Methods and systems for monitoring operation of a quantum computer

Abstract

Systems, methods, and computer-readable media for monitoring an operation of a quantum computer may include (a) an imaging unit configured to passively gather photon data corresponding to the quantum computer during the operation of the quantum computer; (b) an image processing unit configured to generate at least one image corresponding to the operation of the quantum computer based at least in part on the photon data; and (c) a monitoring unit configured to determine a health of the quantum computer based at least in part on the at least one image.

Description

Attorney Docket No. 55436-751.601METHODS AND SYSTEMS FOR MONITORING OPERATION OF A QUANTUM COMPUTERCROSS-REFERENCE

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 717,220, entitled “Methods and Systems for Gawker,” filed on November 6, 2024, which is incorporated by reference herein in its entirety.BACKGROUND

[0002] Quantum computers typically make use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers may be different from digital electronic computers based on transistors. For instance, whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits (qubits), which can be in superpositions of states.

[0003] In neutral-atom quantum computers or simulation devices, qubits may be encoded in optically trapped atoms. The qubit can be represented by a linear superposition of its two orthonormal basis states. The two orthonormal basis states are usually denoted as |0) = [ ] (the “zero state”) and | 1) = (the “one state”). The two orthonormal basis states,{| 0), 11)}, together called the computational basis, span the two-dimensional linear vector (Hilbert) space of the qubit. The basis states can also be combined to form product basis states, e.g., |00), 101), 110), | 11), each called a quantum register. Generally, n qubits are represented by a superposition state vector in 2ndimensional Hilbert space.SUMMARY

[0004] In some cases, systems, methods, computer-readable media, and techniques disclosed herein provide for monitoring operation of a quantum computer. In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein provide for real-time (or near real-time) monitoring of the quantum computer.

[0005] In some cases, to monitor the quantum computer, the systems, the methods, the computer- readable media, and the techniques disclosed herein passively gather photon data corresponding to the quantum computer using an imaging unit. For example, passively gathering photon data may include gathering the photon data with the imaging unit without applying a light or fluorescence onto the quantum computer (as doing so may disturb, obstruct, interrupt, affect, etc.) the quantum computer. Accordingly, the systems, the methods, the computer-readable media, andAttorney Docket No. 55436-751.601 the techniques disclosed herein may advantageously passively monitor the quantum computer without disturbing, obstructing, interrupting, affecting, etc. operation of the quantum computer.

[0006] In some cases, the photon data captured by the imaging unit may be analyzed by an image processing unit (e.g., embodied on a central processing unit (CPU)) to generate one or more images. The one or more images may be analyzed by a monitoring unit (e.g., embodied on a CPU) to monitor the quantum computer. Monitoring the quantum computer may include monitoring a health (e.g., fidelity, calibration, performance, stability, etc.) of the quantum computer. In some cases, if the health of the quantum computer satisfies a threshold, the systems, the methods, the computer-readable media, and the techniques disclosed herein may cause initiation of a calibration of the quantum computer. For example, the calibration may be performed automatically by a control unit, by a control unit in response to user input, manually by a user, etc.

[0007] In some cases, the one or more images may be used to train a machine learning model (e.g., embodied on a CPU) to determine a health of a quantum computer based at least in part on an image generated by the image processing unit. In some cases, the one or more images may be used to train a machine learning model to determine when to calibrate a quantum computer based at least in part on an image.

[0008] In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein may be used for initiating or causing calibration of a quantum computer via the control unit. In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein for monitoring a quantum computer may be integrated into mid-circuit calibration techniques for quantum computers.

[0009] In one aspect, a system for monitoring an operation of a quantum computer, comprises: (a) an imaging unit configured to passively gather photon data corresponding to the quantum computer during the operation of the quantum computer; (b) an image processing unit configured to generate at least one image corresponding to the operation of the quantum computer based at least in part on the photon data; and (c) a monitoring unit configured to determine a health of the quantum computer based at least in part on the at least one image. In some embodiments, the system further comprises a notification unit configured to generate a notification, wherein the notification corresponds to the health of the quantum computer. In some embodiments, the notification is configured to be reviewed by a user of the quantum computer. In some embodiments, the user initiates a calibration of the quantum computer based at least in part on the notification. In some embodiments, the at least one image is used to train machine learning model. In some embodiments, the machine learning model is configured to trigger a calibration of the quantum computer or identify a need for calibration of the quantum computer. In someAttorney Docket No. 55436-751.601 embodiments, the system further comprises a control unit configured to generate a control signal to request a calibration of the quantum computer based at least in part on the health of the quantum computer. In some embodiments, the control unit is configured to generate the control signal at least in part in response to determining the health of the quantum computer satisfies a threshold condition. In some embodiments, the imaging unit is configured to passively gather the photon data without an external light source illuminating the quantum computer during the operation. In some embodiments, the imaging unit is configured to passively gather the photon data without interrupting or affecting the operation of the quantum computer. In some embodiments, the quantum computing operation comprises one or both of a magneto-optical trap operation or a loading operation. In some embodiments, the health of the quantum computer corresponds to one or more of: oven health, beam alignment, or optical focus. In some embodiments, the monitoring unit is configured to determine the health of the quantum computer substantially in real-time with respect to passively gathering the photon data with the imaging unit. In some embodiments, the monitoring unit is configured to determine the health of the quantum computer within a certain time period of passively gathering the photon data with the imaging unit, wherein the certain time period is less than or equal to the amount of time for the health of the quantum computer to change or be expected to change.

[0010] In another aspect, a method for monitoring an operation of a quantum computer, comprises: (a) passively gathering photon data corresponding to the quantum computer during the operation of the quantum computer; (b) generating at least one image corresponding to the operation of the quantum computer based at least in part on the photon data; and (c) determining a health of the quantum computer based at least in part on the at least one image. In some embodiments, the method further comprises generating a notification, wherein the notification corresponds to the health of the quantum computer. In some embodiments, the notification is configured to be reviewed by a user of the quantum computer. In some embodiments, the user initiates a calibration of the quantum computer based at least in part on the notification. In some embodiments, the method further comprises training a machine learning model based at least in part on the at least one image. In some embodiments, the machine learning model is configured to trigger a calibration of the quantum computer or identify a need for calibration of the quantum computer. In some embodiments, the method further comprises generating a control signal to request a calibration of the quantum computer based at least in part on the health of the quantum computer. In some embodiments, the control signal is generated at least in part in response to determining the health of the quantum computer satisfies a threshold condition. In some embodiments, passively gathering the photon data at (a) is performed without an external light source illuminating the quantum computer during the operation. In some embodiments, passivelyAttorney Docket No. 55436-751.601 gathering the photon data at (a) is performed without interrupting or affecting the operation of the quantum computer. In some embodiments, the quantum computing operation comprises one or both of a magneto-optical trap operation or a loading operation. In some embodiments, the health of the quantum computer corresponds to one or more of: oven health, beam alignment, or optical focus. In some embodiments, the health of the quantum computer is determined in (c) substantially in real-time with respect to passively gathering the photon data with the imaging unit in (a). In some embodiments, the health of the quantum computer is determined in (c) within a certain time period of passively gathering the photon data with the imaging unit in (a), wherein the certain time period is less than or equal to the amount of time for the health of the quantum computer to change or be expected to change.

[0011] In another aspect, one or more non-transitory computer-readable media comprising machine-executable code comprising one or more instructions that, when executed, implement the method of any one of the above aspects / embodiments.

[0012] In another aspect, a system for monitoring a quantum computer, comprises: (a) a plurality of optical trapping sites configured to trap a plurality of qubits; (b) an imaging unit configured to obtain one or more observations corresponding to one or both of the plurality of qubits or the plurality of optical trapping sites without applying light to the plurality of qubits; and (c) a control unit configured to initiate a calibration operation on the quantum computer based at least in part on the one or more observations. In some embodiments, the imaging unit is configured to obtain the one or more observations without affecting the plurality of qubits. In some embodiments, the calibration operation corresponds to one or more of: oven health, beam alignment, or optical focus. In some embodiments, the control unit is configured to initiate the calibration operation substantially in real-time with respect to obtaining the one or more observations with the observation unit. In some embodiments, the control unit is configured to initiate the calibration operation within a certain time period of obtaining the one or more observations with the observation unit, wherein the certain time period is less than or equal to the amount of time for the health of the quantum computer to change or be expected to change.

[0013] In another aspect, a method for monitoring a quantum computer, comprises: (a) trapping a plurality of qubits in a plurality of optical trapping sites; (b) obtaining one or more observations corresponding to one or both of the plurality of qubits or the plurality of optical trapping sites without applying light to the plurality of qubits; and (c) initiating a calibration operation on the quantum computer based at least in part on the one or more observations. In some embodiments, obtaining the one or more observations in (b) is performed without affecting the plurality of qubits. In some embodiments, the calibration operation corresponds to one or more of: oven health, beam alignment, or optical focus. In some embodiments, initiating the calibrationAttorney Docket No. 55436-751.601 operation in (c) is performed substantially in real-time with respect to obtaining the one or more observations in (b). In some embodiments, initiating the calibration operation in (c) is performed within a certain time period of obtaining the one or more observations in (b), wherein the certain time period is less than or equal to the amount of time for the health of the quantum computer to change or be expected to change.

[0014] In another aspect, one or more non-transitory computer-readable media comprising machine-executable code comprising one or more instructions that, when executed, implement the method of any one of the above aspects / embodiments.

[0015] Another aspect of the present disclosure provides a system comprising one or more computer processors and computer memory coupled thereto. The computer memory comprises machine executable code that, upon execution by the one or more computer processors, implements any of the methods above or elsewhere herein.

[0016] Additional aspects and advantages of the present disclosure will become readily apparent to those skilled in this art from the following detailed description, wherein only illustrative embodiments of the present disclosure are shown and described. As will be realized, the present disclosure is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the disclosure.Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive.INCORPORATION BY REFERENCEm

[0017] All publications, patents, and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference. To the extent publications and patents or patent applications incorporated by reference contradict the disclosure contained in the specification, the specification is intended to supersede and / or take precedence over any such contradictory material.BRIEF DESCRIPTION OF THE DRAWINGS

[0018] FIG. 1 shows a computer control system that is programmed or otherwise configured to implement methods provided herein;

[0019] FIG. 2 shows an example of a system for performing a non-classical computation;

[0020] FIG. 3A shows an example of an optical trapping unit;

[0021] FIG. 3B shows an example of a plurality of optical trapping sites;

[0022] FIG. 3C shows an example of an optical trapping unit that is partially filled with atoms;Attorney Docket No. 55436-751.601

[0023] FIG. 3D shows an example of an optical trapping unit that is completely filled with atoms;

[0024] FIG. 4 shows an example of an electromagnetic delivery unit;

[0025] FIG. 5 shows an example of a state preparation unit;

[0026] FIG. 6 shows a flowchart for an example of a first method for performing a non-classical computation;

[0027] FIG. 7 shows a flowchart for an example of a second method for performing a non- classical computation;

[0028] FIG. 8 shows a flowchart for an example of a third method for performing a non-classical computation;

[0029] FIG. 9 shows an energy level structure for single-qubit and multi-qubit operations in strontium-87;

[0030] FIG. 10 shows an illustrative system for implementing user and calibration jobs on a quantum computer;

[0031] FIG. 11 shows an illustrative data collection operation with and without monitoring;

[0032] FIG. 12 shows an illustrative system for aggregating monitoring results in a table;

[0033] FIG. 13 shows an illustrative system providing system status information via a monitoring system;

[0034] FIG. 14 shows a plot of system fidelity as a function of time during user jobs and calibration jobs; and

[0035] FIGs. 15A and 15B illustrate examples of methods of the present disclosure.DETAILED DESCRIPTION

[0036] While various embodiments of the invention have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions may occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed.

[0037] Calibration of a quantum computer may be scheduled based on certain rules. For example, calibration may be scheduled for a quantum computer in which user “circuit jobs” compete with “calibration jobs” during the scheduling of operations to be performed on the quantum computer. Such a calibration system 1000 is illustrated in FIG. 10. For example, the calibration system 1000 may schedule calibrations for the quantum computer according to set time intervals. Accordingly, the user of the quantum computer must schedule operations for the quantum computer around these calibrations. In some cases, the calibration system 1000 mayAttorney Docket No. 55436-751.601 schedule calibrations based on existing data gathered during operation of the quantum computer (e.g., when it is determined that a previous calibration may be invalid). In some cases, the calibration system 1000 may schedule calibrations based on a refresh timer, which supposes the calibration is invalid after a certain amount of wall clock time.

[0038] In some cases, the calibration system 1000 may enable manually retriggering calibrations by quantum engineers (QEs) if they observe unusual system performance. In some cases, a user (e.g., a QE) may increase calibration frequency for the calibration system 1000 to guarantee system health or decrease calibration frequency to guarantee availability for quantum computing operations. However, in some cases, without additional monitoring the user may be left to guess the health of a quantum computer based on indirect evidence.

[0039] By contrast, according to the systems, the methods, the computer-readable media, and the techniques disclosed herein, calibration may be performed rationally based on additional system monitoring.

[0040] In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein may enable passively monitoring health of a quantum computer. Passively monitoring a quantum computer may mean monitoring the quantum computer substantially without disturbing, obstructing, interrupting, affecting, etc. the quantum computer. For example, this may be accomplished by collecting photon data (e.g., with an imaging unit) corresponding to the quantum computer using photons that are otherwise already present in or around the quantum computer. These photons may be otherwise already present in or around the quantum computer due to, for example, an operation being performed by the quantum computer. Accordingly, the systems, the methods, the computer-readable media, and the techniques disclosed herein may (i) passively generate images of the quantum computer that would otherwise have not been captured, or (ii) passively view and analyze images of the quantum computer that are already captured during ordinary course of operation of the quantum computer.

[0041] In other words, by collecting photon data corresponding to the quantum computer without providing external or supplemental electromagnetic energy (e.g., light, fluorescence, etc.), the systems, the methods, the computer-readable media, and the techniques disclosed herein may passively monitor the quantum computer. This is in direct contrast with existing approaches for monitoring quantum computers that either (i) predict, based on a time elapsed, that it is time to perform a calibration (which is highly inaccurate), or (ii) fluoresce at least a portion of the quantum computer to monitor the quantum computer (but, at the same time, disturbing, obstructing, interrupting, affecting, etc. the quantum computer).Attorney Docket No. 55436-751.601Examples of Quantum Computer Monitoring

[0042] Generally, the systems, the methods, the computer-readable media, and the techniques disclosed herein may gather (e.g., passively) and analyze data / observations (e.g., photon data, one or more images, etc.) to monitor health (e.g., fidelity, calibration, performance, stability, etc.) of a quantum computer. For example, this monitoring may be performed during user job execution, without scheduling dedicated monitoring jobs. The systems, the methods, the computer-readable media, and the techniques disclosed herein may provide an opportunity to have frequent, low cost information updates on an operating quantum computer. In some cases, the quantum computer may be a neutral atom quantum computer.

[0043] Advantageously, the systems and methods herein may provide particular utility in monitoring quantum computing systems without performing intermittent pre-planned calibrations. For example, by increasing the amount of data collected during quantum computing operations, calibration of quantum computers may be scheduled based on a status of the quantum computer, e.g., rather than as part of scheduled calibration.

[0044] In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein may be used to execute open-loop monitoring of a quantum computer. In some cases, open-loop monitoring may comprise observing a health of a quantum computer during normal operation. In some cases, open-loop monitoring may comprise monitoring the health of the quantum computer without scheduling dedicated jobs on the quantum computer. For example, open -loop monitoring may use asynchronous information published during user circuit jobs.

[0045] In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein for quantum computing monitoring may be used to monitor health (e.g., fidelity, calibration, performance, stability, etc.) of a quantum computer. In some cases, different types of data gathered about components of a quantum computer may include oven health, beam alignment, optical focus, etc. Generally, anything that can be imaged passively (e.g., without disturbing, obstructing, interrupting, affecting, etc. the quantum computer) during a quantum operation may be monitored by the systems, the methods, the computer-readable media, and the techniques disclosed herein.Data Collection

[0046] Shown in FIG. 11 is an example of data collection scheme 1100 for monitoring health (e.g., fidelity, calibration, performance, stability, etc.) of a quantum computer. For example, the data collection scheme 1100 may be performed at least in part during one or more quantum computing operations. As illustrated, the data collection scheme 1100 captures photon data at four points: at a MOT 1105, at loading 1110, at image and preparation 1115, at image 1120.Attorney Docket No. 55436-751.601

[0047] During operation of a quantum computer, a user circuit job may be built from a template that handles atom loading, preparation, readout, or any combination thereof. With the systems, the methods, the computer-readable media, and the techniques disclosed herein, monitor-only images may be inserted into the job template, ensuring key data is collected during user jobs at these key points. For example, health of the MOT may be monitored at 1105. The MOT may be the same as or similar to the MOT 252 or 253. Similarly, a loading operation of loading qubits into an array may be monitored at 1110. The loading operation may be the same as or similar to the loading operation depicted in FIG. 3C. As illustrated, both monitoring (e.g., by an imaging unit) of the MOT at 1105 and the loading operation at 1110 may be performed as monitor-only images, meaning the corresponding images would not have otherwise been captured during ordinary course of a quantum operation.

[0048] As further illustrated, image and preparation of the quantum computer may be monitored at 1115. For example, the preparation of the quantum computer at 1115 may be the same as or similar to preparation performed by the state preparation units 250 of the system 200. Further, an imaging operation of the quantum computer may be monitored at 1120. The imaging operation at 1120 may be the same as or similar to the readout operation performed by the readout units 230 of the system 200. As illustrated, both monitoring (e.g., by an imaging unit) of the image and preparation at 1115 and the imaging operation at 1120 may be performed as circuit images, meaning the corresponding images would have otherwise already been captured during ordinary course of a quantum operation, e.g., by the state preparation units 250 or the readout units 230.

[0049] In some cases, when a user circuit job is executed on or by a quantum computer, photon data may be captured during execution e.g., at one or more of 1105-1120. In some cases, the photon data may be captured by an imaging unit, which may be the same as or similar to one or more of: the one or more readout units 230, the one or more imaging units 215 of FIG. 3A, or other camera or imaging hardware disclosed herein.

[0050] In some cases, the photon data may be used to generate one or more images (e.g., by an image processing unit, which may be embodied on a computing device (such as the CPU 105 of the computer system 101)). In some cases, the image processing unit may be configured to generate the one or more images based at least in part on the photon data. In some cases, the image processing unit may be configured to generate the one or more images using image processing techniques. For example, the image processing techniques may include one or more of: active contouring, adaptive histogram equalization, affine transformation, anisotropic diffusion, background subtraction, bilateral filtering, blob detection, boundary detection, brightness adjustment, canny edge detection, clustering segmentation, color correction, color space conversion, connected-component labeling, comer detection, deconvolution, denoising,Attorney Docket No. 55436-751.601 depth estimation, feature extraction, feature matching, gamma correction, geometric transformation, histogram equalization, image binarization, image compression, image registration, inpainting, integral image, k-means segmentation, morphological operations, noise reduction, object detection, optical flow estimation, panorama stitching, perspective transform, Poisson blending, principal component analysis, radon transform, region growing, Retinex processing, saliency detection, scale-invariant feature transform, segmentation, sharpening, super-resolution, template matching, thresholding, tone mapping, unsharp masking, watershed segmentation, wavelet transform, white balance correction, or the like.

[0051] In some cases, the one or more images (or, in addition or in alternative the photon data) may be published on a system network. For example, the one or more images may be published using a ZMQ PUB / SUB model, which may allow for multiple subscribers. In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein may, alongside the job execution engine, subscribe to the image streams and self-select which images to keep based on metadata in the image messages. In some cases, at least a subset of images may be retained and marked for monitoring while the job engine keeps images relevant to circuit analysis.

[0052] In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein may, in response to a relevant image arriving (e.g., as soon as, shortly thereafter, in real-time, etc.), begin analysis of the image. In some cases, the image may be stored and analyzed. In some cases, the analysis may be stored to a database (DB) table. For example, image metadata (e.g., broadcast as part of the image packet), may be used to interpret the content of the frame and help with analysis.

[0053] As illustrated, the data collection scheme 1100 for monitoring health (e.g., fidelity, calibration, performance, stability, etc.) of a quantum computer is in contrast with using only circuit images, which would result in imaging, for the illustrated case, only at the preparation at 1115 and the imaging at 1120. Accordingly, the systems, the methods, the computer-readable media, and the techniques disclosed herein provide for improved monitoring of a quantum computer, leveraging both circuit images and monitor-only images.Data Storage

[0054] In some cases, a system 1200 implementing quantum computer monitoring may be illustrated by FIG. 12. As illustrated, the system 1200 may be used to improve calibration of a quantum computer in a plurality of ways. For example, the system 1200 may be used to visualize health (e.g., fidelity, calibration, performance, stability, etc.) of the quantum computer (e.g., in real-time or near real-time).Attorney Docket No. 55436-751.601

[0055] As illustrated, data / observations (e.g., photon data, image data, etc.) may be captured by the system 1200 and may be analyzed. For example, as illustrated, an imaging unit 1250 (e.g., comprising an atom camera and a beam camera, as illustrated) may capture photon data of the quantum computer. For example, this photon data may correspond to an atom array, optics (e.g., a beam spot), an oven, etc. of the quantum computer. The imaging unit 1250 may be the same as or similar to the imaging units disclosed elsewhere herein (e.g., with respect to FIG. 11). Further, as disclosed herein, in some cases, the photon data may be further captured during ordinary course of operation of the quantum computer. Such photon data (which may be processed into images referred to in FIG. 11 as circuit images) may be captured at least in part by an imaging unit of the quantum computer execution engine 1210 illustrated in FIG. 12, which may implement one or more operations on the quantum computer. In some cases, as also disclosed herein, the photon data may be processed into images by a computing device (e.g., the computer system 101) implementing an image processing unit 1220, which may be the same as or similar to the image processing unit disclosed elsewhere herein (e.g., with respect to FIG. 11).

[0056] Further, in some cases, data storage may be performed by a results table 1230 as soon as an image is published from the photon data. This may allow a user (e.g., QEs) to observe health of the quantum computer (e.g., in real-time or near real-time), even for long running jobs. In some cases, manual observations inform the user when calibration may be manually retriggered, or if system maintenance may be required. In some cases, the results table 1230 may be implemented on a computing device (e.g., the computer system 101 of FIG. 1), such as in with one or more of a memory, cloud-based storage, a database, etc.

[0057] In some cases, visualizing data with the system 1200 may be performed by polling data from a monitoring results table. In some cases, making decisions based on this data requires an educated observer. In some cases, the educated observer may be a QE. In addition or in alternative, in some cases, making decisions on this data may be performed by a machine learning model, such as an artificial intelligence (Al) agent.Health Monitoring

[0058] Generally, data / observations (e.g., photon data, images, etc.) collected by the systems, the methods, the computer-readable media, and the techniques disclosed herein, such as the system 1200 may be used to monitor health (e.g., fidelity, calibration, performance, stability, etc.) of a quantum computer to inform calibrations or supplement experiment data during calibration as shown in system 1300 of FIG. 13. In another example, data from the system 1200 may be used to inform calibration refresh rates. The system 1300 illustrates how data collected in accordance with the systems, the methods, the computer-readable media, and the techniques disclosed hereinAttorney Docket No. 55436-751.601 may be used to better understand trends about how often, or under what conditions recalibration may be needed for a quantum computer.

[0059] As illustrated, a results table 1330 (which may be the same as or similar to the results table 1230 of FIG. 12) may interface with a calibration table 1335. In some cases, the calibration table 1335 may store one or more calibration processes (e.g., pre-set calibration processes). In some cases, the calibration table 1335 may store one or more calibration parameters (e.g., parameters corresponding to a reset or calibrated state of the quantum computer). In some cases, the calibration table 1335 may store one or more calibration algorithms (e.g., machine learning models) configured to determine how to calibrate a quantum computer based at least in part on the health of the quantum computer (which may be stored in the results table 1330).

[0060] In some cases, a calibration unit 1360 may include (or access) the calibrations table 1360. In some cases, the calibration unit 1360 may determine a threshold is satisfied, indicating a calibration should be performed. In some cases, the calibration unit 1360 may determine which calibration to perform. In some cases, the calibration unit 1360 may determine which components of the quantum computer should be calibrated. In some cases, the calibration unit 1360 may determine to which health states the quantum computer should be calibrated into.

[0061] In some cases, the calibration unit 1360 may operate automatically (e.g., without operator input). In some cases, the calibration unit 1360 may operate in response to operator input (e.g., an operator providing instructions regarding the calibration). In some cases, the calibration unit 1360 may be instructed largely by an operator.

[0062] In some cases, the calibration unit 1360 may provide a control signal to a quantum computer, such as to a quantum computer execution engine 1310 (which may be the same as or similar to the quantum computer execution engine 1210 of FIG. 12).

[0063] In some cases, the calibration unit 1360 may be embodied on a control unit. In some cases, the calibration unit 1360 (or the control unit) may comprise one or more controllers. For example, the one or more controllers may be the same as or similar to other controllers disclosed elsewhere herein. For example, the one or more controllers may be embodied on a computing device such as the computer system 101 of FIG. 1.

[0064] In some cases, the data collected (e.g., photon data, images, etc.) may be used to train, test, and validate Al agents. Advantageously, this may help lead to improved informed refresh rates or rules. In some cases, the data collected does not require dedicated apparatus time to collect meaning data may be passively collected. This may result in more frequent monitoring of quantum computers. In another example, the data collected may be used to supplement or even replace the experiment data that the calibration client collects to regenerate a calibration. ThisAttorney Docket No. 55436-751.601 may help reduce (e.g., minimize) the total number of jobs to run to maintain fresh calibration, which is one goal of calibration improvements, generally.

[0065] In some cases, the data collected (e.g., photon data, image data, etc.) may be used to monitor indicators of tweezer alignment. In some cases, a tweezer may be an optical tweezer. In some cases, the data collected may be used for monitoring purposes of a quantum computer. In some cases, the data collected may be used to help actuate a component of a quantum computer. For example, the data collected may be used by an Al agent to initiate a calibration. In some cases, the data collected may be used to supplement other calibration data. In some cases, the data collected may be used to supplement alignment data in a calibration.

[0066] In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein may be used for monitoring operation of a quantum computer and may comprise: (a) an imaging unit configured to passively gather at least one image of the quantum computer during operation of the quantum computer, wherein the at least one image is gathered during execution of a quantum computing operation; (b) a monitoring unit configured to determine a status of the quantum computer based at least on the at least one image of the quantum computer; and (c) a notification or control unit configured to generate a notification for review by a user (e.g., wherein the notification indicates a status of the quantum computer) or initiate calibration of the quantum computer.Examples of Imaging and Imaging Analysis

[0067] The systems, the methods, the computer-readable media, and the techniques disclosed herein may leverage photon sensors to capture photon data passively. For example, the photon sensors may include one or more imaging units. In some cases, the imaging unit may be the same as or similar to one or more of: the one or more readout units 230, the one or more imaging units 215 of FIG. 3A, or other camera or imaging hardware disclosed herein.

[0068] In some cases, the imaging units (which may be the same as or similar to the imaging unit 1250 of FIG. 12) may capture a red-green-blue (RGB) image, a YUV image, a depth image, a CMOS image, a fluorescence image, a single-atom fluorescence image, an absorption image, a single-atom absorption image, a phase contrast image, a single-atom phase contrast image, a charge-coupled device (CCD) image, an electron-multiplying charge-coupled device (EMCCD) image, an intensified charge-coupled device (ICCD) image, etc. In some cases, the imaging unit may be capable of capturing still images or videos. In some cases, the imaging unit may be capable of capturing visible light (in the range of about 400 nanometers to about 700 nanometers). In some cases, the imaging unit may be capable of capturing infrared light (in the range of about 780 nanometers to about 1000 nanometers).Attorney Docket No. 55436-751.601

[0069] In some cases, in addition or in alternative to photon sensors, the systems, the methods, the computer-readable media, and the techniques disclosed herein may implement one or more other sensors for monitoring a quantum computer. For example, the other sensors may include one or more of: a microphone, a thermal sensor, a thermal imager, an infrared sensor, a laser ranging sensor, a radar sensor, a proximity sensor, an accelerometer, a gyroscope, a pressure sensor, a light sensor, an ultrasonic sensor, a smoke / gas / particulate sensor, a touch sensor, a color sensor, a humidity sensor, a tilt sensor, a photoelectric sensor, a vibration sensor, a position sensor, a pressure sensor, or other suitable sensors. The one or more other sensors may similarly capture sensor data passively (without disturbing, obstructing, interrupting, affecting, etc. operation of the quantum computer) that may be used to determine or predict a health of the quantum computer (e.g., in real-time or near real-time).

[0070] As disclosed herein, in some cases, photon data may not need to be collected directly for the purpose of monitoring the quantum computer (e.g., illustrated as circuit images in FIG. 11). Instead, in some cases, a quantum computing operation may, by its nature, contain image captures (e.g., images of atoms in trap arrays), which can be used by the systems, the methods, the computer-readable media, and the techniques disclosed herein to monitor the quantum computer. In some cases, these images captured for the quantum operation may be modified during compilation to inject additional data capture for monitoring (e.g., image of beam arrays, non-circuit atoms undergoing calibration gates, etc.). Accordingly, in some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein may leverage one or both of images captured directly for the purpose of monitoring the quantum computer (e.g., illustrated as monitor-only images in FIG. 11) and images inherently captured as a part of an operation of the quantum computer (e.g., illustrated as circuit images in FIG. 11).

[0071] As described above, the photon sensors may send sensor data / observations (e.g., photon data, image data, video data, thermal data, audio data, motion data, location data, position data, etc.) or representations or summaries of the sensor data to a processor for processing. Using the sensor data, the processor may generate one or more images corresponding to the quantum computer.

[0072] Based on the one or more images, the systems, the methods, the computer -readable media, and the techniques disclosed herein may analyze the one or more images determine or predict a health (e.g., fidelity, calibration, performance, stability, etc.) of the quantum computer. For example, this analysis may be performed using one or more image processing techniques. These image processing techniques may be classical image processing techniques or machine learning image processing techniques.Attorney Docket No. 55436-751.601Examples of Machine Learning Techniques

[0073] In some cases, the image processing techniques to analyze the one or more images of the quantum computer to determine or predict a health (e.g., fidelity, calibration, performance, stability, etc.) of the quantum computer may implement one or more machine learning (ML) techniques. Further, as disclosed elsewhere herein, the systems, the methods, the computer- readable media, and the techniques disclosed herein may leverage data / observations (e.g., photon data, images, etc.) to train a machine learning model, such as an Al agent.Machine Learning Models

[0074] In some cases, ML may generally involve identifying and recognizing patterns in existing data in order to facilitate making predictions for subsequent data. ML may include a ML model (which may include, for example, a ML algorithm). Machine learning, whether analytical or statistical in nature, may provide deductive or abductive inference based on real or simulated data. The ML model may be a trained model. ML techniques may comprise one or more supervised, semi-supervised, self-supervised, or unsupervised ML techniques. For example, an ML model may be a trained model that is trained through supervised learning (e.g., various parameters are determined as weights or scaling factors). ML may comprise one or more of regression analysis, regularization, classification, dimensionality reduction, ensemble learning, meta learning, association rule learning, cluster analysis, anomaly detection, deep learning, or ultra-deep learning. ML may comprise: k-means, k-means clustering, k-nearest neighbors, learning vector quantization, linear regression, non-linear regression, least squares regression, partial least squares regression, logistic regression, stepwise regression, multivariate adaptive regression splines, ridge regression, principal component regression, least absolute shrinkage and selection operation (LASSO), least angle regression, canonical correlation analysis, factor analysis, independent component analysis, linear discriminant analysis, multidimensional scaling, non-negative matrix factorization, principal components analysis, principal coordinates analysis, projection pursuit, Sammon mapping, t-distributed stochastic neighbor embedding, AdaBoosting, boosting, gradient boosting, bootstrap aggregation, ensemble averaging, decision trees, conditional decision trees, boosted decision trees, gradient boosted decision trees, random forests, stacked generalization, Bayesian networks, Bayesian belief networks, naive Bayes, Gaussian naive Bayes, multinomial naive Bayes, hidden Markov models, hierarchical hidden Markov models, support vector machines, encoders, decoders, auto-encoders, stacked autoencoders, perceptrons, multi-layer perceptrons, artificial neural networks, feedforward neural networks, convolutional neural networks, recurrent neural networks, residual neural networks, physics-informed neural networks, long short-term memory, deep belief networks, deepAttorney Docket No. 55436-751.601Boltzmann machines, deep convolutional neural networks, deep recurrent neural networks, large language models, transformer models, vision transformers, or generative adversarial networks.Training and Validating

[0075] Training the ML model may include, in some cases, selecting one or more untrained data models to train using a training data set. The selected untrained data models may include any type of untrained ML models for supervised, semi -supervised, self-supervised, or unsupervised machine learning. The selected untrained data models may be specified based upon input (e.g., user input) specifying relevant parameters to use as predicted variables or other variables to use as potential explanatory variables. For example, the selected untrained data models may be specified to generate an output (e.g., a prediction) based upon the input. Conditions for training the ML model from the selected untrained data models may likewise be selected, such as limits on the ML model complexity or limits on the ML model refinement past a certain point. The ML model may be trained (e.g., via a computer system such as a server) using the training data set. In some cases, a first subset of the training data set may be selected to train the ML model. The selected untrained data models may then be trained on the first subset of training data set using appropriate ML techniques, based upon the type of ML model selected and any conditions specified for training the ML model. In some cases, due to the processing power requirements of training the ML model, the selected untrained data models may be trained using additional computing resources (e.g., cloud computing resources). Such training may continue, in some cases, until at least one aspect of the ML model is validated and meets selection criteria to be used as a predictive model.

[0076] In some cases, one or more aspects of the ML model may be validated using a second subset of the training data set (e.g., distinct from the first subset of the training data set) to determine accuracy and robustness of the ML model. Such validation may include applying the ML model to the second subset of the training data set to make predictions derived from the second subset of the training data. The ML model may then be evaluated to determine whether performance is sufficient based upon the derived predictions. The sufficiency criteria applied to the ML model may vary depending upon the size of the training data set available for training, the performance of previous iterations of trained models, or user-specified performance requirements. If the ML model does not achieve sufficient performance, additional training may be performed. Additional training may include refinement of the ML model or retraining on a different first subset of the training dataset, after which the new ML model may again be validated and assessed. When the ML model has achieved sufficient performance, in some cases, the ML may be stored for present or future use. The ML model may be stored as sets of parameter values or weights for analysis of further input (e.g., further relevant parameters to useAttorney Docket No. 55436-751.601 as further predicted variables, further explanatory variables, further user interaction data, etc.), which may also include analysis logic or indications of model validity in some instances. In some cases, a plurality of ML models may be stored for generating predictions under different sets of input data conditions. In some cases, the ML model may be stored in a database (e.g., associated with a server).Computer Vision

[0077] In some cases, analyzing the one or more images of the quantum computer may be performed by a computer vision model. Computer vision is a field of artificial intelligence that may use computers to interpret and understand the visual world at least in part by processing one or more of images, videos, or even in some cases, audio. This involves transforming the input by disentangling symbolic information contained in the images, videos, or audio, to provide an output. This disentangled output may then be utilized as further inputs to further models, or as an input to a decision matrix or other process. In this way, computer vision may be used for object recognition, object classification, identification, detection, and other specialized tasks to name a few. In some cases, computer vision may use deep learning models (e.g., convolutional neural networks).

[0078] Computer vision may be utilized in the image analysis of the quantum computer to disentangle symbolic information contained in images. This disentangled information may comprise a health (e.g., fidelity, calibration, performance, stability, etc.) metric of the quantum computer. The disentangled information of the computer vision model may further comprise an input to one or more subsequent computer vision operations to update or further refine the health metric score. The computer vision model may comprise a regressive determination of a health metric for the quantum computer. As an example, a component of the computer vision model may comprise using computer vision to identify a health metric for portions of an image of a portion of the quantum computer. As another example, a component of the computer vision model may further comprise a plurality of subsequent computer vision operations directed to portions of an image possessing a health metric for the quantum computer.

[0079] In some cases, the computer vision model may use stored historical data to update one or more relative size scores or relative amount scores for a given input or set of inputs. As an example, a component of the computer vision model may comprise using computer vision to identify and separate elements of an input or set of inputs. As an example, a component of the computer vision model may further comprise weighting the separate elements of the input or set of inputs by relative size or amount. For example, the computer vision model may recognize one or more elements such as a qubit, a laser, an oven, a trapping site, a light source, etc. and use historical information about the respective elements to predict the health (e.g., fidelity,Attorney Docket No. 55436-751.601 calibration, performance, stability, etc.) of the respective element. As an example, this process may be done iteratively, such as an example where the optical trapping site is recognized and used to subsequently recognize a qubit.

[0080] Computer vision, as disclosed herein, may be used to generate one or more exchangeable representations of the disentangled information of an input or set of inputs. Said exchangeable representations of the disentangled information may take the form of computer readable media such as binary, ASCII, CSV, JSON, XML, and the like. Said exchangeable representations may further comprise a human readable element such as CSV, JSON, XML, YAML, and the like. Computer vision, as disclosed herein, may be used to generate one or more exchangeable representations of disentangled information from a computer vision model to assess a health of a quantum computer as disclosed herein. Computer vision, as disclosed herein, may be used to generate one or more exchangeable representations of disentangled information corresponding to a quantum computer, disclosed herein. In some cases, determination of the quantum computer’s health may further comprise subsequent ML, CNN, DNN, RNN, LLM, and LFM operations as disclosed herein to further refine the one or more overall nutritional scores for an input or set of inputs.

[0081] In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein may leverage object detection as a technique used in computer vision for both (1) identification and (2) localization of objects within an image or a video. Image identification aims to predict the class of an image or an object within an image into one of a category or class. Examples of categories or classes may include, e.g., qubit, MOT, laser beam, missing qubit, electromagnetic delivery unit, etc. Image localization is the process of identifying the correct location of one or multiple objects. Bounding boxes may be used in object detection techniques and image localization within computer vision. Bounding boxes may be annotation markers drawn around objects in an image (e.g., a frame of a video). Bounding boxes may be often, although not always, rectangularly shaped. In some cases, bounding boxes may be applied by humans to training data sets. However, bounding boxes may also be applied to images by a trained machine learning that is trained to detect one or more different objects. In addition or in alternative to bounding boxes, detection and tracking techniques may use any object detection annotation techniques, such as semantic segmentation, instance segmentation, polygon annotation, non-polygon annotation, landmarking, 3D cuboids, etc.

[0082] As disclosed herein, the systems, the methods, the computer -readable media, and the techniques disclosed herein may leverage computer vision techniques for object detection, object tracking, health prediction of the quantum computer, etc. In some cases, one or more elements ofAttorney Docket No. 55436-751.601 object detection, object tracking, health prediction of the quantum computer, etc. may be performed without computer vision (or without machine learning).Examples of Monitoring for Mid-Circuit Calibration

[0083] In some cases, the quantum computer monitoring of the systems, the methods, the computer-readable media, and the techniques disclosed herein may be applied to mid-circuit calibration for quantum computers. In some cases, performing such monitoring for mid-circuit calibration may follow a process that may be the same as or similar to the data collection scheme 1100. Once data / observations (e.g., photon data, images, etc.) are captured, such as via one or both of an imaging unit that may be the same as or similar to the imaging unit 1250 or an image processing unit that may be the same as or similar to the image processing unit 1220, the data may be used for performing a calibration, such as via a control unit which may be the same as or similar to the control unit disclosed herein with respect to the calibration unit 1360 of FIG. 13.

[0084] In some cases, the systems, the methods, the computer-readable media, and the techniques disclosed herein may be used to gather data about sub-system performance. This information is used to inform new data for “passive” calibration, and when the system should trigger “active” calibration. Accordingly, the systems, the methods, the computer-readable media, and the techniques disclosed herein may be used in mid-circuit calibration to create a feedback channel, independent of the final job results, to receive fidelity information. This allows for adjustments to be made before the overall job is complete and analyzed.

[0085] In some cases, mid-circuit calibration may be important for long-running user jobs, as the quantum computer may degrade out of specification over a prolonged job without it. User jobs may, by their nature, contain image captures (e.g. images of atoms in trap arrays) which can be used by the systems, the methods, the computer-readable media, and the techniques disclosed herein to monitor quantum computers. In some cases, the images may be modified during compilation to inject additional data capture for monitoring (e.g., image of beam arrays, noncircuit atoms undergoing calibration gates, etc.). As long-running user jobs execute, monitors of the systems, the methods, the computer-readable media, and the techniques disclosed herein may have access to these images before the jobs are complete via the ZMQ PUB / SUB patterns.

[0086] In some cases, the data analyzed by monitors of the systems, the methods, the computer- readable media, and the techniques disclosed herein mid-job may be used to perform adjustments to improve system performance. These adjustments may be applied within the course of the same user job as the original data was taken. This allows the system to remain in calibration for the duration of the long-running job. An example of making mid-circuit calibration adjustmentsAttorney Docket No. 55436-751.601 includes loading newly-calibrated information about the optimal RF pulse shapes for different quantum operations to the job compiler as a user job is executing.Time-Sharing Jobs and Calibration

[0087] As disclosed herein, in some cases, the systems, the methods, the computer -readable media, and the techniques disclosed herein advantageously help to optimize the frequency at which calibration jobs are scheduled. This allows for more time for user jobs to run on the quantum system, and ensures the system remains within the acceptable health levels.

[0088] FIG. 14 shows a plot 1400 of system fidelity (or health) as a function of time during user jobs and calibration jobs. Specifically, the plot 1400 describes the relationship between job timesharing and system fidelity.

[0089] As illustrated, in some cases, calibration and user jobs require exclusive access to the quantum system, thus may be executed in series. As jobs execute and time passes, the system’s fidelity may degrade due to environmental factors (e.g., humidity, vibrations, etc.) which drift over time.

[0090] The plot 1400 illustrates one example of using pre-determined time intervals to schedule calibrations, rather than timing calibrations based at least in part on monitoring of the quantum computer, as disclosed herein. These time intervals may be established based on historical data about the rate of fidelity decay over time. Without monitoring, there is no guarantee that calibration is executing at the optimal rate. For example, calibrations may be performed more frequently than necessary, reducing efficiency of the system with frequent disruptions. In another example, calibrations may not be performed regularly enough (e.g., because they do not account for a change in conditions that harmed system fidelity), resulting in inaccurate or otherwise problematic operation of the system. In still further examples, the rate of some sub-systems’ fidelity decay cannot be correlated directly with time elapsed, in which case time-based calibration execution is undesirable or unhelpful.

[0091] By contrast, the monitoring of the systems, the methods, the computer-readable media, and the techniques disclosed herein track the system fidelity without requiring dedicated time in the job-execution pipeline. This way calibration jobs can be executed as-needed without overcalibrating (wasting time on the quantum machine) or under-calibrating (allowing the system to drop below acceptable performance). In some cases, in order to ensure the system stays within required fidelity ranges, calibration jobs may be initiated based at least in part on the monitoring by the systems, the methods, the computer-readable media, and the techniques disclosed herein.

[0092] Note that the plot 1400 is a simplified representation. There are many sub-systems within a quantum computer with their own fidelity and calibration routines. These various subsystem performances combine to create the overall system fidelity.Attorney Docket No. 55436-751.601Example Methods for Resonant Cavity Buildup

[0093] FIG. 15A illustrates an example of method 1500A of the present disclosure. In some cases, the method 1500A may comprise: (a) passively gathering photon data corresponding to a quantum computer during an operation of the quantum computer at block 1505A; (b) generating at least one image corresponding to the operation of the quantum computer based at least in part on the photon data at block 1510A; and (c) determining a health of the quantum computer based at least in part on the at least one image at block 1515A.

[0094] In some cases, the method 1500A further comprises generating a notification, wherein the notification corresponds to the health of the quantum computer. In some cases, the notification is configured to be reviewed by a user of the quantum computer. In some cases, the user initiates a calibration of the quantum computer based at least in part on the notification.

[0095] In some cases, the method 1500A further comprises training a machine learning model based at least in part on the at least one image. In some cases, the machine learning model is configured to trigger a calibration of the quantum computer or identify a need for calibration of the quantum computer.

[0096] In some cases, the method 1500A further comprises generating a control signal to request a calibration of the quantum computer based at least in part on the health of the quantum computer. In some embodiments, the control signal is generated at least in part in response to determining the health of the quantum computer satisfies a threshold condition.

[0097] In some cases, passively gathering the photon data at the block 1505A is performed without an external light source illuminating the quantum computer during the operation. In some cases, passively gathering the photon data at the block 1505A is performed without interrupting or affecting the operation of the quantum computer.

[0098] In some cases, the quantum computing operation comprises one or both of a magnetooptical trap operation or a loading operation. In some cases, the health of the quantum computer corresponds to one or more of: oven health, beam alignment, or optical focus.

[0099] In some cases, the health of the quantum computer is determined at the block 1515A substantially in real-time with respect to passively gathering the photon data with the imaging unit at the block 1505A. In some cases, the health of the quantum computer is determined at the block 1515A within a certain time period of passively gathering the photon data with the imaging unit at the block 1505A, wherein the certain time period is less than or equal to the amount of time for the health of the quantum computer to change or be expected to change.

[0100] FIG. 15B illustrates an example of method 1500B of the present disclosure. In some cases, the method 1500B may comprise: (a) trapping a plurality of qubits in a plurality of optical trapping sites of a quantum computer at block 1505B; (b) obtaining one or more observationsAttorney Docket No. 55436-751.601 corresponding to one or both of the plurality of qubits or the plurality of optical trapping sites without applying light to the plurality of qubits at block 1510B; and (c) initiating a calibration operation on the quantum computer based at least in part on the one or more observations at block 1515B.

[0101] In some cases, obtaining the one or more observations at the block 1510B is performed without affecting the plurality of qubits. In some cases, the calibration operation corresponds to one or more of: oven health, beam alignment, or optical focus.

[0102] 1510B In some cases, initiating the calibration operation at the block 1515B is performed within a certain time period of obtaining the one or more observations at the block 1510B, wherein the certain time period is less than or equal to the amount of time for the health of the quantum computer to change or be expected to change. In some cases, initiating the calibration operation at the block 1515B is performed substantially in real-time with respect to obtaining the one or more observations at the block 1510B.

[0103] In some cases, any number of operations of the one or more operations disclosed above with respect to one or both of the methods 1500A or 1500B may be added or removed. Further, the one or more operations disclosed above with respect to one or both of the methods 1500A or 1500B may be performed in any order. Further, at least one of the one or more operations disclosed above with respect to one or both of the methods 1500A or 1500B may be repeated, e.g., iteratively.Example of Systems for Performing a Non-Classical Computation

[0104] FIG. 2 shows an example of a system 200 for performing a non-classical computation. The non-classical computation may comprise a quantum computation. The quantum computation may comprise a gate-model quantum computation.

[0105] The system 200 may comprise one or more trapping units 210. The trapping units may comprise one or more optical trapping units. The optical trapping units may comprise any optical trapping unit described herein, such as an optical trapping unit described herein with respect to FIG. 3A. The optical trapping units may be configured to generate a plurality of optical trapping sites. The optical trapping units may be configured to generate a plurality of spatially distinct optical trapping sites. For instance, the optical trapping units may be configured to generate at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000, or more optical trapping sites. The optical trapping units may be configured to generate at most about 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000,Attorney Docket No. 55436-751.601400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or fewer optical trapping sites. The optical trapping units may be configured to trap a number of optical trapping sites that is within a range defined by any two of the preceding values.

[0106] The optical trapping units may be configured to trap a plurality of atoms. For instance, the optical trapping units may be configured to trap at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000, or more atoms. The optical trapping units may be configured to trap at most about 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or fewer atoms. The optical trapping units may be configured to trap a number of atoms that is within a range defined by any two of the preceding values.

[0107] Each optical trapping site of the optical trapping units may be configured to trap at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more atoms. Each optical trapping site may be configured to trap at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, or fewer atoms. Each optical trapping site may be configured to trap a number of atoms that is within a range defined by any two of the preceding values. Each optical trapping site may be configured to trap a single atom.

[0108] One or more atoms of the plurality of atoms may comprise qubits, as described herein (for instance, with respect to FIG. 4). Two or more atoms may be quantum mechanically entangled. Two or more atoms may be quantum mechanically entangled with a coherence lifetime of at least about 1 microsecond (ps), 2 ps, 3 ps, 4 ps, 5 ps, 6 ps, 7 ps, 8 ps, 9 ps, 10 ps, 20 ps, 30 ps, 40 ps, 50 ps, 60 ps, 70 ps, 80 ps, 90 ps, 100 ps, 200 ps, 300 ps, 400 ps, 500 ps, 600 ps, 700 ps, 800 ps, 900 ps, 1 millisecond (ms), 2 ms, 3 ms, 4 ms, 5 ms, 6 ms, 7 ms, 8 ms, 9 ms, 10 ms, 20 ms, 30 ms, 40 ms, 50 ms, 60 ms, 70 ms, 80 ms, 90 ms, 100 ms, 200 ms, 300 ms, 400 ms, 500 ms, 600 ms, 700 ms, 800 ms, 900 ms, 1 second (s), 2 s, 3 s, 4 s, 5 s, 6 s, 7 s, 8 s, 9 s, 10 s, or more. Two or more atoms may be quantum mechanically entangled with a coherence lifetime of at most about 10 s, 9 s, 8 s, 7 s, 6 s, 5 s, 4 s, 3 s, 2 s, 1 s, 900 ms, 800 ms, 700 ms, 600 ms, 500 ms, 400 ms, 300 ms, 200 ms, 100 ms, 90 ms, 80 ms, 70 ms, 60 ms, 50 ms, 40 ms, 30 ms, 20 ms, 10 ms, 9 ms, 8 ms, 7 ms, 6 ms, 5 ms, 4 ms, 3 ms, 2 ms, 1 ms, 900 ps, 800 ps, 700 ps, 600 ps, 500 ps, 400 ps, 300 ps, 200 ps, 100 ps, 90 ps, 80 ps, 70 ps, 60 ps, 50 ps, 40 ps, 30 ps, 20 ps, 10 ps, 9 ps, 8 ps, 7 ps, 6 ps, 5 ps, 4 ps, 3 ps, 2 ps, 1 ps, or less. Two or more atoms may be quantum mechanicallyAttorney Docket No. 55436-751.601 entangled with a coherence lifetime that is within a range defined by any two of the preceding values. One or more atoms may comprise neutral atoms. One or more atoms may comprise uncharged atoms.

[0109] One or more atoms may comprise alkali atoms. One or more atoms may comprise lithium (Li) atoms, sodium (Na) atoms, potassium (K) atoms, rubidium (Rb) atoms, or cesium (Cs) atoms. One or more atoms may comprise lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, or caesium-133 atoms. One or more atoms may comprise alkaline earth atoms. One or more atoms may comprise beryllium (Be) atoms, magnesium (Mg) atoms, calcium (Ca) atoms, strontium (Sr) atoms, or barium (Ba) atoms. One or more atoms may comprise beryllium-9 atoms, magnesium-24 atoms, magnesium-25 atoms, magnesium-26 atoms, calcium-40 atoms, calcium-42 atoms, calcium-43 atoms, calcium-44 atoms, calcium-46 atoms, calcium-48 atoms, strontium-84 atoms, strontium-86 atoms, strontium-87 atoms, strontium-88 atoms, barium-130 atoms, barium-132 atoms, barium-133 atoms, barium-134 atoms, barium-135 atoms, barium-136 atoms, barium- 137 atoms, or barium-138 atoms. One or more atoms may comprise rare earth atoms. One or more atoms may comprise scandium (Sc) atoms, yttrium (Y) atoms, lanthanum (La) atoms, cerium (Ce) atoms, praseodymium (Pr) atoms, neodymium (Nd) atoms, samarium (Sm) atoms, europium (Eu) atoms, gadolinium (Gd) atoms, terbium (Tb) atoms, dysprosium (Dy) atoms, holmium (Ho) atoms, erbium (Er) atoms, thulium (Tm) atoms, ytterbium (Yb) atoms, or lutetium (Lu) atoms. One or more atoms may comprise scandium -45 atoms, yttrium-89 atoms, lanthanum-139 atoms, cerium-136 atoms, cerium-138 atoms, cerium-140 atoms, cerium-142 atoms, praseodymium-141 atoms, neodymium- 142 atoms, neodymium- 143 atoms, neodymium - 145 atoms, neodymium-146 atoms, neodymium-148 atoms, samarium-144 atoms, samarium-149 atoms, samarium-150 atoms, samarium-152 atoms, samarium-154 atoms, europium-151 atoms, europium-153 atoms, gadolinium- 154 atoms, gadolinium- 155 atoms, gadolinium- 156 atoms, gadolinium-157 atoms, gadolinium- 158 atoms, gadolinium- 160 atoms, terbium-159 atoms, dysprosium-156 atoms, dysprosium- 158 atoms, dysprosium- 160 atoms, dysprosium-161 atoms, dysprosium- 162 atoms, dysprosium- 163 atoms, dysprosium- 164 atoms, erbium- 162 atoms, erbium-164 atoms, erbium-166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium- 171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium- 175 atoms, or lutetium- 176 atoms.

[0110] The plurality of atoms may comprise a single element selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. The plurality of atoms may comprise a mixture of elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. TheAttorney Docket No. 55436-751.601 plurality of atoms may comprise a natural isotopic mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. The plurality of atoms may comprise an isotopically enriched mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. The plurality of atoms may comprise a natural isotopic mixture of one or more elements selected from the group consisting of Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. The plurality of atoms may comprise an isotopically enriched mixture of one or more elements selected from the group consisting of Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. atoms may comprise rare earth atoms. For instance, the plurality of atoms may comprise lithium -6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, caesium-133 atoms, beryllium-9 atoms, magnesium-24 atoms, magnesium-25 atoms, magnesium-26 atoms, calcium-40 atoms, calcium-42 atoms, calcium-43 atoms, calcium-44 atoms, calcium-46 atoms, calcium-48 atoms, strontium-84 atoms, strontium- 86 atoms, strontium-87 atoms, strontium-88 atoms, barium-130 atoms, barium-132 atoms, barium-133 atoms, barium-134 atoms, barium-135 atoms, barium-136 atoms, barium-137 atoms, barium-138 atoms, scandium-45 atoms, yttrium-89 atoms, lanthanum-139 atoms, cerium-136 atoms, cerium-138 atoms, cerium-140 atoms, cerium-142 atoms, praseodymium-141 atoms, neodymium- 142 atoms, neodymium- 143 atoms, neodymium- 145 atoms, neodymium- 146 atoms, neodymium-148 atoms, samarium-144 atoms, samarium-149 atoms, samarium-150 atoms, samarium-152 atoms, samarium-154 atoms, europium-151 atoms, europium-153 atoms, gadolinium- 154 atoms, gadolinium- 155 atoms, gadolinium- 156 atoms, gadolinium-157 atoms, gadolinium-158 atoms, gadolinium- 160 atoms, terbium-159 atoms, dysprosium- 156 atoms, dysprosium-158 atoms, dysprosium- 160 atoms, dysprosium-161 atoms, dysprosium- 162 atoms, dysprosium- 163 atoms, dysprosium- 164 atoms, erbium- 162 atoms, erbium- 164 atoms, erbium - 166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium-171 atoms, ytterbium- 172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium-175 atoms, or lutetium- 176 atoms enriched to an isotopic abundance of at least about 50%, 60%, 70%, 80%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, 99.1%, 99.2%, 99.3%, 99.4%, 99.5%, 99.6%, 99.7%, 99.8%, 99.9%, 99.91%, 99.92%, 99.93%, 99.94%, 99.95%, 99.96%, 99.97%, 99.98%, 99.99%, or more. The plurality of atoms may comprise lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, caesium-133 atoms, beryllium-9 atoms, magnesium-24 atoms, magnesium-25 atoms, magnesium-26 atoms, calcium-40 atoms, calcium-42 atoms, calcium-43 atoms, calcium-44 atoms, calcium-46 atoms, calcium-48 atoms, strontium-Attorney Docket No. 55436-751.60184 atoms, strontium-86 atoms, strontium-87 atoms, strontium-88 atoms, barium- 130 atoms, barium-132 atoms, barium-133 atoms, barium-134 atoms, barium-135 atoms, barium-136 atoms, barium-137 atoms, barium-138 atoms, scandium-45 atoms, yttrium-89 atoms, lanthanum-139 atoms, cerium-136 atoms, cerium-138 atoms, cerium-140 atoms, cerium-142 atoms, praseodymium-141 atoms, neodymium-142 atoms, neodymium-143 atoms, neodymium-145 atoms, neodymium- 146 atoms, neodymium- 148 atoms, samarium- 144 atoms, samarium- 149 atoms, samarium-150 atoms, samarium-152 atoms, samarium-154 atoms, europium-151 atoms, europium-153 atoms, gadolinium- 154 atoms, gadolinium- 155 atoms, gadolinium- 156 atoms, gadolinium-157 atoms, gadolinium- 158 atoms, gadolinium- 160 atoms, terbium-159 atoms, dysprosium-156 atoms, dysprosium- 158 atoms, dysprosium- 160 atoms, dysprosium-161 atoms, dysprosium- 162 atoms, dysprosium- 163 atoms, dysprosium- 164 atoms, erbium- 162 atoms, erbium-164 atoms, erbium-166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium- 171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium-175 atoms, or lutetium-176 atoms enriched to an isotopic abundance of at most about 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50%, or less. The plurality of atoms may comprise lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, caesium-133 atoms, beryllium-9 atoms, magnesium-24 atoms, magnesium-25 atoms, magnesium-26 atoms, calcium-40 atoms, calcium-42 atoms, calcium-43 atoms, calcium-44 atoms, calcium-46 atoms, calcium-48 atoms, strontium-84 atoms, strontium-86 atoms, strontium-87 atoms, strontium-88 atoms, barium-130 atoms, barium-132 atoms, barium-133 atoms, barium-134 atoms, barium-135 atoms, barium-136 atoms, barium-137 atoms, barium-138 atoms, scandium-45 atoms, yttrium-89 atoms, lanthanum- 139 atoms, cerium-136 atoms, cerium-138 atoms, cerium-140 atoms, cerium-142 atoms, praseodymium-141 atoms, neodymium-142 atoms, neodymium-143 atoms, neodymium-145 atoms, neodymium- 146 atoms, neodymium- 148 atoms, samarium- 144 atoms, samarium- 149 atoms, samarium-150 atoms, samarium-152 atoms, samarium-154 atoms, europium-151 atoms, europium-153 atoms, gadolinium- 154 atoms, gadolinium- 155 atoms, gadolinium- 156 atoms, gadolinium-157 atoms, gadolinium- 158 atoms, gadolinium- 160 atoms, terbium-159 atoms, dysprosium-156 atoms, dysprosium- 158 atoms, dysprosium- 160 atoms, dysprosium-161 atoms, dysprosium- 162 atoms, dysprosium- 163 atoms, dysprosium- 164 atoms, erbium- 162 atoms, erbium-164 atoms, erbium-166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium-Attorney Docket No. 55436-751.601171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium-175 atoms, or lutetium-176 atoms enriched to an isotopic abundance that is within a range defined by any two of the preceding values.

[0111] The system 200 may comprise one or more first electromagnetic delivery units 220. The first electromagnetic delivery units may comprise any electromagnetic delivery unit described herein, such as an electromagnetic delivery unit described herein with respect to FIG. 4. The first electromagnetic delivery units may be configured to apply first electromagnetic energy to one or more atoms of the plurality of atoms. Applying the first electromagnetic energy may induce the atoms to adopt one or more superposition states of a first atomic state and a second atomic state that is different from the first atomic state.

[0112] The first atomic state may comprise a first single-qubit state. The second atomic state may comprise a second single-qubit state. The first atomic state or second atomic state may be elevated in energy with respect to a ground atomic state of the atoms. The first atomic state or second atomic state may be equal in energy with respect to the ground atomic state of the atoms.

[0113] The first atomic state may comprise a first hyperfine electronic state and the second atomic state may comprise a second hyperfine electronic state that is different from the first hyperfine electronic state. For instance, the first and second atomic states may comprise first and second hyperfine states on a multiplet manifold, such as a triplet manifold. The first and second atomic states may comprise first and second hyperfine states, respectively, on a3Pi or3P2 manifold. The first and second atomic states may comprise first and second hyperfine states, respectively, on a3Pi or3P2 manifold of any atom described herein, such as a strontium-873Pi manifold or a strontium-873P2 manifold.

[0114] In some cases, the first and second atomic states are first and second hyperfine states of a first electronic state. Optical excitation may be applied between a first electronic state and a second electronic state. The optical excitation may excite the first hyperfine state and / or the second hyperfine state to the second electronic state. A single-qubit transition may comprise a two-photon transition between two hyperfine states within the first electronic state using a second electronic state as an intermediate state. To drive a single-qubit transition, a pair of frequencies, each detuned from a single-photon transition to the intermediate state, may be applied to drive a two-photon transition. In some cases, the first and second hyperfine states are hyperfine states of the ground electronic state. The ground electronic state may not decay by spontaneous or stimulated emission to a lower electronic state. The hyperfine states may comprise nuclear spin states.

[0115] In some cases, the hyperfine states comprise nuclear spin states of a strontium-87 'So manifold and the qubit transition drives one or both of two nuclear spin states of strontium-87xSo-n-Attorney Docket No. 55436-751.601 to a state detuned from or within the3P2 or3Pi manifold. In some cases, the one-qubit transition is a two photon Raman transition between nuclear spin states of strontium-87 'So via a state detuned from or within the3P2 or3Pi manifold. In some cases, the nuclear spin states may be Stark shifted nuclear spin states. A Stark shift may be driven optically. An optical Stark shift may be driven off resonance with any, all, or a combination of a single-qubit transition, a two-qubit transition, a shelving transition, an imaging transition, etc.

[0116] In some cases, the hyperfine states comprise nuclear spin states of a ytterbium.

[0117] The first atomic state may comprise a first nuclear spin state and the second atomic state may comprise a second nuclear spin state that is different from the first nuclear spin state. The first and second atomic states may comprise first and second nuclear spin states, respectively, of a quadrupolar nucleus. The first and second atomic states may comprise first and second nuclear spin states, respectively, of a spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4, or spin- 9 / 2 nucleus. The first and second atomic states may comprise first and second nuclear spin states, respectively, of any atom described herein, such as first and second spin states of strontium-87.

[0118] For first and second nuclear spin states associated with a nucleus comprising a spin greater than 1 / 2 (such as a spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4, or spin-9 / 2 nucleus), transitions between the first and second nuclear spin states may be accompanied by transitions between other spin states on the nuclear spin manifold. For instance, for a spin-9 / 2 nucleus in the presence of a uniform magnetic field, all of the nuclear spin levels may be separated by equal energy. Thus, a transition (such as a Raman transition) designed to transfer atoms from, for instance, an mN = 9 / 2 spin state to an mN = 7 / 2 spin state, may also drive mN = 7 / 2 to mN = 5 / 2, mN = 5 / 2 to mN = 3 / 2, mN = 3 / 2 to mN = 1 / 2, mN = 1 / 2 to mN = -1 / 2, mN = -1 / 2 to mN = -3 / 2, mN = -3 / 2 to mN = -5 / 2, mN = -5 / 2 to mN = -7 / 2, and mN = -7 / 2 to mN = -9 / 2, where mN is the nuclear spin state. Similarly, a transition (such as a Raman transition) designed to transfer atoms from, for instance, an mN = 9 / 2 spin state to an mN = 5 / 2 spin state, may also drive mN = 7 / 2 to mN = 3 / 2, mN = 5 / 2 to mN = 1 / 2, mN = 3 / 2 to mN = -1 / 2, mN = 1 / 2 to mN = -3 / 2, mN = -1 / 2 to mN = -5 / 2, mN = -3 / 2 to mN = -7 / 2, and mN = -5 / 2 to mN = -9 / 2. Such a transition may thus not be selective for inducing transitions between particular spin states on the nuclear spin manifold.

[0119] It may be desirable to instead implement selective transitions between particular first and second spins states on the nuclear spin manifold. This may be accomplished by providing light from a light source that provides an AC Stark shift and pushes neighboring nuclear spin states out of resonance with a transition between the desired transition between the first and second nuclear spin states. For instance, if a transition from first and second nuclear spin states having mN = -9 / 2 and mN = -7 / 2 is desired, the light may provide an AC Stark shift to the mN = -5 / 2 spin state, thereby greatly reducing transitions between the mN = -7 / 2 and mN = -5 / 2 states. Similarly, if aAttorney Docket No. 55436-751.601 transition from first and second nuclear spin states having mN = -9 / 2 and mN = -5 / 2 is desired, the light may provide an AC Stark shift to the mN = -1 / 2 spin state, thereby greatly reducing transitions between the mN = -5 / 2 and mN = -1 / 2 states. This may effectively create a two-level subsystem within the nuclear spin manifold that is decoupled from the remainder of the nuclear spin manifold, greatly simplifying the dynamics of the qubit systems. It may be advantageous to use nuclear spin states near the edge of the nuclear spin manifold (e.g., mN = -9 / 2 and mN = -7 / 2, mN = 7 / 2 and mN = 9 / 2, mN = -9 / 2 and mN = -5 / 2, or mN = 5 / 2 and mN = 9 / 2 for a spin-9 / 2 nucleus) such that only one AC Stark shift is required. Alternatively, nuclear spin states farther from the edge of the nuclear spin manifold (e.g., mN = -5 / 2 and mN = -3 / 2 or mN = -5 / 2 and mN = -1 / 2) may be used and two AC Stark shifts may be implemented (e.g., at mN = -7 / 2 and mN = -1 / 2 or mN = -9 / 2 and mN = 3 / 2).

[0120] Stark shifting of the nuclear spin manifold may shift neighboring nuclear spin states out of resonance with the desired transition between the first and second nuclear spin states and a second electronic state or a state detuned therefrom. Stark shifting may decrease leakage from the first and second nuclear spin state to other states in the nuclear spin manifold. Starks shifts may be achievable up to 100s of kHz for less than 10 mW beam powers. Upper state frequency selectivity may decrease scattering from imperfect polarization control. Separation of different angular momentum states in the3Pi manifold may be many gigahertz from the single and two- qubit gate light. Leakage to other states in the nuclear spin manifold may lead to decoherence. The Rabi frequency for two-qubit transitions (e.g., how quickly the transition can be driven) may be faster than the decoherence rate. Scattering from the intermediate state in the two-qubit transition may be a source of decoherence. Detuning from the intermediate state may improve fidelity of two-qubit transitions.

[0121] Qubits based on nuclear spin states in the electronic ground state may allow exploitation of long-lived metastable excited electronic states (such as a3Po state in strontium-87) for qubit storage. Atoms may be selectively transferred into such a state to reduce cross-talk or to improve gate or detection fidelity. Such a storage or shelving process may be atom -selective using the SLMs or AODs described herein. A shelving transition may comprise a transition between the ' So state in strontium-87 to the3Po or3P2 state in strontium-87.

[0122] The clock transition (also a “shelving transition” or a “storage transition” herein) may be qubit-state selective. The upper state of the clock transition may have a very long natural lifetime, e.g., greater than 1 second. The linewidth of the clock transition may be much narrower than the qubit energy spacing. This may allow direct spectral resolution. Population may be transferred from one of the qubit states into the clock state. This may allow individual qubit states to be read out separately, by first transferring population from one qubit state into the clockAttorney Docket No. 55436-751.601 state, performing imaging on the qubits, then transferring the population back into the ground state from the clock state and imaging again. In some cases, a magic wavelength transition is used to drive the clock transition.

[0123] The clock light for shelving can be atom -selective or not atom-selective. In some cases, the clock transition is globally applied (e.g., not atom selective). A globally applied clock transition may include directing the light without passing through a microscope objective or structuring the light. In some cases, the clock transition is atom-selective. Clock transition which are atom-selective may potentially allow us to improve gate fidelities by minimizing cross-talk. For example, to reduce cross talk in an atom, the atom may be shelved in the clock state where it may not be affected by the light. This may reduce cross-talk between neighboring qubits undergoing transitions. To implement atom-selective clock transitions, the light may pass through one or more microscope objectives and / or may be structured on one or more of a spatial light modulator, digital micromirror device, crossed acousto-optic deflectors, etc.

[0124] The system 200 may comprise one or more readout units 230. The readout units may comprise one or more readout optical units. The readout optical units may be configured to perform one or more measurements of the one or more superposition states to obtain the non- classical computation. The readout optical units may comprise one or more optical detectors. The detectors may comprise one or more photomultiplier tubes (PMTs), photodiodes, avalanche diodes, single-photon avalanche diodes, single-photon avalanche diode arrays, phototransistors, reverse-biased light emitting diodes (LEDs), charge coupled devices (CCDs), or complementary metal oxide semiconductor (CMOS) cameras. The optical detectors may comprise one or more fluorescence detectors. The readout optical unit may comprise one or more objectives, such as one or more objective having a numerical aperture (NA) of at least about 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1, or more. The objective may have an NA of at most about 1, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7, 0.65, 0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1, or less. The objective may have an NA that is within a range defined by any two of the preceding values.

[0125] The one or more readout optical units 230 may make measurements, such as projective measurements, by applying light resonant with an imaging transition. The imaging transition may cause fluorescence. An imaging transition may comprise a transition between the ' So state in strontium-87 to theJPi state in strontium-87. ThexPi state in strontium-87 may fluoresce. The lower state of the qubit transition may comprise two nuclear spin states in the ' So manifold. The one or more states may be resonant with the imaging transition. A measurement may comprise two excitations. In a first excitation, one of the two lower states may be excited to the shelving state (e.g.,3Po state in strontium-87). In a second excitation, the imaging transition may beAttorney Docket No. 55436-751.601 excited. The first transition may reduce cross-talk between neighboring atoms during computation. Fluorescence generated from the imaging transition may be collected on one or more readout optical units 230.

[0126] The imaging units may be used to determine if one or more atoms were lost from the trap. The imaging units may be used to observe the arrangement of atoms in the trap.

[0127] The system 200 may comprise one or more vacuum units 240. The one or more vacuum units may comprise one or more vacuum pumps. The vacuum units may comprise one or more roughing vacuum pumps, such as one or more rotary pumps, rotary vane pumps, rotary piston pumps, diaphragm pumps, piston pumps, reciprocating piston pumps, scroll pumps, or screw pumps. The one or more roughing vacuum pumps may comprise one or more wet (for instance, oil-sealed) or dry roughing vacuum pumps. The vacuum units may comprise one or more high- vacuum pumps, such as one or more cryosorption pumps, diffusion pumps, turbomolecular pumps, molecular drag pumps, turbo-drag hybrid pumps, cryogenic pumps, ions pumps, or getter pumps.

[0128] The vacuum units may comprise any combination of vacuum pumps described herein. For instance, the vacuum units may comprise one or more roughing pumps (such as a scroll pump) configured to provide a first stage of rough vacuum pumping. The roughing vacuum pumps may be configured to pump gases out of the system 200 to achieve a low vacuum pressure condition. For instance, the roughing pumps may be configured to pump gases out of the system 200 to achieve a low vacuum pressure of at most about 103Pascals (Pa). The vacuum units may further comprise one or more high-vacuum pumps (such as one or more ion pumps, getter pumps, or both) configured to provide a second stage of high vacuum pumping or ultra -high vacuum pumping. The high-vacuum pumps may be configured to pump gases out of the system 200 to achieve a high vacuum pressure of at most about 10'3Pa or an ultra-high vacuum pressure of at most about 10'6Pa once the system 200 has reached the low vacuum pressure condition provided by the one or more roughing pumps.

[0129] The vacuum units may be configured to maintain the system 200 at a pressure of at most about IO’6Pa, 9 x IO’7Pa, 8 x IO’7Pa, 7 x IO’7Pa, 6 x IO’7Pa, 5 x IO’7Pa, 4 x IO’7Pa, 3 x IO’7Pa, 2 x 10'7Pa, 10'7Pa, 9 x 10'8Pa, 8 x IO’8Pa, 7 x 10'8Pa, 6 x 10'8Pa, 5 x 10'8Pa, 4 x 10'8Pa, 3 x IO’8Pa, 2 x IO’8Pa, IO’8Pa, 9 x IO’9Pa, 8 x IO’9Pa, 7 x IO’9Pa, 6 x IO’9Pa, 5 x IO’9Pa, 4 x 10’9Pa, 3 x IO’9Pa, 2 x IO’9Pa, IO’9Pa, 9 x IO’10Pa, 8 x IO’10Pa, 7 x IO’10Pa, 6 x IO’10Pa, 5 x IO’10Pa, 4 x IO’10Pa, 3 x IO’10Pa, 2 x IO’10Pa, IO’10Pa, 9 x 10’11Pa, 8 x 10’11Pa, 7 x 10’11Pa, 6 xlO’11Pa, 5 x 10’11Pa, 4 x 10’11Pa, 3 x 10’11Pa, 2 x 10’11Pa, 10’11Pa, 9 x W12Pa, 8 x W12Pa, 7 x IO’12Pa, 6 x IO’12Pa, 5 x 10'12Pa, 4 x 10'12Pa, 3 x 10'12Pa, 2 x 10'12Pa, 10'12Pa, or lower. The vacuum units may be configured to maintain the system 200 at a pressure of at least about 10'12Attorney Docket No. 55436-751.601Pa, 2 x IO’12Pa, 3 x IO’12Pa, 4 x IO’12Pa, 5 x IO’12Pa, 6 x IO’12Pa, 7 x IO’12Pa, 8 x IO’12Pa, 9 x IO’12Pa, IO’11Pa, 2 x IO’11Pa, 3 x IO’11Pa, 4 x IO’11Pa, 5 x IO’11Pa, 6 x IO’11Pa, 7 x IO’11Pa, 8 x IO'11Pa, 9 x IO'11Pa, IO’10Pa, 2 x IO’10Pa, 3 x IO’10Pa, 4 x IO’10Pa, 5 x IO’10Pa, 6 x IO’10Pa,7 x IO’10Pa, 8 x IO’10Pa, 9 x IO’10Pa, IO’9Pa, 2 x IO’9Pa, 3 x IO’9Pa, 4 x IO’9Pa, 5 x IO’9Pa, 6 x IO’9Pa, 7 x IO’9Pa, 8 x IO’9Pa, 9 x IO’9Pa, IO’8Pa, 2 x IO’8Pa, 3 x IO’8Pa, 4 x IO’8Pa, 5 x 10’8Pa, 6 x IO’8Pa, 7 x IO’8Pa, 8 x IO’8Pa, 9 x IO’8Pa, IO’7Pa, 2 x IO’7Pa, 3 x IO’7Pa, 4 x IO’7Pa, 5 x 10'7Pa, 6 x 10'7Pa, 7 x 10'7Pa, 8 x 10'7Pa, 9 x 10'7Pa, 10'6Pa, or higher. The vacuum units may be configured to maintain the system 200 at a pressure that is within a range defined by any two of the preceding values.

[0130] The system 200 may comprise one or more state preparation units 250. The state preparation units may comprise any state preparation unit described herein, such as a state preparation unit described herein with respect to FIG. 5. The state preparation units may be configured to prepare a state of the plurality of atoms.

[0131] The system 200 may comprise one or more atom reservoirs 260. The atom reservoirs may be configured to supply one or more replacement atoms to replace one or more atoms at one or more optical trapping sites upon loss of the atoms from the optical trapping sites. The atom reservoirs may be spatially separated from the optical trapping units. For instance, the atom reservoirs may be located at a distance from the optical trapping units.

[0132] Alternatively or in addition, the atom reservoirs may comprise a portion of the optical trapping sites of the optical trapping units. A first subset of the optical trapping sites may be utilized for performing quantum computations and may be referred to as a set of computationally-active optical trapping sites, while a second subset of the optical trapping sites may serve as an atom reservoir. For instance, the first subset of optical trapping sites may comprise an interior array of optical trapping sites, while the second subset of optical trapping sites comprises an exterior array of optical trapping sites surrounding the interior array. The interior array may comprise a rectangular, square, rectangular prism, or cubic array of optical trapping sites.

[0133] The system 200 may comprise one or more atom movement units 270. The atom movement units may be configured to move the one or more replacement atoms from the one or more atoms reservoirs to the one or more optical trapping sites. For instance, the one or more atom movement units may comprise one or more electrically tunable lenses, acousto-optic deflectors (AODs), or spatial light modulators (SLMs).

[0134] The system 200 may comprise one or more entanglement units 280. The entanglement units may be configured to quantum mechanically entangle at least a first atom of the plurality of atoms with at least a second atom of the plurality of atoms. The first or second atom may be in aAttorney Docket No. 55436-751.601 superposition state at the time of quantum mechanical entanglement. Alternatively or in addition, the first or second atom may not be in a superposition state at the time of quantum mechanical entanglement. The first atom and the second atom may be quantum mechanically entangled through one or more magnetic dipole interactions, induced magnetic dipole interactions, electric dipole interactions, or induced electric dipole interactions. The entanglement units may be configured to quantum mechanically entangle any number of atoms described herein.

[0135] The entanglement units may also be configured to quantum mechanically entangle at least a subset of the atoms with at least another atom to form one or more multi-qubit units. The multiqubit units may comprise two-qubit units, three-qubit units, four-qubit units, or n-qubit units, where n may be 5, 6, 7, 8, 9, 10, or more. For instance, a two-qubit unit may comprise a first atom quantum mechanically entangled with a second atom, a three-qubit unit may comprise a first atom quantum mechanically entangled with a second and third atom, a four-qubit unit may comprise a first atom quantum mechanically entangled with a second, third, and fourth atom, and so forth. The first, second, third, or fourth atom may be in a superposition state at the time of quantum mechanical entanglement. Alternatively or in addition, the first, second, third, or fourth atom may not be in a superposition state at the time of quantum mechanical entanglement. The first, second, third, and fourth atom may be quantum mechanically entangled through one or more magnetic dipole interactions, induced magnetic dipole interactions, electric dipole interactions, or induced electric dipole interactions.

[0136] The entanglement units may comprise one or more Rydberg units. The Rydberg units may be configured to electronically excite the at least first atom to a Rydberg state or to a superposition of a Rydberg state and a lower-energy atomic state, thereby forming one or more Rydberg atoms or dressed Rydberg atoms. The Rydberg units may be configured to induce one or more quantum mechanical entanglements between the Rydberg atoms or dressed Rydberg atoms and the at least second atom. The second atom may be located at a distance of at least about 200 nanometers (nm), 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 micrometer (pm), 2 pm, 3 pm, 4 pm, 5 pm, 6 pm, 7 pm, 8 pm, 9 pm, 10 pm, or more from the Rydberg atoms or dressed Rydberg atoms. The second atom may be located at a distance of at most about 10 pm, 9 pm, 8 pm, 7 pm, 6 pm, 5 pm, 4 pm, 3 pm, 2 pm, 1 pm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm, or less from the Rydberg atoms or dressed Rydberg atoms. The second atom may be located at a distance from the Rydberg atoms or dressed Rydberg atoms that is within a range defined by any two of the preceding values. The Rydberg units may be configured to allow the Rydberg atoms or dressed Rydberg atoms to relax to a lower-energy atomic state, thereby forming one or more two-qubit units. The Rydberg units may be configured to induce the Rydberg atoms or dressed Rydberg atoms to relax to a lower-Attorney Docket No. 55436-751.601 energy atomic state. The Rydberg units may be configured to drive the Rydberg atoms or dressed Rydberg atoms to a lower-energy atomic state. For instance, the Rydberg units may be configured to apply electromagnetic radiation (such as RF radiation or optical radiation) to drive the Rydberg atoms or dressed Rydberg atoms to a lower-energy atomic state. The Rydberg units may be configured to induce any number of quantum mechanical entanglements between any number of atoms of the plurality of atoms.

[0137] The Rydberg units may comprise one or more light sources (such as any light source described herein) configured to emit light having one or more ultraviolet (UV) wavelengths. The UV wavelengths may be selected to correspond to a wavelength that forms the Rydberg atoms or dressed Rydberg atoms. For instance, the light may comprise one or more wavelengths of at least about 200 nm, 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, 370 nm, 380 nm, 390 nm, 400 nm, or more. The light may comprise one or more wavelengths of at most about 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm, or less. The light may comprise one or more wavelengths that are within a range defined by any two of the preceding values. For instance, the light may comprise one or more wavelengths that are within a range from 300 nm to 400 nm.

[0138] The Rydberg units may be configured to induce a two-photon transition to generate an entanglement. The Rydberg units may be configured to induce a two-photon transition to generate an entanglement between two atoms. The Rydberg units may be configured to selectively induce a two-photon transition to selectively generate an entanglement between two atoms. For instance, the Rydberg units may be configured to direct electromagnetic energy (such as optical energy) to particular optical trapping sites to selectively induce a two-photon transition to selectively generate the entanglement between the two atoms. The two atoms may be trapped in nearby optical trapping sites. For instance, the two atoms may be trapped in adjacent optical trapping sites. The two-photon transition may be induced using first and second light from first and second light sources, respectively. The first and second light sources may each comprise any light source described herein (such as any laser described herein). The first light source may be the same or similar to a light source used to perform a single-qubit operation described herein. Alternatively, different light sources may be used to perform a single-qubit operation and to induce a two-photon transition to generate an entanglement. The first light source may emit light comprising one or more wavelengths in the visible region of the optical spectrum (e.g., within a range from 400 nm to 800 nm or from 650 nm to 700 nm). The second light source may emit light comprising one or more wavelengths in the ultraviolet region of the optical spectrum (e.g.,Attorney Docket No. 55436-751.601 within a range from 200 nm to 400 nm or from 300 nm to 350 nm). The first and second light sources may emit light having substantially equal and opposite spatially-dependent frequency shifts.

[0139] The Rydberg atoms or dressed Rydberg atoms may comprise a Rydberg state that may have sufficiently strong interatomic interactions with nearby atoms (such as nearby atoms trapped in nearby optical trapping sites) to enable the implementation of multi -qubit operations. The Rydberg states may comprise a principal quantum number of at least about 50, 60, 70, 80, 90, 100, or more. The Rydberg states may comprise a principal quantum number of at most about 100, 90, 80, 70, 60, 50, or less. The Rydberg states may comprise a principal quantum number that is within a range defined by any two of the preceding values. The Rydberg states may interact with nearby atoms through van der Waals interactions. The van der Waals interactions may shift atomic energy levels of the atoms.

[0140] State selective excitation of atoms to Rydberg levels may enable the implementation of multi -qubit operations. The multi -qubit operations may comprise two-qubit operations, three- qubit operations, or n-qubit operations, where n is 4, 5, 6, 7, 8, 9, 10, or more. Two-photon transitions may be used to excite atoms from a ground state (such as a ' So ground state) to a Rydberg state (such as an n3Si state, wherein n is a principal quantum number described herein). State selectivity may be accomplished by a combination of laser polarization and spectral selectivity. The two-photon transitions may be implemented using first and second laser sources, as described herein. The first laser source may emit pi -polarized light, which may not change the projection of atomic angular momentum along a magnetic field. The second laser may emit circularly polarized light, which may change the projection of atomic angular momentum along the magnetic field by one unit. The first and second qubit levels may be excited to Rydberg level using this polarization. However, the Rydberg levels may be more sensitive to magnetic fields than the ground state so that large splittings (for instance, on the order of 100s of MHz) may be readily obtained. This spectral selectivity may allow state selective excitation to Rydberg levels.

[0141] Multi-qubit operations (such as two-qubit operations, three-qubit operations, four-qubit operations, and so forth) may rely on energy shifts of levels due to van der Waals interactions described herein. Such shifts may either prevent the excitation of one atom conditional on the state of the other or change the coherent dynamics of excitation of the two -atom system to enact a two-qubit operation. In some cases, “dressed states” may be generated under continuous driving to enact two-qubit operations without requiring full excitation to a Rydberg level (for instance, as described in www.arxiv.org / abs / 1605.05207, which is incorporated herein by reference in its entirety for all purposes).Attorney Docket No. 55436-751.601

[0142] The system 200 may comprise one or more second electromagnetic delivery units (not shown in FIG. 2). The second electromagnetic delivery units may comprise any electromagnetic delivery unit described herein, such as an electromagnetic delivery unit described herein with respect to FIG. 4. The first and second electromagnetic delivery units may be the same. The first and second electromagnetic delivery units may be different. The second electromagnetic delivery units may be configured to apply second electromagnetic energy to the one or more multi -qubit units. The second electromagnetic energy may comprise one or more pulse sequences. The first electromagnetic energy may precede, be simultaneous with, or follow the second electromagnetic energy.

[0143] The pulse sequences may comprise any number of pulses. For instance, the pulse sequences may comprise at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, or more pulses. The pulse sequences may comprise at most about 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 pulses. The pulse sequences may comprise a number of pulses that is within a range defined by any two of the preceding values. Each pulse of the pulse sequence may comprise any pulse shape, such as any pulse shape described herein.

[0144] The pulse sequences may be configured to decrease the duration of time required to implement multi -qubit operations, as described herein (for instance, with respect to Example 3). For instance, the pulse sequences may comprise a duration of at least about 10 nanoseconds (ns), 20 ns, 30 ns, 40 ns, 50 ns, 60 ns, 70 ns, 80 ns, 90 ns, 100 ns, 200 ns, 300 ns, 400 ns, 500 ns, 600 ns, 700 ns, 800 ns, 900 ns, 1 microsecond (ps), 2 ps, 3 ps, 4 ps, 5 ps, 6 ps, 7 ps, 8 ps, 9 ps, 10 ps, 20 ps, 30 ps, 40 ps, 50 ps, 60 ps, 70 ps, 80 ps, 90 ps, 100 ps, or more. The pulse sequences may comprise a duration of at most about 100 ps, 90 ps, 80 ps, 70 ps, 60 ps, 50 ps, 40 ps, 30 ps, 20 ps, 10 ps, 9 ps, 8 ps, 7 ps, 6 ps, 5 ps, 4 ps, 3 ps, 2 ps, 1 ps, 900 ns, 800 ns, 700 ns, 600 ns, 500 ns, 400 ns, 300 ns, 200 ns, 100 ns, 90 ns, 80 ns, 70 ns, 60 ns, 50 ns, 40 ns, 30 ns, 20 ns, 10 ns, or less. The pulse sequences may comprise a duration that is within a range defined by any two of the preceding values.

[0145] The pulse sequences may be configured to increase the fidelity of multi -qubit operations, as described herein. For instance, the pulse sequences may enable multi-qubit operations with a fidelity of at least about 0.5, 0.6, 0.7, 0.8, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99, 0.991, 0.992, 0.993, 0.994, 0.995, 0.996, 0.997, 0.998, 0.999, 0.9991, 0.9992, 0.9993, 0.9994, 0.9995, 0.9996, 0.9997, 0.9998, 0.9999, 0.99991, 0.99992, 0.99993, 0.99994, 0.99995, 0.99996, 0.99997, 0.99998, 0.99999, 0.999991, 0.999992, 0.999993, 0.999994, 0.999995, 0.999996, 0.999997, 0.999998, 0.999999, or more. The pulse sequences may enable multi-qubit operations with a fidelity of at most about 0.999999, 0.999998, 0.999997, 0.999996, 0.999995, 0.999994,Attorney Docket No. 55436-751.6010.999993, 0.999992, 0.999991, 0.99999, 0.99998, 0.99997, 0.99996, 0.99995, 0.99994, 0.99993, 0.99992, 0.99991, 0.9999, 0.9998, 0.9997, 0.9996, 0.9995, 0.9994, 0.9993, 0.9992, 0.9991, 0.999, 0.998, 0.997, 0.996, 0.995, 0.994, 0.993, 0.992, 0.991, 0.99, 0.98, 0.97, 0.96, 0.95, 0.94, 0.93, 0.92, 0.91, 0.9, 0.8, 0.7, 0.6, 0.5, or less. The pulse sequences may enable multi-qubit operations with a fidelity that is within a range defined by any two of the preceding values.

[0146] The pulse sequences may enable the implementation of multi-qubit operations on non- adiabatic timescales while maintaining effectively adiabatic dynamics. For instance, the pulse sequences may comprise one or more of shortcut to adiabaticity (STA) pulse sequences, transitionless quantum driving (TQD) pulse sequences, superadiabatic pulse sequences, counterdiabatic driving pulse sequences, derivative removal by adiabatic gate (DRAG) pulse sequences, and weak anharmonicity with average Hamiltonian (Wah Wah) pulse sequences. For instance, the pulse sequences may be similar to those described in M.V. Berry, “Transitionless Quantum Driving,” Journal of Physics A: Mathematical and Theoretical 42(36), 365303 (2009), www.doi.org / 10.1088 / 1751-8113 / 42 / 36 / 365303; Y.-Y. Jau et al., “Entangling Atomic Spins with a Strong Rydberg-Dressed Interaction,” Nature Physics 12(1), 71-74 (2016); T. Keating et al., “Robust Quantum Logic in Neutral Atoms via Adiabatic Rydberg Dressing,” Physical Review A 91, 012337 (2015); A. Mitra et al., “Robust Mblmer-Sbrenson Gate for Neutral Atoms Using Rapid Adiabatic Rydberg Dressing,” www.arxiv.org / abs / 1911.04045 (2019); or L.S. Theis et al., “Counteracting Systems of Diabaticities Using DRAG Controls: The Status after 10 Years,” Europhysics Letters 123(6), 60001 (2018), each of which is incorporated herein by reference in its entirety for all purposes.

[0147] The pulse sequences may further comprise one or more optimal control pulse sequences. The optimal control pulse sequences may be derived from one or more procedures, including gradient ascent pulse engineering (GRAPE) methods, Krotov’s method, chopped basis methods, chopped random basis (CRAB) methods, Nelder-Mead methods, gradient optimization using parametrization (GROUP) methods, genetic algorithm methods, and gradient optimization of analytic controls (GOAT) methods. For instance, the pulse sequences may be similar to those described in N. Khaneja et al., “Optimal Control of Coupled Spin Dynamics: Design of NMR Pulse Sequences by Gradient Ascent Algorithms,” Journal of Magnetic Resonance 172(2), 296- 305 (2005); or J.T. Merrill et al., “Progress in Compensating Pulse Sequences for Quantum Computation,” Advances in Chemical Physics 154, 241-294 (2014), each of which is incorporated by reference in its entirety for all purposes.Attorney Docket No. 55436-751.601Example of Cloud Computing

[0148] The system 200 may be operatively coupled to a digital computer described herein (such as a digital computer described herein with respect to FIG. 1) over a network described herein (such as a network described herein with respect to FIG. 1). The network may comprise a cloud computing network.Example of Optical Trapping Units

[0149] FIG. 3A shows an example of an optical trapping unit 210. The optical trapping unit may be configured to generate a plurality 211 of spatially distinct optical trapping sites, as described herein. For instance, as shown in FIG. 3B, the optical trapping unit may be configured to generate a first optical trapping site 211a, second optical trapping site 211b, third optical trapping site 211c, fourth optical trapping site 21 Id, fifth optical trapping site 21 le, sixth optical trapping site 21 If, seventh optical trapping site 211g, eighth optical trapping site 21 Ih, and ninth optical trapping site 21 li, as depicted in FIG. 3A. The plurality of spatially distinct optical trapping sites may be configured to trap a plurality of atoms, such as first atom 212a, second atom 212b, third atom 212c, and fourth atom 212d, as depicted in FIG. 3A. As depicted in FIG. 3B, each optical trapping site may be configured to trap a single atom. As depicted in FIG. 3B, some of the optical trapping sites may be empty (i.e., not trap an atom).

[0150] As shown in FIG. 3B, the plurality of optical trapping sites may comprise a two- dimensional (2D) array. The 2D array may be perpendicular to the optical axis of optical components of the optical trapping unit depicted in FIG. 3A. Alternatively, the plurality of optical trapping sites may comprise a one-dimensional (ID) array or a three-dimensional (3D) array.

[0151] Although depicted as comprising nine optical trapping sites filled by four atoms in FIG. 3B, the optical trapping unit 210 may be configured to generate any number of spatially distinct optical trapping sites described herein and may be configured to trap any number of atoms described herein.

[0152] Each optical trapping site of the plurality of optical trapping sites may be spatially separated from each other optical trapping site by a distance of at least about 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 pm, 2 pm, 3 pm, 4 pm, 5 pm, 6 pm, 7 pm, 8 pm, 9 pm, 10 pm, or more. Each optical trapping site may be spatially separated from each other optical trapping site by a distance of at most about 10 pm, 9 pm, 8 pm, 7 pm, 6 pm, 5 pm, 4 pm, 3 pm, 2 pm, 1 pm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm, or less. Each optical trapping site maybe spatially separated from each other optical trapping site by a distance that is within a range defined by any two of the preceding values.Attorney Docket No. 55436-751.601

[0153] The optical trapping sites may comprise one or more optical tweezers. Optical tweezers may comprise one or more focused laser beams to provide an attractive or repulsive force to hold or move the one or more atoms. The beam waist of the focused laser beams may comprise a strong electric field gradient. The atoms may be attracted or repelled along the electric field gradient to the center of the laser beam, which may contain the strongest electric field. The optical trapping sites may comprise one or more optical lattice sites of one or more optical lattices. The optical trapping sites may comprise one or more optical lattice sites of one or more one-dimensional (ID) optical lattices, two-dimensional (2D) optical lattices, or three-dimensional (3D) optical lattices. For instance, the optical trapping sites may comprise one or more optical lattice sites of a 2D optical lattice, as depicted in FIG. 3B.

[0154] The optical lattices may be generated by interfering counter -propagating light (such as counter-propagating laser light) to generate a standing wave pattern having a periodic succession of intensity minima and maxima along a particular direction. A ID optical lattice may be generated by interfering a single pair of counter-propagating light beams. A 2D optical lattice may be generated by interfering two pairs of counter-propagating light beams. A 3D optical lattice may be generated by interfering three pairs of counter-propagating lights beams. The light beams may be generated by different light sources or by the same light source. Therefore, an optical lattice may be generated by at least about 1, 2, 3, 4, 5, 6, or more light sources or at most about 6, 5, 4, 3, 2, or 1 light sources.

[0155] Returning to the description of FIG. 3A, the optical trapping unit may comprise one or more light sources configured to emit light to generate the plurality of optical trapping sites as described herein. For instance, the optical trapping unit may comprise a single light source 213, as depicted in FIG. 3A. Though depicted as comprising a single light source in FIG. 3A, the optical trapping unit may comprise any number of light sources, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more light sources or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 light sources. The light sources may comprise one or more lasers. The lasers may be configured to operate at a resolution limit of the lasers. For example, the lasers can be configured to provide diffraction limited spot sizes for optical trapping.

[0156] The lasers may comprise one or more continuous wave lasers. The lasers may comprise one or more pulsed lasers. The lasers may comprise one or more gas lasers, such as one or more helium-neon (HeNe) lasers, argon (Ar) lasers, krypton (Kr) lasers, xenon (Xe) ion lasers, nitrogen (N2) lasers, carbon dioxide (CO2) lasers, carbon monoxide (CO) lasers, transversely excited atmospheric (TEA) lasers, or excimer lasers. For instance, the lasers may comprise one or more argon dimer (Ar2) excimer lasers, krypton dimer (KT2) excimer lasers, fluorine dimer (F2) excimer lasers, xenon dimer (Xe ) excimer lasers, argon fluoride (ArF) excimer lasers, kryptonAttorney Docket No. 55436-751.601 chloride (KrCl) excimer lasers, krypton fluoride (KrF) excimer lasers, xenon bromide (XeBr) excimer lasers, xenon chloride (XeCl) excimer lasers, or xenon fluoride (XeF) excimer lasers. The laser may comprise one or more dye lasers.

[0157] The lasers may comprise one or more metal-vapor lasers, such as one or more heliumcadmium (HeCd) metal-vapor lasers, helium-mercury (HeHg) metal-vapor lasers, heliumselenium (HeSe) metal-vapor lasers, helium-silver (HeAg) metal-vapor lasers, strontium (Sr) metal-vapor lasers, neon-copper (NeCu) metal-vapor lasers, copper (Cu) metal-vapor lasers, gold (Au) metal-vapor lasers, manganese (Mn) metal-vapor laser, or manganese chloride (MnCh) metal-vapor lasers.

[0158] The lasers may comprise one or more solid-state lasers, such as one or more ruby lasers, metal -doped crystal lasers, or metal -doped fiber lasers. For instance, the lasers may comprise one or more neodymium-doped yttrium aluminum garnet (Nd: YAG) lasers, neodymium / chromium doped yttrium aluminum garnet (Nd / Cr: YAG) lasers, erbium-doped yttrium aluminum garnet (Er: YAG) lasers, neodymium-doped yttrium lithium fluoride (Nd:YLF) lasers, neodymium- doped yttrium orthovanadate (ND:YVC>4) lasers, neodymium-doped yttrium calcium oxoborate (Nd:YCOB) lasers, neodymium glass (Nd:glass) lasers, titanium sapphire (Ti:sapphire) lasers, thulium-doped ytrium aluminum garnet (Tm:YAG) lasers, ytterbium -doped ytrrium aluminum garnet (Yb:YAG) lasers, ytterbium-doped glass (Yt:glass) lasers, holmium ytrrium aluminum garnet (Ho: YAG) lasers, chromium-doped zinc selenide (Cr:ZnSe) lasers, cerium-doped lithium strontium aluminum fluoride (Ce:LiSAF) lasers, cerium-doped lithium calcium aluminum fluoride (Ce:LiCAF) lasers, erbium-doped glass (Erglass) lasers, erbium-ytterbium-codoped glass (Er / Yt:glass) lasers, uranium-doped calcium fluoride (U:CaF2) lasers, or samarium-doped calcium fluoride (Sm:CaF2) lasers.

[0159] The lasers may comprise one or more semiconductor lasers or diode lasers, such as one or more gallium nitride (GaN) lasers, indium gallium nitride (InGaN) lasers, aluminum gallium indium phosphide (AlGalnP) lasers, aluminum gallium arsenide (AlGaAs) lasers, indium gallium arsenic phosphide (InGaAsP) lasers, vertical cavity surface emitting lasers (VCSELs), or quantum cascade lasers.

[0160] The lasers may emit continuous wave laser light. The lasers may emit pulsed laser light. The lasers may have a pulse length of at least about 1 femtoseconds (fs), 2 fs, 3 fs, 4 fs, 5 fs, 6 fs, 7 fs, 8 fs, 9 fs, 10 fs, 20 fs, 30 fs, 40 fs, 50 fs, 60 fs, 70 fs, 80 fs, 90 fs, 100 fs, 200 fs, 300 fs, 400 fs, 500 fs, 600 fs, 700 fs, 800 fs, 900 fs, 1 picosecond (ps), 2 ps, 3 ps, 4 ps, 5 ps, 6 ps, 7 ps, 8 ps, 9 ps, 10 ps, 20 ps, 30 ps, 40 ps, 50 ps, 60 ps, 70 ps, 80 ps, 90 ps, 100 ps, 200 ps, 300 ps, 400 ps, 500 ps, 600 ps, 700 ps, 800 ps, 900 ps, 1 nanosecond (ns), 2 ns, 3 ns, 4 ns, 5 ns, 6 ns, 7 ns, 8 ns, 9 ns, 10 ns, 20 ns, 30 ns, 40 ns, 50 ns, 60 ns, 70 ns, 80 ns, 90 ns, 100 ns, 200 ns, 300 ns, 400 ns,Attorney Docket No. 55436-751.601500 ns, 600 ns, 700 ns, 800 ns, 900 ns, 1,000 ns, or more. The lasers may have a pulse length of at most about 1,000 ns, 900 ns, 800 ns, 700 ns, 600 ns, 500 ns, 400 ns, 300 ns, 200 ns, 100 ns, 90 ns, 80 ns, 70 ns, 60 ns, 50 ns, 40 ns, 30 ns, 20 ns, 10 ns, 9 ns, 8 ns, 7 ns, 6 ns, 5 ns, 4 ns, 3 ns, 2 ns, 1 ns, 900 ps, 800 ps, 700 ps, 600 ps, 500 ps, 400 ps, 300 ps, 200 ps, 100 ps, 90 ps, 80 ps, 70 ps, 60 ps, 50 ps, 40 ps, 30 ps, 20 ps, 10 ps, 9 ps, 8 ps, 7 ps, 6 ps, 5 ps, 4 ps, 3 ps, 2 ps, 1 ps, 900 fs, 800 fs, 700 fs, 600 fs, 500 fs, 400 fs, 300 fs, 200 fs, 100 fs, 90 fs, 80 fs, 70 fs, 60 fs, 50 fs, 40 fs, 30 fs, 20 fs, 10 fs, 9 fs, 8 fs, 7 fs, 6 fs, 5 fs, 4 fs, 3 fs, 2 fs, 1 fs, or less. The lasers may have a pulse length that is within a range defined by any two of the preceding values.

[0161] The lasers may have a repetition rate of at least about 1 hertz (Hz), 2 Hz, 3 Hz, 4 Hz, 5 Hz, 6 Hz, 7 Hz, 8 Hz, 9 Hz, 10 Hz, 20 Hz, 30 Hz, 40 Hz, 50 Hz, 60 Hz, 70 Hz, 80 Hz, 90 Hz, 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1 kilohertz (kHz), 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 50 kHz, 60 kHz, 70 kHz, 80 kHz, 90 kHz, 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1 megahertz (MHz), 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 20 MHz, 30 MHz, 40 MHz, 50 MHz, 60 MHz, 70 MHz, 80 MHz, 90 MHz, 100 MHz, 200 MHz, 300 MHz, 400 MHz, 500 MHz, 600 MHz, 700 MHz, 800 MHz, 900 MHz, 1,000 MHz, or more. The lasers may have a repetition rate of at most about 1,000 MHz, 900 MHz, 800 MHz, 700 MHz, 600 MHz, 500 MHz, 400 MHz, 300 MHz, 200 MHz, 100 MHz, 90 MHz, 80 MHz, 70 MHz, 60 MHz, 50 MHz, 40 MHz, 30 MHz, 20 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, 900 Hz, 800 Hz, 700 Hz, 600 Hz, 500 Hz, 400 Hz, 300 Hz, 200 Hz, 100 Hz, 90 Hz, 80 Hz, 70 Hz, 60 Hz, 50 Hz, 40 Hz, 30 Hz, 20 Hz, 10 Hz, 9 Hz, 8 Hz, 7 Hz, 6 Hz, 5 Hz, 4 Hz, 3 Hz, 2 Hz, 1 Hz, or less. The lasers may have a repetition rate that is within a range defined by any two of the preceding values.

[0162] The lasers may emit light having a pulse energy of at least about 1 nanojoule (nJ), 2 nJ, 3 nJ, 4 nJ, 5 nJ, 6 nJ, 7 nJ, 8 nJ, 9 nJ, 10 nJ, 20 nJ, 30 nJ, 40 nJ, 50 nJ, 60 nJ, 70 nJ, 80 nJ, 90 nJ, 100 nJ, 200 nJ, 300 nJ, 400 nJ, 500 nJ, 600 nJ, 700 nJ, 800 nJ, 900 nJ, 1 microjoule (pJ), 2 pj, 3 pj, 4 pj, 5 pj, 6 pj, 7 pj, 8 pj, 9 pj, 10 pj, 20 pj, 30 pj, 40 pj, 50 pj, 60 pj, 70 pj, 80 pj, 90 pj, 100 pj, 200 pj, 300 pj, 400 pj, 500 pj, 600 pj, 700 pj, 800 pj, 900 pj, a least 1 millijoule (mJ), 2 mJ, 3 mJ, 4 mJ, 5 mJ, 6 mJ, 7 mJ, 8 mJ, 9 mJ, 10 mJ, 20 mJ, 30 mJ, 40 mJ, 50 mJ, 60 mJ, 70 mJ, 80 mJ, 90 mJ, 100 mJ, 200 mJ, 300 mJ, 400 mJ, 500 mJ, 600 mJ, 700 mJ, 800 mJ, 900 mJ, a least 1 Joule (J), or more. The lasers may emit light having a pulse energy of at most about 1 J, 900 mJ, 800 mJ, 700 mJ, 600 mJ, 500 mJ, 400 mJ, 300 mJ, 200 mJ, 100 mJ, 90 mJ, 80 mJ, 70Attorney Docket No. 55436-751.601 mJ, 60 mJ, 50 mJ, 40 mJ, 30 mJ, 20 mJ, 10 mJ, 9 mJ, 8 mJ, 7 mJ, 6 mJ, 5 mJ, 4 mJ, 3 mJ, 2 mJ, 1 mJ, 900 pj, 800 pj, 700 juJ, 600 juJ, 500 juJ, 400 juJ, 300 juJ, 200 juJ, 100 juJ, 90 juJ, 80 juJ, 70 juJ, 60 pj, 50 pj, 40 pj, 30 pj, 20 pj, 10 pj, 9 pj, 8 pj, 7 pj, 6 pj, 5 pj, 4 pj, 3 pj, 2 pj, 1 pj, 900 nJ, 800 nJ, 700 nJ, 600 nJ, 500 nJ, 400 nJ, 300 nJ, 200 nJ, 100 nJ, 90 nJ, 80 nJ, 70 nJ, 60 nJ, 50 nJ, 40 nJ, 30 nJ, 20 nJ, 10 nJ, 9 nJ, 8 nJ, 7 nJ, 6 nJ, 5 nJ, 4 nJ, 3 nJ, 2 nJ, 1 nJ, or less. The lasers may emit light having a pulse energy that is within a range defined by any two of the preceding values.

[0163] The lasers may emit light having an average power of at least about 1 microwatt (pW), 2 pW, 3 pW, 4 pW, 5 pW, 6 pW, 7 pW, 8 pW, 9 pW, 10 pW, 20 pW, 30 pW, 40 pW, 50 pW, 60 pW, 70 pW, 80 pW, 90 pW, 100 pW, 200 pW, 300 pW, 400 pW, 500 pW, 600 pW, 700 pW, 800 pW, 900 pW, 1 milliwatt (mW), 2 mW, 3 mW, 4 mW, 5 mW, 6 mW, 7 mW, 8 mW, 9 mW, 10 mW, 20 mW, 30 mW, 40 mW, 50 mW, 60 mW, 70 mW, 80 mW, 90 mW, 100 mW, 200 mW, 300 mW, 400 mW, 500 mW, 600 mW, 700 mW, 800 mW, 900 mW, 1 watt (W), 2 W, 3 W, 4 W, 5 W, 6 W, 7 W, 8 W, 9 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W, 80 W, 90 W, 100 W, 200 W, 300 W, 400 W, 500 W, 600 W, 700 W, 800W, 900 W, 1,000 W, or more. The lasers may emit light having an average power of at most about 1,000 W, 900 W, 800 W, 700 W, 600 W, 500 W, 400 W, 300 W, 200 W, 100 W, 90 W, 80 W, 70 W, 60 W, 50 W, 40 W, 30 W, 20 W, 10 W, 9 W, 8 W, 7 W, 6 W, 5 W, 4 W, 3 W, 2 W, 1 W, 900 mW, 800 mW, 700 mW, 600 mW, 500 mW, 400 mW, 300 mW, 200 mW, 100 mW, 90 mW, 80 mW, 70 mW, 60 mW, 50 mW, 40 mW, 30 mW, 20 mW, 10 mW, 9 mW, 8 mW, 7 mW, 6 mW, 5 mW, 4 mW, 3 mW, 2 mW, 1 mW, 900 pW, 800 pW, 700 pW, 600 pW, 500 pW, 400 pW, 300 pW, 200 pW, 100 pW, 90 pW, 80 pW, 70 pW, 60 pW, 50 pW, 40 pW, 30 pW, 20 pW, 10 pW, 9 pW, 8 pW, 7 pW, 6 pW, 5 pW, 4 pW, 3 pW, 2 pW, 1 pW, or more. The lasers may emit light having a power that is within a range defined by any two of the preceding values.

[0164] The lasers may emit light comprising one or more wavelengths in the ultraviolet (UV), visible, or infrared (IR) portions of the electromagnetic spectrum. The lasers may emit light comprising one or more wavelengths of at least about 200 nm, 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm,360 nm, 370 nm, 380 nm, 390 nm, 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm,470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm,580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm,690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm,800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm,910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, 1,010 nm, 1,020 nm, 1,030 nm, 1,040 nm, 1,050 nm, 1,060 nm, 1,070 nm, 1,080 nm, 1,090 nm, 1,100Attorney Docket No. 55436-751.601 nm, 1,110 nm, 1,120 nm, 1,130 nm, 1,140 nm, 1,150 nm, 1,160 nm, 1,170 nm, 1,180 nm, 1,190 nm, 1,200 nm, 1,210 nm, 1,220 nm, 1,230 nm, 1,240 nm, 1,250 nm, 1,260 nm, 1,270 nm, 1,280 nm, 1,290 nm, 1,300 nm, 1,310 nm, 1,320 nm, 1,330 nm, 1,340 nm, 1,350 nm, 1,360 nm, 1,370 nm, 1,380 nm, 1,390 nm, 1,400 nm, or more. The lasers may emit light comprising one or more wavelengths of at most about 1,400 nm, 1,390 nm, 1,380 nm, 1,370 n, 1,360 nm, 1,350 nm, 1,340 nm, 1,330 nm, 1,320 nm, 1,310 nm, 1,300 nm, 1,290 nm, 1,280 nm, 1,270 n, 1,260 nm,1,250 nm, 1,240 nm, 1,230 nm, 1,220 nm, 1,210 nm, 1,200 nm, 1,190 nm, 1,180 nm, 1,170 n,1,160 nm, 1,150 nm, 1,140 nm, 1,130 nm, 1,120 nm, 1,110 nm, 1,100 nm, 1,090 nm, 1,080 nm,1,070 n, 1,060 nm, 1,050 nm, 1,040 nm, 1,030 nm, 1,020 nm, 1,010 nm, 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm. The lasers may emit light comprising one or more wavelengths that are within a range defined by any two of the preceding values.

[0165] The lasers may emit light having a bandwidth of at least about 1 x 10'15nm, 2 x 10'15nm, 3 x 10’15nm, 4 x 10'15nm, 5 x 10'15nm, 6 x 10'15nm, 7 x 10'15nm, 8 x 10'15nm, 9 x 10'15nm, 1 x 10'14nm, 2 x 10'14nm, 3 x 10'14nm, 4 x 10'14nm, 5 x 10'14nm, 6 x 10'14nm, 7 x 10'14nm, 8 x 10'14nm, 9 x 10'14nm, 1 x 10'13nm, 2 x 10'13nm, 3 x 10'13nm, 4 x 10'13nm, 5 x 10'13nm, 6 x10'13nm, 7 x 10'13nm, 8 x 10'13nm, 9 x 10'13nm, 1 x 10'12nm, 2 x 10'12nm, 3 x 10'12nm, 4 xIO’12nm, 5 x 10'12nm, 6 x 10'12nm, 7 x 10'12nm, 8 x 10'12nm, 9 x 10'12nm, 1 x 10'11nm, 2 x10'11nm, 3 x 10'11nm, 4 x 10'11nm, 5 x 10'11nm, 6 x 10'11nm, 7 x 10'11nm, 8 x 10'11nm, 9 x10'11nm, 1 x 10'10nm, 2 x 10'10nm, 3 x 10'10nm, 4 x 10'10nm, 5 x 10'10nm, 6 x 10'10nm, 7 x10'10nm, 8 x 10'10nm, 9 x 10'10nm, 1 x 10'9nm, 2 x 10'9nm, 3 x 10'9nm, 4 x 10'9nm, 5 x 10'9nm, 6 x 10'9nm, 7 x 10'9nm, 8 x 10'9nm, 9 x 10'9nm, 1 x 10'8nm, 2 x 10'8nm, 3 x 10'8nm, 4 x 10'8nm, 5 x 10'8nm, 6 x 10'8nm, 7 x 10'8nm, 8 x 10'8nm, 9 x 10'8nm, 1 x 10'7nm, 2 x 10'7nm, 3 x 10'7nm, 4 x 10'7nm, 5 x 10'7nm, 6 x 10'7nm, 7 x 10'7nm, 8 x 10'7nm, 9 x 10'7nm, 1 x 10'6nm, 2 x 10'6nm, 3 x 10'6nm, 4 x 10'6nm, 5 x 10'6nm, 6 x 10'6nm, 7 x 10'6nm, 8 x 10'6nm, 9 x 10'6nm, 1 x 10'5nm, 2 x 10'5nm, 3 x 10'5nm, 4 x 10'5nm, 5 x 10'5nm, 6 x 10'5nm, 7 x 10'5nm, 8 x 10'5nm, 9 x 10'5nm, 1 x 10'4nm, 2 x 10'4nm, 3 x 10'4nm, 4 x 10'4nm, 5 x 10'4nm, 6 x 10'4nm, 7 x 10'4nm, 8 x 10'4nm, 9 x 10'4nm, 1 x 10'3nm, or more. The lasers may emit light having a bandwidth of at most aboutl x 10'3nm, 9 x 10'4nm, 8 x 10'4nm, 7 x 10'4nm, 6 x 10'4nm, 5 xAttorney Docket No. 55436-751.60110'4nm, 4 x 10'4nm, 3 x 10'4nm, 2 x 10'4nm, 1 x 10'4nm, 9 x 10'5nm, 8 x 10'5nm, 7 x 10'5nm, 6 x 10'5nm, 5 x 10'5nm, 4 x 10'5nm, 3 x 10'5nm, 2 x 10'5nm, 1 x 10'5nm, 9 x 10'6nm, 8 x 10'6nm, 7 x 10'6nm, 6 x 10'6nm, 5 x 10'6nm, 4 x 10'6nm, 3 x 10'6nm, 2 x 10'6nm, 1 x 10'6nm, 9 x 10'7nm, 8 x 10'7nm, 7 x 10'7nm, 6 x 10'7nm, 5 x 10'7nm, 4 x 10'7nm, 3 x 10'7nm, 2 x 10'7nm, 1 x 10'7nm, 9 x 10'8nm, 8 x 10'8nm, 7 x 10'8nm, 6 x 10'8nm, 5 x 10'8nm, 4 x 10'8nm, 3 x 10'8nm, 2 x 10'8nm, 1 x 10'8nm, 9 x 10'9nm, 8 x 10'9nm, 7 x 10'9nm, 6 x 10'9nm, 5 x 10'9nm, 4 x 10'9nm, 3 x 10'9nm, 2 x 10'9nm, 1 x 10'9nm, 9 x IO'10nm, 8 x IO'10nm, 7 x IO'10nm, 6 x IO'10nm, 5 x IO'10nm, 4 x IO'10nm, 3 x IO'10nm, 2 x IO'10nm, 1 x IO'10nm, 9 x 10'11nm, 8 x 10'11nm, 7 x 10'11nm, 6 x 10'11nm, 5 x 10'11nm, 4 x 10'11nm, 3 x 10'11nm, 2 x 10'11nm, 1 x 10'11nm, 9 x IO’12nm, 8 x 10'12nm, 7 x 10'12nm, 6 x 10'12nm, 5 x 10'12nm, 4 x 10'12nm, 3 x 10'12nm, 2 x IO’12nm, 1 x 10'12nm, 9 x 10'13nm, 8 x 10'13nm, 7 x 10'13nm, 6 x 10'13nm, 5 x 10'13nm, 4 x 10'13nm, 3 x 10'13nm, 2 x 10'13nm, 1 x 10'13nm, 9 x 10'14nm, 8 x 10'14nm, 7 x 10'14nm, 6 x 10'14nm, 5 x 10'14nm, 4 x 10'14nm, 3 x 10'14nm, 2 x 10'14nm, 1 x 10'14nm, 9 x 10'15nm, 8 x 10’15nm, 7 x 10'15nm, 6 x 10'15nm, 5 x 10'15nm, 4 x 10'15nm, 3 x 10'15nm, 2 x 10'15nm, 1 x 10’15nm, or less. The lasers may emit light having a bandwidth that is within a range defined by any two of the preceding values.

[0166] The light sources may be configured to emit light tuned to one or more magic wavelengths corresponding to the plurality of atoms. A magic wavelength corresponding to an atom may comprise any wavelength of light that gives rise to equal or nearly equal polarizabilities of the first and second atomic states. The magic wavelengths for a transition between the first and second atomic states may be determined by calculating the wavelengthdependent polarizabilities of the first and second atomic states and finding crossing points. Light tuned to such a magic wavelength may give rise to equal or nearly equal differential light shifts in the first and second atomic states, regardless of the intensity of the light emitted by the light sources. This may effectively decouple the first and second atomic states from motion of the atoms. The magic wavelengths may utilize one or more scalar or tensor light shifts. The scalar or tensor light shifts may depend on magnetic sublevels within the first and second atomic states.

[0167] For instance, group III atoms and metastable states of alkaline earth or alkaline earth-like atoms may possess relatively large tensor shifts whose angle relative to an applied magnetic field may be tuned to cause a situation in which scalar and tensor shifts balance and give a zero or near zero differential light shift between the first and second atomic states. The angle 0 may be tuned by selecting the polarization of the emitted light. For instance, when the emitted light is linearly polarized, the total polarizability a may be written as a sum of the scalar component ascaiar and the tensor component atenSor'.(Z scalar T (3 COS 0 tens orAttorney Docket No. 55436-751.601

[0168] By choosing Q appropriately, the polarizability of the first and second atomic states may be chosen to be equal or nearly equal, corresponding to a zero or near zero differential light shift and the motion of the atoms may be decoupled.

[0169] The light sources may be configured to direct light to one or more optical modulators (OMs) configured to generate the plurality of optical trapping sites. Ffor instance, the optical trapping unit may comprise an OM 214 configured to generate the plurality of optical trapping sites. Although depicted as comprising one OM in FIG. 3A, the optical trapping unit may comprise any number of OMs, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more OMs or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 OMs. The OMs may comprise one or more digital micromirror devices (DMDs). The OMs may comprise one or more liquid crystal devices, such as one or more liquid crystal on silicon (LCoS) devices. The OMs may comprise one or more spatial light modulators (SLMs). The OMs may comprise one or more acousto-optic deflectors (AODs) or acousto-optic modulators (AOMs). The OMs may comprise one or more electro-optic deflectors (EODs) or electro-optic modulators (EOMs).

[0170] The OM may be optically coupled to one or more optical element to generate a regular array of optical trapping sites. For instance, the OM may be optically coupled to optical element 219, as shown in FIG. 3A. The optical elements may comprise lenses or microscope objectives configured to re-direct light from the OMs to form a regular rectangular grid of optical trapping sites.

[0171] For instance, as shown in FIG. 3A, the OM may comprise an SLM, DMD, or LCoS device. The SLM, DMD, or LCoS device may be imaged onto the back focal plane of the microscope objectives. This may allow for the generation of an arbitrary configuration of optical trapping sites in two or three dimensions.

[0172] Alternatively or in addition, the OMs may comprise first and second AODs. The active regions of the first and second AODs may be imaged onto the back focal plane of the microscope objectives. The output of the first AOD may be optically coupled to the input of the second AOD. In this manner, the second AOD may make a copy of the optical output of the first AOD. This may allow for the generation of optical trapping sites in two or three dimensions.

[0173] Alternatively or in addition, the OMs may comprise static optical elements, such as one or more microlens arrays or holographic optical elements. The static optical elements may be imaged onto the back focal plane of the microscope objectives. This may allow for the generation of an arbitrary configuration of optical trapping sites in two or three dimensions.

[0174] The optical trapping unit may comprise one or more imaging units configured to obtain one or more images of a spatial configuration of the plurality of atoms trapped within the optical trapping sites. For instance, the optical trapping unit may comprise imaging unit 215. AlthoughAttorney Docket No. 55436-751.601 depicted as comprising a single imaging unit in FIG. 3A, the optical trapping unit may comprise any number of imaging units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more imaging units or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 imaging units. The imaging units may comprise one or more lens or objectives. The imaging units may comprise one or more PMTs, photodiodes, avalanche photodiodes, phototransistors, reverse-biased LEDs, CCDs, or CMOS cameras. The imaging unit may comprise one or more fluorescence detectors. The images may comprise one or more fluorescence images, single-atom fluorescence images, absorption images, single-atom absorption images, phase contrast images, or single-atom phase contrast images.

[0175] The optical trapping unit may comprise one or more spatial configuration artificial intelligence (Al) units configured to perform one or more Al operations to determine the spatial configuration of the plurality of atoms trapped within the optical trapping sites based on the images obtained by the imaging unit. For instance, the optical trapping unit may comprise spatial configuration Al unit 216. Although depicted as comprising a single spatial configuration Al unit in FIG. 3A, the optical trapping unit may comprise any number of spatial configuration Al units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more spatial configuration Al units or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 spatial configuration Al units. The Al operations may comprise any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0176] The optical trapping unit may comprise one or more atom rearrangement units configured to impart an altered spatial arrangement of the plurality of atoms trapped with the optical trapping sites based on the one or more images obtained by the imaging unit. For instance, the optical trapping unit may comprise atom rearrangement unit 217. Although depicted as comprising a single atom rearrangement unit in FIG. 3A, the optical trapping unit may comprise any number of atom rearrangement units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more atom rearrangement units or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 atom rearrangement units.

[0177] The optical trapping unit may comprise one or more spatial arrangement artificial intelligence (Al) units configured to perform one or more Al operations to determine the altered spatial arrangement of the plurality of atoms trapped within the optical trapping sites based on the images obtained by the imaging unit. For instance, the optical trapping unit may comprise spatial arrangement Al unit 218. Although depicted as comprising a single spatial arrangement Al unit in FIG. 3A, the optical trapping unit may comprise any number of spatial arrangement Al units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more spatial arrangement Al units or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 spatial arrangement Al units. The Al operations may comprise any machine learning (ML) or reinforcement learning (RL) operations described herein.Attorney Docket No. 55436-751.601

[0178] In some cases, the spatial configuration Al units and the spatial arrangement Al units may be integrated into an integrated Al unit. The optical trapping unit may comprise any number of integrated Al units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more integrated Al units, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 integrated Al units.

[0179] The atom rearrangement unit may be configured to alter the spatial arrangement in order to obtain an increase in a filling factor of the plurality of optical trapping sites. A filling factor may be defined as a ratio of the number of computationally active optical trapping sites occupied by one or more atoms to the total number of computationally active optical trapping sites available in the optical trapping unit or in a portion of the optical trapping unit. For instance, initial loading of atoms within the computationally active optical trapping sites may give rise to a filling factor of less than 100%, 90%, 80%, 70%, 60%, 50%, or less, such that atoms occupy fewer than 100%, 90%, 70%, 60%, 50%, or less of the available computationally active optical trapping sites, respectively. It may be desirable to rearrange the atoms to achieve a filling factor of at least about 50%, 60%, 70%, 80%, 90%, or 100%. By analyzing the imaging information obtained by the imaging unit, the atom rearrangement unit may attain a filling factor of at least about 50%, 60%, 70%, 80%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, 99.1%, 99.2%, 99.3%, 99.4%, 99.5%, 99.6%, 99.7%, 99.8%, 99.9%, 99.91%, 99.92%, 99.93%, 99.94%, 99.95%, 99.96%, 99.97%, 99.98%, 99.99%, or more. The atom rearrangement unit may attain a filling factor of at most about 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50%, or less. The atom rearrangement unit may attain a filling factor that is within a range defined by any two of the preceding values.

[0180] By way of example, FIG. 3C shows an example of an optical trapping unit that is partially filled with atoms. As depicted in FIG. 3C, initial loading of atoms within the optical trapping sites may give rise to a filling factor of 44.4% (4 atoms filling 9 available optical trapping sites). By moving atoms from different regions of the optical trapping unit (not shown in FIG. 3C) to unoccupied optical trapping sites or by moving atoms from an atom reservoir described herein, a much higher filling factor may be obtained, as shown in FIG. 3D.

[0181] FIG. 3D shows an example of an optical trapping unit that is completely filled with atoms. As depicted in FIG. 3D, fifth atom 212e, sixth atom 212f, seventh atom 212g, eighth atom 212h, and ninth atom 212i may be moved to fill unoccupied optical trapping sites. The fifth, sixth, seventh, eighth, and ninth atoms may be moved from different regions of the optical trapping unit (not shown in FIG. 3C) or by moving atoms from an atom reservoir described herein. Thus, the filling factor may be substantially improved following rearrangement of atomsAttorney Docket No. 55436-751.601 within the optical trapping sites. For instance, a filling factor of up to 100% (such 9 atoms filling 9 available optical trapping sites, as shown in FIG. 3D) may be attained.

[0182] Atom rearrangement may be performed by (i) acquiring an image of the optical trapping unit, identifying filled and unfilled optical trapping sites, (ii) determining a set of moves to bring atoms from filled optical trapping sites to unfilled optical trapping sites, and (iii) moving the atoms from filled optical trapping sites to unfilled optical trapping sites. Operations (i), (ii), and (iii) may be performed iteratively until a large filling factor is achieved. Operation (iii) may comprise translating the moves identified in operation (ii) to waveforms that may be sent to an arbitrary waveform generator (AWG) and using the AWG to drive AODs to move the atoms. The set of moves may be determined using the Hungarian algorithm described in W. Lee et al, “Defect-Free Atomic Array Formation Using Hungarian Rearrangement Algorithm,” Physical Review A 95, 053424 (2017), which is incorporated herein by reference in its entirety for all purposes.Example of Electromagnetic Delivery Units

[0183] FIG. 4 shows an example of an electromagnetic delivery unit 220. The electromagnetic delivery unit may be configured to apply electromagnetic energy to one or more atoms of the plurality of atoms, as described herein. The electromagnetic delivery unit may comprise one or more light sources, such as any light source described herein. The electromagnetic energy may comprise optical energy. The optical energy may comprise any repetition rate, pulse energy, average power, wavelength, or bandwidth described herein.

[0184] The electromagnetic delivery unit may comprise one or more microwave or radiofrequency (RF) energy sources, such as one or more magnetrons, klystrons, traveling-wave tubes, gyrotrons, field-effect transistors (FETs), tunnel diodes, Gunn diodes, impact ionization avalanche transit-time (IMP ATT) diodes, or masers. The electromagnetic energy may comprise microwave energy or RF energy. The RF energy may comprise one or more wavelengths of at least about 1 millimeter (mm), 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, 9 mm, 10 mm, 20 mm, 30 mm, 40 mm, 50 mm, 60 mm, 70 mm, 80 mm, 90 mm, 100 mm, 200 mm, 300 mm, 400 mm, 500 mm, 600 mm, 700 mm, 800 mm, 900 mm, 1 meter (m), 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, 9 m, 10 m, 20 m, 30 m, 40 m, 50 m, 60 m, 70 m, 80 m, 90 m, 100 m, 200 m, 300 m, 400 m, 500 m, 600 m, 700 m, 800 m, 900 m, 1 kilometer (km), 2 km, 3 km, 4 km, 5 km, 6 km, 7 km,8 km, 9 km, 10 km, or more. The RF energy may comprise one or more wavelengths of at most about 10 km, 9 km, 8 km, 7 km, 6 km, 5 km, 4 km, 3 km, 2 km, 1 km, 900 m, 800 m, 700 m, 600 m, 500 m, 400 m, 300 m, 200 m, 100 m, 90 m, 80 m, 70 m, 60 m, 50 m, 40 m, 30 m, 20 m, 10 m,9 m, 8 m, 7 m, 6 m, 5 m, 4 m, 3 m, 2 m, I m, 900 mm, 800 mm, 700 mm, 600 mm, 500 mm, 400Attorney Docket No. 55436-751.601 mm, 300 mm, 200 mm, 100 mm, 90 mm, 80 mm, 70 mm, 60 mm, 50 mm, 40 mm, 30 mm, 20 mm, 10 mm, 9 mm, 8 mm, 7 mm, 6 mm, 5 mm, 4 mm, 3 mm, 2 mm, 1 mm, or less. The RF energy may comprise one or more wavelengths that are within a range defined by any two of the preceding values.

[0185] The RF energy may comprise an average power of at least about 1 microwatt (pW), 2 pW, 3 pW, 4 pW, 5 pW, 6 pW, 7 pW, 8 pW, 9 pW, 10 pW, 20 pW, 30 pW, 40 pW, 50 pW, 60 pW, 70 pW, 80 pW, 90 pW, 100 pW, 200 pW, 300 pW, 400 pW, 500 pW, 600 pW, 700 pW, 800 pW, 900 pW, 1 milliwatt (mW), 2 mW, 3 mW, 4 mW, 5 mW, 6 mW, 7 mW, 8 mW, 9 mW, 10 mW, 20 mW, 30 mW, 40 mW, 50 mW, 60 mW, 70 mW, 80 mW, 90 mW, 100 mW, 200 mW, 300 mW, 400 mW, 500 mW, 600 mW, 700 mW, 800 mW, 900 mW, 1 Watt (W), 2 W, 3 W, 4 W, 5 W, 6 W, 7 W, 8 W, 9 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W, 80 W, 90 W, 100 W, 200 W, 300 W, 400 W, 500 W, 600 W, 700 W, 800W, 900 W, 1,000 W, or more. The RF energy may comprise an average power of at most about 1,000 W, 900 W, 800 W, 700 W, 600 W, 500 W, 400 W, 300 W, 200 W, 100 W, 90 W, 80 W, 70 W, 60 W, 50 W, 40 W, 30 W, 20 W, 10 W, 9 W, 8 W, 7 W, 6 W, 5 W, 4 W, 3 W, 2 W, 1 W, 900 mW, 800 mW, 700 mW, 600 mW, 500 mW, 400 mW, 300 mW, 200 mW, 100 mW, 90 mW, 80 mW, 70 mW, 60 mW, 50 mW, 40 mW, 30 mW, 20 mW, 10 mW, 9 mW, 8 mW, 7 mW, 6 mW, 5 mW, 4 mW, 3 mW, 2 mW, 1 mW, 900 pW, 800 pW, 700 pW, 600 pW, 500 pW, 400 pW, 300 pW, 200 pW, 100 pW, 90 pW, 80 pW, 70 pW, 60 pW, 50 pW, 40 pW, 30 pW, 20 pW, 10 pW, 9 pW, 8 pW, 7 pW, 6 pW, 5 pW, 4 pW, 3 pW, 2 pW, 1 pW, or less. The RF energy may comprise an average power that is within a range defined by any two of the preceding values.

[0186] The electromagnetic delivery unit may comprise one or more light sources, such as any light source described herein. For instance, the electromagnetic delivery unit may comprise light source 221. Although depicted as comprising a single light source in FIG. 4, the electromagnetic delivery unit may comprise any number of light sources, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more light sources or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 light sources.

[0187] The light sources may be configured to direct light to one or more OMs configured to selectively apply the electromagnetic energy to one or more atoms of the plurality of atoms. For instance, the electromagnetic delivery unit may comprise OM 222. Although depicted as comprising a single OM in FIG. 4, the electromagnetic delivery unit may comprise any number of OMs, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more OMs or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 OMs. The OMs may comprise one or more SLMs, AODs, or AOMs. The OMs may comprise one or more DMDs. The OMs may comprise one or more liquid crystal devices, such as one or more LCoS devices.Attorney Docket No. 55436-751.601

[0188] The electromagnetic delivery unit may comprise one or more electromagnetic energy artificial intelligence (Al) units configured to perform one or more Al operations to selectively apply the electromagnetic energy to the atoms. For instance, the electromagnetic delivery unit may comprise Al unit 223. Although depicted as comprising a single Al unit in FIG. 4, the electromagnetic delivery unit may comprise any number of Al units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more Al units or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 Al units. The Al operations may comprise any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0189] The electromagnetic delivery unit may be configured to apply one or more single-qubit operations (such as one or more single-qubit gate operations) on the qubits described herein. The electromagnetic delivery unit may be configured to apply one or more two-qubit operations (such as one or more two-qubit gate operations) on the two-qubit units described herein. Each singlequbit or two-qubit operation may comprise a duration of at least about 10 nanoseconds (ns), 20 ns, 30 ns, 40 ns, 50 ns, 60 ns, 70 ns, 80 ns, 90 ns, 100 ns, 200 ns, 300 ns, 400 ns, 500 ns, 600 ns, 700 ns, 800 ns, 900 ns, 1 microsecond (ps), 2 ps, 3 ps, 4 ps, 5 ps, 6 ps, 7 ps, 8 ps, 9 ps, 10 ps, 20 ps, 30 ps, 40 ps, 50 ps, 60 ps, 70 ps, 80 ps, 90 ps, 100 ps, or more. Each single-qubit or two- qubit operation may comprise a duration of at most about 100 ps, 90 ps, 80 ps, 70 ps, 60 ps, 50 ps, 40 ps, 30 ps, 20 ps, 10 ps, 9 ps, 8 ps, 7 ps, 6 ps, 5 ps, 4 ps, 3 ps, 2 ps, 1 ps, 900 ns, 800 ns, 700 ns, 600 ns, 500 ns, 400 ns, 300 ns, 200 ns, 100 ns, 90 ns, 80 ns, 70 ns, 60 ns, 50 ns, 40 ns, 30 ns, 20 ns, 10 ns, or less. Each single-qubit or two-qubit operation may comprise a duration that is within a range defined by any two of the preceding values. The single-qubit or two-qubit operations may be applied with a repetition frequency of at least 1 kilohertz (kHz), 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 50 kHz, 60 kHz, 70 kHz, 80 kHz, 90 kHz, 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1,000 kHz, or more. The single-qubit or two-qubit operations may be applied with a repetition frequency of at most 1,000 kHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, or less. The single-qubit or two-qubit operations may be applied with a repetition frequency that is within a range defined by any two of the preceding values.

[0190] The electromagnetic delivery unit may be configured to apply one or more single-qubit operations by inducing one or more Raman transitions between a first qubit state and a second qubit state described herein. The Raman transitions may be detuned from a3Po or3Pi line described herein. For instance, the Raman transitions may be detuned by at least about 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 50Attorney Docket No. 55436-751.601 kHz, 60 kHz, 70 kHz, 80 kHz, 90 kHz, 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1 MHz, 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 20 MHz, 30 MHz, 40 MHz, 50 MHz, 60 MHz, 70 MHz, 80 MHz, 90 MHz, 100 MHz, 200 MHz, 300 MHz, 400 MHz, 500 MHz, 600 MHz, 700 MHz, 800 MHz, 900 MHz, 1 GHz, or more. The Raman transitions may be detuned by at most about 1 GHz, 900 MHz, 800 MHz, 700 MHz, 600 MHz, 500 MHz, 400 MHz, 300 MHz, 200 MHz, 100 MHz, 90 MHz, 80 MHz, 70 MHz, 60 MHz, 50 MHz, 40 MHz, 30 MHz, 20 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, or less. The Raman transitions may be detuned by a value that is within a range defined by any two of the preceding values.

[0191] Raman transitions may be induced on individually selected atoms using one or more spatial light modulators (SLMs) or acousto-optic deflectors (AODs) to impart a deflection angle and / or a frequency shift to a light beam based on an applied radio-frequency (RF) signal. The SLM or AOD may be combined with an optical conditioning system that images the SLM or AOD active region onto the back focal plane of a microscope objective. The microscope objective may perform a spatial Fourier transform on the optical field at the position of the SLM or AOD. As such, angle (which may be proportional to RF frequency) may be converted into position. For example, applying a comb of radio frequencies to an AOD may generate a linear array of spots at a focal plane of the objective, with each spot having a finite extent determined by the characteristics of the optical conditioning system (such as the point spread function of the optical conditioning system).

[0192] To perform a Raman transition on a single atom with a single SLM or AOD, a pair of frequencies may be applied to the SLM or AOD simultaneously. The two frequencies of the pair may have a frequency difference that matches or nearly matches the splitting energy between the first and second qubit states. For instance, the frequency difference may differ from the splitting energy by at most about 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, 900 Hz, 800 Hz, 700 Hz, 600 Hz, 500 Hz, 400 Hz, 300 Hz, 200 Hz, 100 Hz, 90 Hz, 80 Hz, 70 Hz, 60 Hz, 50 Hz, 40 Hz, 30 Hz, 20 Hz, 10 Hz, 9 Hz, 8 Hz, 7 Hz, 6 Hz, 5 Hz, 4 Hz, 3 Hz, 2 Hz, 1 Hz, or less. The frequency difference may differ from the splitting energy by at least about 1 Hz, 2 Hz, 3 Hz, 4 Hz, 5 Hz, 6 Hz, 7 Hz, 8 Hz, 9 Hz, 10 Hz, 20 Hz, 30 Hz, 40 Hz, 50 Hz, 60 Hz, 70 Hz, 80 Hz, 90 Hz, 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz,Attorney Docket No. 55436-751.6015 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 50 kHz, 60 kHz, 70 kHz, 80 kHz, 90 kHz, 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1 MHz, or more. The frequency difference may differ from the splitting energy by about 0 Hz. The frequency difference may differ from the splitting energy by a value that is within a range defined by any two of the preceding values. The optical system may be configured such that the position spacing corresponding to the frequency difference is not resolved and such that light at both of the two frequencies interacts with a single atom.

[0193] The electromagnetic delivery units may be configured to provide a beam with a characteristic dimension of at least about 10 nm, 50 nm, 75 nm, 100 nm, 125 nm, 150 nm, 175 nm, 200 nm, 225 nm, 250 nm, 275 nm, 300 nm, 325 nm, 350 nm, 375 nm, 400 nm, 425 nm, 450 nm, 475 nm, 500 nm, 525 nm, 550 nm, 575 nm, 600 nm, 625 nm, 650 nm, 675 nm, 700 nm, 725 nm, 750 nm, 775 nm, 800 nm, 825 nm, 850 nm, 875 nm, 900 nm, 925 nm, 950 nm, 975 nm, 1 micrometer (pm), 1.5 pm, 2 pm, 2.5 pm 3 pm, 3.5 pm, 4 pm, 4.5 pm, 5 pm, 5.5 pm, 6 pm, 6.5 pm, 7 pm, 7.5 pm, 8 pm, 8.5 pm, 9 pm, 9.5 pm, 10 pm, or more. The electromagnetic delivery units may be configured to provide a beam with a characteristic dimension of at most about 10 pm, 9.5 pm, 9 pm, 8.5 pm, 8 pm, 7.5 pm, 7 pm, 6.5 pm, 6 pm, 5.5 pm, 5 pm, 4.5 pm, 4 pm, 3.5 pm, 3 pm, 2.5 pm, 2 pm, 1.5 pm, 1 pm, 975 nm, 950 nm, 925 nm, 900 nm, 875 nm, 850 nm, 825 nm, 800 nm, 775 nm, 750 nm, 725 nm, 700 nm, 675 nm, 650 nm, 625 nm, 600 nm, 575 nm, 550 nm, 525 nm, 500 nm, 475 nm, 450 nm, 425 nm, 400 nm, 375 nm, 350 nm, 325 nm, 300 nm, 275 nm, 250 nm, 225 nm, 200 nm, 175 nm, 150 nm, 125 nm, 100 nm, 75 nm, 25 nm, 10 nm, or less.The electromagnetic delivery units may be configured to provide a beam with a characteristic dimension as defined by any two of the proceeding values. For example, the beam can have a characteristic dimension of about 1.5 micrometers to about 2.5 micrometers. Examples of characteristic dimensions include, but are not limited to, a Gaussian beam waist, the full width at half maximum (FWHM) of the beam size, the beam diameter, the 1 / e2width, the D4G width, the D86 width, and the like. For example, the beam may have a Gaussian beam waist of at least about 1.5 micrometers.

[0194] The characteristic dimension of the beam may be bounded at the low end by the size of the atomic wavepacket of an optical trapping site. For example, the beam can be formed such that the intensity variation of the beam over the trapping site is sufficiently small as to be substantially homogeneous over the trapping site. In this example, the beam homogeneity can improve the fidelity of a qubit in the trapping site. The characteristic dimension of the beam may be bounded at the high end by the spacing between trapping sites. For example, a beam can be formed such that it is small enough that the effect of the beam on a neighboring trapping site / atom is negligible. In this example, the effect may be negligible if the effect can beAttorney Docket No. 55436-751.601 minimized by techniques such as, for example, composite pulse engineering. The characteristic dimension may be different from a maximum achievable resolution of the system. For example, a system can have a maximum resolution of 700 nm, but the system may be operated at 1.5 micrometers. In this example, the value of the characteristic dimension may be selected to optimize the performance of the system in view of the considerations described elsewhere herein. The characteristic dimension may be invariant for different maximally achievable resolutions. For example, a system with a maximum resolution of 500 nm and a system with a maximum resolution of 2 micrometers may both be configured to operate at a characteristic dimension of 2 micrometers. In this example, 2 micrometers may be the optimal resolution based on the size of the trapping sites.Example of Integrated Optical Trapping Units and Electromagnetic Delivery Units

[0195] The optical trapping units and electromagnetic delivery units described herein may be integrated into a single optical system. A microscope objective may be used to deliver electromagnetic radiation generated by an electromagnetic delivery unit described herein and to deliver light for trapping atoms generated by an optical trapping unit described herein. Alternatively or in addition, different objectives may be used to deliver electromagnetic radiation generated by an electromagnetic delivery unit and to deliver light from trapping atoms generated by an optical trapping unit.

[0196] A single SLM or AOD may allow the implementation of qubit operations (such as any single-qubit or two-qubit operations described herein) on a linear array of atoms. Alternatively or in addition, two separate SLMs or AODs may be configured to each handle light with orthogonal polarizations. The light with orthogonal polarizations may be overlapped before the microscope objective. In such a scheme, each photon used in a two-photon transition described herein may be passed to the objective by a separate SLM or AOD, which may allow for increased polarization control. Qubit operations may be performed on a two-dimensional arrangement of atoms by bringing light from a first SLM or AOD into a second SLM or AOD that is oriented substantially orthogonally to the first SLM or AOD via an optical relay. Alternatively or in addition, qubit operations may be performed on a two-dimensional arrangement of atoms by using a onedimensional array of SLMs or AODs.

[0197] The stability of qubit gate fidelity may be improved by maintaining overlap of light from the various light sources described herein (such as light sources associated with the optical trapping units or electromagnetic delivery units described herein). Such overlap may be maintained by an optical subsystem that measures the direction of light emitted by the various light sources, allowing closed-loop control of the direction of light emission. The opticalAttorney Docket No. 55436-751.601 subsystem may comprise a pickoff mirror located before the microscope objective. The pickoff mirror may be configured to direct a small amount of light to a lens, which may focus a collimated beam and convert angular deviation into position deviation. A position-sensitive optical detector, such as a lateral -effect position sensor or quadrant photodiode, may convert the position deviation into an electronic signal and information about the deviation may be fed into a compensation optic, such as an active mirror.

[0198] The stability of qubit gate manipulation may be improved by controlling the intensity of light from the various light sources described herein (such as light sources associated with the optical trapping units or electromagnetic delivery units described herein). Such intensity control may be maintained by an optical subsystem that measures the intensity of light emitted by the various light sources, allowing closed-loop control of the intensity. Each light source may be coupled to an intensity actuator, such as an intensity servo control. The actuator may comprise an acousto-optic modulator (AOM) or electro-optic modulator (EOM). The intensity may be measured using an optical detector, such as a photodiode or any other optical detector described herein. Information about the intensity may be integrated into a feedback loop to stabilize the intensity.Example of State Preparation Units

[0199] FIG. 5 shows an example of a state preparation unit 250. The state preparation unit may be configured to prepare a state of the plurality of atoms, as described herein. The state preparation unit may be coupled to the optical trapping unit and may direct atoms that have been prepared by the state preparation unit to the optical trapping unit. The state preparation unit may be configured to cool the plurality of atoms. The state preparation unit may be configured to cool the plurality of atoms prior to trapping the plurality of atoms at the plurality of optical trapping sites.

[0200] The state preparation unit may comprise one or more Zeeman slowers. For instance, the state preparation unit may comprise a Zeeman slower 251. Although depicted as comprising a single Zeeman slower in FIG. 5, the state preparation may comprise any number of Zeeman slowers, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more Zeeman slowers or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 Zeeman slowers. The Zeeman slowers may be configured to cool one or more atoms of the plurality of atoms from a first velocity or distribution of velocities (such an emission velocity from an of an atom source, room temperature, liquid nitrogen temperature, or any other temperature) to a second velocity that is lower than the first velocity or distribution of velocities.Attorney Docket No. 55436-751.601

[0201] The first velocity or distribution of velocities may be associated with a temperature of at least about 50 Kelvin (K), 60 K, 70 K, 80 K, 90 K, 100 K, 200 K, 300 K, 400 K, 500 K, 600 K, 700 K, 800 K, 900 K, 1,000 K, or more. The first velocity or distribution of velocities may be associated with a temperature of at most about 1,000 K, 900 K, 800 K, 700 K, 600 K, 500 K, 400 K, 300 K, 200 K, 100 K, 90 K, 80 K, 70 K, 60 K, 50 K, or less. The first velocity or distribution of velocities may be associated with a temperature that is within a range defined by any two of the preceding values. The second velocity may be at least about 1 meter per second (m / s), 2 m / s, 3 m / s, 4 m / s, 5 m / s, 6 m / s, 7 m / s, 8 m / s, 9 m / s, 10 m / s, or more. The second velocity may be at most about 10 m / s, 9 m / s, 8 m / s, 7 m / s, 6 m / s, 5 m / s, 4 m / s, 3 m / s, 2 m / s, 1 m / s, or less. The second velocity may be within a range defined by any two of the preceding values. The Zeeman slowers may comprise ID Zeeman slowers.

[0202] The state preparation unit may comprise a first magneto-optical trap (MOT) 252. The first MOT may be configured to cool the atoms to a first temperature. The first temperature may be at most about 10 millikelvin (mK), 9 mK, 8 mK, 7 mK, 6 mK, 5 mK, 4 mK, 3 mK, 2 mK, 1 mK, 0.9 mK, 0.8 mK, 0.7 mK, 0.6 mK, 0.5 mK, 0.4 mK, 0.3 mK, 0.2 mK, 0.1 mK, or less. The first temperature may be at least about 0.1 mK, 0.2 mK, 0.3 mK, 0.4 mK, 0.5 mK, 0.6 mK, 0.7 mK, 0.8 mK, 0.9 mK, 1 mK, 2 mK, 3 mK, 4 mK, 5 mK, 6 mK, 7 mK, 8 mK, 9 mK, 10 mK, or more. The first temperature may be within a range defined by any two of the preceding values. The first MOT may comprise a ID, 2D, or 3D MOT.

[0203] The first MOT may comprise one or more light sources (such as any light source described herein) configured to emit light. The light may comprise one or more wavelengths of at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or more. The light may comprise one or more wavelengths of at most about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm,840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm,730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm,620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm,510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm,400 nm, or less. The light may comprise one or more wavelengths that are within a range defined by any two of the preceding values. For instance, the light may comprise one or moreAttorney Docket No. 55436-751.601 wavelengths that are within a range from 400 nm to 1,000 nm, 500 nm to 1,000 nm, 600 nm to 1,000 nm, 650 nm to 1,000 nm, 400 nm to 900 nm, 400 nm to 800 nm, 400 nm to 700 nm, 400 nm to 600 nm, 400 nm to 500 nm, 500 nm to 700 nm, or 650 nm to 700 nm.

[0204] The state preparation unit may comprise a second MOT 253. The second MOT may be configured to cool the atoms from the first temperature to a second temperature that is lower than the first temperature. The second temperature may be at most about 100 microkelvin (pK), 90 pK, 80 pK, 70 pK, 60 pK, 50 pK, 40 pK, 30 pK, 20 pK, 10 pK, 9 pK, 8 pK, 7 pK, 6 pK, 5 pK, 4 pK, 3 pK, 2 pK, 1 pK, 900 nanokelvin (nK), 800 nK, 700 nK, 600 nK, 500 nK, 400 nK, 300 nK, 200 nK, 100 nK, or less. The second temperature may be at least about 100 nK, 200 nK, 300 nK, 400 nK, 500 nK, 600 nK, 700 nK, 800 nK, 900 nK, 1 pK, 2 pK, 3 pK, 4 pK, 5 pK, 6 pK, 7 pK, 8 pK, 9 pK, 10 pK, 20 pK, 30 pK, 40 pK, 50 pK, 60 pK, 70 pK, 80 pK, 90 pK, 100 pK, or more. The second temperature may be within a range defined by any two of the preceding values. The second MOT may comprise a ID, 2D, or 3D MOT.

[0205] The second MOT may comprise one or more light sources (such as any light source described herein) configured to emit light. The light may comprise one or more wavelengths of at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or more. The light may comprise one or more wavelengths of at most about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or less. The light may comprise one or more wavelengths that are within a range defined by any two of the preceding values. For instance, the light may comprise one or more wavelengths that are within a range from 400 nm to 1,000 nm, 500 nm to 1,000 nm, 600 nm to 1,000 nm, 650 nm to 1,000 nm, 400 nm to 900 nm, 400 nm to 800 nm, 400 nm to 700 nm, 400 nm to 600 nm, 400 nm to 500 nm, 500 nm to 700 nm, or 650 nm to 700 nm.

[0206] Although depicted as comprising two MOTs in FIG. 5, the state preparation unit may comprise any number of MOTs, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more MOTs or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 MOTs.Attorney Docket No. 55436-751.601

[0207] The state preparation unit may comprise one or more sideband cooling units or Sisyphus cooling units (such as a sideband cooling unit described in www.arxiv.org / abs / 1810.06626 or a Sisyphus cooling unit described in www.arxiv.org / abs / 1811.06014, each of which is incorporated herein by reference in its entirety for all purposes). For instance, the state preparation unit may comprise sideband cooling unit or Sisyphus cooling unit 254. Although depicted as comprising a single sideband cooling unit or Sisyphus cooling unit in FIG. 5, the state preparation may comprise any number of sideband cooling units or Sisyphus cooling units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more sideband cooling units or Sisyphus cooling units, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 sideband cooling units or Sisyphus cooling units. The sideband cooling units or Sisyphus cooling units may be configured to use sideband cooling to cool the atoms from the second temperature to a third temperature that is lower than the second temperature. The third temperature may be at most about 10 pK, 9 pK, 8 pK, 7 pK, 6 pK, 5 pK, 4 pK, 3 pK, 2 pK, 1 pK, 900 nK, 800 nK, 700 nK, 600 nK, 500 nK, 400 nK, 300 nK, 200 nK, 100 nK, 90 nK, 80 nK, 70 nK, 60 nK, 50 nK, 40 nK, 30 nK, 20 nK, 10 nK, or less. The third temperature may be at most about 10 nK, 20 nK, 30 nK, 40 nK, 50 nK, 60 nK, 70 nK, 80 nK, 90 nK, 100 nK, 200 nK, 300 nK, 400 nK, 500 nK, 600 nK, 700 nK, 800 nK, 900 nK, 1 pK, 2 pK, 3 pK, 4 pK, 5 pK, 6 pK, 7 pK, 8 pK, 9 pK, 10 pK, or more. The third temperature may be within a range defined by any two of the preceding values.

[0208] The sideband cooling units or Sisyphus cooling units may comprise one or more light sources (such as any light source described herein) configured to emit light. The light may comprise one or more wavelengths of at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm,560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm,670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm,780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm,890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm,1,000 nm, or more. The light may comprise one or more wavelengths of at most about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm,880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm,770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm,660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm,550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm,440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or less. The light may comprise one or more wavelengths that are within a range defined by any two of the preceding values. For instance, the light may comprise one or more wavelengths that are within a range from 400 nm to 1,000 nm,Attorney Docket No. 55436-751.601500 nm to 1,000 nm, 600 nm to 1,000 nm, 650 nm to 1,000 nm, 400 nm to 900 nm, 400 nm to 800 nm, 400 nm to 700 nm, 400 nm to 600 nm, 400 nm to 500 nm, 500 nm to 700 nm, or 650 nm to 700 nm.

[0209] The state preparation unit may comprise one or more optical pumping units. For instance, the state preparation unit may comprise optical pumping unit 255. Although depicted as comprising a single optical pumping unit in FIG. 5, the state preparation may comprise any number of optical pumping units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more optical pumping units, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 optical pumping units. The optical pumping units may be configured to emit light to optically pump the atoms from an equilibrium distribution of atomic states to a non-equilibrium atomic state. For instance, the optical pumping units may be configured to emit light to optically pump the atoms from an equilibrium distribution of atomic states to a single pure atomic state. The optical pumping units may be configured to emit light to optically pump the atoms to a ground atomic state or to any other atomic state. The optical pumping units may be configured to optically pump the atoms between any two atomic states. The optical pumping units may comprise one or more light sources (such as any light source described herein) configured to emit light. The light may comprise one or more wavelengths of at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm,580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm,690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm,800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm,910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or more. The light may comprise one or more wavelengths of at most about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or less. The light may comprise one or more wavelengths that are within a range defined by any two of the preceding values. For instance, the light may comprise one or more wavelengths that are within a range from 400 nm to 1,000 nm, 500 nm to 1,000 nm, 600 nm to 1,000 nm, 650 nm to 1,000 nm, 400 nm to 900 nm, 400 nm to 800 nm, 400 nm to 700 nm, 400 nm to 600 nm, 400 nm to 500 nm, 500 nm to 700 nm, or 650 nm to 700 nm.

[0210] The state preparation unit may comprise one or more coherent driving units. For instance, the state preparation unit may comprise coherent driving unit 256. Although depicted asAttorney Docket No. 55436-751.601 comprising a coherent driving unit in FIG. 5, the state preparation may comprise any number of coherent driving units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more coherent driving units or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 coherent driving units. The coherent driving units may be configured to coherently drive the atoms from the non-equilibrium state to the first or second atomic states described herein. Thus, the atoms may be optically pumped to an atomic state that is convenient to access (for instance, based on availability of light sources that emit particular wavelengths or based on other factors) and then coherently driven to atomic states described herein that are useful for performing quantum computations. The coherent driving units may be configured to induce a single photon transition between the non-equilibrium state and the first or second atomic state. The coherent driving units may be configured to induce a two-photon transition between the non-equilibrium state and the first or second atomic state. The two-photon transition may be induced using light from two light sources described herein (such as two lasers described herein).

[0211] The coherent driving units may comprise one or more light sources (such as any light source described herein) configured to emit light. The light may comprise one or more wavelengths of at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or more. The light may comprise one or more wavelengths of at most about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm,860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm,750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm,640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm,530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm,420 nm, 410 nm, 400 nm, or less. The light may comprise one or more wavelengths that are within a range defined by any two of the preceding values. For instance, the light may comprise one or more wavelengths that are within a range from 400 nm to 1,000 nm, 500 nm to 1,000 nm, 600 nm to 1,000 nm, 650 nm to 1,000 nm, 400 nm to 900 nm, 400 nm to 800 nm, 400 nm to 700 nm, 400 nm to 600 nm, 400 nm to 500 nm, 500 nm to 700 nm, or 650 nm to 700 nm.

[0212] The coherent driving units may be configured to induce an RF transition between the nonequilibrium state and the first or second atomic state. The coherent driving units may comprise one or more electromagnetic radiation sources configured to emit electromagnetic radiationAttorney Docket No. 55436-751.601 configured to induce the RF transition. For instance, the coherent driving units may comprise one or more RF sources (such as any RF source described herein) configured to emit RF radiation. The RF radiation may comprise one or more wavelengths of at least about 10 centimeters (cm), 20 cm, 30 cm, 40 cm, 50 cm, 60 cm, 70 cm, 80 cm, 90 cm, 1 meter (m), 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, 9 m, 10 m, or more. The RF radiation may comprise one or more wavelengths of at most about 10 m, 9 m, 8 m, 7 m, 6 m, 5 m, 4 m, 3 m, 2 m, 1 m, 90 cm, 80 cm, 70 cm, 60 cm, 50 cm, 40 cm, 30 cm, 20 cm, 10 cm, or less. The RF radiation may comprise one or more wavelengths that are within a range defined by any two of the preceding values. Alternatively or in addition, the coherent driving units may comprise one or more light sources (such as any light sources described herein) configured to induce a two-photon transition corresponding to the RF transition.Example of Controllers

[0213] The optical trapping units, electromagnetic delivery units, entanglement units, readout optical units, vacuum units, imaging units, spatial configuration Al units, spatial arrangement Al units, atom rearrangement units, state preparation units, sideband cooling units, optical pumping units, coherent driving units, electromagnetic energy Al units, atom reservoirs, atom movement units, or Rydberg excitation units may include one or more circuits or controllers (such as one or more electronic circuits or controllers) that is connected (for instance, by one or more electronic connections) to the optical trapping units, electromagnetic delivery units, entanglement units, readout optical units, vacuum units, imaging units, spatial configuration Al units, spatial arrangement Al units, atom rearrangement units, state preparation units, sideband cooling units, optical pumping units, coherent driving units, electromagnetic energy Al units, atom reservoirs, atom movement units, or Rydberg excitation units. The circuits or controllers may be configured to control the optical trapping units, electromagnetic delivery units, entanglement units, readout optical units, vacuum units, imaging units, spatial configuration Al units, spatial arrangement Al units, atom rearrangement units, state preparation units, sideband cooling units, optical pumping units, coherent driving units, electromagnetic energy Al units, atom reservoirs, atom movement units, or Rydberg excitation units.Example of non-classical computers

[0214] In an aspect, the present disclosure provides a non-classical computer comprising: a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprise at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state; one orAttorney Docket No. 55436-751.601 more electromagnetic delivery units configured to apply electromagnetic energy to one or more qubits of the plurality of qubits, thereby imparting a non-classical operation to the one or more qubits, which non-classical operation includes a superposition between at least the first qubit state and the second qubit state; one or more entanglement units configured to quantum mechanically entangle at least a subset of the plurality of qubits in the superposition with at least another qubit of the plurality of qubits; and one or more readout optical units configured to perform one or more measurements of the one or more qubits, thereby obtaining a non-classical computation.

[0215] In an aspect, the present disclosure provides a non-classical computer comprising a plurality of qubits comprising greater than 60 atoms each trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites.Example of Methods for Performing a Non-Classical Computation

[0216] In an aspect, the present disclosure provides a method for performing a non-classical computation, comprising: (a) generating a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites configured to trap a plurality of atoms, the plurality of atoms comprising greater than 60 atoms; (b) applying electromagnetic energy to one or more atoms of the plurality of atoms, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state that is different from the first atomic state; (c) quantum mechanically entangling at least a subset of the one or more atoms in the one or more superposition states with at least another atom of the plurality of atoms; and (d) performing one or more optical measurements of the one or more superposition state to obtain the non-classical computation.

[0217] FIG. 6 shows a flowchart for an example of a first method 600 for performing a non- classical computation.

[0218] In a first operation 610, the method 600 may comprise generating a plurality of spatially distinct optical trapping sites. The plurality of optical trapping sites may be configured to trap a plurality of atoms. The plurality of atoms may comprise greater than 60 atoms. The optical trapping sites may comprise any optical trapping sites described herein. The atoms may comprise any atoms described herein.

[0219] In a second operation 620, the method 600 may comprise applying electromagnetic energy to one or more atoms of the plurality of atoms, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state that is different from the first atomic state. The electromagnetic energy may comprise any electromagnetic energy described herein. The first atomic state may comprise any first atomicAttorney Docket No. 55436-751.601 state described herein. The second atomic state may comprise any second atomic state described herein.

[0220] In a third operation 630, the method 600 may comprise quantum mechanically entangling at least a subset of the one or more atoms in the one or more superposition states with at least another atom of the plurality of atoms. The atoms may be quantum mechanically entangled in any manner described herein (for instance, as described herein with respect to FIG. 2).

[0221] In a fourth operation 640, the method 600 may comprise performing one or more optical measurements of the one or more superposition state to obtain the non-classical computation. The optical measurements may comprise any optical measurements described herein.

[0222] In an aspect, the present disclosure provides a method for performing a non-classical computation, comprising: (a) providing a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprise at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state; (b) applying electromagnetic energy to one or more qubits of the plurality of qubits, thereby imparting a non-classical operation to the one or more qubits, which non-classical operation includes a superposition between at least the first qubit state and the second qubit state; (c) quantum mechanically entangling at least a subset of the plurality of qubits in the superposition with at least another qubit of the plurality of qubits; and (d) performing one or more optical measurements of the one or more qubits, thereby obtaining said the-classical computation.

[0223] FIG. 7 shows a flowchart for an example of a second method 700 for performing a non- classical computation.

[0224] In a first operation 710, the method 700 may comprise providing a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprise at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state. The optical trapping sites may comprise any optical trapping sites described herein. The qubits may comprise any qubits described herein. The atoms may comprise any atoms described herein. The first qubit state may comprise any first qubit state described herein. The second qubit state may comprise any second qubit state described herein. The first atomic state may comprise any first atomic state described herein. The second atomic state may comprise any second atomic state described herein.

[0225] In a second operation 720, the method 700 may comprise applying electromagnetic energy to one or more qubits of the plurality of qubits, thereby imparting a non-classicalAttorney Docket No. 55436-751.601 operation to the one or more qubits, which non-classical operation includes a superposition between at least the first qubit state and the second qubit state. The electromagnetic energy may comprise any electromagnetic energy described herein.

[0226] In a third operation 730, the method 700 may comprise quantum mechanically entangling at least a subset of the plurality of qubits in the superposition with at least another qubit of the plurality of qubits. The qubits may be quantum mechanically entangled in any manner described herein (for instance, as described herein with respect to FIG. 2).

[0227] In a fourth operation 740, the method 700 may comprise performing one or more optical measurements of the one or more qubits, thereby obtaining the non-classical computation. The optical measurements may comprise any optical measurements described herein.

[0228] In an aspect, the present disclosure provides a method for performing a non-classical computation, comprising: (a) providing a plurality of qubits comprising greater than 60 atoms each trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, and (b) using at least a subset of the plurality of qubits to perform the non-classical computation.

[0229] FIG. 8 shows a flowchart for an example of a third method 800 for performing a non- classical computation.

[0230] In a first operation 810, the method 800 may comprise providing a plurality of qubits comprising greater than 60 atoms each trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites. The qubits may comprise any qubits described herein. The atoms may comprise any atoms described herein. The optical trapping sites may comprise any optical trapping sites described herein.

[0231] In a second operation 820, the method 800 may comprise using at least a subset of the plurality of qubits to perform a non-classical computation.Example of Parallel Addressing of Multi-Qubit Units

[0232] Direct excitation of strontium-87 from the ground state to Rydberg levels would require a laser with a wavelength of approximately 218 nm. Alternatively, the Rydberg excitation operation can be performed using two-photon excitation combining 689 nm and 319 nm light, each detuned from the intermediate3Pi state. The approximately 7 kHz width of the3Pi state provides an effective balance between the two-photon effective Rabi rate and scattering via spontaneous decay from the3Pi. FIG. 9 shows an energy level structure for single-qubit and multi -qubit operations in strontium-87.

[0233] The optical system for single-qubit operations is also designed to work well for multiqubit gates. One of the single-qubit beams is used as one leg of the two-photon excitation schemeAttorney Docket No. 55436-751.601 that drives transitions to the Rydberg electronic manifold. To satisfy the spatially -dependent frequency and phase matching condition, AODs are also used for the UV light. Importantly, the optical systems are matched so that the frequency shift of the UV light from one site to another is identical to that of the 689 nm light. The consequence of this constraint is that the performance of state-of-the-art UV AODs dictate the accessible field of view (FOV) for multi -qubit operations. Further, because one of the single-qubit beams is being used for multi-qubit operations (and the two single-qubit beams are matched), the FOV for single-qubit operations will be the same. A figure of merit for UV AODs is the product of the active aperture and the RF bandwidth of the device. For a fixed beam size in the back focal plane of the objective, increasing either of these quantities results in a larger scan angle of the beams, and thus a larger FOV in the plane of the qubit array. An FOV of approximately 100 pm x 100 pm was achieved, which is sufficient to address an array of approximately 1,000 atoms with a trapping site spacing of 3 pm.Example of Computer Systems

[0234] FIG. 1 shows a computer system 101 that is programmed or otherwise configured to operate any method or system described herein (such as system or method for monitoring operation of a quantum computer described herein). The computer system 101 can regulate various aspects of the present disclosure. The computer system 101 can be an electronic device of a user or a computer system that is remotely located with respect to the electronic device. The electronic device can be a mobile electronic device.

[0235] The computer system 101 includes a central processing unit (CPU, also “processor” and “computer processor” herein) 105, which can be a single core or multi core processor, or a plurality of processors for parallel processing. The computer system 101 also includes memory or memory location 110 (e.g., random-access memory, read-only memory, flash memory), electronic storage unit 115 (e.g., hard disk), communication interface 120 (e.g., network adapter) for communicating with one or more other systems, and peripheral devices 125, such as cache, other memory, data storage and / or electronic display adapters. The memory 110, storage unit 115, interface 120 and peripheral devices 125 are in communication with the CPU 105 through a communication bus (solid lines), such as a motherboard. The storage unit 115 can be a data storage unit (or data repository) for storing data. The computer system 101 can be operatively coupled to a computer network (“network”) 130 with the aid of the communication interface 120. The network 130 can be the Internet, an internet and / or extranet, or an intranet and / or extranet that is in communication with the Internet. The network 130 in some cases is a telecommunication and / or data network. The network 130 can include one or more computer servers, which can enable distributed computing, such as cloud computing. The network 130, inAttorney Docket No. 55436-751.601 some cases with the aid of the computer system 101, can implement a peer-to-peer network, which may enable devices coupled to the computer system 101 to behave as a client or a server.

[0236] The CPU 105 can execute a sequence of machine-readable instructions, which can be embodied in a program or software. The instructions may be stored in a memory location, such as the memory 110. The instructions can be directed to the CPU 105, which can subsequently program or otherwise configure the CPU 105 to implement methods of the present disclosure. Examples of operations performed by the CPU 105 can include fetch, decode, execute, and writeback.

[0237] The CPU 105 can be part of a circuit, such as an integrated circuit. One or more other components of the system 101 can be included in the circuit. In some cases, the circuit is an application specific integrated circuit (ASIC).

[0238] The storage unit 115 can store files, such as drivers, libraries and saved programs. The storage unit 115 can store user data, e.g., user preferences and user programs. The computer system 101 in some cases can include one or more additional data storage units that are external to the computer system 101, such as located on a remote server that is in communication with the computer system 101 through an intranet or the Internet.

[0239] The computer system 101 can communicate with one or more remote computer systems through the network 130. For instance, the computer system 101 can communicate with a remote computer system of a user. Examples of remote computer systems include personal computers (e.g., portable PC), slate or tablet PC’s (e.g., Apple® iPad, Samsung® Galaxy Tab), telephones, Smart phones (e.g., Apple® iPhone, Android-enabled device, Blackberry®), or personal digital assistants. The user can access the computer system 101 via the network 130.

[0240] Methods as described herein can be implemented by way of machine (e.g., computer processor) executable code stored on an electronic storage location of the computer system 101, such as, for example, on the memory 110 or electronic storage unit 115. The machine executable or machine-readable code can be provided in the form of software. During use, the code can be executed by the processor 105. In some cases, the code can be retrieved from the storage unit 115 and stored on the memory 110 for ready access by the processor 105. In some situations, the electronic storage unit 115 can be precluded, and machine-executable instructions are stored on memory 110.

[0241] The code can be pre-compiled and configured for use with a machine having a processor adapted to execute the code or can be compiled during runtime. The code can be supplied in a programming language that can be selected to enable the code to execute in a pre-compiled or as- compiled fashion.Attorney Docket No. 55436-751.601

[0242] Aspects of the systems and methods provided herein, such as the computer system 101, can be embodied in programming. Various aspects of the technology may be thought of as “products” or “articles of manufacture” typically in the form of machine (or processor) executable code and / or associated data that is carried on or embodied in a type of machine readable medium. Machine-executable code can be stored on an electronic storage unit, such as memory (e.g., read-only memory, random-access memory, flash memory) or a hard disk. “Storage” type media can include any or all of the tangible memory of the computers, processors or the like, or associated units thereof, such as various semiconductor memories, tape drives, disk drives and the like, which may provide non-transitory storage at any time for the software programming. All or portions of the software may at times be communicated through the Internet or various other telecommunication networks. Such communications, for example, may enable loading of the software from one computer or processor into another, for example, from a management server or host computer into the computer platform of an application server. Thus, another type of media that may bear the software elements includes optical, electrical and electromagnetic waves, such as used across physical interfaces between local devices, through wired and optical landline networks and over various air-links. The physical elements that carry such waves, such as wired or wireless links, optical links or the like, also may be considered as media bearing the software. As used herein, unless restricted to non-transitory, tangible “storage” media, terms such as computer or machine “readable medium” refer to any medium that participates in providing instructions to a processor for execution.

[0243] Hence, a machine readable medium, such as computer-executable code, may take many forms, including but not limited to, a tangible storage medium, a carrier wave medium or physical transmission medium. Non-volatile storage media include, for example, optical or magnetic disks, such as any of the storage devices in any computer(s) or the like, such as may be used to implement the databases, etc. shown in the drawings. Volatile storage media include dynamic memory, such as main memory of such a computer platform. Tangible transmission media include coaxial cables; copper wire and fiber optics, including the wires that comprise a bus within a computer system. Carrier-wave transmission media may take the form of electric or electromagnetic signals, or acoustic or light waves such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media therefore include for example: a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD or DVD-ROM, any other optical medium, punch cards paper tape, any other physical storage medium with patterns of holes, a RAM, a ROM, a PROM and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave transporting data or instructions, cables or links transporting such a carrier wave, or any otherAttorney Docket No. 55436-751.601 medium from which a computer may read programming code and / or data. Many of these forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to a processor for execution.

[0244] The computer system 101 can include or be in communication with an electronic display 135 that comprises a user interface (UI) 140. Examples of UI’s include, without limitation, a graphical user interface (GUI) and web-based user interface.

[0245] Methods and systems of the present disclosure can be implemented by way of one or more algorithms. An algorithm can be implemented by way of software upon execution by the central processing unit 105. The algorithm can, for example, implement methods for performing a non-classical computation described herein.Machine Learning

[0001] As used in this specification and the appended claims, the terms “Al agent” may refer to a system implementing a machine learning model that may learn via training operations to progressively improve computer performance of a task.

[0002] A machine learning model herein may comprise neural networks and classical machine learning algorithms. A neural network may comprise a perceptron, a convolutional neural network, a recurrent neural network, a long-short-term memory network, a transformer, a residual neural network, or any machine learning model comprising layers of neurons, convolutional filters, the self-attention mechanism, or other architectural component of the listed neural networks. A classical machine learning algorithm may comprise a clustering algorithm, a decision tree-based algorithm, a polynomial regression algorithm, a gaussian regression algorithm, a support vector machine algorithm, a logistic regression algorithm, or other non- neural network based machine learning algorithm.

[0003] Training the ML model may include, in some cases, selecting one or more untrained data models to train using a training data set. The selected untrained data models may include any type of untrained ML models for supervised, semi-supervised, self-supervised, or unsupervised machine learning. The selected untrained data models may be specified based upon input (e.g., user input) specifying relevant parameters to use as predicted variables or other variables to use as potential explanatory variables. For example, the selected untrained data models may be specified to generate an output (e.g., a prediction) based upon the input. Conditions for training the ML model from the selected untrained data models may likewise be selected, such as limits on the ML model complexity (e.g., hyperparameter selection) or limits on the ML model refinement past a certain point (e.g., regularization). The ML model may be trained a computer system described herein using a training data set. In some cases, a first subset of the training dataAttorney Docket No. 55436-751.601 set may be selected to train the ML model. The selected untrained data models may then be trained on the first subset of training data set using appropriate ML techniques, based upon the type of ML model selected and any conditions specified for training the ML model. In some cases, due to the processing power requirements of training the ML model, the selected untrained data models may be trained using additional computing resources (e.g., cloud computing resources). Such training may continue, in some cases, until at least one aspect of the ML model is validated and meets selection criteria to be used as a predictive model.

[0004] In some cases, one or more aspects of the ML model may be validated using a second subset of the training data set (e.g., distinct from the first subset of the training data set) to determine accuracy and robustness of the ML model. Such validation may include applying the ML model to the second subset of the training data set to make predictions derived from the second subset of the training data. The ML model may then be evaluated to determine whether performance is sufficient based upon the derived predictions. The sufficiency criteria applied to the ML model may vary depending upon the size of the training data set available for training, the performance of previous iterations of trained models, or user-specified performance requirements. If the ML model does not achieve sufficient performance, additional training may be performed. Additional training may include refinement of the ML model or retraining on a different first subset of the training dataset, after which the new ML model may again be validated and assessed. When the ML model has achieved sufficient performance, in some cases, the ML may be stored for present or future use. The ML model may be stored as sets of parameter values or weights for analysis of further input (e.g., further relevant parameters to use as further predicted variables, further explanatory variables, further user interaction data, etc.), which may also include analysis logic or indications of model validity in some instances. In some cases, a plurality of ML models may be stored for generating predictions under different sets of input data conditions. In some cases, the ML model may be stored in a database (e.g., associated with a server).Certain Definitions and Additional Considerations

[0246] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. Any reference to “or” herein is intended to encompass “and / or” unless otherwise stated.

[0247] Whenever the term “at least,” “greater than,” or “greater than or equal to” precedes the first numerical value in a series of two or more numerical values, the term “at least,” “greaterAttorney Docket No. 55436-751.601 than” or “greater than or equal to” applies to each of the numerical values in that series of numerical values. For example, greater than or equal to 1, 2, or 3 is equivalent to greater than or equal to 1, greater than or equal to 2, or greater than or equal to 3.

[0248] Whenever the term “no more than,” “less than,” “less than or equal to,” or “at most” precedes the first numerical value in a series of two or more numerical values, the term “no more than,” “less than,” “less than or equal to,” or “at most” applies to each of the numerical values in that series of numerical values. For example, less than or equal to 3, 2, or 1 is equivalent to less than or equal to 3, less than or equal to 2, or less than or equal to 1.

[0249] Where values are described as ranges, it will be understood that such disclosure includes the disclosure of all possible sub-ranges within such ranges, as well as specific numerical values that fall within such ranges irrespective of whether a specific numerical value or specific subrange is expressly stated.

[0250] As used herein, like characters refer to like elements.

[0251] As used herein, the terms “non-classical computation,” “non-classical procedure,” “non- classical operation,” any “non-classical computer” generally refer to any method or system for performing computational procedures outside of the paradigm of classical computing. A non- classical computation, non-classical procedure, non-classical operation, or non-classical computer may comprise a quantum computation, quantum procedure, quantum operation, or quantum computer.

[0252] As used herein, the terms “quantum computation,” “quantum procedure,” “quantum operation,” and “quantum computer” generally refer to any method or system for performing computations using quantum mechanical operations (such as unitary transformations or completely positive trace-preserving (CPTP) maps on quantum channels) on a Hilbert space represented by a quantum device. As such, quantum and classical (or digital) computation may be similar in the following aspect: both computations may comprise sequences of instructions performed on input information to then provide an output. Various paradigms of quantum computation may break the quantum operations down into sequences of basic quantum operations that affect a subset of qubits of the quantum device simultaneously. The quantum operations may be selected based on, for instance, their locality or their ease of physical implementation. A quantum procedure or computation may then consist of a sequence of such instructions that in various applications may represent different quantum evolutions on the quantum device. For example, procedures to compute or simulate quantum chemistry may represent the quantum states and the annihilation and creation operators of electron spin-orbitals by using qubits (such as two-level quantum systems) and a universal quantum gate set (such asAttorney Docket No. 55436-751.601 the Hadamard, controlled-not (CNOT), and rotations) through the so-called Jordan-Wigner transformation or Bravyi-Kitaev transformation.

[0253] Additional examples of quantum procedures or computations may include procedures for optimization such as quantum approximate optimization algorithm (QAOA) or quantum minimum finding. QAOA may comprise performing rotations of single qubits and entangling gates of multiple qubits. In quantum adiabatic computation, the instructions may carry stochastic or non- stochastic paths of evolution of an initial quantum system to a final one.

[0254] Quantum-inspired procedures may include simulated annealing, parallel tempering, master equation solver, Monte Carlo procedures and the like. Quantum -classical or hybrid algorithms or procedures may comprise such procedures as variational quantum eigensolver (VQE) and the variational and adiabatically navigated quantum eigensolver (VanQver).

[0255] A quantum computer may comprise one or more adiabatic quantum computers, quantum gate arrays, one-way quantum computers, topological quantum computers, quantum Turing machines, quantum annealers, Ising solvers, or gate models of quantum computing.

[0256] As used herein, the term “adiabatic” refers to any process performed on a quantum mechanical system in which the parameters of the Hamiltonian are changed slowly in comparison to the natural timescale of evolution of the system.

[0257] As used herein, the term “non-adiabatic” refers to any process performed quantum mechanical system in which the parameters of the Hamiltonian are changed quickly in comparison to the natural timescale of evolution of the system or on a similar timescale as the natural timescale of evolution of the system.

[0258] While preferred embodiments of the present invention have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions will now occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in practicing the invention. It is intended that the following claims define the scope of the invention and that methods and structures within the scope of these claims and their equivalents be covered thereby.

Claims

Attorney Docket No. 55436-751.601CLAIMSWHAT IS CLAIMED IS:

1. A system for monitoring an operation of a quantum computer, comprising:(a) an imaging unit configured to passively gather photon data corresponding to said quantum computer during said operation of said quantum computer;(b) an image processing unit configured to generate at least one image corresponding to said operation of said quantum computer based at least in part on said photon data; and(c) a monitoring unit configured to determine a health of said quantum computer based at least in part on said at least one image.

2. The system of claim 1, further comprising a notification unit configured to generate a notification, wherein said notification corresponds to said health of said quantum computer.

3. The system of claim 2, wherein said notification is configured to be reviewed by a user of said quantum computer.

4. The system of claim 3, wherein said user initiates a calibration of said quantum computer based at least in part on said notification.

5. The system of any one of the preceding claims, wherein said at least one image is used to train machine learning model.

6. The system of claim 5, wherein said machine learning model is configured to trigger a calibration of said quantum computer or identify a need for calibration of said quantum computer.

7. The system of any one of the preceding claims, further comprising a control unit configured to generate a control signal to request a calibration of said quantum computer based at least in part on said health of said quantum computer.

8. The system of claim 6, wherein said control unit is configured to generate said control signal at least in part in response to determining said health of said quantum computer satisfies a threshold condition.

9. The system of any one of the preceding claims, wherein said imaging unit is configured to passively gather said photon data without an external light source illuminating said quantum computer during said operation.

10. The system of any one of the preceding claims, wherein said imaging unit is configured to passively gather said photon data without interrupting or affecting said operation of said quantum computer.

11. The system of any one of the preceding claims, wherein said quantum computing operation comprises one or both of a magneto-optical trap operation or a loading operation.Attorney Docket No. 55436-751.60112. The system of any one of the preceding claims, wherein said health of said quantum computer corresponds to one or more of: oven health, beam alignment, or optical focus.

13. The system of any one of the preceding claims, wherein said monitoring unit is configured to determine said health of said quantum computer substantially in real-time with respect to passively gathering said photon data with said imaging unit.

14. The system of claim 13, wherein said monitoring unit is configured to determine said health of said quantum computer within a certain time period of passively gathering said photon data with said imaging unit, wherein said certain time period is less than or equal to the amount of time for said health of said quantum computer to change or be expected to change.

15. A method for monitoring an operation of a quantum computer, comprising:(a) passively gathering photon data corresponding to said quantum computer during said operation of said quantum computer;(b) generating at least one image corresponding to said operation of said quantum computer based at least in part on said photon data; and(c) determining a health of said quantum computer based at least in part on said at least one image.

16. The method of claim 15, further comprising generating a notification, wherein said notification corresponds to said health of said quantum computer.

17. The method of claim 16, wherein said notification is configured to be reviewed by a user of said quantum computer.

18. The method of claim 17, wherein said user initiates a calibration of said quantum computer based at least in part on said notification.

19. The method of any one of claims 15-18, further comprising training a machine learning model based at least in part on said at least one image.

20. The method of claim 19, wherein said machine learning model is configured to trigger a calibration of said quantum computer or identify a need for calibration of said quantum computer.

21. The method of any one of claims 15-20, further comprising generating a control signal to request a calibration of said quantum computer based at least in part on said health of said quantum computer.

22. The method of claim 21, wherein said control signal is generated at least in part in response to determining said health of said quantum computer satisfies a threshold condition.

23. The method of any one of claims 15-22, wherein passively gathering said photon data at (a) is performed without an external light source illuminating said quantum computer during said operation.Attorney Docket No. 55436-751.60124. The method of any one of claims 15-23, wherein passively gathering said photon data at(a) is performed without interrupting or affecting said operation of said quantum computer.

25. The method of any one of claims 15-24, wherein said quantum computing operation comprises one or both of a magneto-optical trap operation or a loading operation.

26. The method of any one of claims 15-25, wherein said health of said quantum computer corresponds to one or more of: oven health, beam alignment, or optical focus.

27. The method of any one of claims 15-26, wherein said health of said quantum computer is determined in (c) substantially in real-time with respect to passively gathering said photon data with said imaging unit in (a).

28. The method of claim 27, wherein said health of said quantum computer is determined in (c) within a certain time period of passively gathering said photon data with said imaging unit in (a), wherein said certain time period is less than or equal to the amount of time for said health of said quantum computer to change or be expected to change.

29. One or more non-transitory computer-readable media comprising machine-executable code comprising one or more instructions that, when executed, implement the method of any one of claims 15-29.

30. A system for monitoring a quantum computer, comprising:(a) a plurality of optical trapping sites configured to trap a plurality of qubits;(b) an imaging unit configured to obtain one or more observations corresponding to one or both of said plurality of qubits or said plurality of optical trapping sites without applying light to said plurality of qubits; and(c) a control unit configured to initiate a calibration operation on said quantum computer based at least in part on said one or more observations.

31. The system of claim 30, wherein said imaging unit is configured to obtain said one or more observations without affecting said plurality of qubits.

32. The system of claim 30 or 31, wherein said calibration operation corresponds to one or more of: oven health, beam alignment, or optical focus.

33. The system of any one of claims 30-32, wherein said control unit is configured to initiate said calibration operation substantially in real-time with respect to obtaining said one or more observations with said observation unit.

34. The system of claim 33, wherein said control unit is configured to initiate said calibration operation within a certain time period of obtaining said one or more observations with said observation unit, wherein said certain time period is less than or equal to the amount of time for said health of said quantum computer to change or be expected to change.

35. A method for monitoring a quantum computer, comprising:Attorney Docket No. 55436-751.601(a) trapping a plurality of qubits in a plurality of optical trapping sites;(b) obtaining one or more observations corresponding to one or both of said plurality of qubits or said plurality of optical trapping sites without applying light to said plurality of qubits; and(c) initiating a calibration operation on said quantum computer based at least in part on said one or more observations.

36. The method of claim 35, wherein obtaining said one or more observations in (b) is performed without affecting said plurality of qubits.

37. The method of claim 35 or 36, wherein said calibration operation corresponds to one or more of: oven health, beam alignment, or optical focus.

38. The method of any one of claims 35-37, wherein initiating said calibration operation in(c) is performed substantially in real-time with respect to obtaining said one or more observations in (b).

39. The method of claim 38, wherein initiating said calibration operation in (c) is performed within a certain time period of obtaining said one or more observations in (b), wherein said certain time period is less than or equal to the amount of time for said health of said quantum computer to change or be expected to change.

40. One or more non-transitory computer-readable media comprising machine-executable code comprising one or more instructions that, when executed, implement the method of any one of claims 35-39.

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