that is fed to AODs 510a-510d, respectively.

[0055] A technique to circumvent this limitation in an AOD-based Raman system is described below in conjunction with Figures 7A and 7B. Here, a chain 110 of N ions 106 (e.g., a circle hatched with diagonal cross-lines) is divided into two parts: the middle 50% of the ions (chain) and the outer 50% (25% left, 25% right). It can also be said that there are three parts: left (25%), middle (50%), and right (25%). In the AOD-based Raman system of diagram 500 of Figure 5A, the middle and outer parts are addressed by different AOD pairs (since there are two or four AODs). For example, one pair of AODs generates a white elliptical light beam cross section for the outer ions (e.g., 25% of the ions on the left and 25% of the ions on the right) as shown in diagram 700 of Figure 7A, and another pair of AODs generates a diagonally hatched elliptical light beam cross section for the middle ions (e.g., 50% of the ions in the middle).

[0056] Since the system is symmetric around ion (N+1) / 2, diagram 750 in FIG. 7B shows a zoomed-in left half of the ion chain (i.e., the right half is not shown for simplicity). The two upstream AOMs for the diagonally hatched elliptical light beams of the middle ions are adjusted so that their frequency difference matches the correct detuning for ion 3(N+1) / 8+1. This results in a detuning of the AOD for ion 3(N+1) / 8+1 of δ=0. Similarly, the upstream AOMs for the white elliptical light beams of the outer ions are set so that their frequency difference matches the correct detuning for ion (N+1) / 8. This results in a detuning of the AOD for ion (N+1) / 8 of δ=0.

[0057] To match the required frequency for the remaining ions in the chain, the AOD is used to create the appropriate frequency difference. In the above example, this frequency difference is linear in the number of ions, so it is n*δ6, where n is the number of ions away from the δ=0 ion and δ is the calculated frequency difference. The AOD maps frequency to position, resulting in an offset of the light beam proportional to n*δ. This offset, shown as overlapping dashed elliptical light beams, must be kept below the size of the light beams so that a light beam intended for one ion is not at least partially imaged onto other ions, and so that a light beam intended for one ion is imaged onto that ion.

[0058] In one embodiment of an AOD-based Raman system, the frequency difference is symmetric about δ=0 and is the same for both the white elliptical light beam and the dashed elliptical light beam.

[0059] As mentioned above, the AOD-based Raman system described in connection with diagrams 500 and 580 in Figures 5A and 5B, respectively, can include four AODs and four upstream AOMs, generating two pairs of counter-propagating Raman light beams when a single tone is applied to the AOD. In this example, the light beam waist (radius) along the ion chain axis is 1.5 mm, the AOD FOV is 114 mm, and the AOD bandwidth is 80 MHz. The last two numbers mean that the light beam from the AOD travels 114 / 80 = 1.4 mm / MHz.

[0060] If the number of ions in the chain is N=21, then ions N=1 to N=5 are part of the left part, ions N=6 to N=16 are part of the middle part, and ions N=17 to N=21 are part of the right part. In this case, local mode cooling BW=3MHz means that 3MHz must be spanned through 11 distinct (distinguishable) Raman frequencies, each about 300kHz apart. The AOM upstream of the pair of AODs providing the diagonally hatched elliptical light beams for the ions in the middle part can be chosen such that the light beams exactly hitting ions N=8 and N=14 have a Raman frequency detuning of 0.75MHz (detuning=0 corresponds to on-resonance with the lowest frequency radial mode). This Raman pair corresponds to ions N=6 to N=16 with detunings of 0MHz to 1.5MHz.

[0061] The AOM upstream of the pair of AODs providing white elliptical light beams to the ions in the left and right sections can be chosen to have a Raman frequency detuning of 2.25 MHz for the beams that hit exactly the N = 3 and N = 19 ions. This Raman pair corresponds to ions N = 1 to N = 5 and N = 17 to N = 21 with detunings of 1.5 MHz to 3 MHz.

[0062] The tone that needs to be added to each AOD is shifted from the other two by +(-)150kHz, and the + / - signs need to be opposite for the two optical beams of the same Raman pair (to give a net shift of 300kHz).

[0063] Looking at the effect on the first pair of Raman light beams in the above example (the other pair of Raman light beams is analyzed in the same way), we need to send 11 tones to each AOD, but there are only six Raman detunings that must cover the range from 0 MHz to 1.5 MHz. If we take the sensitivity of the AOD to be 1.4 mm / MHz, then the misalignment is n × 210 nm, and the absolute misalignments of the Raman light beam pairs at the six different Raman detunings are 0.42 mm, 0.21 mm, 0 mm, 0.21 mm, 0.42 mm, and 0.63 mm. In such a system, if the light beam waist is 1.5 mm, the light beam waist will be larger than the maximum misalignment and meet the requirement. Since the maximum misalignment is 0.63 mm (or 630 nm), which is a small fraction of the (1.5 mm) light beam waist, the ion power (and therefore the Rabi frequency) will only drop by -30% at worst. Fine-tuning this general scheme can also allow for precise hitting of different ions, for example if it turns out to make cooling of a particular mode of interest more efficient.

[0064] 8 illustrates an example method 800 of using a deflector (e.g., an AOD) for sideband cooling operations. In step 810, the method 800 includes identifying a first group of ions in the ion chain and a second group of ions in the ion chain, where the ions in the first group of ions are different from the ions in the second group of ions.

[0065] In step 820, the method 800 includes providing sideband cooling of the ion chain by applying a first pair of light beams to the first group of ions using a first pair of deflectors.

[0066] In step 830, the method 800 includes providing sideband cooling of the ion chain by applying a second pair of light beams to the second group of ions with a second pair of deflectors.

[0067] In one embodiment of the method 800, the first pair of deflectors includes a pair of AODs and the second pair of deflectors includes a second pair of AODs.

[0068] In one embodiment of method 800, a first set of ions includes ions in a middle portion of the ion chain and a second set of ions includes ions in two outer portions of the ion chain (see, e.g., FIG. 7A). The number of ions in the middle portion of the ion chain may be one more than the number of ions in the two outer portions of the ion chain.

[0069] In one embodiment of method 800, applying a first pair of light beams to a first group of ions using a first pair of deflectors includes individually modulating the first pair of light beams using respective AOMs upstream of the first pair of deflectors (see, e.g., FIG. 5A). Individually modulating the first pair of light beams using respective AOMs comprises matching a frequency difference to a correct detuning for a couple of ions of the first group of ions. All ions in the first group of ions other than the couple of ions are subjected to matching the frequency difference to a correct detuning by the first pair of deflectors.

[0070] In one embodiment of method 800, applying the second pair of light beams to the second group of ions using the second pair of deflectors includes individually modulating the second pair of light beams using respective AOMs upstream of the second pair of deflectors (see, e.g., FIG. 5B). Individually modulating the second pair of light beams using respective AOMs comprises matching a frequency difference to a correct detuning for a couple of ions of the second group of ions. All ions in the second group of ions other than the couple of ions are subjected to a frequency difference matching to a correct detuning by the second pair of deflectors.

[0071] In connection with method 800, a QIP system configured for sideband cooling of an ion chain may be used (see, e.g., FIGS. 5A and 5B). The QIP system includes an ion trap (e.g., ion trap 27) configured to hold the ion chain (e.g., chain 110), where ions in the ion chain (e.g., ions 106) are part of a first group of ions or a second group of ions, and the ions of the first group of ions are different from the ions of the second group of ions. The QIP system also includes a first pair of deflectors configured to apply a first pair of light beams to the first group of ions and a second pair of deflectors configured to apply a second pair of light beams to the second group of ions. The first pair of deflectors includes a pair of AODs, and the second pair of deflectors includes a second pair of AODs (see, e.g., AODs 510a-510d in FIGS. 5A and 5B).

[0072] In other embodiments of the QIP system, a first group of ions includes ions in a middle portion of the ion chain and a second group of ions includes ions in the two outer portions of the ion chain (see, e.g., FIG. 7A). The number of ions in the middle portion of the ion chain may be the same as the number of ions in the two outer portions of the ion chain.

[0073] In another embodiment of the QIP system, the QIP system includes a first pair of AOMs (see, e.g., FIG. 5A ) configured to individually modulate a first pair of light beams upstream of the first pair of deflectors. The first pair of AOMs is further configured to match the frequency difference of the first pair of light beams to the correct detuning for a few ions (several ions of the same type) of the first group of ions. The first pair of deflectors is configured to match the frequency difference for all ions in the first group of ions other than the few ions.

[0074] In another embodiment of the QIP system, the QIP system includes a second pair of AOMs configured to individually modulate the second pair of light beams upstream of the second pair of deflectors (see, e.g., FIG. 5B). The second pair of AOMs is further configured to match the frequency difference of the second pair of light beams to the correct detuning for a few ions (several ions of the same type) of the second group of ions. The second pair of deflectors is configured to match the frequency difference for all ions in the second group of ions other than the few ions.

[0075] The above description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other variations without departing from the spirit or scope of the disclosure. Furthermore, although elements of the described aspects and / or embodiments may be described or claimed in the singular, the plural is contemplated unless limitation to the singular is expressly stated. In addition, unless otherwise stated, all or a portion of any aspect and / or embodiment may be utilized with all or a portion of any other aspect and / or embodiment. Thus, the disclosure should not be limited to the examples and designs described herein, but should be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. 1. A method for sideband cooling of an ion chain, comprising: identifying a first set of ions in the ion chain and a second set of ions in the ion chain, where the ions in the first set of ions are different from the ions in the second set of ions; applying a first pair of light beams to the first group of ions using a first pair of deflectors; applying a second pair of light beams to the second group of ions using a second pair of deflectors to provide sideband cooling of the ion chain; The method includes:

2. The method of claim 1 , wherein the first pair of deflectors includes a pair of acousto-optic deflectors (AODs) and the second pair of deflectors includes a second pair of AODs.

3. The method of claim 1 , wherein the first set of ions includes ions in a middle portion of the ion chain and the second set of ions includes ions in two outer portions of the ion chain.

4. The method of claim 3 , wherein the number of ions in the middle portion of the ion chain is one more than the number of ions in the two outer portions of the ion chain.

5. 2. The method of claim 1 , wherein applying the first pair of light beams to the first group of ions using the first pair of deflectors comprises individually modulating the first pair of light beams using respective acousto-optic modulators (AOMs) upstream of the first pair of deflectors.

6. 6. The method of claim 5, wherein individually modulating the first pair of light beams with each of the AOMs comprises matching a frequency difference to a correct detuning for several ions of the first group of ions.

7. 7. The method of claim 6, wherein all ions in the first group of ions other than the few ions are subjected to the step of matching the frequency difference to a correct detuning by the first pair of deflectors.

8. 2. The method of claim 1 , wherein applying the second pair of light beams to the second group of ions with the second pair of deflectors comprises individually modulating the second pair of light beams with respective AOMs upstream of the second pair of deflectors.

9. 9. The method of claim 8, wherein individually modulating the second pair of light beams with respective AOMs comprises matching a frequency difference to a correct detuning for several ions of the second group of ions.

10. 10. The method of claim 9, wherein all ions in the second group of ions other than the few ions are subjected to matching the frequency difference to the correct detuning by the second pair of deflectors.

11. 1. A quantum information processing (QIP) system configured for sideband cooling of ion chains, comprising: an ion trap configured to hold the chain of ions, where ions in the chain of ions are part of a first set of ions or a second set of ions, and the ions of the first set of ions are different from the ions of the second set of ions; a first pair of deflectors configured to apply a first pair of light beams to the first group of ions; a second pair of deflectors configured to apply a second pair of light beams to the second group of ions.

12. 12. The QIP system of claim 11, wherein the first pair of deflectors includes a pair of acousto-optic deflectors (AODs) and the second pair of deflectors includes a second pair of AODs.

13. The QIP system of claim 11 , wherein the first group of ions includes ions in a middle portion of the ion chain and the second group of ions includes ions in two outer portions of the ion chain.

14. The QIP system of claim 13 , wherein the number of ions in the middle portion of the ion chain is one more than the number of ions in the two outer portions of the ion chain.

15. 12. The QIP system of claim 11, further comprising a first pair of acousto-optic modulators (AOMs) configured to individually modulate the first pair of optical beams upstream of the first pair of deflectors.

16. 16. The QIP system of claim 15, wherein the first pair of AOMs is further configured to match a frequency difference of the first pair of light beams to a correct detuning for several ions of the first population of ions.

17. 17. The QIP system of claim 16, wherein the first pair of deflectors is configured to match the frequency difference for all ions in the first group of ions except for the few ions.

18. 12. The QIP system of claim 11, further comprising a second pair of AOMs configured to individually modulate the second pair of light beams upstream of the second pair of deflectors.

19. 20. The QIP system of claim 18, wherein the second pair of AOMs is further configured to match a frequency difference of the second pair of light beams to a correct detuning for several ions of the second population of ions.

20. 20. The QIP system of claim 19, wherein the second pair of deflectors is configured to match the frequency difference for all ions in the second group of ions other than the few ions.

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