Scalable neutral atom-based quantum computing

Abstract

The present disclosure provides methods and systems for performing non-traditional calculations. The methods and systems generally use a plurality of spatially distinct optical trapping sites for trapping a plurality of atoms; one or more electromagnetic transfer units for applying electromagnetic energy to one or more of the plurality of atoms to induce the atoms to adopt one or more superposition states of a first atomic state and a second atomic state; one or more entanglement units for quantum mechanically entangling at least a subset of one or more atoms in one or more superposition states with other atoms of at least the plurality of atoms; and one or more read units for performing measurements of the superposition states to obtain a non-traditional calculation.

Description

Technology Field

[0001] This application is a partial continuation of U.S. Patent Application No. 16 / 405,877, filed May 7, 2019, with the title of invention "Scalable neutral atom based quantum computing," and claims the benefit of U.S. Provisional Patent Application No. 62 / 760,781, filed November 13, 2018, with the title of invention "Scalable neutral atom based quantum computing," and U.S. Provisional Patent Application No. 62 / 815,985, filed March 8, 2019, with the title of invention "Scalable neutral atom based quantum computing," the entirety of which is incorporated herein by reference for all purposes.

[0002] Statement regarding federally funded research

[0003] This invention was made with the support of the U.S. government under Small Business Innovation Research Grant No. 1843926 awarded by the National Science Foundation. The U.S. government holds specific rights to this invention. Background Technology

[0004] Quantum computers typically use quantum-mechanical phenomena such as superposition and entanglement to perform operations on data. Quantum computers can differ from digital electronic computers based on transistors. For example, digital computers require data to be encoded into binary numbers (bits), each of which always occupies two distinct states (0 or 1), whereas quantum computing uses quantum bits (qubits) that can exist in superposition states.

[0005] The need for methods and systems for performing non-traditional calculations is recognized in this specification.

[0006] The present disclosure provides systems and methods for utilizing atoms (e.g., neutral or uncharged atoms) to perform non-traditional or quantum computations. Atoms can be optically trapped in large arrays. Quantum mechanical states of atoms (e.g., hyperfine states of atoms or nuclear spin states) can be configured to function as quantum bit (qubit)-based states. Qubit states can be manipulated through interaction with optical, radio frequency, or other electromagnetic radiation to perform non-traditional or quantum computations.

[0007] In one aspect, the present disclosure provides a system for performing a non-traditional computation, comprising: one or more optical trapping units configured to generate a plurality of spatially distinct optical trapping sites—the plurality of optical trapping sites configured to trap a plurality of atoms, and the plurality of atoms comprising more than 60 atoms—; one or more electromagnetic transfer units configured to apply electromagnetic energy to one or more of the plurality of atoms to induce the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state distinct from the first atomic state; one or more entanglement units configured to quantum mechanically entangle at least a subset of one or more atoms in the superposition states with at least another atom among the plurality of atoms; and one or more readout optical units configured to perform one or more measurements of one or more superposition states to obtain a non-traditional computation. The non-traditional computation may include a quantum computation. The quantum computation may include a gate-model quantum computation. One or more of the plurality of atoms may include qubits. A first atomic state may include a first single qubit state, and a second atomic state may include a second single qubit state. The energy of the first atomic state or the second atomic state may be elevated relative to the ground atomic state of the atoms. A first atomic state may include a first hyperfine electronic state, and a second atomic state may include a second hyperfine electronic state different from the first hyperfine electronic state. A first atomic state may include a first nuclear spin state, and a second atomic state may include a second nuclear spin state different from the first nuclear spin state. The plurality of atoms may include at least 100 atoms. A plurality of atoms may include neutral atoms. A plurality of atoms may include rare earth atoms. A plurality of atoms may include alkali atoms.Multiple atoms may include alkaline earth atoms. Alkaline earth atoms may include strontium atoms. Strontium atoms may include strontium-87 atoms. The first and second atomic states are strontium-87. 3 It may include first and second hyperfine states on the P1 manifold. The first and second atomic states are strontium-87 3 It may include first and second hyperfine states on a P2 manifold. The first and second atomic states may include first and second hyperfine states on a multiplet manifold. The first and second atomic states may include first and second hyperfine states on a triplet manifold. The first and second atomic states may include first and second nuclear spin states of a quadrupolar nucleus. The first and second atomic states may include first and second nuclear spin states of a spin-9 / 2 nucleus. The first and second atomic states may include first and second nuclear spin states of strontium-87. A subset of one or more atoms in one or more superposition states and other atoms may be quantum mechanically entangled with a coherence lifetime of at least 1 second. Multiple atoms may include a temperature of up to 10 μK (microkelvin). The system, the system up to 10 -6It may further include one or more vacuum units configured to maintain a pressure of Pa (Pascal). Each optical trapping site of the plurality of optical trapping sites may be spatially separated from each other by at least 200 nm (nanometers). Each optical trapping site of the plurality of optical trapping sites may be configured to trap a single atom among a plurality of atoms. One or more optical trapping sites may include one or more optical tweezers. One or more optical trapping sites may include one or more optical grating sites of one or more optical gratings. One or more optical gratings may include one or more members selected from a group consisting of one-dimensional (1D) optical gratings, two-dimensional (2D) optical gratings, and three-dimensional (3D) optical gratings. One or more optical trapping units may include one or more spatial light modulators (SLMs) configured to generate a plurality of optical trapping sites. One or more SLMs may include one or more digital micromirror devices (DMDs) or one or more liquid crystal on silicon (LCoS) devices. One or more optical trapping units may include one or more light sources configured to emit light tuned to one or more magic wavelengths corresponding to a plurality of atoms. One or more optical trapping units may include one or more imaging units configured to acquire one or more images of the spatial configuration of a plurality of atoms trapped within optical trapping sites. One or more images may include one or more members selected from the group consisting of fluorescence images, single-atom fluorescence images, absorption images, single-atom absorption images, phase contrast images, and single-atom phase contrast images.The system may further include one or more spatial configuration AI units configured to perform one or more artificial intelligence (AI) operations to determine the spatial configuration of multiple atoms trapped within optical trapping sites based on one or more images. One or more AI operations may include one or more machine learning (ML) operations. One or more AI operations may include one or more reinforcement learning (RL) operations. One or more optical trapping units may include one or more atomic rearrangement units configured to impart a modified spatial arrangement of multiple atoms trapped within optical trapping sites based on one or more images. The system may further include one or more spatial arrangement AI units configured to perform one or more artificial intelligence (AI) operations to determine a modified spatial arrangement of multiple atoms trapped within optical trapping sites based on one or more images. One or more AI operations may include one or more machine learning (ML) operations. One or more AI operations may include one or more reinforcement learning (RL) operations. One or more atomic rearrangement units may be configured to change the spatial arrangement to obtain an increase in the charge factor of a plurality of optical trapping sites. The charge factor may include a value of at least 70%. The system may further include one or more state preparation units configured to prepare the state of a plurality of atoms. One or more of the state preparation units may be configured to cool a plurality of atoms. One or more of the state preparation units may be configured to cool a plurality of atoms before trapping a plurality of atoms at a plurality of optical trapping sites. One or more of the state preparation units may include a Zeeman slowerer configured to decelerate one or more atoms from a first velocity or a distribution of velocities to a second velocity lower than the first velocity or a distribution of velocities.The Zeeman sloer may include a one-dimensional (1D) Zeeman sloer. The second velocity may be up to 10 m / s (meters per second). One or more of the state preparation units may further include a first magneto-optical trap (MOT) configured to cool one or more atoms to a first temperature. The first MOT may include a three-dimensional (3D) MOT. The first MOT may include one or more light sources configured to emit light having one or more wavelengths within the range of 400 nm to 500 nm. The first temperature may be up to 10 mK (millikelvin). One or more of the state preparation units may further include a second MOT configured to cool one or more atoms from the first temperature to a second temperature lower than the first temperature. The second MOT may include one or more light sources configured to emit light having one or more wavelengths within the range of 400 nm to 1,000 nm. The second temperature may be up to 100 μK (microkelvin). One or more of the state preparation units may further include a sideband cooling unit. The sideband cooling unit may be configured to cool one or more atoms from the second temperature to a third temperature lower than the second temperature using sideband cooling. The sideband cooling unit may include one or more light sources configured to emit light having one or more wavelengths within the range of 400 nm to 1,000 nm. The third temperature may be up to 10 μK (microkelvin). One or more of the state preparation units may include an optical pumping unit configured to emit light to optically pump one or more of the plurality of atoms from an equilibrium atomic state to a non-equilibrium atomic state.The optical pumping unit may include one or more light sources configured to emit light having one or more wavelengths within the range of 400 nm (nanometers) to 1,000 nm. The light may include one or more wavelengths within the range of 650 nm to 700 nm. One or more of the state preparation units may include a coherent driving unit configured to coherently drive one or more atoms from a non-equilibrium atomic state to a first or second atomic state. The coherent driving unit may be configured to induce a two-photon transition between the non-equilibrium state and the first or second atomic state. The coherent driving unit may include one or more light sources configured to emit light having one or more wavelengths within the range of 400 nm to 1,000 nm. The coherent driving unit may be configured to induce a single-photon transition between the non-equilibrium state and the first or second atomic state. The coherent driving unit may include one or more light sources configured to emit light having one or more wavelengths within the range of 400 nm to 1,000 nm. The coherent driving unit may be configured to induce a radio frequency (RF) transition between a non-equilibrium state and a first or second atomic state. The coherent driving unit may include one or more electromagnetic radiation sources configured to emit electromagnetic radiation configured to induce an RF transition. One or more electromagnetic transfer units may include one or more spatial light modulators (SLMs), acousto-optic devices (AODs), or acousto-optic modulators (AOMs) configured to selectively apply electromagnetic energy to one or more of a plurality of atoms.One or more electromagnetic transfer units may include one or more digital micromirror devices (DMDs) or one or more liquid crystal on silicon (LCoS) devices. The system may further include one or more electromagnetic energy AI units configured to perform one or more artificial intelligence (AI) operations to selectively apply electromagnetic energy to one or more atoms. One or more AI operations may include one or more machine learning (ML) operations. One or more AI operations may include one or more reinforcement learning (RL) operations. Electromagnetic energy may include optical energy. Electromagnetic energy may include microwave energy. Electromagnetic energy may include radio frequency (RF) energy. RF energy may include one or more wavelengths of at least 30 millimeters. RF energy may include an average power of 10 Watts or less. One or more electromagnetic transfer units may be configured to implement one or more single-qubit gate operations for one or more qubits. One or more readout optical units may include one or more optical detectors. One or more optical detectors may include one or more cameras. One or more optical detectors may include one or more fluorescence detectors. The system may further include one or more atomic reservoirs configured to supply one or more replacement atoms to replace one or more atoms at one or more of the plurality of optical trapping sites upon the loss of one or more atoms from one or more optical trapping sites. The system may further include one or more atomic transfer units configured to move one or more replacement atoms to one or more optical trapping sites.One or more atomic movement units may include one or more electrically tunable lenses, acousto-optic deflectors (AODs), or spatial light modulators (SLMs). One or more subsets of atoms and other atoms in one or more superposition states may be quantum mechanically entangled through magnetic dipole interactions, induced magnetic dipole interactions, electric dipole interactions, or induced electric dipole interactions. One or more entanglement units may include one or more Rydberg excitation units configured to electronically excite one or more subsets of atoms in one or more superposition states into a Rydberg state or into a superposition state of a Rydberg state and a lower energy atomic state to form one or more Rydberg atoms or dressed Rydberg atoms. One or more Rydberg excitation units may be configured to induce one or more quantum mechanical entanglements between one or more Rydberg atoms or dressed Rydberg atoms and another atom, and the other atom is located at a distance of 10 μm (micrometers) or less from one or more Rydberg atoms or dressed Rydberg atoms. One or more Rydberg units may be configured to drive one or more Rydberg atoms or dressed Rydberg atoms into a lower energy atomic state to form one or more 2-qubit units. One or more electromagnetic transfer units may be configured to implement one or more 2-qubit gate operations for one or more 2-qubit units. One or more Rydberg excitation units may include one or more light sources configured to emit light having one or more ultraviolet (UV) wavelengths. The light may include one or more wavelengths within the range of 300 nm to 400 nm. The system may be operablely coupled to a digital computer via a network.The network may include a cloud network.

[0008] In another aspect, the present disclosure provides a non-traditional computer comprising: a plurality of qubits comprising more than 60 atoms, each atom being trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprises 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 or more electromagnetic transfer units configured to apply electromagnetic energy to one or more qubits of the plurality of qubits to impart a non-traditional operation to one or more qubits, wherein the non-traditional operation comprises at least a superposition between 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 state with at least another qubit among the plurality of qubits; and one or more read optical units configured to perform one or more measurements of one or more qubits to obtain a non-traditional computation.

[0009] In another aspect, the present disclosure provides a non-traditional computer comprising a plurality of qubits, each comprising more than 60 atoms, that are trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites.

[0010] In another aspect, the present disclosure provides a method for performing a non-traditional computation, comprising: (a) generating a plurality of spatially distinct optical trapping sites—the plurality of optical trapping sites are configured to trap a plurality of atoms, and the plurality of atoms comprises more than 60 atoms—; (b) applying electromagnetic energy to one or more of the plurality of atoms to induce the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state distinct from the first atomic state; (c) quantum mechanically entangling at least a subset of one or more atoms in one or more superposition states with at least another atom among the plurality of atoms; and (d) performing one or more optical measurements of one or more superposition states to obtain a non-traditional computation.

[0011] In another aspect, the present disclosure provides a method for performing a non-traditional computation, comprising: (a) providing a plurality of qubits comprising more than 60 atoms, wherein each atom is trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, and the plurality of qubits comprises 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 of the qubits to impart a non-traditional operation to the one or more qubits, wherein the non-traditional operation comprises at least a superposition between 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 state with at least another qubit among the plurality of qubits; and (d) performing one or more optical measurements of one or more qubits to obtain a non-traditional computation.

[0012] In another aspect, the present disclosure provides a method for performing a non-traditional computation, comprising: (a) providing a plurality of qubits each comprising more than 60 atoms trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites; and (b) using a subset of at least a plurality of qubits to perform a non-traditional computation.

[0013] In another aspect, the present disclosure provides a method for performing a non-traditional computation, comprising: (a) providing a plurality of optical trapping sites comprising a plurality of atoms—the plurality of atoms are a plurality of qubits—; (b) changing the spatial arrangement of the plurality of atoms by moving one or more of the plurality of atoms from an occupied trapping site to an unoccupied trapping site; (c) applying electromagnetic energy to one or more of the plurality of atoms to induce the one or more of the atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state—wherein the atoms of the one or more of the atoms in the one or more superposition states are quantum mechanically entangled with other atoms among the plurality of atoms—; and (d) performing one or more measurements of the one or more superposition states.

[0014] In another aspect, the present disclosure provides a method for performing a non-traditional 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 being qubits, and the atoms of the plurality of atoms being trapped by an attractive force at the optical trapping sites of the plurality of optical trapping sites—; (b) applying electromagnetic energy to one or more of the atoms of the plurality of atoms to induce the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state 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 among the plurality of atoms; and (d) performing one or more measurements of the one or more superposition states to obtain the non-traditional computation.

[0015] In another aspect, the present disclosure provides a method for performing a non-traditional computation, comprising: (a) generating a plurality of spatially distinct optical trapping sites—the plurality of optical trapping sites are configured to trap a plurality of atoms, said plurality of atoms are qubits—; (b) applying electromagnetic energy to one or more of said atoms to induce said one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from said first atomic state—said to modulate said electromagnetic energy with at least two optical modulators—; (c) quantum mechanically entangling at least a subset of said one or more atoms in said one or more superposition states with at least another atom among said plurality of atoms; and (d) performing one or more measurements of said one or more superposition states to obtain said non-traditional computation.

[0016] Another aspect of the present disclosure provides a non-transient computer-readable medium comprising machine-executable code that implements any of the methods above or elsewhere in the present specification when executed by one or more computer processors.

[0017] 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 implements any of the methods above or elsewhere in this specification when executed by one or more computer processors.

[0018] Additional aspects and advantages of the present disclosure will be readily apparent to those skilled in the art from the following detailed description, in which only exemplary embodiments of the present disclosure are illustrated and described. As will be recognized, the present disclosure may be subject to other and different embodiments, and some details of the present disclosure may be modified in various obvious respects without departing from the present disclosure. Accordingly, the drawings and description should be regarded as exemplary in nature and not restrictive.

[0019] Integration by reference

[0020] All publications, patents, and patent applications mentioned herein are incorporated by reference into this specification to the same extent as each individual publication, patent, or patent application is specifically and individually indicated as being incorporated by reference. To the extent that the incorporated publications, patents, or patent applications contradict the disclosures contained herein, this specification is intended to replace and / or have priority over any such contradictory material. Brief explanation of the drawing

[0021] Novel features of the present invention are described in detail in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by referring to the following detailed description describing exemplary embodiments in which the principles of the present invention are utilized and the appended drawings (also referred to herein as “Figure” and “FIG”). FIG. 1 illustrates a computer control system programmed or otherwise configured to implement the methods provided in this specification. Figure 2 illustrates an example of a system for performing non-traditional calculations. Figure 3a illustrates an example of an optical trapping unit. FIG. 3b illustrates an example of multiple optical trapping sites. FIG. 3c illustrates an example of an optical trapping unit partially filled with atoms. Figure 3d illustrates an example of an optical trapping unit completely filled with atoms. Figure 4 illustrates an example of an electromagnetic transmission unit. Figure 5 illustrates an example of a state preparation unit. Figure 6 illustrates a flowchart for an example of a first method for performing non-traditional calculations. Figure 7 illustrates a flowchart for an example of a second method for performing non-traditional calculations. Figure 8 illustrates a flowchart for an example of a third method for performing non-traditional calculations. Fig. 9 shows strontium-87. 3 An example of a qubit containing the P2 state is illustrated. Figures 10a and 10b show strontium-87. 1 Stark shift simulations of S0 hyperfine states are illustrated. Figures 11a and 11b illustrate simulations of single-qubit control using Stark shifting. FIGS. 12a and FIGS. 12b illustrate exemplary arrays of trapping light generated by an SLM. Specific details for implementing the invention

[0022] Although various embodiments of the present invention have been illustrated and described herein, it will be apparent to those skilled in the art that such embodiments are provided merely as examples. Now, without departing from the invention, numerous modifications, alterations, and substitutions may be conceived by those skilled in the art. It should be understood that various alternatives to the embodiments of the present invention described herein may be utilized.

[0023] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention pertains. As used in this specification and the appended claims, singular forms (“a,” “an,” and “the”) include plural references unless clearly otherwise indicated by the context. Any reference to “or” in this specification is intended to encompass “and / or” unless otherwise stated.

[0024] Whenever the terms “at least,” “greater than,” or “greater than or equal to” precede the first numeric value in a series of two or more numeric values, the terms “at least,” “greater than,” or “greater than or equal to” apply to each of the numeric values ​​in the series of numeric 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.

[0025] Whenever the terms “less than,” “less than,” “less than or equal to,” or “maximum” precede the first numeric value in a series of two or more numeric values, the terms “less than,” “less than,” “less than,” or “maximum” apply to each of the numeric values ​​in the series of numeric values. For example, 3, 2, or less than or equal to 1 is equivalent to less than or equal to 3, less than or equal to 2, or less than or equal to 1.

[0026] Where values ​​are described as ranges, it will be understood that such disclosure includes all possible sub-ranges within such ranges, as well as disclosure of specific numeric values ​​belonging within such ranges, regardless of whether a specific numeric value or a specific sub-range is explicitly mentioned.

[0027] As used in this specification, similar characters refer to similar elements.

[0028] As used herein, the terms “artificial intelligence,” “artificial intelligence procedure,” “artificial intelligence operation,” and “artificial intelligence algorithm” generally refer to any system or computational procedure that takes one or more actions to improve or maximize the chance of successfully achieving a goal. The term “artificial intelligence” may include “generative modeling,” “machine learning (ML),” and / or “reinforcement learning (RL).”

[0029] As used herein, the terms “machine learning,” “machine learning procedure,” “machine learning operation,” and “machine learning algorithm” generally refer to any system or analytical and / or statistical procedure that progressively improves the computer performance of a task. Machine learning may include machine learning algorithms. A machine learning algorithm may be a trained algorithm. Machine learning (ML) may include one or more supervised, semi-supervised, or unsupervised machine learning techniques. For example, an ML algorithm may be a trained algorithm trained through supervised learning (e.g., various parameters are determined as weights or scaling factors). ML may include one or more of regression analysis, regularization, classification, dimensionality reduction, ensemble learning, meta-learning, association rule learning, cluster analysis, anomaly detection, deep learning, or super-deep learning.ML includes k-means, k-means clustering, k-nearest neighbors, learning vector quantization, linear regression, nonlinear regression, least squares regression, partial least squares regression, logistic regression, stepwise regression, multivariate adaptive regression splines, ridge regression, principal component regression, minimum absolute shrinkage and selection operations, minimum angle regression, canonical correlation analysis, factor analysis, independent component analysis, linear discriminant analysis, multidimensional scaling, non-negative matrix factorization, principal component analysis, principal coordinate analysis, projection tracing, Sammon mapping, t-variance stochastic neighbor embeddings, 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, Autoencoders, Stacked Auto-Encoders, Perceptrons, Multilayer Perceptrons, Artificial Negatives, Feedforward Neural Networks, Convolutional Neural Networks, Recurrent Neural Networks, Long Short-Term Memory, Deep Belief Networks, Deep Boltzmann Machines, Deep Convolutional Neural Networks, Deep Recurrent Neural Networks, or Generative Adversarial Networks, may be included but not limited thereto.

[0030] As used herein, the terms “reinforcement learning,” “reinforcement learning procedure,” “reinforcement learning action,” and “reinforcement learning algorithm” generally refer to any system or computational procedure that takes one or more actions to enhance or maximize some concept of cumulative reward for interaction with an environment. An agent performing a reinforcement learning (RL) procedure may receive positive or negative reinforcements, referred to as “instant rewards,” by taking one or more actions in the environment and, accordingly, placing itself and the environment into various new states.

[0031] The agent's goal may be to improve or maximize some concept of cumulative reward. For example, the agent's goal may be to improve or maximize a "discounted reward function" or an "average reward function." A "Q-function" may represent the maximum cumulative reward obtainable from a state and the action taken from that state. A "value function" and a "generalized benefit estimator" may represent the maximum cumulative reward obtainable from a given state by the actions of the optimal or best choice. RL may utilize any of such concepts of cumulative reward. As used herein, any such function may be referred to as a "cumulative reward function." Thus, computing the best or optimal cumulative reward function may be equivalent to finding the best or optimal policy for the agent.

[0032] The interaction between an agent and its environment can be formulated as one or more Markov Decision Processes (MDPs). RL procedures may not assume knowledge of the exact mathematical models of the MDPs. The MDPs may be completely unknown to the agent, partially known, or completely known. With regard to prior knowledge of the MDPs, RL procedures may lie on a spectrum between two ranges: "model-based" or "model-free." Therefore, RL procedures can target large MDPs where exact methods may not be feasible or available due to the unknown or probabilistic nature of the MDPs.

[0033] RL procedures may be implemented using one or more computer processors as described herein. A digital processing unit may utilize an agent that trains, stores, and later deploys a "policy" to improve or maximize the cumulative reward. The policy may be pursued (e.g., searched) for as long as possible or for a desired period of time. Such optimization problems may be solved by storing an approximation of the optimal policy, by storing an approximation of the cumulative reward function, or by both. In some cases, RL procedures may store one or more tables of approximations for such functions. In other cases, RL procedures may utilize one or more "function approximators."

[0034] Examples of function approximators may include neural networks (e.g., deep neural networks) and probabilistic graphical models (e.g., Boltzmann machines, Helmholtz machines, and Hopfield networks). A function approximator may generate a parameterization of the approximation of the cumulative reward function. Optimization of the function approximator for the parameterization may consist of perturbing the parameters in a direction that enhances or maximizes the cumulative rewards and, accordingly, enhances or optimizes the policy (e.g., in policy gradient methods), or perturbing the function approximator more closely to satisfy Bellman’s optimality criteria (e.g., in temporal difference methods).

[0035] During training, the agent may take actions in the environment to acquire more information about the environment and about good or best choices of policies for survival or better utilization. The agent's actions may be generated randomly (e.g., particularly in the early stages of training) or determined by other machine learning paradigms (e.g., supervised learning, imitation learning, or any other machine learning procedure described herein). The agent's actions may be improved by selecting actions that are closer to the agent's perception of what the reinforced or optimal policy is. Various training strategies may lie on a spectrum between two ranges of off-policy and on-policy methods with respect to choices between exploration and utilization.

[0036] As used herein, the terms “non-traditional computation,” “non-traditional procedure,” “non-traditional operation,” and any “non-traditional computer” generally refer to any method or system for performing computational procedures outside the paradigm of traditional computing. Non-traditional computation, non-traditional procedure, non-traditional operation, or non-traditional computer may include quantum computation, quantum procedure, quantum operation, or quantum computer.

[0037] 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 (e.g., single transformations or completely positive trace-preserving (CPTP) maps on quantum channels) in Hilbert space represented by a quantum device. Thus, quantum and traditional (or digital) computations may be similar in the following aspects: both computations may comprise sequences of instructions performed on input information and subsequently providing an output. Various paradigms of quantum computation may decompose quantum operations into sequences of fundamental quantum operations that simultaneously affect a subset of qubits of a quantum device. Quantum operations may be selected, for example, based on their location or ease of physical implementation. Subsequently, a quantum procedure or computation may consist of such sequences of instructions capable of representing different quantum evolutions on a quantum device in various applications. For example, procedures for computing or simulating quantum chemistry can represent electron spin-orbit annihilation and creation operators and quantum states by using qubits (e.g., 2-level quantum systems) and a set of general-purpose quantum gates (e.g., Hadamard, CNOT (controlled-not), and image rotations) through so-called Jordan-Wigner transformations or Bravyi-Kitaev transformations.

[0038] Additional examples of quantum procedures or computations may include procedures for optimization, such as quantum approximate optimization algorithms (QAOA) or quantum minimum discovery. QAOA may include performing rotations of a single qubit and entanglement gates of multiple qubits. In quantum adiabatic computations, commands may pass probabilistic or non-probabilistic paths of evolution of an initial quantum system to a final quantum system.

[0039] Quantum-inspired procedures may include simulated annealing, parallel tempering, master equation solvers, Monte Carlo procedures, etc. Quantum-traditional or hybrid algorithms or procedures may include procedures such as VQE (variational quantum eigensolver) and VanQver (variational and adiabatically navigationed quantum eigensolver).

[0040] A quantum computer may include one or more adiabatic quantum computers, quantum gate arrays, unidirectional quantum computers, topological quantum computers, quantum Turing machines, quantum annealers, Ising solvers, or gate models of quantum computing.

[0041] A system for performing non-traditional calculations

[0042] In one aspect, the present disclosure provides a system for performing non-traditional computation. The system may include one or more optical trapping units configured to generate a plurality of spatially distinct optical trapping sites—the plurality of optical trapping sites are configured to trap a plurality of atoms, and the plurality of atoms comprises more than 60 atoms—; one or more electromagnetic transfer units configured to apply electromagnetic energy to one or more of the plurality of atoms to induce the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state distinct from the first atomic state; one or more entanglement units configured to quantum mechanically entangle at least a subset of one or more atoms in one or more superposition states with at least another atom among the plurality of atoms; and one or more readout optical units configured to perform one or more measurements of one or more superposition states to obtain non-traditional computation.

[0043] FIG. 2 illustrates an example of a system (200) for performing non-traditional computation. Non-traditional computation may include quantum computation. Quantum computation may include gate-model quantum computation.

[0044] The system (200) may include one or more optical trapping units (210). The optical trapping units may include any optical trapping unit described herein, such as the optical trapping unit described herein in relation to FIG. 3a. The optical trapping units may be configured to create a plurality of spatially distinct optical trapping sites. For example, optical trapping units include 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, It may be configured to generate 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000, or more optical trapping sites. Optical trapping units are up to approximately 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, It may be configured to generate 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or fewer optical trapping sites.Optical trapping units may be configured to trap multiple optical trapping sites within a range defined by any two of the preceding values.

[0045] Optical trapping units can be configured to trap multiple atoms. For example, optical trapping units include 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, It may be configured to trap 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000, or more atoms. Optical trapping units are up to approximately 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, It may be configured to trap 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or fewer atoms. Optical trapping units may be configured to trap multiple atoms within a range defined by any two of the preceding values.

[0046] 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 up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 or fewer atoms. Each optical trapping site may be configured to trap multiple atoms within a range defined by any two of the preceding values. Each optical trapping site may be configured to trap a single atom.

[0047] One or more of the plurality of atoms may include qubits as described herein (e.g., in relation to FIG. 4). Two or more atoms may be quantum mechanically entangled. Two or more atoms have at least about 1 μs (microsecond), 2 μs, 3 μs, 4 μs, 5 μs, 6 μs, 7 μs, 8 μs, 9 μs, 10 μs, 20 μs, 30 μs, 40 μs, 50 μs, 60 μs, 70 μs, 80 μs, 90 μs, 100 μs. μs, 200 μs, 300 μs, 400 μs, 500 μs, 600 μs, 700 μs, 800 μs, 900 μs, 1 ms (millisecond), 2 ms, 3 ms, 4 ms, 5 ms, 6 ms, 7 ms, 8 ms, 9 ms, 10 ms, 20 ms, 30 ms, 40 ms, They can be quantum mechanically entangled with a coherence lifetime of 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 s (second), 2 s, 3 s, 4 s, 5 s, 6 s, 7 s, 8 s, 9 s, 10 s or more.Two or more atoms have up to 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 μs, 800 μs, 700 μs, 600 They may be quantum mechanically entangled with a coherence lifetime of μs, 500 μs, 400 μs, 300 μs, 200 μs, 100 μs, 90 μs, 80 μs, 70 μs, 60 μs, 50 μs, 40 μs, 30 μs, 20 μs, 10 μs, 9 μs, 8 μs, 7 μs, 6 μs, 5 μs, 4 μs, 3 μs, 2 μs, 1 μs, or less. Two or more atoms may be quantum mechanically entangled with a coherence lifetime within a range defined by any two of the preceding values. One or more atoms may include neutral atoms. One or more atoms may include uncharged atoms.

[0048] One or more atoms may include alkali atoms. One or more atoms may include lithium (Li) atoms, sodium (Na) atoms, potassium (K) atoms, rubidium (Rb) atoms, or cesium (Cs) atoms. One or more atoms may include 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 cesium-133 atoms. One or more atoms may include alkaline earth atoms. One or more atoms may include beryllium (Be) atoms, magnesium (Mg) atoms, calcium (Ca) atoms, strontium (Sr) atoms, or barium (Ba) atoms. One or more atoms may include 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-134 atoms, barium-135 atoms, barium-136 atoms, barium-137 atoms, or barium-138 atoms. One or more atoms may include rare earth atoms. One or more atoms may include 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 are 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, It may include ytterbium-171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium-175 atoms, or lutetium-176 atoms.

[0049] A plurality of atoms may include a single element selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. A plurality of atoms may include a mixture of elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. A plurality of atoms may include a natural isotope mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. A plurality of atoms may include an isotope-rich mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. A plurality of atoms may include a natural isotope 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. Multiple atoms may comprise an isotopic-rich 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 atoms may comprise rare earth atoms. For example, a plurality of atoms are lithium-6 atoms, lithium-7 atoms, sodium-23 atoms abundant in 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 greater isotopic abundance, Potassium-39 atoms, Potassium-40 atoms, Potassium-41 atoms, Rubidium-85 atoms, Rubidium-87 atoms, Cesium-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-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 It may contain lutetium-176 atoms. Multiple atoms may comprise up to approximately 99.99%, 99.98%, 99.97%, 99.96%,Lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, abundant in isotopic abundances of 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, or less than the isotopic abundances of 99.95%, 99.93%, 99.92%, 99.91%, 99.91%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50%, or less than the above, Cesium-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-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,It may include 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. Multiple atoms are lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, cesium-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-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, It may include ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium-175 atoms, or lutetium-176 atoms.

[0050] The system (200) may include one or more electromagnetic transfer units (220). The electromagnetic transfer units may include any electromagnetic transfer unit described herein, such as the electromagnetic transfer unit described herein in connection with FIG. 4. The electromagnetic transfer units may be configured to apply electromagnetic energy to one or more of a plurality of atoms. Applying electromagnetic energy may induce the atoms to adopt one or more superposition states of a first atomic state and a second atomic state different from the first atomic state.

[0051] The first atomic state may include a first single-qubit state. The second atomic state may include a second single-qubit state. The first atomic state or the second atomic state may have an increased energy relative to the ground atomic state of the atoms. The first atomic state or the second atomic state may have the same energy relative to the ground atomic state of the atoms.

[0052] The first atomic state may include a first hyperfine electronic state, and the second atomic state may include a second hyperfine electronic state different from the first hyperfine electronic state. For example, the first and second atomic states may include first and second hyperfine states on a multi-fine manifold, such as a triplet manifold. The first and second atomic states are each 3 P1 or 3 It may include first and second hyperfine states on the P2 manifold. The first and second atomic states are of any atom described herein. 3 P1 or 3 P2 manifold, for example, strontium-87 3 P1 manifold or strontium-87 3 Each of the first and second ultrafine states may be included on the P2 manifold.

[0053] Fig. 9 shows strontium-87. 3 An example of a qubit containing the P2 state is illustrated. The left panel of FIG. 9 shows strontium-87. 3 The structure of the abundant energy level in the P2 state is illustrated. The right panel of Fig. 9 shows the strontium-87 3 Illuminates a potential qubit transition within the P2 state, which is (first-order) insensitive to changes in a magnetic field of about 70 Gauss.

[0054] In some cases, the first and second atomic states are the first and second hyperfine states of the first electronic state. Optical excitation may be applied between the first electronic state and the second electronic state. Optical excitation may excite the first hyperfine state and / or the second hyperfine state to the second electronic state. A single-qubit transition may involve a two-photon transition between two hyperfine states within the first electronic state using the second electronic state as an intermediate state. To drive the single-qubit transition, a pair of frequencies, each detuned from the single-photon transition to the intermediate state, may be applied to drive the two-photon transition. In some cases, the first and second hyperfine states are the hyperfine states of the ground electronic state. The ground electronic state may not be attenuated by spontaneous or stimulated emission to a lower electronic state. The hyperfine states may include nuclear spin states. In some cases, the hyperfine states are strontium-87 1 It includes the nuclear spin states of the S0 manifold, and the qubit transition is strontium-87 1 One or both of the two nuclear spin states of S0 3 P2 or 3 It is driven within or from the P1 manifold in a detuned state. In some cases, the 1-qubit transition is 3 P2 or 3 Strontium-87 in or through a detuned state from the P1 manifold 1 It is a two-photon Raman transition between the nuclear spin states of S0. In some cases, the nuclear spin states may be Stark-shifted nuclear spin states. The Stark shift can be optically driven. The optical Stark shift can be driven out of resonance by any one of a single-qubit transition, a two-qubit transition, a shelving transition, an imaging transition, or any combination thereof.

[0055] The first atomic state may include a first nuclear spin state, and the second atomic state may include a second nuclear spin state different from the first nuclear spin state. The first and second atomic states may each include first and second nuclear spin states of a quadrupole nucleus. The first and second atomic states may each include first and second nuclear spin states 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 each include first and second nuclear spin states of any atom described herein, such as first and second spin states of strontium-87.

[0056] In the case of first and second nuclear spin states associated with nuclei containing spins greater than 1 / 2 (e.g., spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4, or spin-9 / 2 nuclei), transitions between the first and second nuclear spin states may entail transitions between other spin states on the nuclear spin manifold. For example, in the case of a spin-9 / 2 nucleus in the presence of a uniform magnetic field, all nuclear spin levels may be separated by the same energy. Thus, for example, m N = m in 9 / 2 spin state N Transitions designed to transfer atoms to a 7 / 2 spin state (e.g., Raman transitions) are also m N = m at 7 / 2 N = to 5 / 2, m N = m at 5 / 2 N = to 3 / 2, m N = m at 3 / 2 N = to 1 / 2, m N = m from 1 / 2 N = to -1 / 2, m N = m at -1 / 2 N = -3 / 2, m N = m at -3 / 2 N = -5 / 2, mN = m at -5 / 2 N = -7 / 2, and m N = m at -7 / 2 N = Can be driven by -9 / 2, where m N is a nuclear spin state. Similarly, for example, m N = m in 9 / 2 spin state N Transitions designed to transfer atoms to a = 5 / 2 spin state (e.g., Raman transitions) are also m N = m at 7 / 2 N = to 3 / 2, m N = m at 5 / 2 N = to 1 / 2, m N = m at 3 / 2 N = to -1 / 2, m N = m from 1 / 2 N = -3 / 2, m N = m at -1 / 2 N = -5 / 2, m N = m at -3 / 2 N = -7 / 2, and m N = m at -5 / 2 N It can be driven by = -9 / 2. Therefore, such a transition may not be selective to induce transitions between specific spin states on the nuclear spin manifold. Instead, it may be desirable to implement selective transitions between specific first and second spin states on the nuclear spin manifold. This can be achieved by providing light from a light source that provides an AC Stark shift and pushes neighboring nuclear spin states out of resonance to transitions between the desired transitions between the first and second nuclear spin states. For example, m N =-9 / 2 and m N If a transition from the first and second nuclear spin states having =-7 / 2 is required, light is m N By providing an AC Stark shift to the =-5 / 2 spin state, m N =-7 / 2 and m N=-5 / 2 can significantly reduce transitions between states. Similarly, m N =-9 / 2 and m N If a transition from the first and second nuclear spin states having =-5 / 2 is required, light is m N By providing an AC Stark shift to the =-1 / 2 spin state, m N =-5 / 2 and m N = -1 / 2 Transitions between states can be significantly reduced. This can greatly simplify the dynamics of qubit systems by effectively creating a 2-level subsystem within the nuclear spin manifold that is decoupled from the rest of the nuclear spin manifold. It may be advantageous to use nuclear spin states near the edges of the nuclear spin manifold so that only one AC Stark shift is required (e.g., m N =-9 / 2 and m N =-7 / 2, m N = 7 / 2 and m N = 9 / 2, m N =-9 / 2 and m N =-5 / 2, or for spin-9 / 2 nuclei, m N = 5 / 2 and m N = 9 / 2). Alternatively, nuclear spin states further from the edge of the nuclear spin manifold (e.g., m N =-5 / 2 and m N =-3 / 2 or m N =-5 / 2 and m N =-1 / 2) can be used, and two AC Stark shifts (e.g., m N =-7 / 2 and m N =-1 / 2 or m N =-9 / 2 and m N = can be implemented in 3 / 2.

[0057] Stark shifting of the nuclear spin manifold can shift neighboring nuclear spin states out of resonance to a desired transition between the first and second nuclear spin states and the second electronic state or a state detuned therefrom. Stark shifting can reduce leakage from the first and second nuclear spin states to other states of the nuclear spin manifold. Stark shifts can be achieved up to 100s kHz for beam powers of less than 10 mW. Upper-state frequency selectivity can reduce scattering from imperfect polarization control. 3 The separation of different angular momentum states in the P1 manifold can be many gigahertz from single and 2-qubit gate light. Leakage to other states in the nuclear spin manifold can result in decoherence. The Rabi frequency for 2-qubit transitions (e.g., how fast the transition can be driven) can be faster than the decoherence rate. Scattering from intermediate states in 2-qubit transitions can be a source of decoherence. Detuning from intermediate states can improve the fidelity of 2-qubit transitions.

[0058] Qubits based on nuclear spin states in the electronic ground state are long-lived metastable excited electronic states (e.g., of strontium-87) for qubit storage 3 The use of the P0 state may be permitted. To reduce crosstalk or improve gate or detection fidelity, atoms may be selectively transferred to this state. Such storage or shelving processes may be atomic-selective using the SLMs or AODs described herein. The shelving transition of strontium-87 1 S0 state and strontium-87 3 P0 or 3 It may include transitions between P2 states.

[0059] Clock transitions (also referred to herein as "shelving transitions" or "storage transitions") may be qubit-state selective. The upper state of a clock transition may have a very long natural lifetime, for example, greater than 1 second. The line width of a clock transition may be much narrower than the qubit energy interval. This may allow for direct spectral resolution. Population may be transferred from one of the qubit states to the clock state. This allows individual qubit states to be read individually by first transferring the population from one qubit state to the clock state, performing imaging on the qubits, and then transferring the population back from the clock state to the ground state and imaging again. In some cases, a magic wavelength transition is used to drive the clock transition.

[0060] The clock light for shelving may be atomic-selective or non-atomic-selective. In some cases, clock transitions are applied globally (e.g., not atomic-selective). Globally applied clock transitions may involve passing through a microscope objective lens or directing the light without structuring it. In some cases, the clock transition is atomic-selective. Atomic-selective clock transitions can potentially allow us to improve gate fidelity by minimizing crosstalk. For example, to reduce crosstalk at an atom, the atom can be shelved into a clock state that may not be affected by the light. This can reduce crosstalk between neighboring qubits undergoing transitions. To implement atomic-selective clock transitions, the light may pass through one or more microscope objective lenses and / or be structured on one or more of spatial light modulators, digital micromirror devices, cross-acoustic-optic deflectors, etc.

[0061] The system (200) may include one or more read-out optical units (230). The read-out optical units may be configured to perform one or more measurements of one or more superposition states to obtain non-traditional calculations. The read-out optical units may include one or more optical detectors. The detectors may include one or more photomultiplier tubes (PMTs), photodiodes, 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 include one or more fluorescence detectors. The reading optical unit may include one or more objective lenses, such as one or more objective lenses 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 greater. The objective lens may have an NA of up to approximately 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 lens may have an NA within a range defined by any two of the preceding values.

[0062] One or more readout optical units (230) can perform measurements, e.g., projection measurements, by applying light that resonates with the imaging transition. The imaging transition can induce fluorescence. The imaging transition is of strontium-87 1It may involve a transition between the S0 state and the 1P1 state of strontium-87. The 1P1 state of strontium-87 can emit fluorescence. The lower state of the qubit transition is 1 The S0 manifold may contain two nuclear spin states. One or more states may resonate with the imaging transition. The measurement may include two excitations. In the first excitation, one of the two lower states is a shelving state (e.g., of strontium-87). 3 It can be excited to the P0 state. In the second excitation, an imaging transition can be excited. The first transition can reduce crosstalk between neighboring atoms during computation. The fluorescence generated from the imaging transition can be collected on one or more readout optical units (230).

[0063] Imaging units can be used to determine whether one or more atoms have been lost from the trap. Imaging units can be used to observe the arrangement of atoms within the trap.

[0064] The system (200) may include one or more vacuum units (240). The one or more vacuum units may include one or more vacuum pumps. The vacuum units may include one or more roughing vacuum pumps, such as 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 include one or more wet (e.g., oil-sealed) or dry roughing vacuum pumps. The vacuum units may include 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, ion pumps, or getter pumps.

[0065] The vacuum units may include any combination of the vacuum pumps described herein. For example, the vacuum units may include one or more roughing pumps (e.g., scroll pumps) configured to provide a first stage of roughing vacuum pumping. The roughing vacuum pumps may be configured to pump gases out of the system (200) to achieve low vacuum pressure conditions. For example, the roughing pumps may be up to about 10 3The system (200) may be configured to pump gases out of the system to achieve a low vacuum pressure of Pa (Pascals). The vacuum units may further include one or more high vacuum pumps (e.g., 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, up to about 10, if the system (200) has reached the low vacuum pressure condition provided by one or more roughing pumps. -3 High vacuum pressure of Pa or up to about 10 -6 It can be configured to pump gases from the system (200) to achieve an ultra-high vacuum pressure of Pa.

[0066] The vacuum units are up to about 10 -6 Pa, 9 x 10 -7 Pa, 8 x 10 -7 Pa, 7 x 10 -7 Pa, 6 x 10 -7 Pa, 5 x 10 -7 Pa, 4 x 10 -7 Pa, 3 x 10 -7 Pa, 2 x 10 -7 Pa, 10 -7 Pa, 9 x 10 -8 Pa, 8 x 10 -8 Pa, 7 x 10 -8 Pa, 6 x 10 -8 Pa, 5 x 10 -8 Pa, 4 x 10 -8 Pa, 3 x 10 -8 Pa, 2 x 10 -8 Pa, 10 -8 Pa, 9 x 10 -9 Pa, 8 x 10 -9 Pa, 7 x 10 -9 Pa, 6 x 10 -9 Pa, 5 x 10 -9 Pa, 4 x 10 -9 Pa, 3 x 10 -9 Pa, 2 x 10 -9 Pa, 10-9 Well, 9 x 10 -10 Well, 8 x 10 -10 Well, 7 x 10 -10 Well, 6 × 10 -10 Well, 5 x 10 -10 Well, 4 × 10 -10 For, 3 × 10 -10 For, 2 × 10 -10 For, 10 -10 Well, 9 x 10 -11 Well, 8 x 10 -11 Well, 7 x 10 -11 Well, 6 × 10 -11 Well, 5 x 10 -11 Well, 4 × 10 -11 For, 3 × 10 -11 For, 2 × 10 -11 For, 10 -11 Well, 9 x 10 -12 Well, 8 x 10 -12 Well, 7 x 10 -12 Well, 6 × 10 -12 Well, 5 x 10 -12 Well, 4 × 10 -12 For, 3 × 10 -12 For, 2 × 10 -12 For, 10 -12 For 또는 그 미만의 압력으로 시스템(200)을 유지하도록 구성될 수 있다. 진공 유닛들은 적어도 약 10 -12 For, 2 × 10 -12 For, 3 × 10 -12 Well, 4 × 10 -12 Well, 5 x 10 -12 Well, 6 × 10 -12 Well, 7 x 10 -12 Well, 8 x 10 -12 Well, 9 x 10 -12 For, 10 -11 For, 2 × 10 -11 For, 3 × 10 -11 Well, 4 × 10 -11 Well, 5 x 10 -11 For, 6 × 10-11 Pa, 7 x 10 -11 Pa, 8 x 10 -11 Pa, 9 x 10 -11 Pa, 10 -10 Pa, 2 x 10 -10 Pa, 3 x 10 -10 Pa, 4 x 10 -10 Pa, 5 x 10 -10 Pa, 6 x 10 -10 Pa, 7 x 10 -10 Pa, 8 x 10 -10 Pa, 9 x 10 -10 Pa, 10 -9 Pa, 2 x 10 -9 Pa, 3 x 10 -9 Pa, 4 x 10 -9 Pa, 5 x 10 -9 Pa, 6 x 10 -9 Pa, 7 x 10 -9 Pa, 8 x 10 -9 Pa, 9 x 10 -9 Pa, 10 -8 Pa, 2 x 10 -8 Pa, 3 x 10 -8 Pa, 4 x 10 -8 Pa, 5 x 10 -8 Pa, 6 x 10 -8 Pa, 7 x 10 -8 Pa, 8 x 10 -8 Pa, 9 x 10 -8 Pa, 10 -7 Pa, 2 x 10 -7 Pa, 3 x 10 -7 Pa, 4 x 10 -7 Pa, 5 x 10 -7 Pa, 6 x 10 -7 Pa, 7 x 10 -7 Pa, 8 x 10 -7 Pa, 9 x 10 -7 Pa, 10 -6The system (200) may be configured to maintain a pressure of Pa or greater. The vacuum units may be configured to maintain the system (200) at a pressure within a range defined by any two of the preceding values.

[0067] The system (200) may include one or more state preparation units (250). The state preparation units may include any state preparation unit described herein, such as the state preparation unit described herein in connection with FIG. 5. The state preparation units may be configured to prepare the state of a plurality of atoms.

[0068] The system (200) may include one or more atomic storage sites (260). The atomic storage sites may be configured to supply one or more replacement atoms to replace one or more atoms at one or more optical trapping sites in the event of loss of atoms from the optical trapping sites.

[0069] The system (200) may include one or more atomic movement units (270). The atomic movement units may be configured to move one or more alternate atoms to one or more optical trapping sites. For example, the one or more atomic movement units may include one or more electrically tunable lenses, acousto-optic deflectors (AODs), or spatial light modulators (SLMs).

[0070] The system (200) may include one or more entanglement units (280). The entanglement units may be configured to quantum mechanically entangle at least a first atom among a plurality of atoms with at least a second atom among a plurality of atoms. The first or second atom may be in a superposition state during quantum mechanical entanglement. Alternatively or in combination, the first or second atom may not be in a superposition state during 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.

[0071] The entanglement units may include one or more Rydberg excitation units. The Rydberg excitation units may be configured to electronically excite at least one first atom to a Rydberg state or to a superposition state of the Rydberg state and a lower energy atomic state to form one or more Rydberg atoms or dressed Rydberg atoms. The Rydberg excitation units may be configured to induce one or more quantum mechanical entanglements between the Rydberg atoms or dressed Rydberg atoms and at least a second atom. The second atom may be located at a distance of at least about 200 nm (nanometers), 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 μm (micrometer), 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, or greater from the Rydberg atoms or dressed Rydberg atoms. The second atom may be located at a maximum distance of about 10 μm, 9 μm, 8 μm, 7 μm, 6 μm, 5 μm, 4 μm, 3 μm, 2 μm, 1 μm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm, or less from the Rydberg atoms or the dressed Rydberg atoms. The second atom may be located at a distance from the Rydberg atoms or the dressed Rydberg atoms within a range defined by any two of the preceding values. Rydberg excitation units may be configured to form one or more 2-qubit units by causing the Rydberg atoms or the dressed Rydberg atoms to relax into a lower energy atomic state. Rydberg excitation units may be configured to induce the Rydberg atoms or the dressed Rydberg atoms to relax into a lower energy atomic state. The Rydberg units here can be configured to drive Rydberg atoms or dressed Rydberg atoms to a lower energy atomic state.For example, Rydberg excitation units can be configured to induce Rydberg atoms or dressed Rydberg atoms into a lower energy atomic state by applying electromagnetic radiation (e.g., RF radiation or optical radiation). Rydberg excitation units can be configured to induce any number of quantum mechanical entanglements between any number of atoms among a plurality of atoms.

[0072] The Rydberg excitation units may include one or more light sources (e.g., 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 the wavelengths forming the Rydberg atoms or the dressed Rydberg atoms. For example, the light may include at least one or more wavelengths of 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 greater than. The light may include one or more wavelengths up to 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 include one or more wavelengths within a range defined by any two of the preceding values. For example, the light may include one or more wavelengths within the range of 300 nm to 400 nm.

[0073] Rydberg excitation units can be configured to induce two-photon transitions to create entanglement. Rydberg excitation units can be configured to induce two-photon transitions to create entanglement between two atoms. Rydberg excitation units can be configured to selectively induce two-photon transitions to selectively create entanglement between two atoms. For example, Rydberg excitation units can be configured to selectively induce two-photon transitions to selectively create entanglement between two atoms by directing electromagnetic energy (e.g., optical energy) to specific optical trapping sites. Two atoms can be trapped at nearby optical trapping sites. For example, two atoms can be trapped at adjacent optical trapping sites. Two-photon transitions can be induced using first and second light from first and second light sources, respectively. The first and second light sources may each include any light source described herein (e.g., any laser described herein). The first light source may be identical or similar to the light source used to perform the single-qubit operation described herein. Alternatively, different light sources may be used to perform the single-qubit operation and to induce two-photon transitions to generate entanglement. The first light source may emit light comprising one or more wavelengths in the visible region of the optical spectrum (e.g., within the range of 400 nm to 800 nm or 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., within the range of 200 nm to 400 nm or 300 nm to 350 nm). The first and second light sources may emit light having substantially identical and opposite space-dependent frequency shifts.

[0074] Rydberg atoms or dressed Rydberg atoms may include Rydberg states capable of having sufficiently strong interatomic interactions with nearby atoms (e.g., nearby atoms trapped in nearby optical trapping sites) to enable the implementation of 2-qubit operations. Rydberg states may include at least about 50, 60, 70, 80, 90, 100, or more principal quantum numbers. Rydberg states may include up to about 100, 90, 80, 70, 60, 50, or less principal quantum numbers. Rydberg states may include principal quantum numbers within a range defined by any two of the preceding values. Rydberg states may interact with nearby atoms through van der Waals interactions. Van der Waals interactions may shift the atomic energy levels of the atoms.

[0075] Selective excitation of atomic states to Rydberg levels can enable the implementation of 2-qubit operations. 2-photon transitions move atoms to the ground state (e.g., 1 From the S0 basis state) to the Rydberg state (e.g., n 3It can be used to excite to the S1 state, where n is the principal quantum number described herein. State selectivity can be achieved by a combination of laser polarization and spectral selectivity. Two-photon transitions can be implemented using first and second laser sources as described herein. The first laser source can emit pi-polarized light, which may not alter the projection of atomic angular momentum along the magnetic field. The second laser can emit circularly polarized light, which may alter the projection of atomic angular momentum along the magnetic field by 1 unit. The first and second qubit levels can be excited to Rydberg levels using these polarizations. However, Rydberg levels may be more sensitive to magnetic fields than the ground state, so large splits (e.g., approximately 100s of MHz) can be easily obtained. Such spectral selectivity may allow state-selective excitation to Rydberg levels.

[0076] 2-qubit operations may rely on energy shifts of levels resulting from van der Waals interactions described herein. Such shifts may prevent the excitation of one atom conditioned on the state of another atom, or alter the coherent dynamics of the excitation of a 2-atom system to execute 2-qubit operations. In some cases, "dressed states" may be generated under continuous driving to execute 2-qubit operations without requiring full excitation to the Rydberg level (e.g., as described in https: / / arxiv.org / abs / 1605.05207, the whole of which is incorporated by reference herein for all purposes).

[0077] Cloud computing

[0078] The system (200) may be operably coupled to a digital computer (e.g., a digital computer described in the present specification in relation to FIG. 1) through a network described in the present specification (e.g., a network described in the present specification in relation to FIG. 1). The network may include a cloud computing network.

[0079] Optical trapping units

[0080] FIG. 3a illustrates an example of an optical trapping unit (210). The optical trapping unit may be configured to create a plurality of spatially distinct optical trapping sites (211) as described herein. For example, as illustrated in FIG. 3b, the optical trapping unit may be configured to create a first optical trapping site (211a), a second optical trapping site (211b), a third optical trapping site (211c), a fourth optical trapping site (211d), a fifth optical trapping site (211e), a sixth optical trapping site (211f), a seventh optical trapping site (211g), an eighth optical trapping site (211h), and a ninth optical trapping site (211i) as illustrated in FIG. 3a. Multiple spatially distinct optical trapping sites may be configured to trap multiple atoms, such as a first atom (212a), a second atom (212b), a third atom (212c), and a fourth atom (212d), as illustrated in FIG. 3a. As illustrated in FIG. 3b, each optical trapping site may be configured to trap a single atom. As illustrated in FIG. 3b, some of the optical trapping sites may be empty (i.e., not trapping atoms).

[0081] As illustrated in FIG. 3b, a plurality of optical trapping sites may comprise a two-dimensional (2D) array. The 2D array may be perpendicular to the optical axes of the optical components of the optical trapping unit illustrated in FIG. 3a. Alternatively, a plurality of optical trapping sites may comprise a one-dimensional (1D) array or a three-dimensional (3D) array.

[0082] Although illustrated in FIG. 3b as comprising nine optical trapping sites filled by four atoms, the optical trapping unit (210) may be configured to generate any number of spatially distinct optical trapping sites as described herein and may be configured to trap any number of atoms as described herein.

[0083] Each of the plurality of optical trapping sites can be spatially separated from each other by a distance of at least about 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 μm, 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm or more. Each optical trapping site may be spatially separated from each other by a distance of up to about 10 μm, 9 μm, 8 μm, 7 μm, 6 μm, 5 μm, 4 μm, 3 μm, 2 μm, 1 μm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm or less. Each optical trapping site may be spatially separated from each other by a distance within a range defined by any two of the preceding values.

[0084] Optical trapping sites may include one or more optical tweezers. Optical tweezers may include one or more focused laser beams to provide an attractive or repulsive force to hold or move one or more atoms. The beam waist of the focused laser beams may include a strong electric field gradient. Atoms may be attracted or repelled along the electric field gradient toward the center of the laser beam, which may contain the strongest electric field. Optical trapping sites may include one or more optical grating sites of one or more optical gratings. Optical trapping sites may include one or more optical grating sites of one or more one-dimensional (1D) optical gratings, two-dimensional (2D) optical gratings, or three-dimensional (3D) optical gratings. For example, optical trapping sites may include one or more optical grating sites of a 2D optical grating, as illustrated in FIG. 3b.

[0085] Optical gratings can be generated by interfering back-propagating light (e.g., back-propagating laser light) to produce a standing wave pattern having a periodic continuum of minimum and maximum intensities along a specific direction. A 1D optical grating can be generated by interfering a single pair of back-propagating light beams. A 2D optical grating can be generated by interfering two pairs of back-propagating light beams. A 3D optical grating can be generated by interfering three pairs of back-propagating light beams. The light beams can be generated by different light sources or by the same light source. Thus, the optical grating can be generated by at least about 1, 2, 3, 4, 5, 6 or more light sources, or by up to about 6, 5, 4, 3, 2, or 1 light source.

[0086] Returning to the description of FIG. 3a, the optical trapping unit may include one or more light sources configured to emit light to create a plurality of optical trapping sites as described herein. For example, the optical trapping unit may include a single light source (213) as illustrated in FIG. 3a. Although FIG. 3a is illustrated as including a single light source, the optical trapping unit may include 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 source. The light sources may include one or more lasers.

[0087] Lasers may include one or more continuous wave lasers. Lasers may include one or more pulsed lasers. Lasers may include 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 example, the lasers may include one or more argon dimer (Ar2) excimer lasers, krypton dimer (Kr2) excimer lasers, fluorine dimer (F2) excimer lasers, xenon dimer (Xe2) excimer lasers, argon fluoride (ArF) excimer lasers, krypton 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 lasers may include one or more dye lasers.

[0088] The lasers may include one or more metal-vapor lasers, such as one or more helium-cadmium (HeCd) metal-vapor lasers, helium-mercury (HeHg) metal-vapor lasers, helium-selenium (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 lasers, or manganese chloride (MnCl2) metal-vapor lasers.

[0089] The lasers may include one or more solid-state lasers, such as one or more ruby ​​lasers, metal-doped crystal lasers, or metal-doped fiber lasers. For example, the lasers include 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:YVO4) lasers, neodymium-doped yttrium calcium oxoborate (Nd:YCOB) lasers, neodymium glass (Nd:glass) lasers, titanium sapphire (Ti:sapphire) lasers, thulium-doped yttrium aluminum garnet (Tm:YAG) lasers, ytterbium-doped yttrium aluminum garnet (Yb:YAG) lasers, It may include ytterbium-doped glass (Yt:glass) lasers, holmium yttrium 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 (Er:glass) lasers, erbium-ytterbium-co-doped glass (Er / Yt:glass) lasers, uranium-doped calcium fluoride (U:CaF2) lasers, or samarium-doped calcium fluoride (Sm:CaF2) lasers.

[0090] Lasers may include 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 (AlGaInP) lasers, aluminum gallium arsenide (AlGaAs) lasers, indium gallium arsenide phosphide (InGaAsP) lasers, vertical cavity surface emission lasers (VCSELs), or quantum cascade lasers.

[0091] Lasers can emit continuous wave laser light. Lasers can emit pulsed laser light. The lasers have pulses 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 ps(picosecond), 2 ps, 3 ps, 4 ps, 5 ps, 6 ps, 7 ps, 8 ps, 9 ps, 10 ps, ​​20 ps, 30ps, 40ps, 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, 500 ns, 600 ns, 700 ns, It can have a pulse length of 800 ns, 900 ns, 1,000 ns or more.The lasers have up to approximately 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. 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, 100ps, 90ps, 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, The pulse length may be 2 fs, 1 fs, or less. Lasers may have a pulse length within a range defined by any two of the preceding values.

[0092] Lasers have frequencies of at least about 1 Hz (hertz), 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 (kilohertz), 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 MHz (megahertz), 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, It can have a repetition rate of 800 MHz, 900 MHz, 1,000 MHz or more.The lasers operate at up to approximately 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, They may have a repetition rate of 2 Hz, 1 Hz, or less. Lasers may have a repetition rate within a range defined by any two of the preceding values.

[0093] 레이저들은 적어도 약 1 nJ(nanojoule), 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 μJ(microjoule), 2 μJ, 3 μJ, 4 μJ, 65 μJ µJ, 8 µJ, 9 µJ, 10 µJ, 20 µJ, 30 µJ, 40 µJ, 50 µJ, 60 µJ, 70 µJ, 80 µJ, 90 µJ, 100 µJ, 200 µJ, 300 µJ, 400 µJ, 500 µJ, 670 µJ, µJ 800 μJ, 900 μJ, 적어도 1 mJ(millijoule), 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, 적어도 1 J(Joule) 펄스 에너지를 갖는 광을 방출할 수 있다.The lasers have power outputs up to 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, 70 mJ, 60 mJ, 50 mJ, 40 mJ, 30 mJ, 20 mJ. mJ, 10 mJ, 9 mJ, 8 mJ, 7 mJ, 6 mJ, 5 mJ, 4 mJ, 3 mJ, 2 mJ, 1 mJ, 900 μJ, 800 μJ, 700 μJ, 600 μJ, 500 μJ, 400 μJ, 300 μJ, 200 μJ, 100 μJ, 90 μJ, 80 μJ, 70 μJ, 60 μJ, 50 μJ, 40 μJ, 30 μJ, 20 μJ, 10 μJ, 9 μJ, 8 μJ, 7 μJ, 6 μJ, 5 μJ, 4 μJ, 3 μJ, 2 μJ, 1 μJ, 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 Lasers can emit light having pulse energy of nJ or less. Lasers can emit light having pulse energy within a range defined by any two of the preceding values.

[0094] The lasers have power outputs of at least about 1 μW (microwatt), 2 μW, 3 μW, 4 μW, 5 μW, 6 μW, 7 μW, 8 μW, 9 μW, 10 μW, 20 μW, 30 μW, 40 μW, 50 μW, 60 μW, 70 μW, 80 μW, 90 μW, 100 μW, 200 μW, 300 μW, 400 μW, 500 μW, 600 μW, 700 μW, 800 μW, 900 μW, 1 mW (milliwatt), 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 light having an average power of 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, 800 W, 900 W, 1,000 W or more It can be released.The lasers have power ratings up to approximately 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. 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, It can emit light having an average power of 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 μW, 800 μW, 700 μW, 600 μW, 500 μW, 400 μW, 300 μW, 200 μW, 100 μW, 90 μW, 80 μW, 70 μW, 60 μW, 50 μW, 40 μW, 30 μW, 20 μW, 10 μW, 9 μW, 8 μW, 7 μW, 6 μW, 5 μW, 4 μW, 3 μW, 2 μW, 1 μW, or more. Lasers can emit light with power within a range defined by any two of the preceding values.

[0095] Lasers can emit light containing one or more wavelengths in the ultraviolet (UV), visible, or infrared (IR) portions of the electromagnetic spectrum. The lasers are 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. 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 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, 1,100 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,It can emit light including one or more wavelengths of 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 greater. Lasers have wavelengths up to approximately 1,400 nm, 1,390 nm, 1,380 nm, 1,370 nm, 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 nm, 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 nm, 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 nm, 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,Lasers can emit light including one or more wavelengths of 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, and 200 nm. Lasers can emit light including one or more wavelengths within a range defined by any two of the preceding values.

[0096] Lasers are at least about 1 x 10 -15 nm, 2 x 10 -15 nm, 3 x 10 -15 nm, 4 x 10 -15 nm, 5 x 10 -15 nm, 6 x 10 -15 nm, 7 x 10 -15 nm, 8 x 10 -15 nm, 9 x 10 -15 nm, 1 x 10 -14 nm, 2 x 10 -14 nm, 3 x 10 -14 nm, 4 x 10 -14 nm, 5 x 10 -14 nm, 6 x 10 -14 nm, 7 x 10 -14 nm, 8 x 10 -14 nm, 9 x 10 -14 nm, 1 x 10 -13 nm, 2 x 10 -13 nm, 3 x 10 -13 nm, 4 x 10 -13 nm, 5 x 10 -13 nm, 6 x 10 -13 nm, 7 x 10 -13 nm, 8 x 10 -13 nm, 9 x 10 -13nm, 1 x 10 -12 nm, 2 x 10 -12 nm, 3 x 10 -12 nm, 4 x 10 -12 nm, 5 x 10 -12 nm, 6 x 10 -12 nm, 7 x 10 -12 nm, 8 x 10 -12 nm, 9 x 10 -12 nm, 1 x 10 -11 nm, 2 x 10 -11 nm, 3 x 10 -11 nm, 4 x 10 -11 nm, 5 x 10 -11 nm, 6 x 10 -11 nm, 7 x 10 -11 nm, 8 x 10 -11 nm, 9 x 10 -11 nm, 1 x 10 -10 nm, 2 x 10 -10 nm, 3 x 10 -10 nm, 4 x 10 -10 nm, 5 x 10 -10 nm, 6 x 10 -10 nm, 7 x 10 -10 nm, 8 x 10 -10 nm, 9 x 10 -10 nm, 1 x 10 -9 nm, 2 x 10 -9 nm, 3 x 10 -9 nm, 4 x 10 -9 nm, 5 x 10 -9 nm, 6 x 10 -9 nm, 7 x 10 -9 nm, 8 x 10 -9 nm, 9 x 10 -9 nm, 1 x 10 -8 nm, 2 x 10 -8 nm, 3 x 10 -8 nm, 4 x 10 -8 nm, 5 x 10 -8 nm, 6 x 10 -8 nm, 7 x 10 -8 nm, 8 x 10-8 nm, 9 x 10 -8 nm, 1 x 10 -7 nm, 2 x 10 -7 nm, 3 x 10 -7 nm, 4 x 10 -7 nm, 5 x 10 -7 nm, 6 x 10 -7 nm, 7 x 10 -7 nm, 8 x 10 -7 nm, 9 x 10 -7 nm, 1 x 10 -6 nm, 2 x 10 -6 nm, 3 x 10 -6 nm, 4 x 10 -6 nm, 5 x 10 -6 nm, 6 x 10 -6 nm, 7 x 10 -6 nm, 8 x 10 -6 nm, 9 x 10 -6 nm, 1 x 10 -5 nm, 2 x 10 -5 nm, 3 x 10 -5 nm, 4 x 10 -5 nm, 5 x 10 -5 nm, 6 x 10 -5 nm, 7 x 10 -5 nm, 8 x 10 -5 nm, 9 x 10 -5 nm, 1 x 10 -4 nm, 2 x 10 -4 nm, 3 x 10 -4 nm, 4 x 10 -4 nm, 5 x 10 -4 nm, 6 x 10 -4 nm, 7 x 10 -4 nm, 8 x 10 -4 nm, 9 x 10 -4 nm, 1 x 10 -3 They can emit light with a bandwidth of nm or greater. Lasers can emit light up to approximately 1 x 10⁻⁶ -3 nm, 9 x 10 -4 nm, 8 x 10 -4nm, 7 x 10 -4 nm, 6 x 10 -4 nm, 5 x 10 -4 nm, 4 x 10 -4 nm, 3 x 10 -4 nm, 2 x 10 -4 nm, 1 x 10 -4 nm, 9 x 10 -5 nm, 8 x 10 -5 nm, 7 x 10 -5 nm, 6 x 10 -5 nm, 5 x 10 -5 nm, 4 x 10 -5 nm, 3 x 10 -5 nm, 2 x 10 -5 nm, 1 x 10 -5 nm, 9 x 10 -6 nm, 8 x 10 -6 nm, 7 x 10 -6 nm, 6 x 10 -6 nm, 5 x 10 -6 nm, 4 x 10 -6 nm, 3 x 10 -6 nm, 2 x 10 -6 nm, 1 x 10 -6 nm, 9 x 10 -7 nm, 8 x 10 -7 nm, 7 x 10 -7 nm, 6 x 10 -7 nm, 5 x 10 -7 nm, 4 x 10 -7 nm, 3 x 10 -7 nm, 2 x 10 -7 nm, 1 x 10 -7 nm, 9 x 10 -8 nm, 8 x 10 -8 nm, 7 x 10 -8 nm, 6 x 10 -8 nm, 5 x 10 -8 nm, 4 x 10 -8 nm, 3 x 10 -8 nm, 2 x 10 -8 nm, 1 x 10 -8 nm, 9 x 10-9 nm, 8 x 10 -9 nm, 7 x 10 -9 nm, 6 x 10 -9 nm, 5 x 10 -9 nm, 4 x 10 -9 nm, 3 x 10 -9 nm, 2 x 10 -9 nm, 1 x 10 -9 nm, 9 x 10 -10 nm, 8 x 10 -10 nm, 7 x 10 -10 nm, 6 x 10 -10 nm, 5 x 10 -10 nm, 4 x 10 -10 nm, 3 x 10 -10 nm, 2 x 10 -10 nm, 1 x 10 -10 nm, 9 x 10 -11 nm, 8 x 10 -11 nm, 7 x 10 -11 nm, 6 x 10 -11 nm, 5 x 10 -11 nm, 4 x 10 -11 nm, 3 x 10 -11 nm, 2 x 10 -11 nm, 1 x 10 -11 nm, 9 x 10 -12 nm, 8 x 10 -12 nm, 7 x 10 -12 nm, 6 x 10 -12 nm, 5 x 10 -12 nm, 4 x 10 -12 nm, 3 x 10 -12 nm, 2 x 10 -12 nm, 1 x 10 -12 nm, 9 x 10 -13 nm, 8 x 10 -13 nm, 7 x 10 -13 nm, 6 x 10 -13 nm, 5 x 10 -13 nm, 4 x 10 -13 nm, 3 x 10 -13 nm, 2 x 10 -13nm, 1 x 10 -13 nm, 9 x 10 -14 nm, 8 x 10 -14 nm, 7 x 10 -14 nm, 6 x 10 -14 nm, 5 x 10 -14 nm, 4 x 10 -14 nm, 3 x 10 -14 nm, 2 x 10 -14 nm, 1 x 10 -14 nm, 9 x 10 -15 nm, 8 x 10 -15 nm, 7 x 10 -15 nm, 6 x 10 -15 nm, 5 x 10 -15 nm, 4 x 10 -15 nm, 3 x 10 -15 nm, 2 x 10 -15 nm, 1 x 10 -15 They can emit light having a bandwidth of nm or less. Lasers can emit light having a bandwidth within a range defined by any two of the preceding values.

[0097] Light sources may be configured to emit light tuned to one or more magic wavelengths corresponding to multiple atoms. The magic wavelength corresponding to an atom may include any wavelength of light that produces identical or nearly identical polarizations of the first and second atomic states. Magic wavelengths for transitions between the first and second atomic states may be determined by calculating the wavelength-dependent polarizations of the first and second atomic states and finding the intersections. Light tuned to such a magic wavelength may produce identical or nearly identical differential light shifts in the first and second atomic states, regardless of the intensity of the light emitted by the light sources. This can effectively decouple the first and second atomic states from the 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.

[0098] For example, the metastable states of Group III atoms and alkaline earth or alkaline earth-like atoms may have relatively large tensor shifts, the angle with respect to the applied magnetic field can be tuned to cause a situation where scalar and tensor shifts are balanced and provide a zero or near-zero differential light shift between the first and second atomic states. The angle θ can be tuned by selecting the polarization of the emitted light. For example, when the emitted light is linearly polarized, the total polarization α is the scalar component α scalar and tensor component α tensor It can be recorded as the sum of:

[0099]

[0100] By appropriately selecting θ, the polarization of the first and second atomic states can be selected to zero or near zero to correspond to a zero or near zero differential optical shift, and the motion of the atoms can be decoupled.

[0101] Light sources may be configured to direct light to one or more optical modulators (OMs) configured to generate a plurality of optical trapping sites. For example, an optical trapping unit may include an OM (214) configured to generate a plurality of optical trapping sites. Although illustrated in FIG. 3a as including one OM, the optical trapping unit may include 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 OM. The OMs may include one or more digital micromirror devices (DMDs). The OMs may include one or more liquid crystal devices, such as one or more LCoS (liquid crystal on silicon) devices. The OMs may include one or more spatial light modulators (SLMs). OMs may include one or more acousto-optic polarizers (AODs) or acousto-optic modulators (AOMs). OMs may include one or more electron-optic polarizers (EODs) or electron-optic modulators (EOMs).

[0102] The OM can be optically coupled to one or more optical elements to create a regular array of optical trapping sites. For example, the OM can be optically coupled to an optical element (219) as shown in FIG. 3a. The optical elements may include lenses or microscope objective lenses configured to redirect light from the OMs to form a regular rectangular grid of optical trapping sites.

[0103] For example, as shown in FIG. 3a, the OM may include an SLM, DMD, or LCoS device. The SLM, DMD, or LCoS device may be imaged on the back focal plane of the microscope objective lens. This may allow for the creation of any configuration of two-dimensional or three-dimensional optical trapping sites.

[0104] Alternatively or in combination, the OMs may include first and second AODs. The active regions of the first and second AODs may be imaged on the back focal plane of the microscope objective lenses. The output of the first AOD may be optically coupled to the input of the second AOD. In this way, the second AOD may make a copy of the optical output of the first AOD. This may allow for the creation of two-dimensional or three-dimensional optical trapping sites.

[0105] Alternatively or in combination, OMs may include static optical elements, such as one or more microlens arrays or holographic optical elements. Static optical elements may be imaged on the back focal plane of the microscope objective lens. This may allow for the creation of any configuration of two-dimensional or three-dimensional optical trapping sites.

[0106] The optical trapping unit may include one or more imaging units configured to acquire one or more images of the spatial configuration of a plurality of atoms trapped within optical trapping sites. For example, the optical trapping unit may include an imaging unit (215). Although illustrated in FIG. 3a as including a single imaging unit, the optical trapping unit may include 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 up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 imaging unit. The imaging units may include one or more lenses or objective lenses. The imaging units may include one or more PMTs, photodiodes, avalanche photodiodes, phototransistors, reverse-bias LEDs, CCDs, or CMOS cameras. The imaging unit may include one or more fluorescence detectors. The images may include one or more fluorescence images, single-atom fluorescence images, absorption images, single-atom absorption images, phase contrast images, or single-atom phase contrast images.

[0107] The optical trapping unit may include one or more spatial configuration AI units configured to perform one or more artificial intelligence (AI) operations to determine the spatial configuration of a plurality of atoms trapped within optical trapping sites based on images acquired by the imaging unit. For example, the optical trapping unit may include a spatial configuration AI unit (216). Although illustrated in FIG. 3a as including a single spatial configuration AI unit, the optical trapping unit may include any number of spatial configuration AI units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more spatial configuration AI units, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 spatial configuration AI unit. The AI ​​operations may include any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0108] The optical trapping unit may include one or more atomic rearrangement units configured to impart a modified spatial arrangement of a plurality of atoms trapped into optical trapping sites based on one or more images acquired by the imaging unit. For example, the optical trapping unit may include an atomic rearrangement unit (217). Although illustrated in FIG. 3a as including a single atomic rearrangement unit, the optical trapping unit may include any number of atomic rearrangement units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 atomic rearrangement units, or more than about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 atomic rearrangement unit.

[0109] The optical trapping unit may include one or more spatial arrangement AI units configured to perform one or more artificial intelligence (AI) operations to determine a modified spatial arrangement of a plurality of atoms trapped within optical trapping sites based on images acquired by the imaging unit. For example, the optical trapping unit may include a spatial arrangement AI unit (218). Although illustrated in FIG. 3a as including a single spatial arrangement AI unit, the optical trapping unit may include any number of spatial arrangement AI units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more spatial arrangement AI units, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 spatial arrangement AI unit. The AI ​​operations may include any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0110] In some cases, spatial configuration AI units and spatial array AI units may be integrated into an integrated AI unit. The optical trapping unit may include any number of integrated AI units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 integrated AI units, or more than about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 integrated AI unit.

[0111] An atomic rearrangement unit may be configured to change the spatial arrangement to obtain an increase in the charge factor of a plurality of optical trapping sites. The charge factor may be defined as the ratio of the number of optical trapping sites occupied by one or more atoms to the total number of available optical trapping sites in the optical trapping unit or in the region of the optical trapping unit. For example, the initial loading of atoms within the optical trapping sites may result in a charge factor of 100%, 90%, 80%, 70%, 60%, 50%, or less, so that the atoms each occupy 100%, 90%, 70%, 60%, 50%, or less of the available optical trapping sites. It may be desirable to rearrange the atoms to achieve a charge factor of at least about 50%, 60%, 70%, 80%, 90%, or 100%. By analyzing imaging information obtained by the imaging unit, the atomic rearrangement unit can achieve a charge 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 atomic rearrangement unit can achieve a charge factor of up to approximately 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 atomic rearrangement unit can achieve a charge factor within a range defined by any two of the preceding values.

[0112] For example, FIG. 3c illustrates an example of an optical trapping unit partially filled with atoms. As shown in FIG. 3c, the initial loading of atoms within the optical trapping sites can produce a charge 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 the atomic reservoir described herein, a much higher charge factor can be obtained, as shown in FIG. 3d.

[0113] FIG. 3d illustrates an example of an optical trapping unit fully charged with atoms. As shown in FIG. 3d, a fifth atom (212e), a sixth atom (212f), a seventh atom (212g), an eighth atom (212h), and a ninth atom (212i) can be moved to charge unoccupied optical trapping sites. The fifth, sixth, seventh, eighth, and ninth atoms can be moved by moving atoms from different regions of the optical trapping unit (not shown in FIG. 3c) or from the atomic reservoir described herein. Thus, the charge factor can be substantially improved after the rearrangement of atoms within the optical trapping sites. For example, a charge factor of up to 100% (nine atoms charging nine available optical trapping sites as shown in FIG. 3d) can be achieved.

[0114] Electromagnetic transmission units

[0115] FIG. 4 illustrates an example of an electromagnetic transfer unit (220). The electromagnetic transfer unit may be configured to apply electromagnetic energy to one or more of a plurality of atoms as described herein. The electromagnetic transfer unit may include one or more light sources, such as any light source described herein. The electromagnetic energy may include optical energy. The optical energy may include any repetition rate, pulse energy, average power, wavelength, or bandwidth described herein.

[0116] The electromagnetic transfer unit may include one or more microwave or radio frequency (RF) energy sources, such as one or more magnetrons, klystrons, traveling wave tubes, gyrotrons, field-effect transistors (FETs), tunnel diodes, gun diodes, IMPATT (impact ionization avalanche transit-time) diodes, or masers. The electromagnetic energy may include microwave energy or RF energy. RF energy is at least about 1 mm (millimeter), 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 m(meter), 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, It may include one or more wavelengths of 400 m, 500 m, 600 m, 700 m, 800 m, 900 m, 1 km (kilometer), 2 km, 3 km, 4 km, 5 km, 6 km, 7 km, 8 km, 9 km, 10 km or more.RF energy is transmitted up to approximately 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, 1 m, 900 mm, 800 mm, 700 mm, 600 mm, 500 mm, 400 mm, 300 mm, 200 mm, 100 mm, 90 mm, 80 mm, It may include one or more wavelengths of 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 include one or more wavelengths within a range defined by any two of the preceding values.

[0117] The RF energy is at least about 1 μW (microwatt), 2 μW, 3 μW, 4 μW, 5 μW, 6 μW, 7 μW, 8 μW, 9 μW, 10 μW, 20 μW, 30 μW, 40 μW, 50 μW, 60 μW, 70 μW, 80 μW, 90 μW, 100 μW, 200 μW, 300 μW, 400 μW, 500 μW, 600 μW, 700 μW, 800 μW, 900 μW, 1 mW (milliwatt), 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 It may include average power of 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 W (Watt), 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, 800 W, 900 W, 1,000 W or more.RF energy can be up to 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 It may include an average power of 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 μW, 800 μW, 700 μW, 600 μW, 500 μW, 400 μW, 300 μW, 200 μW, 100 μW, 90 μW, 80 μW, 70 μW, 60 μW, 50 μW, 40 μW, 30 μW, 20 μW, 10 μW, 9 μW, 8 μW, 7 μW, 6 μW, 5 μW, 4 μW, 3 μW, 2 μW, 1 μW, or less. RF energy may include average power within a range defined by any two of the preceding values.

[0118] The electromagnetic transfer unit may include one or more light sources, such as any light source described herein. For example, the electromagnetic transfer unit may include a light source (221). Although illustrated in FIG. 4 as including a single light source, the electromagnetic transfer unit may include 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 source.

[0119] Light sources may be configured to direct light toward one or more OMs configured to selectively apply electromagnetic energy to one or more of a plurality of atoms. For example, the electromagnetic transfer unit may include an OM (222). Although illustrated in FIG. 4 as including a single OM, the electromagnetic transfer unit may include any number of OMs, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more OMs, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 OM. The OMs may include one or more SLMs, AODs, or AOMs. The OMs may include one or more DMDs. The OMs may include one or more liquid crystal devices, such as one or more LCoS devices.

[0120] The electromagnetic transfer unit may include one or more electromagnetic energy AI units configured to perform one or more artificial intelligence (AI) operations to selectively apply electromagnetic energy to atoms. For example, the electromagnetic transfer unit may include an AI unit (223). Although illustrated in FIG. 4 as including a single AI unit, the electromagnetic transfer unit may include any number of AI units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 AI units, or more than or equal to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 AI unit. The AI ​​operations may include any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0121] The electromagnetic transfer unit may be configured to apply one or more single-qubit operations (e.g., one or more single-qubit gate operations) to the qubits described herein. The electromagnetic transfer unit may be configured to apply one or more 2-qubit operations (e.g., one or more 2-qubit gate operations) to the 2-qubit units described herein. Each single-qubit or 2-qubit operation is at least about 10 ns (nanoseconds), 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 μs (microsecond), 2 μs, 3 μs, 4 μs, 5 μs, 6 μs, 7 μs, 8 μs, 9 μs, 10 μs, 20 μs, 30 μs, 40 μs, 50 μs, 60 μs, 70 μs, 80 μs, 90 μs, 100 μs or It may include a duration exceeding that. Each single-qubit or 2-qubit operation may include a duration of up to approximately 100 μs, 90 μs, 80 μs, 70 μs, 60 μs, 50 μs, 40 μs, 30 μs, 20 μs, 10 μs, 9 μs, 8 μs, 7 μs, 6 μs, 5 μs, 4 μs, 3 μs, 2 μs, 1 μs, 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 include a duration within a range defined by any two of the preceding values.Single-qubit or 2-qubit devices may be applied at a repetition frequency of at least 1 kHz (kilohertz), 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 higher. Single-qubit or 2-qubit operations may be applied at repetition frequencies up to 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. Single-qubit or 2-qubit operations may be applied at repetition frequencies within a range defined by any two of the preceding values.

[0122] The electromagnetic transfer unit may be configured to apply one or more single-qubit operations by inducing one or more Raman transitions between the first qubit state and the second qubit state described herein. The Raman transitions are as described herein. 3 P0 or 3It can be detuned from the P1 line. For example, Raman transitions are 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, 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, 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 It can be detuned to 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. Raman transitions are up to approximately 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 It can be detuned to 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.Raman transitions can be detuned by a value within a range defined by any two of the preceding values.

[0123] Raman transitions can be induced for individually selected atoms using one or more spatial light modulators (SLMs) or acousto-optic deflectors (AODs) to impart a deflection angle and / or frequency shift to the light beam based on an applied radio frequency (RF) signal. The SLM or AOD can be combined with an optical conditioning system that images the SLM or AOD active region on the back focal plane of the microscope objective lens. The microscope objective lens can perform a spatial Fourier transform on the optical field at the location of the SLM or AOD. Thus, an angle (which may be proportional to the RF frequency) can be converted into a position. For example, applying a comb of radio frequencies to the AOD can generate a linear array of spots in the focal plane of the objective lens, each spot having a finite range determined by the characteristics of the optical conditioning system (e.g., the point diffusion function of the optical conditioning system).

[0124] To perform a Raman transition on a single atom with a single SLM or AOD, a pair of frequencies may be applied simultaneously to the SLM or AOD. The two frequencies of the pair may have a frequency difference that matches or nearly matches the separation energy between the first and second qubit states. For example, the frequency difference is up to approximately 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 The separated energy may differ from that of 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 is 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. Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 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, 50 kHz, 60 The frequency difference may differ from the split energy by 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 split energy by about 0 Hz. The frequency difference may differ from the split energy by a value within a range defined by any two of the preceding values. The optical system may be configured such that the positional spacing corresponding to the frequency difference is not resolved and that light at both of the two frequencies interacts with a single atom.

[0125] Integrated optical trapping units and electromagnetic transmission units

[0126] The optical trapping units and electromagnetic transmission units described herein may be integrated into a single optical system. A microscope objective lens may be used to transmit electromagnetic radiation generated by the electromagnetic transmission unit described herein and to transmit light to trapping atoms generated by the optical trapping unit described herein. Alternatively, or in combination, different objective lenses may be used to transmit electromagnetic radiation generated by the electromagnetic transmission unit and to transmit light from trapping atoms generated by the optical trapping unit.

[0127] A single SLM or AOD may allow for the implementation of qubit operations on a linear array of atoms (e.g., any single-qubit or two-qubit operations described herein). Alternatively, or in combination, two distinct SLMs or AODs may be configured to handle light having orthogonal polarizations. Light having orthogonal polarizations may be superimposed before the microscope objective lens. In such a manner, each photon used in the two-photon transition described herein may be delivered to the objective lens by a distinct SLM or AOD, which may allow for increased polarization control. Qubit operations may be performed on a two-dimensional array of atoms by bringing light from the first SLM or AOD through an optical repeater to a second SLM or AOD oriented substantially orthogonally to the first SLM or AOD. Alternatively, or in combination, qubit operations can be performed on a two-dimensional array of atoms by using a one-dimensional array of SLMs or AODs.

[0128] The stability of qubit gate fidelity can be improved by maintaining the superposition of light from various light sources described herein (e.g., light sources associated with optical trapping units or electromagnetic transfer units described herein). Such superposition can be maintained by an optical subsystem that measures the direction of light emitted by various light sources, thereby enabling closed-loop control of the direction of light emission. The optical subsystem may include a pick-off mirror positioned before the microscope objective lens. The pick-off mirror may be configured to direct a small amount of light toward the lens, and the lens may focus the collimated beam and convert an angular deviation into a positional deviation. A position-sensitive optical detector, such as a lateral effect position sensor or a quadrant photodiode, may convert the positional deviation into an electronic signal, and information regarding the deviation may be supplied to a compensating optical unit, such as an active mirror.

[0129] The stability of qubit gate operation can be improved by controlling the intensity of light from various light sources described herein (e.g., light sources associated with optical trapping units or electromagnetic transfer units described herein). Such intensity control can be maintained by an optical subsystem that measures the intensity of light emitted by the various light sources, thereby enabling closed-loop control of the intensity. Each light source can be coupled to an intensity actuator, such as an intensity servo control. The actuator may include an acousto-optical modulator (AOM) or an electro-optical modulator (EOM). The intensity may be measured using an optical detector, such as a photodiode or any other optical detector described herein. Information regarding the intensity may be incorporated into a feedback loop to stabilize the intensity.

[0130] State preparation units

[0131] FIG. 5 illustrates an example of a state preparation unit (250). The state preparation unit may be configured to prepare the state of a plurality of atoms as described herein. The state preparation unit may be coupled to an optical trapping unit and may orient the atoms prepared by the state preparation unit toward the optical trapping unit. The state preparation unit may be configured to cool a plurality of atoms. The state preparation unit may be configured to cool a plurality of atoms before trapping a plurality of atoms at a plurality of optical trapping sites.

[0132] The state preparation unit may include one or more Zeeman sloers. For example, the state preparation unit may include a Zeeman sloer (251). Although illustrated in FIG. 5 as including a single Zeeman sloer, the state preparation may include any number of Zeeman sloers, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more Zeeman sloers, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 Zeeman sloer. The Zeeman sloers may be configured to cool one or more atoms of a plurality of atoms from a first velocity or distribution of velocities (e.g., emission rate from an atomic source, room temperature, liquid nitrogen temperature, or any other temperature) at a second velocity slower than the first velocity or distribution of velocities.

[0133] The first velocity or distribution of velocities may be associated with a temperature of at least about 50 K (Kelvin), 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 greater. The first velocity or distribution of velocities may be associated with a temperature of up to 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 within a range defined by any two of the preceding values. The second velocity may be at least about 1 m / s (meter per second), 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 greater than. 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 than. The second velocity may be within a range defined by any two of the preceding values. Zeeman sloers may include 1D Zeeman sloers.

[0134] The state preparation unit may include 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 up to about 10 mK (millikelvin), 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 greater. The first temperature may be within a range defined by any two of the preceding values. The first MOT may include a 1D, 2D, or 3D MOT.

[0135] The first MOT may include one or more light sources configured to emit light (e.g., any light source described herein). The light is 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. 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, It may include one or more wavelengths of 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.Light has wavelengths up to 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, It may include one or more wavelengths of 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 include one or more wavelengths within a range defined by any two of the preceding values. For example, light may include one or more wavelengths within the range of at least 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.

[0136] The state preparation unit may include a second MOT (253). The second MOT may be configured to cool atoms from a first temperature to a second temperature lower than the first temperature. The second temperature may be up to about 100 μK (microkelvin), 90 μK, 80 μK, 70 μK, 60 μK, 50 μK, 40 μK, 30 μK, 20 μK, 10 μK, 9 μK, 8 μK, 7 μK, 6 μK, 5 μK, 4 μK, 3 μK, 2 μK, 1 μK, 900 nK (nanokelvin), 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 μK, 2 μK, 3 μK, 4 μK, 5 μK, 6 μK, 7 μK, 8 μK, 9 μK, 10 μK, 20 μK, 30 μK, 40 μK, 50 μK, 60 μK, 70 μK, 80 μK, 90 μK, 100 μK, or greater than. The second temperature may be within a range defined by any two of the preceding values. The second MOT may include a 1D, 2D, or 3D MOT.

[0137] The second MOT may include one or more light sources configured to emit light (e.g., any light source described herein). The light is 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. 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, It may include one or more wavelengths of 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.Light has wavelengths up to 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, It may include one or more wavelengths of 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 include one or more wavelengths within a range defined by any two of the preceding values. For example, light may include one or more wavelengths within the range of at least 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.

[0138] Although illustrated in FIG. 5 as including two MOTs, the state preparation unit may include 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 MOT.

[0139] The state preparation unit may include one or more sideband cooling units or Sisyphus cooling units (e.g., the sideband cooling unit described at https: / / arxiv.org / abs / 1810.06626 or the Sisyphus cooling unit described at https: / / arxiv.org / abs / 1811.06014, each of which is incorporated herein by reference in its entirety for all purposes). For example, the state preparation unit may include a sideband cooling unit or a Sisyphus cooling unit (254). Although illustrated in FIG. 5 as comprising a single sideband cooling unit or Sisyphus cooling unit, 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 up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 sideband cooling unit or Sisyphus cooling unit. The sideband cooling units or Sisyphus cooling units may be configured to use sideband cooling to cool atoms from a second temperature to a third temperature lower than the second temperature. The third temperature may be up to about 10 μK, 9 μK, 8 μK, 7 μK, 6 μK, 5 μK, 4 μK, 3 μK, 2 μK, 1 μK, 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 up to 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 μK, 2 μK, 3 μK, 4 μK, 5 μK, 6 μK, 7 μK, 8 μK, 9 μK, 10 μK, or greater. The third temperature may be within a range defined by any two of the preceding values.

[0140] Sideband cooling units or Sisyphus cooling units may include one or more light sources configured to emit light (e.g., any light source described herein). The light is 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. 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, It may include one or more wavelengths of 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.Light has wavelengths up to 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, It may include one or more wavelengths of 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 include one or more wavelengths within a range defined by any two of the preceding values. For example, light may include one or more wavelengths within the range of at least 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.

[0141] The state preparation unit may include one or more optical pumping units. For example, the state preparation unit may include an optical pumping unit (255). Although illustrated in FIG. 5 as including a single optical pumping unit, the state preparation may include 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 up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 optical pumping unit. The optical pumping units may be configured to emit light to optically pump atoms from an equilibrium distribution of atomic states to a non-equilibrium atomic state. For example, the optical pumping units may be configured to emit light to optically pump atoms from an equilibrium distribution of atomic states to a single pure atomic state. Optical pumping units may be configured to emit light to optically pump atoms to a ground atomic state or any other atomic state. Optical pumping units may be configured to optically pump atoms between any two atomic states. Optical pumping units may include one or more light sources configured to emit light (e.g., any light source described herein).The light is 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. 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, It may include one or more wavelengths of 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.Light has wavelengths up to 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, It may include one or more wavelengths of 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 include one or more wavelengths within a range defined by any two of the preceding values. For example, light may include one or more wavelengths within the range of at least 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.

[0142] A state preparation unit may include one or more coherent driving units. For example, a state preparation unit may include a coherent driving unit (256). Although illustrated in FIG. 5 as including coherent driving, the state preparation may include 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 unit. Coherent driving units may be configured to coherently drive atoms from a non-equilibrium state to a first or second atomic state described herein. Accordingly, atoms can be optically pumped into an atomic state convenient for access (e.g., based on the availability of light sources emitting specific wavelengths or based on other factors) and subsequently coherently driven into the atomic states described herein that are useful for performing quantum calculations. Coherent driving units may be configured to induce a single-photon transition between a non-equilibrium state and a first or second atomic state. Coherent driving units may be configured to induce a two-photon transition between a non-equilibrium state and a first or second atomic state. The two-photon transition may be induced using light from two light sources described herein (e.g., two lasers described herein).

[0143] Coherent driving units may include one or more light sources configured to emit light (e.g., any light source described herein). The light is 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. 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, It may include one or more wavelengths of 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.Light has wavelengths up to 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, It may include one or more wavelengths of 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 include one or more wavelengths within a range defined by any two of the preceding values. For example, light may include one or more wavelengths within the range of at least 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.

[0144] Coherent driving units may be configured to induce an RF transition between a non-equilibrium state and a first or second atomic state. Coherent driving units may include one or more electromagnetic radiation sources configured to emit electromagnetic radiation configured to induce an RF transition. For example, coherent driving units may include one or more RF sources configured to emit RF radiation (e.g., any RF source described herein). The RF radiation may include at least one or more wavelengths of about 10 cm (centimeters), 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 greater. RF radiation may include one or more wavelengths up to 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. RF radiation may include one or more wavelengths within a range defined by any two of the preceding values. Alternatively, or in combination, coherent driving units may include one or more light sources (e.g., any light sources described herein) configured to induce a two-photon transition corresponding to an RF transition.

[0145] Controllers

[0146] Optical trapping units, electromagnetic transfer units, entanglement units, readout optical units, vacuum units, imaging units, spatial configuration AI units, spatial array AI units, atomic rearrangement units, state preparation units, sideband cooling units, optical pumping units, coherent driving units, electromagnetic energy AI units, atomic reservoirs, atomic movement units, or Rydberg excitation units may include one or more circuits or controllers (e.g., one or more electronic circuits or controllers) connected to the optical trapping units, electromagnetic transfer units, entanglement units, readout optical units, vacuum units, imaging units, spatial configuration AI units, spatial array AI units, atomic rearrangement units, state preparation units, sideband cooling units, optical pumping units, coherent driving units, electromagnetic energy AI units, atomic reservoirs, atomic movement units, or Rydberg excitation units (by one or more electronic connections). Circuits or controllers may be configured to control optical trapping units, electromagnetic transfer units, entanglement units, readout optical units, vacuum units, imaging units, spatial configuration AI units, spatial arrangement AI units, atomic rearrangement units, state preparation units, sideband cooling units, optical pumping units, coherent driving units, electromagnetic energy AI units, atomic reservoirs, atomic movement units, or Rydberg excitation units.

[0147] Non-traditional computers

[0148] In one aspect, the present disclosure provides a non-traditional computer comprising: a plurality of qubits comprising more than 60 atoms, each atom being trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprises 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 or more electromagnetic transfer units configured to apply electromagnetic energy to one or more qubits of the plurality of qubits to impart a non-traditional operation to one or more qubits, wherein the non-traditional operation comprises at least a superposition between 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 state with at least another qubit among the plurality of qubits; and one or more read optical units configured to perform one or more measurements of one or more qubits to obtain a non-traditional computation.

[0149] In one aspect, the present disclosure provides a non-traditional computer comprising a plurality of qubits each comprising more than 60 atoms trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites.

[0150] Methods for performing non-traditional calculations

[0151] In one aspect, the present disclosure provides a method for performing a non-traditional computation, comprising: (a) generating a plurality of spatially distinct optical trapping sites—the plurality of optical trapping sites are configured to trap a plurality of atoms, and the plurality of atoms comprises more than 60 atoms—; (b) applying electromagnetic energy to one or more of the plurality of atoms to induce the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state distinct from the first atomic state; (c) quantum mechanically entangling at least a subset of one or more atoms in one or more superposition states with at least another atom among the plurality of atoms; and (d) performing one or more optical measurements of one or more superposition states to obtain a non-traditional computation.

[0152] FIG. 6 illustrates a flowchart for an example of a first method (600) for performing non-traditional calculations.

[0153] In the first operation (610), the method (600) may include the step of creating 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 include more than 60 atoms. The optical trapping sites may include any optical trapping sites described herein. The atoms may include any atoms described herein.

[0154] In the second operation (620), the method (600) may include the step of applying electromagnetic energy to one or more of a plurality of atoms to induce one or more atoms to adopt a superposition state of at least one second atomic state that is different from the first atomic state. The electromagnetic energy may include any electromagnetic energy described herein. The first atomic state may include any first atomic state described herein. The second atomic state may include any second atomic state described herein.

[0155] In the third operation (630), the method (600) may include the step of quantum mechanically entangling at least a subset of one or more atoms in one or more superposition states with at least another atom among a plurality of atoms. The atoms may quantum mechanically entangle in any manner described herein (e.g., as described herein in connection with FIG. 2).

[0156] In the fourth operation (640), the method (600) may include the step of performing one or more optical measurements in one or more superimposed states to obtain a non-traditional calculation. The optical measurements may include any optical measurements described herein.

[0157] In one aspect, the present disclosure provides a method for performing a non-traditional computation, comprising: (a) providing a plurality of qubits comprising more than 60 atoms, wherein each atom is trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, and the plurality of qubits comprises 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 of the plurality of qubits to impart a non-traditional operation to the one or more qubits, wherein the non-traditional operation comprises at least a superposition between 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 state with at least another qubit among the plurality of qubits; and (d) performing one or more optical measurements of one or more qubits to obtain the non-traditional computation.

[0158] FIG. 7 illustrates a flowchart for an example of a second method (700) for performing non-traditional calculations.

[0159] In the first operation (710), the method (700) may include the step of providing a plurality of qubits comprising more than 60 atoms, each atom being trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, and the plurality of qubits comprising 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.

[0160] In the second operation (720), the method (700) may include the step of applying electromagnetic energy to one or more of the plurality of qubits to impart a non-traditional operation to the one or more qubits, and the non-traditional operation includes at least a superposition between the first qubit state and the second qubit state. The electromagnetic energy may include any electromagnetic energy described herein.

[0161] In the third operation (730), the method (700) may include the step of quantum mechanically entangling at least a subset of a plurality of qubits that overlap with at least another qubit among the plurality of qubits. The qubits may quantum mechanically entangle in any manner described herein (e.g., as described herein in connection with FIG. 2).

[0162] In the fourth operation (740), the method (700) may include the step of obtaining a non-traditional computation by performing one or more optical measurements of one or more qubits. The optical measurements may include any optical measurements described herein.

[0163] In one aspect, the present disclosure provides a method for performing a non-traditional computation, comprising: (a) providing a plurality of qubits each comprising more than 60 atoms trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites; and (b) using a subset of at least a plurality of qubits to perform a non-traditional computation.

[0164] FIG. 8 illustrates a flowchart for an example of a third method (800) for performing non-traditional calculations.

[0165] In the first operation (810), the method (800) may include the step of providing a plurality of qubits comprising more than 60 atoms each trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites. The qubits may include any qubits described herein. The atoms may include any atoms described herein. The optical trapping sites may include any optical trapping sites described herein.

[0166] In the second operation (820), the method (800) may include the step of using at least a subset of a plurality of qubits to perform a non-traditional calculation.

[0167] computer systems

[0168] FIG. 1 illustrates a computer system (101) programmed or otherwise configured to operate any method or system described herein (e.g., a system or method for performing non-traditional calculations described herein). The computer system (101) may control various aspects of the present disclosure. The computer system (101) may be a computer system located remotely from a user's electronic device or an electronic device. The electronic device may be a mobile electronic device.

[0169] A computer system (101) includes a central processing unit (CPU, also referred to herein as “processor” and “computer processor”) (105), which may 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), a communication interface (120) (e.g., network adapter) for communicating with one or more other systems, and peripheral devices (125), such as a cache, other memory, data storage unit, and / or electronic display adapter. The memory (110), storage unit (115), interface (120), and peripheral devices (125) communicate with the CPU (105) via a communication bus (solid lines), such as a motherboard. The storage unit (115) may be a data storage unit (or data storage) for storing data. A computer system (101) can be operably coupled to a computer network ("network") (130) with the help of a communication interface (120). The network (130) may be the Internet, the Internet and / or an extranet, or an intranet and / or an extranet communicating with the Internet. In some cases, the network (130) is a telecommunications and / or data network. The network (130) may include one or more computer servers capable of enabling distributed computing, such as cloud computing. In some cases, the network (130) may implement a peer-to-peer network with the help of the computer system (101), which may enable devices coupled to the computer system (101) to act as clients or servers.

[0170] The CPU (105) may execute a sequence of machine-readable instructions that may be implemented as a program or software. The instructions may be stored in a memory location such as memory (110). The instructions may be directed to the CPU (105), and the CPU (105) may subsequently be programmed or otherwise configured to implement the methods of the present disclosure. Examples of operations performed by the CPU (105) may include fetching, decoding, execution, and writeback.

[0171] The CPU (105) may be part of a circuit such as an integrated circuit. One or more other components of the system (101) may be included in the circuit. In some cases, the circuit is an application-specific integrated circuit (ASIC).

[0172] The storage unit (115) can store files such as drivers, libraries, and stored programs. The storage unit (115) can store user data, for example, user preferences and user programs. In some cases, the computer system (101) may include one or more additional data storage units located outside the computer system (101), such as on a remote server that communicates with the computer system (101) via an intranet or the Internet.

[0173] A computer system (101) can communicate with one or more remote computer systems through a network (130). For example, the computer system (101) can communicate with a user's remote computer system. Examples of remote computer systems include personal computers (e.g., portable PCs), slates or tablet PCs (e.g., Apple® iPad, Samsung® Galaxy Tab), telephones, smartphones (e.g., Apple® iPhone, Android-enabled devices, Blackberry®), or personal digital assistants. A user can access the computer system (101) through the network (130).

[0174] The methods described herein may be implemented by machine-executable code (e.g., computer processor) stored on electronic storage locations of a computer system (101), such as memory (110) or electronic storage unit (115). Machine-executable or machine-readable code may be provided in the form of software. During use, the code may be executed by the processor (105). In some cases, the code may be retrieved from the storage unit (115) and stored on memory (110) for ready access by the processor (105). In some situations, the electronic storage unit (115) may be excluded, and machine-executable instructions are stored on memory (110).

[0175] The code can be pre-compiled and configured for use with a machine having a processor adapted to execute the code, or it can be compiled at runtime. The code can be supplied in a programming language that can be selected to enable the code to be executed in a pre-compiled or compiled manner.

[0176] The systems and methods provided herein, such as aspects of a computer system (101), may be implemented by programming. Various aspects of the technology may typically be conceived as “products” or “manufactured articles” in the form of associated data that are executed or implemented in the form of machine (or processor) executable code and / or machine-readable media. Machine executable code may be stored on electronic storage units such as memory (e.g., read-only memory, random access memory, flash memory) or hard disks. “Storage” type media may include any or all of the tangible memory of computers, processors, etc., or associated modules thereof, such as various semiconductor memories, tape drives, disk drives, etc., which may provide non-transient storage at any time for software programming. All or part of the software may occasionally be communicated via the Internet or various other telecommunication networks. For example, such communications may enable the loading of software from one computer or processor to another computer or processor, for example, from a management server or host computer to a computer platform of an application server. Accordingly, other types of media capable of holding software elements include, for example, optical, electric, and electromagnetic waves across physical interfaces between local devices, through wired and optical wired networks, and through various air links. Physical elements carrying such waves, such as wired or wireless links, optical links, etc., may also be considered as media holding software. As used herein, terms such as computer or machine "readable medium" refer to any medium participating in providing instructions to a processor for execution, unless limited to non-transient tangible "storage" media.

[0177] Accordingly, machine-readable media, such as computer-executable code, may take many forms, including but not limited to tangible storage media, carrier wave media, or physical transmission media. Non-volatile storage media include optical or magnetic disks, such as any of the storage devices in any computer(s), such as those that may be used to implement databases, etc., as illustrated in the drawings. Volatile storage media include dynamic memory, such as the main memory of such computer platforms. Tangible transmission media include coaxial cables, copper wires, and optical fibers, including wires containing buses within a computer system. Carrier wave transmission media may take the form of electrical or electromagnetic signals, such as those generated during RF (radio frequency) and infrared (IR) data communications, or sound waves or light waves. Accordingly, general forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, or DVD-ROMs, any other optical media, punch cards, paper tapes, any other physical storage media having patterns of holes, RAM, ROM, PROM, EPROM, FLASH-EPROM, any other memory chip or cartridge, carrier waves transmitting data or instructions, cables or links transmitting such carrier waves, or any other media in which a computer can read programming code and / or data. Most of the various forms of computer-readable media may be involved in returning one or more sequences of one or more instructions to a processor for execution.

[0178] The computer system (101) may include or communicate with an electronic display (135) that includes a user interface (UI) (140). Examples of UIs include, without limitation, graphical user interfaces (GUI) and web-based user interfaces.

[0179] The methods and systems of the present disclosure may be implemented by one or more algorithms. The algorithm may be implemented by software during execution by the central processing unit (105). The algorithm may, for example, implement methods for performing non-traditional calculations described herein.

[0180] Examples

[0181] In the following example, the 10 nuclear spin levels of strontium-87 (I = 9 / 2) were modeled to demonstrate a 2-level system (i.e., a qubit). To achieve spectral isolation of qubit transitions, a Stark shift scheme was used to shift unwanted transitions away from the qubit frequency. The isolation schemes can improve effective isolation for achievable Rabi frequencies, reduce the impact on actual qubit states through shifts or residual scattering, may not require perfect polarization control, and may be accessible with reasonable amounts of optical power, etc. 1 S0 or 3 The properties of P1 resonance have been characterized.

[0182] In Fig. 10a, three related nuclear spin states: m that makes the qubit subspace and leakage level 5 / 2. F A toy model was utilized to demonstrate the shifts of the 9 / 2 and 7 / 2 levels. Here, the behavior of a single circularly polarized global AC Stark beam addressing an array of atoms in a 700 Gauss magnetic field was simulated. Additionally, a polarization purity of 100:1 was assumed for the intended circular polarization. 1 From S0 3In each detuning of the AC Stark beam to P1, shifts were experienced for each nuclear spin level. To be clearer, the qubit frequency (m F = 9 / 2 and m F = 7 / 2 (difference between dressed energies) and leakage transition frequency (m F = 7 / 2 and m F = Difference between 5 / 2 dressing states) Both were plotted.

[0183] FIG. 10b illustrates that Stark shifting significantly shifts the leakage transition while having a minimal effect on the qubit frequency. This relates to level splitting at high magnetic fields. 3 This can be made possible by the narrow linewidth of the P1 resonance. Although the frequencies are plotted as signed quantities, the nuances associated with the quantization axis and optical transmission make the absolute values ​​of these frequencies relevant, and in such features, cases appear where Stark shifts push the leakage state very close to the qubit frequency. For each detuning, given the frequency crowding, the maximum available Rabi frequency achievable can be defined. Using this 2-photon Rabi frequency, the pi-pulse time can be inferred, and the number of scattering events caused by the off-resonant interaction of the AC Stark beam can be observed (Fig. 10a).

[0184] Here, no distinction is made between Raman scattering and Rayleigh scattering, and accordingly, it is assumed to be a worst-case scenario for AC Stark-induced scattering errors per gate. To perform single qubit gates, 3 Light was coherently controlled to operate a 2-photon transition using two beams detuned from the P1 resonance. 3 Residual scattering from any of the P1 manifold states can be inherently low due to the 7 kHz linewidth of the transition. Including the effects of the AC Stark shifting beam, 3The diffusion of P1 hyperfine magnetic sublevels can be utilized to separate the energy scales between AC Stark beams detuned from an F = 1 1 / 2 manifold and multi-photon 1Q light detuned from an F = 7 / 2 manifold. Simple toy models involving two ground states and several excited states were sufficient to gain insight into the scaling of powers, spot sizes, and achievable Laby rates. However, the infinite number of accompanying levels, including all of their magnetic sublevels ( 1 S0(F=9 / 2), 3 Due to P1 (F=7 / 2, 9 / 2, 11 / 2), it may be necessary to perform full-scale simulations including all relevant levels. To verify the overall operation, a numerical model was constructed utilizing all 40 levels with multiple optical fields to represent both desired and unwanted polarization. By utilizing simple square pulses, it can be seen that transitions to other nuclear spin states can be suppressed by the AC Stark beam (Figs. 11a and 11b).

[0185] FIGS. 12a and 12b illustrate arrays of trapping light generated by an SLM in a square array and an arbitrary array, etc. 813 nm light from a spatial light modulator (SLM) 1 S0→ 3Holograms were generated by reflecting the magic wavelength for the P0 transition. The active area of ​​the SLM was a 1920x1152 array of square pixels, approximately 9 microns on each side. Each pixel contains a certain volume of liquid crystal that imparts a phase shift to the incident light. This phase shift is controllable by the voltage applied to the pixel, thereby creating an arbitrary pixelated phase mask that can be applied to any unstructured light incident on the surface of the SLM. The SLM is positioned such that a large collimated beam is incident and phase-shifted; subsequently, the light reflected from the SLM is directed through the microscope objective lens. This configuration connected the plane of the SLM to the plane below the lens (where the atomic cloud is formed) by the Fourier conjugate. The complex in-plane electric field in the SLM is the Fourier transform of the pseudo-field in the plane below the microscope objective lens over the volume of the glass cell. The atoms underwent a trapping potential proportional to the electric field strength and consequently underwent lateral confinement. Longitudinal confinement originates from structured light passing through the focus, and its position is also partially determined by the SLM (and thus controllable by the SLM).

[0186] 2,000 traps were generated at a depth of 500 microkelvin, which is more than 1,000 times greater than the recoil energy imparted by scattering photons for imaging or other purposes. This implies that the device must remain well within a regime where hundreds of measurements can be taken without atoms being lost due to heating, even without additional cooling. Once cooled to the atomic motion ground state, the atomic positions are known to be within 20 nm, which enables a significant separation of scales between the atomic positions and the sizes of the laser beams used to drive single and 2-qubit gates or Rydberg interaction length scales. The laser beams driving the gate operations will have a spatial range on the micron scale, and therefore the intensity is level 10-5 It will change from; therefore, a fidelity of .9999 is expected to be easily achievable. In this way, gate fidelity is less sensitive to the positions of the atoms.

[0187] Although preferred embodiments of the present invention have been illustrated and described herein, it will be apparent to those skilled in the art that such embodiments are provided merely as examples. Now, without departing from the present invention, numerous modifications, alterations, and substitutions will be conceived by those skilled in the art. It should be understood that various alternatives to the embodiments of the present invention described herein may be utilized when practicing the present invention. The following claims define the scope of the present invention, and methods and structures and equivalents thereof within the scope of these claims are intended to be covered by the claims.

Claims

Claim 1 A system for performing non-classical computation comprises: one or more state preparation units configured to cool a plurality of atoms — said one or more state preparation units include a first magneto-optical trap (MOT) configured to cool said plurality of atoms to a first temperature —; one or more optical trapping units configured to generate a plurality of spatially distinct optical trapping sites — said plurality of spatially distinct optical trapping sites are configured to trap said plurality of atoms, said plurality of atoms include more than 60 atoms —; one or more electromagnetic transfer units configured to apply electromagnetic energy to one or more of said plurality of atoms to induce said one or more atoms to adopt a superposition state of a first atomic state and at least one second atomic state different from said first atomic state; and one or more entanglement units configured to quantum mechanically entangle at least a subset of said one or more atoms in said superposition states with at least another atom among said plurality of atoms. A system for performing non-traditional calculations, comprising one or more readout optical units configured to perform one or more measurements of one or more superposition states to obtain the non-traditional calculations. Claim 2 In a system for performing non-classical computation, one or more state preparation units configured to cool a plurality of atoms — said one or more state preparation units include a Zeeman slowerer configured to decelerate said plurality of atoms from a first velocity or a distribution of velocities to a second velocity lower than said first velocity or a distribution of velocities — ; A system for performing a non-traditional computation, comprising: one or more optical trapping units configured to generate a plurality of spatially distinct optical trapping sites ― said plurality of spatially distinct optical trapping sites are configured to trap said plurality of atoms, said plurality of atoms include more than 60 atoms ―; one or more electromagnetic transfer units configured to apply electromagnetic energy to one or more of said plurality of atoms to induce said one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from said first atomic state; one or more entanglement units configured to quantum mechanically entangle at least a subset of said one or more atoms in said superposition states with at least another atom among said plurality of atoms; and one or more readout optical units configured to perform one or more measurements of said one or more superposition states to obtain said non-traditional computation. Claim 3 A system for performing non-traditional calculations, wherein, in claim 1 or 2, the non-traditional calculation includes quantum calculation. Claim 4 In paragraph 3, the quantum computation is a system for performing non-traditional computation, including gate-model quantum computation. Claim 5 A system for performing non-traditional calculations, wherein, in claim 1 or 2, the plurality of atoms includes neutral atoms. Claim 6 A system for performing non-traditional calculations according to claim 1 or 2, wherein the plurality of atoms include rare earth atoms. Claim 7 In paragraph 6, a system for performing non-traditional calculations, wherein the rare earth atoms include ytterbium atoms. Claim 8 A system for performing non-traditional calculations according to claim 1 or 2, wherein the plurality of atoms include alkali atoms. Claim 9 A system for performing non-traditional calculations according to claim 1 or 2, wherein the plurality of atoms include alkaline earth atoms. Claim 10 In claim 9, the alkaline earth atoms include strontium atoms, a system for performing non-traditional calculations. Claim 11 In paragraph 10, the above strontium atoms include strontium-87 atoms, a system for performing non-traditional calculations. Claim 12 A system for performing non-traditional calculations according to claim 1 or 2, wherein the plurality of spatially distinct optical trapping sites comprise one or more optical tweezers. Claim 13 A system for performing non-traditional calculations according to claim 1 or 2, wherein the plurality of spatially distinct optical trapping sites comprises one or more optical grating sites of one or more optical gratings. Claim 14 A system for performing non-traditional calculations, wherein the one or more optical gratings comprises one or more members selected from a group consisting of one-dimensional (1D) optical gratings, two-dimensional (2D) optical gratings, and three-dimensional (3D) optical gratings. Claim 15 A system for performing non-traditional calculations according to claim 1 or 2, wherein the one or more optical trapping units comprise one or more spatial light modulators (SLMs) configured to generate the plurality of optical trapping sites. Claim 16 In paragraph 15, the system for performing non-traditional computation comprises one or more SLMs, each comprising one or more digital micromirror devices (DMDs) or one or more LCoS (liquid crystal on silicon) devices. Claim 17 A system for performing non-traditional calculations according to claim 1 or 2, wherein the one or more optical trapping units comprise one or more imaging units configured to acquire one or more images of the spatial configuration of the plurality of atoms trapped within the plurality of spatially distinct optical trapping sites. Claim 18 A system for performing non-traditional computation according to claim 17, wherein the one or more images comprise one or more members selected from the group consisting of fluorescence images, single-atom fluorescence images, absorption images, single-atom absorption images, phase contrast images, and single-atom phase contrast images. Claim 19 A system for performing non-traditional calculations, wherein the one or more optical trapping units comprise one or more atomic rearrangement units configured to impart a modified spatial arrangement of the plurality of atoms trapped within the plurality of spatially distinct optical trapping sites based on the one or more images. Claim 20 In claim 1, the first MOT is a system for performing non-traditional calculations, comprising a three-dimensional (3D) MOT. Claim 21 A system for performing non-traditional calculations according to claim 1, wherein one or more of the state preparation units further comprises a second MOT configured to cool the plurality of atoms from the first temperature to a second temperature lower than the first temperature. Claim 22 A system for performing non-traditional computation according to claim 1 or 2, wherein the one or more electromagnetic transfer units comprise one or more spatial light modulators (SLM), acousto-optic devices (AOD), or acousto-optic modulators (AOM) configured to selectively apply the electromagnetic energy to one or more of the plurality of atoms. Claim 23 In paragraph 22, the system for performing non-traditional computation comprises one or more electromagnetic transfer units, each comprising one or more digital micromirror devices (DMD) or one or more liquid crystal on silicon (LCoS) devices. Claim 24 A system for performing non-traditional calculations, comprising, in claim 1 or 2, further comprising one or more atomic reservoirs configured to supply one or more replacement atoms to replace one or more atoms at one or more optical trapping sites among the plurality of spatially distinct optical trapping sites upon loss of one or more atoms from the one or more optical trapping sites. Claim 25 A system for performing non-traditional calculations according to claim 24, further comprising one or more atomic movement units configured to move the one or more replacement atoms to the one or more optical trapping sites. Claim 26 A system for performing non-traditional calculations, wherein the one or more entanglement units comprise one or more Rydberg excitation units configured to electronically excite the at least subset of the one or more atoms in the one or more superposition states to a Rydberg state or to a superposition state of the Rydberg state and a lower energy atomic state to form one or more Rydberg atoms or a dressed Rydberg atom. Claim 27 In claim 1 or 2, the system is a system for performing non-traditional computations, which is operably coupled to a digital computer via a network. Claim 28 In paragraph 27, the network is a system for performing non-traditional computation, including a cloud computing network. Claim 29 A method for performing non-traditional computation comprises: (a) cooling a plurality of atoms with one or more state preparation units — said one or more state preparation units include a first magneto-optical trap (MOT) configured to cool said plurality of atoms to a first temperature —; (b) generating a plurality of spatially distinct optical trapping sites — said plurality of spatially distinct optical trapping sites are configured to trap a plurality of atoms, said plurality of atoms include more than 60 atoms —; (c) applying electromagnetic energy to one or more of said plurality of atoms to induce said one or more atoms to adopt a superposition state of a first atomic state and at least one second atomic state different from said first atomic state; (d) quantum mechanically entangling at least a subset of said one or more atoms in the superposition state with at least another atom among said plurality of atoms; and (e) a method for performing a non-traditional calculation, comprising the step of performing one or more measurements of one or more superposition states to obtain the non-traditional calculation. Claim 30 A method for performing non-traditional computation comprises: (a) cooling a plurality of atoms with one or more state preparation units — said one or more state preparation units include a Zeeman slowerer configured to decelerate said a plurality of atoms from a first velocity or a distribution of velocities to a second velocity lower than said first velocity or a distribution of velocities —; (b) generating a plurality of spatially distinct optical trapping sites — said one or more spatially distinct optical trapping sites are configured to trap a plurality of atoms, said one or more atoms include more than 60 atoms —; (c) applying electromagnetic energy to one or more of said atoms to induce said one or more atoms to adopt a superposition state of a first atomic state and at least one second atomic state different from said first atomic state; (d) quantum mechanically entangling at least a subset of said one or more atoms in the superposition state with at least another atom among said a plurality of atoms; and (e) a method for performing a non-traditional calculation, comprising the step of performing one or more measurements of one or more superposition states to obtain the non-traditional calculation. 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