Method and system for state-resolved imaging of non-destructive atomic qubits for quantum computing

Abstract

A system and method for state detection for non-classical computation is disclosed that can include acquiring a first plurality of qubits in an array of spatially distinct optical trapping sites, performing one or more qubit gate operations on at least a portion of the first plurality of qubits, performing a measurement operation, and determining that the qubits were in an initial state.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Application No. 63 / 483,160, filed February 3, 2023, which is incorporated herein by reference in its entirety. [Background technology]

[0002] Quantum computers can perform operations on data by exploiting quantum mechanical phenomena such as superposition and entanglement. Quantum computers may differ from transistor-based digital electronic computers. For example, while digital computers encode data into binary digits (bits), each of which can be in one of two definite states (0 or 1), quantum computing uses quantum bits (qubits), which can be in a superposition of states.

[0003] In a neutral atom quantum computer or simulation device, a qubit may be encoded in an optically trapped atom. A qubit can be represented by a linear superposition of its two orthogonal basis states. The two orthogonal basis states are typically:

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[0011] The ability to reliably detect the quantum state of a qubit could be useful in the operation of a quantum computer. In architectures that utilize trapped ions or neutral atoms, the state of the qubit can be read out by collecting photons through an imaging system that spatially or temporally resolves the state of the qubit. Summary of the Invention

[0012] Accurately determining the state of a qubit can present numerous technical challenges. The systems and methods described herein can provide technical solutions for determining the state of a qubit. For example, the systems and methods described herein can provide lossless qubit state detection using fluorescence imaging in a neutral atom quantum computer. Thus, the systems and methods described herein may avoid relying on shelving atoms in metastable clock states, avoid errors due to imperfect transitions to or scattering from clock states, and avoid the complexity of generating moving tune-out tweezers. Furthermore, the systems and methods described herein may detect the states of both qubits nondestructively and, therefore, may be compatible with intermediate circuit detection and error correction schemes.

[0013] In one aspect, the present disclosure provides a method of performing state detection for non-classical computation, the method including: (a) acquiring a first plurality of qubits in an array of spatially distinct optical trapping sites; (b) performing one or more qubit gating operations on at least a portion of the first plurality of qubits; (c) performing a measurement operation, the measurement operation including exposing a second plurality of qubits to electromagnetic energy, the first plurality of qubits including the second plurality of qubits, the electromagnetic energy being configured to selectively drive one qubit of the second plurality of qubits from an initial state to an excited state in the presence of an applied magnetic field, the selectivity of the transition to the excited state being based at least in part on the strength of the applied magnetic field to the first plurality of qubits, the second plurality of qubits, or both; and (d) determining that the qubit was in the initial state, the determining being based at least in part on the qubit returning to the initial state by emitting a photon in response to the electromagnetic energy in (c).

[0014] In some embodiments, the method further includes repeating (c) through (d) multiple times. In some embodiments, the return to the initial state by emitting a photon is a fluorescence transition. In some embodiments, the return to the initial state is from a manifold of excited states, and the strength of the magnetic field determines a separation between states in the manifold of excited states. In some embodiments, the separation between states determines which states resonate with the radiation. In some embodiments, transitions to a single state through the manifold of excited states are allowed by a selection rule for the state of each qubit. In some embodiments, (c) includes exposing a first subset of the second plurality of qubits to a first electromagnetic energy and then exposing a second subset of the second plurality of qubits to a second electromagnetic energy. In some embodiments, the first electromagnetic energy comprises a first polarization and the second electromagnetic energy comprises a second polarization. In some embodiments, the method further includes (e) determining that the first subset of the second plurality of qubits fluoresces in response to exposure to the first radiation and that the second subset of the second plurality of qubits fluoresces in response to exposure to the second radiation. In some embodiments, the method further includes (f) determining, at least in part based on determining in (e), that a plurality (n) of spatially distinct optical trapping sites in the array of spatially distinct optical trapping sites are absent of a qubit. In some embodiments, the first plurality of qubits has up to n more qubits than the second plurality of qubits. In some embodiments, the electromagnetic energy is polarized. In some embodiments, one or more of the electromagnetic energy, the first electromagnetic energy, or the second electromagnetic energy is circularly polarized. In some embodiments, the qubit is in a first state.

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[0021] In another aspect, a system for state detection for non-classical computation is provided, comprising: one or more optical trapping units configured to obtain an array of spatially distinct optical trapping sites, the array including a first plurality of qubits; one or more non-classical computation units configured to perform non-classical computation using at least a portion of the first plurality of qubits; one or more electromagnetic delivery units configured to expose a second plurality of qubits to radiation, the first plurality of qubits including the second plurality of qubits; and one or more measurement units configured to determine or predict that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based, at least in part, on at least one of the second plurality of qubits emitting fluorescence in response to exposure to the radiation.

[0022] In another aspect, a non-transitory computer-readable medium comprising machine-executable code, the machine-executable code including one or more instructions that, when executed, perform a method of performing state detection for non-classical computation on a non-classical computer, the non-classical computer configured to execute the one or more instructions, the method including: (a) acquiring a first plurality of qubits in an array of spatially distinct optical trapping sites; (b) performing a non-classical computation using at least a portion of the first plurality of qubits; (c) exposing a second plurality of qubits to radiation, the first plurality of qubits including the second plurality of qubits; and (d) determining or predicting that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based at least in part on at least one of the second plurality of qubits fluorescing in response to exposure to the radiation.

[0023] In another aspect, the present disclosure provides a method for state-resolved imaging of atomic qubits without disruption, which may include: (a) acquiring a first plurality of qubits in an array of spatially distinct optical trapping sites; (b) performing a non-classical computation using at least some of the first plurality of qubits; (c) exposing a second plurality of qubits to radiation, the first plurality of qubits including the second plurality of qubits; and (d) determining or predicting that a first subset of the second plurality of qubits are each in a first state and a second subset of the second plurality of qubits are each in a second state based, at least in part, on at least one of the second plurality of qubits fluorescing in response to the radiation.

[0024] In some embodiments, exposing the second plurality of qubits to the radiation comprises exposing the second plurality of qubits to a first radiation and then exposing the second plurality of qubits to a second radiation. In some embodiments, the first radiation is first light having a first polarization and the second radiation is second light having a second polarization. In some embodiments, the method further comprises (e) determining that the first subset of the second plurality of qubits fluoresce in response to exposure to the first radiation and that the second subset of the second plurality of qubits fluoresce in response to exposure to the second radiation. In some embodiments, the method further includes (f) determining in (e) that a plurality (n) of spatially distinct optical trapping sites in the array of spatially distinct optical trapping sites are absent of a quantum bit based at least in part on determining that the first subset of the second plurality of quantum bits fluoresces in response to exposure to the first radiation and that the second subset of the second plurality of quantum bits fluoresces in response to exposure to the second radiation.

[0025] In some embodiments, the first plurality of qubits has up to n more qubits than the second plurality of qubits. In some embodiments, the radiation is light. In some embodiments, the light is polarized light. In some embodiments, one or more of the polarized light, the first light, or the second light is circularly polarized light. In some embodiments, the second plurality of qubits is exposed to the radiation while in a magnetic field. In some embodiments, the at least one of the second plurality of qubits that fluoresces in response to exposure to the radiation is the first subset of the second plurality of qubits. In some embodiments, the first state is

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[0030] In another aspect, the present disclosure provides a system for state detection for non-classical computation, which may include one or more optical trapping units configured to obtain an array of spatially distinct optical trapping sites, the array including a first plurality of qubits, one or more non-classical computation units configured to perform non-classical computation using at least a portion of the first plurality of qubits, one or more electromagnetic delivery units configured to expose a second plurality of qubits to radiation, the first plurality of qubits including the second plurality of qubits, and one or more measurement units configured to determine or predict that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based, at least in part, on at least one of the second plurality of qubits emitting fluorescence in response to exposure to the radiation.

[0031] In another aspect, the present disclosure provides a non-transitory computer-readable medium including machine-executable code, the machine-executable code including one or more instructions that, when executed, perform a method for performing state detection for non-classical computation on a non-classical computer configured to execute the one or more instructions. The method may include: (a) obtaining a first plurality of qubits in an array of spatially distinct optical trapping sites; (b) performing a non-classical computation using at least some of the first plurality of qubits; (c) exposing a second plurality of qubits to radiation, the first plurality of qubits including the second plurality of qubits; and (d) determining or predicting that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based, at least in part, on at least one of the second plurality of qubits fluorescing in response to exposure to the radiation.

[0032] Another aspect of the present disclosure provides a system for state-resolved imaging of non-destructive atomic qubits, comprising one or more computer processors and a computer memory coupled thereto, the computer memory including machine-executable code that, when executed by the one or more computer processors, performs any of the operations described above or elsewhere herein.

[0033] Another aspect of the present disclosure provides a non-transitory computer-readable medium containing machine-executable code including one or more instructions that, when executed, perform a method for state-resolved imaging of non-destructive atomic qubits, wherein the non-classical computer is configured to execute the one or more instructions, the method being a method described above or elsewhere herein.

[0034] Additional aspects and advantages of the present disclosure will become readily apparent to those skilled in the art from the following detailed description. In the detailed description, only exemplary embodiments of the present disclosure have been shown and described. As will be realized, the present disclosure is capable of other and different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the present disclosure. Accordingly, the drawings and description should be regarded as illustrative in nature and not restrictive.

[0035] Incorporation by Reference All publications, patents, and patent applications mentioned herein are incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference. In the event that a publication, patent, or patent application incorporated by reference conflicts with the contents of this specification, this specification is intended to supersede and / or supersede such conflicting content. [Brief explanation of the drawings]

[0036] The novel features of the invention are set forth with particularity in the appended claims. The features and advantages of the present invention will be better understood 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" and "FIGs"), in which:

[0037] [Figure 1] 1 shows an example of an energy level diagram for a system that allows for cyclic transitions of the qubit state. [Figure 2] An example of an energy spectrum of an excited state is shown. [Figure 3] 1 shows a schematic diagram of a method for performing state detection for non-classical computation. [Figure 4] 1 shows a schematic diagram of another method for state detection for non-classical computation. [Figure 5A] 1 illustrates an example of a system configured to perform the methods provided herein. [Figure 5B] (Top) A level diagram of an example atomic system that can be used with the methods and systems disclosed herein is shown, and (bottom) experimental data showing two successive single-shot images of a fully filled 10x3 atomic array produced by an example method and system disclosed herein. [Figure 6] 1 illustrates a computer control system programmed or configured to carry out the methods provided herein. [Figure 7] 1 shows an example of state-resolved imaging infidelity. [Figure 8] 10 shows another example of state-resolved imaging infidelity. DETAILED DESCRIPTION OF THE INVENTION

[0038] While various embodiments of the present invention have been shown and described herein, it will be apparent to those skilled in the art that these embodiments are illustrative only. Numerous variations, changes, and substitutions may occur to those skilled in the art without departing from the scope of the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed.

[0039] The systems and methods described herein provide improved methods, e.g., measurement processes, for measuring the state of a qubit. It may be useful to selectively measure the state of a qubit. For example, the state of a qubit may be measured by selecting the state

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[0042] The systems and methods described herein can improve non-destructive state-resolved detection without the use of high magnetic fields (B-fields). In some cases, the detection mechanism may rely on (i) electric dipole selection rules (or angular momentum selection rules) and (ii) purity control of the polarization of the imaging beam. For example, if one qubit state is bright and the other qubit state is dark, false positive atomic detection may occur when detecting the dark state. Furthermore, the systems and methods described herein can detect the state of two hyperfine manifolds (e.g., 87 Rb,87 Sr, 171 In addition, the systems and methods described herein can improve on destructive (e.g., lossy) state-resolved detection methods that remove (e.g., blow away) one qubit state from a trap to detect the presence of an atom.

[0043] The disclosed systems and methods may improve upon atomic measurement methods (e.g., destructive methods) that perform state-independent imaging of the remaining atoms after performing state-selective atom loss. Destructive methods may be unable to distinguish between errors due to atom loss and errors present in the emitted states. Destructive methods may require frequent reloads to address these errors. The disclosed non-destructive methods and systems may be more robust against atom loss and require fewer reload cycles. The disclosed systems and methods may improve upon atomic measurement methods that utilize atom-selectively isolating motion, since at least the additional motion step may be slower, more complex, or both. The disclosed systems and methods may improve upon atomic measurement methods that use additional pulses to selectively shelve and image atoms, since at least the additional pulses may be slower, more complex, or both. The disclosed systems and methods may improve upon methods that select states with selective scattering rates for imaging light or methods that use high-finesse optical resonators, since these methods provide greater flexibility in selecting possible imaging conditions, qubit states, and trap states. Thus, the systems and methods of the present disclosure may alleviate at least some of the above-mentioned drawbacks.

[0044] The systems and methods of the present disclosure may employ narrow linewidth imaging in combination with differential Zeeman shift (e.g., shift in the presence of a magnetic field).

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[0047] In some cases, detecting the state of the qubits may include (A) initializing the qubits to some initial state, (B) performing a quantum computation (e.g., involving atoms going back and forth, where at the end of the computation the atoms are in either a zero state or a one state), and (C) then exposing the qubits to circularly polarized resonant light in the presence of a magnetic field to determine which state each qubit is in.

[0048] The methods and systems disclosed herein have a variety of applications in the field of quantum computing. For example, measurement-based quantum error correction can rely on the ability to determine the state of a subset of qubits (e.g., ancilla qubits) in a processor without revealing or perturbing the state of the remaining qubits (e.g., data qubits or other ancilla qubits). Measurement-based quantum error correction can include neutral 171 This may involve repeated "mid-circuit" measurements (e.g., imaging) in a single-species tweezers array of Yb atomic ancilla qubits. 171Alkaline earth atoms, such as Yb, or lanthanide atoms can be used for quantum computing with the systems and methods described herein. 171 Narrow linewidth transitions in Yb atomic arrays can be used to perform mid-circuit measurements (MCMs), providing non-destructive, state-selective detection. In some cases, site-specific optical shifts can be applied to hide selected atoms in the array from the imaging light, allowing measurements of a subset of qubits while introducing only percentage-level errors into the remaining qubits.

[0049] The systems and methods of the present disclosure may have various useful extensions: For example, the cyclic transitions utilized to detect the state of a qubit may also provide a cooling mechanism (e.g., Doppler cooling) to prevent atoms from escaping the optical trap.

[0050] State-resolved measurements of nondemolition atomic qubits An example of lossless qubit state detection using fluorescence imaging in a neutral atom quantum computer is shown. In some cases, detecting the qubit state may involve (A) initializing the qubit to an initial state, (B) performing a quantum computation (involving atoms going back and forth, such that at the end of the computation, the atoms are in either the zero or one state), and (C) then exposing the qubit to circularly polarized resonant electromagnetic energy (e.g., light of a predetermined wavelength) in the presence of a magnetic field to generate spontaneous or stimulated emission of photons to determine the state of each qubit.

[0051] The present disclosure provides a method for state-resolved imaging of atomic qubits without disruption. In some cases, the method may include (a) acquiring a first plurality of qubits in an array of spatially distinct optical trapping sites, (b) performing a non-classical computation using at least some of the first plurality of qubits, (c) exposing a second plurality of qubits to radiation, the first plurality of qubits including the second plurality of qubits, and (d) determining or predicting that a first subset of the second plurality of qubits are each in a first state and a second subset of the second plurality of qubits are each in a second state based, at least in part, on at least one of the second plurality of qubits fluorescing in response to the radiation.

[0052] The present disclosure provides a method for performing state detection for non-classical computation. In some cases, the method includes: (a) acquiring a first plurality of qubits within an array of spatially distinct optical trapping sites; (b) performing one or more qubit gate operations on at least a portion of the first plurality of qubits; and (c) performing a measurement operation, the measurement operation including exposing a second plurality of qubits to electromagnetic energy, the first plurality of qubits including the second plurality of qubits, the electromagnetic energy configured to selectively drive one qubit of the second plurality of qubits from an initial state to an excited state in the presence of an applied magnetic field, the selectivity of the transition to the excited state being based at least in part on the strength of the applied magnetic field to the first plurality of qubits, the second plurality of qubits, or both. In some cases, the method includes (d) determining that the qubit was in an initial state, where the determining is based at least in part on the qubit returning to the initial state by emitting a photon in response to the electromagnetic energy in (c). In some cases, the method includes repeating (c) through (d) multiple times. In some cases, the initial state is

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[0057] In some cases, the state of the qubit is the first state

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[0060] For example, in some cases, state-resolved detection of atomic qubits may include fluorescence imaging, utilizing cyclic transitions between the qubit state and an excited state that fluoresces photons for imaging. In some cases, the fluorescence of photons for imaging can be performed without losing the atom from the optical trap before or after detection. The cyclic transitions between the qubit state and the excited state can be driven by electromagnetic energy (e.g., a laser) that is resonant with the qubit state and the excited state.

[0061] In some cases, the transition may be a closed two-level system for each qubit state, as shown in Figure 1. For example,

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[0068] In some cases, an applied magnetic field can change the energy levels of excited states through a Zeeman shift, as shown in Figure 2. In some cases, the magnetic field can energetically separate the transition paths of two different qubit states into independent closed systems. In the example of Figure 2, the energy spectrum of the excited states is a function of the magnetic field.

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[0070] Referring again to FIG. 1 , the energy level diagram optionally illustrates the ground state of a qubit (e.g., a spin-½ ytterbium atom, such as ytterbium-171) and excited states to which the qubit can be driven to fluoresce. For example, if the qubit is spin-½, the qubit may have two possible states. In some cases, the qubit may be driven to various states associated with f=½, thus having spin states of −½, −½, +½, and +½. Furthermore, when a zero-state qubit is driven (e.g., with circularly polarized light), selection rules allow the qubit to optionally have one energy level to which it can be driven. Thus, to obtain a state that can be determined or predicted by imaging, one state (e.g., the zero state) may fluoresce and the other state (e.g., the one state) may not fluoresce. The straight arrows in FIG. 1 indicate each energy level that each qubit state can reach based on the selection rules. For example, in the left frame of Figure 1, the zero-state qubit is

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[0079] In some cases, applying a magnetic field can enable this detection based on the difference in fluorescence for different qubit states. In some cases, the magnetic field causes only one energy level transition to resonate and thereby fluoresce for each of the left and right frames in Figure 1. Conversely, in zero magnetic field, qubits in both states may fluoresce. The shift of the upper level in the presence of a magnetic field can be approximately 1-2 megahertz / gauss, while the shift of the ground state level can be approximately several hundred hertz / gauss. Thus, Figure 1 shows that the ground state may shift less than the excited state. It is not strictly necessary for the ground state to shift less than the excited state; rather, it can be simply useful in some cases for the ground state not to shift by the same amount as the excited state.

[0080] In some cases, it may be useful to have a difference in the amount or magnitude of the shift between the ground state and the excited state, such that when a stronger magnetic field is applied, one energy level may be in resonance while the other energy level is out of resonance. In the example shown in the left frame of Figure 1, if the first qubit is in the zero state, photons may scatter from it (e.g., producing a bright spot on the camera), and if the second qubit is in the one state, photons may not scatter from it (e.g., leaving a dark spot on the camera). In some cases, additional complications may arise related to the loss of a qubit. For example, a dark spot on the camera may mean that there is a one-state qubit at the corresponding location in this example, but this may instead mean that a qubit has been lost from the corresponding location. However, as shown in the two frames of Figure 1, a qubit in a certain state may fluoresce when transmitting light polarized in one direction but not when transmitting light polarized in another direction. Therefore, by performing the light bath treatments in both the left and right frames of Figure 1, qubit loss may be identified in a location that does not fluoresce after treatment in either the left or right frame of Figure 1. In some cases, if qubit loss occurs at a sufficiently low rate, one light polarization may be used. In other cases, the first light polarization may be used primarily, and a second light polarization may be used at regular intervals (e.g., every 3 cycles, every 10 cycles, every 100 cycles, etc.) to check for qubit loss. This regular interval may depend on the qubit loss rate. For example, if the qubit loss rate is low, the second light polarization may be used less frequently to check for qubit loss. If qubit loss is detected, the qubit may be replaced.

[0081] In some examples, the methods and systems disclosed herein may be used to induce the formation of Group 2 elements or analogs of Group 2 elements by applying electromagnetic energy (e.g., light of a predetermined wavelength). 1 S0m f=1 / 2, -1 / 2 qubit states (or alternatively,

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[0084] Figure 3 shows a schematic diagram of a method 300 for performing state detection for non-classical computation. Figure 4 shows a schematic diagram of a method 400 for performing state detection for non-classical computation.

[0085] Plurality of Spatially Distinct Optical Trap Sites—At step 310 of method 300, the method may include obtaining a first plurality of qubits in an array of spatially distinct optical trap sites. Step 410 of method 400 may include an example, variation, or embodiment of step 310 of method 300.

[0086] Traps - In some examples, optical traps may be formed by tightly focused light (tweezers), by standing wave gratings, or by imaged masks or gratings. Optical traps may also include various methods of cooling atoms using optical illumination (e.g., lasers) and spatially varying magnetic fields to form the trap. Such optical traps are sometimes called magneto-optical traps (MOTs).

[0087] In some cases, the array is two-dimensional. In some cases, the array is three-dimensional. In some cases, the spatially distinct optical traps include one-dimensional, two-dimensional, or three-dimensional optical traps. In some examples, the array may be linear, two-dimensional, three-dimensional, or may include composite dimensions. Composite dimensions may include, for example, dimensions consisting of internal atomic states or motional states. The spatially distinct optical traps may include single or multiple reservoir regions. In some examples, the array may have a regular, irregular, or quasi-regular geometry.

[0088] In some cases, the array is two-dimensional. For example, a two-dimensional optical trap array can be formed. The two-dimensional array can include an array of rectangular, square, rectangular, or cubic optical trap sites. In some cases, the method further includes determining, at least in part, that a plurality of spatially distinct optical trap sites in the array of spatially distinct optical trap sites are absent of a quantum bit. For example, each optical trap site in the plurality of optical trap sites can be spatially separated from each of the other optical trap sites by a distance of at least about 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 μm, 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, or more. Each optical trap site may be spatially separated from each other optical trap site by a distance of up to about 10 μm, 9 μm, 8 μm, 7 μm, 6 μm, 5 μm, 4 μm, 3 μm, 2 μm, 1 μm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm, or less. Each optical trap site may be spatially separated from each other optical trap site by a distance within a range defined by any two of the aforementioned values. In some cases, the array is three-dimensional. For example, a three-dimensional array of optical traps may be formed.

[0089] Cooling - The array of spatially distinct optical trapping sites may comprise part of an atomic cooling and trapping system. The atomic cooling and trapping system may comprise one or more optical lattices. For example, the atomic cooling and trapping system may comprise a first optical lattice followed by a second optical lattice. In some cases, the optical lattice may be filled by a reservoir trap. In some cases, the reservoir trap may comprise an unstructured or semi-structured optical trap. In some cases, atoms are cooled from a pre-cooled atomic beam by a two-stage magnetic optical trap (at 399 nm). 1 P1 transition followed by 556 nm 3In some cases, the atoms can then be loaded into an optical lattice formed using 532 nm light from an optical trapping system.

[0090] The qubits in the array of spatially distinct traps may be cooled to a temperature. In some cases, the qubits have a temperature of up to 10 microkelvins (μK). In some cases, the qubits have a temperature of up to 10 microkelvins (μK). In some cases, one or more atoms disposed in an optical trap may have a temperature of at least about 1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 300, 400, 500, or more microkelvins. In some cases, one or more atoms disposed within the optical trap may have a temperature of up to about 500, 400, 300, 200, 190, 180, 170, 160, 150, 140, 130, 120, 110, 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 4, 3, 2, 1, or less microkelvin. In some cases, one or more atoms disposed within the optical trap may have a temperature within a range defined by any two of the above values.

[0091] Optical Tweezers—In some cases, the multiple spatially distinct optical traps include optical tweezers. The optical trapping site may include one or more optical tweezers. The optical tweezers may include one or more focused laser beams that provide attractive or repulsive forces to hold or move one or more atoms. The beam waist of the focused laser beam may include a strong electric field gradient. Atoms may be attracted or repelled along the electric field gradient toward the center of the laser beam, which may include the strongest electric field. The optical trapping site may include one or more optical tweezers sites of one or more optical tweezers arrays. The optical trapping site may include one or more optical tweezers sites of one or more one-dimensional (1D) optical tweezers arrays, two-dimensional (2D) optical tweezers arrays, or three-dimensional (3D) optical tweezers arrays. In some cases, the methods and systems described herein may be similarly applied to optical lattices. Optical tweezers may be useful for moving atoms or atomic arrays.

[0092] The site-optical trapping system may be configured to generate multiple optical trapping sites. The optical trapping system may be configured to generate multiple spatially distinct optical trapping sites. Each optical trapping system may include any number of sites disclosed herein. Each optical trapping system may include any number of trapped atoms disclosed herein.

[0093] For example, each optical trapping system may have at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, , 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 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 trap system can accommodate up to approximately 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000, and 10 The optical trapping system may be configured to generate 1,000, 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 trap sites. The optical trapping system may be configured to trap a plurality of optical trap sites within a range defined by any two of the above values.

[0094] Each optical trapping system may be configured to trap a plurality of atoms, for example, 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. For example, the optical trapping system may achieve a total of up to approximately 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 10 ... The optical trapping system may be configured to trap 0, 20,000, 10,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or fewer atoms. The optical trapping system may be configured to trap a number of atoms within a range defined by any two of the above values.

[0095] Trapping Electromagnetic Energy—In some cases, the methods and systems disclosed herein may be configured to form multiple optical trapping sites using trapping electromagnetic energy (e.g., "trapping excitation" herein). The trapping excitation may be generated by a trapping light source.

[0096] The trap excitation may include optical excitation, such as in a magnetic optical trap or optical tweezers. In some cases, the trap excitation is provided by one or more optical trapping systems, as 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 may be split into multiple arrays to form multiple trap arrays with similar properties.

[0097] Atoms—The systems and methods of the present disclosure may be applied to any atomic system that can be cooled and trapped. In some cases, the first plurality of qubits includes a neutral atomic qubit. In some cases, the plurality of atoms includes neutral atoms. In some cases, the plurality of atoms includes a Group 2 element. In some cases, the plurality of atoms includes strontium. In some cases, the plurality of atoms includes an analog of a Group 2 element. In some cases, the plurality of atoms are atoms with two valence electrons. In some cases, the plurality of atoms includes ytterbium. In some cases, the plurality of atoms are qubits.

[0098] The optical trapping system may be configured to trap neutral atoms. In some cases, the optical trapping system may trap alkaline earth or alkaline earth-like atoms. In some cases, the alkaline earth or alkaline earth-like atoms include two valence electrons. In some cases, the alkaline earth or alkaline earth-like atoms include strontium or ytterbium.

[0099] In some cases, one or more atoms may include an alkali atom. One or more atoms may include a lithium (Li) atom, a sodium (Na) atom, a potassium (K) atom, a rubidium (Rb) atom, or a cesium (Cs) atom. One or more atoms may include a lithium-6 atom, a lithium-7 atom, a sodium-23 atom, a potassium-39 atom, a potassium-40 atom, a potassium-41 atom, a rubidium-85 atom, a rubidium-87 atom, or a cesium-133 atom. One or more atoms may include an alkaline earth atom. One or more atoms may include a beryllium (Be) atom, a magnesium (Mg) atom, a calcium (Ca) atom, a strontium (Sr) atom, or a barium (Ba) atom. The one or more atoms may comprise a beryllium-9 atom, a magnesium-24 atom, a magnesium-25 atom, a magnesium-26 atom, a calcium-40 atom, a calcium-42 atom, a calcium-43 atom, a calcium-44 atom, a calcium-46 atom, a calcium-48 atom, a strontium-84 atom, a strontium-86 atom, a strontium-87 atom, a strontium-88 atom, a barium-130 atom, a barium-132 atom, a barium-133 atom, a barium-134 atom, a barium-135 atom, a barium-136 atom, a barium-137 atom, or a barium-138 atom. The one or more atoms may comprise a rare earth atom. The one or more atoms may include a scandium (Sc) atom, a yttrium (Y) atom, a lanthanum (La) atom, a cerium (Ce) atom, a praseodymium (Pr) atom, a neodymium (Nd) atom, a samarium (Sm) atom, a europium (Eu) atom, a gadolinium (Gd) atom, a terbium (Tb) atom, a dysprosium (Dy) atom, a holmium (Ho) atom, an erbium (Er) atom, a thulium (Tm) atom, a ytterbium (Yb) atom, or a lutetium (Lu) atom.One or more atoms may be 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 Atom, Dysprosium-156 Atom, Dysprosium-158 Atom, Dysprosium-160 Atom, Dysprosium-161 Atom, Dysprosium-162 Atom, Dysprosium-163 Atom, Dysprosium-164 Atom, Erbium-162 Atom, Erbium-164 Atom, Erbium-166 Atom, Erbium-167 Atom, Erbium-168 Atom, Erbium The cations may include ytterbium-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.

[0100] In some cases, the plurality of atoms may comprise one element selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. The plurality of atoms may comprise a mixture of elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. The plurality of atoms may comprise a natural isotopic mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. The plurality of atoms may comprise an isotopically enriched mixture of one or more elements selected from the group consisting of Li, Na, K, Rb, Cs, Be, Mg, Ca, Sr, and Ba. The plurality of atoms may comprise a natural isotopic mixture of one or more elements selected from the group consisting of Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. The plurality of atoms may comprise an isotopically enriched mixture of one or more elements selected from the group consisting of Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu. The atoms may comprise rare earth atoms. For example, the plurality of atoms may be lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, or the like enriched to an isotopic abundance of at least about 50%, 60%, 70%, 80%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, 99.1%, 99.2%, 99.3%, 99.4%, 99.5%, 99.6%, 99.7%, 99.8%, 99.9%, 99.91%, 99.92%, 99.93%, 99.94%, 99.95%, 99.96%, 99.97%, 99.98%, 99.99% or more. Potassium-40 atom, potassium-41 atom, rubidium-85 atom, rubidium-87 atom, cesium-133 atom, beryllium-9 atom, magnesium-24 atom, magnesium-25 atom, magnesium-26 atom, calcium-40 atom, calcium-42 atom, calcium-43 atom, calcium-44 atom, calcium-46 atom, calcium-48 atom, strontium-84 atom, strontium-86 atom, strontium-87 atom, strontium-88 atom, barium-130 atom, barium-132 atom, barium-133 atom,Barium-134 atom, barium-135 atom, barium-136 atom, barium-137 atom, barium-138 atom, scandium-45 atom, yttrium-89 atom, lanthanum-139 atom, cerium-136 atom, cerium-138 atom, cerium-140 atom, cerium-142 atom, praseodymium-141 atom, neodymium-142 atom, neodymium-143 atom, neodymium-14 5 atoms, neodymium-146 atom, neodymium-148 atom, samarium-144 atom, samarium-149 atom, samarium-150 atom, samarium-152 atom, samarium-154 atom, europium-151 atom, europium-153 atom, gadolinium-154 atom, gadolinium-155 atom, gadolinium-156 atom, gadolinium-157 atom, gadolinium-158 atom , Gadolinium-160 atom, Terbium-159 atom, Dysprosium-156 atom, Dysprosium-158 atom, Dysprosium-160 atom, Dysprosium-161 atom, Dysprosium-162 atom, Dysprosium-163 atom, Dysprosium-164 atom, Erbium-162 atom, Erbium-164 atom, Erbium-166 atom, Erbium-167 atom, Erbium-168 atom, Erbium-169 atom, Erbium-170 atom, Erbium-171 atom, Erbium-172 atom, Erbium-173 atom, Erbium-174 atom, Erbium-175 atom, Erbium-176 atom, Erbium-177 atom, Erbium-178 atom, Erbium-179 ... The ion-doped fluorine-containing compound may comprise a fluorine-168 atom, an erbium-170 atom, a holmium-165 atom, a thulium-169 atom, a ytterbium-168 atom, a ytterb ...ytterbium-171 atom, a ytterbium-172 atom, a ytterbium-173 atom, a ytterbium-174 atom, a ytterbium-176 atom, a lutetium-175 atom, or a lutetium-176 atom. Multiple atoms have isotopic abundances up to approximately 99.99%, 99.98%, 99.97%, 99.96%, 99.95%, 99.94%, 99.93%, 99.92%, 99.91%, 99.9%, 99.8%, 99.7%, 99.6%, 99.5%, 99.4%, 99.3%, 99.2%, 99.1%, 99%, 98%, 97%, 99.9 ... 6%, 95%, 94%, 93%, 92%, 91%, 90%, 80%, 70%, 60%, 50% or less enriched lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, potassium-41 atoms, rubidium-85 atoms, rubidium-87 atoms, cesium-133 atoms,Beryllium-9 atoms, Magnesium-24 atoms, Magnesium-25 atoms, Magnesium-26 atoms, Calcium-40 atoms, Calcium-42 atoms, Calcium-43 atoms, Calcium-44 atoms, Calcium-46 atoms, Calcium-48 atoms, Strontium-84 atoms, Strontium-86 atoms, Strontium-87 atoms, Strontium-88 atoms, Barium-130 atoms, Barium-132 atoms, Barium-133 atoms, Barium-134 atoms, Barium-135 atoms, Barium-1 36 atoms, barium-137 atoms, barium-138 atoms, scandium-45 atoms, yttrium-89 atoms, lanthanum-139 atoms, cerium-136 atoms, cerium-138 atoms, cerium-140 atoms, cerium-142 atoms, praseodymium-141 atoms, neodymium-142 atoms, neodymium-143 atoms, neodymium-145 atoms, neodymium-146 atoms, neodymium-148 atoms, samarium-144 atoms, samarium-149 atoms, samarium-150 atoms, samarium-152 atoms, samarium Mu-154 atom, Europium-151 atom, Europium-153 atom, Gadolinium-154 atom, Gadolinium-155 atom, Gadolinium-156 atom, Gadolinium-157 atom, Gadolinium-158 atom, Gadolinium-160 atom, Terbium-159 atom, Dysprosium-156 atom, Dysprosium-158 atom, Dysprosium-160 atom, Dysprosium-161 atom, Dysprosium-162 atom, Dysprosium-163 atom, Dysprosium-164 atom, Er ... The plurality of atoms may comprise tungsten-162 atoms, erbium-164 atoms, erbium-166 atoms, erbium-167 atoms, erbium-168 atoms, erbium-170 atoms, holmium-165 atoms, thulium-169 atoms, ytterbium-168 atoms, ytterbium-170 atoms, ytterbium-171 atoms, ytterbium-172 atoms, ytterbium-173 atoms, ytterbium-174 atoms, ytterbium-176 atoms, lutetium-175 atoms, or lutetium-176 atoms. The plurality of atoms may comprise lithium-6 atoms, lithium-7 atoms, sodium-23 atoms, potassium-39 atoms, potassium-40 atoms, or the like enriched in isotopic abundance ratios within a range defined by any two of the foregoing values.Potassium-41 atoms, Rubidium-85 atoms, Rubidium-87 atoms, Cesium-133 atoms, Beryllium-9 atoms, Magnesium-24 atoms, Magnesium-25 atoms, Magnesium-26 atoms, Calcium-40 atoms, Calcium-42 atoms, Calcium-43 atoms, Calcium-44 atoms, Calcium-46 atoms, Calcium-48 atoms, Strontium-84 atoms, Strontium-86 atoms, Strontium-87 atoms, Strontium-88 atoms, Barium-130 atoms, Barium-132 atoms, Barium-13 3 atoms, barium-134 atom, barium-135 atom, barium-136 atom, barium-137 atom, barium-138 atom, scandium-45 atom, yttrium-89 atom, lanthanum-139 atom, cerium-136 atom, cerium-138 atom, cerium-140 atom, cerium-142 atom, praseodymium-141 atom, neodymium-142 atom, neodymium-143 atom, neodymium-145 atom, neodymium-146 atom, neodymium-148 atom, samarium-144 atom, samarium-149 atom, samarium- 150 atom, samarium-152 atom, samarium-154 atom, europium-151 atom, europium-153 atom, gadolinium-154 atom, gadolinium-155 atom, gadolinium-156 atom, gadolinium-157 atom, gadolinium-158 atom, gadolinium-160 atom, terbium-159 atom, dysprosium-156 atom, dysprosium-158 atom, dysprosium-160 atom, dysprosium-161 atom, dysprosium-162 atom, dysprosium-163 atom, dysprosium The thulium-164 atom may include thulium-162 atom, thulium-164 atom, thulium-166 atom, thulium-167 atom, thulium-168 atom, thulium-170 atom, thulium-165 atom, thulium-169 atom, thulium-168 atom, thulium-170 atom, thulium-171 atom, thulium-172 atom, thulium-173 atom, thulium-174 atom, thulium-176 atom, thulium-175 atom, or thulium-176 atom.

[0101] In some cases, the first plurality of qubits includes neutral atoms. In some cases, the second plurality of qubits can include neutral atoms. For example, one or more atoms of the array can include one or more qubits. One or more atoms can be configured for use as one or more qubits. One or more qubits can be configured to perform non-classical computation. For example, one or more qubits can be configured to perform gate-based quantum computation. In another example, one or more qubits can be configured to perform quantum computation. The one or more atoms can include at least about 1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 300, 400, 500, or more atoms. The one or more atoms may include up to about 500, 400, 300, 200, 190, 180, 170, 160, 150, 140, 130, 120, 110, 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 4, 3, 2, or fewer atoms. The one or more atoms may include a number of atoms defined by any two of the above values. For example, the one or more atoms may include from about 75 to about 150 atoms.

[0102] Gate Operation—At step 320 of method 300, the method may include performing a non-classical computation using at least a portion of the first plurality of qubits. At step 420 of method 400, the method may include performing one or more qubit gate operations on at least a portion of the first plurality of qubits. The one or more qubit gate operations may include a subportion of the non-classical computation disclosed herein. For example, the one or more qubit gate operations may include an error-correcting code. In some cases, the methods and systems described herein may facilitate an in-circuit measurement operation on a qubit (e.g., an ancilla qubit) during the non-classical computation. Step 420 of method 400 may include an example, variation, or embodiment of method 320 of method 300.

[0103] Non-classical computation may include gate model quantum computation, quantum annealing procedures, etc. In some cases, a qubit may be in a first state

[0104]

number

[0105]

number

[0106]

number

[0107]

number

[0108] In some cases, the state of the qubit is the first state

[0109]

number

[0110]

number

[0111] Qubit—In some cases, a neutral atom is a qubit. In some cases, the neutral atom includes a Group 2 element. In some cases, the Group 2 element is strontium. In some cases, the neutral atom includes rubidium or cesium. In some cases, the neutral atom includes ytterbium. For example, the first plurality of qubits or the second plurality of qubits can include a neutral atom. One or more atoms can include atoms that are not ionized (e.g., in a neutral state). In some cases, each atom of the one or more atoms can be a neutral atom. For example, each atom of an array of atoms can be not ionized. In some cases, the one or more atoms can include rare earth atoms (e.g., lanthanide series atoms (e.g., ytterbium, neodymium, lanthanum, erbium, etc.), alkali atoms (e.g., sodium, potassium, rubidium, cesium, etc.), alkaline earth atoms (e.g., calcium, strontium (e.g., strontium-87 atom), etc.), etc., or any combination thereof.

[0112] In some cases, the qubits described herein may include nuclear spin qubits. The state of the qubit (e.g.,

[0113]

number

[0114]

number

[0115] Qubit States—In some cases, the qubits described herein may include a first atomic state and a second atomic state. The first atomic state may include the state of a first single qubit. The second atomic state may include the state of a second single qubit. The first atomic state or the second atomic state may be elevated in energy relative to the ground atomic state of the atom, for example, within a manifold of excited states. The first atomic state or the second atomic state may be within the manifold of ground states.

[0116] The first atomic state may include a first hyperfine electronic state, and the second atomic state may include a second hyperfine electronic state different from the first hyperfine electronic state. For example, the first atomic state and the second atomic state may include a first hyperfine state and a second hyperfine state on a multiplet manifold, such as a triplet manifold, a singlet manifold, etc. The first atomic state and the second atomic state may each be: 3 P1, 3 P2, 1 The first and second atomic states may include a first hyperfine state and a second hyperfine state, such as on the S0 manifold. The first and second atomic states may be strontium-87, 3 P1 manifold, strontium-87 3 P2 manifold, strontium-87 1S0 manifold, ytterbium-171 3 P1 manifold, ytterbium-171 3 P2 manifold, ytterbium-171 1 of any atom described herein, such as the S0 manifold. 3 P1, 3 P2, 1 It may include a first hyperfine state and a second hyperfine state on the S0 manifold.

[0117] In some cases, the first and second atomic states are first and second hyperfine states of the first electronic state. Optical excitation may be applied between the first and second electronic states. The optical excitation may excite the first and / or second hyperfine states to the second electronic state. The single qubit transition may include a two-photon transition between two hyperfine states within the first electronic state, using the second electronic state as an intermediate state. To drive the single qubit transition, a pair of frequencies detuned from the single-photon transition to the intermediate state may be applied to drive the two-photon transition. In some cases, the first and second hyperfine states are hyperfine states of the ground electronic state. The ground electronic state may not decay to a lower electronic state by spontaneous or stimulated emission. The hyperfine state may include a nuclear spin state.

[0118] In some cases, the hyperfine state is strontium-87 1 S0 or Ytterbium-171 1 The qubit transition involves the nuclear spin state of the S0 manifold, and the strontium-87 1 S0 or Ytterbium-171 1 One or both of the two nuclear spin states of S0 can be 3 P2 or 3 A state detuned from the P1 manifold, or 3 P2 or 3 In some cases, the single-qubit transition is driven by strontium-87 1 S0 or Ytterbium-171 1is a two-photon Raman transition between the nuclear spin states of S0, 3 P2 or 3 A state detuned from the P1 manifold, or 3 P2 or 3 The nuclear spin state is detuned within the P1 manifold. In some cases, the nuclear spin state may be a Stark-shifted nuclear spin state. The Stark shift may be optically driven. The optical Stark shift may be off-resonance by any, all, or a combination of single-qubit transitions, two-qubit transitions, shelving transitions, imaging transitions, etc.

[0119] In some cases, the hyperfine state includes a nuclear spin state of ytterbium.

[0120] The first atomic state may comprise a first nuclear spin state, and the second atomic state may comprise a second nuclear spin state different from the first nuclear spin state. The first and second atomic states may comprise, respectively, the first and second nuclear spin states of a quadrupolar nucleus. The first and second atomic states may comprise, respectively, 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 comprise, respectively, the first and second nuclear spin states of any atom described herein, such as the first and second spin states of strontium-87.

[0121] For first and second nuclear spin states associated with nuclei containing spins greater than 1 / 2 (such as spin-1, spin-3 / 2, spin-2, spin-5 / 2, spin-3, spin-7 / 2, spin-4, or spin-9 / 2 nuclei), transitions between the first and second nuclear spin states may involve transitions between other spin states on the nuclear spin manifold. For example, for a spin-9 / 2 nucleus in the presence of a uniform magnetic field, all nuclear spin levels may be spaced apart by equal energy. Thus, for example, m N =9 / 2 spin state to m N Transitions designed to move atoms to the spin state of m = 7 / 2 (such as Raman transitions) 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 to m N =-7 / 2 to m N =-9 / 2 (m N is the nuclear spin state). Similarly, for example, m N =9 / 2 spin state to m N Transitions designed to move atoms to the =5 / 2 spin state (such as Raman transitions) are 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 to m N =-5 / 2 to m N =-9 / 2. Therefore, such transitions may not be selective in inducing transitions between specific spin states on the nuclear spin manifold.

[0122] Alternatively, it may be desirable to effect selective transitions between specific first and second spin states on the nuclear spin manifold. This may be accomplished by providing light from a light source that results in an AC Stark shift, which accompanies the transition between the desired first and second nuclear spin states and moves adjacent nuclear spin states off resonance. For example, m N =-9 / 2 and m N If transitions from a first nuclear spin state and a second nuclear spin state with .mu.m and .mu.m are desired, the light N =-5 / 2 spin state, which leads to an AC Stark shift of m N =-7 / 2 state and m N = -5 / 2 state can be significantly reduced. N =-9 / 2 and m N If transitions from a first nuclear spin state and a second nuclear spin state with .mu.m and .mu.m are desired, the light N =-1 / 2 spin state, which leads to an AC Stark shift of m N =-5 / 2 state and m N This effectively creates a two-level subsystem within the nuclear spin manifold that is decoupled from the rest of the nuclear spin manifold, which may significantly simplify the dynamics of the qubit system. Nuclear spin states near the edge of the nuclear spin manifold (e.g., for a spin-9 / 2 nucleus, m N =-9 / 2 and m N =-7 / 2, m N =7 / 2 and m N =9 / 2, m N =-9 / 2 and m N =-5 / 2, or m N =5 / 2 and m N= 9 / 2) can be advantageous, since only one AC Stark shift is required. Alternatively, nuclear spin states further from the edge of the nuclear spin manifold (e.g., m N =-5 / 2 and m N =-3 / 2, or m N =-5 / 2 and m N =-1 / 2) is used, and two AC Stark shifts may be performed (e.g., m N =-7 / 2 and m N =-1 / 2, or m N =-9 / 2 and m N =3 / 2).

[0123] Stark shifting of the nuclear spin manifold may shift adjacent nuclear spin states out of resonance with the desired transition between the first and second nuclear spin states and the second electronic state or states detuned therefrom. Stark shifting may reduce leakage from the first and second nuclear spin states to other states within the nuclear spin manifold. Stark shifting may be achievable up to 100 kHz with beam powers less than 10 mW. Frequency selectivity of the upper states may reduce scattering from imperfect polarization control. 3 The separation of different angular momentum states in the P1 manifold can be many gigahertz from single-qubit and two-qubit gate lights. Leakage to other states in the nuclear spin manifold can lead to decoherence. The Rabi frequency of the two-qubit transition (e.g., how fast the transition can be driven) can be faster than the decoherence rate. Scattering from intermediate states in two-qubit transitions can cause decoherence. Detuning from intermediate states can improve the fidelity of the two-qubit transition.

[0124] Qubits based on the nuclear spin state of the electronic ground state are based on long-lived metastable excited electronic states (such as strontium-87 or ytterbium-171). 3This may allow atoms to be selectively transitioned into such states (e.g., P0 state) for qubit storage. Atoms may be selectively transitioned into such states to reduce crosstalk or improve gating or detection fidelity. Such a storage or shelving process may be atom-selective using the SLM or AOD described herein. Shelving transitions may be achieved using the Strontium-87 or Ytterbium-171 states. 1 From the S0 state, strontium-87 or ytterbium-171 3 P0 state or 3 May include transition to P2 state.

[0125] Clock transitions (also referred to herein as "shelving transitions" or "storage transitions") may be qubit state selective. The upper state of a clock transition may have a very long natural lifetime, e.g., greater than one second. The linewidth of a clock transition may be much narrower than the energy spacing of the qubits. This may enable direct spectral resolution. An ensemble may be moved from one of the qubit states to the clock state. This allows for separate readout of the states of individual qubits by first moving the ensemble from one qubit state to the clock state and imaging the qubit, then moving the ensemble from the clock state to the ground state and imaging again. In some cases, magic wavelength transitions are used to drive the clock transitions.

[0126] The shelving clock light may be atom-selective or non-atom-selective. In some cases, the clock transition is globally applied (e.g., non-atom-selective). Globally applied clock transitions may include directing the light without passing through a microscope objective or structuring the light. In some cases, the clock transition is atom-selective. Atom-selective clock transitions may improve gate fidelity by minimizing crosstalk. For example, to reduce crosstalk within an atom, atoms may be shelved to a clock state that is not affected by light. This may reduce crosstalk between adjacent qubits during the transition. To achieve atom-selective clock transitions, the light may pass through one or more microscope objectives or be structured with one or more spatial light modulators, digital micromirror devices, crossed acousto-optic deflectors, etc.

[0127] Multi-qubit gates—The entanglement unit herein may enable two-qubit gates and multi-qubit gates. For example, the entanglement excitation may be configured to perform an entanglement operation between a first qubit and another qubit different from the first qubit. The entanglement unit may be configured to quantum mechanically entangle at least a first atom of the plurality of atoms with at least a second atom of the plurality of atoms. The first atom or the second atom may be in a superposition state at the time of quantum mechanical entanglement. Alternatively or additionally, the first atom or the second atom may not be in a superposition state at the time of quantum mechanical entanglement. The first atom and the second atom may be quantum mechanically entangled through one or more magnetic dipole interactions, induced magnetic dipole interactions, electric dipole interactions, or induced electric dipole interactions. The entanglement unit may be configured to quantum mechanically entangle any number of atoms described herein.

[0128] The entanglement unit may also be configured to quantum mechanically entangle at least a subset of the atoms with at least another atom to form one or more multi-qubit units. A multi-qubit unit may include a two-qubit unit, a three-qubit unit, a four-qubit unit, or an n-qubit unit (where n may be 5, 6, 7, 8, 9, 10, or more). For example, a two-qubit unit may include a first atom quantum mechanically entangled with a second atom, a three-qubit unit may include a first atom quantum mechanically entangled with a second atom and a third atom, a four-qubit unit may include a first atom quantum mechanically entangled with a second atom, a third atom, and a fourth atom, etc. The first atom, the second atom, the third atom, or the fourth atom may be in a superposition state at the time of quantum mechanical entanglement. Alternatively or additionally, the first atom, the second atom, the third atom, or the fourth atom may not be in a superposition state at the time of quantum mechanical entanglement. The first atom, the second atom, the third atom, and the fourth atom may be quantum mechanically entangled through one or more magnetic dipole interactions, induced magnetic dipole interactions, electric dipole interactions, or induced electric dipole interactions.

[0129] The entanglement unit may include one or more Rydberg units. The Rydberg units may be configured to electronically excite at least a first atom into a Rydberg state or a superposition of a Rydberg state and a lower-energy atomic state, thereby forming one or more Rydberg atoms or dressed Rydberg atoms. The Rydberg units may be configured to induce one or more quantum mechanical entanglements between the Rydberg atom or dressed Rydberg atom and at least a second atom. The second atom may be located at a distance of at least about 200 nanometers (nm), 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, 1 micrometer (μm), 2 μm, 3 μm, 4 μm, 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, or more from the Rydberg atom or dressed Rydberg atom. The second atom may be located at a distance of up to about 10 μm, 9 μm, 8 μm, 7 μm, 6 μm, 5 μm, 4 μm, 3 μm, 2 μm, 1 μm, 900 nm, 800 nm, 700 nm, 600 nm, 500 nm, 400 nm, 300 nm, 200 nm, or less from the Rydberg atom or coated Rydberg atom. The second atom may be located at a distance from the Rydberg atom or coated Rydberg atom within a range defined by any two of the above values. The Rydberg unit may be configured to allow the Rydberg atom or coated Rydberg atom to relax to a lower-energy atomic state, thereby forming one or more two-qubit units. The Rydberg unit may be configured to induce the Rydberg atom or coated Rydberg atom to relax to a lower-energy atomic state. The Rydberg unit may be configured to drive the Rydberg atom or coated Rydberg atom to a lower-energy atomic state. For example, the Rydberg unit may be configured to apply electromagnetic radiation (such as RF radiation or light radiation) to drive the Rydberg atoms or coated Rydberg atoms into a lower energy atomic state.The Rydberg unit may be configured to induce quantum mechanical entanglement between any number of the plurality of atoms.

[0130] The Rydberg unit may include one or more light sources (such as any light source described herein) configured to emit light having one or more ultraviolet (UV) wavelengths. The UV wavelengths may be selected to correspond to wavelengths that form Rydberg atoms or coated Rydberg atoms. For example, the light may include one or more wavelengths of at least about 200 nm, 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, 370 nm, 380 nm, 390 nm, 400 nm, or more. The light may include one or more wavelengths up to about 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm, or less. The light may include one or more wavelengths within a range defined by any two of the above values. For example, the light may include one or more wavelengths within the range of 300 nm to 400 nm.

[0131] The Rydberg unit may be configured to induce two-photon transitions to generate entanglement. The Rydberg unit may be configured to induce two-photon transitions to generate entanglement between two atoms. The Rydberg unit may be configured to selectively induce two-photon transitions to generate entanglement between two atoms. For example, the Rydberg unit may be configured to direct electromagnetic energy (e.g., optical energy) to a specific optical trapping site and selectively induce two-photon transitions to generate entanglement between two atoms. Two atoms may be trapped in nearby optical trapping sites. For example, two atoms may be trapped in adjacent optical trapping sites. The two-photon transitions may be induced using a first light from a first light source and a second light from a second light source, respectively. The first light source and the second light source may each include any light source described herein (e.g., any laser described herein). The first light source may be the same as or similar to the light source used to perform the single qubit operations described herein. Alternatively, different light sources may be used to perform single qubit operations and induce two-photon transitions to generate entanglement. The first light source may emit light including one or more wavelengths in the visible region of the optical spectrum (e.g., within a range of 400 nm to 800 nm, or within a range of 650 nm to 700 nm). The second light source may emit light including one or more wavelengths in the ultraviolet region of the optical spectrum (e.g., within a range of 200 nm to 400 nm, or within a range of 300 nm to 350 nm). The first light source and the second light source may emit light having substantially equal and opposite spatially dependent frequency shifts.

[0132] The Rydberg atom or coated Rydberg atom may include a Rydberg state in which atomic interactions with neighboring atoms (such as neighboring atoms trapped in nearby optical trapping sites) may be strong enough to enable multi-qubit operations. The Rydberg state may include a principal quantum number of at least about 50, 60, 70, 80, 90, 100, or more. The Rydberg state may include a principal quantum number of up to about 100, 90, 80, 70, 60, 50, or less. The Rydberg state may include a principal quantum number within a range defined by any two of the above values. The Rydberg state may interact with neighboring atoms through van der Waals interactions. The van der Waals interactions may shift the energy levels of the atoms.

[0133] State-selective excitation of atoms to Rydberg levels may enable the performance of multi-qubit operations. Multi-qubit operations may include two-qubit operations, three-qubit operations, or n-qubit operations (where n is 4, 5, 6, 7, 8, 9, 10, or more). Two-photon transitions can also be used to excite atoms to the ground state ( 1 S0 ground state) to the Rydberg state (n 3The two-photon transition may be performed using a first laser source and a second laser source, as described herein. The first laser source may emit π-polarized light, which may not change the projection of the atomic angular momentum along the magnetic field. The second laser may emit circularly polarized light, which may change the projection of the atomic angular momentum along the magnetic field by one unit. This polarization may be used to excite the first and second qubit levels to the Rydberg level. However, because the Rydberg level is more sensitive to the magnetic field than the ground state, large splitting (e.g., on the order of 100 MHz) may be easily achieved. This spectral selectivity may enable state-selective excitation to the Rydberg level.

[0134] Multi-qubit operations (e.g., two-qubit, three-qubit, four-qubit, etc.) may rely on energy shifts of levels due to van der Waals interactions as described herein. Such shifts may either prevent the excitation of one atom from being conditional on the state of the other atom, or alter the coherent dynamics of excitations in a two-atom system to perform two-qubit operations. In some cases, "covered states" may be generated under continuous drive to achieve two-qubit operations without requiring full excitation to the Rydberg levels (e.g., as described in www.arxiv.org / abs / 1605.05207, which is incorporated herein by reference in its entirety for all purposes).

[0135] The one-qubit gates, two-qubit gates, and multi-qubit gates may be implemented by one or more nonclassical computation units. The nonclassical computation unit may be configured to perform one-qubit gate operations, two-qubit gate operations, multi-qubit gate operations, and sequences and combinations thereof to perform nonclassical computations. The nonclassical computation unit may include an electromagnetic delivery unit, such as any of the electromagnetic delivery units disclosed herein. The electromagnetic delivery unit disclosed herein for cooling and trapping may be the same electromagnetic delivery unit used for the qubit gate operations or a different electromagnetic delivery unit. The electromagnetic energy may include one or more pulses, pulse sequences, or optical waveforms. The nonclassical computation unit may include one or more entanglement units disclosed herein, one or more Rydberg units disclosed herein, or both. In some cases, the Rydberg unit disclosed herein is an example of an entanglement unit disclosed herein that uses Rydberg excitations to generate entanglement and perform two-qubit or multi-qubit gate operations.

[0136] The non-classical computation may be configured to provide a pulse, pulse sequence, or optical waveform to perform the non-classical computation. The pulse, pulse sequence, or optical waveform may include any number of pulses, pulse sequences, or optical waveforms. For example, the pulse, pulse sequence, or optical waveform may include at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, or more pulses or subwaveforms. A pulse, pulse sequence, or optical waveform may include up to about 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 pulses or subwaveforms. A pulse, pulse sequence, or optical waveform may include a number of pulses or subwaveforms within a range defined by any two of the above values. Each pulse of a pulse sequence may include any pulse shape, such as any pulse shape described herein.

[0137] Pulses, pulse sequences, or optical waveforms may be configured to reduce the time required to perform a multi-qubit operation, as described herein (e.g., with respect to Example 3). For example, a pulse sequence may include a time of at least about 10 nanoseconds (ns), 20 ns, 30 ns, 40 ns, 50 ns, 60 ns, 70 ns, 80 ns, 90 ns, 100 ns, 200 ns, 300 ns, 400 ns, 500 ns, 600 ns, 700 ns, 800 ns, 900 ns, 1 microsecond (μs), 2 μs, 3 μs, 4 μs, 5 μs, 6 μs, 7 μs, 8 μs, 9 μs, 10 μs, 20 μs, 30 μs, 40 μs, 50 μs, 60 μs, 70 μs, 80 μs, 90 μs, 100 μs, or more. The pulse sequence may include a time period of at most about 100 μs, 90 μs, 80 μs, 70 μs, 60 μs, 50 μs, 40 μs, 30 μs, 20 μs, 10 μs, 9 μs, 8 μs, 7 μs, 6 μs, 5 μs, 4 μs, 3 μs, 2 μs, 1 μs, 900 ns, 800 ns, 700 ns, 600 ns, 500 ns, 400 ns, 300 ns, 200 ns, 100 ns, 90 ns, 80 ns, 70 ns, 60 ns, 50 ns, 40 ns, 30 ns, 20 ns, 10 ns, or less. The pulse sequence may include a time period within a range defined by any two of the above values.

[0138] The pulses, pulse sequences, or optical waveforms may be configured to enhance the fidelity of multi-qubit operations, as described herein. For example, the pulses, pulse sequences, or optical waveforms may be at least about 0.5, 0.6, 0.7, 0.8, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99, 0.991, 0.992, 0.993, 0.994, 0.995, 0.996, 0.997, 0.998, 0.999, 0.9991, 0.9992, 0.9993, 0.9994, 0.9995, 0.9996, 0.9997, 0.998, 0.999, 0.9991, 0.9992, 0.9993, 0.9994, 0.9995, 0.9996, 0.9997, 0.998, 0.999, 0.9991, 0.9992, 0.9993, 0.9994, 0.9995, 0.9996, 0.9997, 0.9998, 0.9 ... It may enable multi-qubit operations with fidelity of 0.9998, 0.9999, 0.99991, 0.99992, 0.99993, 0.99994, 0.99995, 0.99996, 0.99997, 0.99998, 0.99999, 0.999991, 0.999992, 0.999993, 0.999994, 0.9999995, 0.999996, 0.999997, 0.999998, 0.999999, or higher. The pulse sequence is approximately 0.999999, 0.999998, 0.999997, 0.999996, 0.999995, 0.999994, 0.999993, 0.999992, 0.999991, 0.99999, 0.99998, 0.99997, 0.99996, 0.99995, 0.99994, 0.99993, 0.99992, 0.99991, 0.9999, 0.9998, 0.9997, 0.9 0.996, 0.995, 0.9994, 0.9993, 0.9992, 0.9991, 0.999, 0.998, 0.997, 0.996, 0.995, 0.994, 0.993, 0.992, 0.991, 0.99, 0.98, 0.97, 0.96, 0.95, 0.94, 0.93, 0.92, 0.91, 0.9, 0.8, 0.7, 0.6, 0.5, or less. The pulse sequence may enable multi-qubit operations with a fidelity that is within a range defined by any two of the above values.

[0139] The pulses, pulse sequences, or optical waveforms may enable multi-qubit operations to be performed on non-adiabatic time scales while maintaining effectively adiabatic dynamics. For example, the pulse sequences may include one or more of a shortcut-to-adiabatic (STA) pulse sequence, a transition-free quantum drive (TQD) pulse sequence, a superadiabatic pulse sequence, a counteradiabatic drive pulse sequence, a derivative removal by adiabatic gate (DRAG) pulse sequence, and a weakly anharmonic by average Hamiltonian (Wah Wah) pulse sequence.For example, pulse sequences have been described in M.V. Berry, "Transitionless Quantum Driving," Journal of Physics A: Mathematical and Theoretical 42(36), 365303 (2009), www.doi.org / 10.1088 / 1751-8113 / 42 / 36 / 365303; Y.-Y. Jau et al., "Entangling Atomic Spins with a Strong Rydberg-Dressed Interaction," Nature Physics 12(1), 71-74 (2016); T. Keating et al., "Robust Quantum Logic in Neutral Atoms via Adiabatic Rydberg Dressing," Physical Review A A) 91, 012337 (2015); A. Mitra et al., "Robust Molmer-Sorenson Gate for Neutral Atoms Using Rapid Adiabatic Rydberg Dressing," www.arxiv.org / abs / 1911.04045 (2019); or L.S. Theis et al., "Counteracting Systems of Diabaticities Using DRAG Controls: The Status after 10 Years," Europhysics Letters 123(6), 60001 (2018), each of which is incorporated herein by reference in its entirety for all purposes.

[0140] The pulse, pulse sequence, or optical waveform may further include one or more optimal control pulse sequences derived from one or more procedures including gradient ascent pulse engineering (GRAPE), Krotov's, chopped basis, chopped random basis (CRAB), Nelder-Mead, gradient optimization using parametrization (GROUP), genetic algorithm, and gradient optimization of analytical control (GOAT). For example, the pulse sequence may be similar to those described in N. Khaneja et al., “Optimal Control of Coupled Spin Dynamics: Design of NMR Pulse Sequences by Gradient Ascent Algorithms,” Journal of Magnetic Resonance 172(2), 296-305 (2005); or J.T. Merrill et al., “Progress in Compensating Pulse Sequences for Quantum Computation,” Advances in Chemical Physics 154, 241-294 (2014), each of which is incorporated by reference in its entirety for all purposes.

[0141] In step 330 of measurement step-method 300, the method may include exposing a second plurality of qubits to radiation. The first plurality of qubits may include the second plurality of qubits. In some cases, the first plurality of qubits is identical to the second plurality of qubits. In some cases, the second plurality of qubits is a selected subset of the qubits being measured. In some cases, step 330 is an embodiment, variation, or example of a measurement step disclosed herein. In some cases, the radiation may include an electromagnetic field disclosed herein.

[0142] At step 430 of method 400, the method may include performing a measuring step. The measuring step may include exposing a second plurality of qubits to electromagnetic energy. The first plurality of qubits may include the second plurality of qubits. In some cases, the first plurality of qubits is identical to the second plurality of qubits. In some cases, the second plurality of qubits is a selected subset of the qubits being measured. In some cases, the electromagnetic energy is configured to selectively drive qubits of the second plurality of qubits from an initial state to an excited state in the presence of an applied magnetic field. In some cases, the selectivity of the transition to the excited state is based at least in part on the strength of the magnetic field applied to the first plurality of qubits, the second plurality of qubits, or both. Step 430 of method 400 may include an example, variation, or embodiment of method 330 of method 300.

[0143] In some cases, step 430 or 330 includes exposing a first subset of the second plurality of qubits to a first electromagnetic energy and then exposing a second subset of the second plurality of qubits to a second electromagnetic energy. In some cases, the first electromagnetic energy includes a first polarization and the second electromagnetic energy includes a second polarization.

[0144] In some cases, method 300 or method 400 further includes determining that a first subset of the second plurality of qubits fluoresces in response to exposure to the first radiation, and that a second subset of the second plurality of qubits fluoresces in response to exposure to the second radiation. 1 S0m f The state may be imaged from either of two counter-propagating imaging beams configured to image one of the states of the =½ and −½ qubits. In some cases, the electromagnetic energy is polarized. In some cases, one or more of the electromagnetic energy, the first electromagnetic energy, or the second electromagnetic energy is circularly polarized. In some cases, the transition is a cyclic transition. In some cases, the beam is 3 P1m f =±3 / 2 states, which provides access to a closed cycle transition with a narrow linewidth (e.g., about 180 kHz). f Scattering from the =±1 / 2 excited states can allow for collective leakage between qubit states, but can be suppressed by the large ratio of the Zeeman shift to the transition linewidth. In some cases, this ratio can include 771 MHz between the -3 / 2 and -1 / 2 states, and 681 MHz between the 1 / 2 and 3 / 2 states, respectively.

[0145] In some cases, the method includes adjusting the strength of the applied magnetic field to a selected measurement state. For example, Figure 2 shows curves of magnetic field strength such that a particular state may be in or out of resonance with a particular measurement state.

[0146] In some cases, the first plurality of qubits has up to n more qubits than the second plurality of qubits. For example, the first plurality of qubits and the second plurality of qubits can be configured in a two-dimensional array of optical trapping sites. The first plurality of qubits can include up to n more qubits than the second plurality of qubits. In some cases, the first plurality of qubits can include at least about 1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 300, 400, 500, or more qubits than the second plurality of qubits. In some cases, the first plurality of qubits can include up to about 500, 400, 300, 200, 190, 180, 170, 160, 150, 140, 130, 120, 110, 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 4, 3, 2, or fewer qubits more than the second plurality of qubits.

[0147] In some cases, the second plurality of qubits has up to n more qubits than the first plurality of qubits. For example, the first plurality of qubits and the second plurality of qubits can be configured in a two-dimensional array of optical trapping sites. The second plurality of qubits can include up to n more qubits than the first plurality of qubits. In some cases, the second plurality of qubits can include at least about 1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 300, 400, 500, or more qubits than the first plurality of qubits. In some cases, the second plurality of qubits can include up to about 500, 400, 300, 200, 190, 180, 170, 160, 150, 140, 130, 120, 110, 100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 4, 3, 2, or fewer qubits more than the first plurality of qubits.

[0148] In some cases, performing the measuring step in the methods and systems disclosed herein includes exposing a first subset of the second plurality of qubits to a first electromagnetic energy and then exposing a second subset of the second plurality of qubits to a second electromagnetic energy. In some cases, the first electromagnetic energy includes a first polarization and the second electromagnetic energy includes a second polarization. In some cases, the method further includes determining that the first subset of the second plurality of qubits fluoresce in response to exposure to the first radiation and that the second subset of the second plurality of qubits fluoresce in response to exposure to the second radiation. For example, the states may be 1 S0m f The qubit state may be imaged from either of two imaging beams configured to image either the =½ and −½ qubit states. The two imaging beams may propagate in counter directions.

[0149] The measuring step may be performed by one or more electromagnetic delivery units, such as, for example, any of the electromagnetic delivery units disclosed herein. In some cases, the electromagnetic delivery unit configured to perform the measuring step is the same as the electromagnetic delivery unit configured to perform the non-classical calculation. In some cases, the electromagnetic delivery unit configured to perform the measuring step is different from the electromagnetic delivery unit configured to perform the non-classical calculation.

[0150] In some cases, the magnetic field (e.g., a 500 Gauss magnetic field) can be selected to minimize unwanted scattering and other potential errors described elsewhere herein while aligning with operational constraints (e.g., mechanical and thermal constraints). The scattered light can be collected by an objective lens (e.g., a high-numerical-aperture objective lens) and imaged onto a camera (e.g., a low-noise digital camera). At each site in the tweezers array, the methods described herein can include applying a threshold to the counts within the integration region to determine whether an atom in the imaged state occupies the site. The methods described herein can include operating at an imaging time (e.g., 5 milliseconds (ms)). At a predetermined imaging time, the methods described herein can include registering or detecting a number of photons (e.g., approximately 30 photons) from the bright atom. In some cases, the imaging time can be selected to balance discrimination, loss, data rate, and robustness against experimental drift.

[0151] State Identification—Methods and systems disclosed herein may provide for selective identification of the state of a qubit. In step 340 of method 300, the method may include determining or predicting that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state, based at least in part on at least one of the qubits fluorescing in response to exposure to the radiation. In some cases, the state of a qubit is identified as a first state or a state by the emission of a photon or the absence of the emission of the photon.

[0152] At step 440 of method 400, the method may include determining that the qubit was in an initial state. This determination may be made at least in part based on the qubit returning to the initial state by emitting photons in response to electromagnetic energy at step 430. Step 440 of method 400 may include an example, variation, or embodiment of method 340 of method 300.

[0153] In some cases, step 340 and / or step 440 includes detecting a photon indicative of a transition between the measurement state and a state of the qubit (e.g., an initial state). In some cases, the photon is generated by returning to the initial state. In some cases, the returning to the initial state is from a manifold of excited states. In some cases, the strength of the magnetic field determines the separation between states in the manifold of excited states. For example, the strength of the magnetic field can include a strength of at least about 100, 200, 300, 400, 500 Gauss, or more. For example, the strength of the magnetic field can include a strength of up to about 500, 400, 300, 200, 100 Gauss, or less. The strength of the magnetic field can include a strength within a range defined by any two of the above values.

[0154] In some cases, the method includes adjusting the strength of an applied magnetic field to a selected measurement state. In some cases, a separation between states determines which states are resonant with the radiation. In some cases, a state selection rule for each qubit allows transitions to a single state having a manifold of excited states.

[0155] In some cases, the returning to the initial state comprises spontaneous emission. In some cases, the returning to the initial state comprises stimulated emission. In some cases, the returning to the initial state by emission of a photon is a fluorescence transition. In some cases, the method includes imaging the photon with a measurement unit.

[0156] In some cases, step 440 or 340 includes imaging the photons with a measurement unit. In some cases, fluorescence associated with the emission of photons can be detected by a measurement unit (e.g., one or more optical detection devices). For example, the optical detection device may be configured to perform state measurements for non-classical computation. The optical detection device may include one or more photomultiplier tubes (PMTs), photodiodes, avalanche diodes, single-photon avalanche diodes, single-photon avalanche diode arrays, phototransistors, reverse-biased light-emitting diodes (LEDs), charge-coupled devices (CCDs), or complementary metal-oxide semiconductor (CMOS) cameras. The optical detection device may include one or more fluorescence detectors. The optical detection device may include one or more objective lenses. For example, one or more objective lenses can have a numerical aperture (NA) of at least about 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1, or more. The objective lenses may have an NA of up to about 1, 0.95, 0.9, 0.85, 0.8, 0.75, 0.7, 0.65, 0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1, or less. The objective lenses may have an NA within a range defined by any two of the above values.

[0157] In some cases, method 400 further includes repeating steps 430 through 440 multiple times. In some cases, method 400 further includes determining that a plurality (n) of spatially distinct optical trapping sites of the array of spatially distinct optical trapping sites lack a qubit based at least in part on determining the fluorescence at 430. In some cases, the first plurality of qubits has up to n more qubits than the second plurality of qubits.

[0158] In some cases, the method is configured to perform an atom cooling step. In some cases, steps 430 through 440 are configured to perform an atom cooling step. For example, achieving low resonant scattering while maintaining cooling from the imaging beam can be achieved by operating at low imaging beam power and a relatively small red-detuning (e.g., on the order of the transition linewidth). This can be facilitated by using a "magic" trap, e.g., where the ground state and excited state can experience the same trapping potential. In some cases, 1 From S0 3 P1m fThe magic wavelength for the =±3 / 2 transition may occur near 483 nm. In some cases, the trapping electromagnetic energy (e.g., light of a predetermined wavelength) may be polarized perpendicular to the magnetic field. In some cases, magic traps can also reduce the uniformity requirements of the array. In some cases, the magic wavelength corresponding to an atom may include any wavelength of light at which the polarizabilities of the first and second states are equal or nearly equal. The magic wavelength for the transition between the first and second states may be determined by calculating the wavelength-dependent polarizabilities of the first and second states and finding the intersection point. Electromagnetic energy (e.g., light) tuned to such a magic wavelength may induce equal or nearly equal differential optical shifts in the first and second states, regardless of the intensity of the light emitted from the light source. In some cases, this may effectively decouple the first and second states from the motion of the atom. In some cases, the magic wavelength may utilize one or more scalar or tensor optical shifts.

[0159] Intermediate-circuit measurements—The ability to determine the quantum state of an atom without losing the atom from an optical trap can be useful for intermediate-circuit measurements. In some systems, such as neutral atom systems, the state of a single atom can be determined by introducing a state-selective loss followed by state-independent imaging of the remaining atoms. Compared to the present disclosure, such an approach may be unable to distinguish between atoms occupying an emitting state and atoms that have already suffered a loss. When used in error-correction protocols, such an approach may require frequent reloading and state preparation of new ancilla qubits.

[0160] A system for state detection for nonclassical computation Disclosed herein is a system for performing state detection for non-classical computation. In some cases, the system can include one or more optical trapping units configured to obtain an array of spatially distinct optical trapping sites, the array including a first plurality of qubits. In some cases, the system can include one or more non-classical computation units configured to perform non-classical computation using at least a portion of the first plurality of qubits. In some cases, the system can include one or more electromagnetic delivery units configured to expose a second plurality of qubits to radiation, the first plurality of qubits including the second plurality of qubits. In some cases, the system can include one or more measurement units configured to determine or predict that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based, at least in part, on at least one of the second plurality of qubits emitting fluorescence in response to exposure to the radiation.

[0161] FIG. 5A shows an example of a system configured to perform state detection for non-classical computation. As shown in the illustrated example, the system may include optical tweezers array sites, a magnetic field, laser beams with opposite circular polarizations and different frequencies applied along the direction of the magnetic field, a high numerical aperture objective lens, and movable tweezers. The system may include at least multiple optical tweezers array sites, shown as a two-dimensional spot array. The system may include magnetic fields, shown as left and right gray coils on either side of the optical tweezers array.

[0162] The system may include various forms of electromagnetic radiation directed to the optical tweezers array. The electromagnetic radiation may be generated by various electromagnetic delivery units disclosed herein. For example, trap optical excitation may be provided from an optical trapping unit to realize an array of spatially distinct optical traps (e.g., a tweezers array herein). For example, measurement electromagnetic energy may be provided from an electromagnetic delivery unit associated with a measurement unit. In the illustrated example, the system may include laser beams with opposite circular polarizations and different frequencies applied along the direction of the magnetic field. Each of the σ- and σ+ may be configured to measure the state of the qubit as disclosed herein. In some cases, light (e.g., fluorescence, spontaneous emission, stimulated emission, etc.) may be directed to the measurement unit to detect the state as disclosed herein. For example, electromagnetic energy from a non-classical computation unit may be directed to the array to perform various gate operations disclosed herein. For example, electromagnetic energy from the measurement unit may be configured to suppress incoherent scattering in the excited state by "hiding" light applied to the qubit at a hidden wavelength. The masking procedures may be similar to those disclosed in commonly owned International Application No. PCT / US2023 / 026730, which is incorporated herein by reference for all purposes.

[0163] FIG. 5A shows the dynamics of individual atoms (e.g., α, β, β) at multiple sites of an optical tweezers array in the presence of a magnetic field (e.g., a 500 Gauss magnetic field). 1711 illustrates a system configured to optically trap Yb atoms. In some cases, the system can include one or more high-numerical-aperture objective lenses (e.g., two objective lenses) configured for site-resolved imaging. In some cases, the one or more objective lenses can be configured to apply trapping light to the target at a trapping wavelength (e.g., 483 nm wavelength). In some cases, the one or more objective lenses can be configured to apply hiding light to the target at a hiding wavelength (e.g., 460 nm wavelength). In some cases, the system can include one or more movable or optical tweezers. In some cases, the one or more movable or optical tweezers can be configured at a trapping wavelength (e.g., 483 nm wavelength). In some cases, the one or more movable or optical tweezers can be configured to reposition atoms between trap sites. In some cases, the system can include one or more electromagnetic energy sources for performing non-classical calculations. In some cases, the measurement unit can be configured to direct one or more lasers configurable at global Raman transition wavelengths (e.g., 556 nm wavelength). In some cases, one or more lasers can be configured to generate lasers that are incident through a hole in the imaging objective and drive global Raman transitions between the states of the qubits.

[0164] FIG. 5B shows (top) a level diagram of an exemplary atomic system usable in the methods and systems disclosed herein, and (bottom) experimental data showing two successive single-shot images of a fully filled 10×3 atomic array produced by an example of the methods and systems disclosed herein.

[0165] Figure 5B (top) shows a system configured with one or more laser beams to perform state detection for non-classical computation. In some cases, one or more laser beams (e.g., two laser beams) have opposite circular polarizations and different frequencies (e.g.,

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[0170] In some cases, state-resolved non-destructive imaging can be demonstrated by performing two successive single-shot images of a fully filled array, as shown in Figure 5B (bottom). In some cases, the array is irradiated with ions prior to the first image.

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[0173] The system may include various forms of electromagnetic radiation directed at the optical tweezers array. The electromagnetic radiation may be generated by various electromagnetic delivery units disclosed herein. In some cases, the electromagnetic energy may include optical energy. The optical energy may include any repetition rate, pulse energy, average power, wavelength, or bandwidth. In some cases, the electromagnetic energy may be provided by a magnetron, klystron, traveling wave tube, gyrotron, field effect transistor (FET), tunnel diode, Gunn diode, impact ionization avalanche transit-time (IMPATT) diode, or maser. In some cases, the electromagnetic energy may be at least about 1 millimeter (mm), 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, 9 mm, 10 mm, 20 mm, 30 mm, 40 mm, 50 mm, 60 mm, 70 mm, 80 mm, 90 mm, 100 mm, 200 mm, 300 mm, 400 mm, 500 mm, 600 mm, 700 mm, 800 mm, 900 mm, 1 meter (m), 2 m , 3m, 4m, 5m, 6m, 7m, 8m, 9m, 10m, 20m, 30m, 40m, 50m, 60m, 70m, 80m, 90m, 100m, 200m, 300m, 400m, 500m, 600m, 700m, 800m, 900m, 1 kilometer (km), 2 km, 3 km, 4 km, 5 km, 6 km, 7 km, 8 km, 9 km, 10 km, or more wavelengths.In some cases, electromagnetic energy can travel up to approximately 10km, 9km, 8km, 7km, 6km, 5km, 4km, 3km, 2km, 1km, 900m, 800m, 700m, 600m, 500m, 400m, 300m, 200m, 100m, 90m, 80m, 70m, 60m, 50m, 40m, 30m, 20m, 10m, 9m, 8m, 7m, 6m, 5m, 4m, 3m, 2 The electromagnetic energy may include one or more of the following wavelengths: m, 1 m, 900 mm, 800 mm, 700 mm, 600 mm, 500 mm, 400 mm, 300 mm, 200 mm, 100 mm, 90 mm, 80 mm, 70 mm, 60 mm, 50 mm, 40 mm, 30 mm, 20 mm, 10 mm, 9 mm, 8 mm, 7 mm, 6 mm, 5 mm, 4 mm, 3 mm, 2 mm, 1 mm, or shorter. In some cases, the electromagnetic energy may include one or more wavelengths within a range defined by any two of the above values.

[0174] In some cases, the electromagnetic energy is at least about 1 microwatt (μW), 2 μW, 3 μW, 4 μW, 5 μW, 6 μW, 7 μW, 8 μW, 9 μW, 10 μW, 20 μW, 30 μW, 40 μW, 50 μW, 60 μW, 70 μW, 80 μW, 90 μW, 100 μW, 200 μW, 300 μW, 400 μW, 500 μW, 600 μW, 700 μW, 800 μW, 900 μW, 1 milliwatt (mW), 2 mW, 3 mW, 4 mW, 5 mW, 6 mW, 7 mW, 8 mW, 9 mW, 10 mW, 20 mW, 30 mW, The average power may include 40mW, 50mW, 60mW, 70mW, 80mW, 90mW, 100mW, 200mW, 300mW, 400mW, 500mW, 600mW, 700mW, 800mW, 900mW, 1 Watt (W), 2W, 3W, 4W, 5W, 6W, 7W, 8W, 9W, 10W, 20W, 30W, 40W, 50W, 60W, 70W, 80W, 90W, 100W, 200W, 300W, 400W, 500W, 600W, 700W, 800W, 900W, 1,000W, or more. In some cases, the electromagnetic energy may be up to approximately 1,000W, 900W, 800W, 700W, 600W, 500W, 400W, 300W, 200W, 100W, 90W, 80W, 70W, 60W, 50W, 40W, 30W, 20W, 10W, 9W, 8W, 7W, 6W, 5W, 4W, 3W, 2W, 1W, 900mW, 800mW, 700mW, 600mW, 500mW, 400mW, 300mW, 200mW, 100mW, 90mW, 80mW, 70mW, 60mW, 50mW , 40 mW, 30 mW, 20 mW, 10 mW, 9 mW, 8 mW, 7 mW, 6 mW, 5 mW, 4 mW, 3 mW, 2 mW, 1 mW, 900 μW, 800 μW, 700 μW, 600 μW, 500 μW, 400 μW, 300 μW, 200 μW, 100 μW, 90 μW, 80 μW, 70 μW, 60 μW, 50 μW, 40 μW, 30 μW, 20 μW, 10 μW, 9 μW, 8 μW, 7 μW, 6 μW, 5 μW, 4 μW, 3 μW, 2 μW, 1 μW, or less. In some cases, the electromagnetic energy can include an average power within a range defined by any two of the above values.

[0175] In some cases, the system can include one or more optical trapping units. The optical trapping units can be configured to generate multiple optical trapping sites. In some cases, the optical trapping units can be configured to generate multiple spatially distinct optical trapping sites. For example, the optical trapping units can 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, It may be configured to generate 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. For example, the optical trap unit may have a maximum of 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, 1 It may be configured to generate 0,000, 9,000, 8,000, 7,000, 6,000, 5,000, 4,000, 3,000, 2,000, 1,000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, or fewer optical trap sites. In some cases, the optical trapping unit may be configured to trap a number of optical trap sites within a range defined by any two of the above values.

[0176] In some cases, the optical trapping unit may be configured to trap a plurality of atoms. For example, the optical trapping unit may be configured to trap at least about 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000, 10,000, 20,000, 30,000, 40,000, 50,000, 60,000, 70 ...0,000, 90,000, 10,000, 12,000, 14,000, 16,000, 18,000, 19,000, 21,000, 22,000, 23,000, 24,000, 25,000, 26,000, 27,000, 28,000, 29,000, 30,000, 31,000, 32,000, 33,000, 34,000, 35,000, 36,000, 37,000, 38,00 It may be configured to trap 0, 40,000, 50,000, 60,000, 70,000, 80,000, 90,000, 100,000, 200,000, 300,000, 400,000, 500,000, 600,000, 700,000, 800,000, 900,000, 1,000,000 or more atoms. For example, the optical trap unit can accommodate up to approximately 1,000,000, 900,000, 800,000, 700,000, 600,000, 500,000, 400,000, 300,000, 200,000, 100,000, 90,000, 80,000, 70,000, 60,000, 50,000, 40,000, 30,000, 20,000 , 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. In some cases, the optical trapping unit may be configured to trap a number of atoms within a range defined by any two of the above values.

[0177] In some cases, each optical trapping site of the optical trapping unit may be configured to trap at least about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more atoms. In some cases, each optical trapping site may be configured to trap up to about 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, or fewer atoms. In some cases, each optical trapping site may be configured to trap a number of atoms within a range defined by any two of the above values. In some cases, each optical trapping site may be configured to trap a single atom.

[0178] In some cases, one or more atoms of the plurality of atoms can include a qubit. Two or more atoms can be quantum mechanically entangled. In some cases, the two or more atoms can be quantum-mechanically entangled for at least about 1 microsecond (μs), 2 μs, 3 μs, 4 μs, 5 μs, 6 μs, 7 μs, 8 μs, 9 μs, 10 μs, 20 μs, 30 μs, 40 μs, 50 μs, 60 μs, 70 μs, 80 μs, 90 μs, 100 μs, 200 μs, 300 μs, 400 μs, 500 μs, 600 μs, 700 μs, 800 μs, 900 μs, 1 millisecond (ms), 2 ms, 3 ms, 4 ms, 5 ms , 6ms, 7ms, 8ms, 9ms, 10ms, 20ms, 30ms, 40ms, 50ms, 60ms, 70ms, 80ms, 90ms, 100ms, 200ms, 300ms, 400ms, 500ms, 600ms, 700ms, 800ms, 900ms, 1 second (s), 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, 10s, or longer coherence lifetimes. In some cases, two or more atoms may be spaced apart by up to about 10s, 9s, 8s, 7s, 6s, 5s, 4s, 3s, 2s, 1s, 900ms, 800ms, 700ms, 600ms, 500ms, 400ms, 300ms, 200ms, 100ms, 90ms, 80ms, 70ms, 60ms, 50ms, 40ms, 30ms, 20ms, 10ms, 9ms, 8ms, 7ms, 6ms, 5ms, 4ms, 3ms, 2ms In some cases, two or more atoms may be quantum mechanically entangled with a coherence lifetime of 1 s, 1 ms, 900 μs, 800 μs, 700 μs, 600 μs, 500 μs, 400 μs, 300 μs, 200 μs, 100 μs, 90 μs, 80 μs, 70 μs, 60 μs, 50 μs, 40 μs, 30 μs, 20 μs, 10 μs, 9 μs, 8 μs, 7 μs, 6 μs, 5 μs, 4 μs, 3 μs, 2 μs, 1 μs, or less. In some cases, two or more atoms may be quantum mechanically entangled with a coherence lifetime within a range defined by any two of the above values.

[0179] In some cases, the laser may include one or more continuous wave lasers. The laser may include one or more pulsed lasers. The laser may include one or more gas lasers, such as one or more helium neon (HeNe) lasers, argon (Ar) lasers, krypton (Kr) lasers, xenon (Xe) ion lasers, nitrogen (N2) lasers, carbon dioxide (CO2) lasers, carbon monoxide (CO) lasers, transversely excited atmospheric (TEA) lasers, or excimer lasers. For example, the laser may include one or more of an argon dimer (Ar2) excimer laser, a krypton dimer (Kr2) excimer laser, a fluorine dimer (F2) excimer laser, a xenon dimer (Xe2) excimer laser, an argon fluoride (ArF) excimer laser, a krypton chloride (KrCl) excimer laser, a krypton fluoride (KrF) excimer laser, a xenon bromide (XeBr) excimer laser, a xenon chloride (XeCl) excimer laser, or a xenon fluoride (XeF) excimer laser. The laser may include one or more dye lasers.

[0180] In some cases, the laser may include one or more metal vapor lasers, such as one or more helium cadmium (HeCd) metal vapor lasers, helium mercury (HeHg) metal vapor lasers, helium selenium (HeSe) metal vapor lasers, helium silver (HeAg) metal vapor lasers, strontium (Sr) metal vapor lasers, neon copper (NeCu) metal vapor lasers, copper (Cu) metal vapor lasers, gold (Au) metal vapor lasers, manganese (Mn) metal vapor lasers, or manganese chloride (MnCl) metal vapor lasers.

[0181] In some cases, the laser may include one or more solid-state lasers, such as one or more ruby ​​lasers, metal-doped crystal lasers, or metal-doped fiber lasers. For example, the laser may include one or more neodymium-doped yttrium aluminum garnet (Nd:YAG) lasers, neodymium / chromium-doped yttrium aluminum garnet (Nd / Cr:YAG) lasers, erbium-doped yttrium aluminum garnet (Er:YAG) lasers, neodymium-doped yttrium lithium fluoride (Nd:YLF) lasers, neodymium-doped yttrium orthovanadate (ND:YVO4) lasers, neodymium-doped yttrium calcium oxoborate (Nd:YCOB) lasers, neodymium-glass (Nd:glass) lasers, titanium sapphire (Ti:sapphire) lasers, thulium-doped yttrium aluminum garnet (Tm:YAG) lasers, ytterbium These may include doped yttrium aluminum garnet (Yb:YAG) lasers, ytterbium-doped glass (Yt:glass) lasers, holmium yttrium aluminum garnet (Ho:YAG) lasers, chromium-doped zinc selenide (Cr:ZnSe) lasers, cerium-doped lithium strontium aluminum fluoride (Ce:LiSAF) lasers, cerium-doped lithium calcium aluminum fluoride (Ce:LiCAF) lasers, erbium-doped glass (Er:glass) lasers, erbium-ytterbium co-doped glass (Er / Yt:glass) lasers, uranium-doped calcium fluoride (U:CaF2) lasers, or samarium-doped calcium fluoride (Sm:CaF2) lasers.

[0182] In some cases, the laser may include one or more semiconductor or diode lasers, such as one or more gallium nitride (GaN) lasers, indium gallium nitride (InGaN) lasers, aluminum gallium indium phosphide (AlGaInP) lasers, aluminum gallium arsenide (AlGaAs) lasers, indium gallium arsenide phosphide (InGaAsP) lasers, vertical cavity surface emitting lasers (VCSELs), or quantum cascade lasers.

[0183] In some cases, the laser may emit continuous wave laser light. The laser may emit pulsed laser light. The laser may emit pulsed laser light of at least about 1 femtosecond (fs), 2 fs, 3 fs, 4 fs, 5 fs, 6 fs, 7 fs, 8 fs, 9 fs, 10 fs, 20 fs, 30 fs, 40 fs, 50 fs, 60 fs, 70 fs, 80 fs, 90 fs, 100 fs, 200 fs, 300 fs, 400 fs, 500 fs, 600 fs, 700 fs, 800 fs, 900 fs, 1 picosecond (ps), 2 ps, 3 ps, 4 ps, 5 ps, 6 ps, 7 ps, 8 ps, 9 ps, 10 ps, ​​20 ps, ​​30 ps, ​​40 ps, ​​50 ps, ​​60 ps, ​​70 ps, ​​80 The pulse length may be ps, 90 ps, ​​100 ps, ​​200 ps, ​​300 ps, ​​400 ps, ​​500 ps, ​​600 ps, ​​700 ps, ​​800 ps, ​​900 ps, ​​1 nanosecond (ns), 2 ns, 3 ns, 4 ns, 5 ns, 6 ns, 7 ns, 8 ns, 9 ns, 10 ns, 20 ns, 30 ns, 40 ns, 50 ns, 60 ns, 70 ns, 80 ns, 90 ns, 100 ns, 200 ns, 300 ns, 400 ns, 500 ns, 600 ns, 700 ns, 800 ns, 900 ns, 1,000 ns, or longer. Lasers have a maximum pulse width of approximately 1,000ns, 900ns, 800ns, 700ns, 600ns, 500ns, 400ns, 300ns, 200ns, 100ns, 90ns, 80ns, 70ns, 60ns, 50ns, 40ns, 30ns, 20ns, 10ns, 9ns, 8ns, 7ns, 6ns, 5ns, 4ns, 3ns, 2ns, 1ns, 900ps, 800ps, 700ps, 600ps, 500ps, 400ps, 300ps, 200ps, 100ps, 90ps, 80ps, 70ps, The pulse length may be 60 ps, ​​50 ps, ​​40 ps, ​​30 ps, ​​20 ps, ​​10 ps, ​​9 ps, 8 ps, 7 ps, 6 ps, 5 ps, 4 ps, 3 ps, 2 ps, 1 ps, 900 fs, 800 fs, 700 fs, 600 fs, 500 fs, 400 fs, 300 fs, 200 fs, 100 fs, 90 fs, 80 fs, 70 fs, 60 fs, 50 fs, 40 fs, 30 fs, 20 fs, 10 fs, 9 fs, 8 fs, 7 fs, 6 fs, 5 fs, 4 fs, 3 fs, 2 fs, 1 fs, or less.The laser may have a pulse length within a range defined by any two of the above values.

[0184] In some cases, the laser may be configured to operate at a frequency of at least about 1 Hertz (Hz), 2 Hz, 3 Hz, 4 Hz, 5 Hz, 6 Hz, 7 Hz, 8 Hz, 9 Hz, 10 Hz, 20 Hz, 30 Hz, 40 Hz, 50 Hz, 60 Hz, 70 Hz, 80 Hz, 90 Hz, 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1 kilohertz (kHz), 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz, 8 kHz, 9 kHz, 10 kHz, 20 kHz, 30 kHz, 40 kHz, 50 kHz, 60 kHz, 70 kHz, 80 kHz, 90 kHz, It may have a repetition rate of 100 kHz, 200 kHz, 300 kHz, 400 kHz, 500 kHz, 600 kHz, 700 kHz, 800 kHz, 900 kHz, 1 megahertz (MHz), 2 MHz, 3 MHz, 4 MHz, 5 MHz, 6 MHz, 7 MHz, 8 MHz, 9 MHz, 10 MHz, 20 MHz, 30 MHz, 40 MHz, 50 MHz, 60 MHz, 70 MHz, 80 MHz, 90 MHz, 100 MHz, 200 MHz, 300 MHz, 400 MHz, 500 MHz, 600 MHz, 700 MHz, 800 MHz, 900 MHz, 1,000 MHz, or higher.Lasers are available in frequencies up to approximately 1,000MHz, 900MHz, 800MHz, 700MHz, 600MHz, 500MHz, 400MHz, 300MHz, 200MHz, 100MHz, 90MHz, 80MHz, 70MHz, 60MHz, 50MHz, 40MHz, 30MHz, 20MHz, 10MHz, 9MHz, 8MHz, 7MHz, 6MHz, 5MHz, 4MHz, 3MHz, 2MHz, 1MHz, 900kHz, 800kHz, 700kHz, 600kHz, 500kHz, 400kHz, 300kHz, 200kHz, 100kHz, 90kHz, 80MHz, 70MHz, 60MHz, 50MHz, 40MHz, 30MHz, 20MHz, 10MHz ...10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, 10MHz, The laser may have a repetition rate of 0 kHz, 70 kHz, 60 kHz, 50 kHz, 40 kHz, 30 kHz, 20 kHz, 10 kHz, 9 kHz, 8 kHz, 7 kHz, 6 kHz, 5 kHz, 4 kHz, 3 kHz, 2 kHz, 1 kHz, 900 Hz, 800 Hz, 700 Hz, 600 Hz, 500 Hz, 400 Hz, 300 Hz, 200 Hz, 100 Hz, 90 Hz, 80 Hz, 70 Hz, 60 Hz, 50 Hz, 40 Hz, 30 Hz, 20 Hz, 10 Hz, 9 Hz, 8 Hz, 7 Hz, 6 Hz, 5 Hz, 4 Hz, 3 Hz, 2 Hz, 1 Hz, or less. The laser may have a repetition rate within a range defined by any two of the above values.

[0185] In some cases, the laser provides a power of at least about 1 nanojoule (nJ), 2 nJ, 3 nJ, 4 nJ, 5 nJ, 6 nJ, 7 nJ, 8 nJ, 9 nJ, 10 nJ, 20 nJ, 30 nJ, 40 nJ, 50 nJ, 60 nJ, 70 nJ, 80 nJ, 90 nJ, 100 nJ, 200 nJ, 300 nJ, 400 nJ, 500 nJ, 600 nJ, 700 nJ, 800 nJ, 900 nJ, 1 microjoule (μJ), 2 μJ, 3 μJ, 4 μJ, 5 μJ, 6 μJ, 7 μJ, 8 μJ, 9 μJ, 10 μJ, 20 μJ, 30 μJ, 40 μJ, 50 μJ, 60 μJ, 70 μJ, 80 μJ, 90 The laser may emit light having a pulse energy of μJ, 100 μJ, 200 μJ, 300 μJ, 400 μJ, 500 μJ, 600 μJ, 700 μJ, 800 μJ, 900 μJ, at least 1 millijoule (mJ), 2 mJ, 3 mJ, 4 mJ, 5 mJ, 6 mJ, 7 mJ, 8 mJ, 9 mJ, 10 mJ, 20 mJ, 30 mJ, 40 mJ, 50 mJ, 60 mJ, 70 mJ, 80 mJ, 90 mJ, 100 mJ, 200 mJ, 300 mJ, 400 mJ, 500 mJ, 600 mJ, 700 mJ, 800 mJ, 900 mJ, at least 1 Joule (J), or more. The laser produces up to approximately 1J, 900mJ, 800mJ, 700mJ, 600mJ, 500mJ, 400mJ, 300mJ, 200mJ, 100mJ, 90mJ, 80mJ, 70mJ, 60mJ, 50mJ, 40mJ, 30mJ, 20mJ, 10mJ, 9mJ, 8mJ, 7mJ, 6mJ, 5mJ, 4mJ, 3mJ, 2mJ, 1mJ, 900μJ, 800μJ, 700μJ, 600μJ, 500μJ, 400μJ, 300μJ, 200μJ, 100μJ, 90μJ, 80μJ, 70μJ, 60μJ, 50μ In some embodiments, the laser may emit light having a pulse energy of 1 nJ, 40 μJ, 30 μJ, 20 μJ, 10 μJ, 9 μJ, 8 μJ, 7 μJ, 6 μJ, 5 μJ, 4 μJ, 3 μJ, 2 μJ, 1 μJ, 900 nJ, 800 nJ, 700 nJ, 600 nJ, 500 nJ, 400 nJ, 300 nJ, 200 nJ, 100 nJ, 90 nJ, 80 nJ, 70 nJ, 60 nJ, 50 nJ, 40 nJ, 30 nJ, 20 nJ, 10 nJ, 9 nJ, 8 nJ, 7 nJ, 6 nJ, 5 nJ, 4 nJ, 3 nJ, 2 nJ, 1 nJ, or less.The laser may emit light having a pulse energy within a range defined by any two of the above values.

[0186] In some cases, the laser has a power of at least about 1 microwatt (μW), 2 μW, 3 μW, 4 μW, 5 μW, 6 μW, 7 μW, 8 μW, 9 μW, 10 μW, 20 μW, 30 μW, 40 μW, 50 μW, 60 μW, 70 μW, 80 μW, 90 μW, 100 μW, 200 μW, 300 μW, 400 μW, 500 μW, 600 μW, 700 μW, 800 μW, 900 μW, 1 milliwatt (mW), 2 mW, 3 mW, 4 mW, 5 mW, 6 mW, 7 mW, 8 mW, 9 mW, 10 mW, 20 mW, 30 mW, 40 mW, The light may emit light having an average power of 50mW, 60mW, 70mW, 80mW, 90mW, 100mW, 200mW, 300mW, 400mW, 500mW, 600mW, 700mW, 800mW, 900mW, 1 Watt (W), 2W, 3W, 4W, 5W, 6W, 7W, 8W, 9W, 10W, 20W, 30W, 40W, 50W, 60W, 70W, 80W, 90W, 100W, 200W, 300W, 400W, 500W, 600W, 700W, 800W, 900W, 1,000W, or more. Lasers are available in a range of powers up to approximately 1,000W, 900W, 800W, 700W, 600W, 500W, 400W, 300W, 200W, 100W, 90W, 80W, 70W, 60W, 50W, 40W, 30W, 20W, 10W, 9W, 8W, 7W, 6W, 5W, 4W, 3W, 2W, 1W, 900mW, 800mW, 700mW, 600mW, 500mW, 400mW, 300mW, 200mW, 100mW, 90mW, 80mW, 70mW, 60mW, 50mW, 40mW, 30 The laser may emit light having an average power of 1000 μW, 20 mW, 10 mW, 9 mW, 8 mW, 7 mW, 6 mW, 5 mW, 4 mW, 3 mW, 2 mW, 1 mW, 900 μW, 800 μW, 700 μW, 600 μW, 500 μW, 400 μW, 300 μW, 200 μW, 100 μW, 90 μW, 80 μW, 70 μW, 60 μW, 50 μW, 40 μW, 30 μW, 20 μW, 10 μW, 9 μW, 8 μW, 7 μW, 6 μW, 5 μW, 4 μW, 3 μW, 2 μW, 1 μW, or more. The laser may emit light having a power within a range defined by any two of the above values.

[0187] In some cases, a laser may emit light comprising one or more wavelengths in the ultraviolet (UV), visible, or infrared (IR) portions of the electromagnetic spectrum. The laser may emit light comprising at least about 200 nm, 210 nm, 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, 370 nm, 380 nm, 390 nm, 400 nm, 410 nm, 420 nm, 430 nm, 440 nm, 450 nm, 460 nm, 470 nm, 480 nm, 490 nm, 500 nm, 510 nm, 520 nm, 530 nm, 540 nm, 550 nm, 560 nm, 570 nm, 580 nm, 590 nm, 600 nm, 610 nm, 620 nm, 630 nm, 640 nm, 650 nm, 660 nm, 670 nm, 680 nm, 690 nm, 700 nm, 710 nm, 720 nm, 730 nm, 740 nm, 750 nm, 760 nm, 770 nm, 780 nm, 790 nm, 800 nm, 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, nm, 540nm, 550nm, 560nm, 570nm, 580nm, 590nm, 600nm, 610nm, 620nm, 630nm, 640nm, 650nm, 660nm, 670nm, 680nm, 690nm, 700nm, 7 10nm, 720nm, 730nm, 740nm, 750nm, 760nm, 770nm, 780nm, 790nm, 800nm, 810nm, 820nm, 830nm, 840nm, 850nm, 860nm, 870nm, 880nm, 890nm, 900nm, 910nm, 920nm, 930nm, 940nm, 950nm, 960nm, 970nm, 980nm, 990nm, 1,000nm, 1,010nm, 1,020nm, 1,030nm, 1,040nm, 1,050nm, 1,060nm, 1,070nm, 1,080nm, 1,090nm, 1,100nm, 1,110nm, 1,120nm, 1,130nm, 1,140nm, 1,150nm, 1,160nm, 1,170nm, 1,1 The device may emit light containing one or more wavelengths of 80nm, 1,190nm, 1,200nm, 1,210nm, 1,220nm, 1,230nm, 1,240nm, 1,250nm, 1,260nm, 1,270nm, 1,280nm, 1,290nm, 1,300nm, 1,310nm, 1,320nm, 1,330nm, 1,340nm, 1,350nm, 1,360nm, 1,370nm, 1,380nm, 1,390nm, 1,400nm, or more.Lasers are available in wavelengths up to approximately 1,400nm, 1,390nm, 1,380nm, 1,370nm, 1,360nm, 1,350nm, 1,340nm, 1,330nm, 1,320nm, 1,310nm, 1,300nm, 1,290nm, 1,280nm, 1,270nm, 1,260nm, 1,250nm, 1,240nm, 1,230nm, 1,220nm, 1,210nm, 1,200nm, 1,190nm, 1,180nm, 1,170nm, 1,160nm, 1,150nm, 1,140nm, 1,130nm, 1,120nm, 1,110nm, 1,100nm, 1,090nm, 1,080nm, 1,070nm, 1,060nm, 1,050nm, 1,040nm, 1,030nm, 1 ,020nm, 1,010nm, 1,000nm, 990nm, 980nm, 970nm, 960nm, 950nm, 940nm, 930nm, 920nm, 910nm, 900nm, 890nm, 880nm, 870nm, 860nm , 850nm, 840nm, 830nm, 820nm, 810nm, 800nm, 790nm, 780nm, 770nm, 760nm, 750nm, 740nm, 730nm, 720nm, 710nm, 700nm, 690nm, 68 0nm, 670nm, 660nm, 650nm, 640nm, 630nm, 620nm, 610nm, 600nm, 590nm, 580nm, 570nm, 560nm, 550nm, 540nm, 530nm, 520nm, 510nm, The laser may emit light comprising one or more wavelengths of 500 nm, 490 nm, 480 nm, 470 nm, 460 nm, 450 nm, 440 nm, 430 nm, 420 nm, 410 nm, 400 nm, 390 nm, 380 nm, 370 nm, 360 nm, 350 nm, 340 nm, 330 nm, 320 nm, 310 nm, 300 nm, 290 nm, 280 nm, 270 nm, 260 nm, 250 nm, 240 nm, 230 nm, 220 nm, 210 nm, 200 nm. The laser may emit light comprising one or more wavelengths within a range defined by any two of the above values.

[0188] In some cases, the laser has a power of at least about 1×10 -15 nm, 2 × 10 -15 nm, 3 × 10-15 nm, 4×10 -15 nm, 5×10 -15 nm, 6×10 -15 nm, 7×10 -15 nm, 8×10 -15 nm, 9×10 -15 nm, 1×10 -14 nm, 2×10 -14 nm、3×10 -14 nm, 4×10 -14 nm, 5×10 -14 nm, 6×10 -14 nm, 7×10 -14 nm, 8×10 -14 nm, 9×10 -14 nm, 1×10 -13 nm, 2×10 -13 nm、3×10 -13 nm, 4×10 -13 nm, 5×10 -13 nm, 6×10 -13 nm, 7×10 -13 nm, 8×10 -13 nm, 9×10 -13 nm, 1×10 -12 nm, 2×10 -12 nm, 3×10 -12 nm, 4×10 -12 nm, 5×10 -12 nm, 6×10 -12 nm, 7×10 -12 nm, 8×10 -12 nm, 9×10 -12 nm, 1×10 -11 nm, 2×10 -11 nm, 3×10 -11 nm, 4×10 -11 nm, 5×10 -11 nm, 6×10 -11 nm, 7×10 -11 nm, 8×10 -11 nm, 9×10 -11 nm, 1×10 -10 nm, 2×10 -10 nm, 3×10 -10 nm, 4×10 -10 nm, 5×10 -10 nm, 6×10 -10 nm, 7×10 -10 nm, 8×10-10 nm, 9×10 -10 nm, 1×10 -9 nm, 2×10 -9 nm, 3×10 -9 nm, 4×10 -9 nm, 5×10 -9 nm, 6×10 -9 nm, 7×10 -9 nm, 8×10 -9 nm, 9×10 -9 nm, 1×10 -8 nm, 2×10 -8 nm, 3×10 -8 nm, 4×10 -8 nm, 5×10 -8 nm, 6×10 -8 nm, 7×10 -8 nm, 8×10 -8 nm, 9×10 -8 nm, 1×10 -7 nm, 2×10 -7 nm, 3×10 -7 nm, 4×10 -7 nm, 5×10 -7 nm, 6×10 -7 nm, 7×10 -7 nm, 8×10 -7 nm, 9×10 -7 nm, 1×10 -6 nm, 2×10 -6 nm, 3×10 -6 nm, 4×10 -6 nm, 5×10 -6 nm, 6×10 -6 nm, 7×10 -6 nm, 8×10 -6 nm, 9×10 -6 nm, 1×10 -5 nm, 2×10 -5 nm, 3×10 -5 nm, 4×10 -5 nm, 5×10 -5 nm, 6×10 -5 nm, 7×10 -5 nm, 8×10 -5 nm, 9×10 -5 nm, 1×10 -4 nm, 2×10 -4 nm, 3×10 -4 nm, 4×10-4 nm, 5 × 10 -4 nm, 6 × 10 -4 nm, 7 × 10 -4 nm, 8 × 10 -4 nm, 9 × 10 -4 nm, 1 × 10 -3 Lasers can emit light with bandwidths up to about 1×10 -3 nm, 9 × 10 -4 nm, 8 × 10 -4 nm, 7 × 10 -4 nm, 6 × 10 -4 nm, 5 × 10 -4 nm, 4 × 10 -4 nm, 3 × 10 -4 nm, 2 × 10 -4 nm, 1 × 10 -4 nm, 9 × 10 -5 nm, 8 × 10 -5 nm, 7 × 10 -5 nm, 6 × 10 -5 nm, 5 × 10 -5 nm, 4 × 10 -5 nm, 3 × 10 -5 nm, 2 × 10 -5 nm, 1 × 10 -5 nm, 9 × 10 -6 nm, 8 × 10 -6 nm, 7 × 10 -6 nm, 6 × 10 -6 nm, 5 × 10 -6 nm, 4 × 10 -6 nm, 3 × 10 -6 nm, 2 × 10 -6 nm, 1 × 10 -6 nm, 9 × 10 -7 nm, 8 × 10 -7 nm, 7 × 10 -7 nm, 6 × 10 -7 nm, 5 × 10 -7 nm, 4 × 10 -7 nm, 3 × 10 -7 nm, 2 × 10 -7 nm, 1 × 10 -7 nm, 9 × 10 -8 nm, 8 × 10 -8 nm, 7 × 10 -8 nm, 6 × 10 -8 nm, 5 × 10-8 nm, 4×10 -8 nm, 3×10 -8 nm, 2×10 -8 nm, 1×10 -8 nm, 9×10 -9 nm, 8×10 -9 nm, 7×10 -9 nm, 6×10 -9 nm, 5×10 -9 nm, 4×10 -9 nm, 3×10 -9 nm, 2×10 -9 nm, 1×10 -9 nm, 9×10 -10 nm, 8×10 -10 nm, 7×10 -10 nm, 6×10 -10 nm, 5×10 -10 nm, 4×10 -10 nm, 3×10 -10 nm, 2×10 -10 nm, 1×10 -10 nm, 9×10 -11 nm, 8×10 -11 nm, 7×10 -11 nm, 6×10 -11 nm, 5×10 -11 nm, 4×10 -11 nm, 3×10 -11 nm, 2×10 -11 nm, 1×10 -11 nm, 9×10 -12 nm, 8×10 -12 nm, 7×10 -12 nm, 6×10 -12 nm, 5×10 -12 nm, 4×10 -12 nm, 3×10 -12 nm, 2×10 -12 nm, 1×10 -12 nm, 9×10 -13 nm, 8×10 -13 nm, 7×10 -13 nm, 6×10 -13 nm, 5×10 -13 nm, 4×10 -13 nm, 3×10 -13 nm, 2×10 -13 nm, 1×10 -13 nm, 9×10-14 nm, 8 × 10 -14 nm, 7 × 10 -14 nm, 6 × 10 -14 nm, 5 × 10 -14 nm, 4 × 10 -14 nm, 3 × 10 -14 nm, 2 × 10 -14 nm, 1 × 10 -14 nm, 9 × 10 -15 nm, 8 × 10 -15 nm, 7 × 10 -15 nm, 6 × 10 -15 nm, 5 × 10 -15 nm, 4 × 10 -15 nm, 3 × 10 -15 nm, 2 × 10 -15 nm, 1 × 10 -15 A laser may emit light having a bandwidth of 1000 nm or less. A laser may emit light having a bandwidth within a range defined by any two of the above values.

[0189] Specific Definitions and Considerations 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, the singular forms "a," "an," and "the" include the plural forms unless the context clearly dictates otherwise. As used herein, the term "or" is intended to include "and / or" unless otherwise indicated.

[0190] When the term "at least," "greater than," or "greater than or equal to" appears before the first number in a sequence of two or more numbers, the term "at least," "greater than," or "greater than or equal to" applies to each number in that sequence. For example, 1, 2, or 3 or more is equivalent to 1 or more, 2 or more, or 3 or more.

[0191] When the term "not greater than," "less than," or "less than or equal to" appears before the first number in a sequence of two or more numbers, the term "not greater than," "less than," or "less than or equal to" applies to each number in that sequence. For example, 3, 2, or 1 or less is equivalent to 3 or less, 2 or less, or 1 or less.

[0192] When values ​​are described as ranges, it will be understood that such disclosure includes all possible subranges within such ranges, as well as specific numerical values ​​falling within such ranges, whether or not a specific numerical value or specific subrange is explicitly stated.

[0193] As used herein, like numbers refer to like elements.

[0194] The terms "about" or "approximately" can mean within an acceptable error range for a particular value, which range depends in part on how the value is measured or determined, e.g., the limitations of the measurement system. For example, "about" can mean within one standard deviation or more, as is customary in the art. Alternatively, "about" can mean within a range of up to 20%, up to 10%, up to 5%, or up to 1% of a given value. When a particular value is described in the application and claims, unless otherwise specified, the term "about" is assumed to mean within an acceptable error range for that particular value.

[0195] As used herein, the terms "nonclassical computation," "nonclassical procedure," "nonclassical process," or "nonclassical computer" refer generally to any method, system, or computer-readable medium for performing a computational procedure that goes beyond the paradigm of classical computation. Nonclassical computation, a nonclassical procedure, a nonclassical process, or a nonclassical computer may include quantum computation, a quantum procedure, a quantum process, or a quantum computer.

[0196] As used herein, the terms “quantum computation,” “quantum procedure,” “quantum process,” and “quantum computer” generally refer to a method, system, or computer-readable medium for performing computations using quantum mechanical processes (e.g., unitary transformations and completely positive trace-preserving (CPTP) maps on quantum channels) on a Hilbert space represented by a quantum device. Thus, quantum computation and classical (or digital) computation may be similar in the following respects: both computations may involve a sequence of instructions performed on input information and then provide an output. Various paradigms of quantum computing may decompose a quantum process into a sequence of elementary quantum processes that simultaneously operate on a subset of qubits of a quantum device. Quantum processes may be selected based on, for example, their locality or ease of physical implementation. Thus, a quantum procedure or quantum computation may consist of a sequence of instructions that may represent different quantum evolutions on a quantum device in various applications. For example, procedures for calculating or simulating quantum chemistry can use qubits (e.g., two-level quantum systems) and universal quantum gate sets (e.g., Hadamard, controlled-NOT (CNOT), π / 8 rotation) to represent quantum states and electron spin-orbit annihilation and creation operators through the so-called Jordan-Wigner or Blaviy-Kitaev transformations.

[0197] Further examples of quantum procedures or quantum computations may include optimization procedures such as quantum approximate optimization algorithms (QAOA) and quantum minimum searches. QAOA may involve performing single-qubit rotations and multi-qubit entanglement gates. Quantum adiabatic computation may direct the probabilistic or non-probabilistic path of evolution from an initial quantum system to a final quantum system.

[0198] Quantum-inspired procedures may include simulated annealing, parallel tempering, master equation solvers, Monte Carlo procedures, etc. Quantum-classical or hybrid algorithms and procedures may include procedures such as variational quantum eigensolvers (VQEs) and variational and adiabatically navigated quantum eigensolvers (VanQver).

[0199] The quantum computer may include one or more of an adiabatic quantum computer, a quantum gate array, a one-way quantum computer, a topological quantum computer, a quantum Turing machine, a quantum annealing device, an Ising solver, or a gate model of quantum computing.

[0200] As used herein, the term "adiabatic" refers to any process taking place on a quantum mechanical system in which the parameters of the Hamiltonian change slowly compared to the timescale of the system's natural evolution.

[0201] As used herein, "non-adiabatic" refers to any process taking place on a quantum mechanical system in which the parameters of the Hamiltonian change rapidly compared to the time scale of the system's natural evolution or change on a time scale similar to the time scale of the system's natural evolution.

[0202] Computer Systems In another aspect, a system for state detection for non-classical computation is provided, the system including: one or more optical trapping units configured to obtain an array of spatially distinct optical trapping sites, the array including a first plurality of qubits; one or more non-classical computation units configured to perform a non-classical computation using at least a portion of the first plurality of qubits; one or more electromagnetic delivery units configured to expose a second plurality of qubits to radiation, the first plurality of qubits including the second plurality of qubits; and one or more measurement units configured to determine or predict that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based at least in part on at least one of the second plurality of qubits fluorescing in response to exposure to the radiation.

[0203] 6 illustrates a computer system 601 programmed or configured to perform any of the methods, systems, computer-readable media, processes, or techniques described herein (such as the systems, methods, computer-readable media, or techniques for state-resolved imaging of non-destructive atomic qubits described herein). The computer system 601 can control various aspects of the present disclosure. The computer system 601 can be a user's electronic device or a computer system located remotely relative to the electronic device. The electronic device can be a mobile electronic device.

[0204] Computer system 601 includes a central processing unit (CPU, also referred to herein as a “processor” and a “computer processor”) 605, which may be a single-core processor or a multi-core processor, or multiple processors for parallel processing. Computer system 601 also includes memory or memory locations 610 (e.g., random access memory, read-only memory, flash memory), an electronic storage unit 615 (e.g., a hard disk), a communication interface 620 (e.g., a network adapter) for communicating with one or more other systems, and peripherals 625, such as cache, other memory, data storage, and / or an electronic display adapter. Memory 610, storage unit 615, interface 620, and peripherals 625 communicate with CPU 605 via a communication bus (solid lines), such as a motherboard. Storage unit 615 may be a data storage unit (or data repository) for storing data. Computer system 601 may be operatively connected to a computer network (“network”) 630 via communication interface 620. Network 630 may be the Internet, an Internet and / or extranet, or an intranet and / or extranet in communication with the Internet. Network 630 may, in some cases, be a telecommunications network and / or a data network. Network 630 may include one or more computer servers that enable distributed computing, such as cloud computing. Network 630 may, in some cases, implement a peer-to-peer network via computer system 601, which may enable devices connected to computer system 601 to function as clients or servers.

[0205] The CPU 605 may execute a series of machine-readable instructions, which may be embodied as a program or software. These instructions may be stored in a memory location, such as the memory 610. These instructions may be sent to the CPU 605, which may then program or configure the CPU 605 to perform the methods of the present disclosure. Examples of operations performed by the CPU 605 may include fetching, decoding, executing, and writing back.

[0206] The CPU 605 may be part of a circuit, such as an integrated circuit. One or more other components of the system 601 may be included in this circuit. In some cases, this circuit is an application specific integrated circuit (ASIC).

[0207] Storage unit 615 may store files such as drivers, libraries, and saved programs. Storage unit 615 may store user data (e.g., user settings and user programs). Computer system 601 may include one or more additional data storage units that are external to computer system 601, such as located on a remote server that communicates with computer system 601 via an intranet or the Internet.

[0208] Computer system 601 can communicate with one or more remote computer systems via network 630. For example, computer system 601 can communicate with a user's remote computer system. Examples of remote computer systems can include a personal computer (e.g., a portable PC), a slate or tablet PC (e.g., an Apple® iPad®, a Samsung® Galaxy Tab), a telephone, a smartphone (e.g., an Apple® iPhone®, an Android®-enabled device, a Blackberry®), or a personal digital assistant. A user can access computer system 601 via network 630.

[0209] The methods described herein may be implemented by machine (e.g., computer processor) executable code stored in an electronic storage location (e.g., memory 610 or electronic storage unit 615) of computer system 601. This machine-executable or machine-readable code may be provided in the form of software. In use, the code is executed by processor 605. In some cases, the code may be retrieved from storage unit 615 and stored in memory 610 for easy access by processor 605. In some cases, electronic storage unit 615 is eliminated, and machine-executable instructions are stored in memory 610.

[0210] The code may be pre-compiled and configured for use on a machine having a processor adapted to execute the code, or it may be compiled at run time. The code may be provided in a selectable programming language so that it can be executed in a pre-compiled or compiled state.

[0211] In another aspect, a non-transitory computer-readable medium is provided that includes machine-executable code, the one or more instructions, that, when executed, perform a method for performing state detection for non-classical computation on a non-classical computer configured to execute the one or more instructions, the method including: (a) obtaining a first plurality of qubits in an array of spatially distinct optical trapping sites; (b) performing a non-classical computation using at least a portion of the first plurality of qubits; (c) exposing a second plurality of qubits to radiation, the first plurality of qubits including the second plurality of qubits; and (d) determining or predicting that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based at least in part on at least one of the second plurality of qubits fluorescing in response to exposure to the radiation.

[0212] Aspects of the systems and methods provided herein, such as computer system 601, can be embodied through programming. Various aspects of the present technology may be thought of as a "product" or "article of manufacture" typically held or embodied on some type of machine-readable medium in the form of machine (or processor) executable code and / or associated data. The machine-executable code may be stored in an electronic storage unit, such as memory (e.g., read-only memory, random-access memory, flash memory) or a hard disk. "Storage" type media may include any or all of the tangible memory of a computer, processor, etc., or their associated modules (such as various semiconductor memories, tape drives, disk drives, etc.) that may provide non-transitory storage for software programming at any time. All or portions of the software may be communicated over the Internet or various other telecommunications networks. Such communication may, for example, enable the software to be loaded from one computer or processor to another, e.g., from a management server or host computer to an application server computer platform. Thus, other types of media that may carry software elements include optical, electrical, and electromagnetic waves, such as those used on physical interfaces between local devices, wired and optical fixed line networks, and various wireless links. Physical elements that carry such waves, such as wired or wireless links, optical links, etc., may also be considered media that carry software. As used herein, terms such as computer or "machine-readable medium" refer to any medium that participates in providing instructions to a processor for execution, unless limited to non-transitory, tangible "storage" media.

[0213] Thus, a machine-readable medium such as computer-executable code (e.g., computer-readable medium) may take many forms, including, but not limited to, tangible storage media, carrier wave media, or physical transmission media. Non-volatile storage media include, for example, optical or magnetic disks, such as any of the storage devices of any computer, such as may be used to implement the illustrated databases, etc. Volatile storage media include dynamic memory, such as the main memory of such a computer platform. Tangible transmission media include coaxial cables, copper wire, and fiber optics (including the wires that comprise a bus within a computer system). Carrier-wave transmission media may take the form of electric or electromagnetic signals, or acoustic or light waves, such as those generated during radio frequency (RF) or infrared (IR) data communications. Thus, common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, other magnetic media, CD-ROMs, DVDs or DVD-ROMs, other optical media, punch cards, paper tape, other physical storage media with patterns of holes, RAM, ROM, PROMs, and EPROMs, FLASH-EPROMs, other memory chips or cartridges, carrier waves carrying data or instructions, cables or links carrying such carrier waves, or other media 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.

[0214] The computer system 601 may include or be in communication with an electronic display 635 that has a user interface (UI) 640. Examples of a UI include, but are not limited to, a graphical user interface (GUI) and a web-based user interface.

[0215] The methods and systems of the present disclosure may be implemented by one or more algorithms, which may be implemented by software executed by the central processing unit 605.

[0216] Specific References This disclosure incorporates the following references for all purposes: (A) M. Martinez-Dorantes et al., "Fast Nondestructive Parallel Readout of Neutral Atom Registers in Optical Potentials," Phys. Rev. Lett. Vol. 119, Issue 18 (2017); (B) Minho Kwon et al., "Parallel low-loss measurement of multiple atomic qubits." University of Wisconsin-Madison, Department of Physics (2018); (C) Margaret E. Shea et al., "Sub-ms, nondestructive, time-resolved quantum-state readout of a single, trapped neutral atom," Phys. Rev. A 102, 053101 (2020); (D) Christopher Monroe et al., "Adaptive and optimal imaging of quantum optical systems for quantum computing," University of Maryland, College Park, U.S. Patent No. 11,262,785; (E) U.S. Patent No. 11,875,227; and (F) Manorcia et al., " 171 Mid-circuit qubit measurement and rearrangement in a Yb atomic array 171"Yb atomic array" arXiv e-prints (2023); (G) Alec Jenkins et al., "Ytterbium Nuclear-Spin Qubits in an Optical Tweezer Array" University of Colorado, National Institute of Standards and Technology, and University of Colorado Department of Physics (2022).

[0217] While preferred embodiments of the present invention have been shown and described herein, it will be apparent to those skilled in the art that these embodiments are illustrative only. It is not intended that the present invention be limited by the specific examples provided herein. While the present invention has been described with reference to the above specification, the description and illustration of the embodiments herein are not meant to be construed in a limiting sense. Numerous variations, changes, and substitutions will occur to those skilled in the art without departing from the invention. Furthermore, it should be understood that all aspects of the present invention are not limited to the specific depictions, configurations, or relative proportions set forth herein, which depend upon a variety of conditions and variables. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in practicing the present invention. Accordingly, it is intended that the present invention encompass all such alternatives, modifications, variations, or equivalents. The following claims define the scope of the present invention, and it is intended that methods and structures within the scope of these claims and their equivalents be covered thereby. [Example]

[0218] Example 1: Simulation of state-resolved imaging infidelity Figure 7 shows a simulation of the state-resolved imaging infidelity as a function of Δ in the two-level system shown in Figure 2. In the simulation, the excited states are 171 Yb 3 P1, 1The states of the S0 manifold are used as the states of the qubit. In some cases, Γ is the spontaneous decay rate, δ is the detuning between the energy level and the pump laser light, and Ω is the Rabi frequency.

[0219] Figure 8 shows another example of state-resolved imaging infidelity as a function of magnetic field in the two-level system shown in Figure 2. In the simulation, the excited state is 171 Yb 3 P1, 1 The state of the S0 manifold is used as the state of the qubit.

[0220] In some cases, the photon emission rate from the excited state is given by Equation 1:

[0221]

number

[0222]

number

[0223]

number

[0224]

number

[0225]

number

[0226] In some cases, assuming ε=0.01 and s=1, the state-resolved imaging infidelity may be calculated or determined as a function of Δ, as shown in Figure 7. In Figure 8, the excited states 171 Yb 3 P1, as the qubit state 1 For S0, the state-resolved imaging infidelity is shown as a function of the B-field. In some cases, ε can be chosen to be 0.01, taking into account the photon collection efficiency of the imaging system. In some cases, ε can be chosen to be 0.001, resulting in approximately 10 photons being collected by the camera, which reduces the photon distribution infidelity to, for example, 1 × 10 -5 can be reduced to below

[0227] Example 2: Experimental Results The experimental system comprised two main vacuum regions (the "MOT chamber" and the "science chamber") connected by a differential pumping tube. Atoms were pumped from a pre-cooled atomic beam into a two-stage magnetic optical trap (at 399 nm) in the MOT chamber. 1 P1 transition followed by 556 nm 3 The atoms were then loaded into an optical lattice formed using 532 nm light and transported vertically 30 cm into a scientific chamber.

[0228] To achieve deep lattices in a power-efficient manner, the waist of the transport beam was moved synchronously with the optical lattice by shifting the positions of two focusing lenses, one for each of the two counterpropagating beams forming the lattice. The alignment between the two beams was actively maintained using a closed-loop piezoelectric steering mirror. Atoms were transported to the optical tweezers array by superimposing the atoms on the optical tweezers array, gradually increasing the power of the optical tweezers, and then gradually decreasing the power of the transport lattice. This resulted in a typical occupancy of a few atoms per optical tweezers. No dissipation occurred during the transport of atoms from the transport lattice to the optical tweezers.

[0229] The two-chamber design allows for a time-static magnetic field. Because the magnetic field did not change during any experimental (e.g., non-classical) sequence, it is possible to simultaneously maintain the magnetic field gradient for MOT formation and a large, uniform bias field in the scientific region while avoiding the time delays associated with switching. The two-stage MOT operates with a constant magnetic field gradient of approximately 18 Gauss / cm in the high-field direction.

[0230] After loading the atoms into the tweezers, m f Using the same parameters used to image the qubit state, the tweezers illuminated the sample with light, inducing light-assisted collisions and projecting them onto a single atom. 1 S0, m f =-1 / 2 3 P1, m f A second tone, corresponding to the transition to m = 1 / 2, is applied, and all atoms are f =1 / 2 state.

[0231] FIG. 5B (bottom) shows experimental data showing two successive single-shot images of a fully filled 10×3 atomic array produced by an example of the methods and systems disclosed herein.

[0232] Table 1, for example, shows imaging errors measured for a base condition with no hidden light applied and for data and ancillary qubits with shielding light applied to the data qubits at a predetermined wavelength. The shielding procedure may be similar to that disclosed in commonly owned International Application PCT / US2023 / 026730, which is incorporated herein by reference for all purposes. The uncertainty may represent the Wilson score interval, and Table 1 shows only the larger direction for visual clarity. Results may be averaged over a 10 × 7 site array. As shown in Table 1, the methods described herein may include characterizing imaging in terms of the precision with which the atom states can be distinguished, the probability of leakage to other qubit states during imaging, and the probability of atom loss. To measure loss from the imaged state, the methods described herein may include repeated imaging and fitting an exponential decay to the measured occupancy. In some cases, the apparent loss from the imaged state may include loss of atoms from traps and transitions to other unmeasured states, including the states of other qubits. The methods described herein may include estimating distinguishability based on the overlap of a double Gaussian function on a count histogram obtained from stochastically occupied sites. In some cases, to characterize the population leakage rate (which may be much smaller than the loss rate) during imaging, the methods described herein may include (i) preparing atoms in one of the qubit states, (ii) pre-imaging the states, and (iii) performing "dummy imaging" of each state. In (ii), this pre-imaging may be possible after selection at occupied sites, since the array may be stochastically loaded for these measurements. In (iii), performing "dummy imaging" may include using default imaging intensity and detuning, but for a longer period selected to strengthen the signal against statistical or systematic readout errors. In some cases, the methods described herein may include imaging the population of one of the qubit states to estimate population shifts.The value can be estimated by dividing the measured collective movement by the ratio of the length of the dummy image to a default value (e.g., 5 ms). Further details on how to determine the error or source of error are provided elsewhere herein.

[0233] [Table 1]

[0234] The largest error channel can be the loss of the imaged state, as shown in Table 1. In some cases, in the range of sufficiently low scattering rates, the methods described herein achieve a regime where the probability of loss is proportional to the number of collected photons, e.g., about 4 × 10 per scattered photon. -6 per collected photon, which can correspond to -4 In some cases, about half of this loss is due to trapped light in traps about 350 microkelvin (μK) deep. 3 This loss mechanism may be explained by the expected Raman scattering from P1. In some cases, this loss mechanism may be due to the need to 1) operate with shallower traps and image slower, or 2) sacrifice state selectivity to allow for metastable 3 P0 and 3 The loss can be eliminated by repumping from the P2 state. In some cases, additional loss in this region can be caused by photoionization. In some cases, at high scattering rates, which may correspond to multiple scattering events per trapping period, the loss probability can increase sharply, which can be due to heating of the atoms. In some cases, the methods described herein can include using operating conditions with scattering rates just below the occurrence of this additional loss.

Claims

1. 1. A method for state detection for non-classical computation, comprising: (a) acquiring a first plurality of qubits within an array of spatially distinct optical trapping sites; (b) performing one or more qubit gate operations on at least a portion of the first plurality of qubits; (c) performing a measurement operation, the measurement operation including exposing a second plurality of qubits to electromagnetic energy, the first plurality of qubits including the second plurality of qubits, the electromagnetic energy configured to selectively drive one qubit of the second plurality of qubits from an initial state to an excited state in the presence of an applied magnetic field, the selectivity of the transition to the excited state being based at least in part on the strength of the applied magnetic field to the first plurality of qubits, the second plurality of qubits, or both; (d) determining that the quantum bit was in the initial state, said determining being based at least in part on the quantum bit returning to the initial state by emitting a photon in response to the electromagnetic energy in (c); A method comprising:

2. The method of claim 1 , further comprising repeating (c) through (d) multiple times.

3. The method of claim 1 , wherein the returning to the initial state by emitting a photon is a fluorescence transition.

4. 10. The method of claim 1, wherein the return to the initial state is from a manifold of excited states, and the strength of the applied magnetic field determines a separation between states in the manifold of excited states.

5. The method of claim 4 , wherein the separation between the states determines which states are resonant with the radiation.

6. 5. The method of claim 4, wherein transitions through the manifold of excited states to a single state are allowed by a selection rule for the state of each qubit.

7. 10. The method of claim 1 , wherein (c) comprises exposing a first subset of the second plurality of qubits to a first electromagnetic energy and then exposing a second subset of the second plurality of qubits to a second electromagnetic energy.

8. The method of claim 7 , wherein the first electromagnetic energy comprises a first polarization and the second electromagnetic energy comprises a second polarization.

9. (e) determining that the first subset of the second plurality of qubits fluoresces in response to exposure to a first radiation and that the second subset of the second plurality of qubits fluoresces in response to exposure to a second radiation.

9. The method of claim 7 or 8, further comprising:

10. (f) determining, based at least in part on determining in (e), that a plurality (n) of spatially distinct optical trapping sites in the array of spatially distinct optical trapping sites are absent of a qubit. The method of claim 5 further comprising:

11. 11. The method of claim 10, wherein the first plurality of qubits has up to n more qubits than the second plurality of qubits.

12. The method of claim 1 , wherein the electromagnetic energy is polarized.

13. 13. The method of any one of claims 8 to 10 or 12, wherein one or more of the electromagnetic energy, the first electromagnetic energy, or the second electromagnetic energy is circularly polarized.

14. The qubit is in a first state [Equation 1] and the second state [Equation 2] The method according to any one of claims 1 to 13, comprising:

15. The initial state is [Equation 3] The method of claim 14, wherein

16. The initial state is [Equation 4] The method of claim 14, wherein

17. The method of any preceding claim, wherein the first plurality of qubits comprises neutral atoms.

18. The method of claim 17 , wherein the neutral atoms comprise Group 2 elements.

19. 19. The method of claim 18, wherein the Group 2 element is strontium.

20. 18. The method of claim 17, wherein the neutral atoms include rubidium or cesium.

21. The method of claim 17 , wherein the neutral atoms include ytterbium.

22. The method of any preceding claim, wherein the qubit has a temperature of up to 10 microkelvin (μK).

23. The method of any one of claims 1 to 22, wherein the array is two-dimensional.

24. The method of any one of claims 1 to 23, wherein the array is three-dimensional.

25. The method of claim 1 , wherein the transition is a cycle transition.

26. The state of the quantum bit is a first state [Equation 5] and the second state [Equation 6] wherein the excited state comprises a manifold of excited states, and a transition between the first state in the manifold and the second state in the manifold comprises two closed two-level systems.

27. 27. The method of claim 26, wherein the state of the qubit is identified as either the first state or the state by the emission of the photon or by the absence of the emission of the photon.

28. The method of claim 1 , wherein the returning to the initial state comprises spontaneous emission and the returning to the initial state comprises stimulated emission.

29. The method of claim 1 , further comprising, prior to (c), adjusting the strength of the applied magnetic field to a selected measurement condition.

30. The method of claim 1 , wherein (d) comprises imaging the photons with a measurement unit.

31. The method of claim 1 , wherein (c) through (d) are configured to perform an atomic cooling process.

32. 1. A system for state detection for non-classical computation, comprising: one or more optical trapping units configured to obtain an array of spatially distinct optical trapping sites, the array including a first plurality of qubits; one or more non-classical computation units configured to perform non-classical computation using at least a portion of the first plurality of qubits; one or more electromagnetic delivery units configured to expose a second plurality of qubits to radiation, the first plurality of qubits comprising the second plurality of qubits; and one or more measurement units configured to determine or predict that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based at least in part on at least one of the second plurality of qubits fluorescing in response to exposure to the radiation; A system comprising:

33. 1. A non-transitory computer-readable medium comprising machine-executable code including one or more instructions that, when executed, perform a method for state detection for non-classical computation on a non-classical computer, the non-classical computer being configured to execute the one or more instructions, the method comprising: (a) acquiring a first plurality of qubits within an array of spatially distinct optical trapping sites; (b) performing a non-classical computation using at least a portion of the first plurality of qubits; and (c) exposing a second plurality of qubits to radiation, the first plurality of qubits comprising the second plurality of qubits; (d) determining or predicting that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based at least in part on at least one of the second plurality of qubits fluorescing in response to exposure to the radiation; a non-transitory computer-readable medium,

34. 1. A method for state detection for non-classical computation, comprising: (a) acquiring a first plurality of qubits within an array of spatially distinct optical trapping sites; (b) performing a non-classical computation using at least a portion of the first plurality of qubits; and (c) exposing a second plurality of qubits to radiation, the first plurality of qubits comprising the second plurality of qubits; (d) determining or predicting that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based at least in part on at least one of the second plurality of qubits fluorescing in response to exposure to the radiation; A method comprising:

35. 35. The method of claim 34, wherein exposing the second plurality of qubits to the radiation comprises exposing the second plurality of qubits to a first radiation and then exposing the second plurality of qubits to a second radiation.

36. 36. The method of claim 35, wherein the first radiation is a first light having a first polarization and the second radiation is a second light having a second polarization.

37. (e) determining that the first subset of the second plurality of qubits fluoresces in response to being exposed to the first radiation, and that the second subset of the second plurality of qubits fluoresces in response to being exposed to the second radiation.

37. The method of claim 35 or 36, further comprising:

38. (f) determining that a plurality (n) of spatially distinct optical trapping sites in the array of spatially distinct optical trapping sites are absent of a qubit based at least in part on determining that the first subset of the second plurality of qubits fluoresces in response to exposure to the first radiation and that the second subset of the second plurality of qubits fluoresces in response to exposure to the second radiation in (e).

38. The method of claim 37, further comprising:

39. 39. The method of claim 38, wherein the first plurality of qubits has up to n more qubits than the second plurality of qubits.

40. 35. The method of claim 34, wherein the radiation is light.

41. 41. The method of claim 40, wherein the light is polarized.

42. 42. The method of any one of claims 36 to 38 or 41, wherein one or more of the polarized light, the first light, or the second light is circularly polarized.

43. 43. The method of any one of claims 1 to 42, wherein the second plurality of qubits is exposed to the radiation while the second plurality of qubits is in a magnetic field.

44. 44. The method of any one of claims 1 to 43, wherein at least one of the second plurality of qubits that fluoresces in response to exposure to the radiation is the first subset of the second plurality of qubits.

45. The first state is [Equation 7] and the second state is [Equation 8] 45. The method of claim 44, wherein:

46. The first state is [Equation 9] and the second state is [Equation 10] 45. The method of claim 44, wherein:

47. 47. The method of any one of claims 1 to 46, wherein the first plurality of qubits comprises neutral atoms.

48. 48. The method of claim 47, wherein the neutral atom comprises a Group 2 element.

49. 49. The method of claim 48, wherein the Group 2 element is strontium.

50. 48. The method of claim 47, wherein the neutral atoms include ytterbium.

51. 51. The method of any preceding claim, wherein the qubit has a temperature of up to 10 microkelvin (μK).

52. The method of any one of claims 1 to 51, wherein the array is two-dimensional.

53. The method of any one of claims 34 to 52, wherein the array is three-dimensional.

54. 1. A system for state detection for non-classical computation, comprising: one or more optical trapping units configured to obtain an array of spatially distinct optical trapping sites, the array including a first plurality of qubits; one or more non-classical computation units configured to perform non-classical computation using at least a portion of the first plurality of qubits; one or more electromagnetic delivery units configured to expose a second plurality of qubits to radiation, the first plurality of qubits comprising the second plurality of qubits; and one or more measurement units configured to determine or predict that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based at least in part on at least one of the second plurality of qubits fluorescing in response to exposure to the radiation; A system comprising:

55. 1. A non-transitory computer-readable medium comprising machine-executable code including one or more instructions that, when executed, perform a method for state detection for non-classical computation on a non-classical computer, the non-classical computer being configured to execute the one or more instructions, the method comprising: (a) acquiring a first plurality of qubits within an array of spatially distinct optical trapping sites; (b) performing a non-classical computation using at least a portion of the first plurality of qubits; and (c) exposing a second plurality of qubits to radiation, the first plurality of qubits comprising the second plurality of qubits; (d) determining or predicting that a first subset of the second plurality of qubits is in a first state and a second subset of the second plurality of qubits is in a second state based at least in part on at least one of the second plurality of qubits fluorescing in response to exposure to the radiation; a non-transitory computer-readable medium,

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