Scalable neutral atom-based quantum computing

Abstract

In one embodiment, the present disclosure provides a method comprising the steps of providing a plurality of atoms. At least one atom of the plurality of atoms can have a different state from one or more other atoms of the plurality of atoms. At least one atom can be excited to an excited state. The excitation can be performed using a non-site-selective excitation beam that spans the plurality of atoms and only interacts with at least one atom.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of U.S. Provisional Application No. 63 / 189,660, filed May 17, 2021, which is incorporated herein by reference.

[0002] STATEMENT REGARDING FEDERALLY FUNDED RESEARCH This invention was made with United States Government support under Small Business Innovation Research Grants Nos. 1843926 and 1951188 awarded by the National Science Foundation. The United States Government has certain rights in this invention. [Background technology]

[0003] Quantum computers typically exploit quantum mechanical phenomena such as superposition and entanglement to perform operations on data. Quantum computers can be different from digital electronic computers, which are based on transistors. For example, while digital computers must encode data into binary digits (bits) where each bit is always in one of two distinct states (0 or 1), quantum computing uses quantum bits (qubits) that can be in a superposition of states. Summary of the Invention [Problem to be solved by the invention]

[0004] There is a need herein for methods and systems for performing non-classical computations.

[0005] The present disclosure provides systems and methods for utilizing atoms (such as neutral or uncharged atoms) to perform non-classical or quantum computations. The atoms may be optically trapped in large arrays. The quantum mechanical states of the atoms (such as the atomic hyperfine or nuclear spin states) may be configured to serve as quantum bit (qubit) basis states. The qubit states may be manipulated by interaction with light, radio frequency, or other electromagnetic radiation, thereby performing non-classical or quantum computations. [Means for solving the problem]

[0006] In one aspect, the present disclosure provides a system for performing non-classical computation, the system including: a plurality of trapping sites configured to trap a plurality of atoms, the plurality of atoms corresponding to a plurality of qubits; an optical unit configured to provide a first light and a second light; a first optical modulator configured to receive the first light and direct the first light along a plurality of first optical paths to at least a subset of the plurality of trapping sites, the at least the subset of trapping sites including at least two trapping sites; a second optical modulator configured to receive the second light and direct the second light along a plurality of second optical paths to at least the subset of the trapping sites; and a controller operatively coupled to the optical unit, the controller configured to instruct the optical unit to emit the first light and to emit the second light to implement one or more multiple qubit operations on at least a subset of atoms of the plurality of atoms trapped at the at least the subset of trapping sites, the at least the subset of atoms including at least two atoms.

[0007] In some embodiments, the first light modulator and the second light modulator are oriented such that the frequency difference between the first light and the second light is substantially constant at each capture site of at least a subset of the capture sites. In some embodiments, the plurality of first light paths includes one or more first positive order light paths and one or more first negative order light paths, and the plurality of second light paths includes one or more second positive order light paths and one or more second negative order light paths. In some embodiments, the first positive order light path and the second negative order light path each terminate at the same capture site of at least a subset of the capture sites, or the first negative order light path and the second positive order light path each terminate at the same capture site of at least a subset of the capture sites. In some embodiments, the first positive order light path is substantially parallel to the second negative order light path, or the first negative order light path is substantially parallel to the second positive order light path. In some embodiments, the first positive order path and the second negative order path each terminate at the same trapping site of at least a subset of the trapping sites, or the first negative order path and the second negative order path each terminate at the same trapping site of at least a subset of the trapping sites. In some embodiments, the first optical modulator or the second optical modulator comprises an acousto-optical deflector (AOD). In some embodiments, the first optical modulator or the second optical modulator comprises a two-dimensional (2D) AOD. In some embodiments, the first optical modulator or the second optical modulator comprises a pair of crossed one-dimensional (1D) AODs. In some embodiments, the one or more qubit operations comprise one or more single qubit operations. In some embodiments, the one or more single qubit operations comprise one or more single qubit gate operations. In some embodiments, the one or more qubit operations comprise one or more two-qubit operations. In some embodiments, the one or more two-qubit operations comprise one or more two-qubit gate operations. In some embodiments, the one or more qubit operations comprise a multi-qubit operation. In some embodiments, the one or more qubit operations include one or more multi-qubit gate operations. In some embodiments, the first wavelength of the first light is different from the second wavelength of the second light.In some embodiments, the first wavelength of the first light is the same as the second wavelength of the second light. In some embodiments, the one or more qubit operations include one or more two-photon excitations of at least a subset of the atoms. In some embodiments, the one or more qubit operations include one or more Rydberg excitations of at least a subset of the atoms. In some embodiments, the first light and the second light arrive at at least a subset of the trapping sites substantially simultaneously. In some embodiments, the first light and the second light overlap at each trapping site of at least a subset of the trapping sites. In some embodiments, the plurality of atoms comprises a 2D array of atoms. In some embodiments, at least a subset of the atoms comprises a one-dimensional (1D) line of atoms of the 2D array of atoms. In some embodiments, the plurality of atoms comprises a three-dimensional (3D) array of atoms. In some embodiments, at least a subset of the atoms comprises a 1D line of atoms of the 3D array of atoms. In some embodiments, at least a subset of the atoms comprises a 2D array of atoms of the 3D array of atoms. The system of claim 1, further comprising one or more phase or wavelength modulators configured to modulate a phase or wavelength of the first light or the second light. In some embodiments, the one or more phase or wavelength modulators are disposed between the optical unit and the first optical modulator or between the optical unit and the second optical modulator. In some embodiments, the one or more phase or wavelength modulators include one or more members selected from the group consisting of an electro-optic modulator (EOM) and an acousto-optic modulator (AOM). In some embodiments, the optical unit comprises a single light source configured to emit light and one or more beam splitters configured to receive the light and split the light into the first light and the second light. In some embodiments, the optical unit comprises a first light source configured to emit the first light and a second light source configured to emit the second light. In some embodiments, the at least a subset of the capture sites includes all of the capture sites of the plurality of capture sites.

[0008] In another aspect, the present disclosure provides a method for performing non-classical computation, the method comprising: (a) activating a non-classical computation unit including (i) a plurality of capture sites, (ii) an optical unit, (ii) a first optical modulator, and (iv) a second optical modulator; (b) using the plurality of capture sites to capture a plurality of atoms, the plurality of atoms corresponding to a plurality of qubits; (c) providing a first light and a second light using the optical unit; and (d) receiving the first light using the first optical modulator and modulating the first light along a plurality of first optical paths. (e) receiving a second light using a second optical modulator and directing the second light along multiple optical paths to at least the subset of the trapping sites, where the at least the subset of the trapping sites comprises at least two trapping sites; and (f) using the first light and the second light to implement one or more qubit operations on at least a subset of the atoms of the plurality of atoms trapped at the at least the subset of the trapping sites, where the at least the subset of atoms comprises at least two atoms.

[0009] In another aspect, the present disclosure provides a method for selecting an atom from a plurality of atoms, the method including: (a) applying a first pulse to the plurality of atoms, the plurality of atoms including the atom and one or more other atoms; (b) applying a second pulse to the atom but not to the one or more other atoms; and (c) applying a third pulse to the plurality of atoms, thereby exciting at least one qubit state of the atom and providing a selected atom.

[0010] In some embodiments, the first pulse comprises a π / 2 pulse. In some embodiments, the second pulse comprises a 2π pulse. In some embodiments, the third pulse comprises a −π / 2 pulse. In some embodiments, the first pulse and the third pulse are opposite in sign to each other. In some embodiments, the selected atom is addressable by a different light than one atom of the plurality of atoms. In some embodiments, (a)-(c) provide a change in state of at least one of the atoms, but not each of the other atoms of the plurality of atoms. In some embodiments, the method further comprises applying a magnetic field across the plurality of atoms. In some embodiments, the first pulse or the third pulse is an electromagnetic pulse and is polarized. In some embodiments, the polarization is circular or π polarization. In some embodiments, the polarization is linear polarization. In some embodiments, the plurality of atoms comprises atoms having two valence electrons. In some embodiments, the first pulse and the third pulse have a ratio of magnitudes of at least about 0.95. In some embodiments, the first pulse and the third pulse are applied to different transitions of the plurality of atoms as the second pulse. In some embodiments, the method further comprises (d) imaging the selected atoms.

[0011] In another aspect, the disclosure provides a method, the method including: (a) providing a plurality of atoms, where at least one atom of the plurality of atoms has a different state than one or more other atoms of the plurality of atoms; and (b) exciting the at least one atom to an excited state, where the excitation is performed using a non-site selective excitation beam across the plurality of atoms that interacts only with the at least one atom.

[0012] In some embodiments, the non-site-selective excitation beam is applied to at least two atoms of the plurality of atoms. In some embodiments, the non-site-selective excitation beam is applied to each atom of the plurality of atoms. In some embodiments, the excited states are Rydberg states. In some embodiments, the excitation is time-domain multiplexed. In some embodiments, the method is at least a part of a universal set of qubit gate operations. In some embodiments, the non-site-selective excitation beam comprises an ultraviolet excitation beam. In some embodiments, the method further comprises, simultaneously with (b), exciting at least another atom of the plurality of atoms using the same excitation beam, where the at least another atom does not interact with the at least one atom. In some implementations, the method further comprises, after (b), exciting at least another atom of the plurality of atoms using the same excitation beam, where the at least another atom does not interact with the at least one atom. In some embodiments, the at least one atom is used in a qubit gate operation. In some embodiments, the method further comprises exciting a second atom and using the second atom with the at least one atom in a two-qubit gate.

[0013] In another aspect, the disclosure provides a method, the method including: (a) selecting an atom from a plurality of atoms; and (b) applying a site-selective pulse to the atom, the site-selective pulse configured to provide a differential shift between a ground state of the atom and a clock manifold compared to the plurality of atoms.

[0014] In some embodiments, the site-selective pulse is an off-resonance pulse. In some embodiments, the site-selective pulse is applied only to the atom and not to the plurality of atoms. In some embodiments, the atom is not addressable by the same light beam as the plurality of atoms as a result of the site-selective pulse. In some embodiments, the method further comprises, after (b), applying a shelving light pulse to the atom and the plurality of atoms. In some embodiments, the shelving light pulse does not interact with the atom.

[0015] Additional aspects and advantages of the present disclosure will become readily apparent to those skilled in the art from the following detailed description, in which only illustrative embodiments of the present disclosure are shown and described. As will be understood, the present disclosure is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the present disclosure. Accordingly, the drawings and description should be regarded as illustrative in nature and not restrictive.

[0016] Citation by reference All publications, patents, and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference. To the extent that the publications and patents or patent applications incorporated by reference conflict with the disclosure contained in the specification, the specification is intended to supersede and / or take precedence over such conflicting material. [Brief description of the drawings]

[0017] The novel features of the invention are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings (herein also referred to as "Figure" and "FIG."). [Figure 1]FIG. 1 illustrates a computer control system programmed or otherwise configured to carry out the methods provided herein. [Diagram 2] FIG. 1 illustrates an example of a system for performing non-classical computation. [Figure 3A] FIG. 2 illustrates an example of a light capture unit. [Figure 3B] FIG. 1 shows an example of multiple light capture sites. [Figure 3C] FIG. 1 shows an example of a light-trapping unit partially filled with atoms. [Figure 3D] FIG. 1 shows an example of a light-trapping unit completely filled with atoms. [Figure 4] FIG. 1 illustrates an example of an electromagnetic delivery unit. [Diagram 5] FIG. 13 illustrates an example of a state preparation unit. [Figure 6] FIG. 2 illustrates a flowchart of a first example method for performing non-classical computation. [Figure 7] FIG. 2 shows a flowchart of an example of a second method for performing non-classical computation. [Figure 8] FIG. 13 is a flowchart of an example of a third method for performing non-classical computation. [Figure 9] FIG. 2 shows an example of a qubit containing the 3P2 state of strontium-87. [Figure 10A] Stark shift simulation of the 1S0 hyperfine state of strontium-87. [Figure 10B] Stark shift simulation of the 1S0 hyperfine state of strontium-87. [Figure 11A] Simulation of single-qubit control by the Stark shift. [Figure 11B] Simulation of single-qubit control by the Stark shift. [Figure 12A] FIG. 1 shows an example of an array of captured light generated by an SLM. [Figure 12B]FIG. 1 shows an example of an array of captured light generated by an SLM. [Figure 13] FIG. 1 illustrates an optical system for delivering four different wavelengths. [Figure 14] FIG. 1 illustrates the trapping and cooling of strontium-87 and strontium-88 atoms using red-light magnetic trapping (MOT). [Figure 15A] FIG. 1 illustrates the energy level structure for single-qubit and multi-qubit operations in strontium-87. [Figure 15B] FIG. 1 illustrates an optical system for delivering light to perform single and multi-qubit operations on multiple trapped atoms in parallel. [Figure 15C] FIG. 1 illustrates an optical system configured to dynamically generate and control beams using a single electro-optic modulator (EOM) and two acousto-optic deflectors (AODs), for each beam, each driven by an RF signal from an arbitrary waveform generator. [Figure 16A] FIG. 1 shows a simulation of two atoms in an initial diatomic state. [Figure 16B] FIG. 13 shows a simulation of two atoms in an initial two-atom state with an inverse adiabatic driving field applied to implement a transition-free quantum driving gate. [Figure 16C] FIG. 13 shows an example of differential removal by adiabatic gate (DRAG) pulse. [Figure 17A] FIG. 13 shows a calibration image of a completely filled 7×7 array of light capture sites. [Figure 17B] FIG. 1 shows labeling of filled and unfilled light capture sites in a 7×7 array. [Figure 17C] FIG. 13 shows 25×25 pixel binning around each light capture site in a 7×7 array. [Figure 17D] FIG. 1 shows the identification of each capture site in a 7×7 array as filled or unfilled. [Figure 17E]FIG. 13 illustrates the transfer from a filled optical trapping site to an unfilled optical trapping site, avoiding collisions between atoms. [Figure 18A] FIG. 1 illustrates the spatial frequency of two light beams steered by separate two-dimensional (2D) AODs in a non-inverting configuration. [Figure 18B] FIG. 1 illustrates the spatial frequency of two light beams steered by separate two-dimensional (2D) AODs in an inverted configuration. [Figure 18C] FIG. 1 illustrates an example of how to address atoms held in a two-dimensional rectangular array, according to one embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] While various embodiments of the present invention have been shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions may occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the present invention described herein may be employed.

[0019] Unless otherwise specified, all technical terms used herein have the same meaning as commonly understood by those skilled in the art to which this invention belongs. As used in this specification and the appended claims, the singular forms "a", "an" and "the" include plural references unless the context clearly dictates otherwise. Any reference to "or" in this specification is intended to include "and / or" unless otherwise specified.

[0020] Whenever the terms "at least," "greater than," or "greater than or equal to" are placed before or after the first number in a series of two or more numbers, the terms "at least," "greater than," or "greater than or equal to" apply to every number in the series. For example, 1, 2, or 3 or more is equivalent to 1 or more, 2 or more, or 3 or more.

[0021] Whenever the terms "no more than," "less than," "less than or equal to," or "at most" appear before or after the first number in a series of two or more numbers, the terms "no more than," "less than," "less than" or "at most" apply to each number in the series. For example, 3, 2, or 1 or less is equivalent to 3 or less, 2 or less, or 1 or less.

[0022] Where values ​​are described as ranges, such disclosure will be understood to include disclosure of all possible subranges within such ranges, as well as specific numerical values ​​falling within such ranges, whether or not a specific numerical value or specific subrange is explicitly stated.

[0023] As used herein, like letters refer to like elements.

[0024] 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 enhance or maximize the likelihood of successfully achieving a goal. The term "artificial intelligence" may include "generative modeling," "machine learning" (ML), and / or "reinforcement learning" (RL).

[0025] 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 computer performance of a task. Machine learning may include a machine learning algorithm. 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 by supervised learning (e.g., various parameters are determined as weights or scaling coefficients). 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 ultra-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, least absolute shrinkage and selection operation, least 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 pursuit, Sammon mapping, stochastic neighbor embedding of t-distribution, AdaBoosting, boosting, gradient boosting, bootstrap aggregation, ensemble averaging, decision trees, conditional decision trees, boosted decision trees, gradient boosted decision trees, random forests, stacked generalization, The neural network may include, but is not limited to, a Bayesian network, a Bayesian belief network, a naive Bayes, a Gaussian naive Bayes, a multinomial naive Bayes, a hidden Markov model, a hierarchical hidden Markov model, a support vector machine, an encoder, a decoder, an autoencoder, a stacked autoencoder, a perceptron, a multilayer perceptron, an artificial neural network, a feedforward neural network, a convolutional neural network, a recurrent neural network, a long short-term memory, a deep belief network, a deep Boltzmann machine, a deep convolutional neural network, a deep recurrent neural network, or a generative adversarial network.

[0026] As used herein, the terms "reinforcement learning," "reinforcement learning procedure," "reinforcement learning operation," and "reinforcement learning algorithm" generally refer to any system or computational procedure that performs one or more actions to reinforce or maximize some concept of a cumulative reward for interacting with an environment. An agent executing a reinforcement learning (RL) procedure may receive positive or negative reinforcement, called an "instantaneous reward," for performing one or more actions in an environment, thereby bringing itself and the environment into various new states.

[0027] The goal of an agent may be to enhance or maximize some notion of cumulative reward. For example, the goal of an agent may be to enhance or maximize a “discounted reward function” or an “average reward function.” A “Q-function” may represent the maximum cumulative reward that can be obtained from a state and an action taken in that state. A “value function” and a “generalized advantage estimator” may represent the maximum cumulative reward that can be obtained from a state given an optimal or best choice of action. RL may utilize any one or more of such notions of cumulative reward. As used herein, such functions may be referred to as “cumulative reward functions.” Thus, computing the best or optimal cumulative reward function may be equivalent to finding the best or optimal policy for an agent.

[0028] The interaction of the agent with its environment may be formulated as one or more Markov Decision Processes (MDPs). RL procedures may not assume knowledge of an exact mathematical model of the MDP. The MDP may be completely unknown, partially known, or completely known to the agent. RL procedures may be in a spectrum between two ranges, "model-based" or "model-free", with respect to prior knowledge of the MDP. As such, RL procedures may target large MDPs where exact methods may be infeasible or unavailable due to the unknown or stochastic nature of the MDP.

[0029] The RL procedure may be implemented using one or more computer processors as described herein. The digital processing unit may utilize an agent that trains, stores, and later deploys a "policy" to enhance or maximize cumulative reward. The policy may be explored (e.g., searched) as far as possible or over a desired period of time. Such optimization problems may be solved by saving an approximation of the optimal policy, saving an approximation of a cumulative reward function, or both. In some cases, the RL procedure may store one or more tables of approximations of such functions. In other cases, the RL procedure may utilize one or more "function approximators."

[0030] 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). The function approximator may create a parameterization that is an approximation of the cumulative reward function. Optimizing the function approximation with respect to the parameterization may consist of perturbing the parameters in a direction that enhances or maximizes the cumulative reward and thus enhances or optimizes the policy (e.g., policy gradient methods), or by perturbing the function approximator to come closer to satisfying Bellman optimality criterion (e.g., time lag methods).

[0031] During training, the agent may perform actions in the environment to acquire more information about the environment and about the appropriate or best choice of policy for survival or better utility. The agent's actions may be randomly generated (e.g., especially in the early stages of training) or may be prescribed by another machine learning paradigm (such as supervised learning, imitation learning, or any other machine learning procedure described herein). The agent's actions may be refined by selecting an action that is closer to the agent's perception of what the enhanced or optimal policy is. Various training strategies may lie on the spectrum between two ranges, off-policy and on-policy, in terms of choosing between exploration and exploitation.

[0032] As used herein, the terms "nonclassical computation," "nonclassical procedure," "nonclassical operation," or any "nonclassical computer" generally refer to any method or system for performing a computational procedure outside the paradigm of classical computing. Nonclassical computation, nonclassical procedure, nonclassical operation, or nonclassical computer may include quantum computation, quantum procedure, quantum operation, or quantum computer.

[0033] 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 in a Hilbert space represented by a quantum device, such as unitary transformations on quantum channels and completely positive trace-preserving (CPTP) maps. Thus, quantum computation and classical (or digital) computation may be similar in the following aspect: both computations may involve a sequence of instructions that are performed on input information and provide an output. Different paradigms of quantum computing may decompose a quantum operation into a sequence of elementary quantum operations that simultaneously affect a subset of qubits of a quantum device. A quantum operation may be selected, for example, based on its locality or ease of physical implementation. A quantum procedure or computation may consist of a sequence of such instructions that may represent different quantum evolutions on a quantum device for various applications. For example, a procedure for calculating or simulating quantum chemistry may be implemented using the so-called Jordan-Wigner transformation. Through the Quantum Transformation (QFT) or Bravyi-Kitaev transformation, quantum states and electron spin-orbit annihilation and creation operators can be represented by using qubits (e.g., two-level quantum systems) and a set of universal quantum gates (e.g., Hadamard, controlled-uncontrolled (CNOT), and π / 8 rotation).

[0034] Additional examples of quantum procedures or computations may include optimization procedures such as quantum approximate optimization algorithms (QAOA) and finding quantum minima. QAOA may include rotating single qubits and performing entanglement gates on multiple qubits. In quantum adiabatic computation, instructions may carry probabilistic or non-probabilistic evolutionary paths from an initial quantum system to a final quantum system.

[0035] Quantum-inspired procedures may include simulated annealing, parallel tempering, master equation solvers, Monte Carlo procedures, etc. Quantum-classical or hybrid algorithms or procedures may include procedures such as the variational quantum eigensolver (VQE) and the variational and adiabatically navigated quantum eigensolver (VanQver).

[0036] The quantum computer may include one or more of an adiabatic quantum computer, a quantum gate array, a one-way quantum computer, a topological quantum computer, a quantum Turing machine, a quantum annealer, an Ising solver, or a gate model of quantum computing.

[0037] As used herein, the term "adiabatic" refers to any process taking place in a quantum mechanical system in which the parameters of the Hamiltonian change slowly compared to the natural timescale of the system's evolution.

[0038] As used herein, the term "non-adiabatic" refers to any process performing quantum mechanical systems in which the parameters of the Hamiltonian change rapidly compared to, or on timescales similar to, the natural timescales of the system's evolution.

[0039] A system for performing non-classical computations In one aspect, the present disclosure provides a system for performing non-classical computations. 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 configured to trap a plurality of atoms, the plurality of atoms including more than 60 atoms, one or more electromagnetic delivery units configured to apply electromagnetic energy to one or more atoms of the plurality of atoms, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state, one or more entanglement units configured to quantum mechanically entangle at least a subset of the one or more atoms in the one or more superposition states with at least another atom of the plurality of atoms, and one or more readout optical units configured to perform one or more measurements of the one or more superposition states to obtain a non-classical computation.

[0040] 2 illustrates an example of a system 200 for performing non-classical computation. The non-classical computation may include quantum computation. The quantum computation may include gate-model quantum computation.

[0041] The system 200 may include one or more capture units 210. The capture units may include one or more light capture units. The light capture units may include any light capture units described herein, such as the light capture units described herein with respect to FIG. 3A. The light capture units may be configured to generate a plurality of light capture sites. The light capture units may be configured to generate a plurality of spatially distinct light capture sites. For example, the ... It may be configured to generate 0, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000, or more light capture sites. The light capture units are available in sizes 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, 1 The light capture unit may be configured to generate 0,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or fewer light capture sites. The light capture unit may be configured to capture a number of light capture sites that are within a range defined by any two of the aforementioned values.

[0042] The light trapping unit can be configured to trap a plurality of atoms. For example, the light trapping unit can trap at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30, In one embodiment, the method may be configured to capture more than 1,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000, or more atoms. The light capture units are at most about 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000 , 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or fewer atoms. The optical capture unit may be configured to capture a number of atoms that are within a range defined by any two of the aforementioned values.

[0043] Each optical capture site of the optical capture unit may be configured to capture at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more atoms. Each optical capture site may be configured to capture up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, or fewer atoms. Each optical capture site may be configured to capture a number of atoms that are within a range defined by any two of the aforementioned values. Each optical capture site may be configured to capture a single atom.

[0044] One or more atoms of the plurality of atoms may include a qubit as described herein (e.g., with respect to FIG. 4). The two or more atoms may be quantum mechanically entangled. The two or more atoms may be quantum entangled for at least about 1 microsecond (μs), 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, 200 μs, 300 μs, 400 μs, 500 μs, 600 μs, 700 μs, 800 μs, 900 μs, 1 millisecond (ms), 2 ms, 3 ms, 4 ms, 5 ms, 6 ms, 7 ms, 8 ms, 9 ms, 10 ms, 10 ms, 15 ms, 20 ms, 25 ms, 30 ms, 40 ms, 50 ms, 60 ms, 70 ms, 80 ms, 90 ms, 100 ms, 200 ms, 300 ms, 400 ms, 500 ms, 600 ms, 700 ms, 800 ms, 900 ms, 1 millisecond (ms), 2 ms, 3 ms, 4 ms, 5 ms, 5 ms, 6 ms, 7 ms, 8 ms, 9 ms, 10 ms, 15 ms, 20 ms, 25 ms, 30 ms, 40 ms, 50 ms, 60 ms, In some embodiments, the quantum mechanical entanglement may be quantum mechanically entangled with a coherence lifetime of 1 s, 6 ms, 7 ms, 8 ms, 9 ms, 10 ms, 20 ms, 30 ms, 40 ms, 50 ms, 60 ms, 70 ms, 80 ms, 90 ms, 100 ms, 200 ms, 300 ms, 400 ms, 500 ms, 600 ms, 700 ms, 800 ms, 900 ms, 1 second (s), 2 s, 3 s, 4 s, 5 s, 6 s, 7 s, 8 s, 9 s, 10 s, or longer. Two or more atoms can be up to about 10s, 9s, 8s, 7s, 6s, 5s, 4s, 3s, 2s, 1s, 900ms, 800ms, 700ms, 600ms, 500ms, 400ms, 300ms, 200ms, 100ms, 90ms, 80ms, 70ms, 60ms, 50ms, 40ms, 30ms, 20ms, 10ms, 9ms, 8ms, 7ms, 6ms, 5ms, 4ms, 3ms, 2ms, 1s ... The atoms may be quantum mechanically entangled with a coherence lifetime of ms, 1 ms, 900 μs, 800 μs, 700 μs, 600 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 shorter. Two or more atoms may be quantum mechanically entangled with a coherence lifetime within a range defined by any two of the aforementioned values. One or more atoms may include neutral atoms. One or more atoms may include uncharged atoms.

[0045] The one or more atoms may include an alkali atom. The one or more atoms may include a lithium (Li) atom, a sodium (Na) atom, a potassium (K) atom, a rubidium (Rb) atom, or a cesium (Cs) atom. The one or more atoms may include a lithium 6 atom, a lithium 7 atom, a sodium 23 atom, a potassium 39 atom, a potassium 40 atom, a potassium 41 atom, a rubidium 85 atom, a rubidium 87 atom, or a cesium 133 atom. The one or more atoms may include an alkaline earth atom. The one or more atoms may include a beryllium (Be) atom, a magnesium (Mg) atom, a calcium (Ca) atom, a strontium (Sr) atom, or a barium (Ba) atom. The 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. The one or more atoms may include a rare earth atom. The one or more atoms may include a scandium (Sc) atom, a yttrium (Y) atom, a lanthanum (La) atom, a cerium (Ce) atom, a praseodymium (Pr) atom, a neodymium (Nd) atom, a samarium (Sm) atom, a europium (Eu) atom, a gadolinium (Gd) atom, a terbium (Tb) atom, a dysprosium (Dy) atom, a holmium (Ho) atom, an erbium (Er) atom, a thulium (Tm) atom, an ytterbium (Yb) atom, or a lutetium (Lu) atom.One or more atoms may be selected from the group consisting of scandium-45, yttrium-89, lanthanum-139, cerium-136, cerium-138, cerium-140, cerium-142, praseodymium-141, neodymium-142, neodymium-143, neodymium-145, neodymium-146, neodymium-148, samarium-144, samarium-149, samarium-150, samarium-152, samarium-154, europium-151, europium-153, gadolinium-154, gadolinium-155, gadolinium-156, gadolinium-157, gadolinium-158, gadolinium-160, terbium-15 9 atoms, dysprosium 156 atoms, dysprosium 158 atoms, dysprosium 160 atoms, dysprosium 161 atoms, dysprosium 162 atoms, dysprosium 163 atoms, dysprosium 164 atoms, erbium 162 atoms, erbium 164 atoms, erbium 166 atoms, erbium 167 atoms, erbium 168 atoms, erbium 170 atoms, holmium 165 atoms, thulium 169 atoms, ytterbium 168 atoms, ytterbium 170 atoms, ytterbium 171 atoms, ytterbium 172 atoms, ytterbium 173 atoms, ytterbium 174 atoms, ytterbium 176 atoms, lutetium 175 atoms, or lutetium 176 atoms.

[0046] The 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. The 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. The plurality of atoms may include a natural isotopic mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. The plurality of atoms may include an isotopically enriched mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. The plurality of atoms may include a natural isotopic mixture of one or more elements selected from the group consisting of Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. The plurality of atoms may include an isotopically enriched mixture of one or more elements selected from the group consisting of Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. The atoms may include rare earth atoms. For example, the plurality of atoms may be selected from the group consisting of lithium 6 atoms, lithium 7 atoms, sodium 23 atoms, potassium 39 atoms, potassium 40 atoms, potassium 41 atoms, rubidium 6 atoms, lithium 7 atoms, sodium 23 atoms, potassium 39 atoms, potassium 40 atoms, potassium 41 atoms, and / or rubidium 7 atoms, enriched to an isotopic abundance of at least about 50%, 60%, 70%, 80%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, 99.1%, 99.2%, 99.3%, 99.4%, 99.5%, 99.6%, 99.7%, 99.8%, 99.9%, 99.91%, 99.92%, 99.93%, 99.94%, 99.95%, 99.96%, 99.97%, 99.98%, 99.99% or more. Umium 85 atom, Rubidium 87 atom, Cesium 133 atom, Beryllium 9 atom, Magnesium 24 atom, Magnesium 25 atom, Magnesium 26 atom, Calcium 40 atom, Calcium 42 atom, Calcium 43 atom, Calcium 44 atom, Calcium 46 atom, Calcium 48 atom, Strontium 84 atom, Strontium 86 atom, Strontium 87 atom, Strontium 88 atom, Barium 130 atom, Barium 132 atom, Barium 134 atom, Barium 135 atom, Barium 136 atom, Barium 137 atom, Barium 138 atom, Scandium 45 atom, Yttrium 89 atom,Lanthanum 139 atom, Cerium 136 atom, Cerium 138 atom, Cerium 140 atom, Cerium 142 atom, Praseodymium 141 atom, Neodymium 142 atom, Neodymium 143 atom, Neodymium 145 atom, Neodymium 146 atom, Neodymium 148 atom, Samarium 144 atom, Samarium 149 atom, Samarium 150 atom, Samarium 152 atom, Samarium 154 atom, Europium 151 atom, Europium 153 atom, Gadolinium 154 atom, Gadolinium 155 atom, Gadolinium 156 atom, Gadolinium 157 atom, Gadolinium 158 atom, Gadolinium 160 atom, Terbium 159 atom, Dysprosium 156 atom , dysprosium 158 atoms, dysprosium 160 atoms, dysprosium 161 atoms, dysprosium 162 atoms, dysprosium 163 atoms, dysprosium 164 atoms, erbium 162 atoms, erbium 164 atoms, erbium 166 atoms, erbium 167 atoms, erbium 168 atoms, erbium 170 atoms, holmium 165 atoms, thulium 169 atoms, ytterbium 168 atoms, ytterbium 170 atoms, ytterbium 171 atoms, ytterbium 172 atoms, ytterbium 173 atoms, ytterbium 174 atoms, ytterbium 176 atoms, lutetium 175 atoms, or lutetium 176 atoms. The plurality of atoms may be lithium 6 atoms enriched to an isotopic abundance of up to about 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50% or less. , 7 lithium atoms, 23 sodium atoms, 39 potassium atoms, 40 potassium atoms, 41 potassium atoms, 85 rubidium atoms, 87 rubidium atoms, 133 cesium atoms, 9 beryllium atoms, 24 magnesium atoms, 25 magnesium atoms, 26 magnesium atoms, 40 calcium atoms, 42 calcium atoms, 43 calcium atoms, 44 calcium atoms, 46 calcium atoms, 48 ​​calcium atoms, 84 strontium atoms, 86 strontium atoms, 87 strontium atoms,Strontium 88, barium 130, barium 132, barium 134, barium 135, barium 136, barium 137, barium 138, scandium 45, yttrium 89, lanthanum 139, cerium 136, cerium 138, cerium 140, cerium 142, praseodymium 141, neodymium 142, neodymium 143, neodymium 145, neodymium 146, neodymium 148, samarium 144, samarium 149, samarium 150, samarium 152, samarium 154, europium 151, europium 153, gadolinium 154, gadolinium 155, gadolinium 156, gadolinium 1 57 atom, gadolinium 158 atom, gadolinium 160 atom, terbium 159 atom, dysprosium 156 atom, dysprosium 158 atom, dysprosium 160 atom, dysprosium 161 atom, dysprosium 162 atom, dysprosium 163 atom, dysprosium 164 atom, erbium 162 atom, erbium 164 atom, erbium 166 atom, erbium In some embodiments, the cations may include cations of 0 to 100 atoms, such as 0 to 100 atoms, ... The plurality of atoms may be selected from the group consisting of 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, or any combination thereof, enriched to an isotopic abundance within a range defined by any two of the preceding values.Barium 136 atom, Barium 137 atom, Barium 138 atom, Scandium 45 atom, Yttrium 89 atom, Lanthanum 139 atom, Cerium 136 atom, Cerium 138 atom, Cerium 140 atom, Cerium 142 atom, Praseodymium 141 atom, Neodymium 142 atom, Neodymium 143 atom, Neodymium 145 atom, Neodymium 146 atom, Neodymium 148 atom, Samarium 144 atom, Samarium 149 atom, Samarium 150 atom, Samarium 152 atom, Samarium 154 atom, Europium 151 atom, Europium 153 atom, Gadolinium 154 atom, Gadolinium 155 atom, Gadolinium 156 atom, Gadolinium 157 atom, Gadolinium 158 atom, Gadolinium 160 atom , terbium 159 atom, dysprosium 156 atom, dysprosium 158 atom, dysprosium 160 atom, dysprosium 161 atom, dysprosium 162 atom, dysprosium 163 atom, dysprosium 164 atom, erbium 162 atom, erbium 164 atom, erbium 166 atom, erbium 167 atom, erbium 168 atom, erbium 170 atom, holmium 165 atom, thulium 169 atom, ytterbium 168 atom, ytterbium 170 atom, ytterbium 171 atom, ytterbium 172 atom, ytterbium 173 atom, ytterbium 174 atom, ytterbium 176 atom, lutetium 175 atom, or lutetium 176 atom.

[0047] The system 200 may include one or more first electromagnetic delivery units 220. The first electromagnetic delivery unit may include any electromagnetic delivery unit described herein, such as the electromagnetic delivery unit described herein with respect to FIG. 4. The first electromagnetic delivery unit may be configured to apply a first electromagnetic energy to one or more atoms of the plurality of atoms. Applying the first electromagnetic energy may induce the atoms to adopt one or more superpositions of a first atomic state and a second atomic state different from the first atomic state.

[0048] The first atomic state may comprise a first single-qubit state. The second atomic state may comprise a second single-qubit state. The first atomic state or the second atomic state may be elevated in energy relative to a ground atomic state of the atom. The first atomic state or the second atomic state may be equal in energy to a ground atomic state of the atom.

[0049] The first atomic state may include a first hyperfine electronic state, and the second atomic state may include a second hyperfine electronic state that is different from the first hyperfine electronic state. For example, the first and second atomic states may include first and second hyperfine states on a multiplet manifold, such as a triplet manifold. The first and second atomic states may be 3 P1 or 3 The first and second atomic states may be included on the P2 manifold, respectively. The first and second atomic states are strontium-87 3 P1 variant or strontium-87 3 of any atom described herein, such as the P2 manifold. 3 P1 or 3 It may include the first and second hyperfine states on the P2 manifold, respectively.

[0050] Figure 9 shows the structure of strontium 87. 3 The left panel of FIG. 9 shows an example of a qubit containing a P2 state. 3 The right panel of Figure 9 shows the rich energy level structure of the P2 state. The right panel of Figure 9 shows the strontium-87 state, which is insensitive (up to first order) to changes in magnetic field around 70 Gauss. 3 1 shows potential qubit transitions within the P2 state.

[0051] In some cases, the first and second atomic states are first and second hyperfine states of the first electronic state. Optical excitation can be applied between the first electronic state and the second electronic state. The optical excitation can excite the first hyperfine state and / or the second hyperfine state to the second electronic state. The single qubit transition can include a two-photon transition between two hyperfine states in the first electronic state using the second electronic state as an intermediate state. A pair of frequencies detuned from the single-photon transition to the intermediate state, respectively, can be applied to drive the single qubit transition to drive the two-photon transition. In some cases, the first and second hyperfine states are hyperfine states of the ground electronic state. The ground electronic state may not decay to a lower electronic state by spontaneous or stimulated emission. The hyperfine state can include a nuclear spin state. In some cases, the hyperfine state can be a strontium-87 1 The qubit transition involves the nuclear spin state of the S0 manifold, strontium-87 1 One or both of the two nuclear spin states of S0 can be 3 P2 or 3 Drive to detuned states from or within the P1 manifold. In some cases, the one-qubit transition is strontium-87 1 is the two-photon Raman transition between the nuclear spin states of S0, 3 P2 or 3 via states detuned from or within the P1 manifold. In some cases, the nuclear spin state may be a Stark-shifted nuclear spin state. The Stark shift may be optically driven. The optical Stark shift may be off-resonance with any, all, or a combination of single-qubit transitions, two-qubit transitions, shelving transitions, imaging transitions, etc.

[0052] 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 include first and second nuclear spin states of quadrupolar nuclei, respectively. The first and second atomic states may include first and second nuclear spin states of spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4, or spin-9 / 2 nuclei, respectively. The first and second atomic states may include first and second nuclear spin states of any atom described herein, such as the first and second spin states of strontium-87, respectively.

[0053] For first and second nuclear spin states associated with nuclei containing spins greater than 1 / 2 (such as 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 involve transitions between other spin states on the nuclear spin manifold. For example, for a spin-9 / 2 nucleus in the presence of a uniform magnetic field, all nuclear spin levels may be separated by equal energy. Thus, for example, m N = 9 / 2 spin state to m N Transitions designed to move atoms to the =7 / 2 spin state (such as Raman transitions) are N =7 / 2 to m N =5 / 2, m N =5 / 2 to m N =3 / 2, m N =3 / 2 to m N = 1 / 2, m N =1 / 2 to m N =-1 / 2, m N =-1 / 2 to m N =-3 / 2, m N =-3 / 2 to m N =-5 / 2, m N =-5 / 2 to m N = -7 / 2, and m N =-7 / 2 to m N =-9 / 2, m N is the nuclear spin state. Similarly, for example, m N = 9 / 2 spin state to mN Transitions designed to move atoms to the m =5 / 2 spin state (such as Raman transitions) are also N =7 / 2 to m N =3 / 2, m N =5 / 2 to m N = 1 / 2, m N =3 / 2 to m N =-1 / 2, m N =1 / 2 to m N =-3 / 2, m N =-1 / 2 to m N =-5 / 2, m N =-3 / 2 to m N = -7 / 2, and m N =-5 / 2 to m N =-9 / 2. Therefore, such transitions may not be selective for inducing transitions between specific spin states on the nuclear spin manifold.

[0054] Alternatively, 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 adjacent nuclear spin states out of resonance with the transition between the desired transition between the first and second nuclear spin states. For example, N =-9 / 2 and m N If transitions from the first and second nuclear spin states with m = -7 / 2 are favored, the light will N =-5 / 2 spin state, thereby providing an AC Stark shift of m N =-7 / 2 and m N =-5 / 2 state transitions are greatly reduced. Similarly, N =-9 / 2 and m N If the transitions from the first and second nuclear spin states with m = -5 / 2 are favored, the light will N =-1 / 2 spin state, thereby providing an AC Stark shift N =-5 / 2 and m N=-1 / 2 state. This effectively creates a two-level subsystem in the nuclear spin manifold that is isolated from the rest of the nuclear spin manifold, greatly simplifying the dynamics of the qubit system. The nuclear spin manifold (e.g., m for a spin 9 / 2 nucleus) can be scaled so that only one AC Stark shift is required. 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 m N =5 / 2 and m N It may be advantageous to use nuclear spin states near 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 to implement two AC Stark shifts (e.g., m N =-7 / 2 and m N =-1 / 2 or m N =-9 / 2 and m N =3 / 2).

[0055] The Stark shift of the nuclear spin manifold can shift adjacent nuclear spin states out of resonance with a desired transition between the first and second nuclear spin states and the second electronic state or states detuned therefrom. The Stark shift can reduce leakage from the first and second nuclear spin states of the nuclear spin manifold into other states. The Stark shift can potentially be achieved up to hundreds of kHz with beam powers less than 10 mW. The frequency selectivity of the upper states can reduce scattering due to imperfect polarization control. 3The separation of different angular momentum states in the P1 manifold can be several gigahertz, which is numerically larger than single- and two-qubit gate light. Leakage into other states of the nuclear spin manifold can lead to decoherence. The Rabi frequency of the two-qubit transition (i.e., how fast the transition can be driven) can be faster than the decoherence rate. Scattering from intermediate states in the two-qubit transition can cause decoherence. Detuning from the intermediate state can improve the fidelity of the two-qubit transition.

[0056] Qubits based on the nuclear spin state of the electronic ground state require long-lived metastable excited electronic states (e.g., strontium-87) for qubit storage. 3 Atoms may be selectively transferred to such states to reduce crosstalk or improve gating or detection fidelity. Such storage or shelving processes may be atom-selective using the SLM or AOD described herein. Shelving transitions may be used to selectively transfer atoms to such states, such as the P0 state of strontium-87. 1 Strontium-87 from the S0 state 3 P0 or 3 This may include a transition to the P2 state.

[0057] The clock transitions (also referred to herein as "shelving transitions" or "storage transitions") can be qubit-state selective. The upper state of the clock transition can have a very long natural lifetime, e.g., greater than 1 second. The linewidth of the clock transition can be much narrower than the energy spacing of the qubits. This can enable direct spectral resolution. The population can be transferred from one of the qubit states to the clock state. This allows individual qubit states to be read out individually by first transferring the population from one qubit state to the clock state, performing imaging on the qubits, and then transferring the population from the clock state back to the ground state and imaging again. In some cases, magic wavelength transitions are used to drive the clock transitions.

[0058] The shelving clock light may or may not be atom-selective. In some cases, the clock transitions are applied globally (e.g., not atom-selective). Globally applied clock transitions may include directing the light without passing through a microscope objective or structuring the light. In some cases, the clock transitions are atom-selective. Atom-selective clock transitions may minimize crosstalk and improve gate fidelity. For example, to reduce atomic crosstalk, atoms may be shelved to a clock state that may not be affected by light. This may reduce crosstalk between adjacent qubits in transition. To implement atom-selective clock transitions, the light passes through one or more microscope objectives and / or is configured with one or more of spatial light modulators, digital micromirror devices, crossed acousto-optic deflectors, etc.

[0059] The system 200 may include one or more readout units 230. The readout units may include one or more readout light units. The readout light units may be configured to perform one or more measurements of one or more superposition states to obtain the non-classical calculations. The readout light units may include one or more photodetectors. The detectors may include one or more photomultiplier tubes (PMTs), photodiodes, avalanche diodes, single-photon avalanche diodes, single-photon avalanche diode arrays, phototransistors, reverse-biased light emitting diodes (LEDs), charge coupled devices (CCDs), or complementary metal oxide semiconductor (CMOS) cameras. The photodetectors may include one or more fluorescence detectors. The readout optical unit may comprise 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 more. The objective lenses may have an NA of up to about 1, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7, 0.65, 0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1 or less. The objective lenses may have an NA within a range defined by any two of the aforementioned values.

[0060] One or more readout light units 230 can perform measurements, such as projection measurements, by applying light that is resonant with the imaging transition. The imaging transition can produce fluorescence. The imaging transition can be the fluorescence of strontium-87. 1 Strontium-87 from the S0 state 1 This may include a transition to the P1 state. 1 The P1 state can emit fluorescence. The substates of the qubit transition are1 The measurement may include two nuclear spin states of the S0 manifold. One or more of the states may be resonant with the imaging transition. The measurement may include two excitations. In the first excitation, one of the two substates may be excited to a shelving state (e.g., the nucleus spin state of strontium-87). 3 P0 state). In the second excitation, an imaging transition can be excited. The first transition can reduce crosstalk between neighboring atoms during calculation. Fluorescence generated from the imaging transition can be collected by one or more readout optical units 230.

[0061] The imaging unit can be used to determine whether one or more atoms have been lost from the trap. The imaging unit can be used to view the array of atoms in the trap.

[0062] 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 one or more rotary pumps, rotary vane pumps, rotary piston pumps, diaphragm pumps, piston pumps, reciprocating piston pumps, scroll pumps, or screw pumps. The one or more roughing vacuum pumps may 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 freeze adsorption pumps, diffusion pumps, turbomolecular pumps, molecular drag pumps, turbodrag hybrid pumps, cryogenic pumps, ion pumps, or getter pumps.

[0063] The vacuum unit may include any combination of vacuum pumps described herein. For example, the vacuum unit may include one or more roughing pumps (such as scroll pumps) configured to provide a first stage of rough vacuum pumping. The roughing vacuum pumps may be configured to evacuate gases from the system 200 to achieve a rough vacuum pressure condition. For example, the roughing pumps may be configured to pump gases from the system 200 to achieve a rough vacuum pressure condition up to about 10 3The vacuum unit may be configured to achieve a low vacuum pressure of up to about 10 Pascals (Pa). The vacuum unit may further include one or more high vacuum pumps (such as one or more ion pumps, getter pumps, or both) configured to provide a second stage of high vacuum pumping or ultra-high vacuum pumping. The high vacuum pumps evacuate gases from the system 200 once the system 200 reaches a low vacuum pressure condition provided by the one or more roughing pumps, up to about 10 Pa. -3 High vacuum pressure of up to approx. 10 Pa -6 The device can be configured to achieve ultra-high vacuum pressures of up to 100 Pa.

[0064] The vacuum unit can be used to reduce the system load by up to 10%. -6 Pa, 9×10 -7 Pa, 8×10 -7 Pa, 7×10 -7 Pa, 6×10 -7 Pa, 5×10 -7 Pa, 4×10 -7 Pa, 3×10 -7 Pa, 2×10 -7 Pa, 10 -7 Pa, 9×10 -8 Pa, 8×10 -8 Pa, 7×10 -8 Pa, 6×10 -8 Pa, 5×10 -8 Pa, 4×10 -8 Pa, 3×10 -8 Pa, 2×10 -8 Pa, 10 -8 Pa, 9×10 -9 Pa, 8×10 -9 Pa, 7×10 -9 Pa, 6×10 -9 Pa, 5×10 -9 Pa, 4×10 -9 Pa, 3×10 -9 Pa, 2×10 -9 Pa, 10 -9 Pa, 9×10 -10 Pa, 8×10 -10 Pa, 7×10 -10 Pa, 6×10 -10 Pa, 5×10 -10 Pa, 4×10 -10Pa, 3×10 -10 Pa, 2×10 -10 Pa, 10 -10 Pa, 9×10 -11 Pa, 8×10 -11 Pa, 7×10 -11 Pa, 6×10 -11 Pa, 5×10 -11 Pa, 4×10 -11 Pa, 3×10 -11 Pa, 2×10 -11 Pa, 10 -11 Pa, 9×10 -12 Pa, 8×10 -12 Pa, 7×10 -12 Pa, 6×10 -12 Pa, 5×10 -12 Pa, 4×10 -12 Pa, 3×10 -12 Pa, 2×10 -12 Pa, 10 -12 The vacuum unit can be configured to maintain the system 200 at a pressure of at least about 10 Pa or less. -12 Pa, 2×10 -12 Pa, 3×10 -12 Pa, 4×10 -12 Pa, 5×10 -12 Pa, 6×10 -12 Pa, 7×10 -12 Pa, 8×10 -12 Pa, 9×10 -12 Pa, 10 -11 Pa, 2×10 -11 Pa, 3×10 -11 Pa, 4×10 -11 Pa, 5×10 -11 Pa, 6×10 -11 Pa, 7×10 -11 Pa, 8×10 -11 Pa, 9×10 -11 Pa, 10 -10 Pa, 2×10 -10 Pa, 3×10 -10 Pa, 4×10 -10 Pa, 5×10 -10 Pa, 6×10 -10 Pa, 7×10 -10 Pa, 8×10 -10 Pa, 9×10 -10Pa, 10 -9 Pa, 2×10 -9 Pa, 3×10 -9 Pa, 4×10 -9 Pa, 5×10 -9 Pa, 6×10 -9 Pa, 7×10 -9 Pa, 8×10 -9 Pa, 9×10 -9 Pa, 10 -8 Pa, 2×10 -8 Pa, 3×10 -8 Pa, 4×10 -8 Pa, 5×10 -8 Pa, 6×10 -8 Pa, 7×10 -8 Pa, 8×10 -8 Pa, 9×10 -8 Pa, 10 -7 Pa, 2×10 -7 Pa, 3×10 -7 Pa, 4×10 -7 Pa, 5×10 -7 Pa, 6×10 -7 Pa, 7×10 -7 Pa, 8×10 -7 Pa, 9×10 -7 Pa, 10 -6 The vacuum unit may be configured to maintain the system 200 at a pressure within a range defined by any two of the aforementioned values.

[0065] The system 200 may include one or more state preparation units 250. The state preparation units may include any state preparation units described herein, such as the state preparation units described herein with respect to Figure 5. The state preparation units may be configured to prepare states of a plurality of atoms.

[0066] The system 200 may include one or more atom reservoirs 260. The atom reservoirs may be configured to provide one or more replacement atoms to replace one or more atoms at one or more optical trapping sites when atoms are lost from the optical trapping sites. The atom reservoirs may be spatially separated from the optical trapping unit. For example, the atom reservoirs may be located at a location remote from the optical trapping unit.

[0067] Alternatively or additionally, the atomic reservoir may comprise a portion of the optical trapping sites of the optical trapping unit. A first subset of the optical trapping sites may be utilized to perform quantum computation and may be referred to as a set of computationally active optical trapping sites, and a second subset of the optical trapping sites may function as the atomic reservoir. For example, the first subset of the optical trapping sites may comprise an internal array of optical trapping sites, and the second subset of the optical trapping sites may comprise an external array of optical trapping sites surrounding the internal array. The internal array may comprise a rectangular, square, rectangular prism, or cubic array of optical trapping sites.

[0068] The system 200 may include one or more atom transfer units 270. The atom transfer units may be configured to transfer one or more replacement atoms from one or more atom reservoirs to one or more optical capture sites. For example, the one or more atom transfer units may include one or more electrically tunable lenses, acousto-optic deflectors (AODs), or spatial light modulators (SLMs).

[0069] The system 200 may include one or more entanglement units 280. The entanglement unit may be configured to quantum-mechanically entangle at least a first atom of the plurality of atoms with at least a second atom of the plurality of atoms. The first or second atom may be in a superposition state when quantum-mechanically entangled. Alternatively or additionally, the first or second atom may not be in a superposition state when quantum-mechanically entangled. The first and second atoms may be quantum-mechanically entangled by one or more magnetic dipole interactions, induced magnetic dipole interactions, electric dipole interactions, or induced electric dipole interactions. The entanglement unit may be configured to quantum-mechanically entangle any number of atoms described herein.

[0070] The entanglement unit may be configured to quantum-mechanically entangle at least a subset of the atoms with at least another atom to form one or more multi-qubit units. The multi-qubit unit may include a two-qubit unit, a three-qubit unit, a four-qubit unit, or an n-qubit unit, where n may be 5, 6, 7, 8, 9, 10, or greater. For example, a two-qubit unit may include a first atom quantum-mechanically entangled with a second atom, a three-qubit unit may include a first atom quantum-mechanically entangled with a second and a third atom, a four-qubit unit may include a first atom quantum-mechanically entangled with a second, a third, and a fourth atom, and so on. The first, second, third, or fourth atoms may be in a superposition state when quantum-mechanically entangled. Alternatively or additionally, the first, second, third, or fourth atom may not be in a superposition state when quantum mechanically entangled. The first, second, third, and fourth atoms may be quantum mechanically entangled by one or more magnetic dipole interactions, induced magnetic dipole interactions, electric dipole interactions, or induced electric dipole interactions.

[0071] The entanglement unit may include one or more Rydberg units. The Rydberg units may be configured to electronically excite at least a first atom into a Rydberg state or into a superposition of a Rydberg state and a lower energy atomic state, thereby forming one or more Rydberg atoms or dressed Rydberg atoms. The Rydberg units may be configured to induce one or more quantum mechanical entanglements between the Rydberg atom or dressed Rydberg atom and at least a second atom. The second atom may be located at a distance of at least about 200 nanometers (nm), 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 micrometer (μm), 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, or greater, from the Rydberg atom or dressed Rydberg atom. The second atom may be located at a distance of at most 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 atom or the dressed Rydberg atom. The second atom may be located at a distance from the Rydberg atom or the dressed Rydberg atom that is within a range defined by any two of the aforementioned values. The Rydberg unit may be configured to allow the Rydberg atom or the dressed Rydberg atom to relax to a lower energy atomic state, thereby forming one or more two-qubit units. The Rydberg unit may be configured to induce the Rydberg atom or the dressed Rydberg atom to relax to a lower energy atomic state. The Rydberg unit can be configured to drive the Rydberg atom or the dressed Rydberg atom to a lower energy atomic state. For example, the Rydberg unit can be configured to apply electromagnetic radiation (such as RF radiation or optical radiation) to drive the Rydberg atom or the dressed Rydberg atom to a lower energy atomic state.The Rydberg unit can be configured to induce any number of quantum mechanical entanglements between any number of atoms in a plurality of atoms.

[0072] The Rydberg unit may include one or more light sources (such as any light sources described herein) configured to emit light having one or more ultraviolet (UV) wavelengths. The UV wavelengths may be selected to correspond to wavelengths that form Rydberg atoms or dressed Rydberg atoms. For example, the light may include one or more wavelengths of at least about 200 nm, 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, 370 nm, 380 nm, 390 nm, 400 nm, or longer. 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 aforementioned values. For example, the light may include one or more wavelengths within a range of 300 nm to 400 nm.

[0073] The Rydberg unit may be configured to induce a two-photon transition to generate entanglement. The Rydberg unit may be configured to induce a two-photon transition to generate entanglement between two atoms. The Rydberg unit may be configured to selectively induce a two-photon transition to selectively generate entanglement between two atoms. For example, the Rydberg unit may be configured to direct electromagnetic energy (such as light energy) to a particular light trapping site to selectively induce a two-photon transition to selectively generate entanglement between two atoms. The two atoms may be trapped in nearby light trapping sites. For example, the two atoms may be trapped in adjacent light trapping sites. The two-photon transition may be induced using first and second light from first and second light sources, respectively. The first and second light sources may each include any light source described herein (such as any laser described herein). The first light source may be the same as or similar to the light source used to perform the single qubit operations described herein. Alternatively, different light sources may be used to perform single qubit operations and induce two-photon transitions to generate entanglement. The first light source may emit light including 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 including 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 equal and opposite spatially dependent frequency shifts.

[0074] The Rydberg atom or dressed Rydberg atom may include a Rydberg state that may have sufficiently strong interatomic interactions with nearby atoms (such as nearby atoms trapped in nearby optical trapping sites) to allow for the implementation of multi-qubit operations. The Rydberg state may include a principal quantum number of at least about 50, 60, 70, 80, 90, 100, or greater. The Rydberg state may include a principal quantum number of up to about 100, 90, 80, 70, 60, 50 or less. The Rydberg state may include a principal quantum number that is within a range defined by any two of the aforementioned values. The Rydberg state may interact with nearby atoms through van der Waals interactions. The van der Waals interactions may shift the atomic energy levels of the atom.

[0075] State-selective excitation of atoms to Rydberg levels can enable the implementation of multi-qubit operations. Multi-qubit operations can include two-qubit operations, three-qubit operations, or n-qubit operations, where n is 4, 5, 6, 7, 8, 9, 10, or more. Two-photon transitions can drive atoms to the ground state ( 1 S0 ground state) to the Rydberg state (n 3 A two-photon transition may be implemented using a first and second laser source as described herein. The first laser source may emit pie-polarized light, which does not change the projection of the atomic angular momentum along the magnetic field. The second laser may emit circularly polarized light, which may change the projection of the atomic angular momentum along the magnetic field by one unit. This polarization may be used to excite the first and second qubit levels to Rydberg levels. However, the Rydberg levels may be more sensitive to the magnetic field than the ground state, so large splittings (e.g., on the order of hundreds of MHz) may be easily obtained. This spectral selectivity may allow state-selective excitation to the Rydberg levels.

[0076] Multiqubit operations (e.g., two-qubit, three-qubit, four-qubit, etc.) may rely on energy shifts of levels due to van der Waals interactions as described herein. Such shifts may prevent excitation of one atom conditional on the state of the other, or may modify the coherent dynamics of excitations in a two-atom system to perform two-qubit operations. In some cases, "dressing states" may be generated under continuous drive to perform two-qubit operations without requiring full excitation to the Rydberg levels (e.g., as described in www.arxiv.org / abs / 1605.05207, which is incorporated by reference in its entirety for all purposes).

[0077] System 200 may include one or more second electromagnetic delivery units (not shown in FIG. 2). The second electromagnetic delivery units may include any electromagnetic delivery units described herein, such as those described herein with respect to FIG. 4. The first and second electromagnetic delivery units may be the same. The first and second electromagnetic delivery units may be different. The second electromagnetic delivery unit may be configured to apply a second electromagnetic energy to one or more multi-qubit units. The second electromagnetic energy may include one or more pulse sequences. The first electromagnetic energy may precede, be simultaneous with, or follow the second electromagnetic energy.

[0078] A pulse sequence may include any number of pulses. For example, a pulse sequence may include at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, or more pulses. A pulse sequence may include up to about 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 pulses. A pulse sequence may include a number of pulses that are within a range defined by any two of the aforementioned values. Each pulse of the pulse sequence may include any pulse shape, including any pulse shape described herein.

[0079] Pulse sequences can be configured to reduce the duration required to implement multi-qubit operations, as described herein (e.g., with respect to Example 3). For example, pulse sequences can include durations of at least about 10 nanoseconds (ns), 20 ns, 30 ns, 40 ns, 50 ns, 60 ns, 70 ns, 80 ns, 90 ns, 100 ns, 200 ns, 300 ns, 400 ns, 500 ns, 600 ns, 700 ns, 800 ns, 900 ns, 1 microsecond (μs), 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 longer. The pulse sequence may include a duration of up to about 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. The pulse sequence may include a duration that is within a range defined by any two of the foregoing values.

[0080] Pulse sequences, as described herein, can be configured to increase the fidelity of multi-qubit operations. For example, pulse sequences can be configured to increase the fidelity of multi-qubit operations by at least about 0.5, 0.6, 0.7, 0.8, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99, 0.991, 0.992, 0.993, 0.994, 0.995, 0.996, 0.997, 0.998, 0.999, 0.9991, 0.9992, 0.9993, 0.9994, 0.9995, 0.9996, 0.9997, 0.999 8, 0.9999, 0.99991, 0.99992, 0.99993, 0.99994, 0.99995, 0.99996, 0.99997, 0.99998, 0.99999, 0.999991, 0.999992, 0.999993, 0.999994, 0.999995, 0.99996, 0.999994, 0.999995, 0.999996, 0.999997, 0.999998, 0.999999, 0.999991, 0.999992, 0.999993, 0.999994, 0.999995, 0.999996, 0.999997, 0.999998, 0.999999, or higher fidelity. The pulse sequence can be up to approximately 0.999999, 0.999998, 0.999997, 0.999996, 0.999995, 0.999994, 0.999993, 0.999992, 0.999991, 0.99999, 0.99998, 0.99997, 0.99996, 0.99995, 0.99994, 0.99993, 0.99992, 0.99991, 0.9999, 0.9998, 0.9997, 0. The pulse sequence may enable multi-qubit operations with a fidelity of 9996, 0.9995, 0.9994, 0.9993, 0.9992, 0.9991, 0.999, 0.998, 0.997, 0.996, 0.995, 0.994, 0.993, 0.992, 0.991, 0.99, 0.98, 0.97, 0.96, 0.95, 0.94, 0.93, 0.92, 0.91, 0.9, 0.8, 0.7, 0.6, 0.5, or less. The pulse sequence may enable multi-qubit operations with a fidelity within a range defined by any two of the aforementioned values.

[0081] Pulse sequences may enable the implementation of multi-qubit operations on nonadiabatic timescales while effectively maintaining adiabatic dynamics. For example, pulse sequences may include one or more of the following: shortcut to adiabaticity (STA) pulse sequences, transitionless quantum driving (TQD) pulse sequences, superadiabatic pulse sequences, inverse adiabatic driving pulse sequences, derivative removal by adiabatic gate (DRAG) pulse sequences, and weak anharmonicity with average Hamiltonian (Wah Wah) pulse sequences.For example, pulse sequences have been described in M.V.Berry, "Transitionless Quantum Driving", Journal of Physics A:Mathematical and Theoretical 42(36), 365303(2009), www.doi.org / 10.1088 / 1751-8113 / 42 / 36 / 365303; Y.-Y.Jau et al., "Entangling Atomic Spins with a Strong Rydberg-Dressed Interaction", Nature Physics 12(1), 71-74(2016); T.Keating et al., "Robust Quantum Logic in Neutral Atoms via Adiabatic Rydberg Dressing", Physical Review A 91, 012337(2015); A.Mitra et al., "Robust Molmer-Sorenson Gate for Neutral Atoms Using Rapid Adiabatic Rydberg "Dressing," www.arxiv.org / abs / 1911.04045 (2019); or L.S. Theis et al., "Counteracting Systems of Diabaticities Using DRAG Controls: The Status after 10 Years," Europhysics Letters 123(6), 60001 (2018), each of which is incorporated by reference in its entirety for all purposes.

[0082] The pulse sequence may further include one or more optimal control pulse sequences, which may be derived from one or more procedures including gradient ascent pulse engineering (GRAPE), Krotov, chopped basis, chopped random basis (CRAB), Nelder-Mead, gradient optimization using parametrization (GROUP), genetic algorithm, and gradient optimization of analytic controls (GOAT). For example, the pulse sequence can be similar to those described in N. Khaneja et al., "Optimal Control of Coupled Spin Dynamics: Design of NMR Pulse Sequences by Gradient Ascent Algorithms," Journal of Magnetic Resonance 172(2), 296-305 (2005); or JT Merrill et al., "Progress in Compensating Pulse Sequences for Quantum Computation," Advances in Chemical Physics 154, 241-294 (2014), each of which is incorporated by reference in its entirety for all purposes.

[0083] Cloud Computing The system 200 may be operatively coupled to a digital computer as described herein (such as the digital computer as described herein with respect to FIG. 1) via a network as described herein (such as the network as described herein with respect to FIG. 1). The network may include a cloud computing network.

[0084] Light Capture Unit FIG. 3A illustrates an example of a light trapping unit 210. The light trapping unit may be configured to generate a plurality of spatially distinct light trapping sites 211 as described herein. For example, as shown in FIG. 3B, the light trapping unit may be configured to generate a first light trapping site 211a, a second light trapping site 211b, a third light trapping site 211c, a fourth light trapping site 211d, a fifth light trapping site 211e, a sixth light trapping site 211f, a seventh light trapping site 211g, an eighth light trapping site 211h, and a ninth light trapping site 211i, as depicted in FIG. 3A. The plurality of spatially distinct light trapping sites may be configured to trap a plurality of atoms, such as a first atom 212a, a second atom 212b, a third atom 212c, and a fourth atom 212d, as depicted in FIG. 3A. As depicted in FIG. 3B, each light trapping site may be configured to trap a single atom. As depicted in FIG. 3B, some of the light trapping sites may be empty (i.e., do not trap atoms).

[0085] As shown in Figure 3B, the plurality of light capture sites may comprise a two-dimensional (2D) array. The 2D array may be perpendicular to the optical axis of the optical components of the light capture unit depicted in Figure 3A. Alternatively, the plurality of light capture sites may comprise a one-dimensional (1D) array or a three-dimensional (3D) array.

[0086] Although depicted in FIG. 3B as including nine light capture sites filled with four atoms, the light capture unit 210 may be configured to generate any number of spatially distinct light capture sites as described herein and may be configured to capture any number of atoms as described herein.

[0087] Each light capture site of the plurality of light capture sites may be spatially separated from each other light capture site by a distance of at least about 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 μm, 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, or more. Each light capture site may be spatially separated from each other light capture site by a distance of at most 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 light trapping site may be spatially separated from each other light trapping site by a distance within a range defined by any two of the aforementioned values.

[0088] The optical trapping site may include one or more optical tweezers. The 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 beam may include a strong electric field gradient. The atoms may be attracted or repelled along the electric field gradient to the center of the laser beam, which may include the strongest electric field. The optical trapping site may include one or more optical lattice sites of one or more optical lattices. The optical trapping site may include one or more optical lattice sites of one or more one-dimensional (1D) optical lattices, two-dimensional (2D) optical lattices, or three-dimensional (3D) optical lattices. For example, the optical trapping site may include one or more optical lattice sites of a 2D optical lattice, as depicted in FIG. 3B.

[0089] Optical lattices can be generated by interfering counter-propagating light (such as counter-propagating laser light) to generate a standing wave pattern with a periodic succession of intensity minima and maxima along a particular direction. A 1D optical lattice can be generated by interfering a pair of counter-propagating light beams. A 2D optical lattice can be generated by interfering two pairs of counter-propagating light beams. A 3D optical lattice can be generated by interfering three pairs of counter-propagating light beams. The light beams can be generated by different light sources or by the same light source. Thus, an optical lattice can be generated by at least about 1, 2, 3, 4, 5, 6, or more light sources, or up to about 6, 5, 4, 3, 2, or 1 light source.

[0090] Returning to the description of FIG. 3A, the light capture unit may include one or more light sources configured to emit light to generate a plurality of light capture sites as described herein. For example, the light capture unit may include a single light source 213 as depicted in FIG. 3A. Although depicted in FIG. 3A as including a single light source, the light capture 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 up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 light source. The light source may include one or more lasers. The laser may be configured to operate at the resolution limit of the laser. For example, the laser may be configured to provide a diffraction-limited spot size for light capture.

[0091] The laser may include one or more continuous wave lasers. The laser may include one or more pulsed lasers. The laser 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 laser may include one or more of an argon dimer (Ar2) excimer laser, a krypton dimer (Kr2) excimer laser, a fluorine dimer (F2) excimer laser, a xenon dimer (Xe2) excimer laser, an argon fluoride (ArF) excimer laser, a krypton chloride (KrCl) excimer laser, a krypton fluoride (KrF) excimer laser, a xenon bromide (XeBr) excimer laser, a xenon chloride (XeCl) excimer laser, or a xenon fluoride (XeF) excimer laser. The laser may include one or more dye lasers.

[0092] The laser 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.

[0093] The laser 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 laser may 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 The laser may include a chromium-doped yttrium aluminum garnet (Yb:YAG) laser, a ytterbium-doped glass (Yt:glass) laser, a holmium-yttrium aluminum garnet (Ho:YAG) laser, a chromium-doped zinc selenide (Cr:ZnSe) laser, a cerium-doped lithium strontium aluminum fluoride (Ce:LiSAF) laser, a cerium-doped lithium calcium aluminum fluoride (Ce:LiCAF) laser, an erbium-doped glass (Er:glass) laser, an erbium and ytterbium co-doped glass (Er / Yt:glass) laser, a uranium-doped calcium fluoride (U:CaF2) laser, or a samarium-doped calcium fluoride (Sm:CaF2) laser.

[0094] The laser 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 emitting lasers (VCSELs), or quantum cascade lasers.

[0095] The laser may emit continuous wave laser light. The laser may emit pulsed laser light. The laser may emit pulsed laser light. The laser may emit pulsed laser light. The laser may emit pulsed laser light. The pulse length may be 80ps, 90ps, 100ps, 200ps, 300ps, 400ps, 500ps, 600ps, 700ps, 800ps, 900ps, 1 nanosecond (ns), 2ns, 3ns, 4ns, 5ns, 6ns, 7ns, 8ns, 9ns, 10ns, 20ns, 30ns, 40ns, 50ns, 60ns, 70ns, 80ns, 90ns, 100ns, 200ns, 300ns, 400ns, 500ns, 600ns, 700ns, 800ns, 900ns, 1,000ns, or longer. Lasers have a maximum of approximately 1,000ns, 900ns, 800ns, 700ns, 600ns, 500ns, 400ns, 300ns, 200ns, 100ns, 90ns, 80ns, 70ns, 60ns, 50ns, 40ns, 30ns, 20ns, 10ns, 9ns, 8ns, 7ns, 6ns, 5ns, 4ns, 3ns, 2ns, 1ns, 900ps, 800ps, 700ps, 600ps, 500ps, 400ps, 300ps, 200ps, 100ps, 90ps, 80ps, 70ps , 60ps, 50ps, 40ps, 30ps, 20ps, 10ps, 9ps, 8ps, 7ps, 6ps, 5ps, 4ps, 3ps, 2ps, 1ps, 900fs, 800fs, 700fs, 600fs, 500fs, 400fs, 300fs, 200fs, 100fs, 90fs, 80fs, 70fs, 60fs, 50fs, 40fs, 30fs, 20fs, 10fs, 9fs, 8fs, 7fs, 6fs, 5fs, 4fs, 3fs, 2fs, 1fs, or shorter. The laser may have a pulse length within a range defined by any two of the foregoing values.

[0096] The laser may be at least about 1 Hertz (Hz), 2 Hz, 3 Hz, 4 Hz, 5 Hz, 6 Hz, 7 Hz, 8 Hz, 9 Hz, 10 Hz, 20 Hz, 30 Hz, 40 Hz, 50 Hz, 60 Hz, 70 Hz, 80 Hz, 90 Hz, 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1 kilohertz (kHz), 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 50 kHz, 60 kHz, 70 kHz, 80 kHz, 90 kHz, 1 In one embodiment, the optical fiber may have a repetition rate of 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1 megahertz (MHz), 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 20 MHz, 30 MHz, 40 MHz, 50 MHz, 60 MHz, 70 MHz, 80 MHz, 90 MHz, 100 MHz, 200 MHz, 300 MHz, 400 MHz, 500 MHz, 600 MHz, 700 MHz, 800 MHz, 900 MHz, 1,000 MHz, or more.The laser operates at frequencies up to approximately 1,000MHz, 900MHz, 800MHz, 700MHz, 600MHz, 500MHz, 400MHz, 300MHz, 200MHz, 100MHz, 90MHz, 80MHz, 70MHz, 60MHz, 50MHz, 40MHz, 30MHz, 20MHz, 10MHz, 9MHz, 8MHz, 7MHz, 6MHz, 5MHz, 4MHz, 3MHz, 2MHz, 1MHz, 900kHz, 800kHz, 700kHz, 600kHz, 500kHz, 400kHz, 300kHz, 200kHz, 100kHz, 90kHz , 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, 900 Hz, 800 Hz, 700 Hz, 600 Hz, 500 Hz, 400 Hz, 300 Hz, 200 Hz, 100 Hz, 90 Hz, 80 Hz, 70 Hz, 60 Hz, 50 Hz, 40 Hz, 30 Hz, 20 Hz, 10 Hz, 9 Hz, 8 Hz, 7 Hz, 6 Hz, 5 Hz, 4 Hz, 3 Hz, 2 Hz, 1 Hz, or less. The laser may have a repetition rate within a range defined by any two of the foregoing values.

[0097] The laser may be at least about 1 nanojoule (nJ), 2 nJ, 3 nJ, 4 nJ, 5 nJ, 6 nJ, 7 nJ, 8 nJ, 9 nJ, 10 nJ, 20 nJ, 30 nJ, 40 nJ, 50 nJ, 60 nJ, 70 nJ, 80 nJ, 90 nJ, 100 nJ, 200 nJ, 300 nJ, 400 nJ, 500 nJ, 600 nJ, 700 nJ, 800 nJ, 900 nJ, 1 microjoule (μJ), 2 μJ, 3 μJ, 4 μJ, 5 μJ, 6 μJ, 7 μJ, 8 μJ, 9 μJ, 10 μJ, 20 μJ, 30 μJ, 40 μJ, 50 μJ, 60 μJ, 70 μJ, 80 μJ, 90 μJ, 1 In one embodiment, the laser may emit light having a pulse energy of at least 100 μJ, 200 μJ, 300 μJ, 400 μJ, 500 μJ, 600 μJ, 700 μJ, 800 μJ, 900 μJ, at least 1 milliJoule (mJ) or more, 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, at least 1 Joule (J), or more. The laser can produce up to about 1J, 900mJ, 800mJ, 700mJ, 600mJ, 500mJ, 400mJ, 300mJ, 200mJ, 100mJ, 90mJ, 80mJ, 70mJ, 60mJ, 50mJ, 40mJ, 30mJ, 20mJ, 10mJ, 9mJ, 8mJ, 7mJ, 6mJ, 5mJ, 4mJ, 3mJ, 2mJ, 1mJ, 900μJ, 800μJ, 700μJ, 600μJ, 500μJ, 400μJ, 300μJ, 200μJ, 100μJ, 90μJ, 80μJ, 70μJ, 60μJ, 50 The laser may emit light having a pulse energy of 1000nJ, 400nJ, 300nJ, 200nJ, 100nJ, 90nJ, 80nJ, 700nJ, 600nJ, 500nJ, 400nJ, 300nJ, 200nJ, 100nJ, 90nJ, 80nJ, 70nJ, 60nJ, 50nJ, 40nJ, 30nJ, 20nJ, 10nJ, 9nJ, 8nJ, 7nJ, 6nJ, 5nJ, 4nJ, 3nJ, 2nJ, 1nJ, or less. The laser may emit light having a pulse energy within a range defined by any two of the aforementioned values.

[0098] The laser may have a power of at least about 1 microwatt (μW), 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 milliwatt (mW), 2 mW, 3 mW, 4 mW, 5 mW, 6 mW, 7 mW, 8 mW, 9 mW, 10 mW, 20 mW, 30 mW, 40 mW, 50 mW, It can emit light having an average power of 60mW, 70mW, 80mW, 90mW, 100mW, 200mW, 300mW, 400mW, 500mW, 600mW, 700mW, 800mW, 900mW, 1 Watt (W), 2W, 3W, 4W, 5W, 6W, 7W, 8W, 9W, 10W, 20W, 30W, 40W, 50W, 60W, 70W, 80W, 90W, 100W, 200W, 300W, 400W, 500W, 600W, 700W, 800W, 900W, 1,000W, or more. Lasers are available in a range of powers up to approximately 1,000W, 900W, 800W, 700W, 600W, 500W, 400W, 300W, 200W, 100W, 90W, 80W, 70W, 60W, 50W, 40W, 30W, 20W, 10W, 9W, 8W, 7W, 6W, 5W, 4W, 3W, 2W, 1W, 900mW, 800mW, 700mW, 600mW, 500mW, 400mW, 300mW, 200mW, 100mW, 90mW, 80mW, 70mW, 60mW, 50mW, 40mW, 30mW , 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. The laser may emit light having a power within a range defined by any two of the aforementioned values.

[0099] Lasers may emit light that includes one or more wavelengths in the ultraviolet (UV), visible, or infrared (IR) portions of the electromagnetic spectrum. Lasers may include at least about 200 nm, 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, 370 nm, 380 nm, 390 nm, 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm 30nm, 540nm, 550nm, 560nm, 570nm, 580nm, 590nm, 600nm, 610nm, 620nm, 630nm, 640nm, 650nm, 660nm, 670nm, 680nm, 690nm, 700nm , 710nm, 720nm, 730nm, 740nm, 750nm, 760nm, 770nm, 780nm, 790nm, 800nm, 810nm, 820nm, 830nm, 840nm, 850nm, 860nm, 870nm, 880 nm, 890nm, 900nm, 910nm, 920nm, 930nm, 940nm, 950nm, 960nm, 970nm, 980nm, 990nm, 1,000nm, 1,010nm, 1,020nm, 1,030nm, 1,040 nm, 1,050nm, 1,060nm, 1,070nm, 1,080nm, 1,090nm, 1,100nm, 1,110nm, 1,120nm, 1,130nm, 1,140nm, 1,150nm, 1,160nm, 1,170nm , 1,180 nm, 1,190 nm, 1,200 nm, 1,210 nm, 1,220 nm, 1,230 nm, 1,240 nm, 1,250 nm, 1,260 nm, 1,270 nm, 1,280 nm, 1,290 nm, 1,300 nm, 1,310 nm, 1,320 nm, 1,330 nm, 1,340 nm, 1,350 nm, 1,360 nm, 1,370 nm, 1,380 nm, 1,390 nm, 1,400 nm, or longer.Lasers are available in a range of wavelengths up to approximately 1,400nm, 1,390nm, 1,380nm, 1,370n, 1,360nm, 1,350nm, 1,340nm, 1,330nm, 1,320nm, 1,310nm, 1,300nm, 1,290nm, 1,280nm, 1,270n, 1,260nm, 1,250nm, 1,240nm, 1,230nm, 1,220nm, 1,210nm, 1,200nm, 1,190nm, 1,180nm, 1,170nm, 1,160nm, 1,150nm, 1,140nm, 1,130nm, 1,120nm, 1,110nm, 1,100nm, 1,090nm, 1,080nm, 1,070nm, 1,060nm, 1,050nm, 1,040nm, 1,030nm, 1,020nm, 1,010nm, 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860 nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 690nm , 680nm, 670nm, 660nm, 650nm, 640nm, 630nm, 620nm, 610nm, 600nm, 590nm, 580nm, 570nm, 560nm, 550nm, 540nm, 530nm, 520nm, 5 The laser may emit light that includes one or more wavelengths of 10 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm. The laser may emit light that includes one or more wavelengths that are within a range defined by any two of the aforementioned values.

[0100] The laser has a power of at least about 1×10 -15 nm, 2 × 10 -15 nm, 3 × 10 -15 nm, 4×10-15 nm, 5×10 -15 nm, 6×10 -15 nm, 7×10 -15 nm, 8×10 -15 nm, 9×10 -15 nm, 1×10 -14 nm, 2×10 -14 nm, 3×10 -14 nm, 4×10 -14 nm, 5×10 -14 nm, 6×10 -14 nm, 7×10 -14 nm, 8×10 -14 nm, 9×10 -14 nm, 1×10 -13 nm, 2×10 -13 nm、3×10 -13 nm, 4×10 -13 nm, 5×10 -13 nm, 6×10 -13 nm, 7×10 -13 nm, 8×10 -13 nm, 9×10 -13 nm, 1×10 -12 nm, 2×10 -12 nm, 3×10 -12 nm, 4×10 -12 nm, 5×10 -12 nm, 6×10 -12 nm, 7×10 -12 nm, 8×10 -12 nm, 9×10 -12 nm, 1×10 -11 nm, 2×10 -11 nm、3×10 -11 nm, 4×10 -11 nm, 5×10 -11 nm, 6×10 -11 nm, 7×10 -11 nm, 8×10 -11 nm, 9×10 -11 nm, 1×10 -10 nm, 2×10 -10 nm, 3×10 -10 nm, 4×10 -10 nm, 5×10 -10 nm, 6×10 -10 nm, 7×10 -10 nm, 8×10 -10 nm, 9×10-10 nm, 1×10 -9 nm, 2×10 -9 nm, 3×10 -9 nm, 4×10 -9 nm, 5×10 -9 nm, 6×10 -9 nm, 7×10 -9 nm, 8×10 -9 nm, 9×10 -9 nm, 1×10 -8 nm, 2×10 -8 nm, 3×10 -8 nm, 4×10 -8 nm, 5×10 -8 nm, 6×10 -8 nm, 7×10 -8 nm, 8×10 -8 nm, 9×10 -8 nm, 1×10 -7 nm, 2×10 -7 nm, 3×10 -7 nm, 4×10 -7 nm, 5×10 -7 nm, 6×10 -7 nm, 7×10 -7 nm, 8×10 -7 nm, 9×10 -7 nm, 1×10 -6 nm, 2×10 -6 nm, 3×10 -6 nm, 4×10 -6 nm, 5×10 -6 nm, 6×10 -6 nm, 7×10 -6 nm, 8×10 -6 nm, 9×10 -6 nm, 1×10 -5 nm, 2×10 -5 nm, 3×10 -5 nm, 4×10 -5 nm, 5×10 -5 nm, 6×10 -5 nm, 7×10 -5 nm, 8×10 -5 nm, 9×10 -5 nm, 1×10 -4 nm, 2×10 -4 nm, 3×10 -4 nm, 4×10 -4 nm, 5×10-4 nm, 6×10 -4 nm, 7×10 -4 nm, 8×10 -4 nm, 9×10 -4 nm, 1×10 -3 The laser can emit light with a bandwidth of up to about 1×10 nm or longer. -3 nm, 9×10 -4 nm, 8×10 -4 nm, 7×10 -4 nm, 6×10 -4 nm, 5×10 -4 nm, 4×10 -4 nm, 3 × 10 -4 nm, 2 × 10 -4 nm, 1×10 -4 nm, 9×10 -5 nm, 8×10 -5 nm, 7×10 -5 nm, 6×10 -5 nm, 5×10 -5 nm, 4×10 -5 nm, 3 × 10 -5 nm, 2 × 10 -5 nm, 1×10 -5 nm, 9×10 -6 nm, 8×10 -6 nm, 7×10 -6 nm, 6×10 -6 nm, 5×10 -6 nm, 4×10 -6 nm, 3 × 10 -6 nm, 2 × 10 -6 nm, 1×10 -6 nm, 9×10 -7 nm, 8×10 -7 nm, 7×10 -7 nm, 6×10 -7 nm, 5×10 -7 nm, 4×10 -7 nm, 3 × 10 -7 nm, 2 × 10 -7 nm, 1×10 -7 nm, 9×10 -8 nm, 8×10 -8 nm, 7×10 -8 nm, 6×10 -8 nm, 5×10 -8 nm, 4×10-8 nm, 3×10 -8 nm, 2×10 -8 nm, 1×10 -8 nm, 9×10 -9 nm, 8×10 -9 nm, 7×10 -9 nm, 6×10 -9 nm, 5×10 -9 nm, 4×10 -9 nm, 3×10 -9 nm, 2×10 -9 nm, 1×10 -9 nm, 9×10 -10 nm, 8×10 -10 nm, 7×10 -10 nm, 6×10 -10 nm, 5×10 -10 nm, 4×10 -10 nm, 3×10 -10 nm, 2×10 -10 nm, 1×10 -10 nm, 9×10 -11 nm, 8×10 -11 nm, 7×10 -11 nm, 6×10 -11 nm, 5×10 -11 nm, 4×10 -11 nm, 3×10 -11 nm, 2×10 -11 nm, 1×10 -11 nm, 9×10 -12 nm, 8×10 -12 nm, 7×10 -12 nm, 6×10 -12 nm, 5×10 -12 nm, 4×10 -12 nm, 3×10 -12 nm, 2×10 -12 nm, 1×10 -12 nm, 9×10 -13 nm, 8×10 -13 nm, 7×10 -13 nm, 6×10 -13 nm, 5×10 -13 nm, 4×10 -13 nm, 3×10 -13 nm, 2×10 -13 nm, 1×10 -13 nm, 9×10 -14 nm, 8×10-14 nm, 7×10 -14 nm, 6×10 -14 nm, 5×10 -14 nm, 4×10 -14 nm, 3 × 10 -14 nm, 2 × 10 -14 nm, 1×10 -14 nm, 9×10 -15 nm, 8×10 -15 nm, 7×10 -15 nm, 6×10 -15 nm, 5×10 -15 nm, 4×10 -15 nm, 3 × 10 -15 nm, 2 × 10 -15 nm, 1×10 -15 A laser may emit light having a bandwidth of 100 .mu.m, or shorter. A laser may emit light having a bandwidth within the range defined by any two of the preceding values.

[0101] The light source may be configured to emit light tuned to one or more magic wavelengths corresponding to the plurality of atoms. The magic wavelengths corresponding to the atoms may include any wavelength of light that induces equal or nearly equal polarizabilities of the first and second atomic states. The magic wavelengths of the transitions between the first and second atomic states may be determined by calculating the wavelength-dependent polarizabilities of the first and second atomic states and finding the intersection point. Light tuned to such magic wavelengths may induce equal or nearly equal differential optical shifts in the first and second atomic states regardless of the intensity of the light emitted from the light source. This may 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 optical shifts. The scalar or tensor optical shifts may depend on magnetic sublevels within the first and second atomic states.

[0102] For example, 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 adjusted to induce a situation where the scalar and tensor shifts are balanced, giving a zero or near-zero differential optical shift between the first and second atomic states. The angle θ can be adjusted by choosing the polarization of the emitted light. For example, if the emitted light is linearly polarized, the total polarizability α can be calculated by dividing the scalar component α scalar and the tensor component α tensor It can be written as the sum of α=α scalar +(3θ-1)α tensor

[0103] By appropriately choosing θ, the polarizabilities of the first and second atomic states can be chosen to be equal or nearly equal, corresponding to a zero or near-zero differential optical shift, allowing the atomic motions to be decoupled.

[0104] The light source may be configured to direct light to one or more optical modulators (OM) configured to generate a plurality of light capture sites. For example, the light capture unit may include an OM 214 configured to generate a plurality of light capture sites. Although depicted in FIG. 3A as including one OM, the light capture 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 OMs. The OM may include one or more digital micromirror devices (DMDs). The OM may include one or more liquid crystal devices, such as one or more liquid crystal on silicon (LCoS) devices. The OM may include one or more spatial light modulators (SLMs). The OM may include one or more acousto-optic deflectors (AODs) or acousto-optic modulators (AOMs). The OM may include one or more electro-optic deflectors (EODs) or electro-optic modulators (EOMs).

[0105] The OM may be optically coupled to one or more optical elements to generate a regular array of light capture sites. For example, the OM may be optically coupled to optical element 219, as shown in FIG. 3A. The optical element may include a lens or microscope objective configured to redirect light from the OM to form a regular rectangular grid of light capture sites.

[0106] For example, as shown in Figure 3A, the OM may include an SLM, DMD, or LCoS device, which may be imaged into the back focal plane of a microscope objective, potentially allowing the generation of any configuration of optical trapping sites in two or three dimensions.

[0107] Alternatively or additionally, the OM may include a first and a second AOD. The active areas of the first and second AOD may be imaged onto the back focal plane of a microscope objective. The output of the first AOD may be optically coupled to the input of the second AOD. In this way, the second AOD may create a copy of the optical output of the first AOD. This may allow the creation of optical trapping sites in two or three dimensions.

[0108] Alternatively or additionally, the OM may comprise one or more static optical elements, such as microlens arrays or holographic optical elements, which may be imaged onto the back focal plane of the microscope objective, potentially allowing the generation of any configuration of optical trapping sites in two or three dimensions.

[0109] The light trapping unit may include one or more imaging units configured to obtain one or more images of the spatial configuration of the atoms trapped within the light trapping site. For example, the light trapping unit may include imaging unit 215. Although depicted in FIG. 3A as including a single imaging unit, the light 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 units. The imaging unit may include one or more lenses or objective lenses. The imaging unit may include one or more PMTs, photodiodes, avalanche photodiodes, phototransistors, reverse-biased 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.

[0110] The optical capture unit may include one or more artificial intelligence (AI) units configured to perform one or more AI operations to determine the spatial configuration of the plurality of atoms captured within the optical capture site based on the image obtained by the imaging unit. For example, the optical capture unit may include a spatial configuration AI unit 216. Although depicted in FIG. 3A as including a single spatial configuration AI unit, the optical capture 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 up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 spatial configuration AI units. The AI ​​operations may include any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0111] The light trapping unit may include one or more atom rearrangement units configured to provide an altered spatial arrangement of the atoms trapped at the light trapping site based on one or more images obtained by the imaging unit. For example, the light trapping unit may include an atom rearrangement unit 217. Although depicted in FIG. 3A as including a single atom rearrangement unit, the light trapping unit may include any number of atom rearrangement units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more atom rearrangement units, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 atom rearrangement units.

[0112] The optical capture unit may include one or more spatial arrangement AI units configured to perform one or more AI operations to determine an altered spatial arrangement of the plurality of atoms captured within the optical capture site based on the image obtained by the imaging unit. For example, the optical capture unit may include a spatial arrangement AI unit 218. Although depicted in FIG. 3A as including a single spatial arrangement AI unit, the optical capture 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 units. The AI ​​operations may include any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0113] In some cases, the spatial configuration AI unit and the spatial arrangement AI unit may be integrated into an integrated AI unit. The light capture unit may include any number of integrated AI units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more integrated AI units, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 integrated AI unit.

[0114] The atom rearrangement unit may be configured to change the spatial arrangement to obtain an increased filling factor of the plurality of light trapping sites. The filling factor may be defined as the ratio of the number of computationally active light trapping sites occupied by one or more atoms to the total number of computationally active light trapping sites available in the light trapping unit or a portion of the light trapping unit. For example, an initial loading of atoms in the computationally active light trapping sites may result in a filling factor of 100%, 90%, 80%, 70%, 60%, 50%, or less, such that the atoms occupy less than 100%, 90%, 70%, 60%, 50%, or less of the available computationally active light trapping sites. It may be desirable to rearrange the atoms to achieve a filling factor of at least about 50%, 60%, 70%, 80%, 90%, or 100%. By analyzing the imaging information obtained by the imaging section, the atomic rearrangement unit may achieve a filling rate 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 greater. The atomic rearrangement unit may achieve a filling rate of up to about 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50% or less. The atomic rearrangement unit may achieve a filling rate within a range defined by any two of the above values.

[0115] As an example, Figure 3C shows an example of a light trapping unit that is partially filled with atoms. As depicted in Figure 3C, the initial loading of atoms in the light trapping sites can result in a filling factor of 44.4% (four atoms filling the nine available light trapping sites). By transferring atoms from a different region of the light trapping unit (not shown in Figure 3C) to the unoccupied light trapping sites or by transferring atoms from an atom reservoir as described herein, much higher filling factors can be obtained, as shown in Figure 3D.

[0116] FIG. 3D illustrates an example of a light trapping unit that is fully filled with atoms. As depicted in FIG. 3D, the fifth atom 212e, the sixth atom 212f, the seventh atom 212g, the eighth atom 212h, and the ninth atom 212i can be moved to fill the unoccupied light trapping sites. The fifth, sixth, seventh, eighth, and ninth atoms can be moved by moving atoms from different regions of the light trapping unit (not shown in FIG. 3C) or from an atom reservoir as described herein. Thus, the filling rate can be significantly improved following the rearrangement of atoms within the light trapping sites. For example, a filling rate of up to 100% (9 atoms filling the 9 available light trapping sites as shown in FIG. 3D) can be achieved.

[0117] The rearrangement of atoms may be performed by (i) acquiring an image of the optical trapping unit and identifying filled and unfilled optical trapping sites, (ii) determining a sequence of movements that move atoms from filled to unfilled optical trapping sites, and (iii) moving atoms from filled to unfilled optical trapping sites. Operations (i), (ii), and (iii) may be performed iteratively until a large fill factor is achieved. Operation (iii) may include converting the movements identified in operation (ii) into a waveform that can be sent to an arbitrary waveform generator (AWG) and using the AWG to drive the AOD to move the atoms. The sequence of movements may be determined using the Hungarian algorithm described in W. Lee et al., "Defect-Free Atomic Array Formation Using Hungarian Rearrangement Algorithm," Physical Review A 95, 053424 (2017), which is incorporated herein by reference in its entirety for all purposes.

[0118] Electromagnetic Delivery Unit 4 illustrates an example of an electromagnetic delivery unit 220. The electromagnetic delivery unit can be configured to apply electromagnetic energy to one or more atoms of the plurality of atoms as described herein. The electromagnetic delivery unit can include one or more light sources, such as any of the light sources described herein. The electromagnetic energy can include optical energy. The optical energy can include any repetition rate, pulse energy, average power, wavelength, or bandwidth described herein.

[0119] The electromagnetic delivery 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, Gunn diodes, impact ionization avalanche transit-time (IMPATT) diodes, or masers. The electromagnetic energy may include microwave energy or RF energy. The RF energy may be at least about 1 millimeter (mm), 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, 9 mm, 10 mm, 20 mm, 30 mm, 40 mm, 50 mm, 60 mm, 70 mm, 80 mm, 90 mm, 100 mm, 200 mm, 300 mm, 400 mm, 500 mm, 600 mm, 700 mm, 800 mm, 900 mm, 1 meter (m), 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, 9 m, 10 m, 12 m, 14 m, 16 m, 18 m, 19 m, 20 m, 21 m, 22 m, 23 m, 24 m, 25 m, 26 m, 27 m, 28 m, 29 m, 30 m, 31 m, 32 m, 33 m, 34 m, 35 m, 36 m, 37 m, 38 m, 39 m, 40 m, 41 m, 42 m, 43 m, 44 m, 45 m, 46 m, 47 m, 48 m, 49 m, 50 m, 50 m, 50 m, 60 m, 70 mm, 80 mm, 90 mm, 100 mm, 200 mm The wavelength may include one or more wavelengths longer than 100 m, 4 m, 5 m, 6 m, 7 m, 8 m, 9 m, 10 m, 20 m, 30 m, 40 m, 50 m, 60 m, 70 m, 80 m, 90 m, 100 m, 200 m, 300 m, 400 m, 500 m, 600 m, 700 m, 800 m, 900 m, 1 kilometer (km), 2 km, 3 km, 4 km, 5 km, 6 km, 7 km, 8 km, 9 km, 10 km, or more. RF energy up to approximately 10km, 9km, 8km, 7km, 6km, 5km, 4km, 3km, 2km, 1km, 900m, 800m, 700m, 600m, 500m, 400m, 300m, 200m, 100m, 90m, 80m, 70m, 60m, 50m, 40m, 30m, 20m, 10m, 9m, 8m, 7m, 6m, 5m, 4m, 3m, 2m, The RF energy may include one or more wavelengths that are within a range defined by any two of the foregoing values.

[0120] The RF energy may be at least about 1 microwatt (μW), 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 milliwatt (mW), 2 mW, 3 mW, 4 mW, 5 mW, 6 mW, 7 mW, 8 mW, 9 mW, 10 mW, 20 mW, 30 mW, 40 mW, 50 mW, 60 mW, 70 mW, 80 mW, 90 mW, 100 mW, 200 mW, 300 mW, 400 mW, 500 mW, 600 mW, 700 mW, 800 mW, 90 ... In some embodiments, the average power may include, for example, 1 W, 50 mW, 60 mW, 70 mW, 80 mW, 90 mW, 100 mW, 200 mW, 300 mW, 400 mW, 500 mW, 600 mW, 700 mW, 800 mW, 900 mW, 1 Watt (W), 2 W, 3 W, 4 W, 5 W, 6 W, 7 W, 8 W, 9 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W, 80 W, 90 W, 100 W, 200 W, 300 W, 400 W, 500 W, 600 W, 700 W, 800 W, 900 W, 1,000 W, or more. RF energy can be up to approximately 1,000W, 900W, 800W, 700W, 600W, 500W, 400W, 300W, 200W, 100W, 90W, 80W, 70W, 60W, 50W, 40W, 30W, 20W, 10W, 9W, 8W, 7W, 6W, 5W, 4W, 3W, 2W, 1W, 900mW, 800mW, 700mW, 600mW, 500mW, 400mW, 300mW, 200mW, 100mW, 90mW, 80mW, 70mW, 60mW, 50mW, 40 The RF energy may include an average power of 1000 uW, 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. The RF energy may include an average power that is within a range defined by any two of the aforementioned values.

[0121] The electromagnetic delivery unit can include one or more light sources, such as any of the light sources described herein. For example, the electromagnetic delivery unit can include light source 221. Although depicted in FIG. 4 as including a single light source, the electromagnetic delivery unit can 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 up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 light source.

[0122] The light source may be configured to direct light to one or more OMs configured to selectively apply electromagnetic energy to one or more atoms of the plurality of atoms. For example, the electromagnetic delivery unit may include OM222. Although depicted in FIG. 4 as including a single OM, the electromagnetic delivery 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 OM may include one or more SLMs, AODs, or AOMs. The OM may include one or more DMDs. The OM may comprise one or more liquid crystal devices, such as one or more LCoS devices.

[0123] The electromagnetic delivery unit may include one or more electromagnetic energy artificial intelligence (AI) units configured to perform one or more AI operations to selectively apply electromagnetic energy to atoms. For example, the electromagnetic delivery unit may include an AI unit 223. Although depicted in FIG. 4 as including a single AI unit, the electromagnetic delivery unit may include any number of AI units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more AI units, or up 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.

[0124] The electromagnetic delivery unit may be configured to apply one or more single-qubit operations (such as one or more single-qubit gate operations) to a qubit as described herein. The electromagnetic delivery unit may be configured to apply one or more two-qubit operations (such as one or more two-qubit gate operations) to a two-qubit unit as described herein. Each single-qubit or two-qubit operation may comprise a duration of at least about 10 nanoseconds (ns), 20 ns, 30 ns, 40 ns, 50 ns, 60 ns, 70 ns, 80 ns, 90 ns, 100 ns, 200 ns, 300 ns, 400 ns, 500 ns, 600 ns, 700 ns, 800 ns, 900 ns, 1 microsecond (μs), 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 more. Each single qubit or two-qubit operation may include a duration of up to about 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 period within a range defined by any two of the foregoing values. Single qubit or two qubit operations may be applied at a repetition rate of at least 1 kilohertz (kHz), 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 50 kHz, 60 kHz, 70 kHz, 80 kHz, 90 kHz, 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1,000 kHz, or more.Single or two-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 or two-qubit operations may be applied at repetition frequencies within the range defined by any two of the foregoing values.

[0125] The electromagnetic delivery unit may be configured to apply one or more single qubit operations by inducing one or more Raman transitions between a first qubit state and a second qubit state as described herein. 3 P0 or 3For example, the Raman transition may be detuned by at least about 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 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 MHz, 60 MHz, 70 MHz, 80 MHz, 90 MHz, 100 MHz, 200 MHz, 300 MHz, 400 MHz, 500 MHz, 600 MHz, 700 MHz, 800 MHz, 900 MHz, 1 GHz, or more. The Raman transitions may be detuned by up to about 1 GHz, 900 MHz, 800 MHz, 700 MHz, 600 MHz, 500 MHz, 400 MHz, 300 MHz, 200 MHz, 100 MHz, 90 MHz, 80 MHz, 70 MHz, 60 MHz, 50 MHz, 40 MHz, 30 MHz, 20 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, or less. The Raman transition may be detuned by a value within a range defined by any two of the aforementioned values.

[0126] Raman transitions may be induced in 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 a light beam based on an applied radio frequency (RF) signal. The SLM or AOD may be combined with an optical conditioning system that images the active area of ​​the SLM or AOD onto the back focal plane of a microscope objective. The microscope objective may perform a spatial Fourier transform on the optical field at the location of the SLM or AOD. In this way, an angle (which may be proportional to the RF frequency) may be converted to a position. For example, applying a radio frequency comb to the AOD may produce a linear array of spots in the focal plane of the objective, each spot having a finite range determined by the properties of the optical conditioning system (such as the point spread function of the optical conditioning system).

[0127] To perform a Raman transition on a single atom using a single SLM or AOD, a pair of frequencies may be applied simultaneously to the SLM or AOD. The two frequencies in the pair may have a frequency difference that matches or nearly matches the splitting energy between the first and second qubit states. For example, the frequency difference may differ from the split energy by up to about 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, 900 Hz, 800 Hz, 700 Hz, 600 Hz, 500 Hz, 400 Hz, 300 Hz, 200 Hz, 100 Hz, 90 Hz, 80 Hz, 70 Hz, 60 Hz, 50 Hz, 40 Hz, 30 Hz, 20 Hz, 10 Hz, 9 Hz, 8 Hz, 7 Hz, 6 Hz, 5 Hz, 4 Hz, 3 Hz, 2 Hz, 1 Hz, or less. The frequency difference may differ from the split energy by at least about 1 Hz, 2 Hz, 3 Hz, 4 Hz, 5 Hz, 6 Hz, 7 Hz, 8 Hz, 9 Hz, 10 Hz, 20 Hz, 30 Hz, 40 Hz, 50 Hz, 60 Hz, 70 Hz, 80 Hz, 90 Hz, 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 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, 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 aforementioned values. The optical system may be configured such that a position interval corresponding to the frequency difference is not resolved and both frequencies of light interact with a single atom.

[0128] The electromagnetic delivery unit is at least about 10 nm, 50 nm, 7 nm, 100 nm, 125 nm, 150 nm, 175 nm, 200 nm, 225 nm, 250 nm, 275 nm, 300 nm, 325 nm, 350 nm, 375 nm, 400 nm, 425 nm, 450 nm, 475 nm, 500 nm, 525 nm, 550 nm, 575 nm, 600 nm, 625 nm, 650 nm, 675 nm, 700 nm, 725 nm, 750 nm, 77 It may be configured to provide a beam having a characteristic dimension of 5 nm, 800 nm, 825 nm, 850 nm, 875 nm, 900 nm, 925 nm, 950 nm, 975 nm, 1 micrometer (μm), 1.5 μm, 2 μm, 2.5 μm, 3 μm, 3.5 μm, 4 μm, 4.5 μm, 5 μm, 5.5 μm, 6 μm, 6.5 μm, 7 μm, 7.5 μm, 8 μm, 8.5 μm, 9 μm, 9.5 μm, 10 μm, or longer. The electromagnetic delivery unit has a maximum of about 10μm, 9.5μm, 9μm, 8.5μm, 8μm, 7.5μm, 7μm, 6.5μm, 6μm, 5.5μm, 5μm, 4.5μm, 4μm, 3.5μm, 3μm, 2.5μm, 2μm, 1.5μm, 1μm, 975nm, 950nm, 925nm, 900nm, 875nm, 850nm, 825nm, 800nm, 775nm, 750nm, 725nm, 700nm, 675nm, 6 The electromagnetic delivery unit may be configured to provide a beam having a characteristic dimension of 50 nm, 625 nm, 600 nm, 575 nm, 550 nm, 525 nm, 500 nm, 475 nm, 450 nm, 425 nm, 400 nm, 375 nm, 350 nm, 325 nm, 300 nm, 275 nm, 250 nm, 225 nm, 200 nm, 175 nm, 150 nm, 125 nm, 100 nm, 75 nm, 25 nm, 10 nm, or less. The electromagnetic delivery unit may be configured to provide the beam with a characteristic dimension defined by any two of the aforementioned values. For example, the beam may have a characteristic dimension of about 1.5 micrometers to about 2.5 micrometers. Examples of characteristic dimensions are the Gaussian beam waist, the full width at half maximum (FWHM) of the beam dimension, the beam diameter, the 1 / e 2The beam may have a Gaussian beam waist of at least about 1.5 micrometers, including but not limited to a D4σ width, a D86 width, etc. For example, the beam may have a Gaussian beam waist of at least about 1.5 micrometers.

[0129] The characteristic dimension of the beam may be limited at the lower end by the size of the atomic wave packet at the optical trapping site. For example, the beam may be shaped such that the intensity variation of the beam over the trapping site is small enough and substantially uniform over the trapping site. In this example, the uniformity of the beam may improve the fidelity of the qubits at the trapping site. The characteristic dimension of the beam may be limited at the upper end by the spacing between the trapping sites. For example, the beam may be shaped such that the effect of the beam on adjacent trapping sites / atoms is small enough that it is negligible. In this example, the effect may be negligible if it can be minimized by techniques such as composite pulse engineering. The characteristic dimension may differ from the maximum achievable resolution of the system. For example, the maximum resolution of the system may be 700 nm, but the system may operate at 1.5 micrometers. In this example, the value of the characteristic dimension may be selected to optimize the performance of the system taking into account considerations described elsewhere herein. The characteristic dimension may be invariant for different maximum achievable resolutions. For example, a system with a maximum resolution of 500 nm and a system with a maximum resolution of 2 micrometers may both be configured to operate with a characteristic dimension of 2 micrometers. In this example, 2 micrometers may be the optimal resolution based on the size of the trapping site.

[0130] Integrated light capture and electromagnetic delivery unit The light capture unit and the electromagnetic delivery unit described herein can be integrated into a single optical system. A microscope objective lens can be used to deliver the electromagnetic radiation generated by the electromagnetic delivery unit described herein and deliver the light for capturing atoms generated by the optical capture unit described herein. Alternatively or additionally, different objective lenses can be used to deliver the electromagnetic radiation generated by the electromagnetic delivery unit and deliver the light from the captured atoms generated by the optical capture unit.

[0131] A single SLM or AOD can allow for the implementation of qubit operations (such as any single-qubit or two-qubit operations described herein) on a linear array of atoms. Alternatively or additionally, two separate SLMs or AODs can be configured, each processing light of orthogonal polarizations. Light of orthogonal polarizations can be superimposed in front of a microscope objective lens. In such a scheme, each photon used in a two-photon transition described herein is passed to the objective lens by a separate SLM or AOD, allowing for improved polarization control. Qubit operations can be performed on a two-dimensional array of atoms by bringing light from a first SLM or AOD through an optical relay to a second SLM or AOD oriented substantially orthogonally to the first SLM or AOD. Alternatively or additionally, qubit operations can be performed on a two-dimensional array of atoms by using a one-dimensional array of SLMs or AODs.

[0132] The stability of the qubit gate fidelity may be improved by maintaining an overlap of light from the various light sources described herein (such as the light sources associated with the light capture units or electromagnetic delivery units described herein). Such overlap is maintained by an optical subsystem that measures the direction of light emitted from the various light sources, thus allowing closed-loop control of the direction of light emission. The optical subsystem may include a pick-off mirror positioned in front of the microscope objective lens. The pick-off mirror may be configured to direct a small amount of light to a lens that can focus the collimated beam and convert the angular deviation into a position deviation. A position-sensitive optical detector, such as a transverse effect position sensor or a quadrant photodiode, may convert the position deviation into an electronic signal and provide information about the deviation to an adaptive optics system, such as an active mirror.

[0133] The stability of the qubit gate operation can be improved by controlling the intensity of light from the various light sources described herein (such as the light sources associated with the optical trapping units or electromagnetic delivery units described herein). Such intensity control is maintained by an optical subsystem that measures the intensity of light emitted by the various light sources, allowing for closed-loop control of the intensity. Each light source can be coupled to an intensity actuator, such as an intensity servo control. The actuator can comprise an acousto-optical modulator (AOM) or an electro-optical modulator (EOM). The intensity can be measured using a photodetector, such as a photodiode or any other photodetector described herein. Information regarding the intensity can be integrated into a feedback loop to stabilize the intensity.

[0134] State Readiness Unit 5 is a diagram illustrating an example of a state preparation unit 250. The state preparation unit may be configured to prepare a state of the plurality of atoms as described herein. The state preparation unit may be coupled to the optical trapping unit and may direct the atoms prepared by the state preparation unit to the optical trapping unit. The state preparation unit may be configured to cool the plurality of atoms. The state preparation unit may be configured to cool the plurality of atoms before trapping the plurality of atoms in the plurality of optical trapping sites.

[0135] The state preparation unit may include one or more Zeeman decelerators. For example, the state preparation unit may include Zeeman decelerator 251. Although depicted in FIG. 5 as including a single Zeeman decelerator, the state preparation may include any number of Zeeman decelerators, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more Zeeman decelerators, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 Zeeman decelerators. The Zeeman decelerator may be configured to cool one or more atoms of the plurality of atoms from a first velocity or velocity distribution (such as an emission velocity from the atom source, room temperature, liquid nitrogen temperature, or other temperature) to a second velocity that is lower than the first velocity or velocity distribution.

[0136] The first velocity or velocity distribution may be associated with a temperature of at least about 50 Kelvin (K), 60K, 70K, 80K, 90K, 100K, 200K, 300K, 400K, 500K, 600K, 700K, 800K, 900K, 1,000K, or higher. The first velocity or velocity distribution may be associated with a temperature of up to about 1,000K, 900K, 800K, 700K, 600K, 500K, 400K, 300K, 200K, 100K, 90K, 80K, 70K, 60K, 50K, or lower. The first velocity or velocity distribution may be associated with a temperature within a range defined by any two of the aforementioned values. The second velocity may be at least about 1 meter per second (m / s), 2 m / s, 3 m / s, 4 m / s, 5 m / s, 6 m / s, 7 m / s, 8 m / s, 9 m / s, 10 m / s, or more. The second velocity may be up to 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 more. The second velocity may be within a range defined by any two of the aforementioned values. The Zeeman reducer may include a 1D Zeeman reducer.

[0137] The state preparation unit may include a first magnetic optical trap (MOT) 252. The first MOT may be configured to cool the atoms to a first temperature. The first temperature may be at most about 10 millikelvin (mK), 9 mK, 8 mK, 7 mK, 6 mK, 5 mK, 4 mK, 3 mK, 2 mK, 1 mK, 0.9 mK, 0.8 mK, 0.7 mK, 0.6 mK, 0.5 mK, 0.4 mK, 0.3 mK, 0.2 mK, 0.1 mK, or lower. 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 higher. The first temperature may be within a range defined by any two of the aforementioned values. The first MOT may include a 1D, 2D, or 3D MOT.

[0138] The first MOT may include one or more light sources (such as any light sources described herein) configured to emit light. The light may be at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, m, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or longer. The light can range up to approximately 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 6 ...90nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or shorter. The light may include one or more wavelengths that are within a range defined by any two of the foregoing values.For example, the light may include one or more wavelengths in the ranges of 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.

[0139] The state preparation unit may include a second MOT 253. The second MOT may be configured to cool the atoms from a first temperature to a second temperature lower than the first temperature. The second temperature may be at most about 100 microkelvin (μK), 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 nanokelvin (nK), 800 nK, 700 nK, 600 nK, 500 nK, 400 nK, 300 nK, 200 nK, 100 nK, or lower. The second temperature may be at least about 100nK, 200nK, 300nK, 400nK, 500nK, 600nK, 700nK, 800nK, 900nK, 1μK, 2μK, 3μK, 4μK, 5μK, 6μK, 7μK, 8μK, 9μK, 10μK, 20μK, 30μK, 40μK, 50μK, 60μK, 70μK, 80μK, 90μK, 100μK, or higher. The second temperature may be within a range defined by any two of the aforementioned values. The second MOT may include a 1D, 2D, or 3D MOT.

[0140] The second MOT may include one or more light sources (such as any light sources described herein) configured to emit light. The light may be at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, m, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or longer. The light can range up to approximately 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 6 ...90nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or shorter. The light may include one or more wavelengths that are within a range defined by any two of the foregoing values.For example, the light may include one or more wavelengths in the ranges of 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] Although depicted 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 up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 MOTs.

[0142] The state preparation unit may comprise one or more sideband or Sisyphus cooling units (such as the sideband cooling units described at www.arxiv.org / abs / 1810.06626 or the Sisyphus cooling units described at www.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 comprise a sideband or Sisyphus cooling unit 254. 5 as including a single sideband or Sisyphus cooling unit, the state preparation may include any number of sideband or Sisyphus cooling units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more sideband or Sisyphus cooling units, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 sideband or Sisyphus cooling units. The sideband or Sisyphus cooling units may be configured to cool atoms from a second temperature to a third temperature lower than the second temperature using sideband cooling. The third temperature can be at most about 10 μK, 9 μK, 8 μK, 7 μK, 6 μK, 5 μK, 4 μK, 3 μK, 2 μK, 1 μK, 900nK, 800nK, 700nK, 600nK, 500nK, 400nK, 300nK, 200nK, 100nK, 90nK, 80nK, 70nK, 60nK, 50nK, 40nK, 30nK, 20nK, 10nK, or lower. The third temperature can be at most about 10 nK, 20 nK, 30 nK, 40 nK, 50 nK, 60 nK, 70 nK, 80 nK, 90 nK, 100 nK, 200 nK, 300 nK, 400 nK, 500 nK, 600 nK, 700 nK, 800 nK, 900 nK, 1 μK, 2 μK, 3 μK, 4 μK, 5 μK, 6 μK, 7 μK, 8 μK, 9 μK, 10 μK, or more. The third temperature can be within a range defined by any two of the foregoing values.

[0143] The sideband or Sisyphus cooling unit may include one or more light sources (such as any of the light sources described herein) configured to emit light. The light may be at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1000 nm, 1020 nm, 1040 nm, 1060 nm, 1080 nm, 1090 nm, 1100 nm, 1110 nm, 1120 nm, 1130 nm, 1140 nm, 1150 nm, 1160 nm, 1170 nm, 1180 nm, 1190 nm m, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or longer. The light can range up to approximately 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 6 ...90nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or shorter. The light may include one or more wavelengths that are within a range defined by any two of the foregoing values.For example, the light may include one or more wavelengths in the ranges of 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] The state preparation unit may include one or more optical pumping units. For example, the state preparation unit may include optical pumping unit 255. Although depicted 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 units. The optical pumping unit 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 unit may be configured to emit light to optically pump atoms from an equilibrium distribution of atomic states to a single pure atomic state. The optical pumping unit may be configured to emit light to optically pump atoms to a ground atomic state or any other atomic state. The optical pumping unit may be configured to optically pump atoms between any two atomic states. The optical pumping unit may include one or more light sources (such as any of the light sources described herein) configured to emit light having a wavelength of at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, m, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or longer.The light can range up to approximately 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 6 ...90nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or shorter. The light may include one or more wavelengths that are within a range defined by any two of the foregoing values. For example, the light may include one or more wavelengths in the ranges of 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.

[0145] The state preparation unit may comprise one or more coherent drive units. For example, the state preparation unit may comprise a coherent drive unit 256. Although depicted in FIG. 5 as including a coherent drive unit, the state preparation may include any number of coherent drive units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more coherent drive units, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 coherent drive units. The coherent drive units may be configured to coherently drive the atoms from a non-equilibrium state to a first or second atomic state described herein. Thus, the atoms may be optically pumped to a convenient atomic state to access (e.g., based on the availability of a light source emitting a particular wavelength, or based on other factors), and then coherently driven to an atomic state described herein that is useful for performing quantum computation. The coherent drive units may be configured to induce a single-photon transition between the non-equilibrium state and the first or second atomic state. The coherent drive unit can be configured to induce a two-photon transition between the non-equilibrium state and the first or second atomic state. The two-photon transition can be induced using light from two light sources as described herein (such as two lasers as described herein).

[0146] The coherent driving unit may include one or more light sources (such as any of the light sources described herein) configured to emit light. The light may be at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, m, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm, or longer. The light can range up to approximately 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 6 ...90nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 780nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790nm, 790 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or shorter. The light may include one or more wavelengths that are within a range defined by any two of the foregoing values.For example, the light may include one or more wavelengths in the ranges of 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.

[0147] The coherent driving unit may be configured to induce an RF transition between the non-equilibrium state and the 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 the RF transition. For example, the coherent driving unit may include one or more RF sources (such as any RF source described herein) configured to emit RF radiation. The RF radiation may include one or more wavelengths of at least about 10 centimeters (cm), 20 cm, 30 cm, 40 cm, 50 cm, 60 cm, 70 cm, 80 cm, 90 cm, 1 meter (m), 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, 9 m, 10 m, or longer. The 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 shorter. The RF radiation may include one or more wavelengths within a range defined by any two of the aforementioned values. Alternatively or additionally, the coherent driving unit may comprise one or more light sources (such as any light sources described herein) configured to induce two-photon transitions corresponding to the RF transitions.

[0148] controller The optical capture unit, electromagnetic delivery unit, entanglement unit, readout optical unit, vacuum unit, imaging unit, spatial configuration AI unit, spatial configuration AI unit, atomic rearrangement unit, state preparation unit, sideband cooling unit, optical pumping unit, coherent drive unit, electromagnetic energy AI unit, atomic reservoir, atom transfer unit, or Rydberg excitation unit may include one or more circuits or controllers (e.g., one or more electronic circuits or controllers) connected to the optical capture unit, electromagnetic delivery unit, entanglement unit, readout optical unit, vacuum unit, imaging unit, spatial configuration AI unit, spatial configuration AI unit, atomic rearrangement unit, state preparation unit, sideband cooling unit, optical pumping unit, coherent drive unit, electromagnetic energy AI unit, atomic reservoir, atom transfer unit, or Rydberg excitation unit (e.g., by one or more electronic connections). The circuit or controller may be configured to control an optical capture unit, an electromagnetic delivery unit, an entanglement unit, a readout optical unit, a vacuum unit, an imaging unit, a spatial configuration AI unit, a spatial arrangement AI unit, an atomic rearrangement unit, a state preparation unit, a sideband cooling unit, an optical pumping unit, a coherent drive unit, an electromagnetic energy AI unit, an atomic reservoir, an atomic transfer unit, or a Rydberg excitation unit.

[0149] Non-Classical Computers In one aspect, the disclosure provides a non-classical computer comprising: a plurality of qubits including more than 60 atoms, each atom being trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, the plurality of qubits including at least a first qubit state and a second qubit state, the first qubit state including a first atomic state and the second qubit state including a second atomic state; one or more electromagnetic delivery units configured to apply electromagnetic energy to one or more qubits of the plurality of qubits, thereby imparting a non-classical operation to the one or more qubits, the non-classical operation including a superposition between at least the first qubit state and the second qubit state; one or more entanglement units configured to quantum mechanically entangle at least a subset of the plurality of qubits in superposition with at least another qubit of the plurality of qubits; and one or more readout optical units configured to perform one or more measurements of the one or more qubits, thereby obtaining a non-classical computation.

[0150] In one aspect, the present disclosure provides a non-classical computer that includes a plurality of qubits, each of which includes more than 60 atoms trapped within one of a plurality of spatially distinct optical trapping sites.

[0151] How to perform non-classical computations In one aspect, the present disclosure provides a method for performing a non-classical computation, the method including: (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 including more than 60 atoms; (b) applying electromagnetic energy to one or more atoms of the plurality of atoms, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state; (c) quantum mechanically entangle at least a subset of the one or more atoms in the one or more superposition states with at least another atom of the plurality of atoms; and (d) performing one or more optical measurements of the one or more superposition states to obtain a non-classical computation.

[0152] FIG. 6 is a flow chart of an example of a first method 600 for performing non-classical computation.

[0153] In a first operation 610, the method 600 may include generating a plurality of spatially distinct optical trapping sites. The plurality of optical trapping sites may be configured to trap a plurality of atoms. The plurality of atoms may include more than 60 atoms. The optical trapping sites may include any optical trapping site described herein. The atoms may include any atoms described herein.

[0154] In a second operation 620, the method 600 may include applying electromagnetic energy to one or more atoms of the plurality of atoms, thereby inducing the one or more atoms to adopt one or more superpositions of a first atomic state and at least a second atomic state 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 a third operation 630, the method 600 may include quantum mechanically entangled at least a subset of the one or more atoms in one or more superposition states with at least another atom of the plurality of atoms. The atoms may be quantum mechanically entangled in any manner described herein (e.g., as described herein with respect to FIG. 2).

[0156] In a fourth operation 640, the method 600 may include performing one or more optical measurements of the one or more superposition states to obtain a non-classical 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-classical computation, the method comprising: (a) 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, the plurality of qubits comprising at least a first qubit state and a second qubit state, the first qubit state comprising a first atomic state and the second qubit state comprising a second atomic state; (b) applying electromagnetic energy to one or more qubits of the plurality of qubits, thereby imparting a non-classical operation to the one or more qubits comprising a superposition between at least the first qubit state and the second qubit state; (c) quantum mechanically entangle at least a subset of the plurality of qubits in the superposition with at least another qubit of the plurality of qubits; and (d) performing one or more optical measurements of the one or more qubits, thereby obtaining the classical computation.

[0158] FIG. 7 is a flow chart of an example of a second method 700 for performing non-classical computation.

[0159] In a first operation 710, the method 700 may include providing a plurality of qubits including more than 60 atoms, each atom being trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, the plurality of qubits including at least a first qubit state and a second qubit state, the first qubit state including a first atomic state and the second qubit state including a second atomic state. The optical trapping site may include any optical trapping site described herein. The qubits may include any qubits described herein. The atoms may include any atoms described herein. The first qubit state may include any first qubit state described herein. The second qubit state may include any second qubit state 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.

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

[0161] In a third operation 730, the method 700 may include quantum mechanically entangled at least a subset of the plurality of qubits in the superposition with at least another qubit of the plurality of qubits. The qubits may be quantum mechanically entangled in any manner described herein (e.g., as described herein with respect to FIG. 2).

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

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

[0164] FIG. 8 is a flowchart illustrating an example of a third method 800 for performing non-classical computation.

[0165] In a first operation 810, the method 800 may include providing a plurality of qubits including 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 qubit described herein. The atoms may include any atom described herein. The optical trapping sites may include any optical trapping sites described herein.

[0166] In a second operation 820, the method 800 may include performing a non-classical computation using at least a subset of the plurality of qubits.

[0167] Selective Excitation In another aspect, the present disclosure provides a method for selecting an atom from a plurality of atoms. A first pulse may be applied to the plurality of atoms. The plurality of atoms may include the atom and one or more other atoms. A second pulse may be applied to the atom but not to the one or more other atoms. A third pulse may be applied to the plurality of atoms. A combination of the first, second, and third pulses may impart a state to the atom to provide the selected atom. For example, the first, second, and third pulses may provide a transient phase that results in the selection of the atom. For example, the phase may be imparted by the second pulse, and after the third pulse, the atom may be in an excited state if the phase was present, or in a ground state if the phase was not present.

[0168] The first pulse may include a π / 2 pulse or a multiple thereof (e.g., a 2n+1 multiple thereof). For example, a 5π / 2 pulse may be used. The second pulse may include a 2π pulse or a multiple thereof (e.g., a 2n multiple thereof, where n is an even number). For example, a 4π pulse may be used. The third pulse may include a -π / 2 pulse or a multiple thereof (e.g., a 2n+1 multiple thereof). For example, a -5π / 2 pulse may be used. In some cases, the first and third pulses may be of equal magnitude and opposite in sign to each other (e.g., a positive first pulse and a negative third pulse). For example, a π first pulse may result in a -π third pulse. The accuracy with which the magnitudes of the first and third pulses match may be important to the function of the disclosed method and system. For example, a good match of the magnitudes of the first and third pulses may result in minimal or no additional energy being added to the atoms, thereby improving fidelity. The magnitudes of the first and third pulses may be within at least about 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 99.9, 99.99, 99.999, 99.9999, 99.9999, or more percent of each other. The magnitudes of the first and third pulses may be within at most about 99.99999, 99.9999, 99.999, 99.9, 99.9, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, or less percent of each other. In some cases, the first and third pulses are pulses of the same type (e.g., same sign, same magnitude, any combination thereof, etc.). For example, the first and third pulses can each be a +π / 2 pulse. In this example, atoms selected to receive the first and third pulses can be placed in an excited state, while atoms that do not receive the first and third pulses can remain in the ground state. In this manner, atoms that do not receive the first and third pulses can be selected (e.g., placed in a different state than the remaining atoms).

[0169] The selected atom may be addressable by light different from one atom of the plurality of atoms. For example, energy added to the qubit state of the selected atom may result in the atom being in a different state than the other atoms of the plurality of atoms. For example, the selected atom may be addressable by light of a different wavelength from the other atoms of the plurality of atoms (e.g., due to the presence of energy in the qubit state of the atom). Thus, the selected atom may be used in the methods described elsewhere herein (e.g., as part of a gate operation, etc.). In this way, the selected atom may be addressable separately from the other atoms of the plurality of atoms.

[0170] The first, second, and third pulses may change the state of at least one of the selected atoms, but not each other atom of the plurality of atoms. For example, the state may be changed because the second pulse is applied to the selected atom. The state change may be the reason for the individual addressability of the selected atom. For example, the state change may be the qubit state of the atom. In this example, the qubit state may be excited relative to the qubit states of other atoms of the plurality of atoms, which may then allow the excitation of the atom to be selectable. The first pulse or the third pulse may be polarized. Examples of polarization include, but are not limited to, circular polarization, linear polarization, π polarization, and the like.

[0171] The method can include applying a magnetic field across the plurality of atoms. The magnetic field can be at least about 0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 10,000, 50,000, or more milliteslas (mT). The magnetic field may be up to about 50,000, 10,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0.5, 0.5, 0.05, 0.01, 0.005, 0.001, or less millitesla. The magnetic field may be uniform across the plurality of atoms. For example, the magnetic field may be the same magnitude for each atom of the plurality of atoms. The magnetic field may not be uniform across the plurality of atoms. For example, the magnetic field may have inherent inhomogeneity, resulting in different atoms having different applied fields. In another example, the magnetic field can be adapted to have different magnetic field strengths for different atoms of the plurality of atoms. The magnetic field can be generated by an electromagnet, a permanent magnet, etc., or any combination thereof. The magnetic field can result in a division of levels (e.g., sublevels of the electronic structure of the atoms). Such division can result in additional states that are accessible compared to atoms that are not in the magnetic field. For example, applying a magnetic field to the plurality of atoms can result in different levels available for use as different manifold states. The magnetic field may not be applied to the plurality of atoms. Instead of a magnetic field, the fine structure of the plurality of atoms can be used to provide the states accessed by the pulse.

[0172] The plurality of atoms may include one or more atoms as described elsewhere herein. For example, the plurality of atoms may include alkaline earth atoms. The plurality of atoms may include two valence electron atoms. Two valence electron atoms may have two electrons in the highest occupied orbital. For example, lanthanum may have [Xe]5d 1 6s 2 and has two electrons in its highest energy orbital. Examples of two-electron atoms include, but are not limited to, alkaline earth atoms (e.g., beryllium, magnesium, calcium, strontium, barium, radium), lanthanides and actinides (e.g., lanthanum, actinium, ytterbium, etc.), transition metals (e.g., scandium, yttrium, etc.), and the like. The multiple atoms may each include the same element. The multiple atoms may each include different elements.

[0173] In another aspect, the present disclosure provides a method. A plurality of atoms can be provided. At least one atom of the plurality of atoms can have a state different from one or more other atoms of the plurality of atoms. The at least one atom can be excited to an excited state. The excitation can be performed using a non-site-selective excitation beam over the plurality of atoms that only interacts with the at least one atom. The state of the at least one atom can be generated as described elsewhere herein (e.g., the at least one atom can be a selected atom).

[0174] The state of the at least one atom may be generated during preparation of the at least one atom (e.g., selection as described elsewhere herein). The state may be the result of a phase that the at least one atom has during a selection operation as described elsewhere herein. For example, an atom having a phase may be selected and placed in an excited state. In another example, an atom without a phase may be selected and placed in a ground state. An atom may be placed in either the ground state or an excited state in the present methods.

[0175] The non-site-selective excitation beam may be generated as described elsewhere herein. The non-site-selective excitation beam may be applied to each atom of the plurality of atoms. For example, the non-site-selective excitation beam may be a beam that is applied simultaneously to all atoms of the plurality of atoms. The non-site-selective excitation beam may be light as described elsewhere herein. For example, the non-site-selective excitation beam may be an ultraviolet excitation beam. The non-site-selective excitation beam may be a read beam. For example, the non-site-selective excitation beam may be configured to read a state from at least one atom. Examples of read beams include beams having wavelengths from about 350 nanometers to about 575 nanometers. For example, the read beam may have a wavelength of 399 nm, 405 nm, 450 nm, etc. The non-site-selective excitation beam may be applied to at least two atoms of the plurality of atoms. For example, the non-site-selective excitation beam may be applied to a subset of the plurality of atoms. The non-site-selective excitation beam may only interact with at least one atom despite being applied to all of the atoms of the plurality of atoms. The existence of different states in the at least one atom can result in the at least one atom interacting with the non-site-selective excitation beam. The excited state can be a Rydberg state. The Rydberg state can be as described elsewhere herein. For example, the atom of the at least one atom can be excited to a Rydberg state.

[0176] The excitation may be time-domain multiplexed. For example, the excitation may excite multiple separate sets of atoms simultaneously. In this example, the atoms may be separated by a sufficient distance such that they do not interact with each other, but may be excited by the same non-site-selective beam. In this example, multiple gate operations may be performed simultaneously using the same non-site-selective beam, thus resulting in time-domain multiplexing of the excitation. The method may include exciting at least another atom of the multiple atoms using the same excitation beam simultaneously with the exciting step. The at least another atom may not interact with the at least one atom. For example, the at least another atom and the at least one atom may be separated such that they do not interact. In another example, the at least another atom and the at least one atom may be configured such that they cannot interact. For example, the states of the at least another atom and the at least one atom may be such that interaction between the states is minimized. The excitation of multiple non-interacting atoms allows the use of multiple gate operations simultaneously using the same excitation beam. For example, single qubit gates and two qubit gates may be prepared using the same excitation beam, but may be non-interacting due to physical separation of the atoms of the qubits. In this way, computations performed by multiple qubits can be parallelized, thereby increasing the speed of the computations.

[0177] The method can be at least part of a universal set of qubit gate operations. For example, the method can be at least part of a qubit gate operation. In this example, the method can be repeated for sufficient other gate operations to form a universal set of qubit gate operations. The universal set of qubit gate operations can be as described elsewhere herein.

[0178] The method may be configured to prepare one or more atoms for imaging. For example, one or more atoms may be left in the atomic ground state, which allows one or more atoms to be read and the remaining atoms of the plurality of atoms not to be read. In this manner, preparing one or more atoms for imaging may be the opposite of preparing one or more atoms for use in a qubit gate operation. The atom selected for reading / imaging may not interact with another atom of the plurality of atoms. For example, the imaging may be imaging of non-interacting atoms. The atoms may not interact, thus preserving the prepared state. In another example, the atoms may interact during imaging. For example, the atoms may be allowed to interact during imaging, thereby completing a quantum computation and imaging the result.

[0179] Selection of atoms (e.g., using a non-site-selective beam to perform site-selective excitation) may be combined with other methods to suppress selectivity errors in selection. For example, atoms not configured to be shelved may be addressed with a site-selective off-resonant beam (e.g., a hidden beam) configured to provide a differential shift between the ground state and the clock manifold. In this example, the off-resonant beam may reduce the likelihood that the shelving light may drive the transition of the atom to the clock state. The off-resonant beam may be combined with methods implemented by the system and described elsewhere herein.

[0180] In some cases, the methods and systems for selecting atoms described elsewhere herein may be used in selective imaging and / or resetting of qubits. For example, selecting atoms of qubits described elsewhere herein may be used to read out a subset of atoms without disturbing the atoms of other qubits. In this example, intermediate circuit measurements may be performed (e.g., atoms may be read out during a quantum computation). This type of measurement may provide the ability to apply conditional operations (e.g., gates), track the progress of measurements, and the like. Furthermore, such intermediate circuit measurements may enable the use of error correction codes in quantum computation, thus improving the quality of programs that may be executed. Intermediate circuit measurements may be combined with a reset operation that may reinitialize the atoms of a qubit. The reinitialization may allow the qubit to be used later in a quantum computation. For example, the qubit may be used in an earlier part of a quantum computation, and the current state may not be needed for the remainder of the computation. In this example, the qubit may be reset to allow the use of the qubit for another part of the computation. The combined intermediate circuit measurement and reset may include shelving (e.g., non-interacting) selected atoms such that they do not interact with the imaging light or the reset light. In this way, non-selected atoms can be imaged and reset without affecting the state of the selected atoms. In some cases, the shelving may include shelving of both qubit states (e.g., not just 0 or 1 states individually). The shelving may include shelving the qubit states (e.g., one or both of the qubit states) to a clock state manifold. In some cases, when both qubit states are shelved, site-selective shelving may be performed for each qubit state individually. For example, the 0 state may be shelved and then the 1 state may be shelved, or vice versa.

[0181] Computer Systems 1 illustrates a computer system 101 programmed or configured to operate any of the methods or systems described herein, such as the systems or methods for performing non-classical computation described herein. The computer system 101 may govern various aspects of the disclosure. The computer system 101 may be a user's electronic device or a computer system located remotely relative to the electronic device. The electronic device may be a mobile electronic device.

[0182] The 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 multiple processors for parallel processing. The computer system 101 also includes memory or storage locations 110 (e.g., random access memory, read-only memory, flash memory), electronic storage 115 (e.g., hard disk), communication interface 120 (e.g., network adapter) for communicating with one or more other systems, and peripheral devices 125, such as cache, other memory, data storage, and / or electronic display adapters. The memory 110, storage 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 repository) for storing data. Computer system 101 may be operatively coupled to a computer network ("network") 130 using communication interface 120. Network 130 may be the Internet, an Internet and / or an extranet, or an intranet and / or an extranet in communication with the Internet. Network 130 may be a telecommunications and / or data network in some cases. Network 130 may include one or more computer servers that enable distributed computing, such as cloud computing. Network 130 may implement a peer-to-peer network, possibly with the aid of computer system 101, that allows devices coupled to computer system 101 to operate as clients or servers.

[0183] CPU 105 may execute a series of machine-readable instructions, which may be embodied in a program or software. The instructions may be stored in a memory location, such as memory 110. The instructions may be directed to CPU 105, which may then program or configure CPU 105 to implement the methods of the present disclosure. Examples of operations performed by CPU 105 may include fetch, decode, execute, and writeback.

[0184] 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).

[0185] The storage unit 115 may store files such as drivers, libraries, and saved programs. The storage unit 115 may store user data, such as user preferences and user programs. The computer system 101 may include one or more additional data storage units, possibly external to the computer system 101, such as located on a remote server that communicates with the computer system 101 through an intranet or the Internet.

[0186] Computer system 101 can communicate with one or more remote computer systems via network 130. For example, computer system 101 can communicate with a user's remote computer system. Examples of remote computer systems include a personal computer (e.g., portable PC), a slate or tablet PC (e.g., Apple® iPad, Samsung® Galaxy Tab), a phone, a smartphone (Apple® iPhone, Android-enabled device, Blackberry®), or a personal digital assistant. A user can access computer system 101 via network 130.

[0187] The methods described herein may be implemented by machine (e.g., computer processor) executable code stored in an electronic storage location of the computer system 101, such as, for example, memory 110 or electronic storage unit 115. The machine executable or machine readable code may be provided in the form of software. In use, the code may be executed by the processor 105. In some cases, the code may be retrieved from storage unit 115 and stored in memory 110 for immediate access by the processor 105. In some circumstances, the electronic storage unit 115 may be omitted and the machine executable instructions are stored in memory 110.

[0188] The code may be pre-compiled and configured for use on a machine with a processor adapted to execute the code, or it may be compiled at run-time. The code may be provided in a programming language that can be selected to allow the code to be executed in a pre-compiled or co-compiled manner.

[0189] Aspects of the systems and methods provided herein, such as computer system 101, may be embodied in programming. Various aspects of the technology may be considered "products" or "articles of manufacture," typically in the form of machine (or processor) executable code and / or associated data, which are held or embodied in some type of machine-readable medium. The machine-executable code may be stored in memory (e.g., read-only memory, random access memory, flash memory) or electronic storage, such as a hard disk. A "storage" type medium may include any or all of the tangible memory of a computer, processor, etc., or associated therewith, modules such as various semiconductor memories, tape drives, disk drives, etc., that may provide non-transitory storage at any time for software programming. All or a portion of the software may be communicated over the Internet or various other telecommunications networks. Such communication may, for example, enable loading of the software from one computer or processor to another, for example, from an administrative server or host computer to an application server computer platform. Thus, another type of medium that may hold software elements includes the light waves, radio waves, and electromagnetic waves used across the physical interfaces between local devices over wired and optical landline telephone networks, as well as various air links. The physical elements that carry such waves, such as wired or wireless links, optical links, etc., may also be considered media that carry software. As used herein, unless limited to non-transitory, tangible "storage" media, terms such as computer or machine "readable medium" refer to any medium that participates in providing instructions to a processor for execution.

[0190] Thus, a machine-readable medium such as a computer executable code may take many forms including, but not limited to, a tangible storage medium, a carrier wave medium, or a physical transmission medium. Non-volatile storage media include optical or magnetic disks, such as any of the storage devices of any computer, such as may be used to implement, for example, the databases shown in the drawings. Volatile storage media include dynamic memory, such as the main memory of such a computer platform. Tangible transmission media include copper wire and optical fibers, including coaxial cables, i.e., the wires that make up a bus within a computer system. Carrier wave transmission media may take the form of electric or electromagnetic signals, or acoustic or light waves such as those generated during radio frequency (RF) and infrared (IR) data communications. Thus, common forms of computer readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, any other magnetic media, CD-ROMs, DVDs, or DVD-ROMs, other optical media, punch cards paper tape, other physical storage media with patterns of holes, RAM, ROM, PROMs and EPROMs, FLASH-EPROMs, other memory chips or cartridges, carrier waves carrying data or instructions, cables or links carrying such carrier waves, or any other medium from which a computer can read programming code and / or data. Many of these forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to a processor for execution.

[0191] The computer system 101 may include or communicate with an electronic display 135 that provides a user interface (UI) 140. Examples of UIs include, but are not limited to, graphical user interfaces (GUIs) and web-based user interfaces.

[0192] The methods and systems of the present disclosure may be implemented by one or more algorithms. The algorithms may be implemented by software upon execution by the central processing unit 105. The algorithms may, for example, implement methods for performing non-classical computations described herein. EXAMPLES

[0193] Example 1: Modeling the Strontium-87 Nuclear Spin Levels In the following example, we model the 10 nuclear spin levels (I=9 / 2) of Strontium-87 to demonstrate a two-level system (i.e., a qubit). To achieve spectral separation of the qubit transitions, we employ a Stark shift scheme to shift the undesired transitions away from the qubit frequency. The separation scheme may improve the effective separation in terms of achievable Rabi frequencies, may reduce the effects on the actual qubit state due to shifts or residual scattering, may not require full polarization control, may be accessible with a reasonable amount of optical power, etc. 1 From S0 3 The properties of the resonance to P1 were characterized.

[0194] In Figure 10A, we use a toy model to show the three relevant nuclear spin states, i.e., the qubit subspace, m F We show shifts of the α = 9 / 2 and 7 / 2 levels, and the leakage level 5 / 2. Here we simulate the operation of a single circularly polarized global ac Stark beam addressing an array of atoms in a magnetic field of 700 Gauss. Furthermore, we assume a polarization purity of 100:1 for the intended circular polarization. The α Stark beam 1 From S0 3 Each detuning to the P1 resonance results in a shift in each nuclear spin level. To clarify further, let F =9 / 2 and m F =7 / 2 dressed energy difference) and the leakage transition frequency (m F =7 / 2 and m F = 5 / 2 dressed difference) are plotted.

[0195] Figure 10B shows that the Stark shift significantly moves the leakage transition with minimal effect on the qubit frequency, compared to the level splitting at high magnetic fields. 3 This can be made possible by the narrow linewidth of the P1 resonance. Although we plotted the frequency as a signed quantity, subtleties related to the quantization axis and light transport make the absolute value of this frequency appropriate, and such features appear where the Stark shift brings the leaky state closer to the qubit frequency. For each detuning, we can define the maximum usable Rabi frequency achievable, taking into account frequency crowding. Using this two-photon Rabi frequency, we can infer the π-pulse time and investigate the number of scattering events generated by non-resonant interactions of AC Stark beams (Figure 10A).

[0196] Since we did not distinguish between Raman and Rayleigh scattering, this is assumed to be the worst-case scenario for AC Stark scattering errors per gate. To perform single-qubit gates, we need to control the light coherently, 3 Two-photon transitions were operated using two beams detuned from the P1 resonance. 3 Residual scattering from any of the P1 manifold states may be inherently low, since the linewidth of the transition is 7 kHz. Including the effects of AC Stark-shifted beams, 3The broadening of the P1 hyperfine magnetic sublevels can be exploited to separate the energy scale between an AC Stark beam detuned from the F=11 / 2 manifold and a multiphoton 1Q light detuned from the F=7 / 2 manifold. A simple toy model including two ground states and a few excited states was sufficient to gain insight into the scaling of power, spot size, and achievable Rabi rate. However, it may be necessary to perform a full-scale simulation including all relevant levels, since it includes an infinite number of levels (1S0 (F=9 / 2), 3P1 (F=7 / 2, 9 / 2, 11 / 2)) including all magnetic sublevels. To verify the complete operation, we built a numerical model utilizing all 40 levels with multiple optical fields to represent both the desired and undesired polarizations. Utilizing a simple square pulse, it can be seen that transitions to other nuclear spin states can be suppressed with an AC Stark beam (Figure 11A and Figure 11B).

[0197] Example 2: Light trapping array 12A and 12B show arrays of captured light generated by an SLM, such as a square array and an arbitrary array. The hologram is generated by emitting 813 nm light ( 1 S0→ 3A phase shift was generated by reflecting the light (magic wavelength of the P0 transition) from the SLM. The active area of ​​the SLM was an array of 1920 × 1152 square pixels, about 9 microns on a side. Each pixel contains a large amount of liquid crystal that imparts a phase shift to the incident light. This phase shift can be controlled by the voltage applied to the pixel, and in this way an arbitrary pixelated phase mask can be generated and applied to any unstructured light incident on the surface of the SLM. The SLM was positioned so that a large collimated beam was incident on it and phase shifted it, and the light reflected from the SLM was directed towards the microscope objective. This configuration connected the plane of the SLM to the plane below the lens (where the atomic cloud was formed) by Fourier conjugation. The complex-valued in-plane electric field at the SLM was the Fourier transform of a similar electric field in the plane below the microscope objective, in the volume of the glass cell. The atoms experienced a trapping potential proportional to the strength of the electric field, and therefore lateral confinement. Longitudinal confinement arises from passing the structured light through a focal spot, the position of which is in part determined (and therefore controllable) by the SLM.

[0198] The light was generated by a titanium-sapphire laser producing about 4 W of optical power at 813 nm. For imaging and other purposes, 2000 traps were generated, each at a depth of 500 microkelvin, well over 1000 times the recoil energy imparted from the scattering of a photon. This means that the device should be in a regime where the atoms can be measured hundreds of times without being lost due to heating, even without additional cooling. Once cooled to the ground state of motion, the positions of the atoms are known to within 20 nm, allowing a large separation in scale between the positions of the atoms and the size of the laser beams used to drive the single and two-qubit gates or the Rydberg interaction length scale. The laser beams driving the gate operations have a spatial extent on the order of one micron, and so their intensities are on the order of 10 -5 , and thus a fidelity of 0.9999 is expected to be easily achievable. In this way, the gate fidelity becomes insensitive to the position of the atoms.

[0199] Example 3: Ultra-high vacuum A quartz cuvette cell constructed of Spectrosil® 2000 quartz glass was utilized as the vacuum cell. Unlike borosilicate glass, this glass does not fluoresce under UV illumination. The cell featured a glass-to-metal transition from quartz to stainless steel that connected the cell to the vacuum pump and atom source. The dimensions of the cell were chosen to avoid clipping of the laser cooling beam and to reduce the numerical aperture of the microscope objective. The cell was assembled using optical contact bonding by Starna Scientific Ltd. The four largest outer surfaces of the cell were coated with a broadband multilayer anti-reflection coating to minimize reflections from 300 nm to 850 nm for both S- and P-polarized light at normal incidence. A magnesium fluoride coating was applied to the small square window of the cell. The vacuum system was operated for several months at 8 × 10 -12 Torr (1.07×10 -9 The pressure was maintained at 100 Pa.

[0200] Example 4: Microscope Objective Lens A microscope objective lens placed directly above the vacuum cell allows for individual trapping, imaging, and addressing of atomic qubits. Due to its high numerical aperture (NA), the objective lens efficiently collects the fluorescence from the atoms during imaging and converts the collimated input beam into a tightly focused spot for trapping atoms at the focal plane. The objective lens is manufactured by Special Optics Inc. and has a high NA (0.65) and a diffraction-limited field of view (FOV) of 300 μm, with 90% transmission at 461 nm and 813 nm. The end of the objective lens facing the vacuum cell is tapered to avoid clipping two of the six laser cooling beams. In addition, the diameter of the objective barrel was limited to fit between the large magnetic coils used for laser cooling, because the power consumption of these coils is highly proportional to their size and spacing. The mechanical housing of the objective lens was made from Ultem, which is non-magnetic and non-conductive.

[0201] The performance of the objective lens was characterized by placing the objective lens and one glass cell window in one arm of a Michelson interferometer. In this arm, the focused beam was retroreflected using a precision ball bearing at the center of the beam focus. The other arm of the Michelson held a reference reflector. The Zernike surface was reconstructed by fitting the resulting spatial interference pattern. The objective lens was mounted directly on the glass cell to eliminate any tilt drift between the cell window and the objective lens. Such tilts of the order of 1 milliradian (mrad) would otherwise cause variations in wavefront quality. The objective lens was epoxied onto a machined McCall mount that contacted the top window of the cell via five brass ball bearings. During this assembly process, the objective lens was interferometrically aligned such that its optical axis was kept perpendicular to the cell.

[0202] Three custom dichroic mirrors from Perkins were used to handle four widely different wavelengths (813 nm, 689 nm, 461 nm, and 319 nm) at the objective. Figure 13 shows the optical system for delivering the four different wavelengths. The three dichroic mirrors are shown as DM01, DM02, and DM03. Note that the 319 nm light enters from the bottom of the cell. The custom coatings on the three dichroic mirrors work in tandem to maintain the arbitrary polarization state of the 813 nm and 689 nm light to perform single-qubit or multi-qubit gates and magic wavelength and / or magnetic angle trapping.

[0203] Example 5: Trapping and Cooling of Atoms Figure 14 shows the trapping and cooling of strontium-87 and strontium-88 atoms using a red MOT.

[0204] Example 6: Imaging To perform the projection measurements, strontium-87 1 S0→ 1Light resonant with the P1 transition is applied to the entire atomic array, and the resulting atomic fluorescence is collected and imaged. 1 For a qubit whose S0 ground state manifold contains two nuclear spin states (both resonant with the imaging light), one of the two states can be considered metastable. 3 The atoms can then be moved to the P0 manifold and measured. This procedure is state-selective, similar to the operation of optical lattice clocks, and is described in Covey et al., "2000 Times Repeated Imaging of Strontium Atoms in Clock-Magic Tweezer Arrays," Physical Review Letters 122(17):173201 (2019), which is incorporated by reference in its entirety for all purposes. This has the added benefit of reducing readout crosstalk from nearby atoms. Each 1 Fluorescence from the S0 atoms is collected through a microscope objective. This light is then imaged onto a scientific CMOS camera, producing an image of the qubit array that is processed to determine the state of each atom. Such images also help determine if atoms have been lost from the array. Because the microscope objective is diffraction limited across the entire atomic array, atoms that are a few microns apart are well resolved.

[0205] Example 7: Single-qubit gated optical transfer The single-qubit scheme was specifically designed to enable single-site addressability. In particular, the two laser beams used to drive single-qubit operations are delivered through the same high-numerical-aperture objective lens used to project the optical tweezers trapping potential. As described herein, three dichroic mirrors combine all relevant beams at the back focal plane of the objective lens. These beams are generated, manipulated, and modulated to perform site-selective single-qubit operations. The two beams used to drive single-qubit operations have orthogonal linear polarizations (one is pi-polarized because it is aligned with the atomic quantization axis, and the other beam is sigma-polarized). Full control of single-qubit operations requires control of the amplitude, frequency, and phase of each beam at individual trapping sites. This control is obtained through a combination of electro-optic modulators (EOMs), acousto-optic deflectors (AODs), and RF control electronics.

[0206] The light used to drive the single-qubit gates is provided by a common amplified laser source phase-locked to an optical frequency comb. Although the overall phase of this light cannot be controlled in each experiment, the laser is a stable local oscillator source that can be modulated with a well-controlled RF source to generate a control field. This global phase sets the global phase of the qubit array, which can only be measured by comparison with an independent qubit array. For maximum flexibility, an electro-optical modulator (EOM) is used to globally phase modulate the red MOT light, the optical pumping, the sideband cooling, and the 689 nm light used for single-qubit operations. This is because these four operations are not typically performed simultaneously. The phase modulation generates symmetric sidebands around a central laser frequency. of states 3 Detuning the laser from the P1 manifold results in a narrow +1 sideband 3 It is chosen to be close enough to the P1 transition to drive the transition. By varying the frequency of this modulation between 5 GHz and 13 GHz, it is possible to use this light to generate excitations even when large bias fields are used to split the manifold of excited states.3 All transitions in the P1 manifold can be treated as resonant.

[0207] The main advantage of this method of generating 689 nm light is that the same beam path is used to generate light for all four beam paths mentioned above. Furthermore, the overall frequency, amplitude, and phase of these resonant beams are controlled using advanced microwave RF sources. The RF that drives the EOM is generated by an arbitrary waveform generator and an IQ mixer to control the complex pulse shape of the laser. For qubit manipulation, this global control is used to generate pulses of any shape with preferred spectral properties.

[0208] Example 8: Parallel addressing of single qubits Acousto-optic deflectors (AODs) are used to generate beams that can be directed to different sites in the qubit array by driving the AODs with different frequencies. This introduces a frequency and phase matching condition that is position-dependent. For single qubit operations, this complication is overcome by using identical AOD paths for the two beams, so that the driven two-photon process remains resonant while the detuning of the intermediate states varies. In other words, the four AOD frequencies are fully constrained by choosing the specific site to address. The two frequencies select the position of the first beam, and the frequency matching condition ensures that the two frequencies of the second beam are the same, up to the offset of the qubit frequency (the split between the two nuclear spin states, about 150 kHz). Using an AOD to generate beams for single qubit operations allows arbitrary addressing of atoms in a single row (or column) at any given time. This is necessary to maintain full control of the amplitude and phase of each. This makes the operation partially serialized. However, the speed at which the pattern can be changed with the AOD is greatly improved compared to SLMs and is much more efficient than DMDs. The AOD also allows full phase control of each beam. This not only allows us to track the phase of each qubit (all rotations within the local qubit frame can be applied), but it can also be used to perform more complex pulse sequences on each qubit. By controlling the amplitude of the RF on each qubit, we can locally scale the pulse area of ​​each qubit operation. Combining both the phase and amplitude of the RF allows us full control over the operation performed on each qubit during a single pulse from the EOM.

[0209] For single-photon operation, a single drive beam is generated with a single 2D AOD system. Unwanted deflections can be filtered out using additional optics. Alternatively or additionally, the transitions can be sufficiently off-resonant to be negligible. Using a single 2D AOD system produces an array of spots whose spacing can be adjusted by tuning the frequency difference of the RF tones driving the acousto-optic crystal, and whose phase can be adjusted by tuning the RF drive phase. By configuring the AODs in a "crossed" configuration (e.g., the first AOD deflects to +1 order and the second AOD deflects to -1 order), lines of deflection that are the same in absolute frequency are created (along a diagonal created relative to the deflection axes of the two AODs).

[0210] As an illustrative example, consider the case where light into a 2D AOD is resonant with a transition of interest. Then, for any RF frequency into the first AOD, if the second AOD is deflected at the same frequency, the optical frequency will return to resonance. The final optical phase of the light driving the transition can be controlled by tuning the relative RF phase of the tones into the two AODs. To parallelize addressing, multiple frequencies can be added to both AODs, and all diagonals where the corresponding frequencies are deflected will be resonant. The remaining deflected spots are off-resonant and can be filtered out, but in many cases (e.g. when driving ultra-narrow "clock" transitions) the extra spots will be too off-resonant for this to be unnecessary.

[0211] There are two main modes of operation for addressing atoms in a square array. First, the AOD can be aligned to the trapping array. In such a case, all spots are aligned to spots in the array, but only the spots along the resonant diagonal are driven. If the detuning is insufficient, a DMD in the image plane of the optical system can be used to dynamically filter out other unwanted spots. Second, the AOD can be aligned at 45 degrees to the atomic array such that a diagonal row of resonant spots aligns with a single row or column of the qubit array. In this case, qubits will be lost at many other spots; however, the remaining spots can be filtered out if desired.

[0212] Example 9: Parallel addressing of multiqubit units Direct excitation of strontium-87 from the ground state to the Rydberg level requires a laser with a wavelength of about 218 nm. Alternatively, the Rydberg excitation can be performed at intermediate 3 This can be done using two-photon excitation combining 689 nm and 319 nm light, which is detuned from the P1 state. 3 The P1 state width of about 7 kHz is the two-photon effective Rabi rate 3 This provides an effective balance between scattering due to spontaneous decay from P1. Figure 15A shows the energy level structure for single and multi-qubit operations in strontium-87.

[0213] The optical system for single-qubit operations is designed to also work well with multi-qubit gates. One of the single-qubit beams is used as one leg of a two-photon excitation scheme that drives the transition to the Rydberg electron manifold. To satisfy the spatially dependent frequency and phase matching condition, the AOD is also used for UV light. Importantly, the optical system is tuned such that the frequency shift of the UV light from one site to the other is the same as the frequency shift of the 689 nm light. As a result of this constraint, the performance of the state-of-the-art UV AOD determines the accessible field of view (FOV) for multi-qubit operations. Furthermore, because one of the single-qubit beams is used for multi-qubit operations (and the two single-qubit beams are coincident), the FOV for single-qubit operations is the same. The figure of merit for a UV AOD is the product of the active numerical aperture and the RF bandwidth of the device. For a fixed beam size in the back focal plane of the objective, increasing either of these quantities increases the scanning angle of the beam and thus the FOV in the plane of the qubit array. An FOV of approximately 100 μm × 100 μm was achieved, sufficient to accommodate an array of approximately 1,000 atoms with a capture site spacing of 3 μm.

[0214] FIG. 15B illustrates an optical system for delivering light to perform single-qubit and multi-qubit operations on multiple trapped atoms in parallel. A first light for performing single-qubit operations on a first qubit (qubit 1) is directed to a first two-dimensional AOD (2D AOD) to allow parallel addressing of a first subset of trapped atoms. A second light for performing single-qubit operations on a second qubit (qubit 2) is directed to a second 2D AOD to allow parallel addressing of a second subset of trapped atoms. A third light for inducing Rydberg interactions on either the first or second subset is delivered through a third 2D AOD to generate multiple entanglements between atoms of the first subset and neighboring atoms of the second subset.

[0215] The third light is generated by an ultraviolet (UV) laser emitting 319 nm light. The UV laser is phase-locked to a frequency comb to provide a narrow linewidth UV laser beam. Amplitude control is provided by an acousto-optic modulator (AOM). Global phase control is achieved by an optical phase stabilization technique. The stabilized global phase of the 319 nm light is combined with active phase modulation of the 689 nm light to provide phase control. The free-space beam is sent to a third 2D AOD, but from the opposite direction to the first and second 2D AODs. The light is directed to the trapped atoms via a customized microscope objective. Counterpropagating beam paths are used to monitor the position of the spot and the effect of the light on the atoms (e.g., via excitation loss spectroscopy) to optimize the alignment. These quantitative effects can also be used to implement an automatic alignment scheme that allows for improved autonomous operation of the system.

[0216] Figure 15C shows an optical system configured to dynamically generate and control the beams using a single electro-optic modulator (EOM) and two acousto-optic deflectors (AODs) per beam, each driven by an RF signal from an arbitrary waveform generator. The AODs are oriented such that the frequency difference between the beams remains constant whenever they overlap at the qubit array. The frequency difference prevents driving unwanted operations, but is easily overcome by the RF drive of the two EOMs. Combining the AODs with an agile RF synthesizer allows full site-by-site control of operations, a major advantage for performing a sequence of quantum operations on an array of atomic qubits, which can be performed in parallel (one row at a time).

[0217] In contrast to single-photon manipulations, two-photon processes are driven by two beams prepared in independent 2D AOD systems. The light beams are passed through a microscope objective (e.g., a confocal microscope system) and focused onto a single site in the atomic array, thus minimizing crosstalk to neighboring qubits. For two-photon transitions, the beams can be either co-propagating or counter-propagating (in this case a confocal microscope can be used).

[0218] Parallel 2D AOD systems are used to drive atomic qubit transitions in an array of atomic qubits. The two beams defined by these parallel 2D AOD systems define the two arms of a two-photon Raman transition between two internal states of the atom (such as electronic or nuclear spin eigenstates). Typically, the polarizations of the two beams are orthogonal, so that the beams can be efficiently combined with a polarizing beam splitter to drive the two legs of the Raman transition. However, the same technique can be used to combine two beams with the same polarization. The polarization through the 2D AOD is typically horizontally linear and vertically linear, but can easily be converted to right- or left-circular.

[0219] FIG. 18C shows an example of how to address atoms held in a two-dimensional rectangular array according to some embodiments of the present disclosure. A two-dimensional AOD configuration can be used to hold the atoms and generate beams from two light sources. The position of the atom in the array is determined by the frequency f0 of the beam from a single light source. v and f0 h The frequency difference Dame pattern (e.g., df v and df h A constant detuning can be maintained across an array of trapping sites by configuring the beams of both the first and second light sources used to drive qubit operations according to (). Simultaneous qubit operations can then be driven at each site in the trapping array. For a particular pattern of frequency difference, the remaining frequency matching condition for driving qubit operations can be achieved by combining additional modulators with one or more (e.g., both) light sources and adjusting the overall alignment offset of the beams generated from each light source.

[0220] In the non-inverted AOD configuration, the deflected beams from the two 2D AODs are in the same direction and all use +1 order deflection. In this configuration, the frequency difference is consistent at all sites in the array, as shown in Figure 18A. In this configuration, the two regions can be overlapped in the atomic plane (e.g., partially overlapping, fully overlapping, etc.). The laser frequency before the modulator is f L , the center frequency of each AOD is f C , the bandwidth of the AOD is Δ AOD , the frequency at which the AOD is driven is f AOD The driving frequency f AOD v and f AOD h Each pair can generate a beam that is focused to a specific location on the atomic plane. The final frequency and position of each beam from the first source is f AOD v1 and f AOD h1 and for the second light source, f1 = f L 1 +fAOD v1 +f AOD h1 and f2=f L 2 +f AOD v2 +f AOD h2 From f AOD v2 and f AOD h2 If the position vs. frequency is the same in the atomic plane of the two source beams, the final frequency difference is f L 1 and f L 2 The constant offset can be equal to the difference between the modulator frequencies of each light source for any particular position in the atomic plane (e.g., (f C h1 -f C h2 )+(f C v1 -f C v2 )). When superimposed the difference can be zero. To drive the qubit transition, the frequency difference can be equal to the qubit frequency. Additional modulators may be added to the optical path to enable frequency matching conditions. The operational detuning remains small and constant at all positions in the atomic array (or resonant if the frequency is properly calibrated). In this configuration, the overall detuning of the two-photon transition from the excited (intermediate) state varies throughout the array. This plays a role in the two-photon Rabi rate of operation, but the change in intermediate state detuning by ~2Δ is small compared to the total intermediate state detuning (hundreds of MHz versus several GHz). In this configuration, by adding a relative shift in frequency between the two input beams (using a detuned laser source or other optics that create a tunable frequency difference), a pure phase modulator can be used to generate shaped pulses that are resonant with only one sideband.

[0221] In the inverse AOD configuration, the two beams are deflected in opposite directions by the AODs using opposite orders of deflection in the AODs (e.g., beam 1 is deflected into the +1 order of the two AODs and beam 2 is deflected into the -1 order of that AOD). When the deflected beams are then combined such that the centers of each deflection bandwidth are aligned, the frequency difference of the two overlapping spots is constant across the array, as shown in Figure 18B. In this configuration, the two regions can be made to overlap in the atomic plane (e.g., partially overlap, fully overlap, etc.). The laser frequency before the modulator is f L , the center frequency of each AOD is f C and the bandwidth of the AOD is given by Δ AOD , the frequency at which the AOD is driven is f AOD The driving frequency f AOD v and f AOD h Each pair can generate a beam that is focused to a specific location on the atomic plane. The final frequency and position of each beam from the first source is f AOD v1 and f AOD h1 and for the second light source, f1=f L 1 +f AOD v1 +f AOD h1 and f2=f L 2 +f AOD v2 +f AOD h2 From f AOD v2 and f AOD h2 If the position vs. frequency is the same in the atomic plane of the two source beams, the net frequency difference is f L 1 and f L 2 (e.g., the additional difference can be the sum of the center frequencies of each modulator, e.g., f C h1 +f C v1 +f C h2+f C v2 ). To drive the qubit transition, this frequency difference can be made equal to the qubit frequency. An additional modulator can be added to the optical path to enable a frequency matching condition. The orientation of the AODs in this configuration keeps the operational detuning constant across the array, but instead of resonant driving, the beam is driven at ~4f c separated (e.g., the frequency from the first beam is ~2f c The frequency from the second beam is shifted up by ~2f c For a fixed constant detuning that is much larger than the two-photon Rabi rate (Ω), it is necessary to make up the difference to drive the resonant operation. This can be achieved in several ways:

[0222] First, electro-optic modulators (EOMs) can be used in one or both of the beam paths to modulate the phase of the beam and generate sidebands at the drive frequency. If the drive frequency is large enough, the off-resonant sidebands are often negligible and the relevant frequency is simply the desired single sideband. Second, f L can be chosen to be different for the two beams (i.e. the frequencies of the beams before the 2D AOD system are different). This can be achieved by using completely separate lasers for the two beams, or by passing one of the beams through a separate acousto-optic modulator or other frequency shifting device before entering the 2D AOD system.

[0223] The advantage of the inverted orientation is that operation remains off-resonance until another subsystem is used to bring the beam into resonance at the desired transition.

[0224] The use of independent 2D AOD systems allows full control of two-photon operation. The Rabi ratio can be adjusted with several amplitude control knobs: the intensity of the laser light in each beam, the power of the RF drive to the AOD, and the power of the RF drive to any EOMs implemented in the system. The relative (local) phase of operation can be adjusted by manipulating the relative phase of the RF applied to the 2D AOD systems. The global operational phase can be manipulated by adjusting the phase of the two beams prior to the 2D AOD system. For example, a different EOM can be used to apply a different phase to each of the two beams.

[0225] Using separate 2D AOD systems also allows one to compensate for the wavelength dependence of the AOD, which can deflect different wavelengths with different efficiency, beam angles, etc. By careful design of the optical system for combining the beams on the target, one can overcome these differences to produce a system that drives resonant two-photon transitions with lasers of different wavelengths.

[0226] Both the non-inverted and inverted methods can be extended to three-dimensional (3D) arrays of atoms by adding an SLM, or a focus-adjustable lens that shifts the position of the focal spot along the beam propagation axis.

[0227] In some cases, if the combination of modulators used to generate coherent drive of the two light sources results in different angle vs. frequency values ​​of the light sources incident on the optical element (e.g., a microscope objective lens) (e.g., the two light sources generate different spots from each modulator with different spacing for the same frequency difference), an additional optical element can be provided. The additional optical element can be configured to correct for the mismatch in angle and frequency. The additional optical element can include a telescope (e.g., multiple lenses configured to collimate and / or focus the light). The magnification of the telescope is

[0228]

number

[0229]

number

[0230] Example 10: Reverse adiabatic operation In the absence of the pulse sequences described herein, multi-qubit operations can be performed by transferring atoms in the ground state to the dressed state and back to the ground state by adiabatically changing the Hamiltonian such that the adiabatic transition to the Rydberg state is minimized. The adiabatic condition imposes limitations that make multi-qubit operations relatively slow. However, faster gates are necessary for overall speed and minimization of decoherence effects. The pulse sequences described herein can achieve faster gates while effectively maintaining adiabatic dynamics.

[0231] For example, inverse adiabatic driving may reduce gate times while minimizing errors resulting from transitions to Rydberg states. Counteradiabatic driving is the addition of one or more driving fields to cancel terms in the Hamiltonian that cause undesired adiabatic transitions. Inverse adiabatic driving achieves effective adiabatic dynamics on time scales shorter than those allowed by the adiabatic condition. One example is the "transitionless quantum driving" (TQD) described herein. TQD is achieved by transforming the full Hamiltonian of the system into a reference frame defined by the instantaneous eigenstates of the Hamiltonian. The Hamiltonian is split into a diagonal part (which does not cause adiabatic transitions between instantaneous eigenstates) and an off-diagonal part (which causes adiabatic transitions). TQD is achieved by adding additional control fields that cancel the off-diagonal adiabatic Hamiltonian. Using this technique, effective adiabatic dynamics can be achieved without having to satisfy the usual slow adiabatic condition. Below is the derivation of the TQD condition for a generic two-level system with a single shaft drive that uses a TQD to counter the adiabatic transition of the Rydberg dressing gate.

[0232] A general problem is to transform a two-level system in the ground state |1> into a dressed state that is a mixture of |1> and excited states |R>, and then return to the ground state as quickly as possible without leaving behind a population of excited states. In a rotating frame, the total Hamiltonian of the driven two-level system (in units of frequency) is (1) H0=Ω(t)δ x +Δ(t)δ z

[0233] where Ω is the Rabi fraction, Δ is the detuning from resonance, and σ x and σ z is the Pauli operator for the two-level system. It is convenient to write the Hamiltonian in a "tilted coordinate system". (2) H'0=Ω eff (t)δ z’

[0234]

number

[0235] In the original basis, the instantaneous eigenstates of H0 are (6)|Φ1>=cos(θ)|1>+sin(θ)|R> (7)|Φ2>=-sin(θ)|1>+cos(θ)|R>

[0236] Next, we transform into an "adiabatic frame" described by these instantaneous eigenstates. The unitary operator corresponding to this transformation is

[0237]

number

[0238] Here, |Φ ad,k > is an instantaneous eigenstate of the adiabatic frame. The transformed Hamiltonian is

[0239]

number

[0240] The second term (W(t)) contains off-diagonal elements that trigger a transition if the adiabatic condition is not satisfied. If U(t) changes slowly enough to make W(t) small enough, the adiabatic condition is satisfied. To achieve effective adiabatic dynamics when this term is not small, an additional control field H c (t) to the original Hamiltonian to cancel the effect of W(t). This is

[0241]

number

[0242] Solving for U(t), we get

[0243]

number

[0244] Using the definition of U(t) given above, it can be written in matrix form:

[0245]

number

[0246] Again, simplifying the expression.

[0247]

number

[0248] This result shows that an inverse adiabatic Hamillsian can be achieved by driving with a field that is 90 degrees out of phase with the original driving field. The form of H(t) can in general be found for the desired H0(t).

[0249] To demonstrate the effectiveness of the transitionless quantum drive of the Rydberg-dressing gate, we simulated a two-atom system. Each atom consisted of two ground (qubit) states and a Rydberg state. Figure 16A shows a simulation of two atoms in an initial two-atom state |00>. By driving the transition from |0> to |r> in each atom and sweeping the detuning towards and away from resonance, the instantaneous eigenstates of the Hamiltonian transform from the bare state to the dressed state and back to the bare state. As shown in Figure 16A, if the ramp is performed too fast and the adiabatic condition is violated, a significant population will remain in the Rydberg state |r0>.

[0250] Figure 16B shows a simulation of two atoms in the initial two-atom state |00> with the addition of an inverse adiabatic driving field applied to implement a non-transition quantum driving gate. The population remaining in the Rydberg state is greatly reduced.

[0251] Inverse adiabatic driving can also be used to suppress unwanted transitions at frequencies other than the driving frequency. This is useful for driving transitions on-resonance while avoiding driving nearby unwanted transitions. Alternatively, off-resonant driving can be used to create dressed states while avoiding excitation to excited states (i.e., adiabatic transitions). An example of inverse adiabatic driving that suppresses unwanted transitions is the "differential removal by adiabatic gate" (DRAG) described herein. Figure 16C shows an example of a DRAG pulse in the time domain (a) and frequency domain (b).

[0252] Example 11: Atomic rearrangement Simulations were performed to determine the time required to perform atomic rearrangements at a 7 × 7 array of optical capture sites. The simulations assume an imaging system with a Hamamatsu Orca-Fusion CMOS digital camera using an external trigger in normal mode. The camera has a region of interest of 2304 (fixed, horizontal) × 256 (vertical) pixels. An exposure of 20 ms, a readout of 4.6 ms (256 vertical lines at 18.65 μs per line), and data transfer latencies of 1.75 ms to 5 ms were assumed.

[0253] The data transferred from the camera can be sliced ​​into a 256x256 array of 16-bit integers. To determine the capture sites, one must first use a calibration image of a fully captured grid (by averaging many capture realizations). Figure 17A shows a calibration image of a fully filled 7x7 array of optical capture sites. The optical capture sites are indexed by coordinates (i,j). This data was used to map capture sites to pixel locations as shown in Table 1.

[0254] [Table 1]

[0255] FIG. 17B shows the labeling of filled and unfilled optical capture sites in a 7×7 array. Binning of the pixels around each capture site was performed. FIG. 17C shows 25×25 pixel binning around each optical capture site in the 7×7 array. The pixels in each bin were averaged. The average value was compared to a threshold extracted from a calibration procedure to determine whether each optical capture site was filled or unfilled. Filled sites were identified with a "1" and unfilled sites with a "0". FIG. 17D shows the identification of each capture site in the 7×7 array as filled or unfilled. Thus, the procedure generated a 7×7 array of binary values ​​indicating whether each site was filled or unfilled. The total processing time to assign the array of binary values ​​was performed in less than 0.5 ms.

[0256] Once the filled and unfilled sites were identified, the next step was to determine the moves to fill the uncaptured sites. This is a combinatorial optimization problem classified as bipartite matching. It can be solved by setting up an adjacency matrix that can efficiently find the optimal matching using algorithms such as the Hungarian matching algorithm described herein. The adjacency matrix d i,j is constructed, where row i is indexed by the target site in the N×N active area, and columns are indexed by the available sites in the full M×M lattice. For example, for a 7×7 array (M=7), an atom can be moved to a computationally active area of ​​5×5 by (N=5). Table 2 shows the entries of the adjacency matrix.

[0257] [Table 2]

[0258] The distance metric is the target (i target ,j target ) and filled sites (i filled ,j filled), the resulting matching produces a collision-free transfer of atoms from a filled to an unfilled light-trapping site. Figure 17E shows a transfer from a filled to an unfilled light-trapping site that avoids collisions between atoms.

[0259] We split the moves into independent subsets and time-ordered them for easy parallelization, as shown in Table 3 below. The process of determining the moves took about 8ms.

[0260] [Table 3]

[0261] The time required for data transfer to the AWG is less than 1 ms. A single maximum latency is introduced in mapping a series of movements to a series of waveforms in the AWG. A single movement may require a ramp-up time of 0.3 ms, a movement of 0.1 ms / μm, and a ramp-down time of 0.3 ms. Assuming a 3 μm spacing between light capture sites and that only movements to adjacent sites are allowed, each movement requires approximately 1 ms. In numerous simulations of a 7 × 7 array, up to 34 movements were made, requiring 34 ms to program the AWG.

[0262] Example 12: Selecting a Qubit Qubits can be shelved from the ground state manifold to a long-lived excited state manifold. Shelving can be performed using a non-site-selective excitation beam and site-resolved single qubit gates. In this way, qubits can be used for qubit gate operations (e.g., single, two, and multi-qubit gate operations) without the use of crossed acousto-optic deflectors. Thus, shelving can be performed on simple equipment that does not use complex alignment procedures.

[0263] An example of a qubit shelving procedure can include applying a first π / 2 pulse to a clock transition of a plurality of qubits. Once the plurality of qubits are excited using the first π / 2 pulse, a second 2π pulse can be applied in a site-selective manner to the qubit selected for shelving. The second pulse can be applied using a light source configured to apply a localized light pulse to each of the plurality of qubits. For example, the second pulse can be applied by the same light source configured to generate a single qubit gate operation. The application of the second pulse can impart some geometric phase to the qubit selected for shelving. A third -π / 2 pulse applied to the clock transition of the plurality of qubits can return all of the qubits to the ground state. However, the qubit that received the second pulse can be placed in a long-lived excited state, which can make the qubit addressable by future pulses.

[0264] An exemplary controlled-phase gate can be implemented by the disclosed methods and systems. In this example, a plurality of qubits can be provided with states |0〉 and |1〉. In this example, a non-site-selective π / 2 pulse can be applied to all of the |0〉 states (e.g., clock states) of the plurality of qubits, while the |1〉 states are left in the qubit manifold (e.g., not excited). A localized 2π pulse can be applied to the two qubits selected to participate in the controlled phase gate. A non-site-selective −π / 2 pulse in the |0〉 states of the plurality of qubits can then return all of the qubits to the qubit manifold, except for the two qubits selected for the controlled phase gate, which may be in the clock manifold. These two atoms can have a state of |Ψ〉=α|c0〉+β|1〉, while the other of the plurality of atoms can have a state of |Ψ〉=α|0〉+β|1〉, where the c term is generated by the application of the 2π pulse.

[0265] With two qubits prepared as described above, a non-site-selective pulse can be applied that is sufficient to promote the qubit from the clock manifold |c0〉 to the Rydberg manifold, but not from the qubit manifold |0〉 to the Rydberg manifold. Here, the two qubits in the Rydberg manifold can interact in a predetermined manner (e.g., as a controlled phase gate). The pulse can be designed such that the qubit returns to the clock state manifold after the pulse (e.g., the qubit can be de-excited to the clock state manifold). The qubit can acquire a phase based on the two-qubit state of the qubit as a result of the non-site-selective pulse. The state of the qubit can be a superposition of the clock manifold state and the qubit manifold state. The clock manifold can be a manifold of excited states. The qubit manifold can be a manifold of unexcited states.

[0266] To return qubits from the clock manifold back to the qubit manifold, a similar process can be performed: a non-site-selective π / 2 pulse can be applied to the |0〉 states of the qubits, another 2π pulse can be applied to two selected qubits to de-excite the qubits from their |0〉 states, and a final −π / 2 pulse can return the qubits to the qubit manifold.

[0267] In another example, the site-selective shelving procedure of this disclosure can be extended to site-selectively perform a class of unitary operations V on the qubit-clock Bloch sphere.

[0268] A unitary operation is the expression

[0269]

number

[0270] Unitary operations are global

[0271]

number

[0272]

number

[0273] This technique can enable a broad category of site-selective composite pulses. Such site-selective composite pulses can reduce shelving errors (e.g., reduce errors in driving atoms into a non-interacting state). For example, a composite rotation of θ about the +X axis can be

[0274]

number

[0275]

number

[0276]

number

[0277]

number

[0278]

number

[0279] While preferred embodiments of the present invention have been shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions will occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in practicing the invention. It is intended that the following claims define the scope of the invention, and that methods and structures within the scope of these claims, and their equivalents, be covered thereby.

Claims

1. 1. A method for selectively altering a state of one of a plurality of atoms, the method comprising: (a) applying a first pulse to the plurality of atoms, the plurality of atoms including the one atom and one or more other atoms; (b) applying a second pulse to the one atom but not to the one or more other atoms, the second pulse not being at a transition frequency of the one atom; (c) applying a third pulse to the atoms, thereby changing the state of the one atom; and The method includes:

2. The method of claim 1 , wherein the first pulse comprises a π / 2 pulse.

3. The method of claim 1 , wherein the second pulse comprises a 2π pulse.

4. The method of claim 1 , wherein the third pulse comprises a −π / 2 pulse.

5. The method of claim 1 , wherein the first pulse and the third pulse are opposite in sign to each other.

6. The method of claim 1, wherein (a) to (c) are configured to impart a change in the state of at least one of the one atoms, but not to impart a change to the one or more other atoms of the plurality of atoms.

7. The method of claim 1, further comprising applying a magnetic field across the plurality of atoms.

8. The method of claim 1, wherein the first pulse, the second pulse, or the third pulse is an electromagnetic pulse or pulse sequence.

9. The method of claim 1, wherein the first pulse or the third pulse includes polarized light.

10. The method of claim 9, wherein the polarized light is linear polarized light, circular polarized light, or π polarized light.

11. The method of claim 1, wherein the plurality of atoms includes an atom having two valence electrons.

12. The method of claim 1, wherein the first pulse and the third pulse have a magnitude ratio of at least about 0.

95.

13. The method of claim 1, wherein the first pulse and the third pulse are at shelving transitions and the second pulse is at a qubit gate transition.

14. The method of claim 1, further comprising the step of: (d) imaging the selected atoms.

15. The method of claim 1, wherein the first pulse and the third pulse are at shelving transitions and the second pulse is at an imaging transition or a qubit reset operation.

16. The method of claim 1, further comprising a step of performing a qubit gate operation on the one atom.

17. The method of claim 16, further comprising the steps of exciting a second atom and performing a two-qubit gate on the second atom and the one atom.

18. A method for selectively exciting one atom of a plurality of atoms to an excited state, the method comprising: (a) selecting said one atom using a selection operation; (b) exciting the one atom to the excited state, the excitation being at least partially achieved by applying a non-site-selective excitation beam across the plurality of atoms, the non-site-selective excitation beam selectively interacting with the one atom based on the selection operation in (a); A method comprising:

19. The method of claim 18, wherein (b) comprises applying the non-site-selective excitation beam to at least two atoms of the plurality of atoms.

20. The method of claim 19, wherein (b) comprises applying the non-site-selective excitation beam to each atom of the plurality of atoms.

21. The method of claim 18, wherein the excited state is a Rydberg state.

22. The method of claim 18, wherein the excitation in (b) is time-domain multiplexed.

23. The method of claim 18, which is at least a part of a universal set of qubit gate operations.

24. The method of claim 18, wherein the non-site-selective excitation beam comprises an ultraviolet excitation beam.

25. The method of claim 18, further comprising, simultaneously with or after (b), a step of exciting at least another atom of the plurality of atoms using the non-site-selective excitation beam, wherein the at least another atom does not interact with the one atom.

26. The method of claim 18, further comprising performing a qubit gate operation on the one atom.

27. The method of claim 26, further comprising the steps of exciting a second atom and performing a two-qubit gate on the second atom and the one atom.

28. The method of claim 1, further comprising: (i) selecting a second atom from the plurality of atoms; (ii) prior to (i), applying a site-selective pulse to the second atom, the applying the site-selective pulse comprising providing the site-selective pulse with a differential shift between a ground state and a clock manifold of the second atom compared to one or more other atoms of the plurality of atoms; A method comprising:

29. The method of claim 28, wherein the site-selective pulse is an off-resonance pulse.

30. The method of claim 28, wherein the site-selective pulse is applied to the one atom and not to the one or more other atoms of the plurality of atoms.

31. The method of claim 28, wherein the one atom is not addressable by the first pulse or the third pulse as is the one or more other atoms of the plurality of atoms as a result of the selecting step in (i).

32. The method of claim 28, wherein the first pulse and the third pulse are at a shelving transition.

33. The method of claim 32, wherein the first pulse and the third pulse do not interact with the one atom.

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