Method and system for continuous operation of a cold atom device using a separate reservoir array

Abstract

Systems and methods for performing successive non-classical computations may include loading a plurality of atoms into a reservoir array, transferring a first subset of the plurality of atoms from the reservoir array into a science array, performing a first non-classical computation using at least a portion of the first subset, determining an atom defect number representing the difference between (i) the number of atoms in the first subset and (ii) the number of atoms of a remaining subset of the first subset that remain in the science array after performing the first non-classical computation, transferring a second subset of the plurality of atoms from the reservoir array into the science array, reloading the reservoir array with additional atoms, and performing a second non-classical computation using at least a portion of one or both of the remaining subset and the second subset.

Description

[Technical Field]

[0001] cross reference This application claims the benefit of U.S. Provisional Application No. 63 / 413,203, filed October 4, 2022, which is incorporated herein by reference in its entirety. [Background technology]

[0002] Quantum computers typically utilize quantum mechanical phenomena such as superposition and entanglement to perform operations on data. Quantum computers can differ from digital electronic computers, which are based on transistors. For example, while digital computers require data to be encoded into binary digits (bits), where each bit is always in one of two distinct states (0 or 1), quantum computing uses quantum bits (qubits), which can be in a superposition of states.

[0003] In a neutral atom quantum computer or simulation device, qubits may be encoded on optically trapped atoms. Because the optical trap may be relatively shallow, atoms may be lost through collisions with residual background gas, through leakage into untrapped or otherwise undesired internal states, or through heating associated with laser interactions or other processes. Typically, in a quantum computer or simulation device, a subset of the entire optical trap array (referred to herein as a "science region") may be filled to perform a calculation or simulation. To perform successive or repeated calculations, it may be important for atoms to be reloaded into the optical trap. Summary of the Invention

[0004] This disclosure describes, in some embodiments, methods and systems that allow a scientific region to be replenished from a reservoir where the scientific region and the reservoir region are different, thereby allowing for refilling of the reservoir without disturbing the atoms in the scientific region, thereby allowing for continuous or quasi-continuous occupancy or coherent operations within the scientific region (over the lifetime of the atoms in the scientific region).

[0005] In one aspect, the present application provides a method for preparing an atomic sample, which may include: (a) trapping a plurality of atoms in a scientific array, the scientific array including a first plurality of spatially distinct optical trapping sites; (b) transferring at least one atom from a reservoir array into the scientific array to increase a fill factor of the scientific array, the reservoir array including a second plurality of spatially distinct optical trapping sites; and (c) transferring at least one atom into the reservoir array to increase the fill factor of the reservoir array, the transferring step in (c) being performed at least in part during the step of (b) transferring at least one atom from the reservoir array into the scientific array.

[0006] In some embodiments, the method further includes repeating (b) and (c) multiple times to maintain fill factor in the scientific array. In some embodiments, the method further includes performing a sensing application using at least a first subset of the plurality of atoms. In some embodiments, the method further includes performing a timing operation using at least a first subset of the plurality of atoms. In some embodiments, the method further includes performing a computation using at least a first subset of the plurality of atoms. In some embodiments, the computation is a non-classical computation, and (c) is performed without substantially stopping the non-classical computation. In some embodiments, performing the non-classical computation includes applying electromagnetic energy to one or more atoms of a first subset of atoms in the science array, thereby inducing the one or more atoms to adopt one or more superpositions of a first atomic state and at least a second atomic state different from the first atomic state; quantum mechanically entangle at least one of the one or more atoms in the one or more superpositions with at least another atom of the first subset of atoms in the science array; and measuring the one or more superpositions to obtain a non-classical result. In some embodiments, the first atomic state and the second atomic state include first and second nuclear spin states of nuclei having nuclear spins of ½ or greater. In some embodiments, the one or more atoms of the first subset of atoms in the one or more superpositions and at least another atom of the first subset of atoms in the science array are quantum mechanically entangled with a coherence lifetime of at least 1 second.

[0007] In some embodiments, the plurality of atoms comprises neutral atoms. In some embodiments, the plurality of atoms comprises a Group 2 element. In some embodiments, the plurality of atoms comprises scandium. In some embodiments, the plurality of atoms comprises a Group 2-like element. In some embodiments, the plurality of atoms comprises an atom with two valence electrons. In some embodiments, the plurality of atoms comprises ytterbium.

[0008] In some embodiments, the plurality of atoms comprises a temperature of at most 10 microKelvin (μK). In some embodiments, one or both of (i) loading the plurality of atoms into the reservoir or (ii) reloading the reservoir array with additional atoms is performed using one or both of a moving optical trap or optical tweezers. In some embodiments, the science array is distinct from the reservoir array. In some embodiments, the science array is physically separated from the reservoir array, optionally by more than 10 cm.

[0009] In some embodiments, the method further includes, subsequent to (a), determining an atom defect number representing the difference between (i) the atom number of the plurality of atoms trapped within the science array and (ii) the atom number of a remaining subset of the plurality of atoms trapped within the science array that remains within the science array after performing at least a portion of the non-classical computation. In some embodiments, the at least one atom transferred from the reservoir array into the science array includes a number of atoms at least equal to the atom defect number. In some embodiments, determining the atom defect number is based on imaging across an imaging axis to determine which sites of a second plurality of spatially distinct optical trapping sites of the science array are occupied. In some embodiments, the science array is physically separated from the reservoir array parallel to the imaging axis, and one or both of (i) transferring the first subset of the plurality of atoms from the reservoir array into the science array or (ii) transferring the second subset of the plurality of atoms from the reservoir array into the science array is performed using one or both of a moving optical trap or optical tweezers.

[0010] In some embodiments, both the science array and the reservoir array are two-dimensional. In some embodiments, both the science array and the reservoir array are three-dimensional. In some embodiments, the science array has a different number of dimensions than the reservoir array. In some embodiments, one or both of the science array or the reservoir array are formed using either optical or non-optical electromagnetic fields. In some embodiments, the second number of sites in the second plurality of light capture sites is equal to the first number of sites in the first plurality of light capture sites. In some embodiments, the second number of sites in the second plurality of light capture sites is greater than the first number of sites in the first plurality of light capture sites.

[0011] In some embodiments, transitioning at least one atom from the reservoir array into the scientific array includes transitioning a first number of atoms, the first number being at least a subset of the at least one atom, from the reservoir array to one or more intermediate arrays, and transitioning a second number of atoms, the second number being up to the first number of atoms, from the one or more intermediate arrays to the scientific array. In some embodiments, the one or more intermediate arrays include at least two intermediate arrays, and the at least second number of atoms is transitioned between the at least two intermediate arrays (i) after the first number of atoms is transitioned from the reservoir array to the at least two intermediate arrays and (ii) before the second number of atoms is transitioned from the at least two intermediate arrays to the scientific array.

[0012] In some embodiments, the method further includes rearranging, within the science array, the positions of at least some of the spatially distinct first plurality of optical capture sites of one or both of (i) the plurality of atoms in the science array or (ii) at least one atom in the science array. In some embodiments, the science array is associated with a first spatial light modulator and the reservoir array is associated with a second spatial light modulator. In some embodiments, the at least one atom transitioned from the reservoir array into the science array is in a dark state, a clock state, or another state forbidden by a selection rule from the optical excitation used for the transition. In some embodiments, the transition of the at least one atom from the reservoir array into the science array is a long-range transition. In some embodiments, the plurality of atoms are qubits.

[0013] In another aspect, the disclosure provides a method for preparing an atomic sample, which may include (a) trapping a plurality of atoms in a scientific array, the scientific array comprising a first plurality of spatially distinct optical trapping sites, (b) inducing at least a first subset of the plurality of atoms in the scientific array to adopt one or more superposition states, and (c) transferring at least one atom from a reservoir array into the scientific array, the reservoir array comprising a second plurality of spatially distinct optical trapping sites, wherein the transferring in (c) is performed substantially without decoherence of the superposition states.

[0014] In some embodiments, the method further includes repeating (c) multiple times to maintain fill factor in the scientific array. In some embodiments, (b) includes performing a sensing application using at least a first subset of the plurality of atoms. In some embodiments, (b) includes performing a timing operation using at least a first subset of the plurality of atoms. In some embodiments, (b) includes performing a computation using at least a first subset of the plurality of atoms. In some embodiments, the computation is a non-classical computation, and (c) is performed without substantially stopping the non-classical computation. In some embodiments, performing the non-classical computation includes applying electromagnetic energy to one or more atoms of a first subset of atoms in the science array, thereby inducing the one or more atoms to adopt one or more superpositions of a first atomic state and at least a second atomic state different from the first atomic state; quantum mechanically entangle at least one of the one or more atoms in the one or more superpositions with at least another atom of the first subset of atoms in the science array; and measuring the one or more superpositions to obtain a non-classical result. In some embodiments, the first atomic state and the second atomic state include first and second nuclear spin states of nuclei having nuclear spins of 1 / 2 or greater. In some embodiments, the one or more atoms of the first subset of atoms in the one or more superpositions and at least another atom of the first subset of atoms in the science array are quantum mechanically entangled with a coherence lifetime of at least 1 second.

[0015] In some embodiments, the method further includes supporting one or more atoms in a reservoir array comprising a second plurality of spatially distinct light capture sites. In some embodiments, the plurality of atoms comprises neutral atoms. In some embodiments, the plurality of atoms comprises Group 2 elements. In some embodiments, the plurality of atoms comprises scandium. In some embodiments, the plurality of atoms comprises a Group 2-like element. In some embodiments, the plurality of atoms comprises atoms with two valence electrons. In some embodiments, the plurality of atoms comprises ytterbium. In some embodiments, the plurality of atoms comprises a temperature of up to 10 microKelvin (μK).

[0016] In some embodiments, one or both of (i) loading multiple atoms into the reservoir or (ii) reloading the reservoir array with additional atoms is performed using one or both of a moving optical trap or optical tweezers. In some embodiments, the science array is different from the reservoir array. In some embodiments, the science array is physically separated from the reservoir array, optionally by more than 10 cm.

[0017] In some embodiments, the method further includes, subsequent to (a), determining an atom defect number representing the difference between (i) the atom number of the plurality of atoms captured within the scientific array and (ii) the atom number of a remaining subset of the plurality of atoms captured within the scientific array that remains within the scientific array after performing at least a portion of the non-classical computation.

[0018] In some embodiments, the at least one atom transitioned from the reservoir array into the science array includes a number of atoms at least equal to the number of atom defects. In some embodiments, determining the number of atom defects is based on imaging across the imaging axis to determine which sites of a second plurality of spatially distinct optical trapping sites of the science array are occupied. In some embodiments, the science array is physically separated from the reservoir array parallel to the imaging axis, and one or both of (i) transitioning the first subset of atoms from the reservoir array into the science array or (ii) transitioning the second subset of atoms from the reservoir array into the science array is performed using one or both of a moving optical trap or optical tweezers.

[0019] In some embodiments, both the science array and the reservoir array are two-dimensional. In some embodiments, both the science array and the reservoir array are three-dimensional. In some embodiments, the science array has a different number of dimensions than the reservoir array. In some embodiments, one or both of the science array or the reservoir array are formed using either optical or non-optical electromagnetic fields. In some embodiments, the second number of sites in the second plurality of light capture sites is equal to the first number of sites in the first plurality of light capture sites. In some embodiments, the second number of sites in the second plurality of light capture sites is greater than the first number of sites in the first plurality of light capture sites.

[0020] In some embodiments, transitioning at least one atom from the reservoir array into the scientific array includes transitioning a first number of atoms, the first number being at least a subset of the at least one atom, from the reservoir array to one or more intermediate arrays, and transitioning a second number of atoms, the second number being up to the first number of atoms, from the one or more intermediate arrays to the scientific array.

[0021] In some embodiments, the one or more intermediate arrays include at least two intermediate arrays, and at least a second number of atoms is transitioned between the at least two intermediate arrays (i) after the first number of atoms is transitioned from the reservoir array to the at least two intermediate arrays, and (ii) before the second number of atoms is transitioned from the at least two intermediate arrays to the science array.

[0022] In some embodiments, the method further includes rearranging, within the science array, the positions of at least some of the spatially distinct first plurality of optical capture sites of one or both of (i) the plurality of atoms in the science array or (ii) at least one atom in the science array. In some embodiments, the science array is associated with a first spatial light modulator and the reservoir array is associated with a second spatial light modulator. In some embodiments, the at least one atom transitioned from the reservoir array into the science array is in a dark state, a clock state, or another state forbidden by a selection rule from the optical excitation used for the transition. In some embodiments, the transition of the at least one atom from the reservoir array into the science array is a long-range transition. In some embodiments, the plurality of atoms are qubits.

[0023] In another aspect, the present disclosure provides a system for preparing an atomic sample, the system comprising one or more atomic transition units configured to perform the method of any aspect or embodiment herein.

[0024] In another aspect, the present disclosure provides a system for preparing an atomic sample, the system may include one or more optical trapping units configured to obtain a scientific array including a first plurality of spatially distinct optical trapping sites, the scientific array including a first plurality of atoms trapped at the first spatially distinct optical trapping sites, and a reservoir array including a second plurality of spatially distinct optical trapping sites, the reservoir array including the second plurality of atoms trapped at the second spatially distinct optical trapping sites, and one or more atom transfer units configured to (a) transfer at least one atom from the reservoir array into the scientific array to increase the fill factor of the scientific array, and (b) transfer at least one atom into the reservoir array to increase the fill factor of the reservoir array, the transfer in (b) being performed at least in part during the transfer of the at least one atom from the reservoir array into the scientific array in (a).

[0025] In another aspect, the present disclosure provides a system for preparing an atomic sample, the system may include one or more optical trapping units configured to obtain a scientific array including a first plurality of spatially distinct optical trapping sites, the scientific array including a first plurality of atoms trapped at the first spatially distinct optical trapping sites, and a reservoir array including a second plurality of spatially distinct optical trapping sites, the reservoir array including the second plurality of atoms trapped at the second spatially distinct optical trapping sites, one or more electromagnetic delivery units configured to induce at least a first subset of the plurality of atoms in the scientific array to adopt one or more superposition states, and one or more atom transfer units configured to transition at least one atom of the second plurality of atoms from the reservoir array into the scientific array, the transition occurring substantially without decoherence of the superposition states.

[0026] In another aspect, the present disclosure provides a method for performing continuous non-classical computations, the method comprising: loading a plurality of atoms into a reservoir array including a first plurality of spatially distinct optical trapping sites configured to trap the plurality of atoms, the plurality of atoms being qubits; transitioning a first subset of the plurality of atoms from the reservoir array into a science array including a second plurality of spatially distinct optical trapping sites configured to trap the plurality of atoms; and performing a first non-classical computation using at least some of the first subset of atoms in the science array; determining (i) the number of atoms in the first subset of atoms and (ii) the number of atoms in the first non-classical computation. The method may include determining a number of missing atoms representing a difference between the number of atoms in a remaining subset of the first subset of atoms remaining in the scientific array after performing the classical computation; transitioning a second subset of atoms from the reservoir array into the scientific array, the second subset of atoms including a number of atoms at least equal to the number of missing atoms; reloading the reservoir array with additional atoms that are quantum bits; and performing a second non-classical computation using at least a portion of one or both of (i) the remaining subset of the first subset of atoms and (ii) the second subset of atoms.

[0027] In some embodiments, performing the first non-classical calculation includes applying electromagnetic energy to one or more atoms of a first subset of atoms in the science array, thereby inducing the one or more atoms to adopt one or more superpositions of a first atomic state and at least a second atomic state different from the first atomic state; quantum mechanically entangle at least one of the one or more atoms in the one or more superpositions with at least another atom of the first subset of atoms in the science array; and measuring the one or more superpositions to obtain the first non-classical result. In some embodiments, the first atomic state and the second atomic state include first and second nuclear spin states of nuclei having nuclear spins greater than ½. In some embodiments, the at least one subset of at least one atom in the one or more superpositions and at least another atom of the first subset of atoms in the science array are quantum mechanically entangled with a coherence lifetime of at least 1 second.

[0028] In some embodiments, the plurality of atoms and the additional atoms both comprise neutral atoms. In some embodiments, the plurality of atoms and the additional atoms both comprise Group 2 elements. In some embodiments, the plurality of atoms and the additional atoms both comprise a temperature of at most 10 microkelvin (μK). In some embodiments, one or both of (i) loading the plurality of atoms into the reservoir or (ii) reloading the additional atoms into the reservoir array is performed using one or both of a moving optical trap or optical tweezers. In some embodiments, the science array is physically separated from the reservoir array. In some embodiments, determining the number of atom defects is based on imaging across an imaging axis to determine which sites of a second plurality of spatially distinct optical capture sites of the science array are occupied. In some embodiments, the science array is physically separated from the reservoir array parallel to the imaging axis, and one or both of (i) transitioning a first subset of atoms from the reservoir array into the science array or (ii) transitioning a second subset of atoms from the reservoir array into the science array is performed using one or both of a moving optical trap or optical tweezers.

[0029] In some embodiments, both the science array and the reservoir array are two-dimensional. In some embodiments, both the science array and the reservoir array are three-dimensional. In some embodiments, the science array has a different number of dimensions than the reservoir array. In some embodiments, one or both of the science array or the reservoir array are formed using either an optical or non-optical electromagnetic field. In some embodiments, a first number of sites in the first plurality of light trapping sites is equal to a second number of sites in the second plurality of light trapping sites. In some embodiments, the first number of sites in the first plurality of light trapping sites is greater than the second number of sites in the second plurality of light trapping sites. In some embodiments, transferring a first subset of atoms from the reservoir array into the science array includes transferring at least a first subset of atoms from the reservoir array to one or more intermediate arrays and transferring the first subset of atoms from the one or more intermediate arrays to the science array. In some embodiments, the one or more intermediate arrays include at least two arrays, and at least a first subset of the atoms is transitioned between the at least two arrays (i) after the at least first subset of the atoms is transitioned from the reservoir array to the at least two arrays and (ii) before the first subset of the atoms is transitioned from the at least two arrays to the science array. In some embodiments, the method further includes rearranging, within the science array, the positions of at least some of the spatially distinct second plurality of light capture sites of one or both of (i) a remaining subset of the first subset of the atoms and (ii) the second subset of the atoms.

[0030] Another aspect of the present disclosure provides a system comprising one or more computer processors and a computer memory coupled thereto, the computer memory including machine-executable code that, when executed by the one or more computer processors, performs any of the methods described above or elsewhere herein.

[0031]

[0013] Further aspects and advantages of the present disclosure will become readily apparent to those skilled in the art from the following detailed description, wherein only illustrative embodiments of the present disclosure are shown and described. As will be realized, the present disclosure is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the present disclosure. Accordingly, the drawings and description are to be regarded as illustrative in nature and not restrictive.

[0032] Citation by reference All publications, patents, and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference. To the extent that the publications and patents or patent applications incorporated by reference conflict with the disclosure contained in the specification, the present specification is intended to supersede and / or supersede such conflicting material. [Brief explanation of the drawings]

[0033] The novel features of the invention are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings (also referred to herein as "Figure" and "FIG.").

[0034] [Figure 1] FIG. 1 illustrates a computer control system programmed or otherwise configured to carry out the methods provided herein. [Figure 2] FIG. 1 illustrates an exemplary process for performing continuous non-classical computations. [Figure 3] FIG. 1 illustrates an exemplary method and system for preparing an atomic sample. [Figure 4] FIG. 1 illustrates another exemplary method and system for preparing an atomic sample. [Figure 5]FIG. 1 illustrates another exemplary method and system for preparing an atomic sample. [Figure 6] FIG. 1 shows data from an experiment on conditional reloading of an ancillary qubit. [Figure 7] FIG. 1 shows experimental data demonstrating coherence during loading on MOT. DETAILED DESCRIPTION OF THE INVENTION

[0035] While various embodiments of the present invention have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions may occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed.

[0036] Unless otherwise specified, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. As used in this specification and the appended claims, the singular forms "a," "an," and "the" include plural references unless the context clearly dictates otherwise. References to "or" herein are intended to encompass "and / or" unless otherwise specified.

[0037] Whenever the terms "at least," "greater than," or "greater than or equal to" appear before the first number in a series of two or more numbers, the terms "at least," "greater than," or "greater than or equal to" apply to each number in the series. For example, 1, 2, or 3 or more is equivalent to 1 or more, 2 or more, or 3 or more.

[0038] Whenever the terms "no more than," "less than," or "less than or equal to" appear before the first number in a series of two or more numbers, the terms "no more than," "less than," or "less than or equal to" apply to each number in the series. For example, 3, 2, or 1 or less is equivalent to 3 or less, 2 or less, or 1 or less.

[0039] Where values ​​are described as ranges, such disclosure will be understood to include disclosure of all possible subranges within such ranges, as well as specific numerical values ​​falling within such ranges, whether or not a specific numerical value or specific subrange is explicitly stated.

[0040] As used herein, like letters refer to like elements.

[0041] The term "about" or "approximately" can mean within an acceptable range of error for a particular value, which depends in part on how the value is measured or determined, e.g., the limitations of the measurement system. For example, "about" can mean within one or more standard deviations, in accordance with practice in the art. Alternatively, "about" can mean within a range of up to 20%, up to 10%, up to 5%, or up to 1% of a given value. When particular values ​​are described in the present application and claims, unless otherwise specified, the term "about" can be assumed to mean within an acceptable range of error for the particular value.

[0042] As used herein, the terms "nonclassical computation," "nonclassical procedure," "nonclassical operation," or any "nonclassical computer" generally refer to any method or system for performing a computational procedure outside the paradigm of classical computing. A nonclassical computation, nonclassical procedure, nonclassical operation, or nonclassical computer may include quantum computation, quantum procedure, quantum operation, or quantum computer.

[0043] As used herein, the terms “quantum computation,” “quantum procedure,” “quantum operation,” and “quantum computer” generally refer to any method or system for performing computations using quantum mechanical operations in a Hilbert space represented by a quantum device (such as unitary transformations on a quantum channel or completely positive trace-preserving (CPTP) maps). Thus, quantum computation and classical (or digital) computation may be similar in the following aspect: both computations may involve a sequence of instructions performed on input information and providing an output. Various paradigms of quantum computing may decompose a quantum operation into a sequence of elementary quantum operations that simultaneously affect a subset of qubits of a quantum device. Quantum operations may be selected, for example, based on their locality or ease of physical implementation. A quantum procedure or computation may consist of a sequence of such instructions, which may represent different quantum evolutions on a quantum device for various applications. For example, procedures for calculating or simulating quantum chemistry can represent quantum states and electron spin-orbit annihilation and creation operators by using qubits (e.g., two-level quantum systems) and universal quantum gate sets (e.g., Hadamard, controlled-uncontrolled (CNOT), and π / 8 rotation) through the so-called Jordan-Wigner or Bravi-Kitaev transformations.

[0044] Further examples of quantum procedures or computations may include optimization procedures such as quantum approximate optimization algorithms (QAOA) and finding quantum minima. QAOA may include rotating a single qubit and performing entanglement gates on multiple qubits. In quantum adiabatic computations, instructions may carry a probabilistic or non-probabilistic evolution path from an initial quantum system to a final quantum system.

[0045] Quantum-inspired procedures may include simulated annealing, parallel tempering, master equation solvers, Monte Carlo procedures, etc. Quantum-classical or hybrid algorithms or procedures may include procedures such as variational quantum eigensolvers (VQEs) and variational and adiabatically navigated quantum eigensolvers (VanQver).

[0046] The quantum computer may include one or more of an adiabatic quantum computer, a quantum gate array, a one-way quantum computer, a topological quantum computer, a quantum Turing machine, a quantum annealer, an Ising solver, or a gate model of quantum computing.

[0047] As used herein, the term "adiabatic" refers to any process taking place in a quantum mechanical system in which the parameters of the Hamiltonian change slowly compared to the natural timescale of the system's evolution.

[0048] As used herein, the term "non-adiabatic" refers to any process-performing 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.

[0049] This disclosure describes, in some embodiments, methods and systems that allow a scientific region to be replenished from a reservoir where the scientific region and the reservoir region are different, thereby allowing for refilling of the reservoir without disturbing the atoms in the scientific region, thereby allowing for continuous or quasi-continuous (over the lifetime of the atoms in the scientific region) occupancy and coherent manipulation within the scientific region.

[0050] In a neutral atom quantum computer or simulation device, qubits may be encoded on optically trapped atoms. Because the optical trap may be relatively shallow, atoms may be lost through collisions with residual background gas, leakage into untrapped or otherwise undesired internal states, or heating associated with laser interactions or other processes. Typically, in a quantum computer or simulation device, a subset of the entire optical trap array (referred to herein as a "science region") may be filled to perform a calculation or simulation. To perform successive or repeated calculations, it may be important for atoms to be reloaded into the optical trap.

[0051] Refilling the science region of a quantum computer or simulation device can be achieved by superimposing a trapping array with a magneto-optical trap (MOT), which creates a dense, cold atomic gas, as well as a consumption mechanism that can trap atoms within the array. This process typically takes a significant amount of time, resulting in the loss of atoms already present in the array and the filling of only a portion of the traps in the array (often approximately 50%). The fill factor of the array can be improved by imaging to determine which sites of the array are occupied and then transferring atoms into unfilled sites in the science region. This transfer may be performed using one or more moving optical traps or tweezers. The trapping sites not within the science region form reservoir regions. In some embodiments, the reservoir region and the science region are two regions of the same array, in the sense that both are formed using the same laser / optical elements. Furthermore, the science array and reservoir array may be refilled simultaneously, causing the loss and decoherence of atoms already present in the science region. The disclosed systems and methods can reduce the loss of atoms, the decoherence of atoms, or both during the refilling process.

[0052] Exemplary Process for Performing Continuous Nonclassical Computation FIG. 2 depicts an exemplary process (200) for performing continuous non-classical computation. In some examples, process (200) may be performed with sufficiently different science and reservoir regions so that the reservoir regions can be filled with sufficiently low atomic disorder within the science region. One way to achieve this is for the reservoir and science regions to be distinct arrays, in the sense that they may be formed using different lasers or different optical elements, rather than subregions of the same array. Furthermore, in some embodiments, the reservoirs may be filled not from the MOT but from a third "transport" array. This last technique may eliminate the use of near-resonant light, potentially enabling continuous coherent operations during the reloading process.

[0053] At a high level, the process (200) may include loading a reservoir array, transferring atoms from the reservoir array to a science array, performing a calculation / simulation using the science array where atoms are lost in the science array, reloading the science array from the reservoir array, and reloading the reservoir array. The science array may contain atoms that are actively used in an application (e.g., quantum computing, optical clocks, sensing, or any other application disclosed herein). The science array in a quantum computer may contain data qubits and ancillary qubits. The reservoir array may contain atoms that are not actively used but that can later be used to replace atoms lost from the science array, e.g., ancillary qubits lost from a quantum computer.

[0054] In some cases, process (200) may begin with both the reservoir array and the science array empty. Once atoms are loaded into the reservoir array, the atoms in the reservoir may then be imaged. In some examples, at least a portion of the atoms in the reservoir array may then be transferred into the science array (e.g., using optical tweezers). Reloading the reservoir array may achieve a full or more full reservoir array, allowing more atoms to be transferred from the reservoir array into the science array. Once the science array is fully populated (or filled to a desired / predetermined amount), computation / simulation may begin. During computation / simulation, the science array may be periodically imaged to determine if and where atoms are missing. If atoms are missing from a site in the science array, atoms may be transferred from the reservoir array to fill the site. This may continue as long as there are enough atoms in the reservoir array. If not, new atoms may be loaded into the reservoir array, and the process continues. As depicted in FIG. 2, the process (200) may, in some instances, be iterative or repetitive, with one or more operations of the process (200) potentially being repeated.

[0055] 2 illustrates an exemplary method and system for performing continuous non-classical computation. The method (200) may include an operation (210). The operation (210) may include carrying a plurality of atoms in a reservoir array including a first plurality of spatially distinct optical trapping sites. The first plurality of optical trapping sites may be configured to trap the plurality of atoms. In some cases, the plurality of atoms are qubits in a non-classical computing system, such as a quantum computer, a quantum annealer, or the like. In some cases, the plurality of atoms includes atoms in an atomic clock.

[0056] The method (200) may include an operation (220). The operation (220) may include transferring a first subset of the plurality of atoms from the reservoir array into a science array. The science array may include a second plurality of spatially distinct optical trapping sites. The second plurality of optical trapping sites may be configured to trap the plurality of atoms.

[0057] In some cases, operations 210 and 220 may be repeated multiple times in operation 215. The operations may be repeated until the scientific array contains sufficient fill for quantum computation, quantum simulation, clock operation, measurement operation, sensing operation, etc.

[0058] The method 200 may include an operation 230. The operation 230 may include performing a first application using at least a portion of a first subset of the plurality of atoms in the scientific array. The application may be quantum computing, quantum simulation, a clock operation, a metrology operation, a sensing operation, or the like.

[0059] The method (200) may include an operation (240). The operation (240) may include determining atomic defects in one or more arrays. The operation may include determining an atomic defect number representing the difference between (i) the number of atoms in a first subset of atoms and (ii) the number of atoms in a remaining subset of the first subset of atoms that remain in the scientific array after performing the first non-classical calculation. The atomic defects may be caused by collisions with residual background gas, by leakage into untrapped or otherwise undesired internal states, by heating associated with laser interaction or other processes.

[0060] The method (200) may include an operation (250). The operation (250) may include transferring a second subset of atoms from the reservoir array into the science array. The operation (250) may include a reloading operation. In some cases, the second subset of atoms includes a number of atoms at least equal to the number of atom deficiencies. In some cases, the second subset of atoms includes a number of atoms less than the number of atom deficiencies. The second subset may be transferred without substantially losing coherence of the atoms in the science array. The second subset may be transferred without substantially ceasing use in the science array.

[0061] In some cases, operations 230, 240, and 220 may be repeated multiple times in operation 255. The operations may be repeated until a quantum computation, quantum simulation, clock operation, measurement operation, etc. is completed. The operations may be repeated as long as there are atoms in the reservoir to be filled in the scientific array.

[0062] The method (200) may include an operation (260). The operation (260) may include reloading the reservoir array with additional atoms. The reservoir may be reloaded from an atom source. The atom source may be a cooled atom source. In some examples, the reservoir region may be filled from a magneto-optical trap (MOT), from an atom beam, from a thermal atom gas, from another optical or other form of electromagnetic trap, or from any other atom source. In some examples, the initial loading of the science region may be direct (from any atom source other than the reservoir array), from the reservoir array, or from a reservoir array separate from the one used for refilling. In some examples, the reservoir region may be smaller, larger, or the same size / number of sites as the science region, and similar techniques may be used to maintain any number of atoms within each site of the science array.

[0063] In some cases, operation 260 may be repeated multiple times in operation 265. Operation 260 may be refilled multiple times to fill the reservoir array. This operation may be repeated so that the applications in operation 230 may be performed continuously.

[0064] In some cases, in operation 275, operations 255 and 265 may both be repeated to maintain fill factor in the scientific array. In some cases, the method may include performing a second non-classical calculation using at least a portion of one or both of (i) a remaining subset of the first subset of atoms and (ii) a second subset of atoms.

[0065] The present disclosure includes various sub-operations of method 200. For example, one or more of the operations of method 200 may be omitted. For example, one or more of the operations of method 200 may be repeated.

[0066] 3 illustrates an exemplary method and system for preparing an atomic sample. The method (300) may include an operation (310). The operation (310) may include trapping a plurality of atoms in a scientific array, the scientific array including a first plurality of spatially distinct optical trapping sites.

[0067] The method (300) may include an operation (320), which may include transitioning at least one atom from a reservoir array into a science array to increase the fill factor of the science array, the reservoir array including a second plurality of spatially distinct light capture sites.

[0068] Operation 320 may include an embodiment, variation, or example of operation 220 of method 200. For example, method 300 may include operation 220. Operation 220 may include transferring a first subset of atoms from a reservoir array into a science array. The science array may include a plurality of spatially distinct light capture sites that are different from the reservoir array.

[0069] In some cases, operation 320 may be repeated multiple times in operation 325. The operations may be repeated until the scientific array includes a sufficient fill factor for quantum computation, quantum simulation, clock operation, measurement operation, sensing operation, etc.

[0070] The method (300) may include an operation (330), which may include transitioning at least one atom into the reservoir array to increase the fill factor of the reservoir array. The operation (330) may be performed at least in part during the transition of the at least one atom from the reservoir array into the science array in the operation (320).

[0071] Operation 330 may include an embodiment, variation, or example of operation 260 of method 200. For example, method 300 may include operation 260. Operation 260 may include reloading the reservoir array with additional atoms. The reservoirs may be reloaded from an atom source. The atom source may be a cooled atom source.

[0072] In some cases, operation 330 may be repeated multiple times in operation 335. Operation 330 may be refilled multiple times to fill the reservoir array. This operation may be repeated so that applications, such as the application in operation 230, may be performed continuously. This operation may be repeated without substantially stopping the application so that applications, such as the application in operation 230, may be performed continuously.

[0073] 4 illustrates another exemplary method and system for preparing an atomic sample. Method 400 may be an embodiment, variation, or example of operation 210 of method 200. Operation 210 may include carrying a plurality of atoms in a reservoir array including a first plurality of spatially distinct optical trapping sites. The first plurality of optical trapping sites may be configured to trap the plurality of atoms. In some cases, the plurality of atoms are qubits in a non-classical computing system, such as a quantum computer or a quantum annealer. In some cases, the plurality of atoms includes atoms in an atomic clock.

[0074] Method 400 may include an embodiment, variation, or example of operation 220 of method 200. Operation 220 may include transitioning a first subset of atoms from a reservoir array into a science array. The science array may include a second plurality of spatially distinct optical trapping sites. The second plurality of optical trapping sites may be configured to trap a plurality of atoms.

[0075] In some cases, operations 210 and 220 may be repeated multiple times in operation 215. The operations may be repeated until the scientific array contains a sufficient fill factor for quantum computation, quantum simulation, clock operation, metrology operation, etc.

[0076] As shown in FIG. 4, method (400) may further include embodiments, variations, or examples of operations (320), (325), (330), and (335) of method (200).

[0077] FIG. 5 illustrates another exemplary method and system for preparing an atomic sample. Method (500) may include operation (510). Operation (510) may include trapping a plurality of atoms within a scientific array, the scientific array including a first plurality of spatially distinct optical trapping sites. Method (500) may include operation (520). Operation (520) may include inducing at least a first subset of the plurality of atoms within the scientific array to adopt one or more superposition states. Method (500) may include operation (530). Operation (530) may include transitioning at least one atom from a reservoir array into the scientific array, the reservoir array including a second plurality of spatially distinct optical trapping sites. Operation (530) may be performed substantially without decoherence of the superposition states created in operation (520).

[0078] In some cases, method 500 may include operation 230. Operation 230 may include performing a first application using at least a portion of a first subset of atoms in a scientific array. The application may be quantum computing, quantum simulation, a clock operation, a metrology operation, or the like. Operation 230 may itself include one or more instances of operation 520. For example, a two-qubit gate may include one or more instances of operation 520 that generate a superposition.

[0079] In some cases, the method (500) may include determining atomic defects in one or more arrays. The operation may include determining an atomic defect number representing the difference between (i) the number of atoms in a first subset of atoms and (ii) the number of atoms in a remaining subset of the first subset of atoms that remain in the scientific array after performing the first non-classical calculation. The atomic defects may arise from collisions with residual background gas, from leakage into untrapped or otherwise undesired internal states, from heating associated with laser interaction or other processes.

[0080] Operation 530 may include an embodiment, variation, or example of operation 250 of method 200. For example, method 500 may include operation 250. Operation 250 may include transferring a second subset of atoms from the reservoir array into the science array. Operation 250 may include a reloading operation. In some cases, the second subset of atoms includes a number of atoms at least equal to the number of atom deficiencies. In some cases, the second subset of atoms includes a number of atoms less than the number of atom deficiencies. The second subset may be transferred without substantially losing coherence of the atoms in the science array. The second subset may be transferred without substantially ceasing use in the science array.

[0081] In some cases, operations 520 and 530 may be repeated multiple times in operation 525. The operations may be repeated until a quantum computation, quantum simulation, clock operation, measurement operation, etc. is completed. The operations may be repeated as long as there are atoms in the reservoir to be filled in the scientific array.

[0082] Method 500 may include embodiments, variations, or examples of operation 260 of method 200. For example, operation 260 may include reloading the reservoir array with additional atoms. The reservoirs may be reloaded from an atom source. The atom source may be a cooled atom source. In some cases, operation 260 may be repeated multiple times in operation 265. Operation 260 may be recharged multiple times to fill the reservoir array. This operation may be repeated so that the applications in operation 230 may be performed continuously.

[0083] Continuous loading A useful error-corrected quantum computer should remove entropy faster than it inputs it. One source of entropy in a trapped-atom quantum computer can be missing atoms. Therefore, it may be useful to continuously calculate and conditionally refill sites in a trapped-atom quantum computer. Continuous operation during a non-classical computation may include refilling missing atoms during the computation. For example, continuous operation in a gate-model quantum computer may include refilling missing atoms between "intermediate circuits" or gate operations in a quantum computation. Continuous operation in a quantum simulator may include refilling atoms during a simulation. Continuous operation in a clock operation may include refilling atoms during the clock's operation. Generally, continuous operation may include refilling atoms during the time the application is being performed.

[0084] A continuous operation may include refilling atoms without substantially stopping the application. Substantially stopping may include not performing recovery operations, such as repeating a previous step, to account for the missing atoms. Such recovery operations may include repeating a calculation or part of a calculation to replace the "missing" portion.

[0085] Similarly, because quantum computing, quantum simulation, clock manipulation, metrology, and quantum sensing can each utilize phenomena such as quantum coherence, it may be useful to maintain coherence while refilling atoms in atom-based implementations of these applications (e.g., atomic clocks, neutral atom quantum computers, etc.). For example, atoms may be refilled without substantial loss of coherence of the atoms in the array. Substantially no loss of coherence may include a contrast reduction of 10% or more on the second timescale. For example, a contrast reduction of less than 10% over 2 seconds and a contrast reduction of about 5% over 2 seconds or more. Substantially no loss of coherence may include a contrast of 0.8 (up to 1) or greater over 1 second.

[0086] The present disclosure provides systems and methods for continuously reloading atoms, which may distinguish between a science array and a reservoir array during atom transitions.

[0087] For example, the arrays may be physically distinct. The systems and methods of the present disclosure may employ different sets or subsets of atoms within the array. For example, each of Figures 2-5 shows a science array and a reservoir array. In some cases, the science array is distinct from the reservoir array. In some cases, the science array is spatially distinct from the reservoir array. For example, the science array may be physically separated from the reservoir array. For example, the science array may be energetically separated from the reservoir array during atom transfer. In some cases, both physical and energetic separation methods may be used to facilitate atom transfer without destroying the science array.

[0088] Physically separating the science array and the reservoir array may be useful, for example, in at least some respects. If the science array and the reservoir array are physically distinct, the reservoir array can be more easily spatially separated from the science region. This allows the reservoir array to be loaded without disturbing the atoms in the science region while loading the reservoir region. For example, disturbances may arise from unwanted scattering during transition, unwanted optical shifts, etc. In some cases, a separate optical system from the trapping excitation may be used to transfer atoms from a first array to a second array disclosed herein. For example, the reservoir array may be loaded from a separate optical potential or array, which may disturb atoms in the science region if the reservoir array and the science array are too close. Using separate optical systems to generate the two arrays may be useful to separate the science array from the reservoir array. The arrays may be further isolated by using a separate (e.g., third) optical system to transfer the atoms.

[0089] In some examples, the reservoir region and the science region may be separated either parallel to or transverse to the axis along which imaging is performed. When the separation is parallel to the imaging axis, atoms may be transported from the reservoir to the science region by translating the focal point of a focused trapping laser or by shifting the phase of a trapping optical lattice. See, for example, the "Long Range Transport" section herein. In some cases, the transport of at least one atom from the reservoir array into the science array is a long range transport.

[0090] Electronic separation of the science array and the reservoir array, for example, may be useful in at least some respects. In some examples, the reservoir region and the science region are distinguished by the internal or motional states occupied by the atoms (perhaps instead of being spatially separated). In some examples, traps may be formed with spatially or temporally incoherent or coherent light, or by non-optical electromagnetic fields.

[0091] In some cases, coherence may be preserved by applying a "hidden" excitation during or partially during the refilling of atoms into the science array. Hidden excitation may include placing the transitioned atoms or atoms already in the array in a dark state, a clock state, or another state forbidden by the selection rules from the optical excitation used for the transition. In some examples, hidden excitation may be applied to atoms in the science array during imaging or excitation of atoms to be transferred to the science portion of the array. In some cases, at least one atom transitioned from the reservoir array into the science array is in a dark state. In some cases, the atom transitioned from the reservoir array into the science array is in a dark state, a clock state, or another state forbidden by the selection rules from the optical excitation used for the transition. See, for example, the "State-Selective Atom Transfer" section herein.

[0092] Optical Trap Optical Traps—The systems and methods of the present disclosure provide for spatially distinct optical traps. The optical traps may include examples of optical trapping sites. For example, the optical traps may include any of the examples of optical trapping sites described herein with respect to FIGS. 2-5.

[0093] The system may include one or more trapping systems. The trapping system may include one or more optical trapping systems. The optical trapping system may comprise any of the optical trapping units described herein. In some examples, the optical trap may be formed by tightly focused light (tweezers), by a standing wave grating, or by an imaged mask or grating. The optical trap may also include various methods in which atoms are cooled with optical illumination, e.g., a laser, and a spatially varying magnetic field to generate the trap. Such optical traps are sometimes referred to as magneto-optical traps (MOTs).

[0094] In some cases, the spatially distinct optical traps include 1D, 2D, or 3D optical traps. In some examples, the array may be linear, 2D, 3D, or may include composite dimensions. Composite dimensions may include, for example, dimensions consisting of internal atomic or motional states. The spatially distinct optical traps may include single or multiple reservoir regions. In some examples, the array may be a regular, irregular, or quasi-regular geometric shape.

[0095] Optical Tweezers - In some cases, multiple spatially distinct optical traps comprise optical tweezers. An optical trapping site may comprise one or more optical tweezers. The optical tweezers may comprise one or more focused laser beams to provide attractive or repulsive forces for holding or moving one or more atoms. The beam waist of the focused laser beam may comprise a strong electric field gradient. Atoms may be attracted or repelled along the electric field gradient toward or toward the center of the laser beam, which may comprise the strongest electric field. An optical trapping site may comprise one or more optical tweezers sites in one or more optical arrays of tweezers. An optical trapping site may comprise one or more optical tweezers sites in one or more one-dimensional (1D) optical arrays of tweezers, two-dimensional (2D) optical arrays of tweezers, or three-dimensional (3D) optical arrays of tweezers. In some cases, the methods and systems described herein may be similarly applied to optical lattices. Optical tweezers may be useful for moving atoms or arrays of atoms.

[0096] Multiple Capture Arrays—The systems and methods of the present disclosure may employ different sets or subsets of atoms within the array. For example, each of Figures 2-5 shows a science array and a reservoir array. In some cases, the science array is distinct from the reservoir array. In some cases, the science array is spatially distinct from the reservoir array. For example, the science array may be physically separate from the science array. In some cases, both the science array and the reservoir array are two-dimensional. In some cases, both the science array and the reservoir array are three-dimensional. In some cases, the science array has a different number of dimensions than the reservoir array.

[0097] In some cases, both the science array and the reservoir array are formed using MOTs. In some cases, both the science array and the reservoir array are formed using optical tweezers. In some cases, either the science array or the reservoir array, or both, are formed using either optical or non-optical electromagnetic fields. In some cases, the science array and the reservoir array comprise spatially distinct MOTs. In some cases, the science array comprises a first MOT in a first chamber and the reservoir array comprises a second MOT in a second chamber. In some cases, the science array and the reservoir array comprise different regions within the same MOT.

[0098] While each of Figures 2-5 illustrates a science array and a reservoir array, the systems and methods of the present disclosure may include one or more additional arrays, e.g., intermediate arrays. For example, improved cooling may be achieved with multi-stage MOTs. For example, a first MOT may be cooled to a first temperature, and a second MOT may be cooled to a second temperature. In some cases, multi-stage MOTs may be useful for spatially separating the arrays. For example, a first MOT generated by a first light irradiation and physically separated from a second MOT may be better insulated from heat, atomic defects, thermal noise, etc., from the second MOT than a different region of the same MOT.

[0099] In some cases, in any of the methods disclosed herein, transitioning at least one atom from the reservoir array into the scientific array includes transitioning a first number of atoms from the reservoir array to one or more intermediate arrays and transitioning a second number of atoms from the one or more intermediate arrays to the scientific array. In some cases, the one or more intermediate arrays include at least two intermediate arrays. In some cases, at least some atoms are transitioned between at least two intermediate arrays (i) after some atoms have been transitioned from the reservoir array to the at least two intermediate arrays and (ii) before some atoms are transitioned from the at least two intermediate arrays to the scientific array.

[0100] The site-light trapping system may be configured to generate multiple light trapping sites. The light trapping system may be configured to generate multiple spatially distinct light trapping sites. As shown in each of Figures 2-5, each array may include spatially distinct light trapping sites. While each light trapping site is shown to have only a single atom, in some cases it may be advantageous to have multiple atoms at a single site. In some cases, it may be preferable to have a single atom at a single site. For example, a single atom at a single site may be easier to cool due to reduced collisions with other atoms.

[0101] In some cases, the second number of sites in the second plurality of light capture sites is equal to the first number of sites in the first plurality of light capture sites. In some cases, the second number of sites in the second plurality of light capture sites is greater than the first number of sites in the first plurality of light capture sites. For example, the number of captures in the science array may be the same as the number of captures in the reservoir array. However, in some cases, it may be more useful to have a greater or lesser number of captures in the reservoir array.

[0102] In some cases, the science array, reservoir array, and any intermediate arrays may each be generated by the same or different optical trapping systems. For example, each trapping system may vary based on the needs of a particular array (science, reservoir, intermediate, etc.). Each optical trapping system may include any number of sites disclosed herein. Each optical trapping system may include any number of trapped atoms disclosed herein.

[0103] For example, each light capture system may have at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 10,000, 12,000, 14,000, 16,000, 18,000, 19,000, 21,000, 22,000, 23,000, 24,000, 25,000, 26,000, 27,000, 28,000, 29,000, 30,000, 31,000, 32,000, 33,000, 34,000, 35,000, 36,000, 37,000, 38,000, 39,000, 40,000, 41,000, 42,000, 43,000, 44,000, 45,000, 46,000, 47,000, 48,000, 49,000, 50 It may be configured to generate 0, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000, or more light capture sites. Each light capture system can accommodate 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, and 1 The light capture system may be configured to generate 0,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or fewer light capture sites. The light capture system may be configured to capture a number of light capture sites within a range defined by any two of the foregoing values.

[0104] Each optical trapping system may be configured to trap a plurality of atoms, for example, at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90 ...120,000, 140,000, 150,000, 160,000, 170,000, 180,000, 190,000, 210,000, 220,000, 230,000, 240,000, 250,000, 260,000, 270,000, 280,000, 290,000, 310,000, 320,000, 330,000, 340,000, 350,000, 360, The optical trapping sites may be configured to trap a total number of atoms in the plurality of optical trapping sites of 0, 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. For example, each optical capture system may have a maximum of 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 atoms. The optical trapping system may be configured to trap a number of atoms that are within a range defined by any two of the foregoing values.

[0105] Trapping Excitation—In some cases, the methods and systems disclosed herein may be configured to form multiple optical trapping sites using a trapping excitation. The trapping excitation may include optical excitations such as magneto-optical traps, optical tweezers, etc. In some cases, the trapping excitation is delivered by one or more optical trapping systems disclosed herein. In some cases, each optical trapping system includes its own trapping excitation (e.g., trapping wavelength, trapping power, trapping focus, number of spots, etc.). In some cases, a single trapping excitation may be split into multiple arrays to form multiple arrays of traps with similar properties.

[0106] In some instances, using separate lasers or optics (e.g., "optical pumping") to form the reservoir array (e.g., compared to the lasers or optics that may be used with the science array) may be useful for one or more reasons. In one example, different laser wavelengths, trapping geometries (e.g., tweezers spot size or spacing), or methods for generating different arrays (e.g., acousto-optic deflectors (AODs), spatial light modulators (SLMs), digital mirror devices (DMDs), microlens arrays, diffraction gratings, standing wave gratings, imaging structures, or others) may be used to generate the reservoir array and the science array. Thus, the properties of each array (e.g., trapping depth, differential polarizability of the associated atomic transitions, trapping spacing, trapping oscillation frequency, etc.) may be optimized for its specific role. In another example, power from a single source is typically limited; by using multiple sources, the total available power can be increased, allowing for the formation of more numerous and / or deeper traps.

[0107] The light capture system may include one or more light sources configured to emit light to generate the multiple light capture sites described herein. For example, the light capture system may include a single light source. In some cases, the light capture system may include any number of light sources, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more light sources, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 light source. The light source may include one or more lasers.

[0108] The light source may be configured to direct light to one or more light modulators (OMs) configured to generate multiple light trapping sites. For example, the light trapping unit may include an OM configured to generate multiple light trapping sites. In some cases, the light trapping unit may include any number of OMs, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more OMs, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 OM. The OM may include one or more digital micromirror devices (DMDs). The OM may include one or more liquid crystal devices, such as one or more liquid crystal on silicon (LCoS) devices. The OM may include one or more spatial light modulators (SLMs). The OM may include one or more acousto-optic deflectors (AODs) or acousto-optic modulators (AOMs). The OM may include one or more electro-optic deflectors (EODs) or electro-optic modulators (EOMs).

[0109] The OM may be optically coupled to one or more optical elements to generate a regular array of light trapping sites. The optical elements may include a lens or microscope objective configured to redirect light from the OM to form a regular rectangular grid of light trapping sites.

[0110] For example, the OM may include an SLM, DMD, or LCoS device, which may be imaged into the back focal plane of a microscope objective, potentially generating either a two-dimensional or three-dimensional configuration of optical trapping sites.

[0111] In some cases, the trapping excitation may be turned on or off during the course of the methods, operations, and applications disclosed herein. For example, the trapping light may be on during the loading stage of the array of optical traps. For example, the trapping light may be turned off during or after the application of a second optical excitation, such as an optical excitation for a non-classical computing operation, clock operation, measurement operation, sensing operation, or other application of the present disclosure. For example, a trap with an initial number of atoms may be provided in a science array. A Rydberg excitation may be applied to form optical coherence between two atoms in the science array. One or more atoms may be added to the science array. The trapping light may be temporarily turned off during the optical excitation to form the coherence.

[0112] In some cases, the capture excitation in each optical capture system is 399 nm. 1 P1 transition followed by 556 nm 3and narrow linewidth transitions of P1 and P2. The capture excitation of each optical capture system is at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm , 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 more. The light has a maximum wavelength of approximately 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 690nm The light may include one or more wavelengths below 400 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or less. The light may include one or more wavelengths within a range defined by any two of the foregoing values.For example, the light may include one or more wavelengths in the ranges of 400 nm to 1,000 nm, 500 nm to 1,000 nm, 600 nm to 1,000 nm, 650 nm to 1,000 nm, 400 nm to 900 nm, 400 nm to 800 nm, 400 nm to 700 nm, 400 nm to 600 nm, 400 nm to 500 nm, 500 nm to 700 nm, or 650 nm to 700 nm.

[0113] atom The systems and methods of the present disclosure may be applied to any atomic system that can be cooled and trapped. In some cases, the plurality of atoms includes neutral atoms. In some cases, the plurality of atoms includes Group 2 elements. In some cases, the plurality of atoms includes scandium. In some cases, the plurality of atoms includes Group 2-like elements. In some cases, the plurality of atoms are atoms with two valence electrons. In some cases, the plurality of atoms includes ytterbium.

[0114] The atom-light trapping system may be configured to trap neutral atoms. In some cases, the light trapping system may trap alkaline earth or alkaline earth-like atoms. In some cases, the alkaline earth-like atoms include two valence electrons. In some cases, the alkaline earth or alkaline earth-like atoms include strontium or ytterbium.

[0115] The one or more atoms may include an alkali atom. The one or more atoms may include a lithium (Li) atom, a sodium (Na) atom, a potassium (K) atom, a rubidium (Rb) atom, or a cesium (Cs) atom. The one or more atoms may include a lithium-6 atom, a lithium-7 atom, a sodium-23 atom, a potassium-39 atom, a potassium-40 atom, a potassium-41 atom, a rubidium-85 atom, a rubidium-87 atom, or a cesium-133 atom. The one or more atoms may include an alkaline earth atom. The one or more atoms may include a beryllium (Be) atom, a magnesium (Mg) atom, a calcium (Ca) atom, a strontium (Sr) atom, or a barium (Ba) atom. The one or more atoms may include beryllium-9 atoms, magnesium-24 atoms, magnesium-25 atoms, magnesium-26 atoms, calcium-40 atoms, calcium-42 atoms, calcium-43 atoms, calcium-44 atoms, calcium-46 atoms, calcium-48 atoms, strontium-84 atoms, strontium-86 atoms, strontium-87 atoms, strontium-88 atoms, barium-130 atoms, barium-132 atoms, barium-133 atoms, barium-134 atoms, barium-135 atoms, barium-136 atoms, barium-137 atoms, or barium-138 atoms. The one or more atoms may include a rare earth atom. The one or more atoms may include a scandium (Sc) atom, a yttrium (Y) atom, a lanthanum (La) atom, a cerium (Ce) atom, a praseodymium (Pr) atom, a neodymium (Nd) atom, a samarium (Sm) atom, a europium (Eu) atom, a gadolinium (Gd) atom, a terbium (Tb) atom, a dysprosium (Dy) atom, a holmium (Ho) atom, an erbium (Er) atom, a thulium (Tm) atom, an ytterbium (Yb) atom, or a lutetium (Lu) atom.One or more atoms may be selected from the group consisting of scandium-45 atom, yttrium-89 atom, lanthanum-139 atom, cerium-136 atom, cerium-138 atom, cerium-140 atom, cerium-142 atom, praseodymium-141 atom, neodymium-142 atom, neodymium-143 atom, neodymium-145 atom, neodymium-146 atom, neodymium-148 atom, samarium-144 atom, samarium-149 atom, samarium-150 atom, samarium-152 atom, samarium-154 atom, europium-151 atom, europium-153 atom, gadolinium-154 atom, gadolinium-155 atom, gadolinium-156 atom, gadolinium-157 atom, gadolinium-158 atom, gadolinium-160 atom, and terbium-159 atom. The element may include a dysprosium-156 atom, a dysprosium-158 atom, a dysprosium-160 atom, a dysprosium-161 atom, a dysprosium-162 atom, a dysprosium-163 atom, a dysprosium-164 atom, an erbium-162 atom, an erbium-164 atom, an erbium-166 atom, an erbium-167 atom, an erbium-168 atom, an erbium-170 atom, a holmium-165 atom, a thulium-169 atom, an ytterbium-168 atom, an ytterbium-170 atom, an ytterbium-171 atom, an ytterbium-172 atom, an ytterbium-173 atom, an ytterbium-174 atom, an ytterbium-176 atom, a lutetium-175 atom, or a lutetium-176 atom.

[0116] Atom Transfer Unit As disclosed herein, the systems and methods disclosed herein may use multiple arrays of optical traps (e.g., a science array, a reservoir array, an intermediate array, etc.). In some cases, the science array is different from the reservoir array. In some cases, the science array is spatially distinct from the reservoir array. For example, the science array may be physically separate from the science array.

[0117] Physically separating the science array and the reservoir array may be useful in at least some respects. For example, if the science array and the reservoir array are physically distinct, the reservoir array can be more easily spatially separated from the science region. This allows the reservoir array to be loaded without disturbing the atoms in the science region while loading the reservoir region. For example, disturbances may arise from unwanted scattering during transition, unwanted optical shifts, etc. In some cases, a separate optical system from the trapping excitation may be used to transfer atoms from a first array to a second array disclosed herein. For example, the reservoir array may be loaded from a separate optical potential or array, which may disturb atoms in the science region if the reservoir array and the science array are too close. Using separate optical systems to generate the two arrays may be useful to separate the science array and the reservoir array. The arrays may be further isolated by using a separate (e.g., third) optical system to transfer the atoms.

[0118] The transfer of atoms between arrays and the rearrangement of atoms within the arrays may be accomplished by an atom transfer unit disclosed herein. The atom transfer unit may include any embodiment, variation, or example of an atom rearrangement unit disclosed herein. For example, operations 220, 250, 320, and 530 described herein may include transferring atoms from a reservoir array to a scientific array.

[0119] In some examples, the present techniques may be combined with methods for stochastically, deterministically, or near-deterministically supporting optical traps or other trapping, such as those disclosed herein. In some examples, atoms in the scientific region may or may not rearrange when the scientific array is replenished. In some examples, atoms may be transitioned between the reservoir region and the scientific region by optical tweezers. In some examples, atoms may be transitioned between the reservoir region and the scientific region by optical lattices. In some examples, atoms may be transitioned between the reservoir region and the scientific region by tunneling / hopping between sites. In some examples, atoms may be moved between the reservoir and the scientific region by autonomous stabilization techniques. The autonomous stabilization techniques may include imaging the initial and / or final occupancy of the scientific region and / or the reservoir region and autonomously updating the occupancy of the sites of the array.

[0120] In some cases, (i) loading multiple atoms into the reservoir or (ii) reloading the reservoir array with additional atoms is performed using one or both of a moving optical trap and optical tweezers. In some cases, optical tweezers may be used to move (e.g., pick and place) a single atom or a subset of atoms between or within the array. In some cases, a moving optical trap may also be used to translate or compress the array. The moving optical trap may implement a tone to sweep atoms from one location to another. The atom transfer unit may be configured to transfer one or more replacement atoms from one or more atom reservoirs to one or more optical trapping sites. For example, the one or more atom transfer units may comprise one or more electrically tunable lenses, acousto-optic deflectors (AODs), or spatial light modulators (SLMs).

[0121] In some cases, the science array is physically separated from the reservoir array parallel to the imaging axis, and one or both of (i) transitioning a first subset of atoms from the reservoir array into the science array or (ii) transitioning a second subset of atoms from the reservoir array into the science array is performed using one or both of a moving optical trap or optical tweezers.

[0122] In some cases, any of methods 200, 300, 400, or 500 may include rearranging, within a scientific array, the positions of spatially distinct light capture sites on at least some of one or both of (i) a plurality of atoms in the scientific array or (ii) at least one atom in the scientific array. In some cases, any of methods 200, 300, 400, or 500 may include rearranging, within a reservoir array, the positions of spatially distinct light capture sites on at least some of one or both of (i) a plurality of atoms in the reservoir array or (ii) at least one atom in the reservoir array.

[0123] The optical trapping systems disclosed herein may include one or more atom rearrangement units configured to alter the spatial arrangement of a plurality of atoms trapped at the optical trapping site based on one or more images obtained by the imaging unit. The optical trapping unit may include any number of atom rearrangement units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more atom rearrangement units, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 atom rearrangement units. In some cases, the science array is associated with a first spatial light modulator and the reservoir array is associated with a second spatial light modulator.

[0124] The atom rearrangement unit may be configured to change the spatial arrangement of the plurality of light trapping sites to obtain an increased fill factor. The fill factor may be defined as the ratio of the number of computationally active light trapping sites occupied by one or more atoms to the total number of computationally active light trapping sites available in the light trapping unit or a portion of the light trapping unit. For example, an initial loading of atoms within the computationally active light trapping sites may result in a fill factor of less than 100%, 90%, 80%, 70%, 60%, 50%, or less, such that atoms occupy less than 100%, 90%, 70%, 60%, 50%, or less of the available computationally active light trapping sites. It may be desirable to rearrange atoms to achieve a fill factor of at least about 50%, 60%, 70%, 80%, 90%, or 100%. By analyzing the imaging information obtained by the imaging unit, the atom rearrangement unit may achieve a fill rate of at least about 50%, 60%, 70%, 80%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, 99.1%, 99.2%, 99.3%, 99.4%, 99.5%, 99.6%, 99.7%, 99.8%, 99.9%, 99.91%, 99.92%, 99.93%, 99.94%, 99.95%, 99.96%, 99.97%, 99.98%, 99.99% or more. The atomic rearrangement unit may achieve a fill factor of up to about 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50%, or less. The atomic rearrangement unit may achieve a fill factor within a range defined by any two of the foregoing values.

[0125] In some cases, the atom repositioning may be performed by (i) acquiring an image of the optical trapping unit and identifying filled and unfilled optical trapping sites, (ii) determining a sequence of movements to move atoms from the filled to the unfilled optical trapping sites, and (iii) moving atoms from the filled to the unfilled optical trapping sites. Operations (i), (ii), and (iii) may be performed iteratively until a large fill factor is achieved. Operation (iii) may include converting the movements identified in operation (ii) into a waveform that can be sent to an arbitrary waveform generator (AWG) and using the AWG to drive the AOD to move the atoms.

[0126] long distance transition As the spatial separation between the science array and the reservoir array increases, the interaction between the two arrays may decrease. However, it may become more difficult to transfer atoms between the arrays. The systems and methods of the present disclosure may incorporate long-range transfer techniques to facilitate greater physical separation.

[0127] In an exemplary long-range transfer technique, an optical lattice may be generated by interfering two counter-directional laser beams whose focal points overlap. Atoms may be transported by simultaneously translating the focal points of the two counter-directional laser beams while translating the phase of the optical lattice, so that the two focal points remain overlapping and track the phase of the lattice throughout the atom's travel. The tight confinement of the optical lattice enables fast transport due to the large restoring force caused by the large intensity gradient created by the lattice. By translating the laser focal point, trap depth can be maximized with minimal laser power throughout the entire trajectory.

[0128] To achieve deep lattices in a power-efficient manner, the waist of the transport beam may be translated in synchronization with the optical lattice by moving the position of two focusing lenses, one for each of the two counter-propagating beams that form the lattice. The alignment between the two beams may be actively maintained using a closed-loop piezoelectric steering mirror. Atoms are transitioned into the optical tweezers array by superimposing the atoms with the array, ramping up the power in the tweezers, and then ramping down the transport lattice.

[0129] In some cases, the long-range transition method may include using one or more electromagnetic waves to cool and trap a plurality of atoms in a one-dimensional optical lattice. In some cases, the long-range transition method may include stopping the cooling of the plurality of atoms in the one-dimensional optical lattice. In some cases, the long-range transition method may include chirping the relative frequency and / or adjusting the focal depth of one or more lenses to maintain trapping of the plurality of atoms. In some cases, the long-range transition method may include changing the angle of one or more electromagnetic waves to transport a set of atoms consisting of the plurality of atoms in the optical lattice. In some cases, the long-range transition method may include performing a computation using the plurality of atoms.

[0130] In some embodiments, chirping the relative frequency comprises translating the phase of the one-dimensional optical lattice. In some embodiments, translating the phase of the one-dimensional optical lattice comprises transporting one or more atoms from a first zone to a second zone. In some embodiments, the first zone is a zone that carries atoms (e.g., a reservoir array) and the second zone is a chemical array. In some embodiments, transporting the one or more atoms from the first zone to the second zone comprises transporting the one or more atoms over a distance. In some embodiments, the distance is at least about 20 cm. In some embodiments, the distance is in a range from about 20 cm to about 100 cm. In some embodiments, translating the phase of the one-dimensional optical lattice comprises changing the angle of a mirror. In some embodiments, adjusting the focal depth of one or more lenses comprises changing the position of one or more lenses.

[0131] Cooling / Preparation The science array and reservoir array may be integrated with the cooling process. In some applications, it may be advantageous for each atom to be in substantially the same state or a substantially determined / determinable state so that applications (e.g., metrology, sensing, optical clocks, non-classical computation, quantum simulation, etc.) can be performed. The optical trapping systems disclosed herein (e.g., science array, reservoir array) may be integrated with the state preparation systems disclosed herein.

[0132] As disclosed above, improved cooling can be achieved with multi-stage MOTs. For example, a first MOT can be cooled to a first temperature, and a second MOT can be cooled to a second temperature. In some cases, multi-stage MOTs can be useful for spatial separation of the array. For example, a first MOT generated by a first light irradiation and physically separated from a second MOT can be better insulated from heat, atomic defects, thermal noise, etc. from the second MOT than a different region of the same MOT. In some cases, a single MOT can include multiple cooling operations. For example, a first cooling operation can be performed using one or more electromagnet delivery units to cool the 399 nm MOT.1 P1 transition followed by 556 nm 3 and delivering a narrow linewidth transition of P1.

[0133] In one example, operations 210 and 260 disclosed herein with respect to methods 200, 300, 400, and 500 may include initially loading and / or reloading the reservoir array with additional atoms. The reservoir may be reloaded from an atom source. The atom source may be a cooled atom source. In some examples, the reservoir region may be filled from a magneto-optical trap (MOT), an atom beam, a thermal atom gas, another optical or other form of electromagnetic trap, or any other atom source. In some examples, the initial loading of the science region (e.g., operation 220 herein) may be direct (from any atom source other than the reservoir array), from the reservoir array, or from a reservoir array separate from the one used for refilling. In some examples, the reservoir region may be smaller, larger, or the same size / number of sites as the science region, and similar techniques may be used to maintain any number of atoms within each site of the science array.

[0134] State Preparation—The systems and methods disclosed herein may include one or more state preparation units. The state preparation unit may include a portion of the atom source. The state preparation unit may be configured to prepare a state of the plurality of atoms as described herein. The state preparation unit may be coupled to the optical trapping unit and may direct atoms prepared by the state preparation unit to the optical trapping unit. The state preparation unit may be configured to cool the plurality of atoms. The state preparation unit may be configured to cool the plurality of atoms before trapping the plurality of atoms in the plurality of optical trapping sites.

[0135] In some cases, the state preparation unit includes one or more atom reservoirs. The atom reservoirs may be configured to provide one or more replacement atoms to replace one or more atoms in one or more optical trapping sites when atoms are lost from the optical trapping sites of the science array or reservoir array. The atom reservoirs may be spatially separated from the optical traps of the science array or reservoir array. For example, the atom reservoirs may be located at a distance from the reservoir array and the optical traps of the science array.

[0136] In some cases, the atomic reservoir may comprise a portion of the optical trapping sites of the optical trapping unit (e.g., the reservoir array is a subset of the chemical array). A first subset of the optical trapping sites may be utilized to perform quantum computations and may be referred to as the set of computationally active optical trapping sites (e.g., the chemical array), and a second subset of the optical trapping sites may function as the atomic reservoir. For example, the first subset of the optical trapping sites may comprise an inner array of optical trapping sites, and the second subset of the optical trapping sites comprises an outer array of optical trapping sites surrounding the inner array. The inner array may comprise a rectangular, square, rectangular prism, or cubic array of optical trapping sites.

[0137] The condition preparation unit may be coupled to the optical trapping unit and may direct atoms prepared by the condition preparation unit to the optical trapping unit. The condition preparation unit may be configured to cool the plurality of atoms. The condition preparation unit may be configured to cool the plurality of atoms before trapping the plurality of atoms in the plurality of optical trapping sites.

[0138] The state preparation unit may include one or more Zeeman decelerators. For example, the state preparation unit may include a Zeeman decelerator. The state preparation may include any number of Zeeman decelerators, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more Zeeman decelerators, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 Zeeman decelerators. The Zeeman decelerator may be configured to cool one or more atoms of the plurality of atoms from a first velocity or velocity distribution (e.g., an emission velocity from the atom source, room temperature, liquid nitrogen temperature, or any other temperature) to a second velocity that is lower than the first velocity or velocity distribution.

[0139] The first velocity or velocity distribution may be associated with a temperature of at least about 50 Kelvin (K), 60K, 70K, 80K, 90K, 100K, 200K, 300K, 400K, 500K, 600K, 700K, 800K, 900K, 1,000K, or higher. The first velocity or velocity distribution may be associated with a temperature of up to about 1,000K, 900K, 800K, 700K, 600K, 500K, 400K, 300K, 200K, 100K, 90K, 80K, 70K, 60K, 50K, or lower. The first velocity or velocity distribution may be associated with a temperature within a range defined by any two of the foregoing values. The second velocity may be at least about 1 meter per second (m / s), 2 m / s, 3 m / s, 4 m / s, 5 m / s, 6 m / s, 7 m / s, 8 m / s, 9 m / s, 10 m / s, or more. The second velocity may be at most about 10 m / s, 9 m / s, 8 m / s, 7 m / s, 6 m / s, 5 m / s, 4 m / s, 3 m / s, 2 m / s, 1 m / s, or less. The second velocity may be within a range defined by any two of the foregoing values. The Zeeman reducer may include a 1D Zeeman reducer.

[0140] The state preparation unit may include one or more magneto-optical traps (MOTs). The one or more MOTs may be configured to cool the atoms to a first temperature. The temperature may be at most about 10 millikelvin (mK), 9 mK, 8 mK, 7 mK, 6 mK, 5 mK, 4 mK, 3 mK, 2 mK, 1 mK, 0.9 mK, 0.8 mK, 0.7 mK, 0.6 mK, 0.5 mK, 0.4 mK, 0.3 mK, 0.2 mK, 0.1 mK, or lower. The first temperature may be at least about 0.1 mK, 0.2 mK, 0.3 mK, 0.4 mK, 0.5 mK, 0.6 mK, 0.7 mK, 0.8 mK, 0.9 mK, 1 mK, 2 mK, 3 mK, 4 mK, 5 mK, 6 mK, 7 mK, 8 mK, 9 mK, 10 mK, or higher. The first temperature may be within a range defined by any two of the foregoing values. The MOT may include a 1D, 2D, or 3D MOT.

[0141] The state preparation unit may comprise one or more sideband or Sisyphus cooling units (such as the sideband cooling units described at www.arxiv.org / abs / 1810.06626 or the Sisyphus cooling units described at www.arxiv.org / abs / 1811.06014, each of which is incorporated by reference in its entirety for all purposes). The state preparation may include any number of sideband or Sisyphus cooling units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more sideband or Sisyphus cooling units, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 sideband or Sisyphus cooling units. The sideband or Sisyphus cooling units may be configured to cool atoms from a second temperature to a third temperature lower than the second temperature using sideband cooling. The third temperature may be at most about 10 μK, 9 μK, 8 μK, 7 μK, 6 μK, 5 μK, 4 μK, 3 μK, 2 μK, 1 μK, 900 nK, 800 nK, 700 nK, 600 nK, 500 nK, 400 nK, 300 nK, 200 nK, 100 nK, 90 nK, 80 nK, 70 nK, 60 nK, 50 nK, 40 nK, 30 nK, 20 nK, 10 nK, or lower. The third temperature may be at most about 10 nK, 20 nK, 30 nK, 40 nK, 50 nK, 60 nK, 70 nK, 80 nK, 90 nK, 100 nK, 200 nK, 300 nK, 400 nK, 500 nK, 600 nK, 700 nK, 800 nK, 900 nK, 1 μK, 2 μK, 3 μK, 4 μK, 5 μK, 6 μK, 7 μK, 8 μK, 9 μK, 10 μK, or more. The third temperature may be within a range defined by any two of the foregoing values.

[0142] The sideband or Sisyphus cooling unit may include one or more light sources (such as any of the light sources described herein) configured to emit light at wavelengths of at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, and 710 nm. , 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 more. The light has a maximum wavelength of approximately 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 690nm The light may include one or more wavelengths below 400 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or less. The light may include one or more wavelengths within a range defined by any two of the foregoing values.For example, the light may include one or more wavelengths in the ranges of 400 nm to 1,000 nm, 500 nm to 1,000 nm, 600 nm to 1,000 nm, 650 nm to 1,000 nm, 400 nm to 900 nm, 400 nm to 800 nm, 400 nm to 700 nm, 400 nm to 600 nm, 400 nm to 500 nm, 500 nm to 700 nm, or 650 nm to 700 nm.

[0143] The state preparation unit may include one or more optical pumping units. The state preparation may include any number of optical pumping units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more optical pumping units, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 optical pumping units. The optical pumping units may be configured to emit light to optically pump atoms from an equilibrium distribution of atomic states to a non-equilibrium atomic state. For example, the optical pumping units may be configured to emit light to optically pump atoms from an equilibrium distribution of atomic states to a single pure atomic state. The optical pumping units may be configured to emit light to optically pump atoms to the ground atomic state or any other atomic state. The optical pumping units may be configured to optically pump atoms between any two atomic states. The optical pumping units may include one or more light sources (such as any of the light sources described herein) configured to emit light. The light may be at least about 400nm, 410nm, 420nm, 430nm, 440nm, 450nm, 460nm, 470nm, 480nm, 490nm, 500nm, 510nm, 520nm, 530nm, 540nm, 550nm, 560nm, 570nm, 580nm, 590nm, 600nm, 610nm, 620nm, 630nm, 640nm, 650nm, 660nm, 670nm, 680nm, 690nm, 700nm, 710nm , 720nm, 730nm, 740nm, 750nm, 760nm, 770nm, 780nm, 790nm, 800nm, 810nm, 820nm, 830nm, 840nm, 850nm, 860nm, 870nm, 880nm, 890nm, 900nm, 910nm, 920nm, 930nm, 940nm, 950nm, 960nm, 970nm, 980nm, 990nm, 1,000nm, or more.The light has a maximum wavelength of approximately 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 690nm The light may include one or more wavelengths below 400 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or less. The light may include one or more wavelengths within a range defined by any two of the foregoing values. For example, the light may include one or more wavelengths in the ranges of 400 nm to 1,000 nm, 500 nm to 1,000 nm, 600 nm to 1,000 nm, 650 nm to 1,000 nm, 400 nm to 900 nm, 400 nm to 800 nm, 400 nm to 700 nm, 400 nm to 600 nm, 400 nm to 500 nm, 500 nm to 700 nm, or 650 nm to 700 nm.

[0144] The state preparation unit may comprise one or more coherent drive units. The state preparation may include any number of coherent drive units, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more coherent drive units, or up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 coherent drive units. The coherent drive units may be configured to coherently drive atoms from a non-equilibrium state to a first or second atomic state described herein. Thus, atoms may be optically pumped to a convenient atomic state to access (e.g., based on the availability of a light source emitting a particular wavelength or other factors) and then coherently driven to an atomic state described herein useful for performing quantum computation. The coherent drive units may be configured to induce single-photon transitions between the non-equilibrium state and the first or second atomic state. The coherent drive units may be configured to induce two-photon transitions between the non-equilibrium state and the first or second atomic state. The two-photon transition may be induced using light from two light sources described herein (such as two lasers described herein).

[0145] The coherent driving unit may include one or more light sources (such as any of the light sources described herein) configured to emit light at wavelengths of at least about 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, and 710 nm. , 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 more. The light has a maximum wavelength of approximately 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm, 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 690nm The light may include one or more wavelengths below 400 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, or less. The light may include one or more wavelengths within a range defined by any two of the foregoing values.For example, the light may include one or more wavelengths in the ranges of 400 nm to 1,000 nm, 500 nm to 1,000 nm, 600 nm to 1,000 nm, 650 nm to 1,000 nm, 400 nm to 900 nm, 400 nm to 800 nm, 400 nm to 700 nm, 400 nm to 600 nm, 400 nm to 500 nm, 500 nm to 700 nm, or 650 nm to 700 nm.

[0146] The coherent drive unit may be configured to induce an RF transition between the non-equilibrium state and the first or second atomic state. The coherent drive unit may include one or more electromagnetic radiation sources configured to emit electromagnetic radiation configured to induce the RF transition. For example, the coherent drive unit may include one or more RF sources (such as any of the RF sources described herein) configured to emit RF radiation. The RF radiation may include one or more wavelengths of at least about 10 centimeters (cm), 20 cm, 30 cm, 40 cm, 50 cm, 60 cm, 70 cm, 80 cm, 90 cm, 1 meter (m), 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, 9 m, 10 m, or longer. The RF radiation may include one or more wavelengths up to about 10 m, 9 m, 8 m, 7 m, 6 m, 5 m, 4 m, 3 m, 2 m, 1 m, 90 cm, 80 cm, 70 cm, 60 cm, 50 cm, 40 cm, 30 cm, 20 cm, 10 cm, or shorter. The RF radiation may include one or more wavelengths within a range defined by any two of the foregoing values. Alternatively or additionally, the coherent driving unit may include one or more light sources (such as any light sources described herein) configured to induce two-photon transitions corresponding to the RF transitions.

[0147] Atom Defects and Imaging Optionally, any of the methods disclosed herein (e.g., (200), (300), (400), (500)) may further include determining an atom defect number representing the difference between (i) the atom number of the plurality of atoms captured within the scientific array and (ii) the atom number of a remaining subset of the plurality of atoms captured within the scientific array that remains within the scientific array after performing at least a portion of the non-classical computation.

[0148] Atomic defects may be determined by imaging one or more atoms in either array. Imaging may be affected by exciting the atoms into an emissive state, such as fluorescent, spontaneously luminescent, stimulated, or phosphorescent. Scattered photons after imaging may be collected by a camera or detector.

[0149] In some cases, atoms may be transferred into the science array to fill the observed missing atoms. For example, at least one atom transferred from the reservoir array into the science array includes a number of atoms at least equal to the number of missing atoms. In some cases, determining the number of missing atoms is based on imaging across an imaging axis to determine which sites of a second plurality of spatially distinct light capture sites of the science array are occupied.

[0150] In some examples, atoms can be transferred between the reservoir region and the science region by autonomous stabilization techniques, which may include imaging the initial and / or final occupancy of the science region and / or the reservoir region and autonomously updating the occupancy of the sites on the array. In this manner, the fill factor of the array may be actively maintained.

[0151] State-selective atom transfer In some cases, coherence may be preserved by applying a "hidden" excitation during or partially during the refilling of atoms into the science array. The hidden excitation may involve placing transitioned atoms or atoms already in the array into a dark state, a clock state, or another state forbidden by the selection rules from the optical excitation used for the transition. In some examples, a hidden excitation may be applied to atoms in the science array during imaging or excitation of atoms to be moved into the science portion of the array.

[0152] In some cases, atoms transitioned from the reservoir array into the science array are in a dark state, a clock state, or another state forbidden by the selection rule from the optical excitation used for the transition. In some cases, additional optical tweezers arrays (separate from the tweezers used for trapping or moving) may be created that can address a subset of atoms with hidden light. For example, optical tweezers addressing a subset of sites with a wavelength where the differential polarizability between the qubit and the imaging transition is large can hide selected qubits from the imaging light. For example, the hidden wavelength is relatively close to detuning (approximately 2 nm) from the imaging transition to another higher transition, resulting in a larger optical shift in the imaging state than in the qubit state, which can cause the imaging light to move off-resonance. In other examples, the hidden transition may place atoms in a metastable state, a different spin state protected by polarization (e.g., shelved by a spin state with a different angular momentum state).

[0153] Purpose In some examples, the atoms in the scientific array may be used for metrology, communication, information storage, computation, simulation, or any other application. In some examples, the present technology (e.g., processes 200, 300, 400, 500, or 600) may be applied to quantum computers or simulation devices that use one or more types of atoms or molecules.

[0154] In some cases, the systems and methods disclosed herein may include performing a sensing application using at least a first subset of the plurality of atoms. For example, the plurality of atoms disclosed herein may be used to sense force. For example, the plurality of atoms disclosed herein may be used to sense distance. The distance sensing application may include using the plurality of atoms for interferometry.

[0155] In some cases, the systems and methods disclosed herein may include performing a timing operation using at least a first subset of the plurality of atoms. For example, one use of the captured atomic array is in an atomic clock. In some cases, the systems and methods disclosed herein may include performing a metrology operation using at least a first subset of the plurality of atoms.

[0156] In some cases, the systems and methods disclosed herein may include performing a computation using at least a first subset of atoms. For example, the computation may be non-classical, and the computation may be performed without substantially stopping the non-classical computation. In some cases, the non-classical computation may include applying electromagnetic energy to one or more atoms of the first subset of atoms in the scientific array, thereby inducing the one or more atoms to adopt one or more superpositions of a first atomic state and at least a second atomic state different from the first atomic state. As disclosed herein, the refill operation may be performed without substantially losing the one or more superpositions. In some cases, the non-classical computation may include quantum mechanically entanglement of at least one of the one or more atoms in the one or more superpositions with at least another atom of the first subset of atoms in the scientific array. As disclosed herein, the refill operation may be performed without substantially losing the entanglement. In some cases, the non-classical computation may include one or more measurement operations. For example, the method may include measuring one or more superposition states to obtain non-classical results.

[0157] In some cases, the application is non-classical computing, and the plurality of atoms are qubits. For example, the qubits may include nuclear spin qubits. A method or system including a nuclear spin qubit may include one or more superpositions of a first atomic state and a second atomic state, the first and second atomic states including a first nuclear spin state and a second nuclear spin state of a nucleus having a nuclear spin of 1 / 2 or greater. In some cases, one or more atoms of the first subset of atoms in the one or more superpositions and at least another atom of the first subset of atoms in the scientific array are quantum mechanically entangled with a coherence lifetime of at least 1 second. In some cases, the qubit states exhibit the coherence characteristics shown in FIG. 6.

[0158] Electromagnetic Delivery Unit—The electromagnetic delivery unit may be configured to apply electromagnetic energy to one or more atoms of the plurality of atoms, as described herein. The electromagnetic delivery unit may include one or more light sources, such as any of the light sources described herein. The electromagnetic energy may include optical energy. The optical energy may include any of the repetition rates, pulse energies, average powers, wavelengths, or bandwidths described herein.

[0159] In some cases, the optical capture unit and the electromagnetic delivery unit described herein may be integrated into a single optical system. A microscope objective lens may be used to deliver the electromagnetic radiation generated by the electromagnetic delivery unit described herein and to deliver the light for capturing atoms generated by the optical capture unit described herein. Alternatively or additionally, different objective lenses may be used to deliver the electromagnetic radiation generated by the electromagnetic delivery unit and to deliver the light for capturing atoms generated by the optical capture unit.

[0160] The electromagnetic delivery unit may be configured to apply a first electromagnetic energy to one or more atoms of the plurality of atoms, the application of the first electromagnetic energy may induce the atoms to adopt one or more superpositions of the first atomic state and a second atomic state different from the first atomic state.

[0161] The first atomic state may comprise a first single-qubit state. The second atomic state may comprise a second single-qubit state. The first atomic state or the second atomic state may be elevated in energy relative to the ground atomic state of the atom. The first atomic state or the second atomic state may be equal in energy to the ground atomic state of the atom.

[0162] The first atomic state may include a first hyperfine electronic state, and the second atomic state may include a second hyperfine electronic state that is different from the first hyperfine electronic state. For example, the first and second atomic states may include first and second hyperfine states on a multiplet manifold, such as a triplet manifold. The first and second atomic states may be 3 P1 or 3 The first and second atomic states may include first and second hyperfine states on the P2 manifold, respectively. The first and second atomic states may include first and second hyperfine states on the P2 manifold, respectively. 3 P1 variant or strontium-87 3 of any of the atoms described herein, such as the P2 manifold. 3 P1 or 3 It may contain the first and second hyperfine states on the P2 manifold, respectively.

[0163] In some cases, the first and second atomic states are first and second hyperfine states of the first electronic state. Optical excitation may be applied between the first electronic state and the second electronic state. The optical excitation may excite the first hyperfine state and / or the second hyperfine state to the second electronic state. The single qubit transition may include a two-photon transition between two hyperfine states within the first electronic state, using the second electronic state as an intermediate state. To drive the single qubit transition, a pair of frequencies detuned from the single-photon transition to the intermediate state may be applied to drive the two-photon transition. In some cases, the first and second hyperfine states are hyperfine states of the ground electronic state. The ground electronic state may not decay to a lower electronic state by spontaneous or stimulated emission. The hyperfine state may include a nuclear spin state.

[0164] In some cases, the hyperfine state is 1 The qubit transition involves the nuclear spin state of the S0 manifold, and the qubit transition is 1 One or both of the two nuclear spin states of S0 can be 3 P2 or 3 Drive to detuned states from or within the P1 manifold. In some cases, one-qubit transitions are driven by strontium-871 is a two-photon Raman transition between the nuclear spin states of S0, 3 P2 or 3 via states detuned from or within the P1 manifold. In some cases, the nuclear spin state may be Stark-shifted. The Stark shift may be optically driven. The optical Stark shift may involve off-resonance with any, all, or a combination of single-qubit, two-qubit, shelving, and imaging transitions.

[0165] In some cases, the hyperfine state includes a nuclear spin state of the ytterbium atom. For example, the one-qubit transition may be a nuclear spin state. For example, the one-qubit transition may be 3 P2 or 3 of ytterbium-171 bound from or within the P1 manifold 1 It may be a transition between the nuclear spin states of S0. In some cases, the transition 1 S0m f =1 / 2, -1 / 2 are 3 P1m f It is combined with either =3 / 2 or -3 / 2.

[0166] The first atomic state may include a first nuclear spin, and the second atomic state may include a second nuclear spin state different from the first nuclear spin state. The first and second atomic states may include first and second nuclear spin states, respectively, of quadrupolar nuclei. The first and second atomic states may include first and second nuclear spin states, respectively, 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 include first and second nuclear spin states, respectively, of any atom described herein, such as the first and second spin states of strontium-87.

[0167] 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), the transition between the first and second nuclear spin states may involve transitions between other spin states on the nuclear spin manifold. For example, for a spin-9 / 2 nucleus in the presence of a uniform magnetic field, all nuclear spin levels may be separated by equal energy. Thus, for example, m N =9 / 2 spin state to m N Transitions designed to move atoms to the =7 / 2 spin state (such as Raman transitions) are N =7 / 2 to m N =5 / 2, m N =5 / 2 to m N =3 / 2, m N =3 / 2 to m N =1 / 2, m N =1 / 2 to m N =-1 / 2, m N =-1 / 2 to m N =-3 / 2, m N =-3 / 2 to m N =-5 / 2, m N =-5 / 2 to m N = -7 / 2, and m N =-7 / 2 to m N = -9 / 2, m N is the nuclear spin state. Similarly, for example, m N =9 / 2 spin state to m N Transitions designed to move atoms to the =5 / 2 spin state (such as Raman transitions) are also N =7 / 2 to m N =3 / 2, m N =5 / 2 to m N =1 / 2, m N =3 / 2 to m N =-1 / 2, m N =1 / 2 to m N =-3 / 2, m N =-1 / 2 to m N =-5 / 2, m N =-3 / 2 to m N = -7 / 2, and m N =-5 / 2 to mN = -9 / 2. Therefore, such transitions may not be selective for inducing transitions between specific spin states on the nuclear spin manifold.

[0168] Alternatively, it may be desirable to implement a selective transition between specific first and second spin states on the nuclear spin manifold. This may be achieved by providing light from a light source that provides an AC Stark shift and pushes adjacent nuclear spin states off resonance with a transition between the desired transition between the first and second nuclear spin states. For example, m N =-9 / 2 and m N If transitions from the first and second nuclear spin states with π = -7 / 2 are desired, the light will N = -5 / 2 spin state, thereby providing an AC Stark shift N =-7 / 2 and m N =-5 / 2 state. Similarly, the transition between N =-9 / 2 and m N If transitions from the first and second nuclear spin states with π = -5 / 2 are desired, the light will N = -1 / 2 spin state, thereby providing an AC Stark shift N =-5 / 2 and m N =-1 / 2 state. This effectively creates a two-level subsystem within the nuclear spin manifold that is isolated from the rest of the nuclear spin manifold, greatly simplifying the dynamics of the qubit system. Nuclear spin states near the edge of the nuclear spin manifold (e.g., m for a spin 9 / 2 nucleus) are chosen so that only one AC Stark shift is required. N =-9 / 2 and m N =-7 / 2, m N =7 / 2 and m N =9 / 2, m N =-9 / 2 and m N =-5 / 2, or m N =5 / 2 and m N= 9 / 2) can be advantageous. Alternatively, it is possible to use nuclear spin states away from the edge of the nuclear spin manifold (e.g., m N =-5 / 2 and m N =-3 / 2 or m N =-5 / 2 and m N =-1 / 2) or perform two AC Stark shifts (e.g., m N =-7 / 2 and m N =-1 / 2 or m N =-9 / 2 and m N =3 / 2).

[0169] Qubits based on the nuclear spin state of the electronic ground state require long-lived metastable excited electronic states (e.g., strontium-87) for quantum storage. 3 P0 state or Ytterbium-171 3 It may be possible to utilize states such as the P1 state. Atoms may be selectively transitioned into such states to reduce crosstalk, improve gating or detection fidelity, or reduce scattering during atomic transitions. Such storage or shelving processes may be atom-selective using the SLM or AOD described herein. Shelving transitions are typically achieved by using the Ytterbium-171 1 From the S0 state to Ytterbium-171 3 P0 or 3 The shelving transition may include a transition to the P2 state of strontium-87. 1 Strontium-87 from the S0 state 3 P0 or 3 This may include a transition to the P2 state.

[0170] Computer Systems FIG. 1 illustrates a computer system (101) programmed or otherwise configured to operate any of the methods, systems, processes, or techniques described herein (e.g., systems or methods for performing continuous non-classical computation described herein). The computer system (101) can govern various aspects of the present disclosure. The computer system (101) may be a user's electronic device or a computer system located remotely relative to the electronic device. The electronic device may be a mobile electronic device.

[0171] The computer system (101) includes a central processing unit (CPU, also referred to herein as "processor" and "computer processor") (105), which may be a single-core or multi-core processor, or multiple processors for parallel processing. The computer system (101) also includes memory or storage locations (110) (e.g., random access memory, read-only memory, flash memory), electronic storage devices (115) (e.g., hard disks), communication interfaces (120) (e.g., network adapters) for communicating with one or more other systems, and peripheral devices (125), such as cache, other memory, data storage, and / or electronic display adapters. The memory (110), storage devices (115), interfaces (120), and peripheral devices (125) communicate with the CPU (105) via a communication bus (solid lines), such as a motherboard. The storage devices (115) may also be data storage devices (or data repositories) for storing data. The computer system (101) may be operatively coupled to a computer network ("network") 130 using the communication interface (120). The network (130) may be the Internet, an Internet and / or extranet, or an intranet and / or extranet in communication with the Internet. The network (130) may, in some cases, be a telecommunications and / or data network. The network (130) may include one or more computer servers that enable distributed computing, such as cloud computing. The network (130) may, in some cases, implement a peer-to-peer network with the help of the computer system (101), allowing devices coupled to the computer system (101) to act as clients or servers.

[0172] The CPU (105) may execute a series of machine-readable instructions, which may be embodied in a program or software. The instructions may be stored in a storage location, such as the memory (110). The instructions may be directed to the CPU (105), which may then be programmed or otherwise configured to implement the methods of the present disclosure. Examples of operations performed by the CPU (105) may include fetch, decode, execute, and writeback.

[0173] The CPU 105 may be part of a circuit, such as an integrated circuit. One or more other components of the system 101 may be included in the circuit. In some cases, the circuit is an application specific integrated circuit (ASIC).

[0174] The storage device (115) can store files such as drivers, libraries, and saved programs. The storage device (115) can store user data, such as user preferences and user programs. The computer system (101) may optionally include one or more additional data storage devices external to the computer system (101), such as those located on remote servers that communicate with the computer system (101) over an intranet or the Internet.

[0175] The computer system (101) can communicate with one or more remote computer systems via a network (130). For example, the computer system (101) can communicate with a user's remote computer system. Examples of remote computer systems include a personal computer (e.g., a portable PC), a slate or tablet PC (e.g., an Apple® iPad, a Samsung® Galaxy Tab), a telephone, a smartphone (an Apple® iPhone, an Android-enabled device, a Blackberry®), or a personal digital assistant. A user can access the computer system (101) via the network (130).

[0176] The methods described herein can be implemented by machine (e.g., computer processor) executable code stored in an electronic storage location of the computer system (101), such as, for example, memory (110) or electronic storage device (115). The machine-executable or machine-readable code may be provided in the form of software. During use, the code may be executed by the processor (105). In some cases, the code may be retrieved from storage device (115) and stored in memory (110) for immediate access by the processor (105). In some situations, the electronic storage device (115) may be omitted, and machine-executable instructions may be stored in memory (110).

[0177] The code may be pre-compiled and configured for use with a machine having a processor adapted to execute the code, or it may be compiled at run-time. The code may be provided in a programming language that can be selected to allow the code to be executed in a pre-compiled or as-compiled manner.

[0178] Aspects of the systems and methods provided herein, such as the computer system (101), may be embodied in programming. Various aspects of the technology can be considered "products" or "articles of manufacture," typically in the form of machine (or processor) executable code and / or associated data, which are held or embodied in some type of machine-readable medium. The machine-executable code may be stored in electronic storage, such as memory (e.g., read-only memory, random-access memory, flash memory) or a hard disk. "Storage"-type media may include any or all of the tangible memory of a computer, processor, etc., or associated modules, such as various semiconductor memory, tape drives, disk drives, etc., that may provide non-transitory storage for software programming at any time. All or portions of the software may be communicated via the Internet or various other telecommunications networks. Such communication may, for example, enable software loading from one computer or processor to another, such as from an administrative server or host computer to an application server computer platform. Thus, other types of media that may hold software elements include the light waves, radio waves, and electromagnetic waves used across physical interfaces between local devices over wired and optical landline networks, as well as various air links. The physical elements that carry such waves, such as wired or wireless links, optical links, etc., may also be considered media that carry software. As used herein, unless limited to non-transitory, tangible "storage" media, terms such as computer or machine "readable medium" refer to any medium that participates in providing instructions to a processor for execution.

[0179] Thus, machine-readable media, such as computer-executable code, may take many forms, including, but not limited to, tangible storage media, carrier wave media, or physical transmission media. Non-volatile storage media include optical or magnetic disks, such as any of the storage devices of any computer, such as those that may be used to implement the databases shown in the figures. Volatile storage media include dynamic memory, such as the main memory of such a computer platform. Tangible transmission media include copper wire and fiber optics, including coaxial cables, i.e., the wires that comprise a bus within a computer system. Carrier-wave transmission media may take the form of electric or electromagnetic signals, or acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Thus, common forms of computer readable media include, for example, a floppy disk, a flexible diskette, a hard disk, magnetic tape, any other magnetic medium, a CD-ROM, a DVD, or a DVD-ROM, any other optical medium, punched cards, paper tape, any other physical storage medium with a pattern of holes, RAM, ROM, PROM and EPROM, FLASH-EPROM, any other memory chip or cartridge, a carrier wave carrying data or instructions, a cable or link carrying such a carrier wave, or any other medium from which a computer can read programming code and / or data. Many of these forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to a processor for execution.

[0180] The computer system (101) may include or communicate with an electronic display (135) that has a user interface (UI) (140). Examples of UIs include, but are not limited to, graphical user interfaces (GUIs) and web-based user interfaces.

[0181] The methods and systems of the present disclosure may be implemented by one or more algorithms, which may be implemented by software when executed by the central processing unit (105). [Example]

[0182] Example 1: Correcting Atomic Defects—Some quantum error correction protocols use intermediate circuit measurements to apply conditional operations to qubits. Additionally, ancillary qubits may typically be reinitialized after a measurement. To demonstrate proof-of-principle of these capabilities, we used intermediate circuit measurements to correct for accidental defects in ancillary qubits while maintaining coherence between the data qubits.

[0183] For this demonstration, we created a fully filled (>98% fill probability) 3 x 4 site subarray by rearranging atoms in a 7 x 10 site array. A single pair of tweezers generated by crossed acousto-optic deflectors (AODs) was used to move individual atoms from the filled sites to the empty sites. The subarray was further subdivided into a checkerboard of data qubits and auxiliary qubits. The atoms remaining in the outer array formed reservoirs and were used to refill the auxiliary sites.

[0184] Figure 6 shows data on the conditional refilling of ancillary qubits. The top panel (a) shows the experimental sequence. While the ancillary sites are repeatedly imaged and refilled, the data qubits are protected from decoherence by a light shift from the hidden beam, indicated by the shaded box. The bottom panel (b) shows the contrast of the data sites for N = 0 (circles), as well as the filling fraction of ancillary sites with conditional refilling (filled diamonds) and without conditional refilling (open diamonds). By 16 cycles, the ancillary filling remains above 98%, with a contrast drop of 0.9(1)% per cycle with conditional refilling. Without refilling, the ancillary filling drops by 1.1(1)% per cycle.

[0185] As detailed in Figure 6, we incorporated N repeated cycles of imaging the intermediate circuit at |1〉 and rearrangement operations on the ancillary qubits within the Ramsey sequence of the data qubit (two π / 2 pulses separated by a time delay). To maintain coherence during optical pumping and imaging, we applied hidden light to the data sites. To reduce sensitivity to static qubit frequency differences between sites, we applied a single spin-echo pulse after N / 2 cycles. While not bound by theory, the qubit frequency difference between sites may arise from the gradient of the applied magnetic field. During each cycle, the ancillary sites identified as empty in the intermediate circuit measurements were refilled with atoms from the reservoir. Optical pumping (OP) of the ancillary qubits after the global π and π / 2 pulses served to reset their internal states to |1〉. To prevent decoherence, hidden light was applied to the data qubits during optical pumping. Optical pumping can scatter fewer photons than imaging (100 μs for OP compared to 5 ms for imaging at similar power levels), and no effect on the contrast of the data qubits from optical pumping was observed.

[0186] By correcting for the loss of auxiliary atoms, we maintained an auxiliary filling rate above 98% for up to 16 imaging and reconfiguration cycles, after which the auxiliary filling rate gradually decreased, likely due to the loss of reservoir atoms in certain experiments. Without correction, for the parameters used in this dataset, the filling rate decreased by 1.1(1)% per imaging cycle. The data qubits exhibited a contrast loss of 0.9(1)% per cycle up to 16 cycles, after which point they deviated from the exponential decay, likely due to non-cancelling coherent errors. For these sequences, we allocated shorter times for larger N to ensure the refilling of the auxiliary states occurred within 10–30 ms, keeping the total Ramsey duration at approximately 600 ms.

[0187] Example 2: Coherence during loading in a MOT—Coherence during loading can arise from magnetic field gradients and scattered light from a magneto-optical trap (MOT) used to trap and cool atoms. It can be useful to maintain qubit coherence in order to perform continuous computations while simultaneously refilling the reservoir.

[0188] Figure 7 shows experimental data demonstrating coherence during MOT loading. The top panel shows the remaining contrast after a Ramsey sequence with (gray dots) and without (black dots) simultaneous MOT manipulation. A single π pulse was used midway through the hold time to eliminate detuning from static detuning errors. A Gaussian fit was applied to the line to guide the eye. The bottom panel shows the relative contrast versus total hold time. The linear fit indicates a further contrast decay rate of 0.03(2) / s in the presence of MOT.

[0189] The present inventors have particularly focused on the 1 From S0 1 An initial MOT was used that operates on a wide transition of P1, which is followed by 1 From S0 3This system poses a higher risk of decoherence than narrow-line MOTs (using narrow P1 transitions). The system utilizes a two-chamber design with a static magnetic field and a 30 cm separation between the MOT and the science region. This physical separation allows atoms in the science region to be loaded into the MOT while remaining coherent. This was confirmed by running standard MOT loading parameters during a Ramsey sequence of qubits (using a single spin echo pulse to eliminate the effects of static detuning errors between qubits). A linear fit yielded a decoherence rate of 0.03(2) / s before the further contrast reduction caused by the MOT. Typical wide-line MOT loading lasts for 200 ms. These experiments demonstrate the feasibility of transporting and loading atoms into the science array while preserving qubit coherence.

[0190] Experimental Setup – Individual 171 Yb atoms were trapped at the site of an array of optical tweezers in the presence of a 500 Gauss magnetic field. The experimental system consists of two main vacuum regions (the "MOT chamber" and the "science chamber") connected by a differential pumping tube. A pre-cooled atomic beam was generated in the MOT chamber (at 399 nm). 1 After the P1 transition at 556 nm 3Atoms are loaded into a two-stage magneto-optical trap (formed using a P1 narrow line transition). They are then loaded into an optical lattice formed using 532 nm light and transported vertically into the scientific chamber by 30 cm. To achieve a deep lattice in a power-efficient manner, the waist of the transport beam is translated in synchronization with the optical lattice by shifting the position of two focusing lenses, one for each of the two counter-propagating beams that form the lattice. The alignment between the two beams is actively maintained using a closed-loop piezoelectric steering mirror. Atoms are transitioned into the optical tweezers array by superimposing the atoms with the array, ramping up the power in the tweezers, and then ramping down the transport lattice. This results in a typical occupancy of several atoms per tweezers. No dissipation is applied to transport the atoms from the transport lattice into the tweezers.

[0191] This two-chamber design allows us to operate in a temporary static magnetic field. The magnetic field remains unchanged during the experimental sequence, avoiding the time delays associated with switching, and simultaneously maintaining the magnetic field gradient to form the MOT and the large, uniform bias field in the scientific region. This two-stage MOT operates in the strong direction with a constant magnetic field gradient of approximately 18 Gauss / cm. After loading the atoms in the tweezers, the m f Light with the same parameters as used to image the =1 / 2 qubit state is applied to induce light-assisted collisions, projecting onto a single atom per tweezers. 1 S0, m f =-1 / 2 3 P1, m f A second tone is applied that addresses the m = 1 / 2 transition, shifting all atoms to m f =1 / 2 state.

[0192] Using light from a single laser incident along two counter-propagating paths, 1 From S0 3Each path has a fiber acousto-optic modulator capable of providing rapid power switching and high extinction. In addition, each path has a fiber-coupled electro-optic modulator (EOM) that can be used to apply sidebands at frequencies up to several GHz.

[0193] Laser beams with opposite circular polarization and different frequencies are applied along the magnetic field direction. 3 P1m f By combining it with either =3 / 2 or -3 / 2, 1 S0m f We selectively imaged two qubit states, =1 / 2 and -1 / 2 (labeled |1> and |0>), which provides access to a closed-cycle transition with a narrow linewidth (about 180 kHz). f Scattering from the ±1 / 2 excited states causes leakage between qubit states, but is suppressed to the transition linewidth by a large ratio of the Zeeman shifts (771 MHz between the -3 / 2 and -1 / 2 states, and 681 MHz between the 1 / 2 and 3 / 2 states, respectively). The scattered light is collected by a high-numerical aperture objective lens and imaged onto a low-noise camera.

[0194] The hidden light comes from a laser with a wavelength of 459.5960(5) nm. 3 P1 to 6s6d 3 When detuned relatively close to the D1 transition (about 2 nm), 1 than the S0 qubit state 3 The P1 state results in a 9-fold larger light shift. 1 S0 manifold and 3 A differential optical shift of up to 74 MHz with a standard deviation of 6 MHz across sites in the array between P1 manifolds is applied to move the imaging light off-resonance.

[0195] While preferred embodiments of the present invention have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. It is not intended that the present invention be limited by the specific examples provided herein. While the present invention has been described with reference to the foregoing specification, the description and illustration of the embodiments herein are not intended to be construed in a limiting sense. Numerous variations, changes, and substitutions will occur to those skilled in the art without departing from the invention. Furthermore, it is to be understood that all aspects of the present invention are not limited to the specific descriptions, configurations, or relative proportions set forth herein, depending upon a variety of conditions and variables. It is to be understood that various alternatives to the embodiments of the present invention described herein may be employed in practicing the invention. Therefore, it is contemplated that the present invention also encompasses any and all such alternatives, modifications, variations, or equivalents. The following claims define the scope of the invention, and it is intended that methods and structures within the scope of these claims and their equivalents be covered thereby.

Claims

1. 1. A method for preparing an atomic sample, the method comprising: (a) trapping a plurality of atoms in a scientific array, the scientific array comprising a first plurality of spatially distinct optical trapping sites; (b) transferring at least one atom from a reservoir array into the science array to increase the fill factor of the science array, the reservoir array including a second plurality of spatially distinct light trapping sites; (c) transferring at least one atom into the reservoir array to increase the fill factor of the reservoir array, the transferring step of (c) being performed at least in part during the transferring of the at least one atom from the reservoir array into the science array of (b); A method comprising:

2. The method of claim 1 , further comprising repeating (b) and (c) multiple times to maintain a fill factor within the scientific array.

3. The method of claim 1 or claim 2, further comprising performing a sensing application using at least a first subset of the plurality of atoms.

4. The method of any one of claims 1 to 3, further comprising performing a timing operation using at least a first subset of said plurality of atoms.

5. The method of any one of claims 1 to 4, further comprising performing a calculation using at least a first subset of the plurality of atoms.

6. 6. The method of claim 5, wherein the computation is a non-classical computation, and (c) is performed without substantially stopping the non-classical computation.

7. performing the non-classical computation applying electromagnetic energy to one or more atoms of the first subset of atoms in the scientific array, thereby inducing the one or more atoms to adopt one or more superpositions of a first atomic state and at least a second atomic state different from the first atomic state; quantum mechanically entangle at least one atom of the one or more atoms in the one or more superposition states with at least another atom of the first subset of atoms in the scientific array; measuring the one or more superposition states to obtain a non-classical result; and The method of claim 6, comprising:

8. 8. The method of claim 7, wherein the first atomic state and the second atomic state comprise first and second nuclear spin states of nuclei having a nuclear spin of 1 / 2 or greater.

9. 9. The method of claim 7 or 8, wherein the one or more atoms of the first subset of atoms in the one or more superposition states and the at least another atom of the first subset of atoms in the scientific array are quantum mechanically entangled with a coherence lifetime of at least 1 second.

10. The method of any one of claims 1 to 9, wherein the plurality of atoms comprises neutral atoms.

11. The method of any one of claims 1 to 10, wherein the plurality of atoms comprises a Group 2 element.

12. The method of claim 11 , wherein the plurality of atoms comprises scandium.

13. The method of any one of claims 1 to 10, wherein the plurality of atoms comprises group 2-like elements.

14. The method of claim 13 , wherein the plurality of atoms includes atoms having two valence electrons.

15. 15. The method of claim 13 or 14, wherein the plurality of atoms includes ytterbium.

16. The method of any one of claims 1 to 15, wherein the plurality of atoms comprises a temperature of at most 10 microkelvin (μK).

17. 17. The method of any one of claims 1 to 16, wherein one or both of (i) loading the plurality of atoms into a reservoir or (ii) reloading the reservoir array with additional atoms is performed using one or both of a moving optical trap or optical tweezers.

18. The method of any one of claims 1 to 17, wherein the scientific array is different from the reservoir array.

19. 20. The method of claim 18, wherein the science array is physically separated from the reservoir array, optionally by more than 10 cm.

20. The method includes (a) followed by:

20. The method of any one of claims 1 to 19, further comprising determining an atom defect number representing the difference between (i) the atom number of the plurality of atoms captured within the scientific array and (ii) the atom number of a remaining subset of the plurality of atoms captured within the scientific array that remains within the scientific array after performing at least a portion of a non-classical computation.

21. 21. The method of claim 20, wherein the at least one atom transitioned from the reservoir array into the scientific array includes a number of atoms at least equal to the number of atom deficiencies.

22. 22. The method of claim 20 or 21, wherein determining the number of atomic defects is based on imaging across an imaging axis to determine which of the second plurality of spatially distinct light capture sites of the scientific array are occupied.

23. the science array being physically separated from the reservoir array parallel to the imaging axis; 23. The method of claim 22, wherein one or both of (i) transferring a first subset of the plurality of atoms from the reservoir array into the science array or (ii) transferring a second subset of the plurality of atoms from the reservoir array into the science array is performed using one or both of a moving optical trap or optical tweezers.

24. The method of any one of claims 1 to 23, wherein both the scientific array and the reservoir array are two-dimensional.

25. The method of any one of claims 1 to 23, wherein both the scientific array and the reservoir array are three-dimensional.

26. The method of any one of claims 1 to 23, wherein the scientific array has a different number of dimensions than the reservoir array.

27. 27. The method of any one of claims 1 to 26, wherein one or both of the scientific array or the reservoir array are formed using either optical or non-optical electromagnetic fields.

28. 28. The method of any one of claims 1 to 27, wherein a second number of sites in the second plurality of light capture sites is equal to a first number of sites in the first plurality of light capture sites.

29. 28. The method of any one of claims 1 to 27, wherein a second number of sites in the second plurality of light capture sites is greater than a first number of sites in the first plurality of light capture sites.

30. Translocating the at least one atom from the reservoir array into the science array includes: transitioning a first number of atoms, the first number being at least a subset of the at least one atom, from the reservoir array to one or more intermediate arrays; transitioning a second number of atoms from the one or more intermediate arrays to the scientific array, the second number of atoms being at most the first number of atoms; 30. The method of any one of claims 1 to 29, comprising:

31. the one or more intermediate arrays include at least two intermediate arrays; 31. The method of claim 30, wherein at least the second number of atoms is transitioned between the at least two intermediate arrays (i) after the first number of atoms is transitioned from the reservoir array to the at least two intermediate arrays, and (ii) before the second number of atoms is transitioned from the at least two intermediate arrays to the science array.

32. 32. The method of any one of claims 1-31, further comprising rearranging, within the scientific array, positions between the first plurality of spatially distinct light capture sites of at least some of one or both of: (i) the plurality of atoms within the scientific array; or (ii) the at least one atom within the scientific array.

33. The method of any one of claims 1 to 31, wherein the scientific array is associated with a first spatial light modulator and the reservoir array is associated with a second spatial light modulator.

34. 33. The method of any one of claims 1 to 32, wherein the at least one atom transitioned from the reservoir array into the science array is in a dark state, a clock state, or another state that is forbidden by a selection rule from the optical excitation used for the transition.

35. 34. The method of any one of claims 1 to 33, wherein the transition of the at least one atom from the reservoir array into the science array is a long-range transition.

36. The method of any one of claims 1 to 34, wherein the plurality of atoms are qubits.

37. 1. A method for preparing an atomic sample, the method comprising: (a) trapping a plurality of atoms in a scientific array, the scientific array comprising a first plurality of spatially distinct optical trapping sites; (b) inducing at least a first subset of the plurality of atoms to adopt one or more superposition states in at least the first subset of the plurality of atoms in the scientific array; (c) transferring at least one atom from a reservoir array into the science array, the reservoir array including a second plurality of spatially distinct optical trapping sites, the transferring in (c) being performed substantially without decoherence of the one or more superposition states; A method comprising:

38. 38. The method of claim 37, further comprising repeating (c) multiple times to maintain a fill factor within the scientific array.

39. 39. The method of claim 37 or 38, wherein (b) comprises performing a sensing application using at least the first subset of the plurality of atoms.

40. 40. The method of any one of claims 37 to 39, wherein (b) comprises performing a timing operation using at least the first subset of the plurality of atoms.

41. 41. The method of any one of claims 37 to 40, wherein (b) comprises performing calculations using at least the first subset of the plurality of atoms.

42. 42. The method of claim 41 , wherein the computation is a non-classical computation, and (c) is performed without substantially stopping the non-classical computation.

43. performing the non-classical computation applying electromagnetic energy to one or more atoms of the first subset of atoms in the scientific array, thereby inducing the one or more atoms to adopt one or more superpositions of a first atomic state and at least a second atomic state different from the first atomic state; quantum mechanically entangle at least one atom of the one or more atoms in the one or more superposition states with at least another atom of the first subset of atoms in the scientific array; measuring the one or more superposition states to obtain a non-classical result; and 43. The method of claim 42, comprising:

44. 44. The method of claim 43, wherein the first atomic state and the second atomic state comprise first and second nuclear spin states of nuclei comprising a nuclear spin of 1 / 2 or greater.

45. 45. The method of claim 43 or 44, wherein the one or more atoms of the first subset of atoms in the one or more superposition states and the at least another atom of the first subset of atoms in the scientific array are quantum mechanically entangled with a coherence lifetime of at least 1 second.

46. 46. ​​The method of any one of claims 37 to 45, further comprising carrying one or more atoms within the reservoir array comprising the second plurality of spatially distinct light capture sites.

47. The method of any one of claims 37 to 46, wherein the plurality of atoms comprises neutral atoms.

48. 48. The method of any one of claims 37 to 47, wherein the plurality of atoms comprises a Group 2 element.

49. 49. The method of claim 48, wherein the plurality of atoms comprises scandium.

50. 48. The method of any one of claims 37 to 47, wherein the plurality of atoms comprises group 2-like elements.

51. 51. The method of claim 50, wherein the plurality of atoms includes atoms having two valence electrons.

52. 52. The method of claim 50 or 51, wherein the plurality of atoms includes ytterbium.

53. 53. The method of any one of claims 37 to 52, wherein the plurality of atoms comprises a temperature of at most 10 microkelvin (μK).

54. 54. The method of any one of claims 37 to 53, wherein one or both of (i) loading the plurality of atoms into a reservoir or (ii) reloading the reservoir array with additional atoms is performed using one or both of a moving optical trap or optical tweezers.

55. The method of any one of claims 37 to 54, wherein the scientific array is different from the reservoir array.

56. 56. The method of claim 55, wherein the science array is physically separated from the reservoir array, optionally by more than 10 cm.

57. The method includes (a) followed by:

47. The method of any one of claims 37-46, further comprising determining an atom defect number representing the difference between (i) the atom number of the plurality of atoms captured within the scientific array and (ii) the atom number of a remaining subset of the plurality of atoms captured within the scientific array that remains within the scientific array after performing at least a portion of a non-classical computation.

58. 58. The method of claim 57, wherein the at least one atom transitioned from the reservoir array into the scientific array includes a number of atoms at least equal to the number of atom deficiencies.

59. 59. The method of claim 57 or 58, wherein determining the number of atomic defects is based on imaging across an imaging axis to determine which of the second plurality of spatially distinct light capture sites of the scientific array are occupied.

60. the science array being physically separated from the reservoir array parallel to the imaging axis; 60. The method of claim 59, wherein one or both of (i) transitioning the first subset of atoms from the reservoir array into the science array or (ii) transitioning the second subset of atoms from the reservoir array into the science array is performed using one or both of a moving optical trap or optical tweezers.

61. 61. The method of any one of claims 37 to 60, wherein both the scientific array and the reservoir array are two-dimensional.

62. 61. The method of any one of claims 37 to 60, wherein both the scientific array and the reservoir array are three-dimensional.

63. 61. The method of any one of claims 37 to 60, wherein the scientific array has a different number of dimensions than the reservoir array.

64. 64. The method of any one of claims 37 to 63, wherein one or both of the scientific array or the reservoir array are formed using either optical or non-optical electromagnetic fields.

65. 65. The method of any one of claims 37 to 64, wherein a second number of sites in the second plurality of light capture sites is equal to a first number of sites in the first plurality of light capture sites.

66. 65. The method of any one of claims 37 to 64, wherein a second number of sites in the second plurality of light capture sites is greater than a first number of sites in the first plurality of light capture sites.

67. Translocating the at least one atom from the reservoir array into the science array includes: transitioning a first number of atoms, the first number being at least a subset of the at least one atom, from the reservoir array to one or more intermediate arrays; transitioning a second number of atoms from the one or more intermediate arrays to the scientific array, the second number of atoms being at most the first number of atoms; 67. The method of any one of claims 37 to 66, comprising:

68. the one or more intermediate arrays include at least two intermediate arrays; 68. The method of claim 67, wherein at least the second number of atoms is transitioned between the at least two intermediate arrays (i) after the first number of atoms is transitioned from the reservoir array to the at least two intermediate arrays, and (ii) before the second number of atoms is transitioned from the at least two intermediate arrays to the science array.

69. 69. The method of any one of claims 37-68, further comprising rearranging, within the scientific array, positions among the first plurality of spatially distinct light capture sites of at least some of one or both of: (i) the plurality of atoms within the scientific array; or (ii) the at least one atom within the scientific array.

70. 70. The method of any one of claims 37 to 69, wherein the scientific array is associated with a first spatial light modulator and the reservoir array is associated with a second spatial light modulator.

71. 71. The method of any one of claims 37-70, wherein the at least one atom transitioned from the reservoir array into the science array is in a dark state, a clock state, or another state that is forbidden by a selection rule from the optical excitation used for the transition.

72. 72. The method of any one of claims 37 to 71, wherein the transition of the at least one atom from the reservoir array into the science array is a long-range transition.

73. 73. The method of any one of claims 37 to 72, wherein the plurality of atoms are qubits.

74. 1. A system for preparing an atomic sample, the system comprising: A system comprising one or more atomic transition units configured to perform the method of any one of claims 1 to 73.

75. 1. A system for preparing an atomic sample, the system comprising: one or more light capture units, a scientific array including a first plurality of spatially distinct optical trapping sites, the scientific array including a first plurality of atoms trapped at the first plurality of spatially distinct optical trapping sites; and a reservoir array including a second plurality of spatially distinct light trapping sites, the second plurality of atoms being trapped in the second plurality of spatially distinct light trapping sites; one or more light capture units configured to obtain one or more atom transfer units, (a) transferring at least one atom from the reservoir array into the science array to increase the fill factor of the science array; (b) one or more atom transfer units configured to transfer at least one atom into the reservoir array to increase the fill factor of the reservoir array, the transfer of (b) being performed at least in part during the transfer of the at least one atom from the reservoir array into the science array of (a); A system comprising:

76. 1. A system for preparing an atomic sample, the system comprising: one or more light capture units, a scientific array including a first plurality of spatially distinct optical trapping sites, the scientific array including a first plurality of atoms trapped at the first plurality of spatially distinct optical trapping sites; and a reservoir array including a second plurality of spatially distinct light trapping sites, the second plurality of atoms being trapped in the second plurality of spatially distinct light trapping sites; one or more light capture units configured to obtain one or more electromagnetic delivery units configured to induce at least a first subset of the plurality of atoms to adopt one or more superposition states in at least the first subset of the plurality of atoms in the scientific array; one or more atom transfer units configured to transfer at least one atom of the second plurality of atoms from the reservoir array into the scientific array, the transfer being performed substantially without decoherence of the one or more superposition states; A system comprising:

77. 1. A method for performing continuous non-classical computation, the method comprising: carrying a plurality of atoms in a reservoir array including a first plurality of spatially distinct optical trapping sites configured to trap the plurality of atoms, the plurality of atoms being qubits; transitioning a first subset of the atoms from the reservoir array into a scientific array including a second plurality of spatially distinct optical trapping sites configured to trap the atoms; performing a first non-classical calculation using at least a portion of the first subset of the atoms in the scientific array; (i) determining an atom defect number representing the difference between the number of atoms in the first subset of atoms and (ii) the number of atoms in a remaining subset of the first subset of atoms that remains in the scientific array after performing the first non-classical calculation; transferring a second subset of the plurality of atoms from the reservoir array into the scientific array, the second subset of the plurality of atoms including a number of atoms at least equal to the number of atom deficiencies; reloading the reservoir array with additional atoms that are qubits; performing a second non-classical calculation using at least a portion of one or both of (i) the remaining subset of the first subset of atoms and (ii) the second subset of atoms. A method comprising:

78. The step of performing the first non-classical computation includes: applying electromagnetic energy to one or more atoms of the first subset of atoms in the scientific array, thereby inducing the one or more atoms to adopt one or more superpositions of a first atomic state and at least a second atomic state different from the first atomic state; quantum mechanically entangle at least one atom of the one or more atoms in the one or more superposition states with at least another atom of the first subset of atoms in the scientific array; measuring the one or more superposition states to obtain a first non-classical result; 78. The method of claim 77, comprising:

79. 79. The method of claim 78, wherein the first atomic state and the second atomic state comprise first and second nuclear spin states of nuclei comprising nuclear spins greater than ½.

80. 80. The method of claim 78 or 79, wherein at least one subset of the at least one atom in the one or more superposition states and at least another atom of the first subset of the plurality of atoms in the scientific array are quantum mechanically entangled with a coherence lifetime of at least 1 second.

81. 81. The method of any one of claims 77 to 80, wherein the plurality of atoms and the further atom both comprise neutral atoms.

82. 82. The method of any one of claims 77 to 81, wherein the plurality of atoms and the further atom both comprise Group 2 elements.

83. 83. A method according to any one of claims 77 to 82, wherein the plurality of atoms and the further atoms both comprise a temperature of at most 10 microkelvin (μK).

84. 84. The method of any one of claims 77 to 83, wherein one or both of (i) loading the plurality of atoms into a reservoir or (ii) reloading the reservoir array with the additional atoms is performed using one or both of a moving optical trap or optical tweezers.

85. 85. The method of any one of claims 77 to 84, wherein the science array is physically separate from the reservoir array.

86. 86. The method of claim 85, wherein determining the number of atomic defects is based on imaging across an imaging axis to determine which sites of the second plurality of spatially distinct light capture sites of the scientific array are occupied.

87. the science array being physically separated from the reservoir array parallel to the imaging axis; One or both of (i) transferring the first subset of the plurality of atoms from the reservoir array into the science array or (ii) transferring the second subset of the plurality of atoms from the reservoir array into the science array is performed using one or both of a moving optical trap or optical tweezers.

87. The method of claim 86.

88. 88. The method of any one of claims 77 to 87, wherein both the scientific array and the reservoir array are two-dimensional.

89. 89. The method of any one of claims 77 to 88, wherein both the scientific array and the reservoir array are three-dimensional.

90. 90. The method of any one of claims 77 to 89, wherein the scientific array has a different number of dimensions than the reservoir array.

91. 91. The method of any one of claims 77 to 90, wherein one or both of the scientific array or the reservoir array are formed using either optical or non-optical electromagnetic fields.

92. 92. The method of any one of claims 77 to 91, wherein a first number of sites in the first plurality of light capture sites is equal to a second number of sites in the second plurality of light capture sites.

93. 93. The method of any one of claims 77 to 92, wherein a first number of sites in the first plurality of light capture sites is greater than a second number of sites in the second plurality of light capture sites.

94. Transitioning the first subset of the plurality of atoms from the reservoir array into the science array includes: transitioning at least the first subset of the plurality of atoms from the reservoir array to one or more intermediate arrays; transitioning the first subset of the plurality of atoms from the one or more intermediate arrays to the scientific array; 94. The method of any one of claims 77 to 93, comprising:

95. the one or more intermediate arrays include at least two arrays; 95. The method of claim 94, wherein at least the first subset of atoms is transitioned between the at least two arrays (i) after the at least the first subset of atoms is transitioned from the reservoir array to the at least two arrays, and (ii) before the first subset of atoms is transitioned from the at least two arrays to the science array.

96. 96. The method of any one of claims 77-95, further comprising rearranging, within the scientific array, positions between the spatially distinct second plurality of light capture sites of at least some of (i) the remaining subset of the first subset of atoms and (ii) one or both of the second subset of atoms.

97. 97. A system for preparing an atomic sample, the system comprising one or more atomic transition units configured to perform the method of claim 96.

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