Scalable neutral atom-based quantum computation

Abstract

The present disclosure provides methods and systems for performing non-classical computations. The methods and systems generally use: a plurality of spatially distinct optical capture sites to capture a plurality of atoms; one or more electromagnetic delivery units to apply electromagnetic energy to one or more atoms of the plurality of atoms to induce the atoms to assume one or more superimposed states of the first atomic state and the second atomic state; one or more entanglement units to quantum mechanically entangle at least one subset of the one or more atoms in the one or more superimposed states with at least another atom of the plurality of atoms; and one or more readout optical units to perform measurements of superimposed states to obtain non-classical calculations.

Description

[0001] This application is a divisional application of the Chinese patent application with the application date of November 12, 2019, application number 201980088695.4, and invention name “Scalable neutral atom-based quantum computing” (the corresponding PCT application with the application date of November 12, 2019 and application number PCT / US2019 / 061029).

[0002] Cross-references

[0003] This application is a continuation-in-part of U.S. Patent Application No. 16 / 405,877, filed on May 7, 2019, entitled “Scalable neutral atom based quantum computing,” which claims the benefit of U.S. Provisional Patent Application No. 62 / 760,781, filed on November 13, 2018, entitled “Scalable neutral atom based quantum computing,” and U.S. Provisional Patent Application No. 62 / 815,985, filed on March 8, 2019, entitled “Scalable neutral atom based quantum computing,” which are incorporated herein by reference in their entirety for all purposes. Background Art

[0004] Quantum computers typically exploit quantum mechanical phenomena such as superposition and entanglement to perform operations on data. Quantum computers may differ from digital electronic computers based on transistors. For example, digital computers need to encode data as binary digits (bits), each of which is always in one of two definite states (0 or 1), while quantum computing uses quantum bits (qubits), which can be in a superposition of states. Summary of the invention

[0005] It is recognized herein that a need exists for methods and systems for performing non-classical computing.

[0006] The present disclosure provides systems and methods for performing non-classical or quantum computing using atoms, such as neutral or uncharged atoms. Atoms can be optically captured in large arrays. The quantum mechanical state of atoms, such as the hyperfine state or nuclear spin state of atoms, can be configured to serve as a quantum bit (qubit) ground state. The qubit state can be manipulated by interaction with optical, radio frequency or other electromagnetic radiation to perform non-classical or quantum computing.

[0007] In one aspect, the present disclosure provides a system for performing non-classical computing, comprising: one or more optical trapping units configured to generate a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites configured to trap a plurality of atoms, the plurality of atoms comprising greater than 60 atoms; one or more electromagnetic delivery units configured to apply electromagnetic energy to one or more atoms in 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 superposition state with at least another atom in the plurality of atoms; and one or more readout optical units configured to perform one or more measurements on the one or more superposition states to obtain non-classical computing. Non-classical computing may include quantum computing. Quantum computing may include gate model quantum computing. One or more atoms in the plurality of atoms may include qubits. The first atomic state may include a first single qubit state and the second atomic state may include a second single qubit state. The first atomic state or the second atomic state may be elevated in energy relative to a base atomic state of the atom. The first atomic state may include a first hyperfine electronic state, and the second atomic state may include a second hyperfine electronic state different from the first hyperfine electronic state. 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 plurality of atoms may include at least 100 atoms. The plurality of atoms may include neutral atoms. The plurality of atoms may include rare earth atoms. The plurality of atoms may include alkali atoms. The plurality of atoms may include alkaline earth atoms. The alkaline earth atoms may include strontium atoms. The strontium atoms may include strontium-87 atoms. The first and second atomic states may include strontium-87 3 The first and second hyperfine states on the P1 manifold. The first and second atomic states can include strontium-87 3The first and second hyperfine states on the P2 manifold. The first and second atomic states may include the first and second hyperfine states on the multit manifold. The first and second atomic states may include the first and second hyperfine states on the triplet manifold. The first and second atomic states may include the first and second nuclear spin states of a quadrupole nucleus. The first and second atomic states may include the first and second nuclear spin states of a spin-9 / 2 nucleus. The first and second atomic states may include the first and second nuclear spin states of strontium-87. One or more atoms in one or more superposition states and a subset of another atom may be quantum mechanically entangled with a coherent lifetime of at least 1 second. The plurality of atoms may include a temperature of up to 10 microkelvins (μK). The system may also include one or more vacuum units configured to maintain the system at a pressure of up to 10-6 Pascals (Pa). Each of the plurality of optical trapping sites may be spatially separated from the other optical trapping sites by at least 200 nanometers (nm). Each of the plurality of optical trapping sites may be configured to capture a single atom of the plurality of atoms. The one or more optical trapping sites may include one or more optical tweezers. One or more optical trapping sites may include one or more optical lattice sites in one or more optical lattices. One or more optical lattices may include one or more members selected from the group consisting of: a one-dimensional (1D) optical lattice, a two-dimensional (2D) optical lattice, and a three-dimensional (3D) optical lattice. One or more optical trapping units may include one or more spatial light modulators (SLMs) configured to generate multiple optical trapping sites. One or more SLMs may include one or more digital micromirror devices (DMDs) or one or more liquid crystal on silicon (LCoS) devices. One or more optical trapping units may include one or more light sources configured to emit light tuned to one or more magic wavelengths corresponding to multiple atoms. One or more optical trapping units may include one or more imaging units configured to obtain one or more images of the spatial configuration of multiple atoms trapped in the optical trapping site. One or more images may include one or more members selected from the group consisting of fluorescence images, single-atom fluorescence images, absorption images, single-atom absorption images, phase contrast images, and single-atom phase contrast images. The system may also include one or more spatial configuration artificial intelligence (AI) units configured to perform one or more AI operations to determine the spatial configuration of multiple atoms trapped in the optical trapping site based on one or more images. The one or more AI operations may include one or more machine learning (ML) operations. The one or more AI operations may include one or more reinforcement learning (RL) operations. The one or more optical trapping units may include one or more atom rearrangement units configured to impart an altered spatial arrangement of a plurality of atoms captured by the optical trapping site based on one or more images.The system may also include one or more spatial arrangement artificial intelligence (AI) units configured to perform one or more AI operations to determine the changed spatial arrangement of multiple atoms trapped within the optical trapping site based on one or more images. The one or more AI operations may include one or more machine learning (ML) operations. The one or more AI operations may include one or more reinforcement learning (RL) operations. One or more atom rearrangement units may be configured to change the spatial arrangement to obtain an increase in the filling factor of the multiple optical trapping sites. The filling factor may include a value of at least 70%. The system may also include one or more state preparation units configured to prepare the state of the multiple atoms. The one or more state preparation units may be configured to cool the multiple atoms. The one or more state preparation units may be configured to cool the multiple atoms before capturing the multiple atoms at the multiple optical trapping sites. One or more of the state preparation units may include a Zeeman slowdown device configured to slow down the one or more atoms from a first speed or speed distribution to a second speed lower than the first speed or speed distribution. The Zeeman slowdown device may include a one-dimensional (1D) Zeeman slowdown device. The second speed may be at most 10 meters per second (m / s). One or more of the state preparation units may also include a first magneto-optical trap (MOT) configured to cool one or more atoms to a first temperature. The first MOT may include a three-dimensional (3D) MOT. The first MOT may include one or more light sources configured to emit light having one or more wavelengths in the range from 400nm to 500nm. The first temperature may be at most 10 millikelvin (mK). One or more of the state preparation units may also include a second MOT configured to cool one or more atoms from the first temperature to a second temperature lower than the first temperature. The second MOT may include one or more light sources configured to emit light having one or more wavelengths in the range from 400nm to 1,000nm. The second temperature may be at most 100 microkelvin (μK). One or more state preparation units may also include a sideband cooling unit. The sideband cooling unit may be configured to use sideband cooling to cool one or more atoms from the second temperature to a third temperature lower than the second temperature. The sideband cooling unit may include one or more light sources configured to emit light having one or more wavelengths in the range from 400nm to 1,000nm. The third temperature may be at most 10 microkelvins (μK). One or more of the state preparation units may include an optical pumping unit configured to emit light to optically pump one or more atoms of the plurality of atoms from an equilibrium atomic state to a non-equilibrium atomic state. The optical pumping unit may include one or more light sources configured to emit light including one or more wavelengths in a range from 400 nanometers (nm) to 1,000 nm. The light may include one or more wavelengths in a range from 650 nm to 700 nm.One or more of the state preparation units may include a coherent drive unit configured to coherently drive one or more atoms from a non-equilibrium atomic state to a first or second atomic state. The coherent drive unit may be configured to induce a two-photon transition between the non-equilibrium state and the first or second atomic state. The coherent drive unit may include one or more light sources configured to emit light having one or more wavelengths in the range of from 400nm to 1,000nm. The coherent drive unit 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 may include one or more light sources configured to emit light having one or more wavelengths in the range of from 400nm to 1,000nm. The coherent drive unit may be configured to induce a radio frequency (RF) transition between the non-equilibrium state and the first or second atomic state. The coherent drive unit may include one or more electromagnetic radiation sources configured to emit electromagnetic radiation configured to induce RF transitions. One or more electromagnetic delivery units may include one or more spatial light modulators (SLMs), acousto-optic devices (AODs), or acousto-optic modulators (AOMs) configured to selectively apply electromagnetic energy to one or more atoms in a plurality of atoms. One or more electromagnetic delivery units may include one or more digital micromirror devices (DMDs) or one or more liquid crystal on silicon (LCoS) devices. The system may also include one or more electromagnetic energy artificial intelligence (AI) units configured to perform one or more AI operations to selectively apply electromagnetic energy to one or more atoms. One or more AI operations may include one or more machine learning (ML) operations. One or more AI operations may include one or more reinforcement learning (RL) operations. The electromagnetic energy may include light energy. The electromagnetic energy may include microwave energy. The electromagnetic energy may include radio frequency (RF) energy. The RF energy may include one or more wavelengths of at least 30 millimeters (mm). The RF energy may include an average power of no more than 10 watts (W). One or more electromagnetic delivery units may be configured to implement one or more single-qubit gate operations on one or more qubits. One or more readout optical units may include one or more optical detectors. One or more optical detectors may include one or more cameras. One or more optical detectors may include one or more fluorescence detectors. The system may also include one or more atom reservoirs configured to supply one or more replacement atoms to replace the one or more atoms at the one or more optical trapping sites when one or more atoms are lost from one or more optical trapping sites in the plurality of optical trapping sites. The system may also include one or more atom moving units configured to move the one or more replacement atoms to the one or more optical trapping sites. The one or more atom moving units may include one or more electrically tunable lenses, acousto-optic deflectors (AODs), or spatial light modulators (SLMs).A subset of one or more atoms in one or more superposition states and another atom can be quantum mechanically entangled through magnetic dipole interaction, induced magnetic dipole interaction, electric dipole interaction or induced electric dipole interaction. One or more entanglement units may include one or more Rydberg excitation units, which are configured to excite a subset of one or more atoms in one or more superposition states to a Rydberg state or to a superposition of a Rydberg state and a low-energy atomic state, thereby forming one or more Rydberg atoms or modified Rydberg atoms. One or more Rydberg excitation units may be configured to induce one or more quantum mechanical entanglements between one or more Rydberg atoms or modified Rydberg atoms and another atom, the other atom being located at a distance of no more than 10 micrometers (μm) from the one or more Rydberg atoms or modified Rydberg atoms. One or more Rydberg units may be configured to drive one or more Rydberg atoms or modified Rydberg atoms to a lower energy atomic state, thereby forming one or more dual qubit units. One or more electromagnetic delivery units may be configured to implement one or more dual qubit gate operations on one or more dual qubit units. The one or more Rydberg excitation cells may include one or more light sources configured to emit light having one or more ultraviolet (UV) wavelengths. The light may include one or more wavelengths in the range from 300 nm to 400 nm. The system may be operably coupled to a digital computer via a network. The network may include a cloud network.

[0008] In another aspect, the present disclosure provides a non-classical computer, comprising: a plurality of qubits comprising greater than 60 atoms, each atom being trapped in one of a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprises at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state; one or more electromagnetic 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 comprising a superposition state between at least the first qubit 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 on the one or more qubits, thereby obtaining a non-classical computation.

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

[0010] On the other hand, the present disclosure provides a method for performing non-classical computing, comprising: (a) generating a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites being configured to trap a plurality of atoms, the plurality of atoms comprising greater than 60 atoms; (b) applying electromagnetic energy to one or more atoms of the plurality of atoms, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state; (c) quantum mechanically entangled 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 on the one or more superposition states to obtain non-classical computing.

[0011] In another aspect, the present invention provides a method of performing non-classical computing, comprising: (a) providing a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site in a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprises at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state; (b) applying electromagnetic energy to one or more qubits in the plurality of qubits, thereby imparting a non-classical operation to the one or more qubits, the non-classical operation comprising a superposition state between at least the first qubit state and the second qubit state; (c) quantum mechanically entangled at least a subset of the plurality of qubits in superposition with at least another qubit in the plurality of qubits; and (d) performing one or more optical measurements on the one or more qubits, thereby obtaining the non-classical computing.

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

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

[0014] In another aspect, the present disclosure demonstrates a method for performing non-classical computing, comprising: (a) generating a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites being configured to trap a plurality of atoms, wherein the plurality of atoms are quantum bits, wherein an atom of the plurality of atoms is trapped in an optical trapping site of the plurality of optical trapping sites by attractive force; (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 entangled 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 measurements on the one or more superposition states to obtain the non-classical computing.

[0015] In another aspect, the present disclosure demonstrates a method for performing non-classical computing, comprising: (a) generating a plurality of spatially distinct optical trapping sites configured to trap a plurality of atoms, wherein the plurality of atoms are quantum bits; (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, wherein the applying comprises modulating the electromagnetic energy with at least two optical modulators; (c) quantum mechanically entangled 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 measurements on the one or more superposition states to obtain the non-classical computing.

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

[0017] Another aspect of the present disclosure provides a system comprising one or more computer processors and a computer memory coupled thereto. The computer memory comprises machine executable code that, when executed by the one or more computer processors, implements any method described above or elsewhere herein.

[0018] Other aspects and advantages of the present disclosure will become apparent to those skilled in the art from the following detailed description, wherein only illustrative embodiments of the present disclosure are shown and described. As will be appreciated, the present disclosure is capable of other different embodiments, and its several details are capable of modification in various obvious respects, all without departing from the present disclosure. Therefore, the drawings and description are to be regarded as illustrative in nature, and not restrictive.

[0019] Incorporated by Reference

[0020] All publications, patents, and patent applications mentioned in this specification are incorporated herein 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. If a publication, patent, or patent application incorporated by reference contradicts the disclosure contained in the specification, the specification is intended to supersede and / or take precedence over any such contradictory material. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The novel features of the present invention are particularly set forth in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by referring to the following detailed description and the accompanying drawings (also referred to herein as "figures") which set forth illustrative embodiments in which the principles of the present invention are utilized, wherein:

[0022] Figure 1 A computer control system is shown that is programmed or otherwise configured to implement the methods provided herein.

[0023] Figure 2 An example of a system for performing non-classical computing is shown.

[0024] Figure 3A An example of an optical capture unit is shown.

[0025] Figure 3B An example of multiple optical trapping sites is shown.

[0026] Figure 3C An example of an optical trapping cell partially filled with atoms is shown.

[0027] Figure 3D An example of an optical trapping cell completely filled with atoms is shown.

[0028] Figure 4 An example of an electromagnetic delivery unit is shown.

[0029] Figure 5 An example of a state preparation unit is shown.

[0030] Figure 6 A flow chart illustrating an example of a first method for performing non-classical computation is shown.

[0031] Figure 7 A flow chart showing an example of a second method for performing non-classical computation is shown.

[0032] Figure 8 A flow chart showing an example of a third method for performing non-classical computing is shown.

[0033] Fig. 9 The inclusion of strontium-87 3 Example of a qubit in the P2 state.

[0034] Fig. 10A and Fig. 10B The strontium-87 1 Stark shift simulation of the S0 hyperfine state.

[0035] Fig.11A and Fig. 11B A simulation of single-qubit control with Stark shift is shown.

[0036] Fig. 12A and Fig. 12B An example array for capturing light generated by an SLM is shown. DETAILED DESCRIPTION

[0037] Although various embodiments of the present invention have been shown and described herein, it will be apparent to those skilled in the art that these embodiments are provided as examples only. Various modifications, variations and substitutions may be envisioned by those skilled in the art without departing from the present invention. It should be understood that various alternatives to the embodiments of the present invention described herein may be adopted.

[0038] Unless otherwise defined, all technical terms used herein have the same meaning as those commonly understood by those of ordinary skill in the art to which the present invention belongs. As used in this specification and the appended claims, the singular forms "a", "an", and "the" include plural forms unless the context clearly dictates otherwise. Any reference to "or" herein is intended to encompass "and / or" unless otherwise indicated.

[0039] When the term "at least", "greater than", or "greater than or equal to" precedes the first value in a series of two or more values, the term "at least", "greater than", or "greater than or equal to" applies to each value in the series. For example, greater than or equal to 1, 2, or 3 is equivalent to greater than or equal to 1, greater than or equal to 2, or greater than or equal to 3.

[0040] When the term "not greater than," "less than," "less than or equal to," or "at most" precedes the first value in a series of two or more values, the term "not greater than," "less than," "less than or equal to," or "at most" applies to each value in the series. For example, less than or equal to 3, 2, or 1 is equivalent to less than or equal to 3, less than or equal to 2, or less than or equal to 1.

[0041] When values ​​are described as ranges, it should be understood that such disclosure includes disclosure of all possible sub-ranges within such ranges as well as specific values ​​falling within such ranges, whether or not a specific value or a specific sub-range is expressly stated.

[0042] As used herein, like characters refer to like elements.

[0043] As used herein, the terms "artificial intelligence," "artificial intelligence process," "artificial intelligence operation," and "artificial intelligence algorithm" generally refer to any system or computing process that takes one or more actions to enhance or maximize the chances of successfully achieving a goal. The term "artificial intelligence" may include "generative modeling," "machine learning" (ML), and / or "reinforcement learning" (RL).

[0044] As used herein, the terms "machine learning," "machine learning process," "machine learning operation," and "machine learning algorithm" generally refer to any system or analytical and / or statistical process performed by a computer that gradually improves 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 factors). ML may include one or more of regression analysis, regularization, classification, dimensionality reduction, ensemble learning, meta-learning, association rule learning, cluster analysis, anomaly detection, deep learning, or ultra-deep learning. ML can include, but is not limited to: 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 operations, 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, t-distributed random neighbor embedding, adaptive boosting (AdaBoosting), boosting, ladder boosting, guided aggregation, ensemble averaging, decision tree, conditional decision tree, boosted decision tree, gradient boosted decision tree, random forest, stacked generalization, Bayesian network, Bayesian belief network, Naive Bayes, Gaussian Naive Bayes, Multinomial Naive Bayes, Hidden Markov Model, Hierarchical Hidden Markov Model, Support Vector Machine, Encoder, Decoder, Autoencoder, Stacked Autoencoder, Perceptron, Multilayer Perceptron, Artificial Neural Network, Feedforward Neural Network, Convolutional Neural Network, Recurrent Neural Network, Long Short-Term Memory, Deep Belief Network, Deep Boltzmann Machine, Deep Convolutional Neural Network, Deep Recurrent Neural Network, or Generative Adversarial Network.

[0045] As used herein, the terms "reinforcement learning," "reinforcement learning process," "reinforcement learning operation," and "reinforcement learning algorithm" are intended to refer to any system or computational process that takes one or more actions to enhance or maximize some notion of the cumulative reward of its interaction with an environment. An agent performing a reinforcement learning (RL) process may receive positive or negative reinforcement, called "immediate rewards," from taking one or more actions in an environment and thereby placing itself and the environment in various new states.

[0046] The goal of the agent may be to enhance or maximize some concept of cumulative reward. For example, the goal of the agent may be to enhance or maximize a "discounted reward function" or an "average reward function". A "Q function" can represent the maximum cumulative reward that can be obtained from a state and the actions taken in that state. "Value functions" and "generalized advantage estimators" can represent the maximum cumulative reward that can be obtained from a state given an optimal or best action selection. RL can utilize any one or more of these cumulative reward concepts. As used herein, any such function can be referred to as a "cumulative reward function". Therefore, calculating the best or optimal cumulative reward function can be equivalent to finding the best or optimal policy for the agent.

[0047] The agent and its interaction with the environment can be formulated as one or more Markov decision processes (MDPs). The RL process may not assume knowledge of the exact mathematical model of the MDP. The MDP may be completely unknown, partially known, or completely known to the agent. With respect to prior knowledge of the MDP, the RL process may be in the range between the two degrees of "model-based" or "model-free". Thus, the RL process may be targeted at large MDPs, where exact methods may not be feasible or available due to the unknown or stochastic nature of the MDP.

[0048] The RL process can be implemented using one or more computer processors described herein. A digital processing unit can train, store, and then deploy a "strategy" using an agent to enhance or maximize a cumulative reward. A strategy can be sought (e.g., searched) over as long a period of time as possible or desired. Such optimization problems can be solved by storing an approximation of the optimal strategy, by storing an approximation of the cumulative reward function, or by both. In some cases, the RL process can store one or more tables of approximated values ​​for such functions. In other cases, the RL process can use one or more "function approximators."

[0049] Examples of function approximators may include neural networks (such as deep neural networks) and probabilistic graphical models (e.g., Boltzmann machines, Helmholtz machines, and Hopfield networks). A function approximator may create a parameterization of an approximation of a cumulative reward function. Optimization of a function approximator in terms of its parameterization may include perturbing parameters by perturbing the function approximator to more closely satisfy Bellman's optimality criterion (such as in temporal difference methods) or in a direction that enhances or maximizes the cumulative reward and thereby enhances or optimizes the policy (such as in policy gradient methods).

[0050] During training, the agent can take actions in the environment to gain more information about the environment and about good or optimal strategy choices for survival or better utility. The agent's actions can be randomly generated (e.g., especially in the early stages of training) or can be dictated by another machine learning paradigm (such as supervised learning, imitation learning, or any other machine learning process described herein). The agent's actions can be refined by selecting actions that are closer to the agent's perception of what an enhanced or optimal strategy is. With respect to the choice between exploration and exploitation, various training strategies can range between two degrees of off-policy and on-policy approaches.

[0051] As used herein, the terms "non-classical computing," "non-classical processes," "non-classical operations," and "non-classical computers" generally refer to any method or system for performing a computational process outside the paradigm of classical computing. Non-classical computing, non-classical processes, non-classical operations, or non-classical computers may include quantum computing, quantum processes, quantum operations, or quantum computers.

[0052] As used herein, the terms "quantum computing", "quantum process", "quantum operation" and "quantum computer" generally refer to any method or system for performing calculations using quantum mechanical operations (such as unitary transformations or completely positive trace preservation (CPTP) mappings on quantum channels) on a Hilbert space represented by a quantum device. As such, quantum computing and classical (or digital) computing may be similar in that both computations may include a sequence of instructions executed on input information and then provide an output. Various paradigms of quantum computing can decompose quantum operations into sequences of elementary quantum operations that simultaneously affect a subset of qubits of a quantum device. Quantum operations can be selected based on, for example, their location or the ease of their physical implementation. A quantum process or computation can then consist of a series of such instructions that can represent different quantum evolutions on a quantum device in various applications. For example, a process of computing or simulating quantum chemistry can be represented by using qubits (such as two-level quantum systems) and universal quantum gate sets (such as Hadamard, non-controlled (CNOT) and π / 8 rotations) through the so-called Jordan-Wigner transformation or Bravyi-Kitaev transformation to represent the quantum states and annihilation and creation operators of electron spin orbits.

[0053] Other examples of quantum processes or computations may include processes for optimization, such as the quantum approximation optimization algorithm (QAOA) or quantum minimum finding. QAOA may include gates that perform rotations of single qubits and entanglement of multiple qubits. In quantum adiabatic computation, instructions may carry a random or non-random evolution path from an initial quantum system to a final quantum system.

[0054] Quantum inspired processes may include simulated annealing, parallel tempering, master equation solvers, Monte Carlo processes, etc. Quantum classical or hybrid algorithms or processes may include processes such as the variational quantum eigensolver (VQE) and the variational and adiabatic navigated quantum eigensolver (VanQver).

[0055] A quantum computer may include one or more adiabatic quantum computers, quantum gate arrays, one-way quantum computers, topological quantum computers, quantum Turing machines, quantum annealers, Ising solvers, or gate models of quantum computing.

[0056] Systems for performing nonclassical computing

[0057] In one aspect, the present disclosure provides a system for performing non-classical computing. The system may include: one or more optical trapping units configured to generate a plurality of spatially different 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 in 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 in the plurality of atoms; and one or more readout optical units configured to perform one or more measurements on the one or more superposition states to obtain non-classical computing.

[0058] Figure 2 An example of a system 200 for performing non-classical computing is shown. Non-classical computing can include quantum computing. Quantum computing can include gate model quantum computing.

[0059] The system 200 may include one or more optical capture units 210. The optical capture unit may include any optical capture unit described herein, such as those described herein with respect to Figure 3AThe optical trapping unit described herein can be configured to generate a plurality of spatially distinct optical trapping sites. For example, the optical trapping unit can be configured to generate at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 2 0,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000 or more optical capture sites. The optical capture unit may be configured to generate 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, 70, 60, 50, 40, 30, 20, 10, or fewer optical trapping sites. The optical trapping unit can be configured to capture a number of optical trapping sites within a range defined by any two of the aforementioned values.

[0060] The optical trapping unit can be configured to trap a plurality of atoms. For example, the optical trapping unit can be configured to trap at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, , 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000 or more atoms. The optical capture unit may be configured to capture up to 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, 3 40, 30, 20, 10, 25, 30, 40, 50, 60, 50, 60, 70, 80, 70, 60, 5 ...

[0061] Each optical trapping site of the optical trapping unit can be configured to capture at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more atoms. Each optical trapping site can be configured to capture at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 or less atoms. Each optical trapping site can be configured to capture a number of atoms within a range defined by any two of the aforementioned values. Each optical trapping site can be configured to capture a single atom.

[0062] One or more atoms in the plurality of atoms may include a qubit, as described herein (e.g., with respect to Figure 4). Two or more atoms may be quantum mechanically entangled. Two or more atoms may be quantum mechanically entangled with a coherence lifetime of at least about 1 microsecond (μs), 2μs, 3μs, 4μs, 5μs, 6μs, 7μs, 8μs, 9μs, 10μs, 20μs, 30μs, 40μs, 50μs, 60μs, 70μs, 80μs, 90μs, 100μs, 200μs, 300μs, 400μs, 500μs, 600μs, 700μs, 800μs, 900μs, 1 millisecond (m s), 2ms, 3ms, 4ms, 5ms, 6ms, 7ms, 8ms, 9ms, 10ms, 20ms, 30ms, 40ms, 50ms, 60ms, 70ms, 80ms, 90ms, 100ms , 200ms, 300ms, 400ms, 500ms, 600ms, 700ms, 800ms, 900ms, 1 second (s), 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, 10s or more. Two or more atoms can be quantum mechanically entangled with a coherence lifetime of 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, 70ms, The lifetime of a quantum leap may be 100 ms, 200 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 less. Two or more atoms may be quantum mechanically entangled, and the coherent lifetime is within the 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.

[0063] One or more atoms may include alkali atoms. One or more atoms may include lithium (Li) atoms, sodium (Na) atoms, potassium (K) atoms, rubidium (Rb) atoms or cesium (Cs) atoms. One or more atoms may include lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms or cesium-133 atoms. One or more atoms may include alkaline earth metal atoms. One or more atoms may include beryllium (Be) atoms, magnesium (Mg) atoms, calcium (Ca) atoms, strontium (Sr) atoms or barium (Ba) atoms. The one or more atoms may include a beryllium-9 atom, a magnesium-24 atom, a magnesium-25 atom, a magnesium-26 atom, a calcium-40 atom, a calcium-42 atom, a calcium-43 atom, a calcium-44 atom, a calcium-46 atom, a calcium-48 atom, a strontium-84 atom, a strontium-86 atom, a strontium-87 atom, a strontium-88 atom, a barium-130 atom, a barium-132 atom, a barium-134 atom, a barium-135 atom, a barium-136 atom, a barium-137 atom, or a barium-138 atom. 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, a ytterbium (Yb) atom, or a lutetium (Lu) atom. The one or more atoms may include scandium-45 atoms, yttrium-89 atoms, lanthanum-139 atoms, cerium-136 atoms, cerium-138 atoms, cerium-140 atoms, cerium-142 atoms, praseodymium-141 atoms, neodymium-142 atoms, neodymium-143 atoms, neodymium-145 atoms, neodymium-146 atoms, neodymium-148 atoms, samarium-144 atoms, samarium-149 atoms, samarium-150 atoms, samarium-152 atoms, samarium-154 atoms, europium-151 atoms, europium-153 atoms, gadolinium-154 atoms, gadolinium-155 atoms, gadolinium-156 atoms, gadolinium-157 atoms, and gadolinium-158 atoms. , gadolinium-160 atoms, terbium-159 atoms, dysprosium-156 atoms, dysprosium-158 atoms, dysprosium-160 atoms, dysprosium-161 atoms, dysprosium-162 atoms, dysprosium-163 atoms, dysprosium-164 atoms, erbium-162 atoms, erbium-164 atoms, erbium-166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium-171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium-175 atoms, or lutetium-176 atoms.

[0064] A plurality of atoms may include a single element selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr and Ba. A plurality of atoms may include a mixture of elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr and Ba. A plurality of atoms may include a natural isotopic mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr and Ba. A plurality of atoms may include an 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. A 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 include lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, 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, and barium-136 atoms. 36 atoms, barium-137 atoms, barium-138 atoms, scandium-45 atoms, yttrium-89 atoms, lanthanum-139 atoms, cerium-136 atoms, cerium-138 atoms, cerium-140 atoms, cerium-142 atoms, praseodymium-141 atoms, neodymium-142 atoms, neodymium-143 atoms, neodymium-145 atoms, neodymium-146 atoms, neodymium-148 atoms, samarium-144 atoms, samarium-149 atoms, samarium-150 atoms, samarium-152 atoms, samarium-154 atoms, europium-151 atoms, europium-153 atoms, gadolinium-154 atoms, gadolinium-155 atoms, gadolinium-156 atoms, and gadolinium-1 57 atoms, gadolinium-158 atoms, gadolinium-160 atoms, terbium-159 atoms, dysprosium-156 atoms, dysprosium-158 atoms, dysprosium-160 atoms, dysprosium-161 atoms, dysprosium-162 atoms, dysprosium-163 atoms, dysprosium-164 atoms, erbium-162 atoms, erbium-164 atoms, erbium-166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium-171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, Lutetium-175 atoms or Lutetium-176 atoms enriched to 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 isotopic abundance.The plurality of atoms may include lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, cesium-133 atoms, beryllium-9 atoms, magnesium-24 atoms, magnesium-25 atoms, magnesium-26 atoms, calcium-40 atoms, calcium-42 atoms, calcium-43 atoms, calcium-44 atoms, calcium-46 atoms, calcium-48 atoms, strontium-84 atoms, strontium-86 atoms, strontium-87 atoms, strontium-88 atoms, barium-130 atoms, barium-132 atoms, barium-134 atoms, barium-135 atoms, barium-136 atoms, 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 7 atoms, gadolinium-158 atoms, gadolinium-160 atoms, terbium-159 atoms, dysprosium-156 atoms, dysprosium-158 atoms, dysprosium-160 atoms, dysprosium-161 atoms, dysprosium-162 atoms, dysprosium-163 atoms, dysprosium-164 atoms, erbium-162 atoms, erbium-164 atoms, erbium-166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium-171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium %, 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 isotopic abundance.The plurality of atoms may include lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, cesium-133 atoms, beryllium-9 atoms, magnesium-24 atoms, magnesium-25 atoms, magnesium-26 atoms, calcium-40 atoms, calcium-42 atoms, calcium-43 atoms, calcium-44 atoms, calcium-46 atoms, calcium-48 atoms, strontium-84 atoms, strontium-86 atoms, strontium-87 atoms, strontium-88 Atoms, barium-130 atoms, barium-132 atoms, barium-134 atoms, barium-135 atoms, barium-136 atoms, barium-137 atoms, barium-138 atoms, scandium-45 atoms, yttrium-89 atoms, lanthanum-139 atoms, cerium-136 atoms, cerium-138 atoms, cerium-140 atoms, cerium-142 atoms, praseodymium-141 atoms, neodymium-142 atoms, neodymium-143 atoms, neodymium-145 atoms, neodymium-146 atoms, neodymium-148 atoms, samarium-1 44 atoms, samarium-149 atoms, samarium-150 atoms, samarium-152 atoms, samarium-154 atoms, europium-151 atoms, europium-153 atoms, gadolinium-154 atoms, gadolinium-155 atoms, gadolinium-156 atoms, gadolinium-157 atoms, gadolinium-158 atoms, gadolinium-160 atoms, terbium-159 atoms, dysprosium-156 atoms, dysprosium-158 atoms, dysprosium-160 atoms, dysprosium-161 atoms, dysprosium-162 atoms, dysprosium-163 atoms, dysprosium-164 atoms , erbium-162 atoms, erbium-164 atoms, erbium-166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium-171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium-175 atoms, or lutetium-176 atoms enriched to an isotopic abundance within the range defined by any two of the above values.

[0065] The system 200 may include one or more electromagnetic delivery units 220. The electromagnetic delivery unit may include any electromagnetic delivery unit described herein, such as those described herein with respect to Figure 4 The electromagnetic delivery unit described herein can be configured to apply electromagnetic energy to one or more atoms in the plurality of atoms. Applying electromagnetic energy can induce the atoms to adopt one or more superposition states of a first atomic state and a second atomic state different from the first atomic state.

[0066] The first atomic state may include a first single qubit state. The second atomic state may include a second single qubit state. The first atomic state or the second atomic state may be elevated in energy relative to a base atomic state of the atom. The energy of the first atomic state or the second atomic state may be equal to the base atomic state of the atom.

[0067] The first atomic state may include a first hyperfine electronic state and the second atomic state may include a second hyperfine electronic state different from the first hyperfine electronic state. For example, the first and second atomic states may include first and second hyperfine states on a multistate manifold such as a triplet manifold. The first and second atomic states may include 3 P1 or 3 The first and second hyperfine states on the P2 manifold. The first and second atomic states may include any of the atoms described herein. 3 P1 or 3 The first and second hyperfine states on the P2 manifold, such as strontium-87 3 P1 manifold or Strontium-87 3 P2 manifold.

[0068] Fig. 9 The inclusion of strontium-87 3 Example of a qubit in the P2 state. Fig. 9 The left panel shows the Sr-87 3 The rich energy level structure of the P2 state. Fig. 9 The right panel shows the Sr-87 3 Potential qubit transitions within the P2 state are insensitive (to first order) to changes in the magnetic field around 70 Gauss.

[0069] In some cases, the first and second atomic states are first and second hyperfine states of a first electronic state. Photoexcitation may be applied between the first electronic state and the second electronic state. Photoexcitation may excite the first hyperfine state and / or the second hyperfine state to the second electronic state. The single qubit transition may include a two-photon transition between two hyperfine states within the first electronic state using the second electronic state as an intermediate state. To drive the single qubit transition, a pair of frequencies may be applied to drive the two-photon transition, each frequency being detuned from the single-photon transition to the intermediate state. In some cases, the first and second hyperfine states are hyperfine states of a ground electronic state. The ground electronic state may not decay to a lower electronic state by spontaneous or stimulated emission. Hyperfine states may include nuclear spin states. In some cases, hyperfine states include strontium-87 1 The nuclear spin state of the S0 manifold, and the quantum bit transition will strontium-87 1 One or both of the two nuclear spin states of S0 are driven to 3 P2 or 3 In some cases, single-qubit transitions are made via 3 P2 or 3 P1 manifold or from its detuned state in Sr-87 1Two-photon Raman transitions between nuclear spin states of S0. In some cases, the nuclear spin state can be a Stark-shifted nuclear spin state. The Stark shift can be driven optically. The optical Stark shift can be driven by any, all, or combination of single-qubit transitions, double-qubit transitions, shelving transitions, imaging transitions, and the like.

[0070] 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 the first and second nuclear spin states of a quadrupole nucleus, respectively. The first and second atomic states may include the first and second nuclear spin states of a spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4, or spin-9 / 2 nucleus, respectively. The first and second atomic states may include the first and second nuclear spin states of any atom described herein, such as the first and second spin states of strontium-87, respectively.

[0071] For first and second nuclear spin states associated with nuclei that include a spin 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 be accompanied by 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 energy levels may be separated by equal energy. Thus, a transition designed to move an atom from, for example, m N =9 / 2 spin state transferred to m N =7 / 2 spin transitions (such as Raman transitions) can also drive: m 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, where m N is the nuclear spin state. Similarly, it is designed to move atoms from, for example, m N =9 / 2 spin state transferred to m N =5 / 2 spin transitions (such as Raman transitions) can also drive: mN =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, this transition may not selectively induce a transition between specific spin states on the nuclear spin manifold. Alternatively, it may be desirable to achieve a selective transition 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 away from resonance with the transition between the desired transition between the first and second nuclear spin states. For example, if it is desired to transition from a state having m N = -9 / 2 and m N = -7 / 2, the first and second nuclear spin states transition, then the light can provide m N = -5 / 2 spin state AC Stark shift, thus greatly reducing m N = -7 / 2 and m N = -5 / 2 state. Similarly, if we want to N = -9 / 2 and m N = -5 / 2, the first and second nuclear spin states transition, then the light can provide m N = -1 / 2 spin state AC Stark shift, thus greatly reducing m N = -5 / 2 and m N = -1 / 2 states. This can effectively create a two-level subsystem within the nuclear spin manifold that is decoupled from the rest of the nuclear spin manifold, greatly simplifying the dynamics of the qubit system. It can be advantageous to use nuclear spin states near the edge of the nuclear spin manifold (e.g., for spin -9 / 2 nuclei, m N = -9 / 2 and m N =-7 / 2, m N =7 / 2 and m N =9 / 2, m N = -9 / 2 and m N = -5 / 2, or m N =5 / 2 and m N=9 / 2), so only one AC Stark shift is required. Alternatively, one can use nuclear spin states that are farther from the edge of the nuclear spin manifold (e.g., m N = -5 / 2 and m N =-3 / 2 or m N = -5 / 2 and m N = -1 / 2) and two AC Stark shifts can be achieved (e.g., at m N = -7 / 2 and m N = -1 / 2 or m N = -9 / 2 and m N =3 / 2).

[0072] Stark shifting of the nuclear spin manifold can deviate adjacent nuclear spin states from resonance with the desired transition between the first and second nuclear spin states and the second electronic state or a state detuned therefrom. Stark shifting can reduce leakage from the first and second nuclear spin states to other states in the nuclear spin manifold. For beam powers less than 10 mW, Stark shifting can reach 100 kHz. Higher state frequency selectivity can reduce scattering caused by imperfect polarization control. 3 The separation of different angular momentum states in the P1 manifold can be many gigahertz different from the single-qubit and two-qubit gate light. Additional states leaking into the nuclear spin manifold can cause decoherence. The Rabi frequency of a two-qubit transition (e.g., how fast a transition can be driven) can be faster than the decoherence rate. Scattering from intermediate states in a two-qubit transition can be a source of decoherence. Detuning from intermediate states can improve the fidelity of two-qubit transitions.

[0073] Qubits based on nuclear spin states in the electronic ground state can allow the use of long-lived metastable excited electronic states (such as those in strontium-87) 3 The P0 state) is used for qubit storage. Atoms can be selectively transferred to this state to reduce crosstalk or improve gate or detection fidelity. Using the SLM or AOD described herein, such storage or shelving processes can be atom selective. Shelving transitions can include 1 S0 state to Sr-87 3 P0 or 3 Transitions between P2 states.

[0074] Clock transitions (also referred to herein as "shelving transitions" or "storage transitions") can be qubit state selective. The higher state of the clock transition can have a very long natural lifetime, for example greater than 1 second. The linewidth of the clock transition can be much narrower than the qubit energy spacing. This can allow direct spectral resolution. The population can be transferred from one of the qubit states to the clock state. This can allow individual single qubit states to be read out - first transferring the population from one qubit state to the clock state, imaging the qubit, and then transferring the population from the clock state back to the ground state and imaging again. In some cases, a magic wavelength transition is used to drive the clock transition.

[0075] The clock light used for shelving can be atom-selective or non-atom-selective. In some cases, the clock transition is globally applied (e.g., not atom-selective). A globally applied clock transition can include guiding light without passing through a microscope objective or structuring the light. In some cases, the clock transition is atom-selective. Atom-selective clock transitions may allow us to improve gate fidelity by minimizing crosstalk. For example, in order to reduce crosstalk in atoms, atoms can be shelved in clock states where they are not affected by light. This can reduce crosstalk between adjacent qubits undergoing transitions. In order to achieve atom-selective clock transitions, light can pass through one or more microscope objectives and / or can be structured on one or more of a spatial light modulator, a digital micromirror device, a cross-acoustic-optic deflector, and the like.

[0076] The system 200 may include one or more readout optical units 230. The readout optical unit may be configured to perform one or more measurements on one or more superposition states to obtain non-classical computations. The readout optical unit may include one or more optical detectors. The detector 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 optical detector may include one or more fluorescence detectors. The readout optical unit may include one or more objective lenses, such as one or more objective lenses having a numerical aperture (NA) of at least about 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1 or more. The objective lens may have a NA of at most about 1, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7, 0.65, 0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1 or less. The objective lens may have a NA within the range defined by any two of the above values.

[0077] One or more readout optical units 230 can perform measurements, such as projection measurements, by applying light that resonates with the imaging transition. The imaging transition may cause fluorescence. The imaging transition may include the 1 S0 state to Sr-87 1 The induction between P1 states. 1 The P1 state may fluoresce. The lower states of the qubit transition may include 1 Two nuclear spin states in the S0 manifold. One or more of the states may be in resonance with the imaging transition. The measurement may include two excitations. In the first excitation, one of the two lower states may be excited to a resting state (e.g., 3 P0 state). In the second excitation, the imaging transition can be excited. The first transition can reduce crosstalk between neighboring atoms during calculations. The fluorescence generated from the imaging transition can be collected on one or more readout optical units 230.

[0078] The imaging unit may also be used to determine if one or more atoms are missing from the trap.The imaging unit may be used to observe the arrangement of atoms in the trap.

[0079] 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 unit may include one or more low vacuum pumps, such as one or more rotary pumps, rotary vane pumps, rotary piston pumps, diaphragm pumps, piston pumps, reciprocating piston pumps, vortex pumps, or screw pumps. The one or more low vacuum pumps may include one or more wet (e.g., oil-sealed) or dry low vacuum pumps. The vacuum unit may include one or more high vacuum pumps, such as one or more cryogenic adsorption pumps, diffusion pumps, turbomolecular pumps, molecular drag pumps, turbo-drag hybrid pumps, cryogenic pumps, ion pumps, or getter pumps.

[0080] The vacuum unit can include any combination of vacuum pumps described herein. For example, the vacuum unit can include one or more low vacuum pumps (such as a scroll pump) configured to provide a first stage low vacuum pumping. The low vacuum pump can be configured to pump gas out of the system 200 to achieve a low vacuum pressure condition. For example, the low vacuum pump can be configured to pump gas out of the system 200 to achieve a low vacuum pressure condition of up to about 10 3 The vacuum unit may also 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. Once the system 200 has reached the low vacuum pressure condition provided by the one or more low vacuum pumps, the high vacuum pump may be configured to pump gas out of the system 200 to achieve a vacuum pressure of up to about 10 -3Pa high vacuum pressure or up to about 10 -6 Pa ultra-high vacuum pressure.

[0081] The vacuum unit may be configured to maintain the system 200 at a pressure of at most about 10 -6 Pa, 9x10 -7 Pa, 8x 10 -7 Pa, 7x10 -7 Pa, 6x 10 -7 Pa, 5x 10 -7 Pa, 4x 10 -7 Pa, 3x 10 -7 Pa, 2x 10 -7 Pa, 10 -7 Pa, 9x 10 -8 Pa, 8x 10 - 8 Pa, 7x 10 -8 Pa, 6x 10 -8 Pa, 5x 10 -8 Pa, 4x 10 -8 Pa, 3x 10 -8 Pa, 2x 10 -8 Pa, 10 -8 Pa, 9x 10 -9 Pa, 8x10 -9 Pa, 7x 10 -9 Pa, 6x 10 -9 Pa, 5x 10 -9 Pa, 4x 10 -9 Pa, 3x 10 -9 Pa, 2x 10 -9 Pa, 10 -9 Pa, 9x 10 - 10 Pa, 8x 10 -10 Pa, 7x 10 -10 Pa, 6x 10 -10 Pa, 5x 10 -10 Pa, 4x 10 -10 Pa, 3x 10 -10 Pa, 2x 10 -10 Pa, 10 -10 Pa, 9x 10 -11 Pa, 8x 10 -11 Pa, 7x 10 -11 Pa, 6x10 -11 Pa, 5x 10 -11 Pa, 4x 10 -11Pa, 3x 10 -11 Pa, 2x10 -11 Pa, 10 -11 Pa, 9x 10 -12 Pa, 8x10 -12 Pa, 7x 10 -12 Pa, 6x 10 -12 Pa, 5x 10 -12 Pa, 4x 10 -12 Pa, 3x10 -12 Pa, 2x 10 -12 Pa, 10 -12 The vacuum unit may be configured to maintain the system 200 at a pressure of at least about 10 -12 Pa, 2x 10 -12 Pa, 3x 10 -12 Pa, 4x 10 -12 Pa, 5x 10 -12 Pa, 6x 10 -12 Pa, 7x 10 -12 Pa, 8x 10 -12 Pa, 9x 10 -12 Pa, 10 -11 Pa, 2x 10 -11 Pa, 3x 10 -11 Pa, 4x 10 -11 Pa, 5x 10 -11 Pa, 6x 10 -11 Pa, 7x10 -11 Pa, 8x 10 -11 Pa, 9x 10 -11 Pa, 10 -10 Pa, 2x 10 -10 Pa, 3x10 -10 Pa, 4x 10 -10 Pa, 5x 10 -10 Pa, 6x10 -10 Pa, 7x 10 -10 Pa, 8x 10 -10 Pa, 9x 10 -10 Pa, 10 -9 Pa, 2x 10 -9 Pa, 3x 10 -9 Pa, 4x 10 -9 Pa, 5x 10 -9 Pa, 6x 10 -9 Pa, 7x 10 -9 Pa, 8x 10 -9 Pa, 9x 10-9 Pa, 10 -8 Pa, 2x 10 -8 Pa, 3x 10 -8 Pa, 4x 10 -8 Pa, 5x 10 -8 Pa, 6x 10 -8 Pa, 7x 10 -8 Pa, 8x 10 -8 Pa, 9x 10 -8 Pa, 10 -7 Pa, 2x 10 -7 Pa, 3x 10 -7 Pa, 4x 10 -7 Pa, 5x 10 -7 Pa, 6x 10 -7 Pa, 7x 10 -7 Pa, 8x 10 -7 Pa, 9x 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.

[0082] System 200 may include one or more state preparation units 250. The state preparation unit may include any state preparation unit described herein, such as Figure 5 A state preparation unit is described. The state preparation unit may be configured to prepare states of a plurality of atoms.

[0083] 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 the atoms at one or more optical trapping sites when one or more atoms are lost from the optical trapping sites.

[0084] The system 200 may include one or more atom moving units 270. The atom moving unit may be configured to move one or more replacement atoms to one or more optical trapping sites. For example, the one or more atom moving units may include one or more electrically tunable lenses, acousto-optic deflectors (AODs), or spatial light modulators (SLMs).

[0085] 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 at the moment of quantum mechanical entanglement. Alternatively or in combination, the first or second atom may not be in a superposition state at the moment of quantum mechanical entanglement. The first atom and the second atom 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.

[0086] The entanglement unit may include one or more Rydberg excitation units. The Rydberg excitation unit may be configured to excite at least a first atomic electron to a Rydberg state or to a superposition of a Rydberg state and a low-energy atomic state, thereby forming one or more Rydberg atoms or modified Rydberg atoms. The Rydberg excitation unit may be configured to induce one or more quantum mechanical entanglements between a Rydberg atom or a modified Rydberg atom and at least a second atom. The second atom may be located at a distance of at least about 200 nanometers (nm), 300nm, 400nm, 500nm, 600nm, 700nm, 800nm, 900nm, 1 micrometer (μm), 2μm, 3μm, 4μm, 5μm, 6μm, 7μm, 8μm, 9μm, 10μm or more from the Rydberg atom or the modified 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 modified Rydberg atom. The second atom may be located at a distance from the Rydberg atom or modified Rydberg atom, the distance being within a range defined by any two of the aforementioned values. The Rydberg excitation unit may be configured to allow the Rydberg atom or modified Rydberg atom to relax to a lower energy atomic state, thereby forming one or more dual qubit units. The Rydberg excitation unit may be configured to induce the Rydberg atom or modified Rydberg atom to relax to a lower energy atomic state. The Rydberg excitation unit may be configured to drive the Rydberg atom or modified Rydberg atom to a lower energy atomic state. For example, the Rydberg excitation cell can be configured to apply electromagnetic radiation (such as RF radiation or optical radiation) to drive the Rydberg atoms or modified Rydberg atoms to a lower energy atomic state. The Rydberg excitation cell can be configured to induce any number of quantum mechanical entanglements between any number of atoms in the plurality of atoms.

[0087] The Rydberg excitation unit may include one or more light sources (such as any light source described herein) configured to emit light having one or more ultraviolet (UV) wavelengths. The UV wavelength may be selected to correspond to the wavelength at which the Rydberg atoms or modified Rydberg atoms are formed. For example, the light may include at least about 200nm, 210nm, 220nm, 230nm, 240nm, 250nm, 260nm, 270nm, 280nm, 290nm, 300nm, 310nm, 320nm, 330nm, 340nm, 350nm, 360nm, 370nm, 380nm, 390nm, 400nm or more wavelengths. The light may include one or more wavelengths of at most about 400nm, 390nm, 380nm, 370nm, 360nm, 350nm, 340nm, 330nm, 320nm, 310nm, 300nm, 290nm, 280nm, 270nm, 260nm, 250nm, 240nm, 230nm, 220nm, 210nm, 200 nanometers 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 from 300nm to 400nm.

[0088] The Rydberg excitation unit may be configured to induce a two-photon transition to generate entanglement. The Rydberg excitation unit may be configured to induce a two-photon transition to generate entanglement between two atoms. The Rydberg excitation unit may be configured to selectively induce a two-photon transition to selectively generate entanglement between two atoms. For example, the Rydberg excitation unit may be configured to guide electromagnetic energy (such as light energy) to a specific optical trapping site to selectively induce a two-photon transition to selectively generate entanglement between two atoms. The two atoms may be trapped in nearby optical trapping sites. For example, two atoms may be trapped in adjacent optical trapping sites. The two-photon transition may be induced using first and second lights 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 or similar to the light source used to perform the single qubit operation 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 of one or more wavelengths included in the visible region of the spectrum (e.g., in the range from 400 nm to 800 nm or from 650 nm to 700 nm). The second light source may emit light of one or more wavelengths included in the ultraviolet region of the spectrum (e.g., in the range from 200 nm to 400 nm or from 300 nm to 350 nm). The first and second light sources may emit light having substantially equal and opposite spatially correlated frequency shifts.

[0089] Rydberg atoms or modified Rydberg atoms may include Rydberg states, which may have sufficiently strong interatomic interactions with nearby atoms (such as nearby atoms captured in nearby optical trapping sites) to enable dual qubit operations. Rydberg states may include principal quantum numbers of at least about 50, 60, 70, 80, 90, 100 or more. Rydberg states may include principal quantum numbers of at most about 100, 90, 80, 70, 60, 50 or less. Rydberg states may include principal quantum numbers within a range defined by any two of the aforementioned values. Rydberg states may interact with nearby atoms through van der Waals interactions. Van der Waals interactions may shift the atomic energy levels of atoms.

[0090] Selectively exciting atoms to Rydberg levels can enable two-qubit operations. Two-photon transitions can be used to transfer atoms from a ground state such as 1 S0 ground state) to a Rydberg state (such as n 3 S1 state, where n is the principal quantum number described in this article). State selectivity can be achieved by a combination of laser polarization and spectral selectivity. As described in this article, a two-photon transition can be achieved using a first and a second laser source. The first laser source can emit pi-polarized light, which does not change the projection of the atomic angular momentum along the magnetic field. The second laser can emit circularly polarized light, which can change the projection of the atomic angular momentum along the magnetic field by one unit. Using this polarization, the first and second qubit energy levels can be excited to Rydberg levels. However, the Rydberg levels can be more sensitive to magnetic fields than the ground state, so large splittings can be easily obtained (for example, on the order of 100 MHz). This spectral selectivity can allow state-selective excitation to Rydberg levels.

[0091] Due to the van der Waals interactions described herein, two-qubit operations can rely on energetic shifts in energy levels. Such shifts may prevent the excitation of one atom from being conditional on the state of the other atom, or change the coherent dynamics of the excitations of the two-atom system to perform two-qubit operations. In some cases, "modified states" can be generated under continuous actuation to perform two-qubit operations without fully exciting to Rydberg levels (e.g., as described in https: / / arxiv.org / abs / 1605.05207, which is incorporated herein by reference in its entirety for all purposes).

[0092] cloud computing

[0093] System 200 can be connected via a network as described herein (such as Figure 1 The network described herein is operatively coupled to a digital computer described herein (such as the one described herein). Figure 1The network may include a cloud computing network.

[0094] Optical capture unit

[0095] Figure 3A An example of an optical trapping unit 210 is shown. The optical trapping unit can be configured to generate a plurality of spatially distinct optical trapping sites 211, as described herein. For example, Figure 3B As shown in FIG. , the optical trapping unit can be configured to generate a first optical trapping site 211a, a second optical trapping site 211b, a third optical trapping site 211c, a fourth optical trapping site 211d, a fifth optical trapping site 211e, a sixth optical trapping site 211f, a seventh optical trapping site 211g, an eighth optical trapping site 211h, and a ninth optical trapping site 211i, as shown in FIG. Figure 3A A plurality of spatially distinct optical 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 shown in FIG. Figure 3A As described in Figure 3B As depicted in , each optical trapping site can be configured to trap a single atom. Figure 3B As shown in , some optical trapping sites may be empty (ie, no atoms are trapped).

[0096] like Figure 3B As shown in , the plurality of optical trapping sites may include a two-dimensional (2D) array. The 2D array may be perpendicular to Figure 3A The optical axis of the optical assembly of the optical trapping unit depicted in . Alternatively, the plurality of optical trapping sites may comprise a one-dimensional (1D) array or a three-dimensional (3D) array.

[0097] Although in Figure 3B 2 is depicted as including nine optical trapping sites populated by four atoms, but the optical trapping unit 210 can be configured to generate any number of spatially distinct optical trapping sites described herein and can be configured to trap any number of atoms described herein.

[0098] Each optical trapping site in the plurality of optical trapping sites can be spatially separated from each other optical trapping site by at least about 200nm, 300nm, 400nm, 500nm, 600nm, 700nm, 800nm, 900nm, 1μm, 2μm, 3μm, 4μm, 5μm, 6μm, 7μm, 8μm, 9μm, 10μm or more. Each optical trapping site can be spatially separated from each other optical trapping site by at most about 10μm, 9μm, 8μm, 7μm, 6μm, 5μm, 4μm, 3μm, 2μm, 1μm, 900nm, 800nm, 700nm, 600nm, 500nm, 400nm, 300nm, 200nm or less. Each optical trapping site can be spatially separated from each other optical trapping site by a distance within a range defined by any two of the foregoing values.

[0099] The optical trapping site may include one or more optical tweezers. The optical tweezers may include one or more focused laser beams to provide attractive or repulsive forces 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 contain the strongest electric field. The optical trapping site may include one or more optical lattice sites in one or more optical lattices. The optical trapping site may include one or more optical lattice sites in 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 two-dimensional optical lattice, such as Figure 3B Described in.

[0100] An optical lattice can be generated by interfering counter-propagating light (such as counter-propagating lasers) to generate a periodic continuous standing wave pattern with intensity minima and maxima along a specific direction. A one-dimensional optical lattice can be generated by interfering a pair of counter-propagating light beams. A two-dimensional 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, the optical lattice can be generated by at least about 1, 2, 3, 4, 5, 6 or more light sources or at most about 6, 5, 4, 3, 2 or 1 light source.

[0101] Back to Figure 3A As described herein, the optical trapping unit may include one or more light sources configured to emit light to generate a plurality of optical trapping sites as described herein. For example, the optical trapping unit may include a single light source 213, such as Figure 3A Although in Figure 3A1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more light sources or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 light source. The light source may include one or more lasers.

[0102] 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, transverse excitation atmosphere (TEA) lasers or excimer lasers. For example, the laser may include one or more argon dimer (Ar2) excimer lasers, krypton dimer (Kr2) excimer lasers, fluorine dimer (F2) excimer lasers, xenon dimer (Xe2) excimer lasers, argon fluoride (ArF) excimer lasers, krypton chloride (KrCl) excimer lasers, krypton fluoride (KrF) excimer lasers, xenon bromide (XeBr) excimer lasers, xenon chloride (XeCl) excimer lasers or xenon fluoride (XeF) excimer lasers. The laser may include one or more dye lasers.

[0103] 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, and the like. N ) metal vapor laser or manganese chloride (MnCl2) metal vapor laser.

[0104] 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-doped / chromium-doped yttrium aluminum garnet (Nd / Cr:YAG) lasers, erbium-doped yttrium aluminum garnet (Er:YAG) lasers, neodymium-doped lithium yttrium fluoride (Nd:YLF) lasers, neodymium-doped yttrium orthovanadate (ND:YVO4) lasers, neodymium-doped calcium yttrium borate (Nd:YCOB) lasers, neodymium glass (Nd:glass) lasers, titanium sapphire (Ti:sapphire) lasers, thulium-doped yttrium aluminum garnet (Tm:YAG) lasers, doped Ytterbium yttrium aluminum garnet (Yb:YAG) laser, ytterbium-doped glass (Yt:glass) laser, holmium yttrium aluminum garnet (Ho:YAG) laser, chromium-doped zinc selenide (Cr:ZnSe) laser, cerium-doped lithium strontium aluminum fluoride (Ce:LiSAF) laser, cerium-doped lithium calcium aluminum fluoride (Ce:LiCAF) laser, erbium-doped glass (Er:glass) laser, erbium-ytterbium co-doped glass (Er / Yt:glass) laser, uranium-doped calcium fluoride (U:CaF2) laser or samarium-doped calcium fluoride (Sm:CaF2) laser.

[0105] 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 phosphide (InGaAsP) lasers, vertical cavity surface emitting lasers (VCSELs), or quantum cascade lasers.

[0106] The laser may emit a continuous wave laser. The laser may emit a pulsed laser. The laser may have a power of at least about 1 femtosecond (fs), 2fs, 3fs, 4fs, 5fs, 6fs, 7fs, 8fs, 9fs, 10fs, 20fs, 30fs, 40fs, 50fs, 60fs, 70fs, 80fs, 90fs, 100fs, 200fs, 300fs, 400fs, 500fs, 600fs, 700fs, 800fs, 900fs, 1 picosecond (ps), 2ps, 3ps, 4ps, 5ps, 6ps, 7ps, 8ps, 9ps, 10ps, 20ps, 30ps, 40ps, 50ps, 60p s, 70ps, 80ps, 90ps, 100ps, 200ps, 300ns, 400ns, 500ns, 600ns, 700ns, 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 more pulse lengths. The laser may have a power of up to about 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 The laser may have a pulse length within the range defined by any two of the foregoing values.

[0107] The laser may have a frequency of 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 z, 5kHz, 6kHz, 7kHz, 8kHz, 9kHz, 10kHz, 20kHz, 30kHz, 40kHz, 50kHz, 60kHz, 70kHz, 80kHz, 90kHz, 100kHz, 200kHz, 300kHz, 400kHz, 500kHz, 600kHz, 700kHz, 800kHz, 900kHz, 1 megahertz (MHz), 2MHz, 3MHz, 4MHz, 5MHz 6MHz, 7MHz, 8MHz, 9MHz, 10MHz, 20MHz, 30MHz, 40MHz, 50MHz, 60MHz, 70MHz, 80MHz, 90MHz, 100MHz, 200MHz, 300MHz, 400MHz, 500MHz, 600MHz, 700MHz, 800MHz, 900MHz, 1,000MHz or higher repetition rate. The laser may have a frequency of up to about 1,000 MHz, 900 MHz, 800 MHz, 700 MHz, 600 MHz, 500 MHz, 400 MHz, 300 MHz, 200 MHz, 100 MHz, 90 MHz, 80 MHz, 70 MHz, 60 MHz, 50 MHz, 40 MHz, 30 MHz, 20 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz Hz, 3Hz, 2Hz, 10Hz, 9Hz, 8Hz, 7Hz, 6Hz, 5Hz, 4Hz, 3Hz, 2Hz, 1Hz or lower repetition rates.The laser can have a repetition rate within the range defined by any two of the aforementioned values.

[0108] The laser may emit a laser having a power of at least about 1 nanojoule (nJ), 2nJ, 3nJ, 4nJ, 5nJ, 6nJ, 7nJ, 8nJ, 9nJ, 10nJ, 20nJ, 30nJ, 40nJ, 50nJ, 60nJ, 70nJ, 80nJ, 90nJ, 100nJ, 200nJ, 300nJ, 400nJ, 500nJ, 600nJ, 700nJ, 800nJ, 900nJ, 1 microjoule (μJ), 2μJ, 3μJ, 4μJ, 5μJ, 6μJ, 7μJ, 8μJ, 9μJ, 10μJ, 20μJ, 30μJ, 40μJ, 50μJ, 60μJ, 70μJ J, 80μJ, 90μJ, 100μJ, 200μJ, 300μJ, 400μJ, 500μJ, 600μJ, 700μJ, 800μJ, 900μJ, at least 1 millijoule (mJ) 2mJ, 3mJ, 4mJ, 5mJ, 6mJ, 7mJ, 8mJ, 9mJ, 10mJ, 20mJ, 30mJ, 40mJ, 50mJ, 60mJ, 70mJ, 80mJ, 90mJ, 100mJ, 200mJ, 300mJ, 400mJ, 500mJ, 600mJ, 700mJ, 800mJ, 900mJ, light with a pulse energy of at least 1 joule (J) or more. The laser may emit a radiation having a power of up to about 1 J, 900 mJ, 800 mJ, 700 mJ, 600 mJ, 500 mJ, 400 mJ, 300 mJ, 200 mJ, 100 mJ, 90 mJ, 80 mJ, 70 mJ, 60 mJ, 50 mJ, 40 mJ, 30 mJ, 20 mJ, 10 mJ, 9 mJ, 8 mJ, 7 mJ, 6 mJ, 5 mJ, 4 mJ, 3 mJ, 2 mJ, 1 mJ, 900 μJ, 800 μJ, 700 μJ, 600 μJ, 500 μJ, 400 μJ, 300 μJ, 200 μJ, 100 μJ, 90 μJ, 80 μJ, The laser may emit light having a pulse energy within a range defined by any two of the foregoing values.

[0109] The laser may emit a power having 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 In some embodiments, the present invention relates to light with an average power of 1 mW, 50 mW, 60 mW, 70 mW, 80 mW, 90 mW, 100 mW, 200 mW, 300 mW, 400 mW, 500 mW, 600 mW, 700 mW, 800 mW, 900 mW, 1 watt (W), 2 W, 3 W, 4 W, 5 W, 6 W, 7 W, 8 W, 9 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W, 80 W, 90 W, 100 W, 200 W, 300 W, 400 W, 500 W, 600 W, 700 W, 800 W, 900 W, 1,000 W or more. The laser may emit a power having a power of up to about 1,000 W, 900 W, 800 W, 700 W, 600 W, 500 W, 400 W, 300 W, 200 W, 100 W, 90 W, 80 W, 70 W, 60 W, 50 W, 40 W, 30 W, 20 W, 10 W, 9 W, 8 W, 7 W, 6 W, 5 W, 4 W, 3 W, 2 W, 1 W, 900 mW, 800 mW, 700 mW, 600 mW, 500 mW, 400 mW, 300 mW, 200 mW, 100 mW, 90 mW, 80 mW, 70 mW, 60 mW, 50 The laser may emit light having an average power of 100 μW, 200 μW, 100 μW, 80 μW, 200 μW, 100 μW, 90 μW, 80 μW, 70 μW, 60 μW, 50 μW, 40 μW, 30 μW, 20 μW, 10 μW, 9 μW, 8 μW, 7 μW, 6 μW, 5 μW, 4 μW, 3 μW, 2 μW, 1 μW or more. The laser may emit light having a power within a range defined by any two of the aforementioned values.

[0110] The laser may emit light comprising one or more wavelengths in the ultraviolet (UV), visible, or infrared (IR) portions of the electromagnetic spectrum. The laser may emit light comprising 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, nm,530nm,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, 87 0nm, 880nm, 890nm, 900nm, 910nm, 920nm, 930nm, 940nm, 950nm, 960nm, 970nm, 980nm, 990nm, 1,000nm, 1,010nm, 1,020nm, 1,03 0nm, 1,040nm, 1,050nm, 1,060nm, 1,070nm, 1,080nm, 1,090nm, 1,100nm, 1,110nm, 1,120nm, 1,130nm, 1,140nm, 1,150nm, 1,16 1,200nm, 1,210nm, 1,220nm, 1,230nm, 1,240nm, 1,250nm, 1,260nm, 1,270nm, 1,280nm, 1,290nm, 1,300nm, 1,310nm, 1,320nm, 1,330nm, 1,340nm, 1,350nm, 1,360nm, 1,370nm, 1,380nm, 1,390nm, 1,400nm or more wavelengths of light.The lasers may emit wavelengths up to about 1,400 nm, 1,390 nm, 1,380 nm, 1,370 nm, 1,360 nm, 1,350 nm, 1,340 nm, 1,330 nm, 1,320 nm, 1,310 nm, 1,300 nm, 1,290 nm, 1,280 nm, 1,270 nm, 1,260 nm, 1,250 nm, 1,240 nm, 1,230 nm, 1,220 nm, 1,210 nm, 1,200 nm, 1,190 nm, 1,180 nm, 1,160 nm, 0nm, 1,150nm, 1,140nm, 1,130nm, 1,120nm, 1,110nm, 1,100nm, 1,090nm, 1,080nm, 1,070n, 1,060nm, 1,050nm, 1,040nm, 1,03 0nm, 1,020nm, 1,010nm, 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870n m, 860nm, 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, 5 The laser may emit light of one or more wavelengths of 20 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm. The laser may emit light of one or more wavelengths included in the range defined by any two of the aforementioned values.

[0111] The laser can emit a radiation having a power of at least about 1 x 10 -15 nm, 2x 10 -15 nm, 3x 10 -15 nm, 4x 10 -15 nm, 5x10-15 nm、6x 10 -15 nm、7x 10 -15 nm、8x 10 -15 nm、9x 10 -15 nm、1x 10 -14 nm、2x 10 -14 nm、3x 10 -14 nm、4x 10 -14 nm、5x10 -14 nm、6x 10 -14 nm、7x 10 -14 nm、8x 10 -14 nm、9x 10 -14 nm、1x 10 -13 nm、2x 10 - 13 nm、3x 10 -13 nm、4x 10 -13 nm、5x 10 -13 nm、6x 10 -13 nm、7x 10 -13 nm、8x 10 -13 nm、9x 10 -13 nm、1x10 -12 nm、2x 10 -12 nm、3x10 -12 nm、4x 10 -12 nm、5x 10 -12 nm、6x 10 -12 nm、7x 10 -12 nm、8x 10 -12 nm、9x 10 -12 nm、1x 10 -11 nm、2x 10 -11 nm、3x 10 -11 nm、4x 10 -11 nm、5x 10 -11 nm、6x 10 -11 nm、7x 10 - 11 nm、8x 10 -11 nm、9x 10 -11 nm、1x10 -10 nm、2x 10 -10 nm、3x 10 -10 nm、4x 10 -10 nm、5x 10 -10 nm、6x10 -10nm、7x 10 -10 nm、8x 10 -10 nm、9x 10 -10 nm、1x 10 -9 nm、2x 10 -9 nm、3x 10 -9 nm、4x 10 -9 nm、5x10 -9 nm、6x 10 -9 nm、7x 10 -9 nm、8x 10 -9 nm、9x 10 -9 nm、1x 10 -8 nm、2x 10 -8 nm、3x 10 -8 nm、4x 10 -8 nm、5x10 -8 nm、6x 10 -8 nm、7x 10 -8 nm、8x 10 -8 nm、9x 10 -8 nm、1x 10 -7 nm、2x 10 -7 nm、3x 10 - 7 nm、4x 10 -7 nm、5x 10 -7 nm、6x 10 -7 nm、7x 10 -7 nm、8x 10 -7 nm、9x 10 -7 nm、1x 10 -6 nm、2x 10 - 6 nm、3x 10 -6 nm、4x 10 -6 nm、5x 10 -6 nm、6x 10 -6 nm、7x 10 -6 nm、8x 10 -6 nm、9x 10 -6 nm、1x 10 - 5 nm、2x 10 -5 nm、3x 10 -5 nm、4x 10 -5 nm、5x 10 -5 nm、6x 10 -5 nm、7x 10 -5nm, 8x 10 -5 nm、9x 10 - 5 nm, 1x 10 -4 nm, 2x 10 -4 nm, 3x10 -4 nm, 4x 10 -4 nm, 5x 10 -4 nm, 6x 10 -4 nm、7x 10 -4 nm, 8x 10 -4 nm、9x 10 -4 nm, 1x 10 -3 nm or more. Lasers can emit light with a bandwidth of up to about 1 x 10 -3 nm、9x 10 - 4 nm, 8x 10 -4 nm、7x 10 -4 nm, 6x 10 -4 nm, 5x10 -4 nm, 4x 10 -4 nm, 3x 10 -4 nm, 2x 10 -4 nm, 1x 10 -4 nm、9x 10 -5 nm, 8x 10 -5 nm、7x 10 -5 nm, 6x 10 -5 nm, 5x 10 -5 nm, 4x 10 -5 nm, 3x 10 -5 nm, 2x 10 -5 nm, 1x10 -5 nm、9x 10 -6 nm, 8x 10 -6 nm、7x 10 -6 nm, 6x10 -6 nm, 5x 10 -6 nm, 4x 10 -6 nm, 3x 10 -6 nm, 2x 10 - 6 nm, 1x 10 -6 nm、9x 10 -7 nm, 8x 10 -7 nm、7x 10 -7 nm, 6x 10 -7 nm, 5x 10 -7nm、4x 10 -7 nm、3x 10 - 7 nm、2x 10 -7 nm、1x 10 -7 nm、9x 10 -8 nm、8x 10 -8 nm、7x10 -8 nm、6x 10 -8 nm、5x 10 -8 nm、4x 10 -8 nm、3x 10 -8 nm、2x 10 -8 nm、1x 10 -8 nm、9x 10 -9 nm、8x 10 -9 nm、7x 10 -9 nm、6x 10 -9 nm、5x 10 -9 nm、4x10 -9 nm、3x 10 -9 nm、2x 10 -9 nm、1x 10 -9 nm、9x 10 -10 nm、8x 10 -10 nm、7x 10 -10 nm、6x 10 -10 nm、5x10 -10 nm、4x 10 -10 nm、3x 10 -10 nm、2x 10 -10 nm、1x 10 -10 nm、9x 10 -11 nm、8x 10 -11 nm、7x 10 -11 nm、6x 10 -11 nm、5x 10 -11 nm、4x 10 -11 nm、3x 10 -11 nm、2x 10 -11 nm、1x10 -11 nm、9x 10 -12 nm、8x 10 - 12 nm、7x 10 -12 nm、6x 10 -12 nm、5x 10 -12 nm、4x 10 -12 nm、3x 10-12 nm, 2x 10 -12 nm, 1x 10 -12 nm, 9x10 -13 nm, 8x 10 -13 nm、7x 10 -13 nm, 6x 10 -13 nm, 5x 10 -13 nm, 4x 10 -13 nm, 3x10 -13 nm, 2x 10 -13 nm, 1x 10 -13 nm、9x 10 -14 nm, 8x 10 -14 nm、7x 10 -14 nm, 6x 10 -14 nm, 5x 10 -14 nm, 4x 10 -14 nm, 3x 10 - 14 nm, 2x 10 -14 nm, 1x 10 -14 nm、9x 10 -15 nm, 8x 10 -15 nm、7x 10 -15 nm, 6x 10 -15 nm, 5x10 -15 nm, 4x10 -15 nm, 3x 10 -15 nm, 2x 10 -15 nm, 1x 10 -15 The laser may emit light having a bandwidth of 100 nm or less. The laser may emit light having a bandwidth within the range defined by any two of the aforementioned values.

[0112] The light source can be configured to emit light tuned to one or more magic wavelengths corresponding to a plurality of atoms. The magic wavelengths corresponding to the atoms can include light of any wavelength that causes equal or nearly equal polarization rates of the first and second atomic states. The magic wavelength for the transition between the first and second atomic states can be determined by calculating the wavelength-dependent polarization rates of the first and second atomic states and finding the crossover point. Regardless of the intensity of the light emitted by the light source, light tuned to such a magic wavelength can cause equal or nearly equal differential optical shifts in the first and second atomic states. This can effectively decouple the first and second atomic states from the motion of the atoms. The magic wavelength can utilize one or more scalar or tensor optical shifts. The scalar or tensor optical shifts can depend on the magnon energy levels within the first and second atomic states.

[0113] For example, metastable states of Group III atoms and alkaline earth or alkaline earth-like atoms may possess relatively large tensor offsets, whose angles relative to the applied magnetic field can be adjusted to result in a situation where the scalar and tensor offsets balance and give a zero or near-zero differential optical offset between the first and second atomic states. The angle θ can be adjusted by selecting the polarization of the emitted light. For example, when the emitted light is linearly polarized, the total degree of polarization α can be written as the scalar component α scalar and the tensor component α tensor The sum of:

[0114] α=α scalar +(3cos 2 θ-1)α tensor

[0115] By appropriately choosing θ, the polarization rates 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, and the motions of the atoms can be decoupled.

[0116] The light source may be configured to direct light to one or more optical modulators (OMs) configured to generate a plurality of optical trapping sites. For example, the optical trapping unit may include an OM 214 configured to generate a plurality of optical trapping sites. Figure 3A The optical capture unit may be depicted as including one OM, but the optical 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 at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 OM. 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).

[0117] The OM can be optically coupled to one or more optical elements to generate a regular array of optical trapping sites. For example, the OM can be optically coupled to an optical element 219, such as Figure 3A The optical element may include a lens or a microscope objective configured to redirect light from the OM to form a regular rectangular grid of optical trapping sites.

[0118] For example, Figure 3A As shown in , the OM can include an SLM, DMD or LCoS device. The SLM, DMD or LCoS device can be imaged onto the back focal plane of the microscope objective. This can allow the generation of arbitrary configurations of optical trapping sites in two or three dimensions.

[0119] Alternatively or in combination, the OM may include a first and a second AOD. The active regions of the first and second AODs may be imaged onto the back focal plane of the 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 make a copy of the light output of the first AOD. This may allow the generation of optical trapping sites in two or three dimensions.

[0120] Alternatively or in combination, the OM may include static optical elements, such as one or more microlens arrays or holographic optical elements. The static optical elements may be imaged onto the back focal plane of the microscope objective. This may allow the generation of arbitrary configurations of optical trapping sites in two or three dimensions.

[0121] The optical trapping unit may include one or more imaging units configured to obtain one or more images of the spatial configuration of the plurality of atoms trapped within the optical trapping site. For example, the optical trapping unit may include imaging unit 215. Figure 3A The optical capture 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 at most 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.

[0122] The optical trapping unit may include one or more spatial configuration artificial intelligence (AI) units configured to perform one or more AI operations to determine the spatial configuration of the plurality of atoms trapped within the optical trapping site based on the image obtained by the imaging unit. For example, the optical trapping unit may include the spatial configuration AI unit 216. Figure 3A 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more spatially configured AI units or at most approximately 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 spatially configured AI unit. The AI ​​operations may include any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0123] The optical trapping unit may include one or more atom rearrangement units configured to impart a changed spatial arrangement of the plurality of atoms trapped by the optical trapping site based on one or more images obtained by the imaging unit. For example, the optical trapping unit may include the atom rearrangement unit 217. Figure 3A The optical trapping unit is depicted as including a single atomic rearrangement unit, but the optical trapping unit may include any number of atomic rearrangement units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more atomic rearrangement units or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 atomic rearrangement unit.

[0124] The optical trapping unit may include one or more spatial arrangement artificial intelligence (AI) units configured to perform one or more AI operations to determine a changed spatial arrangement of the plurality of atoms trapped within the optical trapping site based on the image obtained by the imaging unit. For example, the optical trapping unit may include the spatial arrangement AI unit 218. Figure 3A The optical capture unit may include any number of spatially arranged AI units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more spatially arranged AI units or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 spatially arranged AI unit. The AI ​​operations may include any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0125] In some cases, the spatial configuration AI unit and the spatial arrangement AI unit can be integrated into an integrated AI unit. The optical capture unit can 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 at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 integrated AI unit.

[0126] The atom rearrangement unit can be configured to change the spatial arrangement so as to obtain an increase in the filling factor of the plurality of optical trapping sites. The filling factor can be defined as the ratio of the number of optical trapping sites occupied by one or more atoms to the total number of optical trapping sites available in the optical trapping unit or in the region of the optical trapping unit. For example, the initial loading of atoms within the optical trapping sites can cause a filling factor of less than 100%, 90%, 80%, 70%, 60%, 50% or less, so that the atoms occupy less than 100%, 90%, 70%, 60%, 50% or less of the available optical trapping sites, respectively. It may be desirable to rearrange the atoms to achieve a filling factor of at least about 50%, 60%, 70%, 80%, 90% or 100%. By analyzing the imaging information obtained by the imaging unit, the atomic rearrangement unit can obtain a filling factor of at least about 50%, 60%, 70%, 80%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, 99.1%, 99.2%, 99.3%, 99.4%, 99.5%, 99.6%, 99.7%, 99.8%, 99.9%, 99.91%, 99.92%, 99.93%, 99.94%, 99.95%, 99.96%, 99.97%, 99.98%, 99.99% or more. The atomic rearrangement unit can obtain a filling factor of at most about 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50% or less. The atomic rearrangement unit can obtain a filling factor within the range defined by any two of the aforementioned values.

[0127] For example, Figure 3C An example of an optical trapping cell partially filled with atoms is shown. Figure 3C As depicted in , the initial loading of atoms within the optical trapping sites can result in a filling factor of 44.4% (4 atoms filling 9 available optical trapping sites). Figure 3C Much higher filling factors can be achieved by moving atoms (not shown) to unoccupied optical trapping sites or by moving atoms from the atom reservoirs described herein, such as Figure 3D as shown in .

[0128] Figure 3D An example of an optical trapping cell completely filled with atoms is shown. Figure 3DAs depicted in FIG. 5 , 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 unoccupied optical trapping sites. The fifth, sixth, seventh, eighth, and ninth atoms can be moved from different regions of the optical trapping unit ( Figure 3C The optical trapping sites are arranged in a manner that allows the atoms to be moved (not shown) or by moving atoms from the atom reservoir described herein. Thus, after rearrangement of the atoms within the optical trapping sites, the filling factor can be significantly improved. For example, a filling factor of up to 100% can be obtained (such that 9 atoms fill 9 available optical trapping sites, e.g. Figure 3D ).

[0129] Electromagnetic delivery unit

[0130] Figure 4 An example of an electromagnetic delivery unit 220 is shown. The electromagnetic delivery unit can be configured to apply electromagnetic energy to one or more atoms in the plurality of atoms, as described herein. The electromagnetic delivery unit can include one or more light sources, such as any light source described herein. The electromagnetic energy can include light energy. The light energy can include any repetition rate, pulse energy, average power, wavelength, or bandwidth described herein.

[0131] 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 transfer time (IMPATT) diodes, or microwave masers. The electromagnetic energy may include microwave energy or RF energy. The RF energy may include 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 , 3m, 4m, 5m, 6m, 7m, 8m, 9m, 10m, 20m, 30m, 40m, 50m, 60m, 70m, 80m, 90m, 100m, 200m, 300m, 400m, 500m, 600m, 700m, 800m, 900m, 1 kilometer (km), 2km, 3km, 4km, 5km, 6km, 7km, 8km, 9km, 10km or one or more wavelengths larger. The RF energy may include up to about 10 km, 9 km, 8 km, 7 km, 6 km, 5 km, 4 km, 3 km, 2 km, 1 km, 900 m, 800 m, 700 m, 600 m, 500 m, 400 m, 300 m, 200 m, 100 m, 90 m, 80 m, 70 m, 60 m, 50 m, 40 m, 30 m, 20 m, 10 m, 9 m, 8 m, 7 m, 6 m, 5 m, 4 m, 30 m, The RF energy may include one or more wavelengths within a range defined by any two of the foregoing values.

[0132] The RF energy may include 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 The average power of the power supply may be 100W, 200W, 300W, 400W, 500W, 600W, 700W, 800W, 900W, 100W, 200W, 300W, 400W, 500W, 600W, 700W, 800W, 900W, 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. The RF energy may include up to about 1,000 W, 900 W, 800 W, 700 W, 600 W, 500 W, 400 W, 300 W, 200 W, 100 W, 90 W, 80 W, 70 W, 60 W, 50 W, 40 W, 30 W, 20 W, 10 W, 9 W, 8 W, 7 W, 6 W, 5 W, 4 W, 3 W, 2 W, 1 W, 900 mW, 800 mW, 700 mW, 600 mW, 500 mW, 400 mW, 300 mW, 200 mW, 100 mW, 90 mW, 80 mW, 70 mW, 60 mW, 50 mW, The RF energy may include an average power of 0 mW, 40 mW, 30 mW, 20 mW, 10 mW, 9 mW, 8 mW, 7 mW, 6 mW, 5 mW, 4 mW, 3 mW, 2 mW, 1 mW, 900 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 within a range defined by any two of the foregoing values.

[0133] The electromagnetic delivery unit may include one or more light sources, such as any of the light sources described herein. For example, the electromagnetic delivery unit may include light source 221. Figure 4The electromagnetic delivery unit is depicted as including a single light source, but the electromagnetic delivery unit may include any number of light sources, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more light sources or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 light source.

[0134] The light source may be configured to direct light to one or more OMs that are configured to selectively apply electromagnetic energy to one or more atoms in the plurality of atoms. For example, the electromagnetic delivery unit may include OM 222. Figure 4 , but 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 at most 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 include one or more liquid crystal devices, such as one or more LCoS devices.

[0135] 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 AI unit 223. Figure 4 The EM 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 at most 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.

[0136] 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 the qubits described herein. The electromagnetic delivery unit may be configured to apply one or more double qubit operations (such as one or more double qubit gate operations) to the double qubit units described herein. Each single qubit or double qubit operation may include a duration of at least about 10 nanoseconds (ns), 20ns, 30ns, 40ns, 50ns, 60ns, 70ns, 80ns, 90ns, 100ns, 200ns, 300ns, 400ns, 500ns, 600ns, 700ns, 800ns, 900ns, 1 microsecond (μs), 2μs, 3μs, 4μs, 5μs, 6μs, 7μs, 8μs, 9μs, 10μs, 20μs, 30μs, 40μs, 50μs, 60μs, 70μs, 80μs, 90μs, 100μs, or more. Each single-qubit or two-qubit operation may include a duration of at most 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 duration within a range defined by any two of the foregoing values. Single qubit or two qubit operations may be applied at repetition rates 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 rates of 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 lower.Single-qubit or two-qubit operations can be applied with a repetition frequency within a range defined by any two of the aforementioned values.

[0137] The electromagnetic delivery unit can 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. The Raman transitions can be from the first qubit state described herein to the second qubit state described herein. 3 P0 or 3 The P1 line can be detuned. For example, the Raman transition can 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.

[0138] One or more spatial light modulators (SLM) or acousto-optic deflectors (AOD) can be used to induce Raman transitions on individually selected atoms to impart a deflection angle and / or frequency shift to the light beam based on an applied radio frequency (RF) signal. The SLM or AOD can be combined with an optical adjustment system that images the SLM or AOD active area onto the rear focal plane of a microscope objective. The microscope objective can perform a spatial Fourier transform on the light field at the position of the SLM or AOD. In this way, an angle (which can be proportional to the RF frequency) can be converted into a position. For example, applying a radio frequency comb to an AOD can generate a linear array of light spots on the focal plane of the objective, each light spot having a limited range determined by the characteristics of the optical adjustment system (such as the point spread function of the optical adjustment system).

[0139] To perform a Raman transition on a single atom with a single SLM or AOD, a pair of frequencies can be applied simultaneously to the SLM or AOD. The two frequencies of the pair can have a frequency difference that matches or nearly matches the splitting energy between the first and second qubit states. For example, the frequency difference can differ from the splitting energy by at most approximately 1 MHz, 900kHz, 800kHz, 700kHz, 600kHz, 500kHz, 400kHz, 300kHz, 200kHz, 100kHz, 90kHz, 80kHz, 70kHz, 60kHz, 50kHz, 40kHz, 30kHz, 20kHz, 10kHz, 9kHz, 8kHz, 7kHz, 6kHz, 5kHz, 4kHz, 3kHz, 2kHz, 1kHz, 900Hz, 800Hz, 700Hz, 600Hz, 500Hz, 400Hz, 300Hz, 200Hz, 100Hz, 90Hz, 80Hz, 70Hz, 60Hz, 50Hz, 40Hz, 30Hz, 20Hz, 10Hz, 9Hz, 8Hz, 7Hz, 6Hz, 5Hz, 4Hz, 3Hz, 2Hz, 1Hz or less. The frequency difference may differ from the splitting energy by at least about 1 Hz, 2 Hz, 3 Hz, 4 Hz, 5 Hz, 6 Hz, 7 Hz, 8 Hz, 9 Hz, 10 Hz, 20 Hz, 30 Hz, 40 Hz, 50 Hz, 60 Hz, 70 Hz, 80 Hz, 90 Hz, 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 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 splitting energy by about 0 Hz. The frequency difference may differ from the splitting energy by a value within a range defined by any two of the foregoing values. The optical system may be configured such that the position interval corresponding to the frequency difference is not resolved and such that both frequencies of light interact with a single atom.

[0140] Integrated optical trapping unit and electromagnetic delivery unit

[0141] The optical trapping unit and the electromagnetic delivery unit described herein can be integrated into a single optical system. A microscope objective can be used to deliver the electromagnetic radiation generated by the electromagnetic delivery unit described herein and to deliver light for trapped atoms generated by the optical trapping unit described herein. Alternatively or in combination, different objective lenses can be used to deliver the electromagnetic radiation generated by the electromagnetic delivery unit and to deliver light from trapped atoms generated by the optical trapping unit.

[0142] A single SLM or AOD can allow qubit operations (such as any single qubit or double qubit operations described herein) to be implemented on a linear array of atoms. Alternatively or in combination, two separate SLMs or AODs can be configured to process light with orthogonal polarizations respectively. Light with orthogonal polarizations can be overlapped before the microscope objective. In such a scheme, each photon used in the two-photon transition described herein can be delivered to the objective lens by a separate SLM or AOD, which can allow improved polarization control. By introducing the light from the first SLM or AOD via an optical repeater into a second SLM or AOD oriented substantially orthogonal to the first SLM or AOD, qubit operations can be performed on the two-dimensional arrangement of atoms. Alternatively or in combination, by using a one-dimensional array of SLMs or AODs, qubit operations can be performed on the two-dimensional arrangement of atoms.

[0143] The stability of the qubit gate fidelity can be improved by maintaining an overlap of light from the various light sources described herein, such as light sources associated with the optical capture unit or electromagnetic delivery unit described herein. This overlap can be maintained by an optical subsystem that measures the direction of light emitted by the various light sources, allowing closed-loop control of the light emission direction. The optical subsystem can include a pickup mirror located in front of the microscope objective. The pickup mirror can be configured to direct a small amount of light to a lens that can focus a collimated light beam and convert angular deviations into positional deviations. A position-sensitive optical detector such as a lateral effect position sensor or a quadrant photodiode can convert the positional deviation into an electronic signal, and information about the deviation can be fed into a compensating optical device such as an active mirror.

[0144] 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 light sources associated with the optical trapping unit or electromagnetic delivery unit described herein. This intensity control can be maintained by an optical subsystem that measures the intensity of light emitted by the various light sources, allowing closed-loop control of the intensity. Each light source can be coupled to an intensity actuator, such as an intensity servo control. The actuator can include an acousto-optic modulator (AOM) or an electro-optic modulator (EOM). The intensity can be measured using an optical detector, such as a photodiode or any other optical detector described herein. Information about the intensity can be integrated into a feedback loop to stabilize the intensity.

[0145] State preparation unit

[0146] Figure 5 An example of a state preparation unit 250 is shown. The state preparation unit can be configured to prepare a state of a plurality of atoms, as described herein. The state preparation unit can be coupled to an optical trapping unit and can direct atoms that have been prepared by the state preparation unit to the optical trapping unit. The state preparation unit can be configured to cool a plurality of atoms. The state preparation unit can be configured to cool a plurality of atoms before trapping the plurality of atoms at a plurality of optical trapping sites.

[0147] The state preparation unit may include one or more Zeeman reducers. For example, the state preparation unit may include the Zeeman reducer 251. Figure 5 The state preparation unit is depicted as including a single Zeeman slowdown, but the state preparation unit can include any number of Zeeman slowdowns, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more Zeeman slowdowns or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 Zeeman slowdown. The Zeeman slowdown can 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 an atomic source, room temperature, liquid nitrogen temperature, or any other temperature) to a second velocity that is lower than the first velocity or velocity distribution.

[0148] The first velocity or velocity profile may be associated with a temperature of at least about 50 Kelvin (K), 60 K, 70 K, 80 K, 90 K, 100 K, 200 K, 300 K, 400 K, 500 K, 600 K, 700 K, 800 K, 900 K, 1,000 K, or more. The first velocity or velocity profile may be associated with a temperature of at most about 1,000 K, 900 K, 800 K, 700 K, 600 K, 500 K, 400 K, 300 K, 200 K, 100 K, 90 K, 80 K, 70 K, 60 K, 50 K, or less. The first velocity or velocity profile may be associated with a temperature within a range defined by any two of the foregoing values. The second speed can be at least about 1 meter per second (m / s), 2m / s, 3m / s, 4m / s, 5m / s, 6m / s, 7m / s, 8m / s, 9m / s, 10m / s or greater. The second speed can be at most about 10m / s, 9m / s, 8m / s, 7m / s, 6m / s, 5m / s, 4m / s, 3m / s, 2m / s, 1m / s or lower. The second speed can be within the range defined by any two of the aforementioned values. The Zeeman reducer can include a one-dimensional Zeeman reducer.

[0149] The state preparation unit may include a first magneto-optical trap (MOT) 252. The first MOT may be configured to cool the atoms to a first temperature. The first temperature may be at most about 10 millikelvin (mK), 9mK, 8mK, 7mK, 6mK, 5mK, 4mK, 3mK, 2mK, 1mK, 0.9mK, 0.8mK, 0.7mK, 0.6mK, 0.5mK, 0.4mK, 0.3mK, 0.2mK, 0.1mK or less. The first temperature may be at least about 0.1mK, 0.2mK, 0.3mK, 0.4mK, 0.5mK, 0.6mK, 0.7mK, 0.8mK, 0.9mK, 1mK, 2mK, 3mK, 4mK, 5mK, 6mK, 7mK, 8mK, 9mK, 10mK or more. 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.

[0150] The first MOT may include one or more light sources configured to emit light (such as any of the light sources described herein). The light may include at least about 400nm, 410nm, 420nm, 430nm, 440nm, 450nm, 460nm, 470nm, 480nm, 490nm, 500nm, 510nm, 520nm, 530nm, 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, 880nm, 890nm, 900nm, 910nm, 920nm, 930nm, 940nm, 950nm, 960nm, 970nm, 980nm, 990nm, 1,000nm or one or more wavelengths greater. The light may include up to about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm 400nm, 430nm, 420nm, 410nm, 400nm or less. The light may include one or more wavelengths within the range defined by any two of the aforementioned values.For example, the light may include one or more wavelengths within a range of 400nm to 1,000nm, 500nm to 1,000nm, 600nm to 1,000nm, 650nm to 1,000nm, 400nm to 900nm, 400nm to 800nm, 400nm to 700nm, 400nm to 600nm, 400nm to 500nm, 500nm to 700nm, or 650nm to 700nm.

[0151] 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 microkelvins (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 nanokelvins (nK), 800 nK, 700 nK, 600 nK, 500 nK, 400 nK, 300 nK, 200 nK, 100 nK, or less. The second temperature may be at least about 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 more. The second temperature may be within a range defined by any two of the foregoing values. The second MOT may include 1D, 2D or 3DMOT.

[0152] The second MOT may include one or more light sources configured to emit light (such as any of the light sources described herein). The light may include at least about 400nm, 410nm, 420nm, 430nm, 440nm, 450nm, 460nm, 470nm, 480nm, 490nm, 500nm, 510nm, 520nm, 530nm, 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, 880nm, 890nm, 900nm, 910nm, 920nm, 930nm, 940nm, 950nm, 960nm, 970nm, 980nm, 990nm, 1,000nm or one or more wavelengths greater. The light may include up to about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm 400nm, 430nm, 420nm, 410nm, 400nm or less. The light may include one or more wavelengths within the range defined by any two of the aforementioned values.For example, the light may include one or more wavelengths within a range of 400nm to 1,000nm, 500nm to 1,000nm, 600nm to 1,000nm, 650nm to 1,000nm, 400nm to 900nm, 400nm to 800nm, 400nm to 700nm, 400nm to 600nm, 400nm to 500nm, 500nm to 700nm, or 650nm to 700nm.

[0153] Although in Figure 5 2, 3, 4, 5, 6, 7, 8, 9, 10, or more MOTs or at most approximately 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 MOT.

[0154] The state preparation unit may include one or more sideband cooling units or Sisyphus cooling units (such as the sideband cooling units described in https: / / arxiv.org / abs / 1810.06626 or the Sisyphus cooling units described in https: / / arxiv.org / abs / 1811.06014, each of which is incorporated herein by reference in its entirety for all purposes). For example, the state preparation unit may include the sideband cooling unit or Sisyphus cooling unit 254. Although in Figure 5The state preparation unit is depicted as including a single sideband cooling unit or Sisyphus cooling unit, but the state preparation unit may include any number of sideband cooling units or Sisyphus cooling units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more sideband cooling units or Sisyphus cooling units, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 sideband cooling unit or Sisyphus cooling unit. The sideband cooling unit or Sisyphus cooling unit can be configured to use sideband cooling to cool the atoms from the second temperature to a third temperature lower than the second temperature. The third temperature may be at most approximately 10 μK, 9 μK, 8 μK, 7 μK, 6 μK, 5 μK, 4 μK, 3 μK, 2 μK, 1 μK, 900 nK, 800 nK, 700 nK, 600 nK, 500 nK, 400 nK, 300 nK, 200 nK, 100 nK, 90 nK, 80 nK, 70 nK, 60 nK, 50 nK, 40 nK, 30 nK, 20 nK, 10 nK or less. The third temperature may be at most about 10nK, 20nK, 30nK, 40nK, 50nK, 60nK, 70nK, 80nK, 90nK, 100nK, 200nK, 300nK, 400nK, 500nK, 600nK, 700nK, 800nK, 900nK, 1μK, 2μK, 3μK, 4μK, 5μK, 6μK, 7μK, 8μK, 9μK, 10μK or more. The third temperature may be within a range defined by any two of the foregoing values.

[0155] The sideband cooling unit or Sisyphus cooling unit may include one or more light sources (such as any light source described herein) configured to emit light. The light may include at least about 400nm, 410nm, 420nm, 430nm, 440nm, 450nm, 460nm, 470nm, 480nm, 490nm, 500nm, 510nm, 520nm, 530nm, 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, 880nm, 890nm, 900nm, 910nm, 920nm, 930nm, 940nm, 950nm, 960nm, 970nm, 980nm, 990nm, 1,000nm or one or more wavelengths greater. The light may include up to about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm 400nm, 430nm, 420nm, 410nm, 400nm or less. The light may include one or more wavelengths within the range defined by any two of the aforementioned values.For example, the light may include one or more wavelengths within a range of 400nm to 1,000nm, 500nm to 1,000nm, 600nm to 1,000nm, 650nm to 1,000nm, 400nm to 900nm, 400nm to 800nm, 400nm to 700nm, 400nm to 600nm, 400nm to 500nm, 500nm to 700nm, or 650nm to 700nm.

[0156] The state preparation unit may include one or more optical pumping units. For example, the state preparation unit may include the optical pumping unit 255. Figure 5The state preparation unit is depicted as including a single optical pumping unit, but the state preparation unit 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 at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 optical pumping unit. 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 base 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 configured to emit light (such as any light source described herein). The light may include at least about 400nm, 410nm, 420nm, 430nm, 440nm, 450nm, 460nm, 470nm, 480nm, 490nm, 500nm, 510nm, 520nm, 530nm, 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, 880nm, 890nm, 900nm, 910nm, 920nm, 930nm, 940nm, 950nm, 960nm, 970nm, 980nm, 990nm, 1,000nm or one or more wavelengths greater.The light may include up to about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm 400nm, 430nm, 420nm, 410nm, 400nm or less. The light may include one or more wavelengths within the range defined by any two of the aforementioned values. For example, the light may include one or more wavelengths within a range of 400nm to 1,000nm, 500nm to 1,000nm, 600nm to 1,000nm, 650nm to 1,000nm, 400nm to 900nm, 400nm to 800nm, 400nm to 700nm, 400nm to 600nm, 400nm to 500nm, 500nm to 700nm, or 650nm to 700nm.

[0157] The state preparation unit may include one or more coherent drive units. For example, the state preparation unit may include the coherent drive unit 256. Figure 5In the state preparation unit, it is depicted as including one coherent drive unit, but the state preparation unit 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 at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 coherent drive units. The coherent drive unit can be configured to coherently drive atoms from a non-equilibrium state to the first or second atomic state described herein. Therefore, atoms can be optically pumped to an atomic state that is convenient for access (for example, based on the availability of a light source emitting a specific wavelength or based on other factors), and then coherently driven to the atomic state described herein that is useful for performing quantum computing. The coherent drive unit can be configured to induce a single photon transition between a non-equilibrium state and a first or second atomic state. The coherent drive unit can be configured to induce a two-photon transition between a non-equilibrium state and a first or second atomic state. The two-photon transition can be induced using light from two light sources described herein (such as two lasers described herein).

[0158] The coherent drive unit may include one or more light sources configured to emit light (such as any of the light sources described herein). The light may include at least about 400nm, 410nm, 420nm, 430nm, 440nm, 450nm, 460nm, 470nm, 480nm, 490nm, 500nm, 510nm, 520nm, 530nm, 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, 880nm, 890nm, 900nm, 910nm, 920nm, 930nm, 940nm, 950nm, 960nm, 970nm, 980nm, 990nm, 1,000nm or one or more wavelengths greater. The light may include up to about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm 400nm, 430nm, 420nm, 410nm, 400nm or less. The light may include one or more wavelengths within the range defined by any two of the aforementioned values.For example, the light may include one or more wavelengths within a range of 400nm to 1,000nm, 500nm to 1,000nm, 600nm to 1,000nm, 650nm to 1,000nm, 400nm to 900nm, 400nm to 800nm, 400nm to 700nm, 400nm to 600nm, 400nm to 500nm, 500nm to 700nm, or 650nm to 700nm.

[0159] The coherent drive unit may be configured to induce an RF transition between a non-equilibrium state and a first or second atomic state. The coherent drive unit may include one or more electromagnetic radiation sources configured to emit electromagnetic radiation, the electromagnetic radiation being configured to induce an RF transition. For example, the coherent drive unit may include one or more RF sources configured to emit RF radiation (such as any RF source described herein). 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 more. The RF radiation may include one or more wavelengths of at most about 10 m, 9 m, 8 m, 7 m, 6 m, 5 m, 4 m, 3 m, 2 m, 1 m, 90 cm, 80 cm, 70 cm, 60 cm, 50 cm, 40 cm, 30 cm, 20 cm, 10 cm or less. The RF radiation may include one or more wavelengths within a range defined by any two of the aforementioned values.Alternatively or in combination, the coherent drive unit may include one or more light sources (such as any light source described herein) configured to induce a two-photon transition corresponding to the RF transition.

[0160] Controller

[0161] The optical trapping unit, the electromagnetic delivery unit, the entanglement unit, the readout optical unit, the vacuum unit, the imaging unit, the spatial configuration AI unit, the spatial arrangement AI unit, the atom rearrangement unit, the state preparation unit, the sideband cooling unit, the optical pumping unit, the coherence drive unit, the electromagnetic energy AI unit, the atom reservoir, the atom movement unit or the Rydberg excitation unit may include one or more circuits or controllers (such as one or more electronic circuits or controllers) that are connected (for example, via one or more electronic connections) to the optical trapping unit, the electromagnetic delivery unit, the entanglement unit, the readout optical unit, the vacuum unit, the imaging unit, the spatial configuration AI unit, the spatial arrangement AI unit, the atom rearrangement unit, the state preparation unit, the sideband cooling unit, the optical pumping unit, the coherence drive unit, the electromagnetic energy AI unit, the atom reservoir, the atom movement unit or the Rydberg excitation unit. The circuit or controller can be configured to control an optical trapping 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 atom rearrangement unit, a state preparation unit, a sideband cooling unit, an optical pumping unit, a coherent drive unit, an electromagnetic energy AI unit, an atom reservoir, an atom movement unit or a Rydberg excitation unit.

[0162] Non-classical computers

[0163] In one aspect, the present disclosure provides a non-classical computer comprising: a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site in a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprises at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state; one or more electromagnetic delivery units configured to apply electromagnetic energy to one or more qubits in the plurality of qubits, thereby imparting a non-classical operation to the one or more qubits, the non-classical operation comprising 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 in the plurality of qubits; and one or more readout optical units configured to perform one or more measurements on the one or more qubits, thereby obtaining a non-classical computation.

[0164] In one aspect, the present disclosure provides a non-classical computer comprising: a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites.

[0165] Methods for performing nonclassical computations

[0166] In one aspect, the present disclosure provides a method for performing non-classical computing, comprising: (a) generating a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites being configured to trap a plurality of atoms, the plurality of atoms comprising greater than 60 atoms; (b) applying electromagnetic energy to one or more atoms of the plurality of atoms, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state; (c) quantum mechanically entangled 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 on the one or more superposition states to obtain non-classical computing.

[0167] Figure 6 A flow chart of an example of a first method 600 for performing non-classical computation is shown.

[0168] In a first operation 610, 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 greater than 60 atoms. The optical trapping sites may include any optical trapping sites described herein. The atoms may include any atoms described herein.

[0169] In a second operation 620, 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 superposition states 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.

[0170] In a third operation 630, method 600 may include quantum mechanically entangled at least a subset of the one or more atoms in the one or more superposition states with at least one other atom in the plurality of atoms. The atoms may be quantum mechanically entangled in any manner described herein (e.g., as described herein with respect to Figure 2 described).

[0171] In a fourth operation 640, method 600 may include performing one or more optical measurements on the one or more superposition states to obtain non-classical computations. The optical measurements may include any optical measurements described herein.

[0172] In one aspect, the present disclosure provides a method for performing non-classical computing, comprising: (a) providing a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site in a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprises at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state; (b) applying electromagnetic energy to one or more qubits in the plurality of qubits, thereby imparting a non-classical operation to the one or more qubits, the non-classical operation comprising a superposition between at least the first qubit state and the second qubit state; (c) quantum mechanically entangled at least a subset of the plurality of qubits in superposition with at least another qubit in the plurality of qubits; and (d) performing one or more optical measurements on the one or more qubits, thereby obtaining the classical computing.

[0173] Figure 7 A flow chart of an example of a second method 700 for performing non-classical computation is shown.

[0174] In a first operation 710, method 700 may include providing a plurality of qubits including greater than 60 atoms, each atom trapped within an optical trapping site in a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits include at least a first qubit state and a second qubit state, wherein the first qubit state includes a first atomic state and the second qubit state includes a second atomic state. The optical trapping site may include any optical trapping site described herein. The qubit may include any qubit described herein. The atom may include any atom 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.

[0175] In a second operation 720, method 700 may include applying electromagnetic energy to one or more qubits in the plurality of qubits, thereby imparting a non-classical operation to the one or more qubits, the non-classical operation comprising a superposition between at least a first qubit state and a second qubit state. The electromagnetic energy may include any electromagnetic energy described herein.

[0176] In a third operation 730, method 700 may include quantum mechanically entangled at least a subset of the plurality of qubits in superposition with at least one other qubit in the plurality of qubits. The qubits may be quantum mechanically entangled in any manner described herein (e.g., as described herein with respect to Figure 2 described).

[0177] In a fourth operation 740, method 700 may include performing one or more optical measurements on one or more qubits to obtain a non-classical computation. The optical measurements may include any optical measurements described herein.

[0178] In one aspect, the present disclosure provides a method for performing non-classical computing, comprising: (a) providing a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site in a plurality of spatially distinct optical trapping sites, and (b) performing the non-classical computing using at least a subset of the plurality of qubits.

[0179] Figure 8 A flow chart of an example of a third method 800 for performing non-classical computation is shown.

[0180] In a first operation 810, method 800 may include providing a plurality of qubits including greater than 60 atoms, each atom trapped within an optical trapping site in a plurality of spatially distinct optical trapping sites. The qubit may include any qubit described herein. The atom may include any atom described herein. The optical trapping site may include any optical trapping site described herein.

[0181] In a second operation 820, method 800 may include performing a non-classical computation using at least a subset of the plurality of qubits.

[0182] Computer Systems

[0183] Figure 1 A computer system 101 is shown that is programmed or otherwise configured to operate any method or system described herein (such as a system or method for performing non-classical computing described herein). Computer system 101 can accommodate various aspects of the present disclosure. Computer system 101 can be a user's electronic device or a computer system located remotely relative to the electronic device. The electronic device can be a mobile electronic device.

[0184] The computer system 101 includes a central processing unit (CPU, also referred to herein as a "processor" and "computer processor") 105, which can be a single-core or multi-core processor, or multiple processors for parallel processing. The computer system 101 also includes a memory or memory location 110 (e.g., random access memory, read-only memory, flash memory), an electronic storage unit 115 (e.g., a hard disk), a communication interface 120 (e.g., a network adapter) for communicating with one or more other systems, and peripherals 125, such as cache, other memory, data storage, and / or an electronic display adapter. The memory 110, storage unit 115, interface 120, and peripherals 125 communicate with the CPU 105 via a communication bus (solid line) such as a motherboard. The storage unit 115 can be a data storage unit (or data warehouse) for storing data. The computer system 101 can be operably coupled to a computer network ("network") 130 with the help of the communication interface 120. The network 130 can be the Internet, an intranet and / or an extranet, or an intranet and / or an extranet in communication with the Internet. In some cases, network 130 is a telecommunications and / or data network. Network 130 may include one or more computer servers that may implement distributed computing, such as cloud computing. In some cases, with the help of computer system 101, network 130 may implement a peer-to-peer network that may enable devices coupled to computer system 101 to act as clients or servers.

[0185] The 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 the memory 110. The instructions may be directed to the CPU 105, which may then program or otherwise configure the CPU 105 to implement the methods of the present disclosure. Examples of operations performed by the CPU 105 may include fetching, decoding, executing, and writing back.

[0186] CPU 105 may be part of a circuit, such as an integrated circuit. One or more other components of system 101 may be included in the circuit. In some cases, the circuit is an application specific integrated circuit (ASIC).

[0187] Storage unit 115 may store files, such as drivers, libraries, and saved programs. Storage unit 115 may store user data, such as user preferences and user programs. In some cases, computer system 101 may include one or more additional data storage units located external to computer system 101, such as located on a remote server that communicates with computer system 101 via an intranet or the Internet.

[0188] 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 personal computers (e.g., portable PCs), tablet or slate PCs (e.g., iPad, Galaxy Tab), phones, smartphones (e.g. iPhone, Android-enabled devices, ) or a personal digital assistant. A user can access the computer system 101 via the network 130.

[0189] The methods as described herein may be implemented by machine (e.g., computer processor) executable code stored on an electronic storage location (such as, for example, memory 110 or electronic storage unit 115) of computer system 101. Machine executable or machine readable code may be provided in the form of software. During use, the code may be executed by processor 105. In some cases, the code may be retrieved from storage unit 115 and stored in memory 110 for ready access by processor 105. In some cases, electronic storage unit 115 may be excluded and machine executable instructions are stored on memory 110.

[0190] The code may be precompiled and configured for use with a machine having a processor suitable for executing the code, or may be compiled during runtime. The code may be supplied in a programming language, which may be selected so that the code can be executed in a precompiled or compiled manner.

[0191] Various aspects of the systems and methods provided herein, such as computer system 101, can be embodied in programming. Various aspects of the technology can be considered as "products" or "articles", which are usually present in or embodied in a machine-readable medium in the form of machine (or processor) executable code and / or associated data. Machine executable code can be stored on an electronic storage unit, such as a memory (e.g., read-only memory, random access memory, flash memory) or a hard disk. "Storage" type media can include any or all tangible memories or related modules of computers, processors, etc., such as various semiconductor memories, tape drives, disk drives, etc., which can provide non-temporary storage at any time for software programming. All or part of the software can sometimes communicate through the Internet or various other telecommunications networks. For example, such communication can enable software to be loaded from one computer or processor to another computer or processor, such as from a management server or host computer to a computer platform of an application server. Therefore, another type of medium that can carry software elements includes light, electricity and electromagnetic waves, such as across physical interfaces between local devices, through wired and optical landline networks, and through various air links. Physical elements that carry such waves, such as wired or wireless links, optical links, etc., may also be considered to be the medium that carries the software. As used herein, unless restricted to non-transitory, tangible "storage" media, terms such as computer or machine "readable media" refer to any medium that participates in providing instructions to a processor for execution.

[0192] Thus, machine-readable media such as computer executable code may take a variety of forms, including but not limited to tangible storage media, carrier media, or physical transmission media. Non-volatile storage media include, for example, optical or magnetic disks, such as any storage device in (one or more) any computer, etc., such as may be used to implement the databases shown in the figures, etc. Volatile storage media include dynamic memory, such as the main memory of such a computer platform. Tangible transmission media include coaxial cables; copper wire and optical fiber, including the wires that make up the bus within a computer system. Carrier transmission media may take the form of electrical 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: a floppy disk, a flexible disk, a hard disk, a magnetic tape, any other magnetic medium, a CD-ROM, a DVD or DVD-ROM, any other optical medium, a punched card tape, any other physical storage medium with a pattern of holes, a RAM, a ROM, a PROM and an EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wave that transmits data or instructions, a cable or link that transmits such a carrier wave, 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 transmitting one or more sequences of one or more instructions to a processor for execution.

[0193] Computer system 101 may include or be in communication with electronic display 135, which includes user interface (UI) 140. Examples of UI include, but are not limited to, graphical user interfaces (GUIs) and web-based user interfaces.

[0194] The methods and systems of the present disclosure may be implemented by one or more algorithms. The algorithms may be implemented by software when executed by the central processing unit 105. The algorithms may, for example, implement methods for performing the non-classical computations described herein.

[0195] Example

[0196] In the following example, ten nuclear spin energy levels of strontium-87 (I=9 / 2) are modeled to demonstrate a 2-level system (i.e., a qubit). In order to achieve spectral isolation of qubit transitions, a Stark shift scheme is employed, which shifts unwanted transitions away from the qubit frequency. The isolation scheme can improve effective isolation with respect to achievable Rabi frequencies, can reduce the impact on the actual qubit state via shifts or residual scattering, can not require perfect polarization control, can be accessed with reasonable amounts of optical power, and so on. 1 S0 to 3 The properties of the P1 resonance can be characterized.

[0197] exist Fig. 10A In this paper, a toy model is used to demonstrate the shift of three related nuclear spin states: m F = 9 / 2 and 7 / 2 energy levels, which makes the qubit subspace and leakage energy levels 5 / 2. Here, the behavior of a single circularly polarized global AC Stark beam addressing an atomic array in a 700 Gauss magnetic field is simulated. In addition, a 100:1 polarization purity is assumed as well as the expected circular polarization. 1 S0 to 3 Each time the P1 resonance is detuned, each nuclear spin energy level experiences a shift. To further clarify, the qubit frequency (m F =9 / 2 and m F =7 / 2 modified energy) and leakage transition frequency (m F =7 / 2 and m F =5 / 2 The difference between the modified states) are plotted.

[0198] Fig. 10B It is shown that the Stark shift significantly shifts the leakage transition while having minimal effect on the qubit frequency. This is probably due to 3 The P1 resonance is achieved due to the narrow linewidth of the energy level splitting in high magnetic fields. Although the frequency is plotted as a signed quantity, subtleties associated with the quantization axes and light delivery make the absolute value of this frequency relevant, and hence the signature of the Stark shift pushing the leakage state very close to the qubit frequency. At each detuning, the maximum available Rabi frequency achievable given frequency crowding can be defined. Using this two-photon Rabi frequency, the pi pulse time can be inferred and the number of scattering events that occur due to off-resonant interactions of the AC Stark beam can be viewed ( Fig. 10A ).

[0199] No distinction is made here between Raman and Rayleigh scattering, and therefore a worst-case scenario for AC Stark-induced scattering errors is assumed for each gate. To perform single-qubit gates, the same 3 The two beams are detuned by P1 resonance to coherently control the light to drive the two-photon transition. Due to the 7kHz linewidth of the transition, 3 The residual scattering of the P1 manifold state may be inherently low. Including the effects of the AC Stark offset beam, 3 The expansion of the P1 hyperfine magnetic sublevel can be exploited to separate the energy scale between an AC Stark beam detuned from the F = 11 / 2 manifold and multiphoton 1Q light detuned from the F = 7 / 2 manifold. A simple toy model involving two ground states and a few excited states is sufficient to gain insight into the scaling of power, spot size, and achievable Rabi rates. However, due to the numerous energy levels involved ( 1S0(F=9 / 2), 3 P1 (F = 7 / 2, 9 / 2, 11 / 2)) (including all their magnon energy levels), so it may be necessary to perform full-scale simulations including all relevant energy levels. To verify full operation, a numerical model was built that uses all 40 energy levels and multiple light fields to represent the desired and undesired polarizations. Using simple square wave pulses, it can be seen that transitions to other nuclear spin states can be suppressed with an AC Stark beam ( Fig.11A and Fig. 11B ).

[0200] Fig. 12A and Fig. 12B The captured light arrays generated by the SLM in a square array and an arbitrary array are shown. The holograms are generated by reflecting 813 nm light from a spatial light modulator (SLM) ( 1 S0→ 3 The active area of ​​the SLM is a 1920x1152 square array of pixels with sides of about 9 microns. Each pixel contains a volume of liquid crystal that imparts a phase shift to the incident light. This phase shift can be controlled by a 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 is positioned in such a way that a large collimated beam is incident and phase shifted; the light reflected from the SLM is then directed through the microscope objective. This configuration connects the plane of the SLM to the plane below the lens (where the atomic cloud is formed) via Fourier conjugation. The complex-valued in-plane electric field at the SLM is the Fourier transform of a similar field in the volume of the glass cell, in the plane below the microscope objective. The atoms experience a trapping potential proportional to the strength of the electric field, and therefore experience lateral confinement. Longitudinal confinement comes from structured light passing through the focus, whose position is also partially determined by (and therefore controlled by) the SLM.

[0201] Two thousand traps were created, each 500 microkelvin deep, to give a recoil energy more than 1,000 times greater than that imparted by a scattered photon, for imaging or other purposes. This means that the device should be well within the range where atoms can be measured hundreds of times without being lost due to heating, even without additional cooling. Cooled to their motional ground state, the positions of atoms are known to within 20 nanometers, which allows for significant separation in scale between the positions of atoms and the size of the laser beams used to drive single- and two-qubit gates, or the length scale of the Rydberg interaction. The laser beams driving the gate operations will have a spatial extent on the order of micrometers, and will therefore have intensities on the order of 10 -5 energy levels change; therefore, a fidelity of 0.9999 is expected to be easily achievable. In this way, the gate fidelity is less sensitive to the position of the atoms.

[0202] The present invention provides embodiments including but not limited to the following:

[0203] 1. A system for performing non-classical computing, comprising:

[0204] 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 comprising greater than 60 atoms;

[0205] 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;

[0206] one or more entanglement units configured to quantum mechanically entangle at least a subset of the one or more atoms in the superposition state with at least another atom of the plurality of atoms; and

[0207] One or more readout optical units configured to perform one or more measurements on the one or more superposition states to obtain the non-classical computation.

[0208] 2. The system of embodiment 1, wherein the non-classical computing comprises quantum computing.

[0209] 3. The system of embodiment 2, wherein the quantum computing comprises gate model quantum computing.

[0210] 4. The system of embodiment 1, wherein one or more atoms in the plurality of atoms comprises a qubit.

[0211] 5. The system of embodiment 1, wherein the first atomic state comprises a first single qubit state and the second atomic state comprises a second single qubit state.

[0212] 6. The system of embodiment 1, wherein the first atomic state or the second atomic state is elevated in energy relative to a base atomic state of the atom.

[0213] 7. The system of embodiment 1, wherein the first atomic state comprises a first hyperfine electronic state, and the second atomic state comprises a second hyperfine electronic state different from the first hyperfine electronic state.

[0214] 8. The system of embodiment 1, wherein the first atomic state comprises a first nuclear spin state, and the second atomic state comprises a second nuclear spin state different from the first nuclear spin state.

[0215] 9. The system of embodiment 1, wherein the plurality of atoms comprises at least 100 atoms.

[0216] 10. The system of embodiment 1, wherein the plurality of atoms comprises neutral atoms.

[0217] 11. The system of embodiment 1, wherein the plurality of atoms comprises rare earth atoms.

[0218] 12. The system of embodiment 1, wherein the plurality of atoms comprises alkali atoms.

[0219] 13. The system of embodiment 1, wherein the plurality of atoms comprises alkaline earth atoms.

[0220] 14. The system of embodiment 13, wherein the alkaline earth atoms comprise strontium atoms.

[0221] 15. The system of embodiment 14, wherein the strontium atoms comprise strontium-87 atoms.

[0222] 16. The system of embodiment 15, wherein the first and second atomic states include strontium-87 3 The first and second hyperfine states on the P1 manifold.

[0223] 17. The system of embodiment 15, wherein the first and second atomic states include strontium-87 3 The first and second hyperfine states on the P2 manifold.

[0224] 18. The system of embodiment 1, wherein the first and second atomic states comprise first and second hyperfine states on a multistate manifold.

[0225] 19. The system of embodiment 1, wherein the first and second atomic states comprise first and second hyperfine states on a triplet manifold.

[0226] 20. The system of embodiment 1, wherein the first and second atomic states comprise first and second nuclear spin states of a quadrupole nucleus.

[0227] 21. The system of embodiment 1, wherein the first and second atomic states comprise first and second nuclear spin states of a spin-9 / 2 nucleus.

[0228] 22. The system of embodiment 15, wherein the first and second atomic states comprise first and second nuclear spin states of strontium-87.

[0229] 23. A system according to embodiment 1, wherein the subset of the one or more atoms in the one or more superposition states and the other atom are quantum mechanically entangled with a coherence lifetime of at least 1 second.

[0230] 24. The system of embodiment 1, wherein the plurality of atoms comprises a temperature of at most 10 microKelvin (μK).

[0231] 25. The system of embodiment 1, further comprising one or more vacuum units configured to maintain the system at a pressure of at most 10 -6 Pascal (Pa) pressure.

[0232] 26. The system of embodiment 1, wherein each optical trapping site in the plurality of optical trapping sites is spatially separated from the other optical trapping sites by at least 200 nanometers (nm).

[0233] 27. The system of embodiment 1, wherein each optical trapping site of the plurality of optical trapping sites is configured to trap a single atom of the plurality of atoms.

[0234] 28. The system of embodiment 1, wherein the one or more optical trapping sites comprise one or more optical tweezers.

[0235] 29. The system of embodiment 1, wherein the one or more optical trapping sites comprise one or more optical lattice sites in one or more optical lattices.

[0236] 30. A system according to embodiment 29, wherein the one or more optical lattices include one or more members selected from the group consisting of: a one-dimensional (1D) optical lattice, a two-dimensional (2D) optical lattice, and a three-dimensional (3D) optical lattice.

[0237] 31. The system of embodiment 1, wherein the one or more optical trapping units comprise one or more spatial light modulators (SLMs) configured to generate the plurality of optical trapping sites.

[0238] 32. The system of embodiment 31, wherein the one or more SLMs comprise one or more digital micromirror devices (DMDs) or one or more liquid crystal on silicon (LCoS) devices.

[0239] 33. A system according to embodiment 1, wherein the one or more optical trapping units include one or more light sources configured to emit light tuned to one or more magic wavelengths corresponding to the plurality of atoms.

[0240] 34. A system according to embodiment 1, wherein the one or more optical trapping units include one or more imaging units, and the one or more imaging units are configured to obtain one or more images of the spatial configuration of the multiple atoms trapped within the optical trapping site.

[0241] 35. A system according to embodiment 34, wherein the one or more images include one or more members selected from the group consisting of fluorescence images, single-atom fluorescence images, absorption images, single-atom absorption images, phase contrast images, and single-atom phase contrast images.

[0242] 36. According to embodiment 34, the system also includes one or more spatial configuration artificial intelligence (AI) units, which are configured to perform one or more AI operations to determine the spatial configuration of the multiple atoms captured within the optical trapping site based on the one or more images.

[0243] 37. A system according to embodiment 36, wherein the one or more AI operations include one or more machine learning (ML) operations.

[0244] 38. A system according to embodiment 37, wherein the one or more AI operations include one or more reinforcement learning (RL) operations.

[0245] 39. A system according to embodiment 34, wherein the one or more optical trapping units include one or more atom rearrangement units, and the one or more atom rearrangement units are configured to impart a changed spatial arrangement of the multiple atoms trapped by the optical trapping site based on the one or more images.

[0246] 40. According to embodiment 39, the system also includes one or more spatial arrangement artificial intelligence (AI) units, which are configured to perform one or more AI operations to determine the changed spatial arrangement of the multiple atoms captured within the optical trapping site based on the one or more images.

[0247] 41. A system according to embodiment 40, wherein the one or more AI operations include one or more machine learning (ML) operations.

[0248] 42. A system according to embodiment 40, wherein the one or more AI operations include one or more reinforcement learning (RL) operations.

[0249] 43. The system of embodiment 39, wherein the one or more atom rearrangement units are configured to change the spatial arrangement to obtain an increase in a filling factor of the plurality of optical trapping sites.

[0250] 44. A system according to embodiment 43, wherein the fill factor comprises a value of at least 70%.

[0251] 45. The system according to embodiment 1 further includes one or more state preparation units, wherein the one or more state preparation units are configured to prepare the states of the plurality of atoms.

[0252] 46. ​​A system according to embodiment 45, wherein one or more of the state preparation units are configured to cool the plurality of atoms.

[0253] 47. A system according to embodiment 46, wherein the one or more state preparation units are configured to cool the plurality of atoms before trapping the plurality of atoms at the plurality of optical trapping sites.

[0254] 48. A system according to embodiment 47, wherein one or more of the state preparation units includes a Zeeman slowdown, which is configured to slow down the one or more atoms from a first speed or velocity distribution to a second speed lower than the first speed or velocity distribution.

[0255] 49. A system according to embodiment 48, wherein the Zeeman slowdown comprises a one-dimensional (1D) Zeeman slowdown.

[0256] 50. A system according to embodiment 48, wherein the second speed is at most 10 meters per second (m / s).

[0257] 51. A system according to embodiment 48, wherein one or more of the state preparation units also include a first magneto-optical trap (MOT), and the first magneto-optical trap (MOT) is configured to cool the one or more atoms to a first temperature.

[0258] 52. A system according to embodiment 51, wherein the first MOT comprises a three-dimensional (3D) MOT.

[0259] 53. A system according to embodiment 51, wherein the first MOT comprises one or more light sources configured to emit light having one or more wavelengths in the range from 400 nm to 500 nm.

[0260] 54. A system according to embodiment 51, wherein the first temperature is at most 10 millikelvin (mK).

[0261] 55. A system according to embodiment 54, wherein one or more of the state preparation units further include a second MOT, and the second MOT is configured to cool the one or more atoms from the first temperature to a second temperature lower than the first temperature.

[0262] 56. A system according to embodiment 55, wherein the second MOT includes one or more light sources configured to emit light having one or more wavelengths in the range from 400 nm to 1,000 nm.

[0263] 57. A system according to embodiment 55, wherein the second temperature is at most 100 microKelvin (μK).

[0264] 58. A system according to embodiment 55, wherein one or more of the state preparation units further includes a sideband cooling unit.

[0265] 59. A system according to embodiment 58, wherein the sideband cooling unit is configured to use sideband cooling to cool the one or more atoms from the second temperature to a third temperature lower than the second temperature.

[0266] 60. A system according to embodiment 58, wherein the sideband cooling unit includes one or more light sources, and the one or more light sources are configured to emit light having one or more wavelengths in the range from 400nm to 1,000nm.

[0267] 61. A system according to embodiment 58, wherein the third temperature is at most 10 microKelvin (μK).

[0268] 62. A system according to embodiment 45, wherein one or more of the state preparation units include an optical pumping unit, which is configured to emit light to optically pump one or more atoms of the plurality of atoms from an equilibrium atomic state to a non-equilibrium atomic state.

[0269] 63. The system of embodiment 62, wherein the optical pumping unit comprises one or more light sources configured to emit light at one or more wavelengths comprised in a range from 400 nanometers (nm) to 1,000 nm.

[0270] 64. A system according to embodiment 63, wherein the light comprises one or more wavelengths in the range from 650nm to 700nm.

[0271] 65. A system according to embodiment 62, wherein one or more of the state preparation units includes a coherent driving unit, which is configured to coherently drive the one or more atoms from the non-equilibrium atomic state to the first or second atomic state.

[0272] 66. A system according to embodiment 65, wherein the coherent drive unit is configured to induce a two-photon transition between the non-equilibrium state and the first or second atomic state.

[0273] 67. A system according to embodiment 66, wherein the coherent drive unit includes one or more light sources, and the one or more light sources are configured to emit light having one or more wavelengths in the range from 400nm to 1,000nm.

[0274] 68. A system according to embodiment 65, wherein the coherent drive unit is configured to induce a single-photon transition between the non-equilibrium state and the first or second atomic state.

[0275] 69. A system according to embodiment 68, wherein the coherent drive unit includes one or more light sources, and the one or more light sources are configured to emit light having one or more wavelengths in the range from 400nm to 1,000nm.

[0276] 70. The system of embodiment 65, wherein the coherent drive unit is configured to induce a radio frequency (RF) transition between the non-equilibrium state and the first or second atomic state.

[0277] 71. A system according to embodiment 70, wherein the coherent drive unit includes one or more electromagnetic radiation sources, and the one or more electromagnetic radiation sources are configured to emit electromagnetic radiation configured to induce the RF transition.

[0278] 72. A system according to embodiment 1, wherein the one or more electromagnetic delivery units include one or more spatial light modulators (SLMs), acousto-optic devices (AODs), or acousto-optic modulators (AOMs) configured to selectively apply the electromagnetic energy to one or more atoms among the plurality of atoms.

[0279] 73. The system of embodiment 72, wherein the one or more electromagnetic delivery units comprise one or more digital micromirror devices (DMDs) or one or more liquid crystal on silicon (LCoS) devices.

[0280] 74. The system according to embodiment 72 also includes one or more electromagnetic energy artificial intelligence (AI) units, which are configured to perform one or more AI operations to selectively apply the electromagnetic energy to the one or more atoms.

[0281] 75. A system according to embodiment 74, wherein the one or more AI operations include one or more machine learning (ML) operations.

[0282] 76. A system according to embodiment 74, wherein the one or more AI operations include one or more reinforcement learning (RL) operations.

[0283] 77. The system of embodiment 1, wherein the electromagnetic energy comprises light energy.

[0284] 78. The system of embodiment 1, wherein the electromagnetic energy comprises microwave energy.

[0285] 79. A system according to embodiment 1, wherein the electromagnetic energy includes radio frequency (RF) energy.

[0286] 80. A system according to embodiment 79, wherein the RF energy comprises one or more wavelengths of at least 30 millimeters (mm).

[0287] 81. A system according to embodiment 79, wherein the RF energy comprises an average power of no more than 10 watts (W).

[0288] 82. The system of embodiment 4, wherein the one or more electromagnetic delivery units are configured to perform one or more single-qubit gate operations on the one or more qubits.

[0289] 83. A system according to embodiment 1, wherein the one or more readout optical units include one or more optical detectors.

[0290] 84. The system of embodiment 83, wherein the one or more optical detectors comprise one or more cameras.

[0291] 85. The system of embodiment 83, wherein the one or more optical detectors comprise one or more fluorescence detectors.

[0292] 86. The system according to embodiment 1 further includes one or more atom reservoirs, which are configured to supply one or more replacement atoms to replace the one or more atoms at the one or more optical trapping sites when one or more atoms are lost from one or more optical trapping sites among the multiple optical trapping sites.

[0293] 87. The system according to embodiment 86 further includes one or more atom moving units, which are configured to move the one or more replacement atoms to the one or more optical trapping sites.

[0294] 88. A system according to embodiment 87, wherein the one or more atomic movement units include one or more electrically tunable lenses, acousto-optic deflectors (AODs) or spatial light modulators (SLMs).

[0295] 89. A system according to embodiment 1, wherein the subset of one or more atoms in the one or more superposition states and the other atom are quantum mechanically entangled through a magnetic dipole interaction, an induced magnetic dipole interaction, an electric dipole interaction, or an induced electric dipole interaction.

[0296] 90. A system according to embodiment 1, wherein the one or more entanglement units include one or more Rydberg excitation units, and the one or more Rydberg excitation units are configured to excite the subset of electrons of one or more atoms in the one or more superposition states to a Rydberg state or a superposition of a Rydberg state and a low-energy atomic state, thereby forming one or more Rydberg atoms or modified Rydberg atoms.

[0297] 91. A system according to embodiment 90, wherein the one or more Rydberg excitation units are configured to induce one or more quantum mechanical entanglements between the one or more Rydberg atoms or modified Rydberg atoms and the other atom, wherein the other atom is located at a distance of no more than 10 micrometers (μm) from the one or more Rydberg atoms or modified Rydberg atoms.

[0298] 92. A method according to embodiment 91, wherein the one or more Rydberg cells are configured to drive the one or more Rydberg atoms or modified Rydberg atoms to a lower energy atomic state, thereby forming one or more dual-qubit cells.

[0299] 93. A system according to embodiment 92, wherein the one or more electromagnetic delivery units are configured to implement one or more two-qubit gate operations on the one or more two-qubit units.

[0300] 94. A system according to embodiment 91, wherein the one or more Rydberg excitation units include one or more light sources, and the one or more light sources are configured to emit light having one or more ultraviolet (UV) wavelengths.

[0301] 95. A system according to embodiment 94, wherein the light comprises one or more wavelengths in the range from 300 nm to 400 nm.

[0302] 96. A system according to embodiment 1, wherein the system is operably coupled to a digital computer via a network.

[0303] 97. A system according to embodiment 1, wherein the network includes a cloud computing network.

[0304] 98. A non-classical computer comprising:

[0305] a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site in a spatially distinct plurality of optical trapping sites, wherein the plurality of qubits comprises at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state;

[0306] one or more electromagnetic delivery units configured to apply electromagnetic energy to one or more qubits of the plurality of qubits to impart a nonclassical operation to the one or more qubits, the nonclassical operation comprising a superposition state between at least the first qubit and the second qubit state;

[0307] one or more entangling units configured to quantum mechanically entangle at least a subset of the plurality of qubits in the superposition with at least one other qubit in the plurality of qubits; and

[0308] One or more readout optical units configured to perform one or more measurements on the one or more qubits to obtain a non-classical computation.

[0309] 99. A non-classical computer comprising a plurality of qubits, the qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites.

[0310] 100. A method for performing non-classical computing, comprising:

[0311] (a) generating a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites being configured to trap a plurality of atoms, the plurality of atoms comprising greater than 60 atoms;

[0312] (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 superpositions of a first atomic state and at least a second atomic state different from the first atomic state;

[0313] (c) quantum mechanically entangle at least a subset of the one or more atoms in the one or more superposition states with at least one other atom in the plurality of atoms; and

[0314] (d) performing one or more optical measurements on the one or more superposition states to obtain the non-classical computation.

[0315] 101. A method for performing non-classical computing, comprising:

[0316] (a) providing a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site in a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprises at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state;

[0317] (b) applying electromagnetic energy to one or more qubits of the plurality of qubits, thereby imparting a nonclassical operation to the one or more qubits, the nonclassical operation comprising a superposition state between at least the first qubit state and the second qubit state;

[0318] (c) quantum mechanically entangle at least a subset of the plurality of qubits in the superposition with at least one other qubit of the plurality of qubits; and

[0319] (d) performing one or more optical measurements on the one or more qubits to obtain the non-classical computation.

[0320] 102. A method for performing non-classical computing, comprising: (a) providing a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, and (b) performing the non-classical computing using at least a subset of the plurality of qubits.

[0321] 103. A method for performing non-classical computing, comprising: (a) providing a plurality of optical trapping sites comprising a plurality of atoms, wherein the plurality of atoms are a plurality of quantum bits; (b) moving one or more of the plurality of atoms from an occupied trapping site to an unoccupied trapping site, thereby changing the spatial arrangement of the plurality of atoms; (c) applying electromagnetic energy to one or more of the plurality of atoms to induce the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state, wherein one of the one or more atoms in the one or more superposition states is quantum mechanically entangled with another atom of the plurality of atoms; and (d) performing one or more measurements on the one or more superposition states.

[0322] 104. A method for performing non-classical computing, comprising: (a) generating a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites being configured to trap a plurality of atoms, wherein the plurality of atoms are quantum bits, wherein atoms of the plurality of atoms are trapped in optical trapping sites of the plurality of optical trapping sites by attractive forces; (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 entangled 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 measurements on the one or more superposition states to obtain the non-classical computing.

[0323] 105. A method for performing non-classical computing, comprising: (a) generating a plurality of spatially distinct optical trapping sites, wherein the plurality of optical trapping sites are configured to trap a plurality of atoms, wherein the plurality of atoms are quantum bits; (b) applying electromagnetic energy to one or more 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, wherein the applying comprises modulating the electromagnetic energy with at least two optical modulators; (c) quantum mechanically entangled 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 measurements on the one or more superposition states to obtain the non-classical computing.

[0324] Although preferred embodiments of the present invention have been shown and described herein, it is apparent to those skilled in the art that these embodiments are provided as examples only. Without departing from the present invention, those skilled in the art will now appreciate many variations, changes and substitutions. It should be understood that various alternatives to the embodiments of the present invention described herein may be adopted in practicing the present invention. The following claims are intended to define the scope of the present invention, and are therefore intended to encompass methods and structures within the scope of these claims and their equivalents.

Claims

1. A system for performing non-classical computing, comprising: one or more optical trapping units configured to generate a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites configured to trap a plurality of atoms, the plurality of atoms comprising greater 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 superposition state with at least another atom of the plurality of atoms; and One or more readout optical units configured to perform one or more measurements on the one or more superposition states to obtain the non-classical computation.

2. The system of claim 1, wherein the non-classical computing comprises quantum computing.

3. A non-classical computer comprising: a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site in a spatially distinct plurality of optical trapping sites, wherein the plurality of qubits comprises at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state; one or more electromagnetic delivery units configured to apply electromagnetic energy to one or more qubits of the plurality of qubits to impart a nonclassical operation to the one or more qubits, the nonclassical operation comprising a superposition state between at least the first qubit and the second qubit state; one or more entangling units configured to quantum mechanically entangle at least a subset of the plurality of qubits in the superposition with at least another qubit in the plurality of qubits; and One or more readout optical units configured to perform one or more measurements on the one or more qubits to obtain a non-classical computation.

4. A non-classical computer comprising a plurality of qubits, the qubits comprising greater than 60 atoms, each atom trapped in an optical trapping site of a plurality of spatially distinct optical trapping sites.

5. A method for performing non-classical computing, comprising: (a) generating a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites being configured to trap a plurality of atoms, the plurality of atoms comprising greater than 60 atoms; (b) applying electromagnetic energy to one or more atoms of the plurality of atoms, thereby inducing the one or more atoms to adopt one or more superpositions 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 one other atom in the plurality of atoms; as well as (d) performing one or more optical measurements on the one or more superposition states to obtain the non-classical computation.

6. A method for performing non-classical computing, comprising: (a) providing a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site in a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits comprises at least a first qubit state and a second qubit state, wherein the first qubit state comprises a first atomic state and the second qubit state comprises a second atomic state; (b) applying electromagnetic energy to one or more qubits of the plurality of qubits, thereby imparting a nonclassical operation to the one or more qubits, the nonclassical operation comprising a superposition state 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 one other qubit of the plurality of qubits; and (d) performing one or more optical measurements on the one or more qubits to obtain the non-classical computation.

7. A method for performing non-classical computing, comprising: (a) providing a plurality of qubits comprising greater than 60 atoms, each atom trapped within an optical trapping site of a plurality of spatially distinct optical trapping sites, and (b) performing the non-classical computation using at least a subset of the plurality of qubits.

8. A method for performing non-classical computing, comprising: (a) providing a plurality of optical trapping sites comprising a plurality of atoms, the plurality of atoms being a plurality of qubits; (b) moving one or more of the plurality of atoms from an occupied capture site to an unoccupied capture site, thereby changing the spatial arrangement of the plurality of atoms; (c) applying electromagnetic energy to one or more atoms of the plurality of atoms to induce the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state, wherein an atom of the one or more atoms in the one or more superposition states is quantum mechanically entangled with another atom of the plurality of atoms; and (d) performing one or more measurements on the one or more superposition states.

9. A method for performing non-classical computing, comprising: (a) generating a spatially distinct plurality of optical trapping sites, the plurality of optical trapping sites being configured to trap a plurality of atoms, wherein the plurality of atoms are qubits, wherein atoms of the plurality of atoms are trapped in optical trapping sites of the plurality of optical trapping sites by attractive forces; (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 entangled 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 measurements on the one or more superposition states to obtain the non-classical computation.

10. A method for performing non-classical computing, comprising: (a) generating a plurality of spatially distinct optical trapping sites, the plurality of optical trapping sites being configured to trap a plurality of atoms, wherein the plurality of atoms are qubits; (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, wherein the applying comprises modulating the electromagnetic energy with at least two optical modulators; (c) quantum mechanically entangled 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 measurements on the one or more superposition states to obtain the non-classical computation.

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