Method and equipment for realizing continuous operation of cold atom equipment by using independent reservoir array

Abstract

Systems and methods for performing continuous non-classical calculations 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 scientific array; performing a first non-classical calculation using at least some atoms in the first subset; determining a number of atomic losses representing a difference between (i) the number of atoms in the first subset and (ii) the number of atoms in a remaining subset of the first subset remaining 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 a scientific array; reloading the reservoir array with additional atoms; and performing a second non-classical calculation using at least some atoms in one or both of the remaining subset and the second subset.

Description

[0001] Cross-reference

[0002] This application claims the benefit of U.S. Provisional Application No. 63 / 413,203, filed on Oct. 4, 2022, which is incorporated herein by reference in its entirety. BACKGROUND OF THE DISCLOSURE

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

[0004] In a neutral atom quantum computer or analog device, qubits can be encoded in optically trapped atoms. Since the optical traps may be relatively shallow, the atoms may be lost due to collisions with residual background gas, leakage into un-trapped or other undesired internal states, or heating or other processes associated with interaction with the laser. In a quantum computer or analog device, a subset of the total optically trapped array (referred to herein as the "science area") can typically be filled in order to perform calculations or simulations. In order to perform continuous or repeated calculations, it may be important to reload the atoms into the optical traps. SUMMARY OF THE DISCLOSURE

[0005] The present disclosure describes methods and systems that, in some embodiments, replenish a science area from a reservoir, where the science area and the reservoir area are distinct, such that the reservoir can be refilled without disturbing the atoms within the science area. This allows for continuous or quasi-continuous (beyond the lifetime of the atoms within the science area) occupancy and coherent operations within the science area.

[0006] In one aspect, the present application provides a method for preparing an atomic sample. The method can include: (a) trapping a plurality of atoms into a science array, where the science array includes a plurality of spatially distinct first optical trapping sites; (b) transferring at least one atom from a reservoir array to the science array to increase the fill factor of the science array, where the reservoir array includes a plurality of spatially distinct second optical trapping sites; and (c) transferring at least one atom to the reservoir array to increase the fill factor of the reservoir array, where during the transfer of at least one atom from the reservoir array to the science array in (b), the transfer in (c) is at least partially performed.

[0007] In some embodiments, the method further comprises repeating (b) and (c) multiple times to maintain the fill factor in the science array. In some embodiments, the method further comprises performing a sensing application using at least a first subset of the plurality of atoms. In some embodiments, the method further comprises performing a timing operation using at least a first subset of the plurality of atoms. In some embodiments, the method further comprises 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 wherein (c) is performed substantially without stopping the non-classical computation. In some embodiments, performing the non-classical computation comprises: applying electromagnetic energy to one or more atoms in a first subset of the plurality of atoms in the science array, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state; entangling quantum mechanically at least one of the one or more atoms in one or more superposition states with at least another atom in the first subset of the plurality of atoms in the science array; and measuring the one or more superposition states to obtain a non-classical result. In some embodiments, the first atomic state and the second atomic state comprise a first nuclear spin state and a second nuclear spin state of a nucleus, the nucleus comprising a nuclear spin greater than or equal to 1 / 2. In some embodiments, the one or more atoms in one or more superposition states in the first subset of the plurality of atoms are quantum mechanically entangled with at least another atom in the first subset of the plurality of atoms in the science array with a coherence lifetime of at least 1 second.

[0008] In some embodiments, the plurality of atoms comprise neutral atoms. In some embodiments, the plurality of atoms comprise Group II elements. In some embodiments, the plurality of atoms comprise scandium. In some embodiments, the plurality of atoms comprise Group-II-like elements. In some embodiments, the plurality of atoms comprise atoms having two valence electrons. In some embodiments, the plurality of atoms comprise ytterbium.

[0009] In some embodiments, the plurality of atoms comprise a temperature of at most 10 microkelvin (μK). In some embodiments, one or both of a moving optical trap or an optical tweezer is used to perform one or both of the following: (i) loading the plurality of atoms into a reservoir, or (ii) reloading the reservoir array with additional atoms. 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, wherein the physical separation is greater than 10 cm.

[0010] In some embodiments, after (a), the method further comprises: determining an atomic loss quantity, which represents the difference between (i) the number of atoms among a plurality of atoms captured into the science array and (ii) the number of atoms remaining in the remaining subset that remains in the science array among the plurality of atoms captured into 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 to the science array includes an atomic quantity that is at least equal to the atomic loss quantity. In some embodiments, determining the atomic loss quantity is based on imaging along an imaging axis to determine which of a spatially distinct plurality of second optical trapping sites in the science array are occupied. In some embodiments, the science array and the reservoir array are physically separated parallel to the imaging axis; and one or both of a mobile optical trap or an optical tweezer are used to perform one or both of the following: (i) transferring a first subset of the plurality of atoms from the reservoir array to the science array, or (ii) transferring a second subset of the plurality of atoms from the reservoir array to the science array.

[0011] 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 light or a non-optical electromagnetic field. In some embodiments, a second quantity of sites among the plurality of second optical trapping sites is equal to a first quantity of sites among the plurality of first optical trapping sites. In some embodiments, a second quantity of sites among the plurality of second optical trapping sites is greater than a first quantity of sites among the plurality of first optical trapping sites.

[0012] In some embodiments, transferring at least one atom from the reservoir array to the science array includes: transferring a first quantity of atoms from the reservoir array to one or more intermediate arrays, where the first quantity of atoms is at least a subset of the at least one atom; and transferring a second quantity of atoms from the one or more intermediate arrays to the science array, where the second quantity of atoms is at most the first quantity of atoms. In some embodiments, the one or more intermediate arrays include at least two intermediate arrays; and (i) after transferring the first quantity of atoms from the reservoir array to the at least two intermediate arrays, and (ii) before transferring the second quantity of atoms from the at least two intermediate arrays to the science array, transferring at least the second quantity of atoms between the at least two intermediate arrays.

[0013] In some embodiments, the method further includes: within the science array, rearranging the positions between a plurality of spatially distinct first optical trapping sites of (i) a plurality of atoms in the science array or (ii) at least some of the atoms in the at least one atom in the science array, either or both. 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, at least one atom transferred from the reservoir array to the science array is in a dark state, a clock state, or another state prohibited by the selection rules of the light excitation used for the transfer. In some embodiments, the transfer of at least one atom from the reservoir array to the science array is a long-range transfer. In some embodiments, the plurality of atoms are qubits.

[0014] In another aspect, the present disclosure provides a method for preparing an atomic sample. The method may include: (a) trapping a plurality of atoms in a science array, wherein the science array includes a plurality of spatially distinct first optical trapping sites; (b) inducing at least a first subset of the plurality of atoms to adopt one or more superposition states of at least a first subset of the plurality of atoms in the science array; and (c) transferring at least one atom from a reservoir array to the science array, wherein the reservoir array includes a plurality of spatially distinct second optical trapping sites, and wherein the transfer in (c) is performed substantially without decoherence of the superposition state.

[0015] In some embodiments, the method further includes repeating (c) multiple times to maintain the fill factor in the science 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 wherein (c) is performed substantially without stopping the non-classical computation. In some embodiments, performing the non-classical computation includes: applying electromagnetic energy to one or more atoms in a first subset of the plurality of atoms in the science array, thereby inducing one or more atoms to adopt one or more superposition states of a first atomic state and a second atomic state different from the first atomic state; entangling quantum mechanically at least one of the one or more atoms in one or more superposition states with at least another atom in the first subset of the plurality of atoms in the science array; and measuring the one or more superposition states to obtain a non-classical result. In some embodiments, the first atomic state and the second atomic state include a first nuclear spin state and a second nuclear spin state of a nucleus, the nucleus including a nuclear spin greater than or equal to 1 / 2. In some embodiments, one or more atoms in one or more superposition states in the first subset of the plurality of atoms are quantum mechanically entangled with at least another atom in the first subset of the plurality of atoms in the science array with a coherence lifetime of at least 1 second.

[0016] In some embodiments, the method further includes loading one or more atoms into a reservoir array including a plurality of second optically trapped sites that are spatially distinct. In some embodiments, the plurality of atoms includes neutral atoms. In some embodiments, the plurality of atoms includes Group II elements. In some embodiments, the plurality of atoms includes scandium. In some embodiments, the plurality of atoms includes Group-II-like elements. In some embodiments, the plurality of atoms includes atoms having two valence electrons. In some embodiments, the plurality of atoms includes ytterbium. In some embodiments, the plurality of atoms includes a temperature of at most 10 microkelvin (μK).

[0017] In some embodiments, one or both of a mobile optical trap or an optical tweezer is used to perform one or both of the following: (i) loading the plurality of atoms into the reservoir, or (ii) reloading the reservoir array with additional atoms. 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, wherein the physical separation is greater than 10 cm.

[0018] In some embodiments, after (a), the method further includes determining an atomic loss quantity that represents a difference between (i) the number of atoms among a plurality of atoms captured into the science array and (ii) the number of atoms remaining in a remaining subset of the plurality of atoms captured into the science array that remains in the science array after performing at least a portion of the non-classical computation.

[0019] In some embodiments, the at least one atom transferred from the reservoir array to the science array includes an atomic quantity that is at least equal to the atomic loss quantity. In some embodiments, determining the atomic loss quantity is based on imaging along an imaging axis to determine which of a spatially distinct plurality of second optical trapping sites in the science array are occupied. In some embodiments, the science array and the reservoir array are physically separated parallel to the imaging axis; and one or both of a mobile optical trap or an optical tweezer is used to perform one or both of the following: (i) transfer a first subset of the plurality of atoms from the reservoir array to the science array, or (ii) transfer a second subset of the plurality of atoms from the reservoir array to the science array.

[0020] 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 light or non-optical electromagnetic fields. In some embodiments, a second quantity of sites among the plurality of second optical trapping sites is equal to a first quantity of sites among the plurality of first optical trapping sites. In some embodiments, a second quantity of sites among the plurality of second optical trapping sites is greater than a first quantity of sites among the plurality of first optical trapping sites.

[0021] In some embodiments, transferring at least one atom from the reservoir array to the science array includes: transferring a first quantity of atoms from the reservoir array to one or more intermediate arrays, where the first quantity of atoms is at least a subset of the at least one atom; and transferring a second quantity of atoms from the one or more intermediate arrays to the science array, where the second quantity of atoms is at most the first quantity of atoms.

[0022] In some embodiments, the one or more intermediate arrays include at least two intermediate arrays; and (i) after transferring the first quantity of atoms from the reservoir array to the at least two intermediate arrays, and (ii) before transferring the second quantity of atoms from the at least two intermediate arrays to the science array, transfer at least the second quantity of atoms between the at least two intermediate arrays.

[0023] In some embodiments, the method further includes: rearranging positions between a plurality of spatially distinct first optical trapping sites of (i) a plurality of atoms in the science array or (ii) at least some of the atoms in at least one of the atoms in the science array, or both. 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, at least one atom transferred from the reservoir array to the science array is in a dark state, a clock state, or another state prohibited by the selection rules excited by the light used for the transfer. In some embodiments, the transfer of at least one atom from the reservoir array to the science array is a long-range transfer. In some embodiments, the plurality of atoms are qubits.

[0024] In another aspect, the present disclosure provides a system for preparing an atomic sample, the system including: one or more atom transfer units configured to implement the method of any aspect or embodiment herein.

[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 and one or more atom moving units, the one or more optical trapping units configured to obtain: a science array including a plurality of spatially distinct first optical trapping sites, wherein the science array includes a plurality of first atoms trapped at the plurality of spatially distinct first optical trapping sites; and a reservoir array including a plurality of spatially distinct second optical trapping sites, wherein the reservoir array includes a plurality of second atoms trapped at the plurality of spatially distinct second optical trapping sites, the one or more atom moving units configured to: (a) transfer at least one atom from the reservoir array to the science array to increase the filling factor of the science array; and (b) transfer at least one atom to the reservoir array to increase the filling factor of the reservoir array, wherein during the transfer of at least one atom from the reservoir array to the science array in (a), the transfer in (b) is at least partially performed.

[0026] In another aspect, the present disclosure provides a system for preparing an atomic sample. The system may include one or more optical trapping units, one or more electromagnetic delivery units, and one or more atomic transfer units. The one or more optical trapping units are configured to obtain: a science array including a plurality of first optically trapped sites that are spatially distinct, wherein the science array includes a plurality of first atoms trapped at the plurality of first optically trapped sites that are spatially distinct; and a reservoir array including a plurality of second optically trapped sites that are spatially distinct, wherein the reservoir array includes a plurality of second atoms trapped at the plurality of second optically trapped sites that are spatially distinct. The one or more electromagnetic delivery units are configured to induce at least a first subset of the plurality of atoms to adopt one or more superposition states of at least a first subset of the plurality of atoms in the science array. The one or more atomic transfer units are configured to transfer at least one of the plurality of second atoms from the reservoir array to the science array, wherein the transfer is performed substantially without decoherence of the superposition states.

[0027] In another aspect, the present disclosure provides a method for performing continuous non-classical computing. The method may include: loading a plurality of atoms into a reservoir array including a plurality of first optically trapped sites that are spatially distinct, the plurality of first optically trapped sites being configured to trap a plurality of atoms, wherein the plurality of atoms are qubits; transferring a first subset of the plurality of atoms from the reservoir array to a science array including a plurality of second optically trapped sites that are spatially distinct, the plurality of second optically trapped sites being configured to trap a plurality of atoms; performing a first non-classical computation using at least some of the atoms in the first subset of the plurality of atoms in the science array; determining an atomic loss number representing a difference between (i) the number of atoms in the first subset of the plurality of atoms and (ii) the number of atoms in the remaining subset of the first subset of the plurality of atoms that remain in the science array after performing the first non-classical computation; and transferring a second subset of the plurality of atoms from the reservoir array to the science array, wherein the second subset of the plurality of atoms includes an atomic number at least equal to the atomic loss number; reloading the reservoir array with additional atoms that are qubits; and performing a second non-classical computation using at least some of (i) the remaining subset of the first subset of the plurality of atoms and (ii) one or both of the second subset of the plurality of atoms.

[0028] In some embodiments, performing a first non-classical computation includes: applying electromagnetic energy to one or more atoms in a first subset of a plurality of atoms in a scientific array, thereby inducing one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state; entangling quantum mechanically at least one of the one or more atoms in one or more superposition states with at least another atom in the first subset of the plurality of atoms in the scientific array; and measuring the one or more superposition states to obtain a first non-classical result. In some embodiments, the first atomic state and the second atomic state include a first nuclear spin state and a second nuclear spin state of a nucleus, the nucleus including a nuclear spin greater than 1 / 2. In some embodiments, at least a subset of at least one of the one or more atoms in one or more superposition states is quantum mechanically entangled with at least another atom in the first subset of the plurality of atoms in the scientific array with a coherence lifetime of at least 1 second.

[0029] In some embodiments, both the plurality of atoms and the additional atoms include neutral atoms. In some embodiments, both the plurality of atoms and the additional atoms include group II elements. In some embodiments, both the plurality of atoms and the additional atoms include a temperature of at most 10 microkelvins (μK). In some embodiments, one or both of a mobile optical trap or an optical tweezer are used to perform one or both of the following: (i) loading the plurality of atoms into a reservoir, or (ii) reloading the reservoir array with additional atoms. In some embodiments, the scientific array is physically separated from the reservoir array. In some embodiments, determining the number of atomic losses is based on imaging along an imaging axis to determine which of a plurality of spatially distinct second optical trapping sites in the scientific array are occupied. In some embodiments, the scientific array is physically separated from the reservoir array parallel to the imaging axis; and one or both of a mobile optical trap or an optical tweezer are used to perform one or both of the following: (i) transferring a first subset of the plurality of atoms from the reservoir array to the scientific array, or (ii) transferring a second subset of the plurality of atoms from the reservoir array to the scientific array.

[0030] 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 and the reservoir array are formed using light or non-optical electromagnetic fields. In some embodiments, a first number of sites in the plurality of first optical trapping sites is equal to a second number of sites in the plurality of second optical trapping sites. In some embodiments, a first number of sites in the plurality of first optical trapping sites is greater than a second number of sites in the plurality of second optical trapping sites. In some embodiments, transferring a first subset of the plurality of atoms from the reservoir array to the science array includes: transferring at least a first subset of the plurality of atoms from the reservoir array to one or more intermediate arrays; and transferring the first subset of the plurality 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 (i) after transferring at least a first subset of the plurality of atoms from the reservoir array to the at least two arrays, and (ii) before transferring the first subset of the plurality of atoms from the at least two arrays to the science array, transferring at least a first subset of the plurality of atoms between the at least two arrays. In some embodiments, the method further includes, within the science array, rearranging the positions of at least some of the atoms among (i) a remaining subset of the first subset of the plurality of atoms and (ii) one or both of the plurality of atoms in a second subset at spatially distinct plurality of second optical trapping sites.

[0031] Another aspect of the present disclosure provides a system that includes one or more computer processors and a computer memory coupled to the one or more computer processors. The computer memory includes machine-executable code that, when executed by the one or more computer processors, implements any of the methods described above or elsewhere herein.

[0032] From the following detailed description, other aspects and advantages of the present disclosure will become readily apparent to those skilled in the art, in which only illustrative embodiments of the present disclosure are shown and described. As will be appreciated, the present disclosure is capable of other different embodiments and its several details can be modified in various obvious aspects, all without departing from the disclosure. Accordingly, the drawings and description are to be regarded as illustrative in nature and not restrictive.

[0033] Incorporated by reference

[0034] All publications, patents, and patent applications mentioned in this specification are incorporated herein by reference to the extent that each individual publication, patent, or patent application is specifically and individually indicated to be incorporated by reference. If the publications and patents or patent applications incorporated by reference conflict with the disclosure contained in the specification, the specification is intended to supersede and / or take precedence over any such conflicting material. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] 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 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 "figures"), in which:

[0036] Figure 1 A computer control system programmed or otherwise configured to implement the methods provided herein is shown.

[0037] Figure 2 An example process for performing continuous non-classical computing is illustrated.

[0038] Figure 3 An example method and system for preparing an atomic sample are illustrated.

[0039] Figure 4 Another example method and system for preparing an atomic sample are illustrated.

[0040] Figure 5 Another example method and system for preparing an atomic sample are illustrated.

[0041] Figure 6 Data from an experiment related to conditional reloading of an auxiliary qubit are illustrated.

[0042] Figure 7 Experimental data demonstrating coherence during MOT loading are illustrated. DETAILED DESCRIPTION

[0043] Although various embodiments of the invention have been shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions will occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed.

[0044] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. As used in this specification and the appended claims, unless the context clearly dictates otherwise, the singular forms "a", "an", and "the" include plural forms. Any reference to "or" herein is intended to cover "and / or" unless otherwise stated.

[0045] When the terms "at least", "greater than", or "greater than or equal to" are placed before the first value in a series of two or more numerical values, the terms "at least", "greater than", or "greater than or equal to" apply to each value in the series. For example, greater than or equal to 1, 2, or 3 is equivalent to greater than or equal to 1, greater than or equal to 2, or greater than or equal to 3.

[0046] When the terms "not greater than", "less than", or "less than or equal to" are placed before the first value in a series of two or more numerical values, the terms "not greater than", "less than", or "less than or equal to" apply to each value in the series. For example, less than or equal to 3, 2, or 1 is equivalent to less than or equal to 3, less than or equal to 2, or less than or equal to 1.

[0047] When a value is described as a range, it should be understood that such disclosure includes the disclosure of all possible sub-ranges within such range and specific numerical values falling within such range, whether the specific numerical values or specific sub-ranges are explicitly stated or not.

[0048] As used herein, the same characters refer to the same elements / components.

[0049] The term "about" or "approximately" can mean within an acceptable error range of a particular value, which will depend in part on how the value is measured or determined, e.g., the limitations of the measuring system. For example, in accordance with the practice in the art, "about" can mean within 1 or more standard deviations. Alternatively, "about" can mean a range up to 20%, up to 10%, up to 5%, or up to 1% of a given value. Where a specific value is described in this application and the claims, unless otherwise stated, the term "about" can be considered to mean within an acceptable error range of the specific value.

[0050] As used herein, the terms "non-classical computing", "non-classical process", "non-classical operation", and "non-classical computer" generally refer to any method or system for performing a computational process outside the paradigm of classical computing. Non-classical computing, non-classical processes, non-classical operations, or non-classical computers can include quantum computing, quantum processes, quantum operations, or quantum computers.

[0051] As used herein, the terms "quantum computing", "quantum process", "quantum operation", and "quantum computer" generally refer to any method or system for performing computations using quantum mechanical operations (such as unitary transformations or completely positive trace-preserving (CPTP) maps on quantum channels) on a Hilbert space represented by a quantum device. As such, quantum computing and classical (or digital) computing may be similar in that both can include a sequence of instructions performed on input information and then provide an output. Various paradigms of quantum computing can decompose quantum operations into sequences of elementary quantum operations that simultaneously affect subsets of qubits of a quantum device. Quantum operations can be selected based on, for example, their location or the ease of their physical implementation. A quantum process or computation can then consist of a sequence of such instructions, which can represent different quantum evolutions on a quantum device in various applications. For example, the process of computing or simulating quantum chemistry can represent the quantum states of electron spin orbitals and annihilation and creation operators by using qubits (such as two-level quantum systems) and a universal set of quantum gates (such as Hadamard, controlled-not (CNOT), and π / 8 rotation) through a so-called Jordan-Wigner transformation or Bravyi-Kitaev transformation.

[0052] Additional examples of quantum processes or computations can include processes for optimization, such as the quantum approximate optimization algorithm (QAOA) or quantum minimum finding. QAOA can include performing rotations of single qubits and entanglement gates of multiple qubits. In quantum adiabatic computing, the instructions can carry a random or non-random evolution path of an initial quantum system to a final quantum system.

[0053] Quantum-inspired processes can include simulated annealing, parallel tempering, master equation solvers, Monte Carlo processes, etc. Quantum-classical or hybrid algorithms or processes can include processes such as the variational quantum eigensolver (VQE) and variational and adiabatic navigator quantum eigensolver (VanQver).

[0054] A quantum computer can include one or more adiabatic quantum computers, quantum gate arrays, single-vector quantum computers, topological quantum computers, quantum Turing machines, quantum annealers, Ising solvers, or gate models of quantum computing.

[0055] As used herein, the term "adiabatic" refers to any process performed on a quantum mechanical system in which the parameters of the Hamiltonian change slowly compared to the natural time scale of the system evolution.

[0056] As used herein, the term "non-adiabatic" refers to any process performed on a quantum mechanical system in which the parameters of the Hamiltonian change rapidly compared to or on a time scale similar to the natural time scale of the system evolution.

[0057] The present disclosure describes methods and systems which, in some embodiments, replenish a reservoir from a scientific region, where the scientific region and the reservoir region are distinct, such that the reservoir can be refilled without disturbing the atoms within the scientific region. This allows for continuous or quasi - continuous (beyond the lifetime of the atoms within the scientific region) occupancy and coherent operations within the scientific region.

[0058] In a neutral - atom quantum computer or simulator device, qubits can be encoded in optically trapped atoms. Since optical traps may be relatively shallow, atoms can be lost due to collisions with residual background gas, leakage into untrapped or other unwanted internal states, or heating or other processes associated with interaction with the laser. In a quantum computer or simulator device, typically a subset of the total optically trapped array (referred to herein as the "scientific region") can be filled in order to perform a computation or simulation. In order to perform continuous or repeated computations, it may be important to reload atoms into the optical traps.

[0059] Reloading the scientific region of a quantum computer or simulator device can be achieved by overlapping the trapping array with a magneto - optical trap (MOT) that provides a dense cold - atom gas and a dissipative mechanism that can trap atoms in the array. This process typically takes a long time, results in the loss of atoms already in the array, and only loads a small fraction (typically about 50%) of the traps within the array. The fill factor of the array can be increased by imaging to determine which sites within the array are occupied and then transferring atoms to unoccupied sites within the scientific region. This transfer can be performed using one or more moving optical traps or optical tweezers. The trapping sites not within the scientific region form a reservoir region. In some embodiments, the reservoir region and the scientific region are two regions of the same array, that is, they are both formed using the same lasers / optical elements. Additionally, the scientific array and the reservoir array can be refilled simultaneously, which causes loss and decoherence of those atoms already in the scientific region. The systems and methods of the present disclosure can reduce the loss of atoms, the decoherence of atoms, or both during the refill process.

[0060] Example process for performing continuous non-classical computations

[0061] Figure 2Illustrated is an example process 200 for performing continuous non-classical computing. In some examples, process 200 can be implemented when the science region and the reservoir region are sufficiently different such that the reservoir region can be loaded while causing sufficiently little interference to the atoms in the science region. One way to achieve this is that the reservoir region and the science region are not sub-regions of the same array, but different arrays, that is, they can be formed using different lasers or different optical elements. Additionally, in some embodiments, the reservoir can be loaded from a third "transport" array rather than from a MOT. This last technique can eliminate the use of near-resonant light and thus can allow for continuous coherent operations during the reloading process.

[0062] At a high level, process 200 can include: loading a reservoir array; transferring atoms from the reservoir array to a science array; performing a computation / simulation using the science array where atom loss occurs in the science array; refilling the science array from the reservoir array; and reloading the reservoir array. The science array can include atoms that are being actively used for an application (e.g., quantum computing, optical clock, sensing, or any other application disclosed herein). The science array in a quantum computer can include data qubits and ancillary qubits. The reservoir array can include atoms that are not being actively used but can be used at a later time to replace atoms lost from the science array (e.g., ancillary qubits lost from a quantum computer).

[0063] In some cases, process 200 can start with both the reservoir array and the science array being empty. Once atoms are loaded into the reservoir array, the atoms in the reservoir can be imaged. In some examples, then at least some of the atoms in the reservoir array can be transferred to the science array (e.g., using optical tweezers). The reservoir array can be reloaded to achieve a full or fuller reservoir array and enable further transfer of more atoms from the reservoir array to the science array. Once the science array is fully occupied (or occupied to a desired / predetermined amount), the computation / simulation can begin. During the computation / simulation, the science array can be imaged periodically to determine if atom loss has occurred and where the atom loss has occurred. If a site in the science array has lost an atom, an atom can be transferred from the reservoir array to fill that site. As long as there are sufficient atoms in the reservoir array, this process can continue. When there are not enough atoms in the reservoir array, new atoms can be loaded into the reservoir array and the process continues. As Figure 2 shown, in some examples, process 200 can be iterative or repetitive and one or more operations in process 200 may repeat.

[0064] Figure 2Illustrates an example method and system for performing continuous non-classical computing. Method 200 may include operation 210. Operation 210 may include loading a plurality of atoms into a reservoir array that includes a plurality of first optically trapped sites that are spatially distinct. The plurality of first optically trapped sites may be configured to trap a 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, etc. In some cases, the plurality of atoms include atoms in an atomic clock.

[0065] Method 200 may include operation 220. Operation 220 may include transferring a first subset of the plurality of atoms from the reservoir array to a science array. The science array may include a plurality of second optically trapped sites that are spatially distinct. The plurality of second optically trapped sites may be configured to trap a plurality of atoms.

[0066] In some cases, at operation 215, operations 210 and 220 may be repeated multiple times. The operations may be repeated until the science array includes a fill factor sufficient for quantum computing, quantum simulation, clock operation, metrology operation, sensing operation, etc.

[0067] Method 200 may include operation 230. Operation 230 may include performing a first application using at least some of the atoms in the first subset of the plurality of atoms in the science array. The application may be quantum computing, quantum simulation, clock operation, metrology operation, sensing operation, etc.

[0068] Method 200 may include operation 240. Operation 240 may include determining atomic loss in one or more of the arrays. The operation may include determining an atomic loss quantity that represents the difference between (i) the number of atoms in the first subset of the plurality of atoms and (ii) the number of atoms in the remaining subset of the first subset of the plurality of atoms that remain in the science array after performing the first non-classical computation. Atomic loss may occur due to collisions with residual background gas, leakage into un-trapped or other undesired internal states, heating or other processes associated with interaction with lasers.

[0069] Method 200 may include operation 250. Operation 250 may include transferring a second subset of the plurality of atoms from the reservoir array to the science array. Operation 250 may include a reloading operation. In some cases, the second subset of the plurality of atoms includes at least an atomic quantity equal to the atomic loss quantity. In some cases, the second subset of the plurality of atoms includes an atomic quantity less than the atomic loss quantity. The second subset may be transferred substantially without loss of coherence of the plurality of atoms in the science array. The second subset may be transferred substantially without stopping the application in the science array.

[0070] In some cases, at operation 255, operations 230, 240, and 250 may be repeated multiple times. The operations may be repeated until quantum computing, quantum simulation, clock operations, metrology operations, etc. are completed. The operations may be repeated when there are atoms in the reservoir to be filled into the science array.

[0071] Method 200 may include operation 260. Operation 260 may include reloading the reservoir array with additional atoms. The reservoir may be reloaded from an atomic source. The atomic source may be a cooled atomic source. In some examples, the reservoir region may be filled from a magneto-optical trap (MOT), from an atomic beam, from a thermal atomic gas, from another optical or other form of electromagnetic trap, or from any other atomic source. In some examples, the initial loading of the science region may be done directly (from any atomic source other than the reservoir array), from the reservoir array, or from a reservoir array different from the reservoir array used for replenishment. In some examples, the reservoir region may be smaller than, larger than, or the same as the science region in terms of size / number of sites, and similar techniques may be used to maintain any number of atoms within each site of the science array.

[0072] In some cases, at operation 265, operation 260 may be repeated multiple times. Operation 260 may perform multiple refills to fill the reservoir array. The operations may be repeated such that the applications in operation 230 can be continuously executed.

[0073] In some cases, at operation 275, operations 255 and 265 may be repeated in order to maintain the fill factor in the science array. In some cases, the method may include performing a second non-classical computation using at least some atoms from (i) a remaining subset of a first subset of multiple atoms and (ii) one or both of a second subset of multiple atoms.

[0074] This disclosure includes various sub-operations of method 200. For example, one or more of the operations of method 200 may be removed. For example, one or more of the operations of method 200 may be repeated.

[0075] Figure 3 An example method and system for preparing an atomic sample are shown. Method 300 may include operation 310. Operation 310 may include capturing multiple atoms into a science array, where the science array includes a plurality of spatially distinct first optical trapping sites.

[0076] Method 300 may include operation 320. Operation 320 may include transferring at least one atom from a reservoir array to the science array to increase the fill factor of the science array, where the reservoir array includes a plurality of spatially distinct second optical trapping sites.

[0077] Operation 320 may include an implementation, 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 a plurality of atoms from a reservoir array into a science array. The science array may include a plurality of spatially distinct optical trapping sites from the reservoir array.

[0078] In some cases, at operation 325, operation 320 may be repeated multiple times. The operation may be repeated until the science array includes a fill factor sufficient for quantum computing, quantum simulation, clock operation, metrology operation, sensing operation, etc.

[0079] Method 300 may include operation 330. Operation 330 may include transferring at least one atom into the reservoir array to increase the fill factor of the reservoir array. Operation 330 may be at least partially performed during transferring at least one atom from the reservoir array into the science array at operation 320.

[0080] Operation 330 may include an implementation, 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 reservoir array may be reloaded from an atomic source. The atomic source may be a cooled atomic source.

[0081] In some cases, at operation 335, operation 330 may be repeated multiple times. Operation 330 may be refilled multiple times to fill the reservoir array. The operation may be repeated such that an application, such as the application in operation 230, can be continuously performed. The operation may be repeated such that an application, such as the application in operation 230, can be performed substantially without stopping the application.

[0082] Figure 4 Another example method and system for preparing an atomic sample are shown. Method 400 may be an implementation, variation, or example of operation 210 of method 200. Operation 210 may include loading a plurality of atoms into a reservoir array that includes a plurality of spatially distinct first optical trapping sites. The plurality of first optical trapping sites may be configured to trap a 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, etc. In some cases, the plurality of atoms include atoms in an atomic clock.

[0083] Method 400 may include an implementation, variation, or example of operation 220 of method 200. Operation 220 may include transferring a first subset of a plurality of atoms from the reservoir array into a science array. The science array may include a plurality of spatially distinct second optical trapping sites. The plurality of second optical trapping sites may be configured to trap a plurality of atoms.

[0084] In some cases, at operation 215, operations 210 and 220 may be repeated multiple times. The operations may be repeated until the science array includes a fill factor sufficient for quantum computing, quantum simulation, clock operations, metrology operations, etc.

[0085] As Figure 4 shown, method 400 may also include implementations, variations, or examples of operations 320, 325, 330, and 335 of method 200.

[0086] Figure 5 Another example method and system for preparing an atomic sample are shown. Method 500 may include operation 510. Operation 510 may include trapping a plurality of atoms in a science array, where the science array includes a plurality of spatially distinct first optical trapping sites. Method 500 may include operation 520. Operation 520 may include inducing at least a first subset of the plurality of atoms to adopt one or more superposition states of at least a first subset of the plurality of atoms in the science array. Method 500 may include operation 530. Operation 530 may include transferring at least one atom from a reservoir array to the science array, where the reservoir array includes a plurality of spatially distinct second optical trapping sites. Operation 530 may be performed substantially without decohering the superposition states generated at operation 520.

[0087] In some cases, method 500 may include operation 230. Operation 230 may include performing a first application using at least some of the atoms in a first subset of the plurality of atoms in the science array. The application may be quantum computing, quantum simulation, clock operations, metrology operations, etc. Operation 230 itself may include one or more instances of operation 520. For example, a two-qubit gate may include one or more instances of generating a superposition at operation 520.

[0088] In some cases, method 500 may include determining atomic loss in one or more of the arrays. The operation may include determining an atomic loss quantity that represents the difference between (i) the number of atoms in a first subset of the plurality of atoms and (ii) the number of atoms in the remaining subset of the first subset of the plurality of atoms that remain in the science array after performing a first non-classical computation. Atomic loss may occur due to collisions with residual background gas, leakage into un-trapped or other undesired internal states, heating associated with interaction with lasers, or other processes.

[0089] Operation 530 may include an implementation, 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 a plurality of atoms from a reservoir array into a science array. Operation 250 may include a reloading operation. In some cases, the second subset of the plurality of atoms includes an atom number that is at least equal to the atom loss number. In some cases, the second subset of the plurality of atoms includes an atom number that is less than the atom loss number. The second subset may be transferred substantially without loss of coherence of the plurality of atoms in the science array. The second subset may be transferred substantially without stopping the application in the science array.

[0090] In some cases, at operation 525, operations 520 and 530 may be repeated multiple times. The operations may be repeated until quantum computing, quantum simulation, clock operation, metrology operation, etc. are completed. The operations may be repeated when there are atoms in the reservoir to be filled into the science array.

[0091] Method 500 may include an implementation, variation, or example of operation 260 of method 200. For example, 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 cases, at operation 265, operation 260 may be repeated multiple times. Operation 260 may perform multiple refills to fill the reservoir array. The operations may be repeated such that the application in operation 230 can be continuously executed.

[0092] Continuous loading

[0093] A useful error-correcting quantum computer should remove entropy faster than entropy can be input. One source of entropy in a trapped-atom quantum computer may be atom loss. Thus, it may be useful to computationally conditionally and continuously refill the sites in a trapped-atom quantum computer. Continuous operations during non-classical computing may include refilling lost atoms during the operations of the computation. For example, continuous operations in a gate-model quantum computer may include refilling lost atoms between the "mid-circuit" or gate operations of the quantum computation. Continuous operations in a quantum simulator may include refilling atoms during the simulation. Continuous operations in a clock operation may include refilling atoms during the operations of the clock. Generally, continuous operations may include refilling atoms during the time of implementing the application.

[0094] Continuous operations may include refilling atoms substantially without stopping the application. Substantially not stopping may include not performing recovery operations such as repeating previous steps to cope with atom loss. Such recovery operations may include repeating the computation or a part of the computation to replace the "lost" part.

[0095] Similarly, since each of quantum computing, quantum simulation, clock operation, metrology, and quantum sensing can utilize phenomena such as quantum coherence, it may be useful to maintain coherence while refilling atoms in atomic-based implementations of these applications (e.g., atomic clocks, neutral atom quantum computers, etc.). For example, atoms can be refilled substantially without loss of coherence of the atoms in the array. Substantially no loss of coherence can include a contrast loss of about 10% or better on a second timescale. For example, the contrast loss is less than 10% within 2 seconds, and the contrast loss is approximately 5% or better within 2 seconds. Substantially no loss of coherence can include a contrast better than 0.8 (up to 1) within 1 second.

[0096] The present disclosure provides systems and methods for continuous atomic reloading. The systems and methods of the present disclosure can distinguish between a science array and a reservoir array during atomic transfer.

[0097] For example, the arrays can be physically distinguishable. The systems and methods of the present disclosure can employ different sets or subsets of atoms within the arrays. For example, Figures 2 to 5 each of which shows a science array and a reservoir array. In some cases, the science array is different from the reservoir array. In some cases, the science array is spatially different from the reservoir array. For example, the science array can be physically separated from the reservoir array. For example, during atomic movement, the science array can be energetically separated from the reservoir array. In some cases, both the physical separation method and the energy separation method can facilitate atomic movement without disrupting the science array.

[0098] For example, the physical separation of the science array and the reservoir array may be useful in at least some aspects. If the science array and the reservoir array are physically different, the reservoir array can be more easily separated spatially from the science region. This can allow loading into the reservoir array without disturbing the atoms in the science region during loading of the reservoir region. For example, during transfer, interference may occur due to unwanted scattering, unwanted optical shifts, etc. In some cases, an optical system separated from trap excitation can be used to move atoms from a first array disclosed herein to a second array. For example, the reservoir array can be loaded from a separate optical potential or array, which may interfere with the atoms in the science region if the reservoir array and the science array are too close. Using a separate optical system to generate the two arrays can help separate the science array and the reservoir array. Using a separate (e.g., third) optical system to move atoms can further isolate the arrays.

[0099] In some examples, the reservoir region and the science region can be separated parallel or transverse to the axis along which imaging is performed. If separated parallel to the imaging axis, atoms can be transferred from the reservoir region to the science region by translating the focus of the focusing capture laser or by offsetting the phase of the captured optical lattice. For example, see the section "Long-Range Transport" in this document. In some cases, the transfer of at least one atom from the reservoir array to the science array is a long-range transfer.

[0100] For example, the electronic separation of the science array and the reservoir array may be useful in at least some respects. In some examples, the reservoir region and the science region are distinguished by internal or motional states occupied by atoms (perhaps not spatially separated). In some examples, the trap can be formed with light that is incoherent or coherent in space or time, or by a non-optical electromagnetic field.

[0101] In some cases, coherence can be protected by applying "hidden" excitations during or part of the reloading of atoms into the science array. Hidden excitations can include placing the atoms being transferred or already in the array into a dark state, a clock state, or another state prohibited by the selection rules of the light excitation used for transfer. In some examples, hidden excitations can be applied to the atoms in the science array during the imaging or excitation of the atoms to be moved into the science part of the array. In some cases, at least one atom transferred from the reservoir array to the science array is in a dark state. In some cases, the atoms transferred from the reservoir array to the science array are in a dark state, a clock state, or another state prohibited by the selection rules of the light excitation used for transfer. For example, see the section "State-Selected Atom Movement" in this document.

[0102] Optical trapping

[0103] Optical traps - The systems and methods of the present disclosure provide a plurality of optically distinct traps. Examples of a plurality of optical traps can include a plurality of optical capture sites. For example, a plurality of optical traps can include any example of the plurality of optical capture sites described herein with reference to Figures 2 - 5 any example of the plurality of optical capture sites described.

[0104] The system can include one or more capture systems. The capture system can include one or more optical capture systems. The optical capture system can include any optical capture unit described herein. In some examples, the optical trap can be formed by tightly focused light (optical tweezers), or by a standing-wave lattice, or by an imaging mask or grating. Optical trapping can also additionally include various methods in which atoms are cooled with optical illumination (e.g., laser) and a spatially varying magnetic field to create a trap. Such optical traps can be referred to as magneto-optical traps (MOT).

[0105] In some cases, multiple optically distinct optical traps include 1D, 2D, or 3D optical traps. In some examples, the array can be linear, two-dimensional, three-dimensional, or can involve synthetic dimensions. For example, the synthetic dimension can include a dimension constituted by internal atomic states or motion states. Multiple optically distinct optical traps can include single or multiple reservoir regions. In some examples, the array can be of regular, irregular, or quasi-regular geometric shapes.

[0106] Optical tweezers - In some cases, multiple optically distinct optical traps include optical tweezers. The optically trapped sites can include one or more optical tweezers. The optical tweezers can include one or more focused laser beams to provide an attractive or repulsive force to hold or move one or more atoms. The waist of the focused laser beam can include a strong electric field gradient. The atoms can be attracted or repelled along the electric field gradient to the center of the laser beam, which may contain the strongest electric field. The optically trapped sites can include one or more optically trapped sites in one or more optical tweezer arrays. The optically trapped sites can include one or more optically trapped sites in one or more one-dimensional (1D) optical tweezer arrays, two-dimensional (2D) optical tweezer arrays, or three-dimensional (3D) optical tweezer arrays. In some cases, the methods and systems described herein can be similarly applied to optical lattices. Optical tweezers can be useful in moving atoms or arrays of atoms.

[0107] Multiple trapping arrays - The systems and methods of the present disclosure can employ different sets or subsets of atoms within an array. For example, Figures 2 - 5 each of which shows a science array and a reservoir array. In some cases, the science array is different from the reservoir array. In some cases, the science array is spatially different from the reservoir array. For example, the science array can be physically separated 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 from the reservoir array.

[0108] 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, one or both of the science array or the reservoir array are formed using light or non-optical electromagnetic fields. In some cases, the science array and the reservoir array include spatially distinct MOTs. In some cases, the science array includes a first MOT in a first chamber, and the reservoir array includes a second MOT in a second chamber. In some cases, the science array and the reservoir array include different regions within the same MOT.

[0109] While Figures 2 - 5Each of them shows a scientific array and a reservoir array, but the systems and methods of the present disclosure may include one or more additional arrays, e.g., an intermediate array. For example, improved cooling effects can be achieved through a multi-stage MOT. 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, a multi-stage MOT can contribute to the spatial separation of the arrays. For example, compared to different regions of the same MOT, a first MOT generated by a first optical illumination and physically separated from the second MOT can better isolate heat, atomic losses, thermal noise, etc. from the second MOT.

[0110] In some cases, in any of the methods disclosed herein, transferring at least one atom from a reservoir array to a scientific array includes: transferring a first quantity of atoms from the reservoir array to one or more intermediate arrays, and transferring a second quantity 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, (i) after transferring a certain quantity of atoms from the reservoir array to at least two intermediate arrays, and (ii) before transferring the quantity of atoms from the at least two intermediate arrays to the scientific array, the at least certain quantity of atoms is transferred between the at least two intermediate arrays.

[0111] Sites - The optical trapping system can be configured to generate a plurality of optical trapping sites. The optical trapping system can be configured to generate a plurality of spatially distinct optical trapping sites. As Figures 2 - 5 shown in each of them, each array can include a plurality of spatially distinct optical trapping sites. Although each optical trapping site is shown as having only a single atom, in some cases, it may be advantageous to have more than one atom in a single site. In some cases, having a single atom in a single site may be preferred. For example, a single atom in a single site may be easier to cool due to fewer collisions with other atoms.

[0112] In some cases, the second quantity of sites in the plurality of second optical trapping sites is equal to the first quantity of sites in the plurality of first optical trapping sites. In some cases, the second quantity of sites in the plurality of second optical trapping sites is greater than the first quantity of sites in the plurality of first optical trapping sites. For example, the number of traps in the scientific array can be the same as the number of traps in the reservoir array. However, in some cases, it may be more useful to have a greater or fewer number of traps in the reservoir array.

[0113] In some cases, each of the science array, the reservoir array, and any intermediate arrays can be generated by the same or different optical trapping systems. For example, each optical trapping system can be varied based on the requirements of a particular array (science array, reservoir array, intermediate array, etc.). Each optical trapping system can include any number of sites disclosed herein. Each optical trapping system can include any number of trapped atoms disclosed herein.

[0114] For example, each optical trapping system can be configured to generate at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000 or more optical trapping sites. Each optical trapping system can be configured to generate at most about 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10 or fewer optical trapping sites. One or more optical trapping systems can be configured to trap an optical trapping site in a range defined by any two of the foregoing values.

[0115] Each optical trapping system can be configured to trap multiple atoms. For example, each optical trapping system can be configured to trap a total of at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000 or more atoms at multiple optical trapping sites. For example, one or more optical trapping systems can be configured to trap a total of at most about 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10 or fewer atoms at multiple optical trapping sites. One or more optical trapping systems can be configured to trap atoms in a range defined by any two of the foregoing values.

[0116] Trap excitation - In some cases, the methods and systems disclosed herein can be configured to use trap excitation to form multiple optical trapping sites. Trap excitation can include optical excitation, such as optical excitation in magneto-optical traps, optical tweezers, etc. In some cases, trap excitation is delivered by one or more of the optical trapping systems disclosed herein. In some cases, each optical trapping system includes its own trap excitation (e.g., trap wavelength, trap power, trap focus, number of spots, etc.). In some cases, a single trap excitation can be split into multiple arrays to form multiple trap arrays with similar characteristics.

[0117] In some examples, for one or more reasons, it may be useful to use a separate laser or optical device (e.g., "optical excitation") to form a reservoir array (e.g., as compared to lasers or optical devices that may be used with a science array). In one example, different laser wavelengths, trap geometries (e.g., tweezer spot size or spacing), or methods for generating different arrays (e.g., acousto-optic deflectors (AODs), spatial light modulators (SLMs), digital micromirror devices (DMDs), microlens arrays, diffraction gratings, standing wave lattices, imaging structures, or others) may be used to create a reservoir array and a science array. Thus, the properties of each array (trap depth, differential polarization rate on the associated atomic transition, trap spacing, trap oscillation frequency, etc.) can be optimized for its specific role. In another example, the power from a single light source is typically limited, and by using multiple light sources, the total available power can be increased, allowing for the formation of more and / or deeper traps.

[0118] One or more optical trapping systems may include one or more light sources configured to emit light to generate a plurality of optical trapping sites as described herein. For example, one or more optical trapping systems may include a single light source. In some cases, one or more optical trapping systems may include any number of light sources, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more light sources or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 light source. The light source may include one or more lasers.

[0119] The light source may be configured to direct light to one or more optical modulators (OMs) configured to generate a plurality of optical trapping sites. For example, an optical trapping unit may include an OM configured to generate a plurality of optical trapping sites. In some cases, an optical trapping unit may include any number of OMs, such as at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more OMs, or at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 OM. The 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).

[0120] The OM may be optically coupled to one or more optical elements to generate a regular array of optical trapping sites. The optical elements may include lenses or microscope objectives configured to redirect light from the OM to form a regular rectangular grid of optical trapping sites.

[0121] For example, the OM may include an SLM, DMD, or LCoS device. The SLM, DMD, or LCoS device may image onto the rear focal plane of the microscope objective. This may allow for the generation of optically trapped sites in arbitrary configurations in two or three dimensions.

[0122] In some cases, trap excitation may be turned on or off during the course of the methods, operations, and applications disclosed herein. For example, trap light may be turned on during the loading phase of an optical trap array. For example, trap light may be turned off during or after the phase in which a second optical excitation (e.g., for applications such as non-classical computing operations, clock operations, metrology operations, sensing operations, etc. of the present disclosure) is applied. For example, a trap may be provided with an initial number of atoms in a science array. A Rydberg excitation may be applied to form an optical coherence between two atoms in the science array. One or more atoms may be added to the science array. Trap light may be temporarily turned off during the application of the optical excitation to form the coherence.

[0123] In some cases, trap excitation of each optical trapping system includes a 1 P1 transition at 399 nm, followed by a 3P1 narrow line transition. The trap excitation of each optical trapping system may include one or more wavelengths of at least approximately 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm or greater. The light may include one or more wavelengths of at most approximately 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 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 within the range 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.

[0124] Atom

[0125] The systems and methods of the present disclosure can 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 II elements. In some cases, the plurality of atoms includes scandium. In some cases, the plurality of atoms includes group-II-like elements. In some cases, the plurality of atoms includes atoms having two valence electrons. In some cases, the plurality of atoms includes ytterbium.

[0126] An atom-optical trapping system can be configured to trap neutral atoms. In some cases, the optical trapping system can trap alkaline earth metal atoms or alkaline-earth-metal-like atoms. In some cases, the alkaline-earth-metal-like atoms include two valence electrons. In some cases, the alkaline earth metal atoms or alkaline-earth-metal-like atoms include strontium or ytterbium.

[0127] One or more atoms may include alkali atoms. One or more atoms may include lithium (Li) atoms, sodium (Na) atoms, potassium (K) atoms, rubidium (Rb) atoms, or cesium (Cs) atoms. One or more atoms may include lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, or cesium-133 atoms. One or more atoms may include alkaline earth metal atoms. One or more atoms may include beryllium (Be) atoms, magnesium (Mg) atoms, calcium (Ca) atoms, strontium (Sr) atoms, or barium (Ba) atoms. One or more atoms may include beryllium-9 atoms, magnesium-24 atoms, magnesium-25 atoms, magnesium-26 atoms, calcium-40 atoms, calcium-42 atoms, calcium-43 atoms, calcium-44 atoms, calcium-46 atoms, calcium-48 atoms, strontium-84 atoms, strontium-86 atoms, strontium-87 atoms, strontium-88 atoms, barium-130 atoms, barium-132 atoms, barium-133, barium-134 atoms, barium-135 atoms, barium-136 atoms, barium-137 atoms, or barium-138 atoms. One or more atoms may include rare earth atoms. One or more atoms may include scandium (Sc) atoms, yttrium (Y) atoms, lanthanum (La) atoms, cerium (Ce) atoms, praseodymium (Pr) atoms, neodymium (Nd) atoms, samarium (Sm) atoms, europium (Eu) atoms, gadolinium (Gd) atoms, terbium (Tb) atoms, dysprosium (Dy) atoms, holmium (Ho) atoms, erbium (Er) atoms, thulium (Tm) atoms, ytterbium (Yb) atoms, or lutetium (Lu) atoms. One or more atoms may include scandium-45 atoms, yttrium-89 atoms, lanthanum-139 atoms, cerium-136 atoms, cerium-138 atoms, cerium-140 atoms, cerium-142 atoms, praseodymium-141 atoms, neodymium-142 atoms, neodymium-143 atoms, neodymium-145 atoms, neodymium-146 atoms, neodymium-148 atoms, samarium-144 atoms, samarium-149 atoms, samarium-150 atoms, samarium-152 atoms, samarium-154 atoms, europium-151 atoms, europium-153 atoms, gadolinium-154 atoms, gadolinium-155 atoms, gadolinium-156 atoms, gadolinium-157 atoms, gadolinium-158 atoms, gadolinium-160 atoms, terbium-159 atoms, dysprosium-156 atoms, dysprosium-158 atoms, dysprosium-160 atoms, dysprosium-161 atoms, dysprosium-162 atoms, dysprosium-163 atoms, dysprosium-164 atoms, erbium-162 atoms, erbium-164 atoms, erbium-166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium-171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium-175 atoms, or lutetium-176 atoms.

[0128] Atom transfer unit

[0129] As disclosed herein, the systems and methods described 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 different from the reservoir array. For example, the science array may be physically separated from the science array.

[0130] The physical separation of 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 area. This can allow loading into the reservoir array without disturbing the atoms in the science area when loading the reservoir area. For example, during transfer, interference may occur due to unwanted scattering, unwanted optical shifts, etc. In some cases, an optical system separate from trap excitation can be used to move atoms from a first array disclosed herein to a second array. For example, the reservoir array can be loaded from a separate optical potential or array, which may interfere with the atoms in the science area if the reservoir array and the science array are too close. Using separate optical systems to generate the two arrays can help separate the science array and the reservoir array. Using a separate (e.g., third) optical system to move atoms can further isolate the arrays.

[0131] Moving atoms between arrays and rearranging atoms within an array can be achieved by the atom moving unit disclosed herein. The atom moving unit may include any implementation, variation, or example of the atom rearrangement unit disclosed herein. For example, operations 220, 250, 320, and 530 described herein may include moving atoms from a reservoir array to a science array.

[0132] In some examples, the present technology may be combined with methods for probabilistic loading, deterministic loading, or near-deterministic loading of optical traps or other traps (such as the methods disclosed herein). In some examples, when replenishing the science array, the atoms within the science area may or may not be rearranged. In some examples, atoms can be transferred between the reservoir area and the science area by optical tweezers. In some examples, atoms can be transferred between the reservoir area and the science area by an optical lattice. In some examples, atoms can be transferred between the reservoir area and the science area by tunneling / jumping between sites. In some examples, atoms can be transferred between the reservoir area and the science area by an autonomous stabilization technique. The autonomous stabilization technique may include imaging the initial occupancy and / or final occupancy of the science area and / or the reservoir area, and autonomously updating the occupancy of the sites of the array.

[0133] In some cases, one or both of a mobile optical trap or an optical tweezer are used to perform one or both of the following: (i) loading multiple atoms into a reservoir, or (ii) reloading an array of reservoirs with additional atoms. In some cases, an optical tweezer can be used to move (e.g., pick and place) a single atom or subset of atoms between or within arrays. In some cases, a mobile optical trap can be used to translate or compress an array. A mobile optical trap can implement tuning for sweeping atoms from one location to another. An atom mover unit can be configured to move one or more replacement atoms from one or more atom reservoirs to one or more optical trapping sites. For example, one or more atom mover units can include one or more electro - tunable lenses, an acousto - optic deflector (AOD), or a spatial light modulator (SLM).

[0134] In some cases, the science array is physically separated from the reservoir array parallel to the imaging axis; and one or both of a mobile optical trap or an optical tweezer are used to perform one or both of the following: (i) transferring a first subset of multiple atoms from the reservoir array to the science array, or (ii) transferring a second subset of multiple atoms from the reservoir array to the science array.

[0135] In some cases, any one of methods 200, 300, 400, or 500 can include: within the science array, rearranging the positions of at least some of the atoms among a plurality of spatially distinct optical trapping sites of (i) multiple atoms in the science array or (ii) at least one atom in the science array. In some cases, any one of methods 200, 300, 400, or 500 can include: within the reservoir array, rearranging the positions of at least some of the atoms among a plurality of spatially distinct optical trapping sites of (i) multiple atoms in the reservoir array or (ii) at least one atom in the reservoir array.

[0136] One or more of the optical trapping systems disclosed herein can include one or more atom rearrangement units configured to impart an altered spatial arrangement of multiple atoms captured by optical trapping sites based on one or more images obtained by an imaging unit. The optical trapping unit can 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 at most about 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 atom rearrangement unit. 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.

[0137] The atomic rearrangement unit can be configured to change the spatial arrangement in order to obtain an increase in the filling factor of multiple optical trapping sites. The filling factor can be defined as the ratio of the number of computationally active optical trapping sites occupied by one or more atoms to the total number of computationally active optical trapping sites available in the optical trapping unit or a portion of the optical trapping unit. For example, the initial loading of atoms within a computationally active optical trapping site may result in a filling factor of less than 100%, 90%, 80%, 70%, 60%, 50% or less, such that the atoms occupy less than 100%, 90%, 70%, 60%, 50% or less of the available computationally active optical trapping sites, respectively. Rearrangement of the atoms may be required to achieve a filling factor of at least approximately 50%, 60%, 70%, 80%, 90% or 100%. By analyzing the imaging information obtained by the imaging unit, the atomic rearrangement unit can obtain a filling factor of at least approximately 50%, 60%, 70%, 80%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, 99.1%, 99.2%, 99.3%, 99.4%, 99.5%, 99.6%, 99.7%, 99.8%, 99.9%, 99.91%, 99.92%, 99.93%, 99.94%, 99.95%, 99.96%, 99.97%, 99.98%, 99.99% or more. The atomic rearrangement unit can achieve a filling factor of at most approximately 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 96%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50% or less. The atomic rearrangement unit can obtain a filling factor within the range defined by any two of the foregoing values.

[0138] In some cases, atomic rearrangement can be performed by the following operations: (i) acquiring an image of the optical trapping unit, identifying the filled and unfilled optical trapping sites, (ii) determining a set of movements to move the atoms from the filled optical trapping sites to the unfilled optical trapping sites, and (iii) moving the atoms from the filled optical trapping sites to the unfilled optical trapping sites. Operations (i), (ii) and (iii) can be performed iteratively until a large filling factor is obtained. Operation (iii) can include converting the movements identified in operation (ii) into waveforms that can be sent to an arbitrary waveform generator (AWG) and using the AWG to drive an AOD to move the atoms.

[0139] Long-range transfer

[0140] As the spatial separation between the scientific array and the reservoir array increases, the interaction between the two arrays may decrease; however, it may become more difficult to move atoms between the arrays. The systems and methods of the present disclosure can incorporate long-range transfer techniques to facilitate a greater physical separation.

[0141] In an exemplary long-range transfer technique, an optical lattice can be created by interfering two opposing laser beams whose foci overlap with each other. Atoms can be transported by translating the phase of the optical lattice while simultaneously translating the foci of the two opposing laser beams so that the two foci remain overlapping and also track the phase of the lattice during the entire travel of the atoms. The tight confinement of the optical lattice enables rapid transport due to the large restoring force caused by the high-intensity gradient created by the optical lattice. Translating the laser foci allows maximizing the trap depth with minimal laser power throughout the trajectory.

[0142] To achieve a deep lattice in an energy-efficient manner, the beam waist of the transport beam can be translated synchronously with the optical lattice by moving the positions of two focusing lenses, with one focusing lens used for each of the two counter-propagating beams that form the lattice. A closed-loop piezoelectric steering mirror can be used to actively maintain the alignment between the two beams. The atoms are transferred into the optical tweezer array by overlapping the atoms with the array, increasing the power of the optical tweezer, and then decelerating the transport lattice.

[0143] In some cases, the long-range transfer method can include cooling and trapping a plurality of atoms within a one-dimensional optical lattice using one or more electromagnetic waves. In some cases, the long-range transfer method can include stopping the cooling of the plurality of atoms within the one-dimensional optical lattice. In some cases, the long-range transfer method can include chirping the relative frequencies and / or adjusting the focal depth of one or more lenses to maintain the trapping of the plurality of atoms. In some cases, the long-range transfer method can include changing the angle of one or more electromagnetic waves to transport a group of the plurality of atoms within the optical lattice. In some cases, the long-range transfer method can include using the plurality of atoms to perform calculations.

[0144] In some embodiments, the chirp relative frequency includes translating the phase of a one-dimensional optical lattice. In some embodiments, translating the phase of the one-dimensional lattice includes transporting one or more atoms from a first region to a second region. In some embodiments, the first region is an atomic loading region (e.g., a reservoir array), and the second region is a science array. In some embodiments, transporting one or more atoms from the first region to the second region includes transporting the one or more atoms a certain distance. In some embodiments, the distance is at least about 20 cm. In some embodiments, the distance ranges from about 20 cm to about 100 cm. In some embodiments, translating the phase of the one-dimensional optical lattice includes changing the angle of a mirror. In some embodiments, adjusting the depth of focus of one or more lenses includes changing the position of the one or more lenses.

[0145] Cooling / state preparation

[0146] The science array and the reservoir array can be integrated with the cooling process. For some applications, it may be advantageous for each atom to be in substantially the same state or in a substantially determined / determinable state such that applications (e.g., metrology, sensing, optical clocks, non-classical computing, quantum simulation, etc.) can be performed. The optical trapping systems (e.g., systems for the science array, reservoir array) disclosed herein can be integrated with the state preparation systems disclosed herein.

[0147] As disclosed above, improved cooling effects can be achieved through multi-stage MOT. For example, a first MOT can cool to a first temperature, and a second MOT can cool to a second temperature. In some cases, multi-stage MOT can contribute to the spatial separation of the arrays. For example, compared to different regions of the same MOT, the first MOT generated by the first optical illumination and physically separated from the second MOT can better isolate heat, atomic loss, thermal noise, etc. from the second MOT. In some cases, a single MOT can include multiple cooling operations. For example, a first cooling operation can include using one or more electromagnetic delivery units to deliver the 1 P1 transition at 399 nm, and subsequently delivering the 3 P1 narrow-line transition at 556 nm.

[0148] In an example, operations 210 and 260 disclosed herein with respect to methods 200, 300, 400, and 500 can include initially loading a reservoir array and / or reloading the reservoir array with additional atoms. The reservoir can be reloaded from an atomic source. The atomic source can be a cooled atomic source. In some examples, the reservoir region can be filled from a magneto-optical trap (MOT), from an atomic beam, from a thermal atomic gas, from another optical or other form of electromagnetic trap, or from any other atomic source. In some examples, the initial loading of the science region (e.g., operation 220 herein) can be performed directly (from any atomic source other than the reservoir array), from the reservoir array, or from a reservoir array different from the reservoir array used for replenishment. In some examples, the reservoir region can be smaller than, larger than, or the same as the science region in terms of size / number of sites, and similar techniques can be used to maintain any number of atoms within each site of the science array.

[0149] State preparation - The systems and methods disclosed herein can include one or more state preparation units. The state preparation unit can include a portion of an atomic source. The state preparation unit can be configured to prepare the states of a plurality of atoms as described herein. The state preparation unit can be coupled to an optical trapping unit and can direct the atoms that have been prepared by the state preparation unit to the optical trapping unit. The state preparation unit can be configured to cool a plurality of atoms. The state preparation unit can be configured to cool a plurality of atoms prior to trapping the plurality of atoms at a plurality of optical trapping sites.

[0150] In some cases, the state preparation unit includes one or more atomic reservoirs. The atomic reservoir can be configured to provide one or more replacement atoms to replace one or more atoms at one or more optical trapping sites when the atoms are lost from the optical trapping sites of the science array or the reservoir array. The atomic reservoir can be spatially separated from the optical traps of the science array or the reservoir array. For example, the atomic reservoir can be located at a distance from the optical traps of the reservoir array and the science array.

[0151] In some cases, the atomic reservoir can include a portion of the optical trapping sites of the optical trapping unit (e.g., the reservoir array is a subset of the science array). A first subset of the optical trapping sites can be used to perform quantum computing and can be referred to as a set of computationally active optical trapping sites (e.g., the science array), while a second subset of the optical trapping sites can serve as an atomic reservoir. For example, the first subset of the optical trapping sites can include an internal array of optical trapping sites, while the second subset of the optical trapping sites includes an external array of optical trapping sites near the internal array. The internal array can include a rectangular array, a square array, a rectangular prism array, or a cubic array of optical trapping sites.

[0152] The state preparation unit may be coupled to the optical trapping unit and may direct atoms that have been prepared by the state preparation unit to the optical trapping unit. The state preparation unit may be configured to cool a plurality of atoms. The state preparation unit may be configured to cool the plurality of atoms before trapping the plurality of atoms at a plurality of optical trapping sites.

[0153] 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 unit may contain 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 at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 Zeeman decelerator. The Zeeman decelerator may be configured to cool one or more of the plurality of atoms from a first velocity or velocity distribution (such as an emission velocity from an atomic source, room temperature, liquid nitrogen temperature or any other temperature) to a second velocity that is lower than the first velocity or velocity distribution.

[0154] 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 at most 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), 2m / s, 3m / s, 4m / s, 5m / s, 6m / s, 7m / s, 8m / s, 9m / s, 10m / s or greater. The second velocity may be at most about 10m / s, 9m / s, 8m / s, 7m / s, 6m / s, 5m / s, 4m / s, 3m / s, 2m / s, 1m / s or less. The second velocity may be within a range defined by any two of the foregoing values. The Zeeman decelerator may include a 1D Zeeman decelerator.

[0155] The state preparation unit may include one or more magneto-optical traps (MOTs). The one or more MOTs may be configured to cool 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.

[0156] The state preparation unit may include one or more sideband cooling units or Sisyphus cooling units (such as the sideband cooling unit described in www.arxiv.org / abs / 1810.06626 or the Sisyphus cooling unit described in www.arxiv.org / abs / 1811.06014, each of which is hereby incorporated by reference in its entirety for all purposes). The state preparation may include any number of sideband cooling units or Sisyphus cooling units, such as at least approximately 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 or more sideband cooling units or Sisyphus cooling units, or at most approximately 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 sideband cooling unit or Sisyphus cooling unit. The sideband cooling unit or Sisyphus cooling unit may be configured to cool an atom from a second temperature to a third temperature lower than the second temperature using sideband cooling. The third temperature may be at most approximately 10 μK, 9 μK, 8 μK, 7 μK, 6 μK, 5 μK, 4 μK, 3 μK, 2 μK, 1 μK, 900 nK, 800 nK, 700 nK, 600 nK, 500 nK, 400 nK, 300 nK, 200 nK, 100 nK, 90 nK, 80 nK, 70 nK, 60 nK, 50 nK, 40 nK, 30 nK, 20 nK, 10 nK or lower. The third temperature may be at most approximately 10 nK, 20 nK, 30 nK, 40 nK, 50 nK, 60 nK, 70 nK, 80 nK, 90 nK, 100 nK, 200 nK, 300 nK, 400 nK, 500 nK, 600 nK, 700 nK, 800 nK, 900 nK, 1 μK, 2 μK, 3 μK, 4 μK, 5 μK, 6 μK, 7 μK, 8 μK, 9 μK, 10 μK or higher. The third temperature may be within a range defined by any two of the foregoing values.

[0157] The sideband cooling unit or the Sisyphus cooling unit may include one or more light sources (such as any of the light sources described herein) configured to emit light. The light may include one or more wavelengths of at least approximately 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm or greater. The light may include one or more wavelengths of at most approximately 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 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 the range defined by any two of the foregoing values.For example, the light may include one or more wavelengths in the range 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.

[0158] The state preparation unit may include one or more optical pumping units. 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 at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 optical pumping unit. The optical pumping unit may be configured to emit light to optically pump atoms from an equilibrium distribution of atomic states to a non-equilibrium atomic state. For example, the optical pumping unit may be configured to emit light to optically pump atoms from an equilibrium distribution of atomic states to a single pure atomic state. The optical pumping unit may be configured to emit light to optically pump atoms to a ground atomic state or any other atomic state. The optical pumping unit may be configured to optically pump atoms between any two atomic states. The optical pumping unit may include one or more light sources (such as any light source described herein) configured to emit light. The light may include one or more 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, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm or greater.The light may include one or more wavelengths of at most about 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 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 within the range 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.

[0159] The state preparation unit may include 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 at most about 10, 9, 8, 7, 6, 5, 4, 3, 2 or 1 coherent drive unit. The coherent drive unit may be configured to coherently drive an atom from a non-equilibrium state to the first atomic state or the second atomic state described herein. Thus, the atom may be optically pumped to an accessible atomic state (e.g., based on the availability of a light source emitting a specific wavelength or based on other factors), and then coherently driven to an atomic state useful for performing quantum computing described herein. The coherent drive unit may be configured to induce a single-photon transition between the non-equilibrium state and the first atomic state or the second atomic state. The coherent drive unit may be configured to induce a two-photon transition between the non-equilibrium state and the first atomic state or the second atomic state. Light from two light sources described herein (such as two lasers described herein) may be used to induce the two-photon transition.

[0160] The coherent drive unit may include one or more light sources configured to emit light (such as any light source described herein). The light may include one or more wavelengths of at least approximately 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 810 nm, 820 nm, 830 nm, 840 nm, 850 nm, 860 nm, 870 nm, 880 nm, 890 nm, 900 nm, 910 nm, 920 nm, 930 nm, 940 nm, 950 nm, 960 nm, 970 nm, 980 nm, 990 nm, 1,000 nm or greater. The light may include one or more wavelengths of at most approximately 1,000 nm, 990 nm, 980 nm, 970 nm, 960 nm, 950 nm, 940 nm, 930 nm, 920 nm, 910 nm, 900 nm, 890 nm, 880 nm, 870 nm, 860 nm, 850 nm, 840 nm, 830 nm, 820 nm, 810 nm, 800 nm, 790 nm, 780 nm, 770 nm, 760 nm, 750 nm, 740 nm, 730 nm, 720 nm, 710 nm, 700 nm, 690 nm, 680 nm, 670 nm, 660 nm, 650 nm, 640 nm, 630 nm, 620 nm, 610 nm, 600 nm, 590 nm, 580 nm, 570 nm, 560 nm, 550 nm, 540 nm, 530 nm, 520 nm, 510 nm, 500 nm, 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 the range defined by any two of the foregoing values.For example, the light can include one or more wavelengths in the range 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.

[0161] The coherent drive unit can be configured to induce an RF transition between a non-equilibrium state and a first atomic state or a second atomic state. The coherent drive unit can include one or more electromagnetic radiation sources configured to emit electromagnetic radiation, which is configured to induce the RF transition. For example, the coherent drive unit can include one or more RF sources (such as any RF source described herein) configured to emit RF radiation. The RF radiation can include 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 greater. The RF radiation can include one or more wavelengths of at most about 10 m, 9 m, 8 m, 7 m, 6 m, 5 m, 4 m, 3 m, 2 m, 1 m, 90 cm, 80 cm, 70 cm, 60 cm, 50 cm, 40 cm, 30 cm, 20 cm, 10 cm or less. The RF radiation can include one or more wavelengths within the range defined by any two of the foregoing values. Alternatively or in addition, the coherent drive unit can include one or more light sources (such as any light source described herein) configured to induce a two-photon transition corresponding to the RF transition.

[0162] Atom loss and imaging

[0163] In some cases, any one of the methods disclosed herein (e.g., methods 200, 300, 400, 500) can further include determining an atomic loss number, which represents the difference between (i) the number of atoms among a plurality of atoms captured in the science array and (ii) the number of atoms remaining in the remaining subset of the plurality of atoms captured in the science array that are still in the science array after at least part of the non-classical calculation is performed.

[0164] Atomic loss can be determined by imaging one or more atoms in any array. Imaging can be affected by exciting the atoms into an emission state (e.g., a fluorescent state, a spontaneous emission state, a state undergoing stimulated emission, a phosphorescent state). Photons scattered after imaging can be collected on a camera or detector.

[0165] In some cases, atoms can be moved into a science array to fill in observed missing atoms. For example, at least one atom transferred from a reservoir array to a science array includes an atom quantity that is at least equal to the atom loss quantity. In some cases, determining the atom loss quantity is based on imaging along an imaging axis to determine which of a spatially distinct plurality of second optical trapping sites in the science array are occupied.

[0166] In some examples, atoms can be transferred between a reservoir region and a science region by an autonomous stabilization technique. The autonomous stabilization technique can include imaging the initial occupancy and / or final occupancy of the science region and / or the reservoir region, and autonomously updating the occupancy of sites in the array. In this method, the fill factor of the array can be actively maintained.

[0167] State-selected atom transfer

[0168] In some cases, coherence can be protected by applying "hidden" excitations during or part of the time during which atoms are reloaded into the science array. Hidden excitations can include placing the atoms being transferred or already in the array into a dark state, a clock state, or another state prohibited by the selection rules of the light excitation used for transfer. In some examples, hidden excitations can be applied to atoms in the science array during the imaging or excitation of atoms to be moved into the science portion of the array.

[0169] In some cases, atoms transferred from a reservoir array to a science array are in a dark state, a clock state, or another state prohibited by the selection rules of the light excitation used for transfer. In some cases, an additional optical tweezer array (separate from the tweezers used for trapping or moving) can be generated, and the additional optical tweezer array can address a subset of atoms with hidden light. For example, the optical tweezers addressing a subset of sites can hide selected qubits from imaging light at wavelengths having a large differential polarization rate between the qubit and the imaging transition. For example, the hidden wavelength can be relatively detuned (about 2 nm) from the imaging transition to another higher transition, resulting in a larger light shift of the imaging state than that of the qubit state, thus pushing the imaging light off resonance. In other examples, the hidden transition can place the atoms in a metastable state, a different spin state protected by polarization (e.g., shelving by spin states having different angular momentum states).

[0170] Application

[0171] In some examples, the atoms in a scientific array can be used for metrology, communication, information storage, computing, simulation, or any other application. In some examples, the present technology (e.g., processes 200, 300, 400, 500, or 600) can be applied to quantum computers or simulation devices that use one or more classes of atoms or molecules.

[0172] In some cases, the methods and systems disclosed herein can include using at least a first subset of a plurality of atoms to perform sensing applications. For example, the plurality of atoms disclosed herein can be used for force sensing. For example, the plurality of atoms disclosed herein can be used for distance sensing. Distance sensing applications can include using a plurality of atoms for interferometry.

[0173] In some cases, the methods and systems disclosed herein can include using at least a first subset of a plurality of atoms to perform timing operations. For example, one use of a trapped atom array is in an atomic clock. In some cases, the methods and systems disclosed herein can include using at least a first subset of a plurality of atoms to perform metrology operations.

[0174] In some cases, the methods and systems disclosed herein can include using at least a first subset of a plurality of atoms to perform computing. For example, the computing can be non-classical computing, and the computing can be performed substantially without stopping the non-classical computing. In some cases, non-classical computing can include applying electromagnetic energy to one or more atoms in a first subset of a plurality of atoms in a scientific array, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state. As disclosed herein, a refilling operation can be performed substantially without loss of one or more superposition states. In some cases, non-classical computing can include entangling at least one atom in one or more superposition states with at least another atom in a first subset of a plurality of atoms in a scientific array. As disclosed herein, a refilling operation can be performed substantially without loss of entanglement. In some cases, non-classical computing can include one or more measurement operations. For example, the method can include measuring one or more superposition states to obtain a non-classical result.

[0175] In some cases, the application is for non - classical computing and multiple atoms are qubits. For example, the qubits can include nuclear spin qubits. A method or system including nuclear spin qubits can include one or more superposition states of a first atomic state and a second atomic state, where the first atomic state and the second atomic state include a first nuclear spin state and a second nuclear spin state of a nucleus, and the nucleus includes a nuclear spin greater than or equal to 1 / 2. In some cases, one or more atoms in a first subset of multiple atoms in one or more superposition states are quantum mechanically entangled with at least another atom in the first subset of multiple atoms in a science array with a coherence lifetime of at least 1 second. In some cases, the qubit states exhibit coherent properties as Figure 6 shown.

[0176] Electromagnetic delivery unit - The electromagnetic delivery unit can be configured to apply electromagnetic energy to one or more of the multiple atoms as described herein. The electromagnetic delivery unit can include one or more light sources, such as any light source described herein. The electromagnetic energy can include light energy. The light energy can include any repetition rate, pulse energy, average power, wavelength, or bandwidth described herein.

[0177] In some cases, the optical trapping unit and the electromagnetic delivery unit described herein can be integrated into a single optical system. A microscope objective can be used to deliver the electromagnetic radiation generated by the electromagnetic delivery unit described herein and to deliver the light used to trap the atoms generated by the optical trapping unit described herein. Alternatively or additionally, different objectives can be used to deliver the electromagnetic radiation generated by the electromagnetic delivery unit and to deliver the light for trapping the atoms generated by the optical trapping unit.

[0178] One or more electromagnetic delivery units can be configured to apply a first electromagnetic energy to one or more of the multiple atoms. Applying the first electromagnetic energy can induce the atoms to adopt one or more superposition states of a first atomic state and a second atomic state different from the first atomic state.

[0179] The first atomic state can include a first single - qubit state. The second atomic state can include a second single - qubit state. The first atomic state or the second atomic state can be elevated in energy relative to the ground atomic state of the atom. The energy of the first atomic state or the second atomic state can be equal to the ground atomic state of the atom.

[0180] The first atomic state can include a first hyperfine electron state and the second atomic state can include a second hyperfine electron state different from the first hyperfine electron state. For example, the first atomic state and the second atomic state can include a first hyperfine state and a second hyperfine state on a multiplet manifold such as a triplet manifold. The first atomic state and the second atomic state can respectively include in 3 P1 or 3The first and second hyperfine states on the P2 manifold. The first and second atomic states can respectively include those of any atom described herein 3 P1 or 3 The first and second hyperfine states on the P2 manifold, such as strontium-87 3 The P1 manifold or strontium-87 3 The P2 manifold.

[0181] In some cases, the first and second atomic states are the first and second hyperfine states of the first electronic state. Optical excitation can be applied between the first and second electronic states. The optical excitation can excite the first and / or second hyperfine state to the second electronic state. A single-qubit transition can 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 can be applied to drive the two-photon transition, each frequency detuned from a single-photon transition to the intermediate state. In some cases, the first and second hyperfine states are the hyperfine states of the ground electronic state. The ground electronic state may not decay to a lower electronic state by spontaneous or stimulated emission. The hyperfine state can include a nuclear spin state.

[0182] In some cases, the hyperfine state includes strontium-87 1 The nuclear spin states of the S0 manifold, and the qubit transition drives one or both of the two nuclear spin states of strontium-87 1 To a state detuned from the 3 P2 or 3 The P1 manifold or detuned within the 3 P2 or 3 The P1 manifold. In some cases, the single-qubit transition is a two-photon Raman transition between the nuclear spin states of strontium-87 3 Via a state detuned from the 3 P2 or 3 The P1 manifold or detuned within the 3 P2 or 1 The P1 manifold. In some cases, the nuclear spin state can be a Stark-shifted nuclear spin state. The Stark shift can be optically driven. The optical Stark shift can be driven to be detuned from the resonance of any one, all, or a combination of single-qubit transitions, two-qubit transitions, shelving transitions, imaging transitions, etc.

[0183] In some cases, the hyperfine state includes the nuclear spin state of a ytterbium atom. For example, the single-qubit transition can be a nuclear spin state. For example, the single-qubit transition can be from 3 P2 or 3 Coupled to the P1 manifold or within the 3 P2 or 3 Coupled within the P1 manifold of ytterbium-1711 Transitions between nuclear spin states of S0. In some cases, ytterbium-171 1 S0 m f = 1 / 2, -1 / 2 is coupled to 3 P1 m f = any one of 3 / 2, -3 / 2.

[0184] The first atomic state may include a first nuclear spin state and the second atomic state may include a second nuclear spin state different from the first nuclear spin state. The first and second atomic states may respectively include the first and second nuclear spin states of a quadrupolar nucleus. The first and second atomic states may respectively include the first and second nuclear spin states of a spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4 or spin-9 / 2 nucleus. The first and second atomic states may respectively include the first and second nuclear spin states of any atom described herein, such as the first and second spin states of strontium-87.

[0185] For the first and second nuclear spin states associated with a nucleus having a spin greater than 1 / 2 (such as a spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4 or spin-9 / 2 nucleus), the transition between the first and second nuclear spin states may be accompanied by transitions between other spin states on the nuclear spin manifold. For example, for a spin-9 / 2 nucleus in the presence of a uniform magnetic field, all nuclear spin energy levels may be separated by equal energies. Thus, a transition designed to transfer an atom from, for example, m N = 9 / 2 spin state to m N = 7 / 2 spin state (such as a Raman transition) can also drive: m N = 7 / 2 to m N = 5 / 2, m N = 5 / 2 to m N = 3 / 2, m N = 3 / 2 to m N = 1 / 2, m N = 1 / 2 to m N = -1 / 2, m N = -1 / 2 to m N = -3 / 2, m N = -3 / 2 to m N = -5 / 2, m N = -5 / 2 to m N = -7 / 2 and m N = -7 / 2 to m N = -9 / 2, where m N is the nuclear spin state. Similarly, a transition designed to transfer an atom from, for example, m N= 9 / 2 spin state transfer to m N Transitions to the m = 5 / 2 spin state (such as Raman transitions) can also be driven: m N = 7 / 2 to m N = 3 / 2, m N = 5 / 2 to m N = 1 / 2, m N = 3 / 2 to m N = -1 / 2, m N = 1 / 2 to m N = -3 / 2, m N = -1 / 2 to m N = -5 / 2, m N = -3 / 2 to m N = -7 / 2, and m N = -5 / 2 to m N = -9 / 2. Thus, such transitions may not selectively induce transitions between specific spin states on the nuclear spin manifold.

[0186] Alternatively, it may be desirable to achieve selective transitions between specific first and second spin states on the nuclear spin manifold. This can be achieved by providing light from a light source that provides an AC Stark shift and pushes adjacent nuclear spin states away from resonance with the transitions between the desired transitions between the first and second nuclear spin states. For example, if a transition from a first nuclear spin state with m N = -9 / 2 and m N = -7 / 2 to a second nuclear spin state is desired, the light can provide an AC Stark shift to the m N = -5 / 2 spin state, thus greatly reducing the transition between m N = -7 / 2 and m N = -5 / 2 states. Similarly, if a transition from a first nuclear spin state with m N = -9 / 2 and m N = -5 / 2 to a second nuclear spin state is desired, the light can provide an AC Stark shift to the m N = -1 / 2 spin state, thus greatly reducing the transition between m N = -5 / 2 and m N = -1 / 2 states. This can effectively create a two-level subsystem within the nuclear spin manifold that is decoupled from the rest of the nuclear spin manifold, greatly simplifying the dynamics of the qubit system. It may be advantageous to use nuclear spin states near the edge of the nuclear spin manifold (e.g., for spin-9 / 2 nuclei, m N = -9 / 2 and m N = -7 / 2, m N = 7 / 2 and m N = 9 / 2, m N= -9 / 2 and m N = -5 / 2, or m N = 5 / 2 and m N = 9 / 2), such that only one AC Stark shift is required. Alternatively, nuclear spin states further from the edge of the nuclear spin manifold can be used (e.g., m N = -5 / 2 and m N = -3 / 2 or m N = -5 / 2 and m N = -1 / 2) and two AC Stark shifts can be achieved (e.g., at m N = -7 / 2 and m N = -1 / 2 or m N = -9 / 2 and m N = 3 / 2).

[0187] Qubits based on nuclear spin states in the electronic ground state can allow the use of long-lived metastable excited electronic states (such as the 3 P0 state in strontium-87 or the 3 P1 state in ytterbium-171) for qubit storage. Atoms can be selectively transferred to such states to reduce crosstalk, improve gate or detection fidelity, or reduce scattering during atomic transfer. Using the SLM or AOD described herein, such storage or shelving processes can be atom-selective. Shelving transitions can include transitions from the 1 S0 state in ytterbium-171 to the 3 P0 or 3 P2 state in ytterbium-171. Shelving transitions can include transitions from the 1 S0 state in strontium-87 to the 3 P0 or 3 P2 state in strontium-87.

[0188] Computer system

[0189] Figure 1 A computer system 101 is shown that is programmed or otherwise configured to operate any of the methods, systems, processes, or techniques described herein (such as the systems or methods for performing continuous non-classical computing described herein). The computer system 101 can mediate various aspects of the present disclosure. The computer system 101 can be an electronic device of a user or a computer system remote from the electronic device. The electronic device can be a mobile electronic device.

[0190] The computer system 101 includes a central processing unit (CPU, also referred to herein as “processor” and “computer processor”) 105, which can be a single-core or multi-core processor, or multiple processors for parallel processing. The computer system 101 also includes a memory or memory location 110 (such as random access memory, read-only memory, flash memory), an electronic storage unit 115 (such as a hard disk), a communication interface 120 (such as a network adapter) for communicating with one or more other systems, and peripheral devices 125, such as caches, other memories, data storage, and / or an electronic display adapter. The memory 110, storage unit 115, interface 120, and peripheral devices 125 communicate with the CPU 105 via a communication bus (solid lines), such as a motherboard. The storage unit 115 can be a data storage unit (or data repository) for storing data. The computer system 101 can be operatively coupled to a computer network (“network”) 130 with the help of the communication interface 120. The network 130 can be the Internet, an intranet, and / or an extranet, or an intranet and / or an extranet that is communicating with the Internet. In some cases, the network 130 is a telecommunications and / or data network. The network 130 can include one or more computer servers, which can implement distributed computing, such as cloud computing. In some cases, with the help of the computer system 101, the network 130 can implement a peer-to-peer network, which can enable devices coupled to the computer system 101 to act as clients or servers.

[0191] The CPU 105 can execute a series of machine-readable instructions, which can be embodied in a program or software. The instructions can be stored in a memory location, such as the memory 110. The instructions can be directed to the CPU 105, which can then program or otherwise configure the CPU 105 to implement the methods of the present disclosure. Examples of operations performed by the CPU 105 can include fetching, decoding, executing, and writing back.

[0192] The CPU 105 can be part of a circuit, such as an integrated circuit. One or more other components of the system 101 can be included in the circuit. In some cases, the circuit is an application-specific integrated circuit (ASIC).

[0193] The storage unit 115 can store files, such as drivers, libraries, and saved programs. The storage unit 115 can store user data, such as user preferences and user programs. In some cases, the computer system 101 can include one or more additional data storage units located outside the computer system 101, such as on a remote server that communicates with the computer system 101 via an intranet or the Internet.

[0194] The computer system 101 can communicate with one or more remote computer systems via the network 130. For example, the computer system 101 can communicate with the user's remote computer system. Examples of remote computer systems include personal computers (such as portable PCs), slate or tablet PCs (e.g., iPad, Galaxy Tab), telephones, smartphones (e.g., iPhone, Android - enabled devices, ) or personal digital assistants. The user can access the computer system 101 via the network 130.

[0195] The methods described herein can be implemented by machine (e.g., computer processor) - executable code stored on an electronic storage location of the computer system 101, such as, for example, the memory 110 or the electronic storage unit 115. The machine - executable or machine - readable code can be provided in the form of software. During use, the code can be executed by the processor 105. In some cases, the code can be retrieved from the storage unit 115 and stored in the memory 110 for ready access by the processor 105. In some situations, the electronic storage unit 115 can be excluded and the machine - executable instructions are stored on the memory 110.

[0196] The code can be pre - compiled and configured to be used with a machine having a processor suitable for executing the code, or can be compiled during run - time. The code can be supplied in a programming language, and the programming language can be chosen such that the code can be executed in a pre - compiled or just - in - time compiled manner.

[0197] Aspects of the systems and methods provided herein, such as computer system 101, may be embodied in programming. Aspects of the technology may be considered a "product" or "article of manufacture", which typically exists or is embodied in a machine-readable medium in the form of machine (or processor) executable code and / or associated data. The machine executable code may be stored on an electronic storage unit, such as a memory (e.g., read-only memory, random access memory, flash memory) or a hard disk. A "storage" type medium may include any or all tangible memories of a computer, processor, etc., or associated modules thereof, such as various semiconductor memories, tape drives, disk drives, etc., which can provide non-transitory storage for software programming at any time. All or part of the software can sometimes be communicated via the Internet or various other telecommunications networks. For example, such communication can enable the software to be loaded from one computer or processor to another, such as from a management server or host computer to the computer platform of an application server. Thus, another type of medium that can carry software elements includes optical, electrical, and electromagnetic waves, such as those used across physical interfaces between local devices, through wired and optical landline networks, and through various air links. Physical elements carrying such waves, such as wired or wireless links, optical links, etc., can also be considered media carrying software. As used herein, unless limited to non-transitory, tangible "storage" media, terms such as computer or machine "readable media" refer to any medium that participates in providing instructions to a processor for execution.

[0198] Thus, machine-readable media such as computer-executable code can take many forms, including but not limited to tangible storage media, carrier media, or physical transmission media. Non-volatile storage media includes, for example, optical or magnetic disks, any of the storage devices in a storage device such as (one or more) any computer, such as can be used to implement databases shown in the figures. Volatile storage media includes dynamic memory, such as the main memory of such a computer platform. Tangible transmission media includes coaxial cables; copper wire and fiber optics, including the wires that make up a bus within a computer system. Carrier transmission media can take the form of electrical or electromagnetic signals, or acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Thus, common forms of computer-readable media include, for example: floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs or DVD-ROMs, any other optical media, punched card tapes, any other physical storage media with a hole pattern, RAM, ROM, PROM, and EPROM, FLASH-EPROM, any other memory chip or cartridge, carrier waves that carry data or instructions, cables or links that carry such carrier waves, or any other medium from which a computer can read programming code and / or data. Many of these forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to a processor for execution.

[0199] Computer system 101 may include or communicate with an electronic display 135 that includes a user interface (UI) 140. Examples of UIs include, but are not limited to, graphical user interfaces (GUIs) and web-based user interfaces.

[0200] The methods and systems of the present disclosure may be implemented by one or more algorithms. The algorithms may be implemented by software when executed by a central processing unit 105.

[0201] Example

[0202] Example 1: Atom loss correction - In some quantum error correction protocols, the results of intermediate circuit measurements are used to apply conditional operations to qubits. Additionally, ancillary qubits can typically be re-initialized after measurement. As a proof-of-principle demonstration of these capabilities, we use the results of intermediate circuit measurements to correct for occasional loss of ancillary qubits while maintaining coherence between data qubits.

[0203] For this demonstration, we create a fully filled (filling probability higher than 98%) 3×4 qubit subarray by rearranging atoms from a 7×10 site array. A single tweezer generated by a crossed acousto-optic deflector (AOD) is used to move individual atoms from the filled sites to the empty sites. The subarray is further divided into a checkerboard pattern of data qubits and ancillary qubits. Atoms remaining in the outer array form a reservoir for refilling the ancillary sites.

[0204] Figure 6 Data related to the conditional reloading of the ancillary qubits is shown. The upper panel (a) shows the experimental sequence. During repeated imaging and reloading of the ancillary sites, the data qubits are protected from decoherence by an optical shift from a hidden beam, as indicated by the shaded box. The lower panel (b) shows the contrast of the data sites relative to the N = 0 case (circles), and the filling fraction of the ancillary sites in the case of conditional reloading (filled diamonds) and unconditional reloading (open diamonds). Up to 16 cycles, the ancillary filling remains above 98%, and in the case of conditional reloading, the contrast loss per cycle is 0.9(1)%. In the case of no reloading, the ancillary filling drops 1.1(1)% per cycle.

[0205] As Figure 6 Detailed as follows, we embed N repeated intermediate circuit imaging cycles in the |1> state and rearrangement operations on the ancillary qubits in the Ramsey sequence (two π / 2 pulses separated by a time delay) of the data qubits. During optical pumping and imaging, hidden light is applied to the data sites to maintain coherence. We apply a single spin echo pulse after N / 2 cycles to reduce the sensitivity to the static differences in qubit frequencies between the sites. Without being limited by theory, the differences in qubit frequencies between the sites may be caused by the gradients of the applied magnetic field. In each cycle, the ancillary sites identified as empty in the intermediate circuit measurement are refilled with atoms from the reservoir. Optical pumping (OP) of the ancillary qubits after the global π pulse and the π / 2 pulse is used to reset their internal state to the |1> state. Hidden light is applied to the data qubits during optical pumping to prevent decoherence. The scattered photons required for optical pumping can be fewer than those required for imaging (at a similar power level, we used 100 μs for OP compared to 5 ms for imaging), and we did not observe the effect of optical pumping on the contrast of the data qubits.

[0206] By correcting for the loss of ancilla atoms, we maintained the ancilla fill fraction above 98% over 16 imaging and reloading cycles, after which it slowly decreased, presumably due to the lack of reservoir atoms in some trials. Without correction, for the parameters used in this dataset, the fill decreased by 1.1(1)% per imaging cycle. For the data qubits, the contrast loss per cycle was 0.9(1)% over 16 cycles, after which it began to deviate from exponential decay, presumably due to uncorrected coherent errors. In these sequences, the ancilla state was refilled within 10 - 30 ms, with shorter times assigned to higher N to keep the total Ramsey duration approximately 600 ms.

[0207] Example 2: Coherence during MOT loading - Coherence during reloading can be caused by magnetic field gradients and scattered light from the magneto - optical trap (MOT) used to collect and cool the atoms. Maintaining qubit coherence may be useful for performing continuous calculations while replenishing the reservoir.

[0208] Figure 7 Experimental data demonstrating coherence during MOT loading are shown. The top panel shows the remaining contrast after Ramsey sequences with (grey dots) and without (black dots) synchronous MOT operation. A single π - pulse was used in the middle of the hold time to cancel dephasing due to static detuning errors. The lines are Gaussian fits to guide the eye. The bottom panel shows the relative contrast versus the total hold time. The linear fit shows that in the presence of the MOT, the additional contrast decay rate is 0.03(2) / s.

[0209] Specifically, we used an initial MOT operating on the broad 1 S0 to 1 P1 transition near 399 nm, compared to a subsequent narrow - line MOT (using the narrow 1 S0 to 3 P1 transition), where this broad 1 S0 to 1The risk of decoherence caused by P1 transitions is greater. Our system employs a two-chamber design with a static magnetic field, and there is a 30-cm physical separation between the MOT region and the science region. This physical separation allows us to load atoms into the MOT while the atoms in the science region remain coherent. We confirmed this by running our standard MOT loading parameters during the Ramsey sequence on the qubits (using a single spin-echo pulse to eliminate the effect of static detuning errors between the qubits). From a linear fit to the additional contrast loss caused by the MOT, we obtained a decoherence rate of 0.03(2) / s. Our typical broad-line MOT loading lasted 200 ms. These experiments demonstrated the feasibility of transporting and loading atoms into our science array while maintaining qubit coherence.

[0210] Experimental setup - In the presence of a 500-Gauss magnetic field, a single 171 Yb atom is trapped at the sites of an optical tweezer array. Our experimental system consists of two main vacuum regions ("MOT chamber" and "science chamber") connected by a differential pumping tube. Atoms are loaded from a pre-cooled atomic beam into a two-stage magneto-optical trap in the MOT chamber (using the 1 P1 transition at 399 nm, followed by using the 3 P1 narrow-line transition to form this two-stage magneto-optical trap). Then the atoms are loaded into an optical lattice formed using 532-nm light and transported vertically 30 cm into the science chamber. To achieve a deep lattice in an energy-efficient manner, the beam waist of the transport beam is translated synchronously with the optical lattice by moving the positions of two focusing lenses, and one focusing lens is used for each of the two counter-propagating beams that form the lattice. A closed-loop piezoelectric steering mirror is used to actively maintain the alignment between the two beams. The atoms are transferred to the optical tweezer array by overlapping the atoms with the array, increasing the power of the optical tweezers, and then slowing down the transport lattice. This results in several atoms typically occupying each tweezer. Transferring the atoms from the transport lattice to the tweezers does not require the application of dissipation.

[0211] Our two-chamber design allows us to operate under a temporarily static magnetic field. During the experimental sequence, the magnetic field is not changed, which both avoids the time delay associated with switching and allows us to simultaneously maintain the magnetic field gradient for MOT formation and the large and uniform bias magnetic field in our science region. Our two-stage MOT operates with a constant field gradient of approximately 18 Gauss / cm in the strong direction. After loading the atoms into the tweezers, we apply light with the same parameters as those used for imaging the m f = 1 / 2 qubit state to induce light-assisted collisions and project a single atom onto each tweezer. During this time, the treatment 1 S0, m f=-1 / 2 to 3 P1, m f The second tuning of the =1 / 2 transition to transfer all atoms to m f =1 / 2 state.

[0212] We use light from a single laser incident along two counter-propagating paths to address the 1 S0 to 3 P1 transition. Each path has a fiber optic acousto-optic modulator, which can provide fast power switching and high extinction. Additionally, each path has a fiber-coupled electro-optic modulator (EOM), which can be used to apply sidebands with frequencies up to several GHz.

[0213] Laser beams with opposite circular polarizations and different frequencies are applied along the direction of the magnetic field to selectively image the two-qubit state by coupling the two qubit states 1 S0 m f =1 / 2, -1 / 2 (which we label as |1>, |0>) to 3 P1 m f =3 / 2, -3 / 2. This provides the utilization of the narrow linewidth (about 180 kHz) closed-loop transition. Scattering from the m f =±1 / 2 excited state (which would allow population leakage between qubit states) is suppressed due to the large ratio of the Zeeman shift (771 MHz and 681 MHz between the -3 / 2 and -1 / 2 states and between the 1 / 2 and 3 / 2 states respectively) to the transition linewidth. The scattered light is collected by a high numerical aperture objective lens and imaged onto a low-noise camera.

[0214] The hidden light is sourced from a laser at a wavelength of 459.5960(5) nm. This wavelength is 3 relatively detuned (about 2 nm) from the 3 P1 transition to the 3 6s6d 1 D1 transition, resulting in 1 a light shift of the 3 P1 state that is about 9 times the light shift of the

[0215] While the preferred embodiments of the present invention have been shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. The present invention is not intended to be limited by the specific examples provided in the specification. Although the present invention has been described with reference to the foregoing specification, the description and illustration of the embodiments herein are not to be construed in a limiting sense. Many variations, changes and substitutions will now occur to those skilled in the art without departing from the present invention. In addition, it should be understood that all aspects of the present invention are not limited to the specific descriptions, configurations or relative proportions set forth herein which depend on various conditions and variables. It should be understood that various alternatives of the embodiments of the present invention described herein may be employed in practicing the present invention. Accordingly, it is contemplated that the present invention should also cover any such alternatives, modifications, variations or equivalents. The appended claims are intended to define the scope of the present invention and thereby cover methods and structures within the scope of these claims and their equivalents.

Claims

1. A method for preparing an atomic sample, the method comprising: (a) capturing a plurality of atoms into a science array, wherein the science array includes a plurality of first optically trapped sites that are spatially distinct; (b) transferring at least one atom from a reservoir array to the science array to increase the fill factor of the science array, wherein the reservoir array includes a plurality of second optically trapped sites that are spatially distinct; and (c) transferring at least one atom to the reservoir array to increase the fill factor of the reservoir array, wherein during the transfer of the at least one atom from the reservoir array to the science array in (b), the transfer in (c) is at least partially performed.

2. The method according to claim 1, further comprising: repeating (b) and (c) multiple times to maintain the fill factor in the science array.

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

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

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

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

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

8. The method according to claim 7, wherein the first atomic state and the second atomic state include a first nuclear spin state and a second nuclear spin state of a nucleus, the nucleus having a nuclear spin greater than or equal to 1 / 2.

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

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

11. The method according to any one of claims 1-10, wherein the plurality of atoms includes group II elements.

12. The method according to claim 11, wherein the plurality of atoms includes scandium.

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

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

15. The method according to claim 13 or 14, wherein the plurality of atoms comprises ytterbium.

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

17. The method according to any one of claims 1-16, wherein one or both of a mobile optical trap or an optical tweezer is used to perform one or both of the following: (i) loading the plurality of atoms into the reservoir, or (ii) reloading the reservoir array with the additional atoms.

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

19. The method according to claim 18, wherein the science array is physically separated from the reservoir array, optionally, wherein the physical separation is greater than 10 cm.

20. The method according to any one of claims 1-19, wherein after (a), the method further comprises: determining an atomic loss quantity, the atomic loss quantity representing the difference between (i) the number of atoms among the plurality of atoms captured in the science array and (ii) the number of atoms remaining in the remaining subset of the plurality of atoms captured in the science array after at least a portion of the performing of the non-classical calculation and still in the science array.

21. The method according to claim 20, wherein the at least one atom transferred from the reservoir array to the science array comprises an atomic quantity at least equal to the atomic loss quantity.

22. The method according to claim 20 or 21, wherein determining the atomic loss quantity is based on imaging along an imaging axis to determine which of the spatially distinct plurality of second optical trapping sites of the science array are occupied.

23. The method according to claim 22, wherein: the science array and the reservoir array are physically separated parallel to the imaging axis; and one or both of a mobile optical trap or an optical tweezer is used to perform one or both of the following: (i) transferring the first subset of the plurality of atoms from the reservoir array to the science array, or (ii) transferring the second subset of the plurality of atoms from the reservoir array to the science array.

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

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

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

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

28. The method according to any one of claims 1-27, wherein a second number of sites in the plurality of second optical trapping sites is equal to a first number of sites in the plurality of first optical trapping sites.

29. The method according to any one of claims 1-27, wherein a second number of sites in the plurality of second optical trapping sites is greater than a first number of sites in the plurality of first optical trapping sites.

30. The method according to any one of claims 1-29, wherein transferring the at least one atom from the reservoir array to the scientific array comprises: transferring a first number of atoms from the reservoir array to one or more intermediate arrays, wherein the first number of atoms is at least a subset of the at least one atom; and transferring a second number of atoms from the one or more intermediate arrays to the scientific array, wherein the second number of atoms is at most the first number of atoms.

31. The method according to claim 30, wherein: the one or more intermediate arrays comprise at least two intermediate arrays; and (i) after transferring the first number of atoms from the reservoir array to the at least two intermediate arrays, and (ii) before transferring the second number of atoms from the at least two intermediate arrays to the scientific array, transferring at least the second number of atoms between the at least two intermediate arrays.

32. The method according to any one of claims 1-31, further comprising: within the scientific array, rearranging the positions of at least some of the atoms among the spatially distinct plurality of first optical trapping sites in (i) the plurality of atoms in the scientific array or (ii) the at least one atom in the scientific array.

33. The method according to any one of claims 1-31, 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. The method according to any one of claims 1-32, wherein the at least one atom transferred from the reservoir array to the scientific array is in a dark state, a clock state, or another state prohibited by a selection rule excited by light used for the transfer.

35. The method according to any one of claims 1-33, wherein the transfer of the at least one atom transferred from the reservoir array to the scientific array is a long-range transfer.

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

37. A method for preparing an atomic sample, the method comprising: (a) trapping a plurality of atoms in a scientific array, wherein the scientific array comprises a plurality of spatially distinct first optical trapping sites; (b) Inducing at least a first subset of the plurality of atoms to adopt one or more superposition states of at least a first subset of the plurality of atoms in the science array; And (c) Transferring at least one atom from the reservoir array to the science array, wherein the reservoir array includes a plurality of spatially distinct second optical trapping sites, and wherein the transfer in (c) is performed substantially without decohering the superposition state.

38. The method according to claim 37, further comprising: Repeating (c) multiple times to maintain the filling factor in the science array.

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

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

41. The method according to any one of claims 37 - 40, wherein (b) includes performing a computation using at least the first subset of the plurality of atoms.

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

43. The method according to claim 42, wherein performing the non - classical computation includes: Applying electromagnetic energy to one or more atoms in the first subset of the plurality of atoms in the science array, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and a second atomic state different from the first atomic state; Entangling quantum mechanically at least one of the one or more atoms in the one or more superposition states with at least another atom in the first subset of the plurality of atoms in the science array; And Measuring the one or more superposition states to obtain a non - classical result.

44. The method according to claim 43, wherein the first atomic state and the second atomic state include a first nuclear spin state and a second nuclear spin state of a nucleus, and the nucleus includes a nuclear spin greater than or equal to 1 / 2.

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

46. The method according to any one of claims 37 - 45, further comprising: Loading one or more atoms into the reservoir array including the plurality of spatially distinct second optical trapping sites.

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

48. The method according to any one of claims 37 - 47, wherein the plurality of atoms include group II elements.

49. The method according to claim 48, wherein the plurality of atoms include scandium.

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

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

52. The method according to claim 50 or 51, wherein the plurality of atoms comprises ytterbium.

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

54. The method according to any one of claims 37 - 53, wherein one or both of a moving optical trap or an optical tweezer is used to perform one or both of the following: (i) loading the plurality of atoms into the reservoir, or (ii) reloading the reservoir array with the additional atoms.

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

56. The method according to claim 55, wherein the science array is physically separated from the reservoir array, optionally, wherein the physical separation is greater than 10 cm.

57. The method according to any one of claims 37 - 46, wherein after (a), the method further comprises: determining an atomic loss number, the atomic loss number representing the difference between (i) the number of atoms in the plurality of atoms captured in the science array and (ii) the number of atoms remaining in the remaining subset of the plurality of atoms captured in the science array after at least a portion of the performing of the non - classical calculation and still in the science array.

58. The method according to claim 57, wherein the at least one atom transferred from the reservoir array to the science array comprises an atomic number at least equal to the atomic loss number.

59. The method according to claim 57 or 58, wherein determining the atomic loss number is based on imaging along an imaging axis to determine which of the spatially distinct plurality of second optical trapping sites in the science array are occupied.

60. The method according to claim 59, wherein: the science array and the reservoir array are physically separated parallel to the imaging axis; and one or both of a moving optical trap or an optical tweezer is used to perform one or both of the following: (i) transferring a first subset of the plurality of atoms from the reservoir array to the science array, or (ii) transferring a second subset of the plurality of atoms from the reservoir array to the science array.

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

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

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

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

65. The method according to any one of claims 37 - 64, wherein the second number of sites in the plurality of second optical trapping sites is equal to the first number of sites in the plurality of first optical trapping sites.

66. The method according to any one of claims 37 - 64, wherein the second number of sites in the plurality of second optical trapping sites is greater than the first number of sites in the plurality of first optical trapping sites.

67. The method according to any one of claims 37 - 66, wherein transferring the at least one atom from the reservoir array to the scientific array comprises: transferring a first number of atoms from the reservoir array to one or more intermediate arrays, wherein the first number of atoms is at least a subset of the at least one atom; and transferring a second number of atoms from the one or more intermediate arrays to the scientific array, wherein the second number of atoms is at most the first number of atoms.

68. The method according to claim 67, wherein: the one or more intermediate arrays comprise at least two intermediate arrays; and (i) after transferring the first number of atoms from the reservoir array to the at least two intermediate arrays, and (ii) before transferring the second number of atoms from the at least two intermediate arrays to the scientific array, transferring at least the second number of atoms between the at least two intermediate arrays.

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

70. The method according to any one of claims 37 - 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. The method according to any one of claims 37 - 70, wherein the at least one atom transferred from the reservoir array to the scientific array is in a dark state, a clock state, or another state prohibited by the selection rules excited by the light used for the transfer.

72. The method according to any one of claims 37 - 71, wherein the transfer of the at least one atom transferred from the reservoir array to the scientific array is a long - range transfer.

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

74. A system for preparing an atomic sample, the system comprising: one or more atom transfer units configured to implement the method according to any one of the preceding claims.

75. A system for preparing an atomic sample, the system comprising: One or more optical trapping units configured to obtain: A science array including a plurality of first optically trapped sites that are spatially distinct, where the science array includes a plurality of first atoms trapped at the spatially distinct plurality of first optically trapped sites; And A reservoir array including a plurality of second optically trapped sites that are spatially distinct, where the reservoir array includes a plurality of second atoms trapped at the spatially distinct plurality of second optically trapped sites; One or more atom transfer units configured to: (a) Transfer at least one atom from the reservoir array into the science array to increase the fill factor of the science array; and (b) Transfer at least one atom into the reservoir array to increase the fill factor of the reservoir array, where during the transfer of the at least one atom from the reservoir array into the science array in (a), the transfer in (b) is at least partially performed.

76. A system for preparing an atomic sample, the system including: One or more optical trapping units configured to obtain: A science array including a plurality of first optically trapped sites that are spatially distinct, where the science array includes a plurality of first atoms trapped at the spatially distinct plurality of first optically trapped sites; And A reservoir array including a plurality of second optically trapped sites that are spatially distinct, where the reservoir array includes a plurality of second atoms trapped at the spatially distinct plurality of second optically trapped sites; 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 of at least a first subset of the plurality of atoms in the science array; And One or more atom transfer units configured to transfer at least one atom of the plurality of second atoms from the reservoir array into the science array, where the transfer is performed substantially without decohering the superposition state.

77. A method for performing continuous non - classical computation, including: Loading a plurality of atoms into a reservoir array including a plurality of first optically trapped sites that are spatially distinct, the plurality of first optically trapped sites being configured to trap the plurality of atoms, where the plurality of atoms are qubits; Transferring a first subset of the plurality of atoms from the reservoir array into a science array including a plurality of second optically trapped sites that are spatially distinct, the plurality of second optically trapped sites being configured to trap the plurality of atoms; Performing a first non - classical computation using at least some of the first subset of the plurality of atoms in the science array; Determine an atomic loss quantity, the atomic loss quantity representing the difference between (i) the number of atoms in the first subset of the plurality of atoms and (ii) the number of atoms in the remaining subset of the first subset of the plurality of atoms that remain in the science array after performing the first non-classical computation; Transfer a second subset of the plurality of atoms from the reservoir array into the science array, wherein the second subset of the plurality of atoms includes an atomic quantity that is at least equal to the atomic loss quantity; Reload the reservoir array with additional atoms, the additional atoms being qubits; And Perform a second non-classical computation using (i) the remaining subset of the first subset of the plurality of atoms and (ii) at least some of the atoms in one or both of the second subset of the plurality of atoms.

78. The method according to claim 77, wherein performing the first non-classical computation includes: Applying electromagnetic energy to one or more atoms in the first subset of the plurality of atoms in the science array, thereby inducing the one or more atoms to adopt one or more superposition states of a first atomic state and at least a second atomic state different from the first atomic state; Entangling quantum mechanically at least one of the one or more atoms in the one or more superposition states with at least another atom in the first subset of the plurality of atoms in the science array; And Measuring the one or more superposition states to obtain a first non-classical result.

79. The method according to claim 78, wherein the first atomic state and the second atomic state include a first nuclear spin state and a second nuclear spin state of a nucleus, the nucleus including a nuclear spin greater than 1 / 2.

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

81. The method according to any one of claims 77-80, wherein the plurality of atoms and the additional atoms both include neutral atoms.

82. The method according to any one of claims 77-81, wherein the plurality of atoms and the additional atoms both include Group II elements.

83. The method according to any one of claims 77-82, wherein the plurality of atoms and the additional atoms both include a temperature of at most 10 microkelvin (μK).

84. The method according to any one of claims 77-83, wherein a mobile optical trap or one or two of optical tweezers is used to perform one or two of the following: (i) loading the plurality of atoms into the reservoir, or (ii) reloading the reservoir array with the additional atoms.

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

86. The method according to claim 85, wherein determining the number of atomic losses is based on imaging along an imaging axis to determine which of the spatially distinct plurality of second optical trapping sites in the science array are occupied.

87. The method according to claim 86, wherein: the science array and the reservoir array are physically separated parallel to the imaging axis; and one or both of a movable optical trap or an optical tweezer are used to perform one or both of the following: (i) transfer the first subset of the plurality of atoms from the reservoir array to the science array, or (ii) transfer the second subset of the plurality of atoms from the reservoir array to the science array.

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

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

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

91. The method according to any one of claims 77 - 90, wherein one or both of the science array or the reservoir array are formed using light or a non-optical electromagnetic field.

92. The method according to any one of claims 77 - 91, wherein a first number of sites in the plurality of first optical trapping sites is equal to a second number of sites in the plurality of second optical trapping sites.

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

94. The method according to any one of claims 77 - 93, wherein transferring the first subset of the plurality of atoms from the reservoir array to the science array includes: transferring at least the first subset of the plurality of atoms from the reservoir array to one or more intermediate arrays; and transferring the first subset of the plurality of atoms from the one or more intermediate arrays to the science array.

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

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

97. A system for preparing an atomic sample, the system comprising: One or more atomic transfer units configured to implement the method of claim 96.

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