Continuous reloading of atomic qubits including two optical conveyor belts

Abstract

Devices and methods for reloading atomic qubits into a quantum computer via two optical conveyor belts are provided.

Description

HQU-01825 HU 9844 CONTINUOUS RELOADING OF ATOMIC QUBITS INCLUDING TWO OPTICAL CONVEYOR BELTS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No.63 / 772,191, filed March 14, 2025 and U.S. Provisional Application No.63 / 656,377 filed on June 5, 2024, which are each hereby incorporated by reference in their entirety. BACKGROUND

[0002] Embodiments of the present disclosure relate to quantum computers, and more specifically, to continuous reloading of atomic qubits including via two optical conveyor belts. BRIEF SUMMARY

[0003] In various embodiments, devices for moving atoms are provided, comprising: an atom reservoir, configured to generate a cloud of atoms; a computation chamber, comprising an active zone configured to hold an array of atoms and adapted to perform quantum gates thereon; a differential vacuum tube operably connected to the atom reservoir and the computation chamber; at least one laser source configured to generate a first beam having a first frequency and a second beam having a second frequency; a first optical lattice generator configured to generate a first optical lattice based on the first beam, the first optical lattice generator adapted to detune the first frequency; and a second optical lattice generator configured to generate a second optical lattice based on the second beam, the second optical lattice generator adapted to detune the second frequency. The first optical lattice extends from the atom reservoir, through the differential vacuum tube, and into the computation chamber without passing through the active zone. The second optical lattice extends from the differential vacuum tube to the computational chamber, passing through the active zone. The first and the second optical lattices intersect, thereby forming a handover region.HQU-01825 HU 9844

[0004] In some embodiments, the device further comprises a magneto-optical trap adapted to trap atoms within the atom reservoir, and to load the atoms into the first optical lattice.

[0005] In some embodiments, each of the first and the second optical lattice generators comprises a retroreflector and an acousto-optical modulator.

[0006] In some embodiments, the device further comprises an array of optical tweezers adapted to form an array of atoms in the active zone.

[0007] In some embodiments, the differential vacuum tube forms an aperture configured to prevent photons spontaneously scattered from atoms disposed in the atom reservoir from reaching the active zone.

[0008] In some embodiments, the first and the second optical lattices intersect at an angle that is greater than zero and less than 90 degrees.

[0009] In various embodiments, methods for moving atoms are provided. Atoms are trapped within the atom reservoir. The first beam having the first frequency and the second beam having the second frequency is generated. The first optical lattice is generated based on the first beam. Atoms are loaded within the atom reservoir into the first optical lattice. The first frequency is detuned, thereby moving the atoms in the first optical lattice from the atom reservoir to the handover region. The second optical lattice is generated based on the second beam. The atoms are transferred from the first optical lattice to the second optical lattice. The second frequency is detuned, thereby moving the atoms from the handover region to the active zone. The array of atoms is formed in the active zone.

[0010] In some embodiments, transferring the atoms from the first optical lattice to the second optical lattice comprises reducing power of the first beam and increasing power of the second beam.

[0011] In various embodiments, devices for continuous loading of qubits for quantum computation are provided, comprising: a computation chamber, the computation chamber comprising an active zone, an imaging zone, and a reservoir zone; at least one moveable optical tweezer configured to convey atoms from the delivery zone to the imaging zone and from the imaging zone to the active zone; at least one imaging laser configured to illuminate the imaging zone; at least one image sensor configured to detect atoms in the imaging zone upon illumination by the imaging laser; and a shielding laser configured to illuminate the active zone when the imaging laser illuminates the imaging zone, the shielding laser inducing a state shift on atoms in the active zone that suppresses response to scattering from the imaging laser. The active zone is configured to hold a first array of atoms and adapted to perform quantum gates thereon. The delivery zone is configured to provide a supply ofHQU-01825 HU 9844 atoms, and the imaging zone is configured to hold a second array of atoms. The imaging zone and the active zone are separated by a distance sufficient to reduce a photo scattering decoherence probability to less than or equal to 0.01.

[0012] In some embodiments, the first array and the second array of atoms are trapped by optical tweezers generated through a common objective.

[0013] In some embodiments, the device further comprises an acousto-optical device (AOD) configured to generate the at least one moveable optical tweezer.

[0014] In some embodiments, the shielding laser has a wavelength about 1530nm or about 776nm.

[0015] In some embodiments, the device further comprises at least one cooling laser configured to illuminate the imaging zone, the cooling laser configured to cool atoms in the presence of a finite B-field.

[0016] In some embodiments, the device further comprises at least one initialization laser configured to illuminate the imaging zone and initialize atoms therein as qubits.

[0017] In some embodiments, the imaging zone and the active zone are separated by at least 200μm.

[0018] In some embodiments, the at least one moveable optical tweezer configured to capture atoms from the delivery zone with laser-free dissipation.

[0019] In various embodiments, systems for quantum computation are provided comprising a device for moving atoms according to any of the foregoing embodiments and a device for continuous loading of qubits for quantum computation according to any of the foregoing embodiments, wherein the first optical lattice is configured to deliver atoms to the delivery zone. BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0020] Fig.1 is a schematic view of a quantum information architecture according to embodiments of the present disclosure.

[0021] Fig.2 is a level diagram showing key87Rb atomic levels according to embodiments of the present disclosure.

[0022] Fig.3 is a schematic view of a quantum processing unit (QPU) according to embodiments of the present disclosure.HQU-01825 HU 9844

[0023] Fig.4A-4B are schematic views of an atomic qubit loading system according to embodiments of the present disclosure.

[0024] Fig.5 is a graph showing detuning and power over time for optical lattices according to embodiments of the present disclosure.

[0025] Fig.6 is a schematic view of an atomic qubit loading system configured to operate with a quantum processing unit (QPU) according to embodiments of the present disclosure.

[0026] Fig.7 is a schematic view of an atomic qubit loading system according to embodiments of the present disclosure.

[0027] Fig.8 is a schematic view of optical lattices according to embodiments of the present disclosure.

[0028] Fig.9 is a graph of transported atoms versus acceleration according to embodiments of the present disclosure.

[0029] Fig.10 is a graph of handover efficiency versus ramp time according to embodiments of the present disclosure.

[0030] Fig.11 is an image of an array of atoms according to embodiments of the present disclosure.

[0031] Fig.12 is an image of an array of atoms according to embodiments of the present disclosure.

[0032] Fig.13 is a schematic view of an array of atoms loaded from a qubit loading system according to embodiments of the present disclosure.

[0033] Fig.14 is a graph of filling fraction versus number of pulls according to embodiments of the present disclosure.

[0034] Fig.15 is a graph of pulled atoms versus number of pulls according to embodiments of the present disclosure.HQU-01825 HU 9844

[0035] Fig.16 is a graph of atoms in reservoir versus number of pulls according to embodiments of the present disclosure.

[0036] Figs.17A-D illustrate an exemplary continuous reloading architecture according to embodiments of the present disclosure.

[0037] Fig.18 is a schematic view of an apparatus for quantum computation according to embodiments of the present disclosure.

[0038] Fig.19 is a schematic representation of continuous loading of atomic qubits according to various embodiments of the present disclosure.

[0039] Fig.20 is a cutaway view of an apparatus for quantum computation according to embodiments of the present disclosure.

[0040] Fig.21 is a representation of a lattice array showing atom loading and a timeline of operation of an apparatus for quantum computation according to embodiments of the present disclosure.

[0041] Fig.22 is a plot of atoms pulled versus number of pulls according to embodiments of the present disclosure.

[0042] Figs.23A-23F are representations of qubit coherence over time according to embodiments of the present disclosure.

[0043] Fig.24 is a schematic representation of qubit shielding according to embodiments of the present disclosure.

[0044] Fig.25A-25C is a representation of finite field operations, including a cooling curve, initialization scheme and array rearrangement according to embodiments of the present disclosure, respectively.HQU-01825 HU 9844 DETAILED DESCRIPTION

[0045] Neutral atoms recently became one of the most promising platforms for quantum computing. One major obstacle to perform deep quantum circuits involving a large number of qubits is atom loss occurring during the algorithm. Loss can occur during qubit-readout, gate operations (in particular two-qubit Rydberg gates), and eventually due to collisions with background atoms in the vacuum chamber.

[0046] Performing deep quantum algorithms that are not limited by atom loss requires to continuously load new atoms into the system. This enables replacing data qubits by fresh atoms after teleporting the quantum information encoded in logical qubits before the occurred atom loss decoheres the information encoded in logical qubits. Furthermore, fresh atoms can be used as ancilla qubits for detecting errors in the circuit. The reloading scheme should fulfill several requirements. First, it should be scalable and fast, such that continuous operation does not come with the cost of data rates lower than non-continuous schemes. Second, reloading fresh atoms should preserve the quantum coherence of nearby data qubits.

[0047] Loading atoms into tweezers may be performed from a single conveyor belt. In such a scheme, atoms can be laser-cooled far from the computing zone. As a consequence, the preparation of the reservoir does not require near-resonant photon scattering to cool atoms close to data qubits. Furthermore, local densities are enhanced by the lattice structure, increasing collision rates between atoms as a key element of the loading scheme. In contrast to schemes where atoms are loaded from two-dimensional lattice reservoirs where reloading has to be slow such that atoms do not heat up when moved over the lattice, pulling atoms out of the reservoir perpendicular to the lattice can be fast. Finally, the conveyor belt can be used to connect two vacuum chambers via a differential pumping tube, separating an area with higher pressure where the magneto-optical trap (MOT) is loaded from an area with better vacuum where quantum algorithms are performed.HQU-01825 HU 9844

[0048] A remaining challenge in single conveyor belt schemes is to protect data qubits from the photons scattered during the magneto-optical trap (MOT) used to load the optical conveyor belt. Even if the MOT is tens of centimeters away, the amount of spontaneously scattered photons can be large enough to increase decoherence rates of quantum algorithms.

[0049] The present disclosure addresses this remaining problem by using two optical conveyor belts. The optical lattice conveyor belt transports the atoms from the MOT chamber through a differential pumping tube into the science chamber. Because the aperture of the differential pumping tube connecting both chambers is small, photons scattered from the MOT can only illuminate a small solid angle in the science chamber. By transferring the atoms to a second lattice, which is slightly angled relative to the first lattice, the atoms leave the illuminated area during the final transport stage in the second lattice.

[0050] A quantum bit (qubit) is the fundamental building block for a quantum computer. By analogy to classical bits which are used to store information in traditional computers (each bitis 0 or 1), qubits can occupy two distinct states labeled|0^and|1^, or any quantumsuperposition of the two states. In various applications, multiple qubits are entangled in order to build multi-qubit quantum gates.

[0051] Bits and qubits are each encoded in the state of real physical systems. For example, a classical bit (0 or 1) may be encoded in whether a capacitor is charged or discharged, or whether a switch is ‘on’ or ‘off’.

[0052] The term qudit (quantum digit) denotes the unit of quantum information that can berealized in suitable ^^-level quantum systems. A collection of qubits that can be measured to^^ states can implement an ^^-level qudit.

[0053] Quantum bits are encoded in quantum systems with two (or more) distinct quantum states. There are many physical realizations that may be employed. One example is based on individual particles such as atoms, ions, or molecules which are isolated in vacuum. TheseHQU-01825 HU 9844 isolated atoms, ions, and molecules have many distinct quantum states that correspond to different orientations of electron spins, nuclear spins, electron orbits, and molecular rotations / vibrations.

[0054] In principle, a qubit may be encoded in any pair of quantum states of the atom / ion / molecule. In practice, a key parameter of qubits is described by their quantum coherence properties. Coherence measures the lifetime of the qubit before its information is lost. It has a close analogy with classical bits: if you prepare a classical bit in the 0 state, then after some time it may randomly be flipped to 1 due to environmental noise. Quantummechanically, the same error may occur:|0^may randomly flip to|1^after somecharacteristic timescale. However, qubits may suffer from additional errors: for example, a superposition state (|0^+|1^) / √2 may randomly flip to (|0^-|1^) / √2. In real quantum computers, the qubits must be encoded in quantum states which have long coherence properties.

[0055] Quantum computers generally can contain many qubits, each encoded in its own atom / molecule / ion / etc. Beyond simply containing the qubits, the quantum computer should be able to (1) initialize the qubits, (2) manipulate the state of the qubits in a controlled way, and (3) read out the final states of the qubits. When it comes to manipulation of the qubits, this is usually broken down into two types: one type of qubit manipulation is a so-called single-qubit gate, which means an operation that is applied individually to a qubit. This may, for example, flip the state of the qubit from |0^to |1^, or it may take |0^to a superpositionstate (|0^+|1^) / √2. The second necessary type of qubit manipulation is a multi-qubit gate,which acts collectively on two or more qubits, including those that are entangled. A multi- qubit gate is realized through some form of interaction between the qubits. The various quantum computing platforms (having various physical encodings of qubits) rely on differentHQU-01825 HU 9844 physical mechanisms both for single-qubit gates as well as multi-qubit gates according to the physical system that is storing the qubit.

[0056] In various embodiments of a quantum computer, a qubit is encoded in two near- ground-state energy levels of an atom, ion, or molecule. An example of this is a hyperfine qubit. Such a qubit is encoded in two electronic ground states that differ by the relative orientation of the nuclear spin with respect to the outer electron spin. Pairs of such states can be chosen so that they are particularly robust / insensitive to environmental perturbations, leading to long coherence times. These states are split in energy by the hyperfine interaction energy of the atom / ion / molecule, which is the interaction energy between the nuclear spin and the electron spin. The robustness of the qubit can be understood as the energy splitting between the two states being particularly stable. For this reason, such states are called clock states because the stable energy splitting can form an excellent frequency-reference and as such forms the basis for atomic clocks. Typical hyperfine splitting between these qubit states is in the 1 – 13 GHz frequency range.

[0057] To perform single-qubit gates on such a hyperfine qubit, it is possible to apply coherent microwave radiation at the exact frequency of the energy splitting between states. However, there are two drawbacks to this approach. First, microwaves cannot be applied to just one qubit without affecting adjacent qubits. This is because qubits are encoded in particles that are typically just a few microns apart from one another, and microwaves cannot be focused to such a small scale due to their large wavelength. Second, the microwave intensity is fairly limited and as such the maximum speed of single-qubit gates is correspondingly limited.

[0058] An alternative approach is based on stimulated Raman transitions. In this case, a laser field, also referred to herein as a Raman pulse, is applied to the atoms / ions / molecules. The laser field is nearly (but not exactly) resonant with an optical transition from one of theHQU-01825 HU 9844 ground states to an optically excited state. The laser field contains multiple frequency components separated in frequency by exactly the amount equal to the hyperfine splitting of the qubit. The atom / ion / molecule can absorb a photon from one frequency component and coherently emit into a different frequency component, and in doing so it changes its state. This approach benefits from the capability of focusing the laser field onto individual particles or subsets of particles in the quantum computer. The laser field can also be applied with high intensity, enabling much faster gate operations.

[0059] Neutral atom quantum computers encode qubits in individual neutral atoms. The neutral atoms are trapped in a vacuum chamber and levitated by trapping lasers. Most commonly, the trapping lasers are individual optical tweezers, which are individual tightly focused laser beams that trap an individual atom at the focus. Alternatively, individual atoms may be trapped in an optical lattice, which is formed from standing waves of laser light which produce a periodic structure of nodes / antinodes.

[0060] A typical approach for encoding a qubit in neutral atoms is the hyperfine qubit approach, in which two ground states split by several GHz form the qubit. Multi-qubit gates in neutral atom quantum computers are realized using a third atomic state, which is a highly- excited Rydberg state. When one atom is excited to a Rydberg state, neighboring atoms are prevented from being excited to the Rydberg state. This conditional behavior forms the basis for multi-qubit gates, such as a controlled-NOT gate. The Rydberg state is used temporarily to mediate the multi-qubit gate, and then the atoms are returned back from the Rydberg state to the ground state levels to preserve their coherence.

[0061] Trapped ion quantum computers use atomic species that are ionized, meaning they have a net charge. In most cases, many ions are trapped in one large trapping potential formed by electrodes in a vacuum chamber. The ions are pulled to the minimum of the trapping potential, but inter-ion Coulomb repulsion causes them to form a crystal structureHQU-01825 HU 9844 centered in the middle of the trapping potential. Most commonly, the ions arrange into a linear chain. Other ways to trap ions are also possible, such as using optical tweezers, or trapping ions individually with local electric fields with a more complex on-chip electrode structure.

[0062] Qubits are encoded in trapped ions in multiple ways. One common approach is to use ground-state hyperfine levels, as described for neutral atoms. In trapped ions with hyperfine- qubit encoding, as with neutral atoms, single-qubit gates may use microwave radiation or stimulated Raman transitions.

[0063] Unlike in neutral atoms, trapped ion hyperfine qubits rely heavily on stimulated Raman transitions for performing multi-qubit gates. Stimulated Raman transitions may be used to control both the hyperfine state of the ion but also to change the motional state of the ion (i.e., add momentum). This can be understood as absorbing a photon moving in one direction and emitting a photon in a different direction, such that the difference in photon momentum is absorbed by the ion. Since many ions are often trapped in one collective trapping potential and are mutually repelling one another, changing the motional state of one ion affects other ions in the system, and this mechanism forms the basis for multi-qubit gates.

[0064] According to various embodiments of a quantum computer, individual particles (atoms / ions / molecules) can first be trapped in an array and arranged into particular configurations. Next, one or more particles are prepared in a desired quantum state. Quantum circuits can then be implemented by a sequence of qubit operations acting on individual qubits (single-qubit gates) or on groups of two or more qubits (multi-qubit gates). Finally, the state of the particles can be read out in order to observe the result of the quantum circuit. The readout can be accomplished using an observation system that typically includes an electron-multiplied CCD (EMCCD) camera image to detect particles’ loaded positions,HQU-01825 HU 9844 and a second camera image to read out the particles’ final states by, for example, detecting fluorescence emitted by the particles in their final states.

[0065] Quantum information platforms rely on interactions between qubits, either for performing quantum gates or for performing analog many-body simulation. Qubits often interact in a local way, however, which limits the connectivity of the circuit or the analog simulation and constrains the possible computations. While some platforms can communicate in a nonlocal way through the use of a shared bus (e.g., trapped ions), these shared-bus approaches are limited to small systems and thus still require a way to dynamically move qubits around in order to truly scale up the platform.

[0066] Neutral atom arrays can be dynamically reconfigured while preserving quantum coherence and entanglement between qubits, by storing quantum information in hyperfine states and shuttling atoms in optical tweezers. This approach offers a scalable way to realize a quantum information system with large numbers of qubits and arbitrary programmability – where any qubit can perform an entangling gate with any other qubit in the array. Using high-fidelity two-qubit Rydberg gates, various quantum information circuits are described herein that leverage the programmability and nonlocal connectivity achievable with these approaches. Examples of high fidelity Rydberg gates are described in Levine, et al., Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms, Phys. Rev. Lett., vol. 123, issue 17, https: / / link.aps.org / doi / 10.1103 / PhysRevLett.123.170503, and Evered, et al., High-Fidelity Parallel Entangling Gates on a Neutral Atom Quantum Computer, arXiv:2304.05420 [quant-ph], https: / / arxiv.org / abs / 2304.05420, which are hereby incorporated by reference.

[0067] As set out in more detail below, the methods provided herein enable a variety of computational scenarios. In some scenarios, a plurality of neutral atom are moved in parallel between multiple regions in space. For example, a source of illumination may be directed toHQU-01825 HU 9844 a first region, and atoms are moved in and out of that region between the application of pulses by the source of illumination. Similarly, a camera may be directed to an imaging region, and atoms are moved in and out of that imaging region for imaging. Similarly, atoms may be moved in and out of the blockade radius of other atoms, thereby allowing the application of gates to the different groups of atoms at different stages of an algorithm or layers of a quantum circuit.

[0068] It will be appreciated that various stabilizer codes entail the readout of ancilla qubits, and the present disclosure allows the physical relocation of ancilla qubits to an imaging region separate from the data qubits. In this way, readout of ancilla qubits may be provided without destruction of the data qubits.

[0069] More generally, an array of atoms may be moved between multiple arrangements to facilitate both digital gates between different selections of atoms and analog evolution of the array as a whole. As used herein, an arrangement of an array of atoms or a plurality of atoms refers to the positioning of those atoms relative to each other. It will be appreciated that certain arrangements provide connectivity between qubits that enable particular gates or analog evolution according to a particular Hamiltonian. One advantage of the methods provided herein is that atoms may be moved into proximity of atoms that were not adjacent within an array. A non-adjacent atom is one that is not within a unit cell in a regular lattice or that is not a nearest neighbor in an irregular array. For example, in a rectangular lattice, each atom has eight atoms that are within a unit cell thereof, and thus has eight adjacent atoms (disregarding edges).

[0070] As defined further below, atoms are moved adiabatically in order to preserve entanglement. As used herein, the term adiabatic movement refers to movement that avoids a transition of the subject atom within its trap. For example, where the first time-derivative of the acceleration of the subject atom is not greater than a predetermined value, the movementHQU-01825 HU 9844is considered adiabatic. Typically, adiabatic movement occurs when ^^^^^^^^ <(^^^^^^^^ ^^^^ ^^^^^^^^) × (^^^^^^^^ ^^^^^^^^^^^^^^^^^^)ଷ. In physics, jerk or jolt is the term given to the rateat which an object’s acceleration changes with respect to time.

[0071] In addition to adiabatic movement, in some embodiments dynamical decoupling is applied during the movement. As set out further below, a ^^-pulse during movement cancels out dephasing induced by the trap differential light shift. The trap differential light shift changes when the atom is moving (depending on its acceleration) because it will move in the trap, and so sample a different portion of the light intensity and hence have a different differential light shift.

[0072] Generally speaking, the more pulses applied, the more decoupling from fluctuations. For example, fluctuations may come from laser intensity fluctuations at different displacement positions of the atom, or different magnetic fields in space.

[0073] In embodiments where acceleration and deceleration are symmetric, both change the differential light shift in the same way. Accordingly, in such embodiments it is advantageous to apply a ^^-pulse at the midpoint of the motion. In this way, the changes in differential light shift induced by acceleration and deceleration cancel each other out.

[0074] Referring to Fig.1, a quantum information architecture 100 enabled by coherent transport of neutral atoms is illustrated. Qubits are transported to perform entangling gates with distant qubits, enabling programmable and nonlocal connectivity. Atom shuttling is performed using optical tweezers, with high parallelism in two dimensions and betweenmultiple zones allowing selective manipulations. The inset shows the atomic levels used: the|0^, |1^ qubit states refer to the ^^ி = 0 clock states of 87Rb, and |^^^ is a Rydberg state usedfor generating entanglement between qubits, which are further described with regard to Fig. 2.HQU-01825 HU 9844

[0075] Fig.2 is a level diagram 200 showing key87Rb atomic levels used. The Rydberg excitation scheme from |1^ to |^^^ is composed of a two-photon transition driven by a 420-nmlaser and a 1013-nm laser. A DC magnetic field of ^^ = 8.5^^ is applied throughout this work.

[0076] As noted above, quantum information systems derive their power from controllable interactions that generate quantum entanglement. However, the natural, local character of interactions limits the connectivity of quantum circuits and simulations. Nonlocal connectivity can be engineered via a global shared quantum data bus, but these approaches are limited in either control or size.

[0077] According to various embodiments of the present disclosure, this long-standing challenge is addressed through dynamically reconfigurable arrays of entangled neutral atoms, shuttled by optical tweezers in two spatial dimensions. Hyperfine states are used for storing and transporting quantum information in between quantum operations, and excitation into Rydberg states is used for generating entanglement. Highly parallel operations are enabled via selective qubit operations in distinct zones that qubits are dynamically shuttled between. Taken together, these ingredients enable a powerful quantum information architecture, which is employed to realize applications including entangled state generation, creation of topological surface and toric code states, and hybrid analog-digital quantum simulations.

[0078] Within this architecture, programming a specific quantum circuit entails control over only a few optical degrees of freedom. Arbitrary tweezer positions in space are controlled by a computer-generated hologram, hundreds of atoms are dynamically reconfigured in parallel by two waveforms in a 2D acousto-optic deflector (AOD), and qubit operations are realized by pulsing optical beams. This flexible optical control enables sophisticated quantum circuits with only a few classical controls. This architecture enables an inherently scalable approach: larger codes require no increase in the number of classical controls.HQU-01825 HU 9844

[0079] Various quantum circuits are realizable with this approach, including quantum error correction (QEC) codes such as the surface and Steane codes, with fidelities in this disclosure already comparable to state-of-the-art experiments in other platforms. Moreover, the parallelized, nonlocal connectivity is used to create the toric code state on a torus.

[0080] Referring to Fig.3, a quantum processing unit (QPU) 300 according to embodiments of the present disclosure is illustrated. This design is centered around efficient classical control over many logical qubits in parallel using optical beams. Single-qubit logical gates can be realized transversally, for example, by illuminating all physical qubits within the same logical qubit block by an optical beam. Two-qubit logical gates can also be realized transversally, by interlacing two logical arrays of qubits and applying a global optical pulse for entangling each twin of the pair. For such a gate to be transversal, it must interact only corresponding qubits from the different logical arrays, such that the first qubit of the first logical array interacts with the first qubit of the second logical array, and so on.

[0081] Neutral atom systems have the potential for utility scale computing: for example, millions of identical neutral atom qubits may be trapped in mm-scale regions of space. The key challenge is the classical control required to assemble these qubits into a large-scale quantum processor. Full programmability of single physical qubits generally requires highly complicated classical control techniques in order to operate on millions of qubits. In contrast, the architectures provided herein allow for full programmability of single logical qubits while only requiring a few classical controls per logical qubit. This enables reaching utility-scale by encoding logical qubits into blocks that can be efficiently controlled in parallel. Using advanced optical microscopy systems (such as those utilized for modern industrial-scale lithography) with high numerical aperture and large field of view exceeding several millimeters, and appropriately scaled trapping laser power, direct trapping and manipulation of over a million qubits is possible. Further scaling is possible by creating 10-100 suchHQU-01825 HU 9844 processing units, each under its own microscope objective, and then connecting these units together utilizing photonic links and / or optical lattice transport. This allows for sufficient space, resolution, and power density for enacting high-fidelity control over 10M qubits and beyond.

[0082] QPU 300 is segmented into several key zones: a storage zone 311, entangling zone 312, readout zone 313, atom loading zone 304, and remote entangling zone 305. Storage zone 311, entangling zone 312, and readout zone 313 form processor core 301, which in some embodiments contains 104to 106qubits in a footprint of 0.5-5mm. Fresh atoms are continuously reloaded from distant atom loading zone 304, and a distant remote entangling zone 305 (using optical interconnects and / or lattice transport) delivers remote Bell pair entanglement resources.

[0083] In storage zone 311, idle logical qubits are stored for long times, utilizing the long qubit coherence times and high fidelity single-qubit gates, such that an error-correction cycle is only required before a logical two-qubit gate. For coherence times of 10-100 second, and assuming performance 10x below threshold, then roughly 1% single-qubit dephasing errors can be tolerated before a round of ^^ cycles of error correction. This corresponds to approximately 0.1-1 second of allowed storage time before the requirement for correction. Due to the all-to-all connectivity provided by the presently described architectures, idled logical qubits can simply be kept in the storage zone, safe from additional errors. Logical qubits are thus stored in dense blocks, shuttled out when they are needed in the algorithm, and only error-corrected before a two-qubit gate, greatly reducing the error correctionoverhead. In various exemplary devices, atoms are stored at densities of approximately1 / (2^^^^)ଶ in the dense storage zone, and densities of approximately 1 / (10^^^^)ଶ in theactive zone.HQU-01825 HU 9844

[0084] The active logical qubits are manipulated in active zone 312. By utilizing qubit transport, all combinations of two-qubit gates can be performed in a fixed region of space. This significantly reduces the classical control complexity. For example, all two-qubit gates can be performed using a single, global optical beam, which is dramatically simpler than addressing each individual qubit. This exceptional degree of parallelism for logical qubit control is a significant advantage of the present architecture relative to alternatives such as those involving individual control of atomic qubits.

[0085] Readout zone 313 allows selectively reading out a subset of qubits mid-circuit without disturbing the other qubits. This readout happens in parallel with a global beam and a camera, again requiring only one set of classical controls.

[0086] Outside of the core processor 301, atoms are constantly reloaded from loading zone 304 and transported into the core processor for running arbitrarily long circuits. Remote Bell pairs with other processing units are generated using optical links and / or optical lattice transport 305 and are shuttled into the core processor 301 for creating remote logical entanglement. This allows interconnection of 10-100 single processing units into one error- corrected, utility-scale quantum computer.

[0087] The architecture provided above allows for mid-circuit readout. In particular, this architecture may be paired with fast imaging in the readout zone and a classical control loop. In addition, various methods may be used to suppress crosstalk errors and detect / correct for loss. Arbitrarily long circuit depths may be achieved with continuous reloading of atoms and further crosstalk suppression.

[0088] To connect multiple units, many high-fidelity, long-distance Bell pairs may be generated in parallel, using lattice transport and / or photonic links.

[0089] It will be appreciated that the present architecture is suitable for logical state preservation by repetitive mid-circuit measurement and correction. In addition, a surfaceHQU-01825 HU 9844 code logical qubit may be implemented, for example by moving ancillas from a storage zone reservoir, entangling with data qubits for syndrome extraction, and moving to the readout zone. This allows fast mid-circuit readout and feedback while preserving coherence on data qubits. In various embodiments, the data qubits are protected by placing the imaging zone ~50 microns away, thereby suppressing crosstalk from the readout beam and scattered light from the ancilla atoms.

[0090] In various embodiments, a fast classical control loop uses ancilla measurements to determine errors on the data qubits, and to detect and correct qubit loss. Lost qubits may then be replaced with reservoir atoms. In order to reach surface code distances several times larger than the largest codes created in alternative systems, local detuning patterns may be utilized for space-efficient use of the entangling zone.

[0091] The presently described architectures may also be used to perform algorithms with logical qubits. The zoned approach combined with efficient optical control over many logical qubits in parallel allows construction of large-scale processors. In an exemplary use case, ~10 logical qubits are encoded in the active zone and moved to the storage zone. After encoding all logical qubits, the algorithm is run with appropriate logical single-qubit and logical two-qubit gates. The flexible, local single-qubit control required for logical single- qubit gates is implemented with Raman light from a 2D AOD illuminating the grid of a single code block. Logical two-qubit gates are realized transversally in the entangling zone. Mid- circuit readout is used for the non-Clifford gate-teleportation sequence, followed by fast feedback for logical single-qubit rotation.

[0092] It will be appreciated that while certain operating parameter are provided below by way of example, increased fidelity in two-qubit gate errors may be achieved through various further optimizations. For example, increasing Rydberg laser power and detuning will reduce laser scattering errors and also suppress other errors by increasing gate speed. Cooling atomsHQU-01825 HU 9844 to the motional ground state (thereby suppressing Doppler dephasing errors), and utilizing 10x higher laser power, theoretically results in >99.8% gate fidelities. Further improvements can be made with continued increases in laser power, but alternative routes such as single- photon excitation to Rydberg P states or alkaline-earth-based systems, are also available. Processor speed can be increased to a ~10 microsecond logical qubit cycle time by increasing collection efficiency or utilizing cavity-based or ensemble-based readout schemes, or by increasing movement speed with deeper optical tweezers.

[0093] To reach arbitrarily deep circuits, atoms may be continuously reloaded. Accordingly, some embodiments employ loading into a distant magneto-optical trap (MOT) and transporting atoms in an optical lattice conveyor belt.

[0094] In various embodiments, cross-talk during readout is suppressed by moving the ancilla atoms away from the data qubits.

[0095] Further scaling of the quantum processors can be achieved by connecting more than one microscope objective, either through atom transport or optical communication links. In various embodiments, the first approach utilizes the novel capabilities of atom rearrangement, combined with the use of optical lattice conveyor belts to coherently transport qubits between multiple active optical control regions and distribute entanglement. In various embodiments, the second approach utilizes photon-mediated entanglement between distinct atom array nodes with >104qubits. High entanglement rates can be achieved through parallel nanophotonic or bulk optical cavities, and the large sizes of atom arrays can provide further parallelism. This approach also enables modular construction of quantum processor units, flexibly rewired and linked together.

[0096] Referring to Fig.4A-4B, a scheme 400 to continuously reload atoms for quantum computing is illustrated. An atomic reservoir 404 is reloaded from a MOT chamber 408 into a computation chamber (right) which are connected via a differential pumping tube 416 usingHQU-01825 HU 9844 two optical conveyor belts 420a, 420b.In some embodiments, each of the optical conveyor belts 420a, 420b are produced by first and the second optical lattice generators 426, which may comprise a retroreflector and an acousto-optical modulator (AOM), according to embodiments of the present disclosure. The atoms are accelerated and decelerated by ramping the detuning of the retro-reflected lasers, optical conveyor belts 420a, 420b. In various embodiments, one or more of the optical conveyor belts 420a, 420b may be directed by a reflector 422. Fig.5 illustrates an exemplary graph 500 of detuning power over time of the optical conveyor belts 420a, 420b. During transfer between both conveyor belts, the lattices are static. Because only light scattered from the MOT 408 that propagates along the first optical lattice 420a (the differential pumping tube 416 acts as an aperture) will enter the science chamber 424, the angle between both conveyor belts 420a, 420b protects data qubits from decoherence. According to embodiments of the present disclosure, science region 424 may be approximately 10 cm long. The optical conveyor belts 420a, 420b travel through vacuum 425 into a neck 427 and intersect, forming a handover region 428, which can be seen in Fig.8, specifically. During the transport in the second conveyor belt, the atoms leave the area which is illuminated by the light scattered from the atoms in the MOT 408 (see also Figs.7-8). In various embodiments, a small differential pumping tube 416, such as one having a diameter of one millimeter, combined with the two-lattice architecture described herein, blocks direct line-of-sight between the MOT source and the science region for extra isolation.

[0097] Referring to Fig.6, tweezers can be loaded from an optical lattice 420a, 420b by overlapping the tweezer with the lattice, further illustrated in Figs.17A-17C. The process can be efficient and fast (a few milliseconds) and does not require additional laser cooling during loading. In various embodiments, the tweezers can overlap the lattice in about one ms, with a pullout in about 1.6 ms, resulting in a total time of 2.6 ms per pull, shownHQU-01825 HU 9844 schematically in Fig.13. After loading, atoms can be pulled into an imaging zone, cooled and rearranged, and used for quantum algorithms. Figs.14-16 illustrate graphs of filling fraction versus number of pulls, accumulated atoms versus number of pulls and atoms in reservoir versus number of pulls, respectively, and according to embodiments of the present disclosure.

[0098] As shown in Fig.8, the optimum angle during reloading depends on several factors. On the one hand, the angle has to be large enough such that the final computation zone is safely located far away from the solid angle illuminated by the photons scattered from the MOT. The illuminated solid angle depends critically on the size of the differential pumping tube 416 (which has to be large enough to not introduce aberrations to the optical lattice), the design of the differential pumping (rescattering of photons within the tube should be avoided), as well as the position of the pumping tube (the further away from the MOT and the closer to the final location, the better). On the other hand, the angle should be as small as possible such that the atom transfer efficiency between both optical conveyor belts is large and heating during hand-over is minimized.

[0099] The waists of the conveyor belts 420a, 420b are chosen based on the transport distance such that beam divergence is not a problem and atoms can be held against gravity over the whole transport. The laser frequency of the conveyor belt is also an important parameter. For a laser frequency closer to resonance (e.g., several hundreds of gigahertz), heating rates from off-resonant scattering increase and lifetimes in the lattice can be below a second. However, if the reloading cycle of the lattice reservoir is only hundred milliseconds and heating rates from moving tweezers through the reservoir during the loading process are larger than heating from off-resonant scattering, then having a further detuned lattice at larger intensities is not helpful.

[0100] Architectures provided herein are non-destructive for data qubits and are scalable and fast. The conveyor belt provided herein provides reservoir preparation without (local) photonHQU-01825 HU 9844 scattering; lattice-enhanced densities (collisional loading); and fast pulling perpendicular to lattice.

[0101] Hand-over between two conveyor belts is provided. A differential pumping tube acts as an aperture without direct line-of-sight.

[0102] Referring to Fig.7, details of the lattice arrangement are provided. In MOT 408, millions of atoms scatter millions of photons per second. For quantum computing purposes, where near-resonant light can decohere qubits, it is beneficial if these photons do not illuminate data qubits. This is achieved by transporting atoms using two optical conveyor belts. The differential pumping tube where the atoms travel through in the first lattice transport blocks most of the scattered light such that scattered light can only illuminate a small solid angle at the other side of the pumping tube. The computing zone (or active zone) where qubits are stored is in the "dark region" outside of the illuminated area. The further away the aperture is located from the MOT, the smaller the illuminated area (and as a consequence, the smaller the angle between both conveyor belts that can be chosen).

[0103] Referring to Fig.8, the angle between both conveyor belts is crucial to shield atoms from the scattered light from the MOT. However, it is also beneficial to not have an angle which is too large, where the hand-over efficiency between both lattices is small. The larger the overlap between the atom cloud and both optical lattices at the overlap region, the larger the efficiency. Graphs of transported atoms versus their acceleration is illustrated in Fig.9 and handover efficiency versus ramp time is illustrated in Fig.10.

[0104] In exemplary embodiments, the following transport parameters are employed: Beam waists:Speed:Acceleration: ^^ ଶ^^௧ ≈ 4000^^ / ^^Hand-over time: ^^ோ ≲ 5^^^^HQU-01825 HU 9844

[0105] In exemplary embodiments, the time from the MOT through lattice loading and PGC is 150ms. More than 100,000 atoms are provided per 200 ms.

[0106] In exemplary embodiments, tweezers are overlapped with the lattice reservoir of40,000 atoms. Overlap time for loading is given by ^^^ ≲ 5^^^^. In some embodiments, activecooling is not employed. In exemplary embodiments, 1,000 atoms are retrieved from the reservoir.

[0107] In exemplary embodiments, the following parameters are employed: • Location of differential pumping tube: As far away as possible from the MOT, and as close as possible to the final location (both distances are typically between 10-50 cm and also depend on the details of the vacuum chamber). • Angle between conveyor belts: in a range of more than about 2◦-and less than about 90◦, such as in a range of between about 3◦and about 6◦. For the hand-over it is beneficial to have the angle as small as possible (efficiency in the atom transport will decrease), at the same time it has to be large enough such that scattered light from the MOT does not illuminate the atomic array.

[0108] In an exemplary embodiment where the angle is about 4.5◦, the two distances are 39 cm and 15 cm, and such that the total transport distance is 54cm, a reservoir of 100000 atoms can be delivered at a temperature of a few tens of microkelvins every 200 ms, which can then be used to refill atomic arrays. Figs.11 and 12 illustrate atomic arrays according to embodiments of the present disclosure.

[0109] In optical conveyor belts, atoms can be moved with speeds of tens of m / s, acceleration and deceleration values can be thousands of m / s2. Beam waists of the conveyor belts are typically between 100 µm (small transport distances) and 500 µm (large transport distances). The trade-off is that a more focused beam (smaller waist) will diverge faster and therefore not be able to hold atoms over a larger distance.HQU-01825 HU 9844

[0110] The loading of the tweezers happens by overlapping tweezers with the optical lattices and then pulling atoms out. If atomic densities are high enough, loading can rely only on collisions between atoms. If one has enough tweezers available, one can in principle load thousands of atoms from the reservoir at once.

[0111] Dynamic reconfiguration in 2D tweezer arrays

[0112] Exemplary experiments utilize the apparatus described below. Inside the vacuum cell,87Rb atoms are loaded from a magneto-optical trap into a backbone array of programmable optical tweezers generated by a spatial light modulator (SLM). Atoms are rearranged in parallel into defect-free target positions in this SLM backbone by additional optical tweezers generated from a crossed 2D acousto-optic deflector (AOD). Following the rearrangement procedure, selected atoms are transferred from the static SLM traps back into the mobile AOD traps, and then these mobile atoms are moved to their starting positions in the quantum circuit. During this entire process, the atoms are cooled with polarization gradient cooling. Before running the quantum circuit, a camera image of the atoms in their initial starting positions is taken. Following the circuit, a final camera image is taken todetect qubit states|0^(atom presence) and|1^(atom loss, following resonant pushout). Alldata are postselected on finding perfect rearrangement of the AOD and SLM atoms before running the circuit. In some embodiments, each atom remains in a single static or single mobile trap throughout the duration of the quantum circuit.

[0113] The crossed AOD system is composed of two independently controlled AODs (AA Opto Electronic DTSX-400) for ^^ and ^^ control of the beam positions. Both AODs are driven by independent arbitrary waveforms which are generated by a dual-channel arbitrary waveform generator (AWG) (M4i.6631-x8 by Spectrum Instrumentation) and then amplified through independent MW amplifiers (Minicircuits ZHL-5W-1). The time-domain arbitrary waveforms are composed of multiple frequency tones corresponding to the ^^ and ^^ positionsHQU-01825 HU 9844 of columns and rows, which are independently changed as a function of time for steering around the AOD-trapped atoms dynamically; the full ^^ and ^^ waveforms are calculated by adding together the time-domain profile of all frequency components with a given amplitude and phase for each component. For running quantum circuits, the positions of the AOD atoms at each gate location are programmed and then smoothly interpolated (with a cubic profile) the AOD frequencies as a function of time between gate positions. The cubic profileenacts a constant jerk onto the atoms, which allows movement of roughly 5 − 10 × faster(without heating and loss) than if moving at a constant velocity (linear profile). In the movement protocol, stretches, compressions, and translations of the AOD trap array are applied: i.e., the AOD rows and columns never cross each other in order to avoid atom loss and heating associated with two frequency components crossing each other.

[0114] The AOD tweezer intensity is homogenized throughout the whole atom trajectory in order to minimize dephasing induced by a time-varying magnitude of differential light shifts. To this end, a reference camera is used in the image plane to gauge the intensity of each AOD tweezer at each gate location and homogenized by varying the amplitude of each frequency component; during motion between two locations the amplitude of each individual frequency component is interpolated.

[0115] The SLM tweezer light (830 nm) and the AOD tweezer light (828 nm) are generated by two separate, free-running Ti:sapphire lasers (M Squared, 18-W pump). Projected througha 0.5 NA objective, the SLM tweezers have a waist of roughly ∼ 900 ^^^^ (∼ 1000 ^^^^ forAODs). When loading the atoms, the trap depths are ∼ 2^^ × 16^^^^^^, with radial trapfrequencies of ∼ 2^^ × 80^^^^^^, and when running quantum circuits the trap depths are ∼2^^ × 4^^^^^^, with radial trap frequencies of ∼ 2^^ × 40^^^^^^.HQU-01825 HU 9844

[0116] Raman laser system

[0117] Fast, high-fidelity single-qubit manipulations are critical ingredients of the quantum circuits demonstrated in this work. To this end, a high-power 795-nm Raman laser system isused for driving global single-qubit rotations between ^^ி = 0 clock states. This Raman lasersystem is based on dispersive optics. 795-nm light (Toptica TA pro, 1.8W) is phase- modulated by an electro-optic modulator (Qubig), which is driven by microwaves at 3.4 GHz (Stanford Research Systems SRS SG384) that are doubled to 6.8 GHz and amplified. The laser phase modulation is converted to amplitude modulation for driving Raman transitions through use of a Chirped Bragg Grating (Optigrate). IQ control of the SG384 is used for frequency and phase control of the microwaves, which are imprinted onto the laser amplitude modulation and thus provide direct frequency and phase control over the hyperfine qubit drive.

[0118] The Raman laser illuminates the atom plane from the side in a circularly polarized elliptical beam with waists of 40^^^^ and 560^^^^ on the thin axis and the tall axis, respectively, with a total average optical power of 150^^^^ on the atoms. The large verticalextent ensures < 1% inhomogeneity across the atoms, and shot-to-shot fluctuations in thelaser intensity are also < 1%. The Raman laser is operated at a blue-detuned intermediate-state detuning of 180 GHz, resulting in two-photon Rabi frequencies of 1 MHz and anestimated scattering error per ^^ pulse of 7 × 10ିହ (i.e. 1 scattering event per 15000 ^^pulses).

[0119] Qubit coherence and dynamical decoupling

[0120] In the 830-nm traps, hyperfine qubit coherence is characterized by ^^∗ଶ = 4^^^^ (notplotted here), ^^ଶ = 1.5^^ (XY16 with 128 total ^^ pulses), and ^^^ = 4 s (including atom loss).The experiments described herein are performed in a DC magnetic field of 8.5 Gauss. Coherence can be further improved by using further-detuned optical tweezers (with trapHQU-01825 HU 9844depth held constant, the tweezer differential lightshifts decrease as 1 / Δ and 1 / ^^^ decreases as1 / Δଷ) and shielding against magnetic field fluctuations. For practical QEC operation, atomloss can be detected in a hardware-efficient manner and the atom then replaced from a reservoir, which could in principle be continuously reloaded by a MOT for reaching arbitrarily deep circuits.

[0121] The transport sequences are accompanied with dynamical decoupling sequences. The number of pulses used is a tradeoff between preserving qubit coherence while minimizing pulse errors. In various embodiments, there is an interchange between two types of dynamical decoupling sequences: XY8 / XY16 sequences, composed of phase-alternated individual ^^-pulses which are self-correcting for amplitude and detuning errors, and CPMG- type dynamical decoupling sequences composed of robust BB1 pulses. The CPMG-BB1 sequence is more robust to amplitude errors but incurs more scattering error. The sequence may be empirically optimized for any given experiment by choosing between these different sequences and a variable number of decoupling ^^ pulses, optimizing on either single-qubit coherence (including the movement) or the final signal. Typically, decoupling sequences are composed of a total 12-18 ^^ pulses.

[0122] Movement effects on atom heating and loss

[0123] The following discusses the effects of movement on atom loss and heating in the harmonic oscillator potential given by the tweezer trap. Motion of the trap potential is equivalent to the non-inertial frame of reference where the harmonic oscillator potential isstationary, but the atom experiences a fictitious force given by ^^(^^) = −^^ ^^(^^), where ^^ isthe mass of the particle and ^^(^^) is the acceleration of the trap as a function of time. The average vibrational quantum number increase Δ^^ is given byHQU-01825 HU 9844 Equation 1 where ^^^(^^^) is the Fourier transform of ^^(^^) evaluated at the trap frequency ^^^, and the zeropoint size of the particle ^^௭^^ ≡Δ^^ is the same for all initial levels of theoscillator. Experimentally, an acceleration profile ^^(^^) = ^^^^ is applied to the atom, from time−^^ / 2 to +^^ / 2 to move a distance ^^ with constant jerk ^^. Calculating |^^^(^^)|ଶ, simplifyusing ^^^^^ ≫ 1, and assume a small range of trap frequencies to average the oscillatoryterms, results inEquation 2

[0124] Several relevant insights can be gleaned from this formula. First, this expression indicates the ability to move large distances ^^ with comparably small increases in time ^^.Furthermore, to maintain a constant Δ^^, the movement time ^^ ∝ ^^ ଷ / ସ^ି . Moreover, toperform a large number of moves ^^ for a deep circuit, Δ^^ ∝ ^^ / ^^ସ can be estimated,suggesting that the number of moves can be increased from, e.g., 5 to 80 by slowing each move from 200^^^^ to 400^^^^. Move speed could be further improved with different ^^(^^)profiles, but inevitably with finite resources such as trap depth, quantum speed limits will eventually prevent arbitrarily fast motion of qubits across the array.

[0125] Equation 2 is now compared to experimental observations. Atom loss is observed with movement of 55 ^^m in 200^^^^ under a constant negative jerk. This speed limit isconsistent with the above estimates: using ^^^ = 2^^ × 40^^^^^^ and ^^௭^^ = 38^^^^, it ispredicted that Δ^^ ≈ 6 for this move, corresponding to the onset of tangible heating at thismove speed. More quantitatively, a Poisson distribution is assumed with mean ^^ andHQU-01825 HU 9844 variance ^^ and integrate the population above some critical ^^^^௫upon which the atom willleave the trap. From this analysis, atom retention is given by

[0126] Additional heating and loss during the circuit can also be caused by repeated short drops for performing two-qubit gates, where the tweezers are briefly turned off to avoid anti- trapping of the Rydberg state and light shifts of the ground-Rydberg transition. However, drop-recapture measurements suggest the 500-ns drops used experimentally have a negligible effect until hundreds of drops per atom (corresponding to hundreds of CZ gates). Atom loss and heating as a function of number of drops are well-described by a diffusion model, whichwould then predict that reducing atom temperature by a factor of 2 × (reducing thermalvelocity by √2 ×) and reducing drop time ^^ௗ^^^ by 2 ×, together would increase the numberof possible CZ gates per atom to thousands.

[0127] Two-qubit CZ gates implementation

[0128] Two-qubit gates and calibrations may be implemented using the techniques provided herein. Specifically, the two-qubit CZ gate is implemented by two global Rydberg pulses, with each pulse at detuning Δ and length ^^, and with a phase jump ^^ between the two pulses. The pulse parameters are chosen such that qubit pairs, adjacent and under the Rydberg blockade constraint, will return from the Rydberg state back to the hyperfine qubit manifold with a phase depending on the state of the other qubit. The numerical values for these pulseparameters are:Δ = −0.377371Ω^^ = −0.621089 × (2^^)^^ = 0.683201 / [Ω / (2^^)]

[0129] Exemplary experiments are operated with a two-photon Rydberg Rabi frequency ofΩ / 2^^ = 3.6^^^^^^, giving a theoretical ^^ = 190^^^^ and a theoretical Δ / (2^^) = −1.36^^^^^^.The negative detuning sign is chosen to help minimize excitation into the ^^^ = +1 / 2HQU-01825 HU 9844Rydberg state which is detuned by about 24 MHz under the field of 8.5 G (and experiences a3 × lower coupling to the Rydberg laser than the desired ^^^ = −1 / 2 state due to reducedClebsch-Gordan coefficients). In this work strong blockade between adjacent qubits is provided, with Rydberg-Rydberg interactions ^^^ / 2^^ ranging from 200 MHz to 1 GHz.

[0130] Managing spurious phases during CZ gates

[0131] The two-qubit gate induces both an intrinsic single-qubit phase, as well as spurious phases which are primarily induced by the differential light shift from the 420-nm laser. Under certain configurations, the 420-nm-induced differential light shift on the hyperfinequbit can be exceedingly large (> 8^^^^^^), yielding phase accumulations on the hyperfinequbit of ≈ 6^^. Small, percent-level variations of the 420-nm intensity can thus lead tosignificant qubit dephasing.

[0132] This 420-induced-phase issue may be addressed by performing an echo sequence: after the CZ gate, the 1013-nm Rydberg laser is turned off, a Raman ^^ pulse is applied, and then the 420-nm laser is pulsed again to cancel the phase induced by the 420 light during the CZ gate. This method echoes out the 420-induced phase, but comes at a cost of a factor of two increase in the 420-induced scattering error, which is the dominant source of error in two-qubit CZ gates.

[0133] Echo between CZ gates. To address these various issues, a Raman ^^ pulse is performed between each CZ gate to echo out spurious gate-induced phases on the hyperfine qubit. This approach has several advantages. The 420-induced phase is now cancelled by pairs of CZ gates, without explicitly applying additional 420-nm pulses to echo each individual CZ gate, thereby reducing the scattering error of the CZ gate in this work by a factor of approximately two. This echo technique, having reduced the scattering error incurred during each gate, roughly compensates the increased scattering rate incurred by spreading optical power over more space in 2D, thereby giving comparable gate fidelities toHQU-01825 HU 9844the two-qubit CZ gate fidelities of ≥ 97.4(2)%. Further, the echo between CZ gates alsocancels the intrinsic single-qubit phase of the CZ gate, removing errors in the calibration of this parameter, as well as canceling any other gate-induced spurious single-qubit phases suchas a ≈ 0.01 rad phase induced by pulsing the traps off for 500 ns for the two-qubit gate. Ininstances where the number of CZ gates is odd, the echo for the final CZ gate is performed.

[0134] Sign of intermediate-state detuning. To further suppress the effect of the spurious, 420-induced phase, the 420-nm laser is operated to be red-detuned (by 2 GHz) from the 6^^ଷ / ଶtransition. For red detunings, the light shift on the |0^state and the |1^state are of the samesign, minimizing the differential light shift, while for blue detunings < 6.8^^^^^^, the light shifton the|0^state and the|1^state have opposite signs and amplify the differential light shift.

[0135] Sensitivity to axial trap oscillations

[0136] In typical Rydberg excitation timescales with optical tweezers, the axial trap oscillation frequencies of several kHz are inconsequential. Here, with circuits running as long as 1.2 ms, with Rydberg pulses throughout, the axial trap oscillations can have important effects. In particular, the axial oscillations cause the atoms to make oscillations in / out of theRydberg beams: at estimated axial temperature of ∼ 25^^^^ and axial oscillation frequency of6^^^^^^, an axial spread ^〈^^ଶ〉 ≈ 1.3^^^^ is estimated. For 20-micron-waist beams, the effectof this positional spread is relatively small on the pulse parameters of the CZ gate, but can be significant on the sensitive 420-induced phase that should be canceled by echoing out thephase induced by CZ gates separated by ∼ 200^^^^. When using 20-micron-waist beams, anda 2.5-GHz blue detuning of the 420-nm laser, the dephasing due to the axial trap oscillations is significant. To remedy this deleterious effect, the beam waist of the 420-nm laser is increased to 35 microns (while maintaining constant intensity) and the laser frequency is changed to be 2-GHz red-detuned, together resulting in a significant reduction in the dephasing associated with improper echoing of the 420-nm pulse.HQU-01825 HU 9844

[0137] Rydberg beam shaping and homogeneity

[0138] The Rydberg beams are shaped into tophats of variable size through wavefront control using the phase profile on a spatial light modulator (SLM). This ability allows matching the height of the beam profile to the experiment zone size of any given experiment, thereby maximizing the 1013-nm light intensity and CZ gate fidelities. The Rydberg beam homogeneity is optimized until peak-to-peak inhomogenities are below <1%. To this end, all aberrations are corrected up to the window of the vacuum chamber, which yields an inhomogeneity on the atoms of several percent that is attributed to imperfections of the final window. To further optimize the homogeneity, aberration corrections are tuned on the tophat through Zernike polynomial corrections to the phase profile in the SLM plane (Fourier plane). With this procedure peak-to-peak inhomogeneities are reduced to <1% over a range of 40-50 ^^m in the atom plane.

[0139] Coherent mapping protocol

[0140] A coherent mapping protocol is provided to transfer a generic many-body state in the{|1^, |^^^} basis to the long-lived and non-interacting {|0^, |1^} basis. To achieve thismapping, immediately following the Rydberg dynamics, a Raman ^^ pulse is applied to map|1^ → |0^, and then a subsequent Rydberg ^^ -pulse to map |^^^ → |1^.

[0141] Even for perfect Raman and Rydberg ^^ pulses (on isolated atoms), there are three key sources of infidelity associated with this mapping process: (1) Any population in blockade-violating states (i.e., two adjacent atoms both in|^^^) will be strongly shifted off-resonance for the final Rydberg ^^ pulse. As such, this atomic population will be left in the Rydberg state and lost. (2) Long-range interactions, e.g., from next-nearest-neighbors, will detune the final Rydberg ^^ pulse from resonance and thus reduce pulse fidelity. Since the long-rangeHQU-01825 HU 9844 interactions are not the same for all many-body microstates, this effect cannot be mitigated by a simple shift of the detuning. (3) Dephasing of the state occurs throughout the duration of the Raman ^^ pulse, predominantly from Doppler shifts between the ground states |0^, |1^and the Rydberg state |^^^. Although these random on-site detunings are also present during the many-body dynamics, turning the Rydberg drive Ω off allows the system to freely accumulate phase errors and particular sensitivity to dephasing errors.

[0142] The above error mechanisms are mitigated as follows. To minimize errors from (1), ஐమmany-body dynamics are performed with ଶ^మబ ≈ 0.01. This minimizes the probability of anatom to violate blockade to be on the order of 1%. To help minimize errors from (2), theamplitude of the 420-nm laser is increased for the final ^^ pulse by a factor of 2 ×, such that^ಿಿಿ ଶ^ ஐ ^ = 0.005 (where ^^ேேே are the interactions with next-nearest neighbors), reducingpulse errors from long-range interactions to on the order of 1%. Finally, to reduce errors from (3), a fast Raman ^^ pulse is performed, leaving only 150 ns between ending the many- body Rydberg dynamics and beginning the Rydberg ^^ pulse. The 150-ns gap is comparablyshort relative to the ^^∗ଶ ≈ 3 − 4^^^^ of the {|^^^, |^^^} basis, leading to a random phaseaccumulation of order ∼ 0.02 × 2^^ ^^^^^^ per particle, but is further compounded by havingentangled states of N particles in one copy accumulating a random phase relative to entangled states of N particles in the second copy.

[0143] The global Raman beam induces a light-shift-induced phase shift of ≈ ^^ on |0^, |1^relative to|^^^during the Raman ^^ pulse. Similarly, the global 420-nm laser also induces alight-shift-induced phase shift of ≈ ^^ between |0^ and |1^ during the Rydberg ^^ pulse.While the measurements performed here are interferometric (in other words, the singlet stateHQU-01825 HU 9844 measured is invariant under global rotations) and thus not affected by these global phase shifts, these phase shifts can be measured and accounted for where relevant.

[0144] Continuous Reloading Architectures

[0145] In various embodiments, qubit reloading architectures are provide including: a reservoir zone or delivery zone where an optical conveyor belt as described above optionally delivers atoms, and from which tweezers are loaded; a local imaging / readout / cooling zone which is illuminated with an imaging / readout / cooling laser beam; and a computation zone where qubits are stored and quantum algorithms take place.

[0146] In various embodiments, atoms are imaged and reloaded at identical magnetic fields as the one used during encoding of qubits. In order to decouple operations in the different zone, an objective with a large field-of-view is used such that zones can be separated by hundreds of micrometers. Even if the local imaging beam is mainly illuminating the readout / imaging zone, due to reflections at mirrors / lenses or due to the tails of the imaging beam, the imaging beam intensity in the computation zone is not strictly zero. Various embodiments therefore use a shielding-beam that illuminates the computation zone and shifts the imaging transition of all atoms within the computation zone away from the laser frequency of the local imaging laser, such that switching the imaging beam on has even less impact on the qubits in the computation zone.

[0147] In various embodiments, atoms are moved between the zones using AOD tweezers, as described elsewhere herein.

[0148] Referring now to Figs.17A-17D, an exemplary zoned architecture for continuous loading is schematically illustrated. In various embodiments, a schematic for continuously reloading atoms into a quantum computer is shown in Fig.6 with increasing granularity. For example and without limitation, Fig.17A illustrates a zoomed-in schematic view of a regionHQU-01825 HU 9844 1701 where tweezers 1702 (represented by circles for the purposes of this disclosure) are overlapped with the lattice 1703 (represented by stripes for the purposes of this disclosure).

[0149] Gentle loading: Usually, loading atoms into tweezers 1702 requires laser cooling such that atoms falling into a conservative tweezer potential remain trapped and are not moving out again. When loading atoms from an atomic reservoir (a standing conveyor belt in certain embodiments described herein), this introduces problems because the cooling light can affect the atomic reservoir and photons scattered at the reservoir can also affect the coherence of nearby qubits. Various embodiments of the present disclosure enable loading the tweezers in the absence of laser cooling. Two mechanisms are provided to achieve this: stochastic loading and collisional loading. In stochastic loading, if the density in the lattice is high enough, such that the probability to find an atom within the volume of a tweezer is high, one can load tweezers stochastically. If there is an atom in the volume of the tweezer the moment the tweezer is switched on, the atom will be captured. In collisional loading, if two atoms collide within the tweezer potential, the redistribution of energy and momentum in the collision process can get one of the two atoms trapped after the collision. Fig.17B illustrates a schematic of stochastic loading, according to various embodiments of the present disclosure. As shown, an atom located within in the tweezer volume when the tweezer potential is diabatically switched on remains trapped within the tweezer 1702. Referring to Fig.17C, an illustration of an atom collision in various embodiments of the present disclosure. As shown in Fig.17C, when two atoms collide within an optical trap, exchange of energy and momentum can lead to trapping of one of the atoms after the collision. Fig.17D illustrates estimated tweezer loading rates at various parameters such as number of atoms and temperature. One may find that if atom numbers are too low or temperatures too high, loading can be inefficient. for the purposes of this disclosure, Fig.17D, radial and axial trap frequencies ^^^ = 2^^ × 500^^^^ and ^^^ = 2^^ × 500^^^^^^ areHQU-01825 HU 9844assumed. For the subfigure on the lower right, the radial trap frequency has been increased to^^^ = 2^^ × 1500^^^^. In various embodiments, this may compress the lattice reservoir andtherefore increases the loading rate at the center but decreases the area of the reloading zone.

[0150] In various exemplary embodiments, different loading rates are achieved. In a first exemplary embodiment, 200 qubits are provided, with a 2Q gate every 100 ^^^^ and 0.1% loss, yielding 2,000 qubits / sec. In a second exemplary embodiments, 1,000 qubits are provided, with a 2Q gate every 100 ^^^^ and 0.1% loss, yielding 10,000 qubits / sec. In a third exemplary embodiments, 10,000 qubits are provided, with a 2Q gate every 100 ^^^^ and 0.1% loss, yielding 100,000 qubits / sec. In a fourth exemplary embodiment, 1,000,000 qubits are provided, with a 2Q gate every 100 ^^^^ and 0.1% loss, yielding 10,000,000 qubits / sec.

[0151] The density of the atoms trapped in the lattice depends on the atom number ^^ per lattice site, the atom temperature ^^, and the radial and axial trapping frequencies ^^^and ^^௭. Within one lattice site, it is given byయwith ^^^the peak density, ^^ the radial distance from the center of thereservoir, and ^^ the axial distance from the lattice site.

[0152] Radially, the reservoir density varies slowly and can be assumed to be constant over the length scale of the tweezer. Axially, where the lattice compresses the atom cloud intopancakes much thinner than the tweezer waist ^^௧௪௭ ≈ 800^^^^, this is not true. Here, becausethe tweezer position relative to the lattice sites ^^ = 0 is unknown and varies among tweezers,ഊ^ೌ^lattice-averaged loading rates are calculated, denoted as ^ ^ర^^௧ ≡ ఒ^ೌ^ ^ିഊ^ೌ^ ^^^^ .ర

[0153] Switching the tweezer on diabatically, the probability to stochastically capture anatom at the center of the reservoir ^^ = 0 can be approximated viaHQU-01825 HU 9844with ^^௧௪௭the effective tweezer volume.

[0154] An atom moving through a background gas collides with a rate Γ(^^, ^^) =^^(^^, ^^)^^^^^^^, with ^^^^^the thermal relative velocity between two atoms, ^^ =4^^^^ଶ the scattering cross section, ^^ ≈ 98^^ 87^ the s-wave scattering length for Rb, and ^^^ theBohr radius. Consequently, the density of collisions is given by ^^^(^^, ^^)where the factor ^ଶ avoids double counting. At ^^ = 0, the lattice-averaged collisional densityis given by ^^^^(0, ^^)^^^௧ = ^ଶ ^^^ଶ(0, ^^)^^^௧^^^^^^^. Within a reservoir overlap time Δ^^, weestimate the number of loaded atoms to bewhere we introduced the probabilitythat a collision loads one atom, which can be high the tweezer potential represents the largest energy scale in the system. ^^^ௗand also ^^௧௪௭depend on the depth of the tweezer and the lattice and the atom temperature.

[0155] Estimated number of loaded atoms ^^^௧ + ^^^^^ for various parameters are included inFig. 17D. Furthermore, it is assumed that ^^ ଶ గ௪మ^^^௧௪௭ ≈ ^^௧௪௭ ^^ோ, with ^^ோ = ఒ^^^ the Rayleighlength, and ^^௧௪௭the tweezer wavelength. Obtaining large enough loading rates requires to operate in a high-density regime, which can be obtained by either increasing the overall atom number, lowering the temperature, or increasing the radial lattice confinement.

[0156] It is found that if one loads tweezers from a colder reservoir, iterative loading can be more difficult because every loading iteration increases the temperature in the lattice and therefore decreases the density. The initial atom number in the reservoir can be increased to a level where loading rates are high even at the highest temperatures available in the latticeHQU-01825 HU 9844 potential, enabling many loading iterations. In various embodiments, iterative assembly may be performed in an interleaved manner to minimize heating effects.

[0157] In various embodiments, when tweezers 1702 are created by AODs, the relative frequency between neighboring tweezers 1702 should not match the axial lattice trap frequency, otherwise the oscillating interference signal can heat atoms in the lattice, which lowers the reservoir lifetime.

[0158] Formation of Array of Particles Using Optical Tweezers

[0159] Optical trapping of neutral atoms is a powerful technique for isolating atoms in vacuum. Atoms are polarizable, and the oscillating electric field of a light beam induces an oscillating electric dipole moment in the atom. The associated energy shift in an atom from the induced dipole, averaged over a light oscillation period, is called the AC Stark shift. Based on the AC Stark shift induced by light that is detuned (i.e., offset in wavelength) from atomic resonance transitions, atoms are trapped at local intensity maxima (for red detuned, that is, longer wavelength trap light), because the atoms are attracted to light below the resonance frequency. The AC Stark shift is proportional to the intensity of the light. Thus, the shape of the intensity field is the shape of an associated atom trap. Optical tweezers utilize this principle by focusing a laser to a micron-scale waist, where individual atoms are trapped at the focus. Two-dimensional (2D) arrays of optical tweezers are generated by, for example, illuminating a spatial light modulator (SLM), which imprints a computer-generated hologram on the wavefront of the laser field. The 2D array of optical tweezers is overlapped with a cloud of laser-cooled atoms in a magneto-optical trap (MOT). The tightly focused optical tweezers operate in a “collisional blockade” regime, in which single atoms are loaded from the MOT, while pairs of atoms are ejected due to light-assisted collisions, ensuring that the tweezers are loaded with at most single atoms, but the loading is probabilistic, such that the trap is loaded with a single atom with a probability of about 50-60%.HQU-01825 HU 9844

[0160] To prepare deterministic atom arrays, a real-time feedback procedure identifies the randomly loaded atoms and rearranges them into pre-programmed geometries. Atom rearrangement requires moving atoms in tweezers which can be smoothly steered to minimize heating, by using, for example, acousto-optic deflectors (AODs) to deflect a laser beam by a tunable angle which is controlled by the frequency of an acoustic waveform applied to the AOD crystal. Dynamic tuning of the acoustic frequency translates into smooth motion of an optical tweezer. A multi-frequency acoustic wave creates an array of laser deflections, which, after focusing through a microscope objective, forms an array of optical tweezers with tunable position and amplitude that are both controlled by the acoustic waveform. Atoms are rearranged by using an additional set of dynamically moving tweezers that are overlaid on top of the SLM tweezer array.

[0161] To reiterate, a local beam geometry of two counter-propagating beams in 1D which have opposite circular polarization and are colinear to the B-field is employed. After pulling atoms from the lattice in around 5ms, they are handed over to SLM backbone array and simultaneously PGC cool, which also parity projects into single atoms. An image is then taken to verify loading, and atoms are rearranged while EIT cooling simultaneously. Then, the qubit state is prepared. According to embodiments of the present disclosure, all these operations are performed at finite field, i.e., there is no need to ramp the magnetic field in the science region for imaging / cooling. It can be seen that one can achieve low temperatures when cooling only in 1D. According to embodiments of the present disclosure, this sequence can also include fast state initialization, which relies on each of the counter-propagating beams addressing both the 2-2’ and the 1-0’ transition simultaneously. The 0 qubit state is dark by selection rules, and given the two beams and closing all transitions at the same time, only a few scattering events are necessary to pump into it. That way, a >98% state preparation fidelity in around 10 µs can be achieved. According to embodiments of theHQU-01825 HU 9844 present disclosure, rearrangement of atom arrays can be performed row-by-row, which enables pre-computation of waveforms, depicted in Fig.25C.

[0162] Exemplary Hardware

[0163] Optical tweezer arrays constitute a powerful and flexible way to construct large scale systems composed of individual particles. Each optical tweezer traps a single particle, including, but not limited to, individual neutral atoms and molecules for applications in quantum technology. Loading individual particles into such tweezer arrays is a stochastic process, where each tweezer in the system is filled with a single particle with a finite probability p<1, for example p~0.5 in the case of many neutral atom tweezer implementations. To compensate for this random loading, real-time feedback may be obtained by measuring which tweezers are loaded and then sorting the loaded particles into a programmable geometry. This may be performed by moving one particle at a time, or in parallel.

[0164] Parallel sorting may be achieved by using two acousto-optic deflectors (AODs) to generate multiple tweezers that can pick up particles from an existing particle-trapping structure, move them simultaneously, and release them somewhere else. This can include moving particles around within a single trapping structure (e.g., tweezer array) or transporting and sorting particles from one trapping system to another (e.g., between one tweezer array and another type of optical / magnetic trap). This sorting is flexible and allows programmed positioning of each particle. Each movable trap is formed by the AODs and its position is dynamically controlled by the frequency components of the radiofrequency (RF) drive field for the AODs. Since the RF drive of the AODs can be controlled in real time and can include any combination of frequency components, it is possible to generate any grid of traps (such as a line of arbitrarily positioned traps), move the rows or columns of the grid,HQU-01825 HU 9844 and add or remove rows and columns of the grid, by changing the number, magnitude, and distribution of the frequency components in the RF drive fields of the AODs.

[0165] In an exemplary embodiment, an optical tweezer array is created using a liquid crystal on silicon spatial light modulator (SLM), which can programmatically create flexible arrangements of tweezers. These tweezers are fixed in space for a given experimental sequence and loaded stochastically with individual atoms, such that each tweezer is loaded with probability p ~ 0.5. A fluorescence image of the loaded atoms is taken, to identify in real-time which tweezers are loaded and which are empty.

[0166] After detecting which tweezers are loaded, movable tweezers overlapping the optical tweezer array can dynamically reposition atoms from their starting locations to fill a target arrangement of traps with near-unity filling. The movable tweezers are created with a pair of crossed AODs. These AODs can be used to create a single moveable trap which moves one atom at a time to fill the target arrangement or to move many atoms in parallel.

[0167] Referring to Fig.18, a schematic view is provided of an apparatus 1800 for quantum computation according to embodiments of the present disclosure. As shown in Fig.18, using a beam generated by a light source 1802 (for example, a coherent light source, in some example embodiments – a monochromatic light source), SLM 1804 forms an array of trapping beams (i.e., a tweezer array) which is imaged onto trapping plane 1808 in vacuum chamber 1810 by an optical train that, in the example embodiment shown in Fig.18, comprises elements 1806a, 1806c, 1806d, and a high numerical aperture (NA) objective 1806e. Other suitable optical trains can be employed, as would be easily recognized by a person of ordinary skill in the art. Using a beam generated by light source 1812 (for example, a coherent light source; in some example embodiments - a monochromatic light source), a pair of AODs 1814 and 1816, having non-parallel directions of acoustic wave propagation (for example, orthogonal directions) creates dynamically movable sorting beams.HQU-01825 HU 9844 By using the optical train, such as the one depicted in Fig.18 (elements 1817, 1806b, 1806c, 1806d, and 1806e), the sorting beams are overlapped with the trapping beams. It is understood that other optical train can be used to achieve the same result. For example, source 1802 and 1812 can be a single source, and the trapping beam and the sorting beam are generated by a beam splitter.

[0168] The dynamic movement of the steering beams is accomplished by employing two non-parallel AODs 1814, 1816, arranged in series. In the example embodiment depicted in Fig.18, one AOD defines the direction of “rows” (“horizontal” – the ‘X’ AOD) and the other AOD defines the direction of “columns” (“vertical” – the ‘Y’ AOD). Each AOD is driven with an arbitrary RF waveform from an arbitrary waveform generator 1820, which is generated in real-time by a computer 1822 which processes the feedback routine after analyzing the image of where atoms are loaded. If each AOD is driven with a single frequency component, then a single steering beam (“AOD trap”) is created in the same plane 1808 as the SLM trap array. The frequency of the X AOD drive determines the horizontal position of the AOD trap, and the frequency of the Y AOD drive determines the vertical position; in this way, a single AOD trap can be steered to overlap with any SLM trap.

[0169] In Fig.18, laser 1802 projects a beam of light onto SLM 1804. SLM 1804 can be controlled by computer 1822 in order to generate a pattern of beams (“trapping beams” or “tweezer array”). The pattern of beams is focused by lens 1806a, passes through mirror 1806b, and is collimated by lens 1806c on mirror 1806d. The reflected light passes through objective 1806e to focus an optical tweezer array in vacuum chamber 1810 on trapping plane 1808. The laser light of the optical tweezer array continues through objective 1824a, and passes through dichroic mirror 1824b to be detected by charge-coupled device (CCD) camera 1824c.HQU-01825 HU 9844

[0170] Vacuum chamber 1810 may be illuminated by an additional light source (not pictured). Fluorescence from atoms trapped on the trapping plane also passes through objective 1824a, but is reflected by dichroic mirror 1824b to electron-multiplying CCD (EMCCD) camera 1824d. In this example, laser 1812 directs a beam of light to AODs 1814, 1816. AODs 1814, 1816 are driven by arbitrary wave generator (AWG) 1820, which is in turn controlled by computer 1822. Crossed AODs 1814, 1816 emit one or more beams as set forth above, which are directed to focusing lens 1817. The beams then enter the same optical train 1806b…1806e as described above with regard to the optical tweezer array, focusing on trapping plane 1808.

[0171] Referring now to Fig.19, a schematic representation of continuous loading of atomic qubits is illustrated according to various embodiments of the present disclosure. The reloading of lost atomic qubits is critical for realizing deep quantum circuits running useful algorithms. Atom loss may be approximately 0.1% per circuit layer, necessitating replacement. The population may be left in a Rydberg state. There may be losses during imaging. Fig.19 includes an optical lattice conveyor belt. An “optical lattice” is a periodic potential for trapping atoms formed by standing-wave interference of two counter- propagating laser beams, and the periodicity is fully determined by the standing wave interference. In various embodiments, the two counter-propagating laser beams may be detuned in frequency relative to one another, the standing wave becomes a moving wave and transports atoms spatially. In various embodiments, the optical lattice conveyor belt may be capable of bringing in greater than one million fresh atoms at a time from a distant cold atom source. In various embodiments, the distant cold atom source may be 50 centimeters away to avoid affecting data qubits. In various embodiments, an optical tweezer array may be overlapped with the optical lattice reservoir to extract single atoms. A “tweezer array” is a regular pattern of individually focused laser spots each of which are capable of trapping aHQU-01825 HU 9844 single atom. In various embodiments, spatial patterns may be programmable by one or more users and do not have to be a regular geometry. In various embodiments, the optical lattice conveyor belt may not require cooling lasers to load the optical tweezers from the optical lattice atom reservoir. As shown in Fig.19, the loaded optical tweezer array may be moved to a localized imaging and state preparation zone. In various embodiments, the localized imaging and state preparation zone may include one or more spatially confined laser beams configured to verify loading and initialize qubit state without affecting data qubits in the computational zone. Further, local imaging and state preparation zone may include efficient cooling and imaging at finite B-field to avoid the need to ramp fields for qubit replenishment, as shown in Fig.25A-25B. With continued reference to Fig.19, fresh qubits may be moved back into the computational zone. In various embodiments, a large field-of-view microscope objective may allow sufficient spatial separation between the aforementioned zones to suppress cross-talk therebetween. For example and without limitation, a laser at 1530 nm illuminating the computational zone may further shield qubits there to suppress the effect of reloading one or more laser beams, local imaging and state preparation lasers on qubit state, a schematic view of which is illustrated in Fig.24. Further, the decoherence of qubit due to inhomogeneities can be prolonged by applying dynamical decoupling techniques, such as 256 dynamical decoupling pulses.

[0172] Fig.23A illustrates Rabi oscillations, analyzed for every row of the atom array independently. These data are used to align the Rabi-oscillation laser beam with the atoms — if the alignment is optimized, the Rabi oscillations are highest in the central row. Fig.23B likewise shows Rabi oscillations for different rows. These oscillations characterize quantum coherence, which is maintained during reloading. Fig.23C illustrates coherence contrast without MOT operation, with MOT operating at 30% duty cycle, and 100% duty cycle. The effect of the 1530 nm laser to suppress qubit decoherence is shown in Fig.23D-23E. Fig.HQU-01825 HU 9844 23F illustrates Ramsey contrast of exemplary qubits. The continuous loading of atomic qubits without decoherence on remaining data qubits and at a sufficiently high rate to sustain large- scale quantum operations may be accomplished according to various embodiments of the disclosure.

[0173] Referring now to Fig.21, a sequence of continuous atom loading is shown. Continuous loading of atoms as described herein may load atoms with a greater than 50% fill rate. In some embodiments, the loading mechanism may be collision between atoms. For example, 40 rounds of loading over a period of 100 ms may load greater than 10,000 single atoms, such as 40,000 single atoms, as shown in Fig.22. In some embodiments, small movements of lattices, such as about 30 µm every 3 pulls refreshes the loading. In some embodiments, the MOT is loaded during pulling of atoms from the reservoir, in this manner, tweezers may be loaded from the reservoir continuously, which are in turn dropped and imaged into the SLM array. In some embodiments, instead of the entire state preparation sequence being performed, the atoms are only imaged. In this way, a highly deterministic atom flux in the tweezers of about 75,000 atoms per second is illustrated in Fig.21. The only instance in which no reservoir is present is when atoms are transferred from one lattice to another, however, as the previous qubit preparation sequence, which may include cooling, imaging, rearrangement and state initialization takes longer than the transfer, reservoir replenishment is continuous. A visual representation of this sequence is illustrated in Fig.21. In some embodiments, said sequence may be timed in the following manner: loading of MOT in 50 ms, cooling and loading of lattice in 20 ms, moving source lattice in 50 ms, lattice handover in 10 ms, move second lattice in 30 ms, load atoms in 100 ms, and cooling and imaging in 20 ms. In some embodiments, lattice handover to cooling and imaging may occur in 150 ms. In some embodiments, the continuous loading can be used to iteratively build a larger storage zone array. Graphs of probability density versus loading fraction of MOT andHQU-01825 HU 9844 lattices shown in Fig.22 indicate that simply overlapping tweezers with the lattice is enough to achieve loading that is as effective as loading from the MOT directly.

[0174] According to embodiments of the present disclosure, an apparatus for quantum computation may include an optical lattice reservoir as described herein. In various embodiments, optical lattice reservoir may include over a million atoms, said apparatus configured to extract greater than 40,000 single atoms in tweezers. The apparatus may include an imaging and state preparation zone as described herein, said zone may also be configured to reload atoms continuously. In various embodiments, the optical lattice reservoir may be spaced from the imaging and state preparation zone by 220 um. In various embodiments the imaging and state preparation zone may be formed in an array having a side length of 50 µm. According to embodiments of the present disclosure, the apparatus may include a computational zone, such as in a 3000 qubit loaded tweezer array, having a side length of 110 µm. In various embodiments, the computational zone may be spaced from the imaging and state preparation zone by 220 µm. In various embodiments, the optical lattice reservoir may be spaced from the computational zone by 600 µm.

[0175] It will be appreciated that alternative optical trains may be employed to produce an optical tweezer array suitable for use as set out herein.

[0176] The descriptions of the various embodiments of the present disclosure have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

HQU-01825 HU 9844 CLAIMS What is claimed is:

1. A device for moving atoms, comprising: an atom reservoir, configured to generate a cloud of atoms; a computation chamber, comprising an active zone configured to hold an array of atoms and adapted to perform quantum gates thereon; a differential vacuum tube operably connected to the atom reservoir and the computation chamber; at least one laser source configured to generate a first beam having a first frequency and a second beam having a second frequency; a first optical lattice generator configured to generate a first optical lattice based on the first beam, the first optical lattice generator adapted to detune the first frequency; and a second optical lattice generator configured to generate a second optical lattice based on the second beam, the second optical lattice generator adapted to detune the second frequency, wherein: the first optical lattice extends from the atom reservoir, through the differential vacuum tube, and into the computation chamber without passing through the active zone; the second optical lattice extends from the differential vacuum tube to the computational chamber, passing through the active zone; and the first and the second optical lattices intersect, thereby forming a handover region.

2. The device of Claim 1, comprising a magneto-optical trap adapted to trap atoms within the atom reservoir, and to load the atoms into the first optical lattice.

3. The device of any one of Claims 1 or 2, wherein each of the first and the second optical lattice generators comprises a retroreflector and an acousto-optical modulator.

4. The device of any one of Claims 1-3, further comprising an array of optical tweezers adapted to form an array of atoms in the active zone.HQU-01825 HU 9844 5. The device of any one of Claims 1-4, wherein the differential vacuum tube forms an aperture configured to prevent photons spontaneously scattered from atoms disposed in the atom reservoir from reaching the active zone.

6. The device of any one of Claim 1-5, wherein the first and the second optical lattices intersect at an angle that is greater than zero and less than 90 degrees.

7. A method of moving atoms in a device comprising: an atom reservoir, configured to generate a cloud of atoms; a computation chamber, comprising an active zone configured to hold an array of atoms and adapted to perform quantum gates thereon;; a differential vacuum tube operably connected to the atom reservoir and the computation chamber; at least one laser source configured to generate a first beam having a first frequency and a second beam having a second frequency; a first optical lattice generator configured to generate a first optical lattice based on the first beam, the first optical lattice generator adapted to detune the first frequency; and a second optical lattice generator configured to generate a second optical lattice based on the second beam, the second optical lattice generator adapted to detune the second frequency, wherein: the first optical lattice extends from the atom reservoir, through the differential vacuum tube, and into the computation chamber without passing through the active zone; the second optical lattice extends from the differential vacuum tube to the computational chamber passing through the active zone; and the first and the second optical lattices intersect, thereby forming a handover region, the method comprising: trapping atoms within the atom reservoir; generating the first beam having the first frequency and the second beam having the second frequency;HQU-01825 HU 9844 generating the first optical lattice based on the first beam; loading atoms within the atom reservoir into the first optical lattice; detuning the first frequency, thereby moving the atoms in the first optical lattice from the atom reservoir to the handover region; generating the second optical lattice based on the second beam; transferring the atoms from the first optical lattice to the second optical lattice; detuning the second frequency, thereby moving the atoms from the handover region to the active zone; and forming the array of atoms in the active zone.

8. The method of Claim 7, wherein transferring the atoms from the first optical lattice to the second optical lattice comprises reducing power of the first beam and increasing power of the second beam.

9. A device for continuous loading of qubits for quantum computation, comprising: a computation chamber, the computation chamber comprising an active zone, an imaging zone, and a reservoir zone, wherein the active zone is configured to hold a first array of atoms and adapted to perform quantum gates thereon, the delivery zone is configured to provide a supply of atoms, and the imaging zone is configured to hold a second array of atoms, wherein the imaging zone and the active zone are separated by a distance sufficient to reduce a photon scattering decoherence probability to less than or equal to 0.01; at least one moveable optical tweezer configured to convey atoms from the delivery zone to the imaging zone and from the imaging zone to the active zone; at least one imaging laser configured to illuminate the imaging zone; at least one image sensor configured to detect atoms in the imaging zone upon illumination by the imaging laser; and a shielding laser configured to illuminate the active zone when the imaging laser illuminates the imaging zone, the shielding laser inducing a state shift on atoms in the active zone that suppresses response to scattering from the imaging laser.HQU-01825 HU 9844 10. The device of Claim 9, wherein the first array and the second array of atoms are trapped by optical tweezers generated through a common objective.

11. The device of any one of Claims 9-10, further comprising: an acousto-optical device (AOD) configured to generate the at least one moveable optical tweezer.

12. The device of any one of Claims 9-11, wherein the shielding laser has a wavelength about 1530nm or about 776nm.

13. The device of any one of Claims 9-12, further comprising: at least one cooling laser configured to illuminate the imaging zone, the cooling laser configured to cool atoms in the presence of a finite B-field.

14. The device of any one of Claims 9-13, further comprising: at least one initialization laser configured to illuminate the imaging zone and initialize atoms therein as qubits.

15. The device of any one of Claims 9-14, wherein the imaging zone and the active zone are separated by at least 200^^^^.

16. The device of any one of Claims 9-15, wherein the at least one moveable optical tweezer configured to capture atoms from the delivery zone with laser-free dissipation.

17. A system for quantum computation comprising: the device of any one of Claims 1-6 and the device of any one of Claims 9-16, wherein the first optical lattice is configured to deliver atoms to the delivery zone.

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