Scalable neutral atom-based quantum computing

Abstract

The present disclosure provides methods and systems for performing non-classical computation. The methods and systems generally use: a plurality of optically distinct optical trapping sites to trap a plurality of atoms; one or more electromagnetic delivery units to apply electromagnetic energy to one or more of the plurality of atoms to induce the atom to adopt one or more superposition states of a first atomic state and a second atomic state; one or more entangling units to quantum mechanically entangle at least a subset of the one or more atoms in the one or more superposition states with at least another atom of the plurality of atoms; and one or more readout optical units to perform a measurement of the superposition state to obtain a non-classical computation.

Description

[0001] Cross-references

[0002] This application claims the benefit of U.S. Provisional Patent Application No. 62 / 984,174, filed March 2, 2020, which is incorporated herein by reference in its entirety. Background Technology

[0003] Quantum computers typically utilize quantum mechanical phenomena such as superposition and entanglement to perform operations on data. Quantum computers may differ from transistor-based digital electronic computers. For example, digital computers need to encode data as binary digits (bits), each digit always being in one of two definite states (0 or 1), while quantum computing uses qubits, which can be in a superposition of states. Summary of the Invention

[0004] This paper recognizes the need for methods and systems for performing non-classical computations.

[0005] This disclosure provides systems and methods for performing non-classical or quantum computing using atoms, such as neutral or uncharged atoms. Atoms can be optically trapped in large arrays. The quantum mechanical states of the atoms (such as hyperfine states or nuclear spin states) can be configured as the ground states of qubits. The qubit states can be manipulated through interactions with optical, radio frequency, or other electromagnetic radiation, thereby performing non-classical or quantum computing.

[0006] In one aspect, this disclosure provides a method for performing non-classical computation that may include: (a) activating a non-classical computation unit comprising: (i) one or more trapping units that trap a plurality of atoms, the plurality of atoms being a plurality of qubits; (ii) one or more first electromagnetic delivery units; (iii) one or more Rydberg units; (iv) one or more second electromagnetic delivery units; and (v) one or more readout units; (b) applying a first electromagnetic energy to one or more atoms of the plurality of atoms using one or more first electromagnetic delivery units, thereby inducing 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 using one or more Rydberg units to form one or more multi-qubit units; (d) applying a second electromagnetic energy comprising one or more pulse sequences to one or more multi-qubit units using one or more second electromagnetic delivery units, thereby implementing one or more multi-qubit gate operations on one or more multi-qubit units, wherein the one or more pulse sequences comprise one or more non-adiabatic pulses maintaining adiabatic dynamics; and (e) performing one or more measurements on one or more superposition states using one or more readout units to obtain a non-classical computation. One or more pulse sequences may include one or more members selected from the group consisting of: adiabatic (STA) pulse sequence shortcuts, transition-free quantum drive (TQD) pulse sequences, superadiabatic pulse sequences, antiadiabatic drive pulse sequences, adiabatic derivative elimination (DRAG) pulse sequences, and weakly anharmonic (Wah Wah) pulse sequences with average Hamiltonian. The first and second electromagnetic delivery units may be the same. The first and second electromagnetic delivery units may be different. One or more pulse sequences may also include one or more optimal control pulse sequences. One or more optimal control pulse sequences may originate from one or more processes selected from the group consisting of: gradient rising pulse engineering (GRAPE) methods, Krotov methods, chopper basis methods, chopper random basis (CRAB) methods, Nelder-Mead methods, gradient optimization using parameterized methods (GROUP), genetic algorithm methods, and gradient optimization of analytical control (GOAT) methods. One or more pulse sequences may include a duration of at least 10 nanoseconds (ns). One or more pulse sequences may include a duration of at most 100 microseconds (μs). One or more multi-qubit gate operations may include a fidelity of at least 0.9. One or more multi-qubit gate operations can include a fidelity of up to 0.999999.The method may further include using one or more Rydberg units to excite at least one atomic electron of one or more atoms in one or more superposition states to a Rydberg state, thereby forming one or more Rydberg atoms, or by continuously driving one or more atoms in one or more superposition states via transitions to Rydberg states, thereby forming one or more modified Rydberg atoms. The method may further include using one or more Rydberg units to induce one or more quantum mechanical entanglements between one or more Rydberg atoms or modified Rydberg atoms and at least one other atom located at a distance of no more than 10 micrometers (μm) from one or more Rydberg atoms or modified Rydberg atoms. The method may further include using one or more Rydberg units to drive one or more Rydberg atoms or modified Rydberg atoms to a lower energy atomic state, thereby forming one or more multi-qubit units. One or more trapping units may include one or more optical trapping units. The method may further include using one or more optical trapping units to generate multiple spatially distinct optical trapping sites. The method may further include using each of the multiple spatially distinct optical trapping sites to trap at most one atom from a plurality of atoms. One or more of the multi-qubit units may include biqubit units. One or more of the multi-qubit gate operations may include two-qubit gate operations. In some embodiments, (c) further includes implementing one or more multi-qubit gate operations on one or more multi-qubit units. In some embodiments, in (c), quantum mechanical entanglement of at least a subset of one or more atoms using one or more Rydberg units includes using one or more pulse sequences. In some embodiments, the one or more pulse sequences include one or more non-adiabatic pulses that maintain adiabatic dynamics. In some embodiments, generating entanglement via a Rydberg unit may be a gate operation. In some embodiments, pulse shaping or pulse sequences may be applied via a Rydberg unit.

[0007] On the other hand, this disclosure provides a system for performing non-classical computation, comprising: one or more capture units; one or more first electromagnetic delivery units; one or more Rydberg units; one or more second electromagnetic delivery units; one or more readout units; and one or more controllers coupled to the one or more capture units, the one or more first electromagnetic units, the one or more Rydberg units, the one or more second electromagnetic delivery units, and the one or more readout units, wherein the one or more controllers are configured to: (i) direct the one or more capture units to capture a plurality of atoms, the plurality of atoms being a plurality of qubits; and (ii) direct the one or more first electromagnetic delivery units to apply a first electromagnetic energy to one or more of the plurality of atoms, thereby inducing the one or more atoms to employ a first electromagnetic energy. (iii) One or more Rydberg units are directed to quantum mechanically entangle at least a subset of one or more atoms in one or more superposition states with at least another atom among a plurality of atoms to form one or more multi-qubit units; (iv) One or more second electromagnetic delivery units are directed to apply a second electromagnetic energy comprising one or more pulse sequences to one or more multi-qubit units to realize one or more multi-qubit gate operations on one or more multi-qubit units, wherein the one or more pulse sequences comprise one or more non-adiabatic pulses that maintain adiabatic dynamics; and (v) One or more readout units are directed to perform one or more measurements on one or more superposition states to obtain non-classical computations.

[0008] Although this document describes multi-qubit Rydberg gate systems, the methods and systems disclosed herein can be used in many different gate systems. For example, the methods and systems described herein can be applied to single-qubit gates. In another example, a qubit is encoded as... 87 Sr (e.g., m) F = -9 / 2 and m F = -7 / 2 1 S0 state, for example Figure 15A In a system with two nuclear spin states, the remaining nuclear spin states can exist outside the qubit subspace, and a population of these states can constitute leakage error. Two-photon transitions driving a single-qubit gate can also drive leakage transitions to nuclear spin states outside the qubit subspace. By selectively shifting the nuclear spin states, leakage transitions can be offset from the frequency of the qubit transition. As described elsewhere in this paper, the use of DRAG pulses implemented on two-photon transitions can suppress leakage transitions, which could allow for faster, higher-fidelity single-qubit gates.

[0009] Other aspects and advantages of this disclosure will become readily apparent to those skilled in the art from the following detailed description, in which only illustrative embodiments of the disclosure are shown and described. As will be appreciated, other different embodiments of the disclosure are possible, and several details thereof can be modified in various obvious ways, all without departing from the scope of the disclosure. Therefore, the drawings and description are to be considered illustrative in nature and not restrictive.

[0010] Incorporation

[0011] All publications, patents, and patent applications mentioned in this specification are incorporated herein by reference to the extent that each individual publication, patent, or patent application is specifically and individually indicated as incorporated by reference. If any publication, patent, or patent application incorporated by reference contradicts the disclosure contained in this specification, this specification is intended to supersede and / or take precedence over any such contradictory material. Attached Figure Description

[0012] The novel features of the invention are specifically set forth in the appended claims. A better understanding of the features and advantages of the invention will be obtained by referring to the following detailed description of illustrative embodiments in which the principles of the invention are utilized, along with the accompanying drawings (also referred to herein as “Figures”), wherein:

[0013] Figure 1 A computer control system is shown that is programmed or otherwise configured to implement the methods provided herein.

[0014] Figure 2 An example of a system for performing non-classical calculations is shown.

[0015] Figure 3A An example of an optical capture unit is shown.

[0016] Figure 3B Examples of multiple optical capture sites are shown.

[0017] Figure 3C An example of an optical trapping unit partially filled with atoms is shown.

[0018] Figure 3D An example of an optical trapping unit that is completely filled with atoms is shown.

[0019] Figure 4 An example of an electromagnetic delivery unit is shown.

[0020] Figure 5 An example of a state preparation unit is shown.

[0021] Figure 6A flowchart is shown as an example of a first method for performing non-classical computations.

[0022] Figure 7 A flowchart is shown as an example of a second method for performing non-classical calculations.

[0023] Figure 8 A flowchart is shown as an example of a third method for performing non-classical computations.

[0024] Figure 9 The image shows a product containing strontium-87. 3 An example of a P2 state qubit.

[0025] Figure 10A and Figure 10B Strontium-87 is shown. 1 Simulation of Stark migration in the S0 hyperfine state.

[0026] Figure 11A and Figure 11B A simulation of single-qubit control with Stark shift is shown.

[0027] Figure 12A and Figure 12B An example array is shown that captures light generated by SLM.

[0028] Figure 13 An optical system for delivering four different wavelengths is shown.

[0029] Figure 14 The use of a red magneto-optical trap (MOT) to trap and cool strontium-87 and strontium-88 atoms is shown.

[0030] Figure 15A The energy level structures for single-qubit and multi-qubit operations in Strontium-87 are shown.

[0031] Figure 15B An optical system for delivering light to perform single-qubit and multi-qubit operations in parallel on multiple trapped atoms is shown.

[0032] Figure 15C An optical system configured to dynamically generate and control beams using a single electro-optic modulator (EOM) and two acousto-optic deflectors (AOD) for each beam is shown, each beam being driven by an RF signal from an arbitrary waveform generator.

[0033] Figure 16A A simulation of two atoms in the initial diatomic state is shown.

[0034] Figure 16B A simulation of two atoms in the initial diatomic state is shown, with an antiadiabatic driving field applied to implement a transitionless quantum driving gate.

[0035] Figure 16C Numerical simulations of a diatomic system with a Rydberg blockade that has undergone Rydberg modification gates are shown.

[0036] Figure 16D Examples of DRAG pulses in the time domain (a) and frequency domain (b) are shown.

[0037] Figure 16E A simulation example of optimizing DRAG pulse parameters to minimize error is shown. Figure 17A A calibrated image of the light-capturing sites of a fully filled 7x7 array is shown.

[0038] Figure 17B The markings of filled and unfilled optical capture sites in the 7x7 array are shown.

[0039] Figure 17C The diagram shows a 25x25 pixel grid around each optical capture point in the 7x7 array.

[0040] Figure 17D The diagram shows how each capture site in the 7x7 array is identified as either filled or unfilled.

[0041] Figure 17E The movement of optical trapping sites from filled to unfilled avoids collisions between atoms. Detailed Implementation

[0042] While various embodiments of the invention have been shown and described herein, it will be readily understood by those skilled in the art that these embodiments are provided by way of example only. Many variations, modifications, and substitutions will occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed.

[0043] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include the plural forms unless the context clearly specifies otherwise. Unless otherwise stated, any reference to “or” herein is intended to cover “and / or.”

[0044] When the terms "at least," "greater than," or "greater than or equal to" precede the first value in a series of two or more values, the terms "at least," "greater than," or "greater than or equal to" apply 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.

[0045] When the terms “not greater than,” “less than,” “less than or equal to,” or “at most” precede the first value in two or more series of values, the terms “not greater than,” “less than,” “less than or equal to,” or “at most” apply to each value in that 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.”

[0046] When a value is described as a range, it should be understood that such disclosure includes disclosure of all possible subranges within such range as well as specific values ​​falling within such range, whether or not the specific value or specific subrange is explicitly specified.

[0047] As used in this article, the same character refers to the same element.

[0048] As used herein, the terms “artificial intelligence,” “artificial intelligence process,” “artificial intelligence operation,” and “artificial intelligence algorithm” generally refer to any system or computational 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).”

[0049] 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 to progressively improve a task. Machine learning can include machine learning algorithms. Machine learning algorithms can be trained algorithms. Machine learning (ML) can include one or more supervised, semi-supervised, or unsupervised machine learning techniques. For example, an ML algorithm can be a trained algorithm trained through supervised learning (e.g., various parameters are determined as weights or scaling factors). ML can 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, learned vector quantization, linear regression, nonlinear regression, least squares regression, partial least squares regression, logistic regression, stepwise regression, multivariate adaptive regression splines, ridge regression, principal component regression, minimum absolute contraction and selection operations, minimum angle regression, canonical correlation analysis, factor analysis, independent component analysis, linear discriminant analysis, multidimensional scaling, nonnegative matrix factorization, principal component analysis, principal coordinate analysis, projection tracking, Sammon Mapping, t-distributed random neighborhood embedding, adaptive boosting (AdaBoosting), boosting, gradient boosting, guided aggregation, ensemble averaging, decision trees, conditional decision trees, boosting decision trees, gradient boosting decision trees, random forests, stacked generalization, Bayesian networks, Bayesian belief networks, Naive Bayes, Gaussian Naive Bayes, Multinomial Naive Bayes, Hidden Markov Models, Hierarchical Hidden Markov Models, Support Vector Machines, encoders, decoders, autoencoders, stacked autoencoders, perceptrons, multilayer perceptrons, artificial neural networks, feedforward neural networks, convolutional neural networks, recurrent neural networks, long short-term memory, deep belief networks, deep Boltzmann machines, deep convolutional neural networks, deep recurrent neural networks, or generative adversarial networks.

[0050] As used herein, the terms “reinforcement learning,” “reinforcement learning process,” “reinforcement learning operation,” and “reinforcement learning algorithm” are proposed to refer to any system or computational process that takes one or more actions to enhance or maximize the cumulative reward of its interaction with the environment. An agent performing a reinforcement learning (RL) process can receive positive or negative reinforcement, referred to as “immediate reward,” from taking one or more actions in the environment and thus placing itself and the environment into various new states.

[0051] An agent's objective might be to enhance or maximize some concept of cumulative reward. For example, an agent's objective might be to enhance or maximize a "discounted reward function" or an "average reward function." A "Q-function" can represent the maximum cumulative reward obtainable from a state and the action taken in that state. A "value function" and a "generalized advantage estimator" can represent the maximum cumulative reward obtainable from a state given an optimal or best action choice. RL can utilize any one or more of these cumulative reward concepts. As used in this paper, any such function can be called a "cumulative reward function." Therefore, computing the optimal or best cumulative reward function is equivalent to finding the optimal or best policy for the agent.

[0052] An agent and its interaction with the environment can be formulated as one or more Markov decision processes (MDPs). RL processes may not assume knowledge of the exact mathematical model of the MDP. The MDP can be completely unknown, partially known, or completely known to the agent. Regarding prior knowledge of the MDP, RL processes may fall between the levels of "model-based" and "model-free." Thus, RL processes may be designed for large MDPs, where precise methods may be infeasible or unavailable due to the unknown or stochastic nature of the MDP.

[0053] RL processes can be implemented using one or more computer processors as described in this paper. The digital processing unit can train and store the agent, then deploy a "policy" to enhance or maximize the cumulative reward. The policy can be sought (e.g., searched) over a period of as long as possible or desired. Such optimization problems can be solved by storing approximations of the optimal policy, by storing approximations of the cumulative reward function, or both. In some cases, the RL process can store one or more tables of approximations for such functions. In other cases, the RL process can use one or more "function approximators".

[0054] Examples of function approximators can include neural networks (such as deep neural networks) and probabilistic graphical models (such as Boltzmann machines, Helmholtz machines, and Hopfield networks). Function approximators can create parameterizations that approximate the cumulative reward function. Optimization of the parameterization of a function approximator can include perturbing the parameters in a direction that enhances or maximizes the cumulative reward and thus enhances or optimizes the policy (such as in the policy gradient method) to get closer to satisfying Bellman's optimality criterion.

[0055] During training, the agent can take actions in the environment to gain more information about the environment and about good or optimal policy 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 prescribed 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 more closely reflect the agent's perception of what an enhanced or optimal policy is. Regarding the choice between exploration and exploitation, various training strategies can fall between two degrees of off-policy and on-policy approaches.

[0056] As used herein, the terms “non-classical computing,” “non-classical process,” “non-classical operation,” and “non-classical computer” generally refer to any method or system for performing computational processes outside the paradigm of classical computing. Non-classical computing, non-classical process, non-classical operation, or non-classical computer may include quantum computing, quantum process, quantum operation, or quantum computer.

[0057] As used herein, the terms “quantum computing,” “quantum process,” “quantum operation,” and “quantum computer” generally refer to any method or system used to perform computations on a Hilbert space represented by a quantum device using quantum mechanical operations such as unitary transformations or fully normal trace preservation (CPTP) mappings on quantum channels. Thus, quantum computing and classical (or digital) computing can be similar in that both can consist of a sequence of instructions to be executed on input information and then provide an output. Various paradigms of quantum computing can decompose quantum operations into a sequence of fundamental quantum operations that simultaneously affect a subset of qubits on the quantum device. Quantum operations can be chosen based on, for example, their location or the ease of their physical realization. A quantum process or computation can then consist of a series of instructions that can represent different quantum evolutions on a quantum device in various applications. For example, computational or simulation processes in quantum chemistry can be represented by quantum states of electron spin orbitals and annihilation and creation operators using qubits (such as two-level quantum systems) and universal sets of quantum gates (such as Hadamard, uncontrolled (CNOT), and π / 8 spin) via the so-called Jordan-Wigner transformation or Bravyi-Kitaev transformation.

[0058] Other examples of quantum processes or computations can include processes for optimization, such as quantum approximation optimization algorithms (QAOA) or quantum minimum searches. QAOA can include performing single-qubit rotations and entanglement gates for multiple qubits. In quantum adiabatic computation, instructions can carry random or non-random evolution paths from the initial quantum system to the final quantum system.

[0059] The process of quantum excitation can include simulated annealing, parallel tempering, master equation solvers, Monte Carlo processes, etc. Quantum classical or hybrid algorithms or processes can include processes such as variational quantum feature solvers (VQE) and variational and adiabatic guided quantum feature solvers (VanQver).

[0060] A quantum computer may include one or more adiabatic quantum computers, quantum gate arrays, single-vector quantum computers, topological quantum computers, quantum Turing machines, quantum annealers, Ising solvers, or gate models of quantum computing.

[0061] As used in this paper, the term "adiabatic" refers to any process performed on a quantum mechanical system in which the parameters of the Hamiltonian change slowly compared to the natural timescale of the system's evolution.

[0062] As used in this paper, the term “non-adiabatic” refers to any process performed on a quantum mechanical system in which the parameters of the Hamiltonian change rapidly compared to or on a timescale similar to the natural timescale of the system’s evolution.

[0063] Systems for performing non-classical calculations

[0064] In one aspect, this disclosure provides a system for performing non-classical computation. The system may include: one or more optical trapping units configured to generate a plurality of spatially distinct optical trapping sites configured to trap a plurality of atoms, the plurality of atoms comprising more than 60 atoms; one or more electromagnetic delivery units configured to apply electromagnetic energy to one or more of the plurality of atoms, thereby inducing one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state; one or more entanglement units configured to quantum mechanically entangle at least a subset of the one or more atoms in the one or more superposition states with at least another atom of the plurality of atoms; and one or more readout optical units configured to perform one or more measurements on the one or more superposition states to obtain non-classical computation.

[0065] Figure 2 An example of a system 200 for performing non-classical computation is shown. Non-classical computation may include quantum computation. Quantum computation may include gate model quantum computation.

[0066] System 200 may include one or more capture units 210. A capture unit may include one or more optical capture units. An optical capture unit may include any optical capture unit described herein, such as those described herein. Figure 3AAn optical capturing unit is described. The optical capturing unit can be configured to generate multiple optical capturing sites. The optical capturing unit can be configured to generate multiple spatially distinct optical capturing sites. For example, the optical capturing unit can be configured to generate at least approximately 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 can be configured to generate up to approximately 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30, 000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10 or fewer optical capture sites. The optical capture unit can be configured to capture a plurality of optical capture sites within a range defined by any two of the foregoing values.

[0067] The optical trapping unit can be configured to trap multiple atoms. For example, the optical trapping unit can be configured to trap at least approximately 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, or 10,000 atoms. 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 acquisition unit can be configured to acquire up to approximately 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 3 0,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10 or fewer atoms. The optical trapping unit can be configured to trap a number of atoms within the range defined by any two of the foregoing values.

[0068] Each optical trapping site in the optical trapping unit can be configured to trap at least approximately 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more atoms. Each optical trapping site can be configured to trap up to approximately 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 or fewer atoms. Each optical trapping site can be configured to trap a plurality of atoms within a range defined by any two of the foregoing values. Each optical trapping site can be configured to trap a single atom.

[0069] One or more atoms among a plurality of atoms may include qubits, as described herein (e.g., regarding...). Figure 4Two or more atoms can be quantum mechanically entangled. The coherence lifetime of two or more atoms can be quantum mechanically entangled with a coherence lifetime of at least approximately 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, or 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 coherent lifetimes of at most approximately 10 s, 9 s, 8 s, 7 s, 6 s, 5 s, 4 s, 3 s, 2 s, 1 s, 900 ms, 800 ms, 700 ms, 600 ms, 500 ms, 400 ms, 300 ms, 200 ms, 100 ms, 90 ms, 80 ms, 70 ms, 60 ms, 50 ms, 40 ms, 30 ms, 20 ms, 10 ms, 9 ms, 8 ms, 7 ms, 6ms, 5ms, 4ms, 3ms, 2ms, 1ms, 900µs, 800µs, 700µs, 600µs, 500µs, 400µs, 300µs, 200µs, 100µs, 90µs, 80µs, 70µs, 60µs, 50µs, 40µs, 30µs, 20µs, 10µs, 9µs, 8µs, 7µs, 6µs, 5µs, 4µs, 3µs, 2µs, 1µs or less. Two or more atoms can be quantum mechanically entangled, with a coherent lifetime 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.

[0070] 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. One or more atoms may include beryllium-9 atoms, magnesium-24 atoms, magnesium-25 atoms, magnesium-26 atoms, calcium-40 atoms, calcium-42 atoms, calcium-43 atoms, calcium-44 atoms, calcium-46 atoms, calcium-48 atoms, strontium-84 atoms, strontium-86 atoms, strontium-87 atoms, strontium-88 atoms, barium-130 atoms, barium-132 atoms, barium-134 atoms, barium-135 atoms, barium-136 atoms, barium-137 atoms, or barium-138 atoms. One or more atoms may include rare earth atoms. One or more atoms may include scandium (Sc) atoms, yttrium (Y) atoms, lanthanum (La) atoms, cerium (Ce) atoms, praseodymium (Pr) atoms, neodymium (Nd) atoms, samarium (Sm) atoms, europium (Eu) atoms, gadolinium (Gd) atoms, terbium (Tb) atoms, dysprosium (Dy) atoms, holmium (Ho) atoms, erbium (Er) atoms, thulium (Tm) atoms, ytterbium (Yb) atoms, or lutetium (Lu) atoms. One or more atoms 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.

[0071] Multiple atoms may include a single element selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. Multiple atoms may include a mixture of elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. Multiple atoms may include a naturally occurring mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. Multiple 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. Multiple atoms may include a naturally occurring mixture of one or more elements selected from the group consisting of Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. Multiple atoms may include isotopic enriched mixtures of one or more elements selected from the group consisting of Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. Atoms may include rare earth atoms.For example, multiple 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-1 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, 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 or lutetium-176 atoms enriched to at least approximately 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 of isotopic abundance.Multiple atoms can 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. Atoms, Barium-137 atoms, Barium-138 atoms, Scandium-45 atoms, Yttrium-89 atoms, Lanthanum-139 atoms, Cerium-136 atoms, Cerium-138 atoms, Cerium-140 atoms, Cerium-142 atoms, Praseodymium-141 atoms, Neodymium-142 atoms, Neodymium-143 atoms, Neodymium-145 atoms, Neodymium-146 atoms, Neodymium-148 atoms, Samarium-144 atoms, Samarium-149 atoms, Samarium-150 atoms, Samarium-152 atoms, Samarium-154 atoms, Europium-151 atoms, Europium-153 atoms, Gadolinium-154 atoms, Gadolinium-155 atoms, Gadolinium-156 atoms, Gadolinium-15 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 -175 atoms or lutetium-176 atoms, enriched to at most approximately 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50% or less of the isotopic abundance.Multiple atoms can 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, and strontium-88 atoms. 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, erbium-164, erbium-166, erbium-167, erbium-168, erbium-170, holmium-165, thulium-169, ytterbium-168, ytterbium-170, ytterbium-171, ytterbium-172, ytterbium-173, ytterbium-174, ytterbium-176, lutetium-175, or lutetium-176 atoms, enriched to isotopic abundances within the range defined by any two of the aforementioned values.

[0072] System 200 may include one or more first electromagnetic delivery units 220. The first electromagnetic delivery unit may include any electromagnetic delivery unit described herein, such as those described herein. Figure 4 The electromagnetic delivery unit is described. The first electromagnetic delivery unit can be configured to apply a first electromagnetic energy to one or more atoms among a plurality of atoms. Applying the first electromagnetic energy can induce the atom to adopt one or more superposition states of a first atomic state and a second atomic state different from the first atomic state.

[0073] The first atomic state may include a first single-qubit state. The second atomic state may include a second single-qubit state. The first or second atomic state may be higher in energy than the basic atomic state of the atom. The energy of the first or second atomic state may be equal to that of the basic atomic state of the atom.

[0074] 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 the first and second hyperfine states on a multiplicity manifold, such as a triplet manifold. The first and second atomic states may respectively include 3 P1 or 3 The first and second hyperfine states on the P2 manifold. The first and second atomic states can be included, respectively, of any atom described herein. 3 P1 or 3 First and second hyperfine states on the P2 manifold, such as Strontium-87 3 P1 manifold or Strontium-87 3 P2 manifold.

[0075] Figure 9 The image shows a product containing strontium-87. 3 An example of a P2 state qubit. Figure 9 The left panel shows Strontium-87. 3 The rich energy level structure of the P2 state. Figure 9 The right panel shows Strontium-87. 3 The potential qubit transition in the P2 state is insensitive to changes in the magnetic field near 70 Gauss (for first order).

[0076] In some cases, the first and second atomic states are first and second hyperfine states of the first electronic state. Photoexcitation can be applied between the first and second electronic states. Photoexcitation can excite the first and / or second hyperfine states to the second electronic state. Single-qubit transitions can include two-photon transitions between two hyperfine states within the first electronic state, using the second electronic state as an intermediate state. To drive a single-qubit transition, a pair of frequencies can be applied to drive the two-photon transition, each frequency detuning from the single-photon transition to the intermediate state. In some cases, the first and second hyperfine states are hyperfine states of the ground electronic state. The ground electronic state may not decay to a lower electronic state through spontaneous or stimulated emission. Hyperfine states can include nuclear spin states. In some cases, hyperfine states include strontium-87. 1 The nuclear spin state of the S0 manifold, and the qubit transition will strontium-87 1 One or both of the two nuclear spin states of S0 drive the spin to the point where... 3 P2 or 3 Within or from the detuned state of the P1 manifold. In some cases, single-qubit transitions are via... 3 P2 or 3 Within the P1 manifold or from its detuned state, in Strontium-87 1Two-photon Raman transitions between S0 nuclear spin states. In some cases, the nuclear spin states can be Stark-shifted nuclear spin states. Stark shifting can be optically driven. Optical Stark shifting can be driven by any, all, or a combination of single-qubit transitions, two-qubit transitions, shelving transitions, imaging transitions, etc.

[0077] The first atomic state may include a first nuclear spin state and the second atomic state may include a second nuclear spin state different from the first nuclear spin state. The first and second atomic states may each include the first and second nuclear spin states of a tetrapolar nucleus. The first and second atomic states may each include the first and second nuclear spin states of spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4, or spin-9 / 2 nuclei. The first and second atomic states may each include the first and second nuclear spin states of any atom described herein, such as the first and second spin states of strontium-87.

[0078] For first and second nuclear spin states associated with nuclei containing spins greater than 1 / 2 (such as spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4, or spin-9 / 2 nuclei), transitions between the first and second nuclear spin states may be accompanied by transitions between other spin states on the nuclear spin manifold. For example, for a spin-9 / 2 nucleus with a uniform magnetic field, all nuclear spin energy levels may be separated by equal energies. Therefore, transitions from, for example, m... N = 9 / 2 spin state transfer to m N = 7 / 2 spin state 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 This is a nuclear spin state. Similarly, it is designed to transfer atoms from, for example, m... N = 9 / 2 spin state transfer to mN =5 / 2 spin state transitions (such as Raman transitions) can also drive: m N = 7 / 2 to m N =3 / 2, m N =5 / 2 to m N =1 / 2, m N =3 / 2 to m N = -1 / 2, m N =1 / 2 to m N = -3 / 2, m N = -1 / 2 to m N = -5 / 2, m N = -3 / 2 to m N = -7 / 2, and m N = -5 / 2 to m N = -9 / 2. Therefore, this transition may not be selectively induced between specific spin states on the nuclear spin manifold.

[0079] Alternatively, selective transitions between specific first and second spin states on a nuclear spin manifold may be desirable. This can be achieved by providing light from a source that provides an AC-Stark shift and pushes adjacent nuclear spin states away from resonance with the desired transition between the first and second nuclear spin states. For example, if the desired transition is from a manifold with m N = -9 / 2 and m N If the first and second nuclear spin states transition by a ratio of -7 / 2, then light can be provided up to m. N = -5 / 2 spin state AC Stark shift, thus greatly reducing m N = -7 / 2 and m N = -5 / 2 states for transitions. Similarly, if we expect to transition from a state with m N = -9 / 2 and m N If the first and second nuclear spin states transition by a ratio of -5 / 2, then light can be provided up to m. N = -1 / 2 spin state AC Stark shift, thus greatly reducing m N = -5 / 2 and m N = Transitions between -1 / 2 states. This can effectively create a two-level subsystem within the nuclear spin manifold, decoupled from the rest of the nuclear spin manifold, greatly simplifying the dynamics of the qubit system. Using nuclear spin states near the edge of the nuclear spin manifold can be advantageous (e.g., for a spin-9 / 2 nucleus, m N = -9 / 2 and m N = -7 / 2, m N = 7 / 2 and m N = 9 / 2, mN = -9 / 2 and m N = -5 / 2, or m N =5 / 2 and m N = 9 / 2), thus requiring only one AC Stark offset. Alternatively, nuclear spin states further from the edge of the nuclear spin manifold (e.g., m) can be used. N = -5 / 2 and m N = -3 / 2 or m N = -5 / 2 and m N = -1 / 2) and can achieve two AC Stark offsets (e.g., in m N = -7 / 2 and m N = -1 / 2 or m N = -9 / 2 and m N =3 / 2).

[0080] Stark shift of the nuclear spin manifold can deflect adjacent nuclear spin states from resonances with desired transitions between the first and second nuclear spin states and the second electronic state, or from their detuned states. Stark shift 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 shift 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 a P1 manifold can differ from single-qubit and two-qubit gated light by many gigahertz. Leakage of other states into the nuclear spin manifold can lead to decoherence. The Rabi frequency of a two-qubit transition (e.g., how fast it can drive the transition) may be faster than the rate of decoherence. Scattering from intermediate states in a two-qubit transition can be a source of decoherence. Detuning from intermediate states can improve the fidelity of the two-qubit transition.

[0081] Quantum bits based on nuclear spin states in their electronic ground state can allow the excitation of electronic states using long-lived metastable states (such as those in Strontium-87). 3 The P0 state is used for qubit storage. Atoms can selectively transition to this state to reduce crosstalk or improve gate or detection fidelity. Such storage or shelving processes can be atom-selective using the SLM or AOD described herein. Shelving transitions can include those from Strontium-87. 1 S0 state to Strontium-87 3 P0 or 3 Transitions between P2 states.

[0082] Clock transitions (also referred to herein as "shelved transitions" or "stored transitions") can be state-selective for qubits. The higher states of a clock transition can have very long natural lifetimes, such as greater than 1 second. The linewidth of a clock transition can be much narrower than the qubit energy interval. This allows for direct spectral resolution. A population can transition from one of the qubit states to the clock state. This allows for the readout of individual single-qubit states—first transitioning the population from one qubit state to the clock state, imaging the qubit, and then transitioning the population back from the clock state to the ground state and imaging again. In some cases, magic wavelength transitions are used to drive clock transitions.

[0083] The clock light used for restoring the light can be atomically selective or non-atomic selective. In some cases, the clock transition is globally applied (e.g., not atomically selective). Globally applied clock transitions can involve guiding light without passing through a microscope objective or constructing light. In some cases, the clock transition is atomically selective. Atomically selective clock transitions may allow us to improve gate fidelity by minimizing crosstalk. For example, to reduce crosstalk in an atom, the atom can be rested in a clock state in which it is unaffected by light. This can reduce crosstalk between adjacent qubits undergoing the transition. To achieve atomically selective clock transitions, the light can pass through one or more microscope objectives and / or can be structured on one or more of spatial light modulators, digital micromirror devices, cross-acoustic-optic deflectors, etc.

[0084] System 200 may include one or more readout units 230. Each readout unit may include one or more readout optics. Each readout optics unit may be configured to perform one or more measurements of one or more superimposed states to obtain non-classical calculations. Each readout optics unit may include one or more optical detectors. Detectors may include one or more photomultiplier tubes (PMTs), photodiodes, avalanche diodes, single-photon avalanche diodes, single-photon avalanche diode arrays, phototransistors, reverse-biased light-emitting diodes (LEDs), charge-coupled devices (CCDs), or complementary metal-oxide-semiconductor (CMOS) cameras. Optical detectors may include one or more fluorescence detectors. Each readout optics unit may include one or more objectives, such as one or more objectives having a numerical aperture (NA) of at least approximately 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. Objective lenses may have an NA of at most approximately 1, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7, 0.65, 0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1, or less. Objective lenses may have an NA within the range defined by any two of the aforementioned values.

[0085] One or more readout optics 230 can perform measurements, such as projection measurements, by applying an optical resonance with an imaging transition. The imaging transition may result in fluorescence. The imaging transition may include those in strontium-87. 1 From S0 state to Strontium-87 1 Transitions between states P1. In Strontium-87 1 The P1 state may emit fluorescence. Lower states of a qubit transition may include... 1 Two nuclear spin states in the S0 manifold. One or more states may resonate with the imaging transition. A measurement may include two excitations. In the first excitation, one of the two lower states may be excited to a shelved state (e.g., in Strontium-87). 3 (P0 state). In the second excitation, an imaging transition may be excited. The first transition can reduce crosstalk between adjacent atoms during the calculation. The fluorescence generated from the imaging transition can be collected on one or more readout optical units 230.

[0086] An imaging unit can be used to determine whether one or more atoms have been lost from a trap. An imaging unit can also be used to observe the arrangement of atoms within a trap.

[0087] System 200 may include one or more vacuum units 240. The one or more vacuum units may include one or more vacuum pumps. The vacuum units may include one or more low-vacuum pumps, such as one or more rotary pumps, rotary vane pumps, rotary piston pumps, diaphragm pumps, piston pumps, reciprocating piston pumps, scroll pumps, or screw pumps. The one or more low-vacuum pumps may include one or more wet (e.g., oil-sealed) or dry low-vacuum pumps. The vacuum units may include one or more high-vacuum pumps, such as one or more cryogenic adsorption pumps, diffusion pumps, turbomolecular pumps, molecular dragged pumps, turbo-drafted mixing pumps, cryogenic pumps, ion pumps, or getter pumps.

[0088] The vacuum unit may include any combination of vacuum pumps described herein. For example, the vacuum unit may include one or more low-vacuum pumps (such as vortex pumps) configured to provide a first-stage low-vacuum pump. The low-vacuum pump may be configured to pump gas out of system 200 to achieve low vacuum pressure conditions. For example, the low-vacuum pump may be configured to pump gas out of system 200 to achieve up to approximately 10 3 The vacuum unit may also include one or more high-vacuum pumps (such as one or more ion pumps, bubbling pumps, or both) configured to provide a second-stage high-vacuum pump or ultra-high-vacuum pump. Once system 200 has reached the low-vacuum pressure conditions provided by one or more low-vacuum pumps, the high-vacuum pumps may be configured to pump gas out of system 200 to achieve up to approximately 10 Pascals (Pa). -3 A high vacuum pressure of Pa or at most approximately 10 Pa -6 Ultra-high vacuum pressure of Pa.

[0089] The vacuum unit can be configured to maintain the system 200 at a temperature of up to approximately 10. -6 Pa, 9x10 -7 Pa, 8x10 -7 Pa, 7x10 -7 Pa, 6x10 -7 Pa, 5x10 -7 Pa, 4x10 -7 Pa, 3x10 -7 Pa, 2x10 -7 Pa, 10 -7 Pa, 9x10 -8 Pa, 8x10 -8 Pa, 7x10 -8 Pa, 6x10 -8 Pa, 5x10 -8 Pa, 4x10 -8 Pa, 3x10 -8 Pa, 2x10 -8 Pa, 10 -8 Pa, 9x10-9 Pa, 8x10 -9 Pa, 7x10 -9 Pa, 6x10 -9 Pa, 5x10 -9 Pa, 4x10 -9 Pa, 3x10 -9 Pa, 2x10 -9 Pa, 10 -9 Pa, 9x10 -10 Pa, 8x10 -10 Pa, 7x10 -10 Pa, 6x10 -10 Pa, 5x10 -10 Pa, 4x10 -10 Pa, 3x10 -10 Pa, 2x10 -10 Pa, 10 -10 Pa, 9x10 -11 Pa, 8x10 - 11 Pa, 7x10 -11 Pa, 6x10 -11 Pa, 5x10 -11 Pa, 4x10 -11 Pa, 3x10 -11 Pa, 2x10 -11 Pa, 10 -11 Pa, 9x10 -12 Pa, 8x10 -12 Pa, 7x10 -12 Pa, 6x10 -12 Pa, 5x10 -12 Pa, 4x10 -12 Pa, 3x10 -12 Pa, 2x10 -12 Pa, 10 -12 At a pressure of Pa or lower. The vacuum unit can be configured to maintain the system 200 at a pressure of at least approximately 10 Pa. -12 Pa, 2x10 -12 Pa, 3x10 -12 Pa, 4x10 -12 Pa, 5x10 -12 Pa, 6x10 -12 Pa, 7x10 -12 Pa, 8x10 -12 Pa, 9x10 -12 Pa, 10 -11 Pa, 2x10 -11 Pa, 3x10 - 11Pa, 4x10 -11 Pa, 5x10 -11 Pa, 6x10 -11 Pa, 7x10 -11 Pa, 8x10 -11 Pa, 9x10 -11 Pa, 10 -10 Pa, 2x10 -10 Pa, 3x10 -10 Pa, 4x10 -10 Pa, 5x10 -10 Pa, 6x10 -10 Pa, 7x10 -10 Pa, 8x10 -10 Pa, 9x10 -10 Pa, 10 -9 Pa, 2x10 - 9 Pa, 3x10 -9 Pa, 4x10 -9 Pa, 5x10 -9 Pa, 6x10 -9 Pa, 7x10 -9 Pa, 8x10 -9 Pa, 9x10 -9 Pa, 10 -8 Pa, 2x10 -8 Pa, 3x10 -8 Pa, 4x10 -8 Pa, 5x10 -8 Pa, 6x10 -8 Pa, 7x10 -8 Pa, 8x10 -8 Pa, 9x10 -8 Pa, 10 -7 Pa, 2x10 -7 Pa, 3x10 -7 Pa, 4x10 -7 Pa, 5x10 -7 Pa, 6x10 -7 Pa, 7x10 -7 Pa, 8x10 -7 Pa, 9x10 -7 Pa, 10 -6 At a pressure of Pa or higher. The vacuum unit can be configured to maintain the system 200 at a pressure within the range defined by any two of the aforementioned values.

[0090] System 200 may include one or more state preparation units 250. State preparation units may include any state preparation unit described herein, such as those described herein. Figure 5 The described state preparation unit. A state preparation unit can be configured to prepare the states of multiple atoms.

[0091] System 200 may include one or more atomic reservoirs 260. The atomic reservoirs may be configured to provide one or more replacement atoms to replace one or more atoms at one or more optical trapping sites when atoms are lost from the optical trapping sites. The atomic reservoirs may be spatially separated from the optical trapping units. For example, the atomic reservoirs may be located at a distance from the optical trapping units.

[0092] Alternatively or additionally, the atomic reservoir may include a portion of the optical trapping sites of the optical trapping units. A first subset of the optical trapping sites may be used to perform quantum computing and may be referred to as a set of computationally active optical trapping sites, while a second subset of the optical trapping sites may serve as an atomic library. For example, the first subset of the optical trapping sites may include an inner array of optical trapping sites, while the second subset of the optical trapping sites includes an outer array of optical trapping sites near the inner array. The inner array may include a rectangular array, a square array, a rectangular prism array, or a cubic array of optical trapping sites.

[0093] System 200 may include one or more atom moving units 270. The atom moving units may be configured to move one or more substitutional atoms from one or more atom reservoirs 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).

[0094] System 200 may include one or more entanglement units 280. An entanglement unit may be configured to quantum mechanically entangle at least one first atom among a plurality of atoms with at least one second atom among a plurality of atoms. The first or second atom may be in a superposition state when quantum mechanically entangled. Alternatively or additionally, the first or second atom may not be in a superposition state when quantum mechanically entangled. The first and second atoms may be quantum mechanically entangled through one or more magnetic dipole interactions, induced magnetic dipole interactions, electric dipole interactions, or induced electric dipole interactions. An entanglement unit may be configured to quantum mechanically entangle any number of atoms as described herein.

[0095] Entanglement units can also be configured to quantum mechanically entangle at least a subset of atoms with at least one other atom to form one or more multi-qubit units. Multi-qubit units can include two-qubit units, three-qubit units, four-qubit units, or n-qubit units, where n can be 5, 6, 7, 8, 9, 10, or more. For example, a two-qubit unit can include a first atom quantum mechanically entangled with a second atom, a three-qubit unit can include a first atom quantum mechanically entangled with a second and a third atom, a four-qubit unit can include a first atom quantum mechanically entangled with a second, third, and fourth atom, and so on. The first, second, third, or fourth atom may be in a superposition state when quantum mechanically entangled. Alternatively or additionally, the first, second, third, or fourth atom may not be in a superposition state when quantum mechanically entangled. The first, second, third, and fourth atoms can be quantum mechanically entangled through one or more magnetic dipole interactions, induced magnetic dipole interactions, electric dipole interactions, or induced electric dipole interactions.

[0096] The entangled unit may include one or more Rydberg units. The Rydberg unit may be configured to electronically excite at least a first atom to a Rydberg state or a superposition of a Raedberg state and a lower-energy atomic state, thereby forming one or more Rydberg atoms or modified Rydberg atoms. The Rydberg unit may be configured to induce one or more quantum mechanical entanglements between the Rydberg atom or modified Rydberg atom and at least a second atom. The second atom may be located at a distance of at least approximately 200 nanometers (nm), 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 micrometer (μm), 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, or more from the Rydberg atom or modified Rydberg atom. The second atom can be located at a distance of at most approximately 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 distance of the second atom from the Rydberg atom or modified Rydberg atom can be within the range defined by any two of the foregoing values. The Rydberg unit can be configured to allow the Rydberg atom or modified Rydberg atom to relax to a lower energy atomic state, thereby forming one or more two-qubit units. The Rydberg unit can be configured to induce the Rydberg atom or modified Rydberg atom to relax to a lower energy atomic state. The Rydberg unit can be configured to drive the Rydberg atom or modified Rydberg atom to a lower energy atomic state. For example, a Rydberg unit can be configured to apply electromagnetic radiation (e.g., RF radiation or light radiation) to drive a Rydberg atom or a modified Rydberg atom to a lower-energy atomic state. A Rydberg unit can be configured to induce any number of quantum mechanical entanglements between any number of atoms of a plurality of atoms.

[0097] A Rydberg 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 wavelengths may be selected to correspond to the wavelengths of the Rydberg atoms that form or modify the Rydberg atoms. For example, the light may include wavelengths of at least about 200 nm, 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, 370 nm, 380 nm, 390 nm, 400 nm, 390 nm, 400 nm, or more. Light may include one or more wavelengths of up to approximately 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm, or fewer. Light may include one or more wavelengths within the range defined by any two of the foregoing values. For example, light may include one or more wavelengths in the range of 300 nm to 400 nm.

[0098] Rydberg units can be configured to induce two-photon transitions to generate entanglement. Rydberg units can be configured to induce two-photon transitions to generate entanglement between two atoms. Rydberg units can be configured to selectively induce two-photon transitions to selectively generate entanglement between two atoms. For example, a Rydberg unit can be configured to direct electromagnetic energy (e.g., light energy) to a specific optical trapping site to selectively induce two-photon transitions, thereby selectively generating entanglement between two atoms. The two atoms may be trapped at nearby optical trapping sites. For example, the two atoms may be trapped in adjacent optical trapping sites. First light and second light from a first source and a second source can be used, respectively, to induce two-photon transitions. The first source and the second source can each include any source described herein (e.g., any laser described herein). The first source can be the same as or similar to the source used to perform the single-qubit operations described herein. Alternatively, different sources can be used to perform the single-qubit operations and induce two-photon transitions to generate entanglement. The first light source may emit light of one or more wavelengths including those in the visible region of the spectrum (e.g., in the range of 400 nm to 800 nm or 650 nm to 700 nm). The second light source may emit light of one or more wavelengths including those in the ultraviolet region of the spectrum (e.g., in the range of 200 nm to 400 nm or 300 nm to 350 nm). The first and second light sources may emit light having substantially equal and opposite spatially correlated frequency shifts.

[0099] Rydberg atoms or modified Rydberg atoms can include Rydberg states that may have sufficiently strong interatomic interactions with nearby atoms (e.g., atoms trapped near optical trapping sites) to enable multi-qubit operations. Rydberg states can include at least about 50, 60, 70, 80, 90, 100 or more principal quantum numbers. Rydberg states can include at most about 100, 90, 80, 70, 60, 50 or fewer principal quantum numbers. Rydberg states can include principal quantum numbers within the range defined by any two of the foregoing values. Rydberg states may interact with nearby atoms through van der Waals interactions. Van der Waals interactions may alter the atomic energy levels of the atom.

[0100] Selectively exciting an atom to a Rydberg level enables multi-qubit operations. Multi-qubit operations can include two-qubit, three-qubit, or n-qubit operations, where n is 4, 5, 6, 7, 8, 9, 10, or more. Two-photon transitions can be used to excite an atom from its ground state (e.g., ...) 1 The ground state (S0) is excited to a Rydberg state (e.g., n). 3 The S1 state (where n is the principal quantum number described in this paper). State selectivity can be achieved through a combination of laser polarization and spectral selectivity. As described in this paper, two-photon transitions can be achieved using first and second laser sources. The first laser source can emit π-polarized light, which may not change the projection of the atomic angular momentum along the magnetic field. The second laser can emit circularly polarized light, which may 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 the Rydberg level. However, the Rydberg level may be more sensitive to the magnetic field than the ground state, and thus large splits (e.g., approximately 100 s MHz) can be easily obtained. This spectral selectivity allows for state-selective excitation to the Rydberg level.

[0101] Multi-qubit operations (such as two-qubit, three-qubit, four-qubit, etc.) may rely on energy shifts in energy levels due to van der Waals interactions as described herein. Such shifts can prevent the excitation of one atom, conditional on the state of another atom, or alter the coherent excitation dynamics of a diatomic system to implement a two-qubit operation. In some cases, “modified states” can be generated under continuous drive to implement a two-qubit operation without requiring full excitation to the Rydberg level (e.g., as described in www.arxiv.org / abs / 1605.05207, which is incorporated herein by reference in its entirety for all purposes).

[0102] System 200 may include one or more second electromagnetic delivery units ( Figure 2(Not shown in the image). The second electromagnetic delivery unit may include any electromagnetic delivery unit described herein, such as those described herein. Figure 4 The electromagnetic delivery unit is described. The first and second electromagnetic delivery units can be the same. The first and second electromagnetic delivery units can also be different. The second electromagnetic delivery unit can be configured to apply a second electromagnetic energy to one or more multi-qubit units. The second electromagnetic energy can include one or more pulse sequences. The first electromagnetic energy can precede, occur simultaneously with, or follow the second electromagnetic energy.

[0103] A pulse sequence may include any number of pulses. For example, a pulse sequence may include at least approximately 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000 or more pulses. A pulse sequence may include up to approximately 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 pulses. A pulse sequence may include a certain number of pulses within the range defined by any two of the foregoing values. Each pulse in a pulse sequence can include any pulse shape, such as any pulse shape described herein.

[0104] Pulse sequences can be configured to reduce the duration required to achieve multi-qubit operations, as described herein (e.g., with respect to Example 3). For example, pulse sequences can include durations of at least approximately 10 nanoseconds (ns), 20 ns, 30 ns, 40 ns, 50 ns, 60 ns, 70 ns, 80 ns, 90 ns, 100 ns, 200 ns, 300 ns, 400 ns, 500 ns, 600 ns, 700 ns, 800 ns, 900 ns, 1 microsecond (µs), 2µs, 3µs, 4µs, 5µs, 6µs, 7µs, 8µs, 9µs, 10µs, 20µs, 30µs, 40µs, 50µs, 60µs, 70µs, 80µs, 90µs, 100µs, or more. Pulse sequences may include durations of up to approximately 100µs, 90µs, 80µs, 70µs, 60µs, 50µs, 40µs, 30µs, 20µs, 10µs, 9µs, 8µs, 7µs, 6µs, 5µs, 4µs, 3µs, 2µs, 1µs, 900ns, 800ns, 700ns, 600ns, 500ns, 400ns, 300ns, 200ns, 100ns, 90ns, 80ns, 70ns, 60ns, 50ns, 40ns, 30ns, 20ns, 10ns, or less. Pulse sequences may include durations within the range defined by any two of the foregoing values.

[0105] Pulse sequences can be configured to increase the fidelity of multi-qubit operations, as described herein. For example, pulse sequences can be implemented with at least approximately 0.5, 0.6, 0.7, 0.8, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99, 0.991, 0.992, 0.993, 0.994, 0.995, 0.996, 0.997, 0.998, 0.999, 0.9991, 0.9992, 0.9993, 0.9994, 0.9995, 0.9996, 0.999 7. Multi-qubit operations with fidelity of 0.9998, 0.9999, 0.99991, 0.99992, 0.99993, 0.99994, 0.99995, 0.99996, 0.99997, 0.99998, 0.99999, 0.999991, 0.999992, 0.999993, 0.999994, 0.999995, 0.999996, 0.999997, 0.999998, 0.999999 or higher. The pulse sequence can achieve values ​​of up to approximately 0.999999, 0.999998, 0.999997, 0.999996, 0.999995, 0.999994, 0.999993, 0.999992, 0.999991, 0.99999, 0.99998, 0.99997, 0.99996, 0.99995, 0.99994, 0.99993, 0.99992, 0.99991, 0.9999, 0.9998, Multi-qubit operations with fidelity of 0.9997, 0.9996, 0.9995, 0.9994, 0.9993, 0.9992, 0.9991, 0.999, 0.998, 0.997, 0.996, 0.995, 0.994, 0.993, 0.992, 0.991, 0.99, 0.98, 0.97, 0.96, 0.95, 0.94, 0.93, 0.92, 0.91, 0.9, 0.8, 0.7, 0.6, 0.5, or less. Pulse sequences can realize multi-qubit operations with fidelity within the range defined by any two of the aforementioned values.

[0106] Pulse sequences can enable multi-qubit operations on non-adiabatic timescales while effectively maintaining adiabatic dynamics. For example, pulse sequences can include one or more of the following: adiabatic (STA) pulse sequence shortcuts, transition-free quantum drive (TQD) pulse sequences, hyperadiabatic pulse sequences, antiadiabatic drive pulse sequences, adiabatic derivative elimination (DRAG) pulse sequences, and weakly anharmonic (Wah Wah) pulse sequences with average Hamiltonian. For example, the pulse sequences might resemble those described in MV Berry, “Transition-free quantum drive,” Acta Physica Sinica A: Mathematica & Theory 42(36), 365303 (2009), www.doi.org / 10.1088 / 1751-8113 / 42 / 36 / 365303; Y.-Y. Jau et al., “Entangled atomic spins with strong Rydberg modified interactions,” Nature Physics 12(1), 71-74 (2016); T. Keating et al., “Robust quantum logic in neutral atoms via adiabatic Rydberg modification,” Physical Review A 91, 012337 (2015); A. Mitra et al., “Robust Mölmer-Sörenson gates in neutral atoms using fast adiabatic Rydberg modification,” www.arxiv.org / abs / 1911.04045 (2019); or LS The pulse sequence of Theis et al., “Using DRAG control to combat non-adiabatic systems: state 10 years later,” European Physical Letters 123(6), 60001(2018), each of which is incorporated herein by reference in its entirety for all purposes.

[0107] Pulse sequences may also include one or more optimally controlled pulse sequences. Optimally controlled pulse sequences may originate from one or more processes, including the Gradient Ascending Pulse Engineering (GRAPE) method, the Krotov method, the chopper basis method, the chopper random basis method (CRAB), the Nelder-Mead method, the GROUP method using parameterized gradient optimization, the genetic algorithm method, and the Gradient Optimization of Analytical Control (GOAT) method. For example, pulse sequences may resemble those described in N. Khaneja et al., “Optimal Control of Coupled Spin Dynamics: Design of NMR Pulse Sequences via Gradient Ascending Algorithm,” Journal of Magnetic Resonance 172(2), 296-305 (2005); or J.M. Merrill et al., “Procedures for Compensating Pulse Sequences in Quantum Computation,” Progress in Chemical Physics 154, 241-294 (2014), each of which is incorporated herein by reference in its entirety for all purposes. Pulse sequences may also include composite pulses. Examples of composite pulses include, but are not limited to, broadband (e.g., BB1), narrowband, passband, compensated off-resonance pulse sequences (CORPSE), short composite rotations of varying lengths (SCROFULOUS), Solovay-Kitaev (SK) sequences, and Knill pulses. Composite pulses can be used in systems with single-qubit gates.

[0108] cloud computing

[0109] System 200 can be accessed via networks described herein (such as those described herein). Figure 1 The network described herein is operatively coupled to the digital computer described herein (such as the one described herein). Figure 1 The aforementioned digital computer. The network may include a cloud computing network.

[0110] Optical capture unit

[0111] Figure 3A An example of an optical capturing unit 210 is shown. The optical capturing unit can be configured to generate multiple spatially distinct optical capturing sites 211, as described herein. For example, as... Figure 3B As shown, the optical capturing unit can be configured to generate a first optical capturing site 211a, a second optical capturing site 211b, a third optical capturing site 211c, a fourth optical capturing site 211d, a fifth optical capturing site 211e, a sixth optical capturing site 211f, a seventh optical capturing site 211g, an eighth optical capturing site 211h, and a ninth optical capturing site 211i, as shown. Figure 3A As depicted in the figure. Multiple spatially distinct optical trapping sites can be configured to trap multiple atoms, such as a first atom 212a, a second atom 212b, a third atom 212c, and a fourth atom 212d, as shown in the figure. Figure 3A As described in the text. For example... Figure 3B As depicted, each optical trapping site can be configured to trap a single atom. Figure 3B As shown, some optical trapping sites may be empty (i.e., uncaptured atoms).

[0112] like Figure 3B As shown, multiple optical capture points can comprise a two-dimensional (2D) array. The 2D array can be perpendicular to... Figure 3A The optical axis of the optical components of the optical trapping unit depicted in the figure. Alternatively, the multiple optical trapping sites may comprise a one-dimensional (1D) array or a three-dimensional (3D) array.

[0113] Although Figure 3B The optical trapping unit 210 is described as comprising nine optical trapping sites filled with four atoms, but the optical trapping unit 210 can be configured to generate any number of spatially distinct optical trapping sites as described herein and can be configured to trap any number of atoms as described herein.

[0114] Each of the multiple optical trapping sites may be spatially separated from each other by a distance of at least approximately 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 µm, 2 µm, 3 µm, 4 µm, 5 µm, 6 µm, 7 µm, 8 µm, 9 µm, 10 µm or greater. Each optical trapping site may also be spatially separated from each other by a distance of at most approximately 10 µm, 9 µm, 8 µm, 7 µm, 6 µm, 5 µm, 4 µm, 3 µm, 2 µm, 1 µm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm or less. Each optical trapping site may also be spatially separated from each other by a distance within the range defined by any two of the aforementioned values.

[0115] Optical trapping sites can include one or more optical tweezers. Optical tweezers can 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 can include a strong electric field gradient. Atoms can be attracted or repelled along the electric field gradient to the center of the laser beam, which may contain the strongest electric field. Optical trapping sites can include one or more optical lattice sites in one or more optical latticees. Optical trapping sites can include one or more optical lattice sites in one-dimensional (1D), two-dimensional (2D), or three-dimensional (3D) optical lattices. For example, optical trapping sites can include one or more optical lattice sites in one or more two-dimensional optical lattices, such as... Figure 3B As depicted in the text.

[0116] Optical lattices can be generated by interfering with back-propagating light (such as back-propagating laser light) to produce periodic, continuous standing wave patterns with minimum and maximum intensities along a specific direction. One-dimensional optical lattices can be generated by interfering with a pair of back-propagating beams. Two-dimensional optical lattices can be generated by interfering with two pairs of back-propagating beams. 3D optical lattices can be generated by interfering with three pairs of back-propagating beams. The beams can be generated from different light sources or from the same light source. Therefore, optical lattices can be generated from at least approximately 1, 2, 3, 4, 5, 6 or more light sources, or at most approximately 6, 5, 4, 3, 2 or 1 light source.

[0117] Return to Figure 3A As described herein, an optical trapping unit may include one or more light sources configured to emit light to generate multiple optical trapping sites as described herein. For example, an optical trapping unit may include a single light source 213, such as... Figure 3A As depicted in [the text]. Although in [the text] Figure 3A The image is described as including a single light source, but the optical capture unit may include any number of light sources, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more light sources, or 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.

[0118] The laser may include one or more continuous-wave lasers. The laser may include one or more pulsed lasers. The laser may include one or more gas lasers, such as one or more helium-neon (HeNe) lasers, argon (Ar) lasers, krypton (Kr) lasers, xenon (Xe) ion lasers, nitrogen (N2) lasers, carbon dioxide (CO2) lasers, carbon monoxide (CO) lasers, transversely excited 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. Lasers may include one or more dye lasers.

[0119] 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, and manganese (m) metal vapor lasers. N Metal vapor laser or manganese chloride (MnCl2) metal vapor laser.

[0120] 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 Nd:YAG lasers, Nd / Cr:YAG lasers, Er:YAG lasers, Nd:YLF lasers, Nd:YVO4 lasers, Nd:YCOB lasers, Nd:glass lasers, Ti:sapphire lasers, Tm:YAG lasers, and others. Yttrium aluminum garnet (Yb:YAG) lasers, ytterbium-doped glass (Yt:glass) lasers, holmium-ytterbium aluminum garnet (Ho:YAG) lasers, chromium-doped zinc selenide (Cr:ZnSe) lasers, cerium-doped lithium strontium aluminum fluoride (Ce:LiSAF) lasers, cerium-doped lithium calcium aluminum fluoride (Ce:LiCAF) lasers, erbium-doped glass (Er:glass) lasers, erbium-ytterbium co-doped glass (Er / Yt:glass) lasers, uranium-doped calcium fluoride (U:CaF2) lasers, or samarium-doped calcium fluoride (Sm:CaF2) lasers.

[0121] Lasers may include one or more semiconductor lasers or diode lasers, such as one or more gallium nitride (GaN) lasers, indium gallium nitride (InGaN) lasers, aluminum gallium indium phosphide (AlGaInP) lasers, aluminum gallium arsenide (AlGaAs) lasers, indium gallium phosphide (InGaAsP) lasers, vertical cavity surface-emitting lasers (VCSELs) or quantum cascade lasers.

[0122] Lasers can emit continuous-wave laser light. Lasers can also emit pulsed laser light. Lasers can have pulsed light outputs of at least approximately 1 femtosecond (fs), 2 fs, 3 fs, 4 fs, 5 fs, 6 fs, 7 fs, 8 fs, 9 fs, 10 fs, 20 fs, 30 fs, 40 fs, 50 fs, 60 fs, 70 fs, 80 fs, 90 fs, 100 fs, 200 fs, 300 fs, 400 fs, 500 fs, 600 fs, 700 fs, 800 fs, 900 fs, 1 picosecond (ps), 2 ps, 3 ps, 4 ps, 5 ps, 6 ps, 7 ps, 8 ps, 9 ps, 10 ps, ​​20 ps, ​​30 ps, ​​40 ps, ​​50 ps, ​​and 60 ps. Pulse lengths of s, 70ps, 80ps, 90ps, 100ps, 200ps, 300ps, 400ps, 500ps, 600ps, 700ps, 800ps, 900ps, 1 nanosecond (ns), 2ns, 3ns, 4ns, 5ns, 6ns, 7ns, 8ns, 9ns, 10ns, 20ns, 30ns, 40ns, 50ns, 60ns, 70ns, 80ns, 90ns, 100ns, 200ns, 300ns, 400ns, 500ns, 600ns, 700ns, 800ns, 900ns, 1,000ns, or more. Lasers can have speeds of up to approximately 1,000 ns, 900 ns, 800 ns, 700 ns, 600 ns, 500 ns, 400 ns, 300 ns, 200 ns, 100 ns, 90 ns, 80 ns, 70 ns, 60 ns, 50 ns, 40 ns, 30 ns, 20 ns, 10 ns, 9 ns, 8 ns, 7 ns, 6 ns, 5 ns, 4 ns, 3 ns, 2 ns, 1 ns, 900 ps, ​​800 ps, ​​700 ps, ​​600 ps, ​​500 ps, ​​400 ps, ​​300 ps, ​​200 ps, ​​100 ps, ​​90 ps, ​​and 80 ps. Pulse lengths of s, 70ps, 60ps, 50ps, 40ps, 30ps, 20ps, 10ps, 9ps, 8ps, 7ps, 6ps, 5ps, 4ps, 3ps, 2ps, 1ps, 900fs, 800fs, 700fs, 600fs, 500fs, 400fs, 300fs, 200fs, 100fs, 90fs, 80fs, 70fs, 60fs, 50fs, 40fs, 30fs, 20fs, 10fs, 9fs, 8fs, 7fs, 6fs, 5fs, 4fs, 3fs, 2fs, 1fs, or less. The laser can have pulse lengths within the range defined by any two of the foregoing values.

[0123] Lasers can have frequencies of at least approximately 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, etc. kHz, 100kHz, 200kHz, 300kHz, 400kHz, 500kHz, 600kHz, 700kHz, 800kHz, 900kHz, 1 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 rates. Lasers can have frequencies up to approximately 1,000MHz, 900MHz, 800MHz, 700MHz, 600MHz, 500MHz, 400MHz, 300MHz, 200MHz, 100MHz, 90MHz, 80MHz, 70MHz, 60MHz, 50MHz, 40MHz, 30MHz, 20MHz, 10MHz, 9MHz, 8MHz, 7MHz, 6MHz, 5MHz, 4MHz, 3MHz, 2MHz, 1MHz, 900kHz, 800kHz, 700kHz, 600kHz, 500kHz, 400kHz, 300kHz, 200kHz, and 100kHz. Hz, 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 lower repetition rates.The laser can have a repetition rate within the range defined by any two of the aforementioned values.

[0124] The laser can emit wavelengths of at least approximately 1 nanojoule (nJ), 2 nJ, 3 nJ, 4 nJ, 5 nJ, 6 nJ, 7 nJ, 8 nJ, 9 nJ, 10 nJ, 20 nJ, 30 nJ, 40 nJ, 50 nJ, 60 nJ, 70 nJ, 80 nJ, 90 nJ, 100 nJ, 200 nJ, 300 nJ, 400 nJ, 500 nJ, 600 nJ, 700 nJ, 800 nJ, 900 nJ, 1 microjoule (µJ), 2 µJ, 3 µJ, 4 µJ, 5 µJ, 6 µJ, 7 µJ, 8 µJ, 9 µJ, 10 µJ, 20 µJ, 30 µJ, 40 µJ, 50 µJ, 60 µJ, and 70 µJ. J, 80µJ, 90µJ, 100µJ, 200µJ, 300µJ, 400µJ, 500µJ, 600µJ, 700µJ, 800µJ, 900µJ, at least 1 millijoules (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 pulse energy of at least 1 joule (J) or more. The laser can emit pulses with frequencies up to approximately 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, and 80 µJ. The laser can emit light with pulse energies of 70µJ, 60µJ, 50µJ, 40µJ, 30µJ, 20µJ, 10µJ, 9µJ, 8µJ, 7µJ, 6µJ, 5µJ, 4µJ, 3µJ, 2µJ, 1µJ, 900nJ, 800nJ, 700nJ, 600nJ, 500nJ, 400nJ, 300nJ, 200nJ, 100nJ, 90nJ, 80nJ, 70nJ, 60nJ, 50nJ, 40nJ, 30nJ, 20nJ, 10nJ, 9nJ, 8nJ, 7nJ, 6nJ, 5nJ, 4nJ, 3nJ, 2nJ, 1nJ, or less. The laser can emit light with pulse energies within the range defined by any two of the foregoing values.

[0125] Lasers can emit power at least approximately 1 microwatt (µW), 2µW, 3µW, 4µW, 5µW, 6µW, 7µW, 8µW, 9µW, 10µW, 20µW, 30µW, 40µW, 50µW, 60µW, 70µW, 80µW, 90µW, 100µW, 200µW, 300µW, 400µW, 500µW, 600µW, 700µW, 800µW, 900µW, 1 milliwatt (mW), 2mW, 3mW, 4mW, 5mW, 6mW, 7mW, 8mW, 9mW, 10mW, 20mW, 30mW, 40µW, etc. Light with average power of mW, 50mW, 60mW, 70mW, 80mW, 90mW, 100mW, 200mW, 300mW, 400mW, 500mW, 600mW, 700mW, 800mW, 900mW, 1 watt (W), 2W, 3W, 4W, 5W, 6W, 7W, 8W, 9W, 10W, 20W, 30W, 40W, 50W, 60W, 70W, 80W, 90W, 100W, 200W, 300W, 400W, 500W, 600W, 700W, 800W, 900W, 1,000W or more. The laser can emit power at frequencies up to approximately 1,000W, 900W, 800W, 700W, 600W, 500W, 400W, 300W, 200W, 100W, 90W, 80W, 70W, 60W, 50W, 40W, 30W, 20W, 10W, 9W, 8W, 7W, 6W, 5W, 4W, 3W, 2W, 1W, 900mW, 800mW, 700mW, 600mW, 500mW, 400mW, 300mW, 200mW, 100mW, 90mW, 80mW, 70mW, 60mW, 50mW, 60mW, and 50mW. The laser emits light with average power ranging from mW, 40mW, 30mW, 20mW, 10mW, 9mW, 8mW, 7mW, 6mW, 5mW, 4mW, 3mW, 2mW, 1mW, 900µW, 800µW, 700µW, 600µW, 500µW, 400µW, 300µW, 200µW, 100µW, 90µW, 80µW, 70µW, 60µW, 50µW, 40µW, 30µW, 20µW, 10µW, 9µW, 8µW, 7µW, 6µW, 5µW, 4µW, 3µW, 2µW, 1µW, or more. The laser can emit light with power within the range defined by any two of the foregoing values.

[0126] Lasers can emit light including one or more wavelengths from the ultraviolet (UV), visible, or infrared (IR) portions of the electromagnetic spectrum. Lasers can emit wavelengths including at least approximately 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, and 520 nm. nanometer , 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 Light of one or more wavelengths, including 0nm, 1,170nm, 1,180nm, 1,190nm, 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, etc.The laser can emit wavelengths including up to approximately 1,400 nm, 1,390 nm, 1,380 nm, 1,370 nm, 1,360 nm, 1,350 nm, 1,340 nm, 1,330 nm, 1,320 nm, 1,310 nm, 1,300 nm, 1,290 nm, 1,280 nm, 1,270 nm, 1,260 nm, 1,250 nm, 1,240 nm, 1,230 nm, 1,220 nm, 1,210 nm, 1,200 nm, 1,190 nm, 1,180 nm, 1,170 nm, and 1,1 60nm, 1,150nm, 1,140nm, 1,130nm, 1,120nm, 1,110nm, 1,100nm, 1,090nm, 1,080nm, 1,070nm, 1,060nm, 1,050nm, 1,040nm, 1,0 30nm, 1,020nm, 1,010nm, 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870 nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700n m, 690nm, 680nm, 670nm, 660nm, 650nm, 640nm, 630nm, 620nm, 610nm, 600nm, 590nm, 580nm, 570nm, 560nm, 550nm, 540nm, 530nm, The laser emits light of one or more wavelengths from the range defined by any two of the foregoing values: 520nm, 510nm, 500nm, 490nm, 480nm, 470nm, 460nm, 450nm, 440nm, 430nm, 420nm, 410nm, 400nm, 390nm, 380nm, 370nm, 360nm, 350nm, 340nm, 330nm, 320nm, 310nm, 300nm, 290nm, 280nm, 270nm, 260nm, 250nm, 240nm, 230nm, 220nm, 210nm, and 200nm.

[0127] The laser can emit light with a wavelength of at least approximately 1x10⁻⁶. -15 nm, 2x10 -15 nm, 3x10 -15 nm, 4x10 -15 nm, 5x10- 15 nm、6x10 -15 nm、7x10 -15 nm、8x10 -15 nm、9x10 -15 nm、1x10 -14 nm、2x10 -14 nm、3x10 -14 nm、4x10 -14 nm、5x10 -14 nm、6x10 -14 nm、7x10 -14 nm、8x10 -14 nm、9x10 -14 nm、1x10 -13 nm、2x10 -13 nm、3x10 -13 nm、4x10 -13 nm、5x10 -13 nm、6x10 -13 nm、7x10 -13 nm、8x10 -13 nm、9x10 -13 nm、1x10 -12 nm、2x10 -12 nm、3x10 -12 nm、4x10 -12 nm、5x10 -12 nm、6x10 -12 nm、7x10 -12 nm、8x10 -12 nm、9x10 -12 nm、1x10 -11 nm、2x10 -11 nm、3x10 -11 nm、4x10 -11 nm、5x10 -11 nm、6x10 -11 nm、7x10 -11 nm、8x10 -11 nm、9x10 -11 nm、1x10 -10 nm、2x10 -10 nm、3x10 -10 nm、4x10 -10 nm、5x10 -10 nm、6x10 -10 nm、7x10 -10 nm、8x10 -10 nm、9x10-10 nm、1x10 -9 nm、2x10 - 9 nm、3x10 -9 nm、4x10 -9 nm、5x10 -9 nm、6x10 -9 nm、7x10 -9 nm、8x10 -9 nm、9x10 -9 nm、1x10 -8 nm、2x10 - 8 nm、3x10 -8 nm、4x10 -8 nm、5x10 -8 nm、6x10 -8 nm、7x10 -8 nm、8x10 -8 nm、9x10 -8 nm、1x10 -7 nm、2x10 - 7 nm、3x10 -7 nm、4x10 -7 nm、5x10 -7 nm、6x10 -7 nm、7x10 -7 nm、8x10 -7 nm、9x10 -7 nm、1x10 -6 nm、2x10 - 6 nm、3x10 -6 nm、4x10 -6 nm、5x10 -6 nm、6x10 -6 nm、7x10 -6 nm、8x10 -6 nm、9x10 -6 nm、1x10 -5 nm、2x10 - 5 nm、3x10 -5 nm、4x10 -5 nm、5x10 -5 nm、6x10 -5 nm、7x10 -5 nm、8x10 -5 nm、9x10 -5 nm、1x10 -4nm, 2x10 - 4 nm, 3x10 -4 nm, 4x10 -4 nm, 5x10 -4 nm, 6x10 -4 nm, 7x10 -4 nm, 8x10 -4 nm, 9x10 -4 nm, 1x10 -3 Lasers can emit light with a bandwidth of at most approximately 1 x 10 nm. -3 nm, 9x10 -4 nm, 8x10 -4 nm, 7x10 -4 nm, 6x10 -4 nm, 5x10 -4 nm, 4x10 -4 nm, 3x10 -4 nm, 2x10 -4 nm, 1x10 -4 nm, 9x10 -5 nm, 8x10 -5 nm, 7x10 -5 nm, 6x10 -5 nm, 5x10 -5 nm, 4x10 -5 nm, 3x10 -5 nm, 2x10 -5 nm, 1x10 -5 nm, 9x10 -6 nm, 8x10 -6 nm, 7x10 -6 nm, 6x10 -6 nm, 5x10 -6 nm, 4x10 -6 nm, 3x10 -6 nm, 2x10 -6 nm, 1x10 -6 nm, 9x10 -7 nm, 8x10 -7 nm, 7x10 -7 nm, 6x10 -7 nm, 5x10 -7 nm, 4x10 -7 nm, 3x10 -7 nm, 2x10 -7 nm, 1x10 -7 nm, 9x10 -8 nm, 8x10 -8 nm, 7x10-8 nm、6x10 -8 nm、5x10 -8 nm、4x10 -8 nm、3x10 -8 nm、2x10 -8 nm、1x10 -8 nm、9x10 -9 nm、8x10 -9 nm、7x10 -9 nm、6x10 -9 nm、5x10 -9 nm、4x10 -9 nm、3x10 -9 nm、2x10 -9 nm、1x10 -9 nm、9x10 -10 nm、8x10 -10 nm、7x10 -10 nm、6x10 - 10 nm、5x10 -10 nm、4x10 -10 nm、3x10 -10 nm、2x10 -10 nm、1x10 -10 nm、9x10 -11 nm、8x10 -11 nm、7x10 -11 nm、6x10 -11 nm、5x10 -11 nm、4x10 -11 nm、3x10 -11 nm、2x10 -11 nm、1x10 -11 nm、9x10 -12 nm、8x10 -12 nm、7x10 -12 nm、6x10 -12 nm、5x10 -12 nm、4x10 -12 nm、3x10 -12 nm、2x10 -12 nm、1x10 -12 nm、9x10 -13 nm、8x10 -13 nm、7x10 -13 nm、6x10 -13 nm、5x10 -13 nm、4x10 -13 nm、3x10-13 nm, 2x10 -13 nm, 1x10 -13 nm, 9x10 -14 nm, 8x10 -14 nm, 7x10 -14 nm, 6x10 -14 nm, 5x10 -14 nm, 4x10 -14 nm, 3x10 -14 nm, 2x10 -14 nm, 1x10 -14 nm, 9x10 -15 nm, 8x10 -15 nm, 7x10 -15 nm, 6x10 -15 nm, 5x10 -15 nm, 4x10 -15 nm, 3x10 -15 nm, 2x10 -15 nm, 1x10 -15 Lasers can emit light with a bandwidth of nm or less.

[0128] A light source can be configured to emit light tuned to one or more magic wavelengths corresponding to multiple atoms. The magic wavelengths corresponding to atoms can include any wavelength of light that causes equal or nearly equal polarization rates in 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 this magic wavelength can cause equal or nearly equal differential light shifts in the first and second atomic states. This effectively decouples the first and second atomic states from the motion of the atoms. The magic wavelength can utilize one or more scalar or tensor light shifts. Scalar or tensor light shifts can depend on the magneton energy levels within the first and second atomic states.

[0129] For example, group III atoms and metastable states of alkaline earths or similar alkaline earths may have relatively large tensor shifts, the angle of which relative to the applied magnetic field can be tuned to induce a balance between scalar and tensor shifts, and to impart zero or near-zero differential optical shift between the first and second atomic states. (Angle) θ Tuning can be achieved by selecting the polarization of the emitted light. For example, when the emitted light is linearly polarized, the total polarization index α can be written as the scalar component α. scalar and tensor components α tensor The sum:

[0130]

[0131] By choosing appropriately θ The polarization rates of the first and second atomic states can be chosen to be equal or nearly equal, corresponding to zero or near-zero differential optical offset, and the motion of the atoms can be decoupled.

[0132] The light source can be configured to direct light to one or more optical modulators (OMs), which are configured to generate multiple optical trapping sites. For example, the optical trapping unit may include an OM214 configured to generate multiple optical trapping sites. Although in Figure 3A The device is described as including one optical acquisition unit (OM), but the optical acquisition 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. An OM may include one or more digital micromirror devices (DMDs). An OM may include one or more liquid crystal devices, such as one or more liquid crystal on silicon (LCoS) devices. An OM may include one or more spatial light modulators (SLMs). An OM may include one or more acousto-optic deflectors (AODs) or acousto-optic modulators (AOMs). An OM may include one or more electro-optic deflectors (EODs) or electro-optic modulators (EOMs).

[0133] An optical element (OM) can be optically coupled to one or more optical elements to generate a regular array of optical trapping sites. For example, an OM can be optically coupled to optical element 219, such as... Figure 3A As shown in the diagram. Optical elements may include lenses or microscope objectives configured to redirect light from the OM to form a regular rectangular grid of optical capture sites.

[0134] For example, such as Figure 3A As shown, the OM can include an SLM, DMD, or LCoS device. The SLM, DMD, or LCoS device can image onto the back focal plane of the microscope objective. This allows for the generation of optical capture sites in arbitrary configurations in two or three dimensions.

[0135] Alternatively or additionally, the OM may include a first AOD and a second AOD. The active regions of the first AOD and the second AOD can be imaged onto the back focal plane of the microscope objective. The output of the first AOD can be optically coupled to the input of the second AOD. In this way, the second AOD can replicate the optical output of the first AOD. This can allow the generation of optical trapping sites in two or three dimensions.

[0136] Alternatively or additionally, the OM may include static optical elements, such as one or more microlens arrays or holographic optical elements. Static optical elements can be imaged onto the back focal plane of a microscope objective. This allows for the generation of optical capture sites in arbitrary configurations in two or three dimensions.

[0137] An optical trapping unit may include one or more imaging units configured to acquire one or more images of the spatial configuration of a plurality of atoms trapped within an optical trapping site. For example, an optical trapping unit may include imaging unit 215. Although in Figure 3A The image is described as comprising a single imaging unit, but 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 unit. The imaging unit may include one or more lenses or objectives. 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 image 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.

[0138] The optical capture 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 multiple atoms captured within the optical capture site based on an image obtained by the imaging unit. For example, the optical capture unit may include spatial configuration AI unit 216. While in Figure 3A The optical capture unit is described as comprising a single spatially configured AI unit, but may include any number of spatially configured AI units, such as at least approximately 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more, or at most approximately 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1. AI operations may include any machine learning (ML) or reinforcement learning (RL) operations described herein.

[0139] The optical trapping unit may include one or more atomic rearrangement units configured to impart a modified spatial arrangement of multiple atoms trapped through the optical trapping site based on one or more images obtained by the imaging unit. For example, the optical trapping unit may include atomic rearrangement unit 217. Although in Figure 3AThe unit is described as comprising 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.

[0140] The optical capture unit may include one or more spatial arrangement artificial intelligence (AI) units configured to perform one or more AI operations to determine a modified spatial arrangement of multiple atoms captured within the optical capture site based on an image obtained by the imaging unit. For example, the optical capture unit may include spatial arrangement AI unit 218. While in Figure 3A The object is described as comprising a single spatially arranged AI unit, but 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 units. The AI ​​operation may include any machine learning (ML) or reinforcement learning (RL) operation described herein.

[0141] In some cases, spatial configuration AI units and spatial arrangement AI units can be integrated into an integrated AI unit. The optical capture unit may include any number of integrated AI units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more integrated AI units, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 integrated AI unit.

[0142] Atom rearrangement units can be configured to alter the spatial arrangement to achieve an increase in the fill factor of multiple optical trapping sites. The fill factor can be defined as the ratio of the number of computationally active optical trapping sites occupied by one or more atoms to the total number of computationally active optical trapping sites available in the optical trapping unit or a portion of the optical trapping unit. For example, the initial loading of atoms within a computationally active optical trapping site may result in a fill factor of less than 100%, 90%, 80%, 70%, 60%, 50%, or less, such that the atoms occupy less than 100%, 90%, 70%, 60%, 50%, or less of the available computationally active optical trapping sites, respectively. Atom rearrangement may be necessary to achieve a fill factor of at least approximately 50%, 60%, 70%, 80%, 90%, or 100%. By analyzing the imaging information obtained by the imaging unit, the atomic rearrangement unit can obtain a fill factor of at least approximately 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. Atomic rearrangement units can achieve fill factors of up to approximately 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50%, or less. Atomic rearrangement units can obtain fill factors within the range defined by any two of the aforementioned values.

[0143] For example, Figure 3C An example of an optical trapping unit partially filled with atoms is shown. (e.g.) Figure 3C As depicted, the initial loading of atoms within the optical trapping sites can cause a fill factor of 44.4% (4 atoms fill 9 available optical trapping sites). This is achieved by transferring atoms from different regions of the optical trapping unit ( Figure 3C A much higher fill factor can be obtained by moving atoms (not shown) to an unoccupied optical trapping site or by moving atoms from the atom reservoir described herein, such as Figure 3D As shown in the image.

[0144] Figure 3DAn example of an optical trapping unit completely filled with atoms is shown. Figure 3D As depicted, 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 (Not shown) is moved or moved by moving atoms from the atom reservoir described herein. Therefore, after the atoms are rearranged within the optical trapping sites, the fill factor can be significantly improved. For example, a fill factor of up to 100% can be obtained (such as 9 atoms filling 9 available optical trapping sites, as...). Figure 3D (as shown in the image).

[0145] Atomic rearrangement can be achieved by (i) acquiring an image of the optical trapping cells and identifying filled and unfilled optical trapping sites, (ii) determining a set of moves to move atoms from filled optical trapping sites to unfilled optical trapping sites, and (iii) moving atoms from filled optical trapping sites to unfilled optical trapping sites. Operations (i), (ii), and (iii) can be performed iteratively until a large fill factor is obtained. Operation (iii) may include converting the moves identified in operation (ii) into waveforms that can be sent to an arbitrary waveform generator (AWG) and using the AWG to drive the AOD to move atoms. The set of moves can be determined using the Hungarian algorithm described in W. Lee et al., “Forming Defect-Free Atom Arrays Using the Hungarian Rearrangement Algorithm,” Physical Review A 95,053424 (2017), which is incorporated herein by reference in its entirety for all purposes.

[0146] Electromagnetic delivery unit

[0147] 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 of a plurality of atoms, as described herein. The electromagnetic delivery unit may include one or more light sources, such as any light source described herein. The electromagnetic energy may include light energy. The light energy may include any repetition rate, pulse energy, average power, wavelength, or bandwidth described herein.

[0148] 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 propagation time (IMPATT) diodes, or microwave masers. The electromagnetic energy may include microwave energy or RF energy. The RF energy may include at least approximately 1 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, or 2 meters. One or more wavelengths of 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 km, 2km, 3km, 4km, 5km, 6km, 7km, 8km, 9km, 10km or greater. RF energy can include up to approximately 10km, 9km, 8km, 7km, 6km, 5km, 4km, 3km, 2km, 1km, 900m, 800m, 700m, 600m, 500m, 400m, 300m, 200m, 100m, 90m, 80m, 70m, 60m, 50m, 40m, 30m, 20m, 10m, 9m, 8m, 7m, 6m, 5m, 4m, 3 One or more wavelengths of m, 2m, 1m, 900mm, 800mm, 700mm, 600mm, 500mm, 400mm, 300mm, 200mm, 100mm, 90mm, 80mm, 70mm, 60mm, 50mm, 40mm, 30mm, 20mm, 10mm, 9mm, 8mm, 7mm, 6mm, 5mm, 4mm, 3mm, 2mm, 1mm, or smaller. RF energy can include one or more wavelengths within the range defined by any two of the foregoing values.

[0149] RF energy can include at least approximately 1 microwatt (μW), 2µW, 3µW, 4µW, 5µW, 6µW, 7µW, 8µW, 9µW, 10µW, 20µW, 30µW, 40µW, 50µW, 60µW, 70µW, 80µW, 90µW, 100µW, 200µW, 300µW, 400µW, 500µW, 600µW, 700µW, 800µW, 900µW, 1 milliwatt (mW), 2mW, 3mW, 4mW, 5mW, 6mW, 7mW, 8mW, 9mW, 10mW, 20mW, 30mW, 40 Average power ratings: mW, 50mW, 60mW, 70mW, 80mW, 90mW, 100mW, 200mW, 300mW, 400mW, 500mW, 600mW, 700mW, 800mW, 900mW, 1 watt (W), 2W, 3W, 4W, 5W, 6W, 7W, 8W, 9W, 10W, 20W, 30W, 40W, 50W, 60W, 70W, 80W, 90W, 100W, 200W, 300W, 400W, 500W, 600W, 700W, 800W, 900W, 1,000W, or more. RF power can include up to approximately 1,000W, 900W, 800W, 700W, 600W, 500W, 400W, 300W, 200W, 100W, 90W, 80W, 70W, 60W, 50W, 40W, 30W, 20W, 10W, 9W, 8W, 7W, 6W, 5W, 4W, 3W, 2W, 1W, 900mW, 800mW, 700mW, 600mW, 500mW, 400mW, 300mW, 200mW, 100mW, 90mW, 80mW, 70mW, 60mW, 5 Average power of 0mW, 40mW, 30mW, 20mW, 10mW, 9mW, 8mW, 7mW, 6mW, 5mW, 4mW, 3mW, 2mW, 1mW, 900µW, 800µW, 700µW, 600µW, 500µW, 400µW, 300µW, 200µW, 100µW, 90µW, 80µW, 70µW, 60µW, 50µW, 40µW, 30µW, 20µW, 10µW, 9µW, 8µW, 7µW, 6µW, 5µW, 4µW, 3µW, 2µW, 1µW, or less. RF energy can include average power within the range defined by any two of the foregoing values.

[0150] The electromagnetic delivery unit may include one or more light sources, such as any light source described herein. For example, the electromagnetic delivery unit may include light source 221. Although depicted in Figure 42 as including a single light source, 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.

[0151] The light source can be configured to direct light to one or more OMs, which are configured to selectively apply electromagnetic energy to one or more atoms among a plurality of atoms. For example, the electromagnetic delivery unit may include OM222. Although in Figure 4 The device is described as comprising a single OM, 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. An OM may include one or more SLMs, AODs, or AOMs. An OM may include one or more DMDs. An OM may include one or more liquid crystal devices, such as one or more LCoS devices.

[0152] 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. Although in Figure 4 The description is intended to include a single AI unit, but the electromagnetic delivery unit may include any number of AI units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more AI units or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 AI unit. The AI ​​operation may include any machine learning (ML) or reinforcement learning (RL) operation described herein.

[0153] The electromagnetic delivery unit can 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 can also be configured to apply one or more two-qubit operations (such as one or more two-qubit gate operations) to the two-qubit units described herein. Each single-qubit or two-qubit operation can include a duration of at least approximately 10 nanoseconds (ns), 20 ns, 30 ns, 40 ns, 50 ns, 60 ns, 70 ns, 80 ns, 90 ns, 100 ns, 200 ns, 300 ns, 400 ns, 500 ns, 600 ns, 700 ns, 800 ns, 900 ns, 1 microsecond (µs), 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 up to approximately 100µs, 90µs, 80µs, 70µs, 60µs, 50µs, 40µs, 30µs, 20µs, 10µs, 9µs, 8µs, 7µs, 6µs, 5µs, 4µs, 3µs, 2µs, 1µs, 900ns, 800ns, 700ns, 600ns, 500ns, 400ns, 300ns, 200ns, 100ns, 90ns, 80ns, 70ns, 60ns, 50ns, 40ns, 30ns, 20ns, 10ns, or less. Each single-qubit or two-qubit operation may include a duration within the range defined by any two of the foregoing values. Single-qubit or dual-qubit operation can be applied at repetition frequencies of at least 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, 1,000 kHz or higher. Single-qubit or dual-qubit operation can be applied at repetition frequencies 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 at a repetition frequency within a range defined by any two of the aforementioned values.

[0154] 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. Raman transitions can occur from the states described herein... 3 P0 or 3 The P1 line may be detuned. For example, the Raman transition may be detuned at least approximately 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 higher. Raman transitions can be detuned up to approximately 1 GHz, 900 MHz, 800 MHz, 700 MHz, 600 MHz, 500 MHz, 400 MHz, 300 MHz, 200 MHz, 100 MHz, 90 MHz, 80 MHz, 70 MHz, 60 MHz, 50 MHz, 40 MHz, 30 MHz, 20 MHz, 10 MHz, 9 MHz, 8 MHz, 7 MHz, 6 MHz, 5 MHz, 4 MHz, 3 MHz, 2 MHz, 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 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. Raman transitions can be detuned by a value that is within the range defined by any two of the aforementioned values.

[0155] One or more spatial light modulators (SLMs) or acousto-optic deflectors (AODs) 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 active region of the SLM or AOD onto the back focal plane of a microscope objective. The microscope objective can perform a spatial Fourier transform on the light field at the location of the SLM or AOD. Thus, an angle (which can be proportional to the RF frequency) can be converted into a position. For example, applying an RF comb to the AOD can generate a linear array of light spots on the focal plane of the objective, each spot having a finite range determined by characteristics of the optical adjustment system, such as the point spread function of the optical adjustment system.

[0156] 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 this 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 be at most approximately 1 MHz, 900 kHz, 800 kHz, 700 kHz, 600 kHz, 500 kHz, 400 kHz, 300 kHz, 200 kHz, 100 kHz, 90 kHz, 80 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, 900 Hz, 800 Hz, 700 Hz, 600 Hz, 500 Hz, 400 Hz, 300 Hz, 200 Hz, 100 Hz, 90 Hz, 80 Hz, 70 Hz, 60 Hz, 50 Hz, 40 Hz, 30 Hz, 20 Hz, 10 Hz, 9 Hz, 8 Hz, 7 Hz, 6 Hz, 5 Hz, 4 Hz, 3 Hz, 2 Hz, 1 Hz or less in terms of splitting energy. The frequency difference can be at least approximately 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, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1 mHz or more from the splitting energy. The frequency difference can be approximately 0 Hz from the splitting energy. The frequency difference can differ from the splitting energy by a value that falls within the range defined by any two of the aforementioned values. The optical system can be configured such that the positional spacing corresponding to the frequency difference is unresolved and that light of both frequencies interacts with a single atom.

[0157] Integrated optical capture unit and electromagnetic delivery unit

[0158] The optical trapping unit and electromagnetic delivery unit described herein can be integrated into a single optical system. A microscope objective can be used to deliver electromagnetic radiation generated by the electromagnetic delivery unit described herein, and to deliver light used to trap atoms generated by the optical trapping unit described herein. Alternatively or additionally, different targets can be used to deliver electromagnetic radiation generated by the electromagnetic delivery unit and light from the trapped atoms generated by the optical trapping unit.

[0159] A single SLM or AOD can allow qubit operations (such as any single-qubit or two-qubit operations described herein) to be performed on a linear array of atoms. Alternatively or additionally, two separate SLMs or AODs can be configured to each process light with orthogonal polarization. Light with orthogonal polarization can be superimposed in front of a microscope objective. In such a scheme, each photon used in the two-photon transitions described herein can be passed to the objective via a separate SLM or AOD, which allows for increased polarization control. By introducing light from a first SLM or AOD into a second SLM or AOD, qubit operations can be performed on a two-dimensional arrangement of atoms, which is substantially orthogonal to the first SLM or AOD via an optocoupler. Alternatively or additionally, qubit operations can be performed on a two-dimensional arrangement of atoms using a one-dimensional array of SLMs or AODs.

[0160] The stability of qubit gate fidelity can be improved by maintaining the overlap of light from the various light sources described herein, such as those associated with the optical trapping unit or electromagnetic delivery unit described herein. This overlap can be maintained by an optical subsystem that measures the direction of light emitted from the various light sources, thus allowing closed-loop control of the light emission direction. The optical subsystem may include a pickup mirror located in front of the microscope objective. The pickup mirror can be configured to guide a small amount of light to a lens that can focus and collimate the beam and convert angular deviation into positional deviation. Position-sensitive optical detectors, such as lateral effect position sensors or quadrant photodiodes, can convert the positional deviation into an electronic signal, and information about the deviation can be fed into compensating optics, such as active mirrors.

[0161] The stability of qubit gate operation can be improved by controlling the intensity of light from various light sources described herein, such as those 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 from the various light sources, thus allowing closed-loop control of the intensity. Each light source can be coupled to an intensity actuator, such as an intensity servo controller. The actuator may 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.

[0162] State preparation unit

[0163] Figure 5 An example of a state preparation unit 250 is shown. The state preparation unit can be configured to prepare the states of multiple atoms, as described herein. The state preparation unit can be coupled to an optical trapping unit and can guide atoms already prepared by the state preparation unit to the optical trapping unit. The state preparation unit can be configured to cool the multiple atoms. The state preparation unit can be configured to cool the multiple atoms before trapping them at multiple optical trapping sites.

[0164] The state preparation unit may include one or more Zeeman reducers. For example, the state preparation unit may include Zeeman reducer 251. Although in Figure 5 The state preparation unit is depicted as including a single Zeeman reducer, but it may contain any number of Zeeman reducers, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more Zeeman reducers, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 Zeeman reducer. The Zeeman reducer may be configured to cool one or more atoms from a first velocity or velocity distribution (such as the emission velocity from the atomic source, room temperature, liquid nitrogen temperature, or any other temperature) to a second velocity below the first velocity or velocity distribution.

[0165] The first velocity or velocity distribution can be associated with a temperature of at least approximately 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 higher. The first velocity or velocity distribution can be associated with a temperature of at most approximately 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 lower. The first velocity or velocity distribution can be associated with a temperature within the range defined by any two of the foregoing values. The second speed can be at least approximately 1 m / s, 2 m / s, 3 m / s, 4 m / s, 5 m / s, 6 m / s, 7 m / s, 8 m / s, 9 m / s, 10 m / s or greater. The second speed can be at most approximately 10 m / s, 9 m / s, 8 m / s, 7 m / s, 6 m / s, 5 m / s, 4 m / s, 3 m / s, 2 m / s, 1 m / s or lower. The second speed can be within the range defined by any two of the foregoing values. The Zeeman reducer can include a one-dimensional Zeeman reducer.

[0166] The state preparation unit may include a first magneto-optical trap (MOT) 252. The first MOT may be configured to cool atoms to a first temperature. The first temperature may be up to about 10 mK, 9 mK, 8 mK, 7 mK, 6 mK, 5 mK, 4 mK, 3 mK, 2 mK, 1 mK, 0.9 mK, 0.8 mK, 0.7 mK, 0.6 mK, 0.5 mK, 0.4 mK, 0.3 mK, 0.2 mK, 0.1 mK or lower. The first temperature may be at least about 0.1 mK, 0.2 mK, 0.3 mK, 0.4 mK, 0.5 mK, 0.6 mK, 0.7 mK, 0.8 mK, 0.9 mK, 1 mK, 2 mK, 3 mK, 4 mK, 5 mK, 6 mK, 7 mK, 8 mK, 9 mK, 10 mK or higher. The first temperature can be within the range defined by any two of the aforementioned values. The first MOT can include 1D, 2D, or 3D MOT.

[0167] The first MOT may include one or more light sources (such as any light source described herein) configured to emit light. The light may include at least approximately 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, or 700nm. One or more wavelengths of 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 greater. Light can include up to approximately 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, etc. One or more wavelengths of 690nm, 680nm, 670nm, 660nm, 650nm, 640nm, 630nm, 620nm, 610nm, 600nm, 590nm, 580nm, 570nm, 560nm, 550nm, 540nm, 530nm, 520nm, 510nm, 500nm, 490nm, 480nm, 470nm, 460nm, 450nm, 440nm, 430nm, 420nm, 410nm, 400nm, or smaller. Light may include one or more wavelengths within the range defined by any two of the foregoing values.For example, light may include one or more wavelengths in the 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.

[0168] The state preparation unit may include a second MOT253. The second MOT may be configured to cool atoms from a first temperature to a second temperature below the first temperature. The second temperature may be up to approximately 100 micro Kelvin (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 nano Kelvin (NK), 800 nK, 700 nK, 600 nK, 500 nK, 400 nK, 300 nK, 200 nK, 100 nK, or lower. The second temperature can be at least approximately 100 nK, 200 nK, 300 nK, 400 nK, 500 nK, 600 nK, 700 nK, 800 nK, 900 nK, 1 μK, 2 μK, 3 μK, 4 μK, 5 μK, 6 µK, 7 µK, 8 µK, 9 µK, 10 µK, 20 µK, 30 µK, 40 µK, 50 µK, 60 µK, 70 µK, 80 µK, 90 µK, 100 µK, or higher. The second temperature can be within the range defined by any two of the foregoing values. The second MOT can include 1D, 2D, or 3D MOT.

[0169] The second MOT may include one or more light sources configured to emit light (such as any light source described herein). The light may include at least approximately 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, or 700 nm. One or more wavelengths of 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 greater. Light can include up to approximately 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, etc. One or more wavelengths of 690nm, 680nm, 670nm, 660nm, 650nm, 640nm, 630nm, 620nm, 610nm, 600nm, 590nm, 580nm, 570nm, 560nm, 550nm, 540nm, 530nm, 520nm, 510nm, 500nm, 490nm, 480nm, 470nm, 460nm, 450nm, 440nm, 430nm, 420nm, 410nm, 400nm, or smaller. Light may include one or more wavelengths within the range defined by any two of the foregoing values.For example, light may include one or more wavelengths in the 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.

[0170] Although Figure 5 The state preparation unit is described as including two MOTs, but the state preparation unit may include any number of MOTs, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more MOTs or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 MOT.

[0171] The state preparation unit may include one or more sideband cooling units or Sisyphus cooling units (such as the sideband cooling unit described in www.arxiv.org / abs / 1810.06626 or the Sisyphus cooling unit described in www.arxiv.org / abs / 1811.06014, each of which is incorporated herein by reference in its entirety for all purposes). For example, the state preparation unit may include a sideband cooling unit or Sisyphus cooling unit 254. Although in Figure 5The description includes a single sideband cooling unit or a Sisyphus cooling unit. State preparation 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, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1. The sideband cooling unit or Sisyphus cooling unit may be configured to use sideband cooling to cool atoms from a second temperature to a third temperature below the second temperature. The third temperature can 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 can be at most approximately 10 nK, 20 nK, 30 nK, 40 nK, 50 nK, 60 nK, 70 nK, 80 nK, 90 nK, 100 nK, 200 nK, 300 nK, 400 nK, 500 nK, 600 nK, 700 nK, 800 nK, 900 nK, 1 µK, 2 µK, 3 µK, 4 µK, 5 µK, 6 µK, 7 µK, 8 µK, 9 µK, 10 µK or more. The third temperature can be within the range defined by any two of the foregoing values.

[0172] 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 approximately 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, or 700 nm. One or more wavelengths of 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 greater. Light can include up to approximately 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, etc. One or more wavelengths of 690nm, 680nm, 670nm, 660nm, 650nm, 640nm, 630nm, 620nm, 610nm, 600nm, 590nm, 580nm, 570nm, 560nm, 550nm, 540nm, 530nm, 520nm, 510nm, 500nm, 490nm, 480nm, 470nm, 460nm, 450nm, 440nm, 430nm, 420nm, 410nm, 400nm, or smaller. Light may include one or more wavelengths within the range defined by any two of the foregoing values.For example, light may include one or more wavelengths in the 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.

[0173] The state preparation unit may include one or more optical pumping units. For example, the state preparation unit may include optical pumping unit 255. Although in Figure 5The process is described 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, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1. 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). Light can include at least approximately 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, and 700nm. One or more wavelengths of 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 greater.Light can include up to approximately 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, etc. One or more wavelengths of 690nm, 680nm, 670nm, 660nm, 650nm, 640nm, 630nm, 620nm, 610nm, 600nm, 590nm, 580nm, 570nm, 560nm, 550nm, 540nm, 530nm, 520nm, 510nm, 500nm, 490nm, 480nm, 470nm, 460nm, 450nm, 440nm, 430nm, 420nm, 410nm, 400nm, or smaller. Light may include one or more wavelengths within the range defined by any two of the foregoing values. For example, light may include one or more wavelengths in the 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.

[0174] The state preparation unit may include one or more coherent driving units. For example, the state preparation unit may include coherent driving unit 256. Although in Figure 5The state preparation unit is described as including one coherent driving unit, but may include any number of coherent driving units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1. The coherent driving unit may be configured to coherently drive atoms from a non-equilibrium state to a first or second atomic state as described herein. Thus, atoms may be optically pumped to an easily accessible atomic state (e.g., based on the availability of a light source emitting a specific wavelength or based on other factors) and then coherently driven to an atomic state as described herein that is useful for performing quantum computing. The coherent driving unit may be configured to induce single-photon transitions between a non-equilibrium state and a first or second atomic state. The coherent driving unit may be configured to induce two-photon transitions between a non-equilibrium state and a first or second atomic state. Two-photon transitions may be induced using light from two light sources described herein, such as two lasers described herein.

[0175] The coherent driving 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 approximately 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, or 700 nm. One or more wavelengths of 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 greater. Light can include up to approximately 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, etc. One or more wavelengths of 690nm, 680nm, 670nm, 660nm, 650nm, 640nm, 630nm, 620nm, 610nm, 600nm, 590nm, 580nm, 570nm, 560nm, 550nm, 540nm, 530nm, 520nm, 510nm, 500nm, 490nm, 480nm, 470nm, 460nm, 450nm, 440nm, 430nm, 420nm, 410nm, 400nm, or smaller. Light may include one or more wavelengths within the range defined by any two of the foregoing values.For example, light may include one or more wavelengths in the 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.

[0176] A coherent driving unit can be configured to induce RF transitions between a non-equilibrium state and a first or second atomic state. The coherent driving unit may include one or more electromagnetic radiation sources configured to emit electromagnetic radiation that is also configured to induce RF transitions. For example, the coherent driving 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 wavelengths of at least about 10 cm, 20 cm, 30 cm, 40 cm, 50 cm, 60 cm, 70 cm, 80 cm, 90 cm, 1 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 fewer. RF radiation may include one or more wavelengths within the range defined by any two of the foregoing values. Alternatively or additionally, the coherent driving unit may include one or more light sources (such as any light source described herein) configured to induce two-photon transitions corresponding to RF transitions.

[0177] controller

[0178] The optical capture unit, electromagnetic delivery unit, entanglement unit, readout optics unit, vacuum unit, imaging unit, spatial configuration AI unit, spatial arrangement AI unit, atomic rearrangement unit, state preparation unit, sideband cooling unit, optical pumping unit, coherent driving unit, electromagnetic energy AI unit, atomic storage unit, atomic movement unit, or Rydberg excitation unit may include one or more circuits or controllers (such as one or more electronic circuits or controllers) which (e.g., via one or more electronic connections) are connected to the optical capture unit, electromagnetic delivery unit, entanglement unit, readout optics unit, vacuum unit, imaging unit, spatial configuration AI unit, spatial arrangement AI unit, atomic rearrangement unit, state preparation unit, sideband cooling unit, optical pumping unit, coherent driving unit, electromagnetic energy AI unit, atomic storage unit, atomic movement unit, or Rydberg excitation unit. The circuit or controller can be configured to control an optical capture unit, an electromagnetic delivery unit, an entanglement unit, a readout optical unit, a vacuum unit, an imaging unit, a spatial configuration AI unit, a spatial arrangement AI unit, an atomic rearrangement unit, a state preparation unit, a sideband cooling unit, an optical pumping unit, a coherent driving unit, an electromagnetic energy AI unit, an atomic library, an atomic movement unit, or a Rydberg excitation unit.

[0179] Non-classical computers

[0180] In one aspect, this disclosure provides a non-classical computer comprising: a plurality of qubits comprising more than 60 atoms, each atom being trapped within an optical trapping site among a plurality of spatially distinct optical trapping sites, wherein the plurality of qubits includes 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; one or more electromagnetic delivery units configured to apply electromagnetic energy to one or more of the plurality of qubits to impart a non-classical operation to the one or more qubits, the non-classical operation including a superposition between at least the first qubit state and the second qubit state; one or more entanglement units configured to quantum mechanically entangle at least a subset of the plurality of qubits in the superposition with at least another qubit of the plurality of qubits; and one or more readout optical units configured to perform one or more measurements on the one or more qubits to obtain a non-classical computation.

[0181] In one aspect, this disclosure provides a non-classical computer comprising: a plurality of qubits comprising more than 60 atoms, each atom being trapped within an optical trapping site among a plurality of spatially distinct optical trapping sites.

[0182] Methods for performing non-classical computation

[0183] In one aspect, this disclosure provides a method for performing non-classical computation, comprising: (a) generating a plurality of spatially distinct optical trapping sites configured to trap a plurality of atoms, the plurality of atoms comprising more than 60 atoms; (b) applying electromagnetic energy to one or more of the plurality of atoms to induce 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 computation.

[0184] Figure 6 A flowchart is shown as an example of a first method 600 for performing non-classical calculations.

[0185] In the 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 more than 60 atoms. The optical trapping sites may include any optical trapping site described herein. The atoms may include any atoms described herein.

[0186] In the second operation 620, method 600 may include: applying electromagnetic energy to one or more atoms of a 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.

[0187] In the third operation 630, method 600 may include: quantum mechanically entangled at least a subset of one or more atoms in one or more superposition states with at least another atom of a plurality of atoms. Atoms can be quantum mechanically entangled in any manner described herein (e.g., as per this document's description of...). Figure 2 (as described).

[0188] In the fourth operation 640, method 600 may include performing one or more optical measurements on one or more superposition states to obtain a nonclassical calculation. The optical measurements may include any optical measurements described herein.

[0189] In one aspect, this disclosure provides a method for performing non-classical computation, comprising: (a) providing a plurality of qubits comprising more than 60 atoms, each atom being trapped within an optical trapping site among 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 of the plurality of qubits to impart 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 the superposition with at least another qubit of the plurality of qubits; and (d) performing one or more optical measurements on the one or more qubits to obtain the classical computation.

[0190] Figure 7 A flowchart is shown as an example of a second method 700 for performing non-classical calculations.

[0191] In the first operation 710, method 700 may include: providing a plurality of qubits comprising more than 60 atoms, each atom being trapped within an optical trapping site among 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.

[0192] In the second operation 720, method 700 may include: applying electromagnetic energy to one or more qubits of a plurality of qubits to impart 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.

[0193] In the third operation 730, method 700 may include: quantum mechanically entangled at least a subset of a plurality of qubits in a superposition with at least another qubit of the plurality of qubits. The qubits can be quantum mechanically entangled in any manner described herein (e.g., as per this document's description of...). Figure 2 (as described).

[0194] In the 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.

[0195] In one aspect, this disclosure provides a method for performing non-classical computation, comprising: (a) providing a plurality of qubits comprising more than 60 atoms, each atom being trapped within an optical trapping site among a plurality of spatially distinct optical trapping sites; and (b) using at least a subset of the plurality of qubits to perform non-classical computation.

[0196] Figure 8 A flowchart is shown as an example of a third method 800 for performing non-classical calculations.

[0197] In the first operation 810, method 800 may include: providing a plurality of qubits comprising more than 60 atoms, each atom being trapped within an optical trapping site among a plurality of spatially distinct optical trapping sites. The qubits may include any qubit described herein. The atoms may include any atom described herein. The optical trapping sites may include any optical trapping sites described herein.

[0198] In the second operation 820, method 800 may include: performing non-classical computation using at least a subset of a plurality of qubits.

[0199] Computer System

[0200] Figure 1 A computer system 101 is illustrated, which is programmed or otherwise configured to operate any of the methods or systems described herein (such as systems or methods for performing the non-classical calculations described herein). The computer system 101 can regulate various aspects of this disclosure. The computer system 101 can be a user's electronic device or a computer system located remotely relative to an electronic device. The electronic device can be a mobile electronic device.

[0201] Computer system 101 includes a central processing unit (CPU, also referred to herein as a “processor” and “computer processor”) 105, which may be a single-core or multi-core processor, or multiple processors for parallel processing. Computer system 101 also includes memory or memory locations 110 (e.g., random access memory, read-only memory, flash memory), electronic storage units 115 (e.g., hard disks), communication interfaces 120 for communicating with one or more other systems (e.g., network adapters), and peripheral devices 125, such as caches, other memories, data storage, and / or electronic display adapters. Memory 110, storage units 115, interfaces 120, and peripheral devices 125 communicate with CPU 105 via a communication bus (solid line) such as a motherboard. Storage units 115 may be data storage units (or data warehouses) for storing data. Computer system 101 may be operatively coupled to a computer network (“network”) 130 with the aid of communication interface 120. Network 130 may be the Internet, an intranet and / or an extranet, or an intranet and / or extranet communicating 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 can enable distributed computing, such as cloud computing. In some cases, with the assistance of computer system 101, network 130 can implement a peer-to-peer network, which allows devices coupled to computer system 101 to act as clients or servers.

[0202] CPU 105 can execute a series of machine-readable instructions, which can be embodied in a program or software. The instructions can be stored in a memory location such as memory 110. The instructions can be directed to CPU 105, which can then be programmed or otherwise configured to implement the methods of this disclosure. Examples of operations performed by CPU 105 can include fetching, decoding, executing, and writing back.

[0203] 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).

[0204] 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 outside computer system 101, such as those located on a remote server communicating with computer system 101 via an intranet or the Internet.

[0205] 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 PCs (e.g., Apple® iPad, Samsung® Galaxy Tab), telephones, smartphones (e.g., Apple® iPhone, Android-enabled devices, Blackberry®), or personal digital assistants. Users can access computer system 101 via network 130.

[0206] The method described herein can be implemented using machine-executable code (e.g., a computer processor) stored in an electronic storage location (such as, for example, memory 110 or electronic storage unit 115) of computer system 101. The machine-executable or machine-readable code can be provided in the form of software. During use, the code can be executed by processor 105. In some cases, the code can be retrieved from storage unit 115 and stored in memory 110 for access by processor 105 at any time. In some cases, electronic storage unit 115 can be excluded, and machine-executable instructions are stored on memory 110.

[0207] Code can be pre-compiled and configured for use with machines that have processors suitable for executing the code, or it can be compiled during runtime. Code can be supplied in a programming language, and the programming language can be selected so that the code can be executed either pre-compiled or compiled.

[0208] The aspects of the systems and methods presented herein, such as computer system 101, can be embodied in a programmable manner. These aspects of the technology can be considered “products” or “artifacts,” typically existing 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 electronic storage units, such as memory (e.g., read-only memory, random access memory, flash memory) or hard disks. “Storage” media can include any or all tangible memory or related modules of a computer, processor, etc., such as various semiconductor memories, tape drives, disk drives, etc., which can readily provide non-transitory storage for software programming. All or part of the software can sometimes communicate via the Internet or various other telecommunications networks. For example, such communication can enable software to be loaded from one computer or processor to another, such as from a management server or host computer to a computer platform for an application server. Therefore, another type of medium that can carry software elements includes optical, electrical, and electromagnetic waves, such as those used through physical interfaces between local devices, via wired and optical terrestrial networks, and via various air links. Physical elements carrying such waves, such as wired or wireless links, optical links, etc., can also be considered as media carrying software. As used herein, unless limited to non-transitory, tangible "storage" media, terms such as "computer or machine-readable medium" refer to any medium involved in providing instructions to a processor for execution.

[0209] Therefore, machine-readable media, such as computer executable code, can take many forms, including but not limited to tangible storage media, carrier media, or physical transmission media. Non-volatile storage media include, for example, optical discs or disks, any storage device such as one or more computers, etc., such as those that can be used to implement the database shown in the diagram. Volatile storage media include dynamic memory, such as the main memory of a computer platform. Tangible transmission media include coaxial cables; copper wires and optical fibers, including wires that form the bus within a computer system. Carrier transmission media can take the form of electrical or electromagnetic signals, or sound or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Therefore, common forms of computer-readable media include, for example: floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs or DVD-ROMs, any other optical media, punched cardstock magnetic tapes, any other physical storage media with a perforated pattern, RAM, ROM, PROM and EPROM, FLASH-EPROM, any other memory chips or cassettes, carrier waves for transmitting data or instructions, cables or links for transmitting such carrier waves, or any other media from which a computer may read programming code and / or data. Many of these forms of computer-readable media may involve transmitting one or more sequences of one or more instructions to a processor for execution.

[0210] Computer system 101 may include or communicate with an electronic display 135, the electronic display 135 including a user interface (UI) 140. Examples of UIs include, but are not limited to, graphical user interfaces (GUIs) and web-based user interfaces.

[0211] The methods and systems disclosed herein can be implemented by one or more algorithms. These algorithms can be implemented in software when executed by the central processing unit 105. For example, the algorithms can implement methods for performing the non-classical computations described herein.

[0212] Example

[0213] Example 1: Modeling the spin level of Strontium-87 nucleus

[0214] In the following example, ten nuclear spin levels of Strontium-87 (I = 9 / 2) are modeled to demonstrate a two-level system (i.e., a qubit). To achieve spectral isolation of qubit transitions, a Stark shift scheme is employed, which shifts unwanted transitions away from the qubit frequency. Isolation schemes can improve effective isolation with respect to achievable Rabi frequencies, can reduce the influence on the actual qubit state via shift or residual scattering, do not require perfect polarization control, can be accessed using reasonable amounts of optical power, and so on. 1 S0 to3 The properties of P1 resonance can be characterized.

[0215] exist Figure 10A In this study, 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 quantum bit space and leakage energy level 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. Furthermore, a polarization purity of 100:1 and the expected circular polarization are assumed. The AC-Stark beam from... 1 S0 to 3 Each detuning of the P1 resonance causes a shift in the spin energy level of each nucleus. To further clarify, the qubit frequency (m F =9 / 2 and m F =7 / 2 difference in energy between modifications) and leakage transition frequency (m F =7 / 2 and m F The differences between the states modified by =5 / 2 are all plotted.

[0216] Figure 10B The study shows that the Stark shift significantly moves the leakage transition while having minimal impact on the qubit frequency. This is likely due to... 3 The P1 resonance is achieved relative to the narrow linewidth of energy level splitting in a high magnetic field. Although the frequency is plotted as a signed quantity, subtleties associated with the quantization axis and optical delivery make the absolute value of this frequency relevant, and thus exhibit the characteristic of Stark shifts pushing the leaky state very close to the qubit frequency. At each detuning, the maximum usable Rabi frequency achievable under a given frequency congestion can be defined. Using this two-photon Rabi frequency, the pi pulse time can be inferred, and the number of scattering events occurring due to the off-resonant interaction of the AC Stark beam can be observed. Figure 10A ).

[0217] There is no distinction between Raman scattering and Rayleigh scattering here, and therefore the worst-case scenario of the AC-Stark induced scattering error for each gate is assumed. To perform single-qubit gates, a method using... 3 Two beams, resonantly detuned at P1, are used to coherently control the light to drive two-photon transitions. Due to the 7kHz linewidth of the transition, from any... 3 Residual scattering in the P1 manifold state may be inherently low. This includes the effects of the AC Stark deflected beam. 3The extension of the P1 hyperfine magnetic sublevel can be used to separate the energy scale between an AC Stark beam detuned by an F = 11 / 2 manifold and a multiphoton 1Q beam detuned by an F = 7 / 2 manifold. A simple toy model involving two ground states and several excited states is sufficient to gain in-depth understanding of power scaling, spot size, and achievable Rabi rates. However, due to the countless number of energy levels involved (…),… 1 S0 (F=9 / 2) 3 P1 (F=7 / 2, 9 / 2, 11 / 2) (including all their magneton levels) may require full-scale simulations encompassing all relevant levels. To verify full operation, a numerical model was built that utilizes all 40 levels and multiple optical fields to represent both desired and undesired polarizations. Using a simple square-wave pulse, it can be seen that transitions to other nuclear spin states can be suppressed using an AC Stark beam. Figure 11A and Figure 11B ).

[0218] Example 2: Optical capture array

[0219] Figure 12A and Figure 12B An array is shown that captures light generated by a spatial light modulator (SLM), such as a square array or an arbitrary array. This is achieved by reflecting light from the spatial light modulator (SLM). 1 S0→ 3 Holograms are generated using 813nm light (the "magic wavelength" of the P0 transition). The active region of the SLM is a 1920x1152 square pixel array with sides approximately 9 micrometers long. Each pixel contains a certain amount 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, allowing the generation of arbitrary pixelated phase masks that can be applied to any unstructured light incident on the surface of the SLM. The SLM is positioned such that a large collimated beam is incident and phase-shifted; the light reflected from the SLM is then guided through the microscope objective. This configuration connects the plane of the SLM to the plane below the lens (where the atomic cloud forms) via Fourier conjugation. The in-plane electric field at the SLM is a Fourier transform of a similar field in the volume of the glass cuvette in the plane below the microscope objective. The atoms experience a trapping potential proportional to the electric field strength, thus undergoing lateral confinement. Longitudinal confinement arises from the structured light passing through the focal point, the position of which is also partially determined by (and thus controllable by) the SLM.

[0220] Light is generated by a Ti:sapphire laser that produces approximately 4W of optical power at 813nm. 2000 traps are created at depths of 500 microKelvin each, far exceeding 1000 times the recoil energy imparted by scattered photons, for imaging or other purposes. This means the device must be in a state where atoms can be measured hundreds of times without being lost due to heating, even without additional cooling. Cooled to their ground state, the atomic positions are known to be within 20nm, which significantly separates the atomic positions from the scale of the laser beam used to drive single-qubit and two-qubit gates or Rydberg interactions. The laser beams driving the gates will reach a spatial scale on the micrometer scale, thus the intensity will be in the range of 10... -5 The gate fidelity varies by level; therefore, a fidelity of 0.9999 is expected to be easily achieved. In this way, the gate fidelity is less sensitive to the position of atoms.

[0221] Example 3: Ultra-high vacuum

[0222] A quartz cuvette composed of Spectrosil® 2000 quartz glass is used as a vacuum cell. Unlike borosilicate glass, this glass does not fluoresce under ultraviolet light. The cell features a glass-metal transition from quartz to stainless steel, connecting the cell to the vacuum pump and atomic source. The cell size was chosen to avoid clamping the laser cooling beam and reducing the numerical aperture of the microscope objectives. The cell was assembled by Starna Scientific Ltd. using optical contact bonding. The four largest outer surfaces of the cell are coated with broadband multilayer antireflective films to minimize reflections of S-polarized and P-polarized light from 300 nm to 850 nm at perpendicular incident angles. A magnesium fluoride coating is applied to the small square window of the cell. The vacuum system is maintained at 8 x 10 for several months. - 12 Torr (1.07x10) -9 Pressure (Pa).

[0223] Example 4: Microscope objective lens

[0224] The microscope objective is positioned directly above the vacuum cell, allowing for individual capture, imaging, and addressing of atomic qubits. Due to its high numerical aperture (NA), the objective efficiently collects fluorescence from atoms during imaging and transforms the collimated input beam into a tightly focused point to capture atoms in the focal plane. Manufactured by Special Optical Inc., the objective features a high numerical aperture (0.65) and a 300 μm diffraction-limited field of view (FOV) with 90% transmittance at 461 nm and 813 nm. The objective's end facing the vacuum cell is tapered to avoid pinching two of the six laser-cooled beams. Furthermore, the diameter of the objective tube is limited between the large magnetic coils used for laser cooling, as the power dissipation of these coils is strongly proportional to their size and spacing. The objective's mechanical housing is made of Ultem, as it is non-magnetic and non-conductive.

[0225] The objective lens is characterized by its placement on one arm of a Michelson interferometer, where a glass cell window is mounted. In this arm, the focused beam undergoes retroreflection using precision ball bearings centered on the beam focal point. The other arm of the Michelson interferometer houses a reference reflector. The Zernike surface is reconstructed by fitting the resulting spatial interference pattern. The objective lens is mounted directly on the glass cell to eliminate tilt deviation between the cell window and the objective lens. This tilt, approximately 1 milliradian (mrad), would otherwise result in a change in wavefront quality. The objective lens is epoxy-bonded to a machined macro mount, which contacts the top window of the cell via five brass ball bearings. During this assembly, the objective lens is interferometrically aligned so that its optical axis remains perpendicular to the cell.

[0226] Perkins manufactures three custom-made dichroic mirrors to handle four distinct wavelengths in the objective lens (813nm, 689nm, 461nm, and 319nm). Figure 13 An optical system for providing four different wavelengths is shown. The three dichroic mirrors are designated DM01, DM02, and DM03. Note that 319 nm light enters from the bottom of the pool. Custom coatings on the three dichroic mirrors work together to maintain arbitrary polarization states of 813 nm and 689 nm light to perform single-qubit or multi-qubit gates, as well as magic wavelength and / or magnetic angle trapping.

[0227] Example 5: Atom trapping and cooling

[0228] Figure 14 The use of red MOT to trap and cool strontium-87 and strontium-88 atoms is shown.

[0229] Example 6: Imaging

[0230] In order to perform projection measurements, it will be used with Strontium-87 1 S0→ 1The light from the P1 transition resonance is applied to the entire atomic array, while the resulting atomic fluorescence is collected and imaged. For in 1 The S0 ground-state manifold contains qubits of two nuclear spin states (both of which resonate with imaging light), and one of these states can transition to a metastable state before measurement. 3 P0 manifold. This process is identical to optical lattice clock operation and is state-selective, as illustrated in Covey et al.'s "2000 Times Repeated Imaging of Strontium Atoms in Clock-Magic Tweezer Arrays". Physical Review Letters As described in 122(17):173201(2019), it is incorporated herein by reference in its entirety for all purposes. This provides the additional benefit of reducing crosstalk readouts from nearby atoms. From each 1 The fluorescence of the S0 atoms is collected through our microscope objective. This light is then imaged onto a scientific CMOS camera, producing an image of the qubit array, which is processed to determine the state of each atom. Such an image also helps determine if any atoms have been lost from the array. Because the microscope objective is diffraction-limited across the entire atomic array, atoms separated by multiple micrometers are well resolved.

[0231] Example 7: Single-qubit gated optical delivery

[0232] The single-qubit scheme is specifically designed to achieve unit-point addressability. Specifically, two laser beams used to drive the single-qubit operation are delivered through the same high numerical aperture objective, which is used to project the optical tweezers trapping potential. As described herein, three dichroic mirrors combine all relevant beams in the back focal plane of the composite mirror. These beams are generated, manipulated, and modulated to perform site-selective single-qubit operations. The two beams used to drive the single-qubit operation have orthogonal linear polarizations (one aligned with the atomic quantization axis, thus pi-polarized, and the other sigma-polarized). To achieve complete control over the single-qubit operation, amplitude, frequency, and phase control of each beam is required at each individual trapping site. This control is achieved through a combination of an electro-optic modulator (EOM), an acousto-optic deflector (AOD), and RF control electronics.

[0233] The light used to drive the single-qubit gate was provided by a conventional amplified laser source, which was phase-locked to an optical frequency comb. While the global phase of this light was not controlled in each experiment, the laser is a stable local oscillator and can be modulated with a well-controlled RF source to generate a control field. This global phase sets the global phase of the qubit array, which cannot be measured without comparison to the individual qubit arrays. For maximum flexibility, an electro-optic modulator (EOM) was used to globally phase modulate the 689nm light used for red MOT, optical pumping, sideband cooling, and single-qubit operations, as these four operations are generally not performed simultaneously. Phase modulation resulted in the generation of symmetrical sidebands around the central laser frequency. 3 Laser detuning of the P1 state manifold ensures that only the +1st order sideband is sufficiently close to narrow. 3 The P1 transition drives the transition. This optical resonant addressing can be achieved by varying the modulation frequency between 5 GHz and 13 GHz, even when using a large bias field to split the excited-state manifold. 3 All transitions in the P1 manifold.

[0234] The main advantage of this method for generating 689nm light is that it uses the same beam path to generate light for all four beam paths described above. Furthermore, the global frequency, amplitude, and phase of these resonant beams are controlled using an advanced microwave RF source. The RF driving the EOM is generated by an arbitrary waveform generator and an IQ mixer, providing control over the complex pulse shape of the laser. For qubit operations, this global control is used to generate pulses of arbitrary shapes with good spectral characteristics.

[0235] Example 8: Parallel addressing of a single qubit

[0236] Acousto-optic deflectors (AODs) are used to generate beams that can be driven at different frequencies to manipulate different locations within a qubit array. This introduces position-dependent frequency and phase-matching conditions. For single-qubit operations, this complexity is overcome by using the same AOD path for both beams, so that the driven two-photon process remains resonant when intermediate state detuning occurs. In other words, the four AOD frequencies are entirely constrained by the selection of the specific site to be processed. Two frequencies select the position of the first beam, and the frequency-matching condition forces the two frequencies of the second beam to be identical until a shift in the qubit frequency (a split between the two nuclear spin states, approximately 150 kHz) occurs. Using AODs to generate beams for single-qubit operations allows arbitrary addressing of atoms in a single row (or column) at any given time. This is necessary to maintain complete control over the amplitude and phase of each. This results in partial serialization of the operation. However, compared to SLMs, AODs significantly increase the speed of mode alteration and are more efficient than DMDs. Full phase control of each beam can also be achieved using AODs. This not only allows for tracking the phase of each qubit (allowing all rotations to be applied within a local qubit frame), but also enables the execution of more complex pulse sequences on each qubit. By controlling the amplitude of the RF of each qubit, the pulse region of operation for each qubit can be locally scaled. Combining the phase and amplitude of the RF, the operation performed on each qubit can be fully controlled during a single pulse from the EOM.

[0237] Example 9: Parallel addressing of multi-qubit units

[0238] Direct excitation of strontium-87 from its ground state to the Rydberg level would require a laser with a wavelength of approximately 218 nm. Alternatively, Rydberg excitation can be performed using two-photon excitation combining 689 nm and 319 nm light, with each photon excitation starting from the middle. 3 P1 state is detuned. 3 The approximately 7kHz width of the P1 state at the two-photon-efficient Rabi rate and via 3 An effective balance is provided between the scattering of P1 spontaneous decay and the scattering. Figure 15A The energy level structures for single-qubit and multi-qubit operations in Strontium-87 are shown.

[0239] The optical system used for single-qubit operations is also designed for multi-qubit gates. One of the single-qubit beams is used as a branch of a two-photon excitation scheme that drives transitions to the Rydberg electron manifold. To satisfy spatially dependent frequency and phase matching conditions, the AOD is also used for UV light. Importantly, the optical system is matched, so the frequency shift of UV light from one site to another is the same as the frequency shift of 689 nm light. As a result of this constraint, the performance of state-of-the-art UVAODs determines the accessible field of view (FOV) for multi-qubit operations. Moreover, because one of the single-qubit beams is used for multi-qubit operations (and the two single-qubit beams are matched), the FOV for single-qubit operations will be the same. The quality factor of a UVAOD is the product of the device's active aperture and RF bandwidth. For a fixed beam size in the objective's back focal plane, increasing any of these quantities results in a larger beam scanning angle, thus leading to a larger FOV in the qubit array plane. An FOV of approximately 100µm x 100µm was achieved, which is sufficient to handle arrays of approximately 1,000 atoms with a trap site spacing of 3µm.

[0240] Figure 15B An optical system for delivering light to perform single-qubit and multi-qubit operations in parallel on multiple trapped atoms is illustrated. A first light for performing a single-qubit operation on a first qubit (qubit 1) is directed to a first two-dimensional access point (2D AOD), allowing parallel addressing of a first subset of the trapped atoms. A second light for performing a single-qubit operation on a second qubit (qubit 2) is directed to a second 2D AOD, allowing parallel addressing of a second subset of the trapped atoms. A third light for inducing Rydberg interactions in either the first or second subset is delivered via a third 2D AOD, generating multiple entanglements between atoms in the first subset and adjacent atoms in the second subset.

[0241] The third beam is generated by an ultraviolet (UV) laser emitting 319 nm light. The UV laser is phase-locked to a frequency comb, providing a narrow-linewidth UV laser beam. Amplitude control is provided via an acousto-optic modulator (AOM). Global phase control is achieved through optical phase stabilization techniques. The stabilized global phase of the 319 nm light is combined with active phase modulation of the 689 nm light to provide phase control. The free-space beam is sent into the third 2D AOD, but in the opposite direction to the first and second 2D AODs. The light is then guided to the trapped atoms through a custom-designed microscope objective. The backpropagation beam path is used to monitor the position of the point and the effect of the light on the atoms (e.g., by exciting the loss spectrum) to optimize alignment. These quantitative effects can also be used to implement automated alignment schemes to allow for improved autonomous operation of the system.

[0242] Figure 15CAn optical system configured to dynamically generate and control beams using a single electro-optic modulator (EOM) and two acousto-optic deflectors (AODs) for each beam, each beam driven by an RF signal from an arbitrary waveform generator, is illustrated. Orientation of the AODs ensures that the frequency difference between the beams remains constant as they overlap in the qubit array. This frequency difference prevents the driving of undesirable operations but is easily overcome by the RF drive of the two EOMs. The combination of the AODs and the agile RF synthesizer also provides comprehensive, point-by-point control over operations that can be performed in parallel (one line at a time), a key advantage for implementing sequences of quantum operations on atomic qubit arrays.

[0243] Example 10: Inverse adiabatic drive

[0244] Without the pulse sequence described herein, multi-qubit operations can be performed by transferring atoms from the ground state to a modified state and returning to the ground state adiabatic by altering the Hamiltonian, thereby minimizing the adiabatic transition to the Rydberg state. The adiabatic condition imposes constraints, making multi-qubit operations relatively slow. However, to minimize overall speed and decoherence effects, faster gates are needed. The pulse sequence described herein enables faster gate maintenance while efficiently preserving adiabatic kinetics.

[0245] For example, antiadiabatic driving can reduce gate time while minimizing errors caused by transitions to Rydberg states. Antiadiabatic driving involves adding one or more driving fields to cancel out terms in the Hamiltonian that cause unwanted adiabatic transitions. Antiadiabatic driving efficiently realizes adiabatic dynamics on shorter timescales than allowed by adiabatic conditions. One example, as described in this paper, is “transition-free quantum driving” (TQD). TQD is accomplished by transforming the total Hamiltonian of the system into a reference coordinate system defined by the instantaneous eigenstates of the Hamiltonian. The Hamiltonian is divided into a diagonal part (which does not cause nonadiabatic transitions between instantaneous eigenstates) and an off-diagonal part (which does cause nonadiabatic transitions). TQD is achieved by adding an additional control field that cancels out the off-diagonal, nonadiabatic Hamiltonian. Using this technique, efficient adiabatic dynamics can be realized without satisfying the usual slow adiabatic conditions. The following is a derivation of the TQD condition for a general two-stage system with a single-axis drive, using TQD to cancel the non-adiabatic transition of the Rydberg modified gate.

[0246] The general problem is the ground state. The two-level system is transformed into and excited state The mixture is modified and returns to the ground state as quickly as possible, without leaving any population in the excited state. In the rotating coordinate system, the total Hamiltonian (in frequency) of the two-level system under driving is expressed as:

[0247] (1)

[0248] here, It is the Rabi rate. It is from the detuning of resonance, σ x and σ z It is the Pauli operator on a two-level system. It is very useful to describe the Hamiltonian in an "tilted reference frame":

[0249] (2)

[0250] (3)

[0251] (4)

[0252] (5)

[0253] In the original cardinality, The instantaneous eigenstates are:

[0254] (6)

[0255] (7)

[0256] We now transform into an "adiabatic coordinate system" described by these instantaneous eigenstates. The unitary operator corresponding to this transformation is:

[0257] (8)

[0258] here, It is an instantaneous eigenstate in an adiabatic coordinate system. The Hamiltonian of the transformation is:

[0259] (9)

[0260] The second item ( This includes off-diagonal elements that cause transitions when adiabatic conditions are not met. The change is slow enough to make When this term is sufficiently small, the adiabatic condition is satisfied. To achieve effective adiabatic kinetics when this term is not small, we add an additional control field to the original Hamiltonian to eliminate... The impact. This can be achieved by setting the following:

[0261] (10)

[0262] according to Solution:

[0263] (11)

[0264] Before use The definition can be expressed in matrix form:

[0265] (12)

[0266] Simplify the expression again:

[0267] (13)

[0268] (14)

[0269] This result demonstrates that the anti-adiabatic Hamiltonian can be achieved through field driving that is 90 degrees out of phase with the original driving field. Typically, the desired [mechanism / method] can be found. form .

[0270] To demonstrate the effectiveness of the transition-free quantum drive of the Rydberg modification gate, a 2-atom system was simulated. Each atom comprises two ground states (qubits) and one Rydberg state. These two atomic states can be qubit states |00>, |01>, |10>, or |11>, single-excited Rydberg states |0R>, |R0>, |R1>, or double-excited Rydberg states |RR>. In the presence of Rydberg blocking, transitions to |RR> can be suppressed. The Rydberg modification gate can be configured to apply one or more driving fields to transform a pair of atoms (e.g., a pair of atoms starting with a superposition of qubit states) into a mixture of qubit and Rydberg states. The atomic pairs can enable the diatomic state to acquire a conditional phase dependent on the initial state. At the end of the gate, the atom can return to the qubit space, while any atom remaining in the Rydberg level can be a source of error. Figure 16A A simulation of two atoms in the initial diatomic state is shown. This is achieved by driving |0> to |0> on each atom. r The transition of the Hamiltonian sweeps the detuning to resonance, then moves away from resonance. The instantaneous eigenstate of the Hamiltonian transforms from the bare state to the modified state, and then back to the bare state. For example... Figure 16A As shown, if the ramp is executed too quickly, violating the adiabatic conditions, the significant population remains in the Reedberg state.

[0271] Figure 16B A simulation of two atoms in the initial diatomic state is shown, with an antiadiabatic driving field added to implement a transition-free quantum driving gate. The population retained in the Rydberg state is greatly reduced. Figure 16CNumerical simulations of a diatomic system with a Rydberg blockade that has undergone Rydberg-modified gates are shown, with (with TQD) and without (without TQD) the addition of an antiadiabatic driving field configured to realize TQD. In this example, for the initial state |01>, applying TQD reduces the residual population in the Rydberg state. In this example, the gate parameter can be chosen to emphasize the violation of the adiabatic condition to demonstrate the effect of TQD. In some cases with more than about two energy levels (e.g., the 9-level system described elsewhere in this paper), essentially transition-free quantum driving can be realized over multiple transitions. Such driving can be observed even with different Rabi rates.

[0272] Antiadiabatic driving can also be used to suppress unwanted transitions at frequencies other than the driving frequency. This can be used to drive transitions at resonances while avoiding unwanted transitions near the drive. Alternatively, nonresonant driving can be used to create modified states while avoiding excitation to excited states (i.e., adiabatic transitions). As described in this paper, an example of antiadiabatic driving for suppressing unwanted transitions is "adiabatic derivative elimination" (DRAG). Figure 16D Examples of DRAG pulses in the time domain (a) and frequency domain (b) are shown. Non-resonant DRAG pulses can be used to generate controlled phase gates in Rydberg atoms. A pulse with a smooth amplitude profile can be applied at the non-resonant frequency of the qubit-to-Rydberg transition. Application at the non-resonant frequency can cause the qubit atom to enter or leave the Rydberg modified state. DRAG pulses can be designed to minimize transitions driven at specific frequency offsets from the pulse carrier frequency. By adjusting the position of the spectral aperture in the spectrum of the pulse shape, gate errors caused by the population left in the Rydberg state can be minimized. Figure 16E A simulation example of optimizing DRAG pulse parameters to minimize error is shown. The spectral aperture position with minimum error can be used as the spectral aperture position, thereby improving the overall fidelity of the system.

[0273] Example 11: Atomic rearrangement

[0274] Simulations were performed to determine the time requirements for atomic rearrangement at the light-trapping sites of a 7x7 array. The simulations assumed the imaging system consisted of a Hamamatsu Orca-Fusio NCMOS digital camera in normal mode and an external trigger. The camera had a region of interest of 2304 (fixed, horizontal) x 256 (vertical) pixels. An exposure time of 20 ms, a readout time of 4.6 ms (256 vertical lines, 18.65 μs per line), and a data delivery delay of 1.75 ms to 5 ms were assumed.

[0275] The data delivered from the camera can be divided into a 256x256 array of 16-bit integers. To determine the capture site, we must first use a calibrated image of the complete capture lattice (by averaging over many capture implementations). Figure 17A A calibrated image of the light-capturing sites of a fully filled 7x7 array is shown. The light-capturing sites are indexed by coordinates (i, j). This data is used to map the capture sites to pixel locations, as shown in Table 1.

[0276] Table 1: Calibration image index coordinates mapped to pixel locations:

[0277]

[0278] Figure 17B The markings for filled and unfilled optical capture sites are shown in the 7x7 array. Passing is performed on the pixels surrounding each capture site. Figure 17C The diagram shows a 25x25 pixel band around each optical capture point in a 7x7 array. Pixels in each band are averaged. The average is compared to a threshold extracted from the calibration process to determine whether each optical capture point is filled or unfilled. Filled points are marked with "1", while unfilled points are marked with "0". Figure 17D The diagram illustrates how each capture site in a 7x7 array is identified as either filled or unfilled. Therefore, the process produces a 7x7 array of binary values ​​indicating whether each site is filled or unfilled. The total processing time for assigning the binary value array is less than 0.5 ms.

[0279] Once the filled and unfilled sites are located, the next step is to determine the movement of the filled, uncaptured sites. This is a combinatorial optimization problem categorized as binary matching. It can be solved by constructing an adjacency matrix from which the optimal match can be efficiently found using algorithms such as the Hungarian matching algorithm described in this paper. Constructing the adjacency matrix , among which The columns are indexed by the target sites in the NxN active region, and by the available sites in the complete MxM lattice. For example, in the case of a 7x7 array (M = 7), atoms can be moved to a 5x5 (N = 5) calculated active region. Table 2 shows the entries in the adjacency matrix.

[0280] Table 2: Adjacency matrix of a 7x7 array with 5x5 computed active area

[0281]

[0282] When the distance metric is the target and filling sites When the squared distance between them is used, the resulting match produces a collisionless movement of atoms from the filled optical trapping site to the unfilled optical trapping site. Figure 17E The movement from filled to unfilled optical trapping sites is shown to avoid collisions between atoms.

[0283] The moves are divided into independent subsets and ordered by time to facilitate parallelization, as shown in Table 3 below. The process of determining the move takes approximately 8 ms.

[0284] Table 3: Time-ordered list of atomic movements in a 7x7 atomic array

[0285]

[0286] Delivering data to the AWG takes less than 1 ms. A single maximum delay is introduced when mapping the movement set to a set of waveforms in the AWG. A single movement may require 0.3 ms for uphill time, 0.1 ms / μm for movement, and 0.3 ms for downhill time. Assuming a spacing of 3 μm between optical capture points and allowing movement only to adjacent points, each movement takes approximately 1 ms. Many simulations of a 7x7 array can perform up to 34 movements, requiring 34 ms to program the AWG.

[0287] While preferred embodiments of the invention have been shown and described herein, these embodiments will be apparent to those skilled in the art if provided by way of example only. Many variations, modifications, and substitutions will now occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in the practice of the invention. The following claims are intended to define the scope of the invention and thereby cover the methods and structures within the scope of these claims and their equivalents.

Claims

1. A method for performing non-classical computation, comprising: (a) Capturing multiple atoms at one or more capture units, wherein the multiple atoms are multiple qubits; (b) Applying a first electromagnetic energy to one or more of the plurality of atoms using one or more first electromagnetic delivery units, 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) Entangling at least a subset of the one or more atoms in the one or more superposition states with at least another atom of the plurality of atoms using one or more Rydberg units to form one or more multi-qubit units, the one or more multi-qubit units comprising two or more qubits, wherein the quantum mechanical entanglement in (c) comprises parallel addressing of each of the two or more qubits using a second electromagnetic energy comprising one or more pulse sequences via one or more second electromagnetic delivery units, thereby implementing one or more multi-qubit gate operations on the one or more multi-qubit units, wherein the one or more pulse sequences comprise one or more non-adiabatic pulses maintaining adiabatic dynamics; and (d) Perform one or more measurements on the one or more superposition states using one or more readout units to obtain the non-classical computation.

2. The method of claim 1, wherein the one or more pulse sequences comprise one or more members selected from the group consisting of: adiabatic (STA) pulse sequence shortcuts, transition-free quantum drive (TQD) pulse sequences, superadiabatic pulse sequences, antiadiabatic drive pulse sequences, and adiabatic derivative elimination (DRAG) pulse sequences.

3. The method according to claim 1, wherein the one or more first electromagnetic delivery units and the one or more second electromagnetic delivery units are identical.

4. The method according to claim 1, wherein the one or more first electromagnetic delivery units and the one or more second electromagnetic delivery units are different.

5. The method according to claim 1, wherein the one or more pulse sequences further include one or more optimal control pulse sequences.

6. The method of claim 5, wherein the one or more optimal control pulse sequences originate from one or more processes selected from the group consisting of: Gradient Ascending Pulse Engineering (GRAPE) method, Krotov method, chopper basis method, chopper random basis (CRAB) method, Nelder-Mead method, gradient optimization method using parameterization, genetic algorithm method, and gradient optimization method for analytical control.

7. The method according to any one of claims 1-6, wherein the one or more pulse sequences comprise a duration of at least 10 nanoseconds (ns).

8. The method according to any one of claims 1-7, wherein the one or more pulse sequences comprise a duration of up to 100 microseconds (μs).

9. The method according to any one of claims 1-8, wherein the one or more multi-qubit gate operations comprise a fidelity of at least 0.

9.

10. The method according to any one of claims 1-9, wherein the one or more multi-qubit gate operations comprise a fidelity of up to 0.9999.

11. The method of claim 1, further comprising using the one or more Rydberg units to excite at least one atomic electron of the one or more atoms in the one or more superposition states to a Rydberg state, thereby forming one or more Rydberg atoms, or by continuously driving the one or more atoms in the one or more superposition states via transitions to Rydberg states, thereby forming one or more Rydberg-modified atoms.

12. The method of claim 11, further comprising inducing one or more quantum mechanical entanglements between the one or more Rydberg atoms or Rydberg-modified atoms and the at least one other atom using the one or more Rydberg units, wherein the at least one other atom is located at a distance of no more than 10 micrometers (μm) from the one or more Rydberg atoms or Rydberg-modified atoms.

13. The method of claim 12, further comprising using the one or more Rydberg units to drive the one or more Rydberg atoms or Rydberg-modified atoms to a lower energy atomic state, thereby forming the one or more multi-qubit units.

14. The method according to any one of claims 1-13, wherein the one or more capturing units comprise one or more optical capturing units.

15. The method of claim 14, further comprising using the one or more optical capturing units to generate a plurality of spatially distinct optical capturing sites.

16. The method of claim 15, further comprising using each of the plurality of spatially distinct optical trapping sites to trap at most one atom of the plurality of atoms.

17. The method according to any one of claims 1-16, wherein the one or more multi-qubit units comprise dual-qubit units.

18. The method of claim 17, wherein the one or more multi-qubit gate operations include two-qubit gate operations.

19. A system for performing non-classical computation, comprising: One or more controllers communicatively coupled to one or more capture units, one or more first electromagnetic delivery units, one or more Rydberg units, one or more second electromagnetic delivery units, and one or more readout units, wherein the one or more controllers are configured to: (i) Guide the one or more capturing units to capture a plurality of atoms, wherein the plurality of atoms are a plurality of qubits; (ii) The one or more first electromagnetic transfer units are guided to apply a first 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; (iii) Guiding the one or more Rydberg units to quantum mechanically entangle at least a subset of the one or more atoms in the one or more superposition states with at least another atom of the plurality of atoms to form one or more multi-qubit units, the one or more multi-qubit units comprising two or more qubits, wherein the guidance in (iii) comprises using one or more second electromagnetic delivery units to perform parallel addressing of each of the two or more qubits using a second electromagnetic energy comprising one or more pulse sequences, thereby implementing one or more multi-qubit gate operations on the one or more multi-qubit units, wherein the one or more pulse sequences comprise one or more non-adiabatic pulses maintaining adiabatic dynamics; and (iv) Instruct the one or more readout units to perform one or more measurements on the one or more superposition states to obtain the nonclassical computation.

Images