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Quantum computers must achieve large-scale, fault-tolerant operation to deliver on their promise of transformational processing power [1-4]. This will require thousands or millions of high-fidelity quantum gates and similar numbers of qubits [5]. Demonstrations using neutral-atom qubits trapped and manipulated by lasers have shown that this modality can provide high two-qubit gate (CZ) fidelities and scalable operation [6-10]. However, the gates in these demonstrations are driven by lasers that do not resolve individual qubits, with universal computation enabled by physical mid-circuit shuttling of the qubits. This relatively slow operation will greatly extend runtimes for useful, large-scale computation. Here we demonstrate a universal neutral-atom quantum computer with gate rates limited by optical switching times, rather than shuttling, by individually addressing tightly focused laser beams at an array of single atoms. We achieve CZ fidelity of 99.35(4)% and local single qubit RZ gate fidelity of 99.902(8)%. Moreover, we demonstrate non-destructive readout of alkali-atom qubits with sub-percent loss, which boosts operational speed. This technique also enables us to measure 99.73(3)% CZ fidelity with atom-loss events excluded, which is a record among long lived neutral-atom qubits and highlights the path to higher fidelity and error correction. Our results represent a critical step towards large-scale, fault-tolerant neutral-atom quantum computers that can execute computations on practical timescales.

We propose and analyze an approach for fast syndrome measurements in an array of rubidium and cesium atomic qubits. The scheme works by implementing an inter-species $\textsf{CNOT}_k$ gate, entangling one cesium ancilla qubit with $k\geq 1$ rubidium qubits which are then used for state measurement. Utilizing Rydberg states with different inter- and intra-species interaction strengths, the proposal provides a syndrome measurement fidelity of $\mathcal{F}>0.9999$ in less than 5 $\mu$s of integration time., Comment: Minor edits to text and additional references added

We propose an implementation of bivariate bicycle codes (Nature {\bf 627}, 778 (2024)) based on long-range Rydberg gates between stationary neutral atom qubits. An optimized layout of data and ancilla qubits reduces the maximum Euclidean communication distance needed for non-local parity check operators. An optimized Rydberg gate pulse design enables $\sf CZ$ entangling operations with fidelity ${\mathcal F}>0.999$ at a distance greater than $12~\mu\rm m$. The combination of optimized layout and gate design leads to a quantum error correction cycle time of $\sim 1.2~\rm ms$ for a $[[144,12,12]]$ code, an order of magnitude improvement over previous designs.

We propose a scheme for two-qubit gates between a flying photon and an atom in a cavity. The atom-photon gate setup consists of a cavity and a Mach-Zehnder interferometer with doubly degenerate ground and excited state energy levels mediating the atom-light interaction. We provide an error analysis of the gate and model important errors, including spatial mode mismatch between the photon and the cavity, spontaneous emission, cavity losses, detunings, and random fluctuations of the cavity parameters and frequencies. Error analysis shows that the gate protocol is more robust against experimental errors compared to previous atom-photon gates and achieves higher fidelity., Comment: 6 figures, final version

We demonstrate qubit state measurements assisted by a supervised convolutional neural network (CNN) in a neutral atom quantum processor. We present two CNN architectures for analyzing neutral atom qubit readout data: a compact 5-layer single-qubit CNN architecture and a 6-layer multi-qubit CNN architecture. We benchmark both architectures against a conventional Gaussian threshold analysis method. In a sparse array (9 {\mu}m atom separation) which experiences negligible crosstalk, we observed up to 32% and 56% error reduction for the multi-qubit and single-qubit architectures respectively, as compared to the benchmark. In a tightly spaced array (5 {\mu}m atom separation), which suffers from readout crosstalk, we observed up to 43% and 32% error reduction in the multi-qubit and single-qubit CNN architectures respectively, as compared to the benchmark. By examining the correlation between the predicted states of neighboring qubits, we found that the multi-qubit CNN architecture reduces the crosstalk correlation up to 78.5%. This work demonstrates a proof of concept for a CNN network to be implemented as a real-time readout processing method on a neutral atom quantum computer, enabling faster readout time and improved fidelity., Comment: additional data added

In this study, we simulated the algorithmic performance of a small neutral atom quantum computer and compared its performance when operating with all-to-all versus nearest-neighbor connectivity. This comparison was made using a suite of algorithmic benchmarks developed by the Quantum Economic Development Consortium. Circuits were simulated with a noise model consistent with experimental data from Nature 604, 457 (2022). We find that all-to-all connectivity improves simulated circuit fidelity by $10\%-15\%$, compared to nearest-neighbor connectivity.

We demonstrate reduction of the dc polarizability of Cesium atom Rydberg states in a 77 K environment utilizing microwave field dressing. In particular we reduce the polarizability of $52P_{3/2}$ states which have resonances at 5.35 GHz to $51D_{5/2}$, suitable for interfacing Rydberg atoms to superconducting resonators in a cryogenic environment. We measure the polarizability of the Rydberg states using Magneto-Optical-Trap (MOT) loss spectroscopy. Using an off-resonant radio-frequency (RF) dressing field coupling $52P_{3/2}$ and $51D_{5/2}$ we demonstrate a reduction in dc polarizability of the $ 52P_{3/2}$ states over 80$\%$. Experimental findings are in good agreement with a numerical model of the atom-dressing field system developed using the Shirley-Floquet formalism. We also demonstrate that the dc polarizability reduction is highly anisotropic, with near total nulling possible when the dc and dressing fields are aligned, but only a factor of two reduction in polarizability when the fields are orthogonal. These results may aid in stabilizing Rydberg resonances against varying dc fields present near surfaces, enabling advancement in the development of hybrid Rydberg atom - superconducting resonator quantum gates., Comment: figure labeling corrected, and polarizability values added

We demonstrate mid-circuit measurements in a neutral atom array by shelving data qubits in protected hyperfine-Zeeman sub-states while non-destructively measuring an ancilla qubit. Measurement fidelity was enhanced using microwave repumping of the ancilla during the measurement. The coherence of the shelved data qubits was extended during the ancilla readout with dynamical decoupling pulses, after which the data qubits are returned to mf = 0 computational basis states. We demonstrate that the quantum state of the data qubits is well preserved up to a constant phase shift with a state preparation and measurement (SPAM) corrected process fidelity of F = 97.0(5)%. The measurement fidelity on the ancilla qubit after correction for state preparation errors is F = 94.9(8)% and F = 95.3(1.1)% for |0> and |1> qubit states, respectively. We discuss extending this technique to repetitive quantum error correction using quadrupole recooling and microwave-based quantum state resetting., Comment: v3: additional appendices with fidelity analysis added

We propose to integrate dark-state based localization techniques into a neutral atom quantum computing architecture and numerically investigate two specific schemes. The first scheme implements state-selective projective measurement by scattering photons from a specific qubit with very little cross talk on the other atoms in the ensemble. The second scheme performs a single-qubit phase gate on the target atom with an incoherent spontaneous emission probability as low as 0.01. Our numerical simulations in rubidium (Rb) atoms show that for both of these schemes a spatial resolution at the level of tens of nanometers using near-infrared light can be achieved with experimentally realistic parameters.

We present a technique for rapid site-selective control of the quantum state of particles in a large array using a combination of a fast deflector (e.g. an acousto-optic deflector) and a relatively slow spatial light modulator. The use of spatial light modulators for site-selective quantum state manipulation has been limited due to slow transition times preventing rapid, consecutive quantum gates. By partitioning the spatial light modulator into multiple segments, and using a fast deflector to transition between them, it is possible to substantially reduce the average time increment between scanner transitions by increasing the number of gates that can be performed for a single spatial light modulator full frame setting. We analyze the performance of this device in two different configurations: in configuration 1, each segment of the spatial light modulator addresses the full qubit array; in configuration 2, each segment of the spatial light modulator addresses a sub-array and an additional fast deflector positions that sub-array with respect to the full qubit array. With these hybrid scanners we calculate qubit addressing rates that are tens to hundreds of times faster than using an SLM alone., Comment: 8 figures, minor revisions

We introduce SupercheQ, a family of quantum protocols that achieves asymptotic advantage over classical protocols for checking the equivalence of files, a task also known as fingerprinting. The first variant, SupercheQ-EE (Efficient Encoding), uses n qubits to verify files with 2^O(n) bits -- an exponential advantage in communication complexity (i.e. bandwidth, often the limiting factor in networked applications) over the best possible classical protocol in the simultaneous message passing setting. Moreover, SupercheQ-EE can be gracefully scaled down for implementation on circuits with poly(n^l) depth to enable verification for files with O(n^l) bits for arbitrary constant l. The quantum advantage is achieved by random circuit sampling, thereby endowing circuits from recent quantum supremacy and quantum volume experiments with a practical application. We validate SupercheQ-EE's performance at scale through GPU simulation. The second variant, SupercheQ-IE (Incremental Encoding), uses n qubits to verify files with O(n^2) bits while supporting constant-time incremental updates to the fingerprint. Moreover, SupercheQ-IE only requires Clifford gates, ensuring relatively modest overheads for error-corrected implementation. We experimentally demonstrate proof-of-concepts through Qiskit Runtime on IBM quantum hardware. We envision SupercheQ could be deployed in distributed data settings, accompanying replicas of important databases.

The fidelity of gate operations on neutral atom qubits is often limited by fluctuations of the laser drive. Here, we quantify the sensitivity of quantum gate fidelities to laser phase and intensity noise. We first develop models to identify features observed in laser self-heterodyne noise spectra, focusing on the effects of white noise and servo bumps. In the weak-noise regime, characteristic of well-stabilized lasers, we show that an analytical theory based on a perturbative solution of a master equation agrees very well with numerical simulations that incorporate phase noise. We compute quantum gate fidelities for one- and two-photon Rabi oscillations and show that they can be enhanced by an appropriate choice of Rabi frequency relative to spectral noise peaks. We also analyze the influence of intensity noise with spectral support smaller than the Rabi frequency. Our results establish requirements on laser noise levels needed to achieve desired gate fidelities., Comment: v3: added analysis of the Lambda configuration

We present an approach for trapping cold atoms in a 2D optical trap array generated with a novel 4f filtering scheme and custom transmission mask without any active device. The approach can be used to generate arrays of bright or dark traps, or both simultaneously with a single wavelength for forming two-species traps. We demonstrate the design by creating a 2D array of 1225 dark trap sites, where single Cs atoms are loaded into regions of near-zero intensity in an approximately Gaussian profile trap. Moreover, we demonstrate a simple solution to the problem of out-of-focus trapped atoms, which occurs due to the Talbot effect in periodic optical lattices. Using a high power yet low cost spectrally and spatially broadband laser, out-of-focus interference is mitigated, leading to near perfect removal of Talbot plane traps., Comment: v3: minor revisions

We propose and analyze a Cesium lattice optical clock (CLOC) which has the potential for high performance and simple operation in a compact form factor using a forbidden optical transition in Cs atoms at 685 nm. Cs atoms are trapped in a 3D optical lattice using a magic trap wavelength of $\lambda_{\textrm m}=803~\textrm nm$. To reduce sensitivity to magnetic fields the atoms are probed on two cycling transitions with equal magnitude, but opposite magnetic shifts. Operation of the clock requires only three diode lasers at 685, 803, 852 nm and is simplified compared to other higher-performance optical clocks that rely on alkaline earth atoms or single trapped ions. Analysis shows a quantum noise limited stability of $8.4\times 10^{-16}/\sqrt\tau$ and the potential for reaching 1 ns timing uncertainty at 1 month with realistic system parameters.

Development of a network for remote entanglement of quantum processors is an outstanding challenge in quantum information science. We propose and analyze a two-species architecture for remote entanglement of neutral atom quantum computers based on integration of optically trapped atomic qubit arrays with fast optics for photon collection. One of the atomic species is used for atom-photon entanglement, and the other species provides local processing. We compare the achievable rates of remote entanglement generation for two optical approaches: free space photon collection with a lens and a near-concentric, long working distance resonant cavity. Laser cooling and trapping within the cavity removes the need for mechanical transport of atoms from a source region, which allows for a fast repetition rate. Using optimized values of the cavity finesse, remote entanglement generation rates $> 10^3~\rm s^{-1}$ are predicted for experimentally feasible parameters., Comment: v3: minor revisions

Gate model quantum computers promise to solve currently intractable computational problems if they can be operated at scale with long coherence times and high fidelity logic. Neutral atom hyperfine qubits provide inherent scalability due to their identical characteristics, long coherence times, and ability to be trapped in dense multi-dimensional arrays\cite{Saffman2010}. Combined with the strong entangling interactions provided by Rydberg states\cite{Jaksch2000,Gaetan2009,Urban2009}, all the necessary characteristics for quantum computation are available. Here we demonstrate several quantum algorithms on a programmable gate model neutral atom quantum computer in an architecture based on individual addressing of single atoms with tightly focused optical beams scanned across a two-dimensional array of qubits. Preparation of entangled Greenberger-Horne-Zeilinger (GHZ) states\cite{Greenberger1989} with up to 6 qubits, quantum phase estimation for a chemistry problem\cite{Aspuru-Guzik2005}, and the Quantum Approximate Optimization Algorithm (QAOA)\cite{Farhi2014} for the MaxCut graph problem are demonstrated. These results highlight the emergent capability of neutral atom qubit arrays for universal, programmable quantum computation, as well as preparation of non-classical states of use for quantum enhanced sensing., Comment: 4 figures and supplemental material. V2 details on phase estimation and RB data included

When a quantum system is put into an excited state, it will decay back to the ground state through a process termed spontaneous emission. It is generally assumed that spontaneous emission between different individual emitters would not be coherent with each other; to produce coherent light one would need population inversion and stimulated emission. In this work, we show that an optically-thin ensemble of 11,000 radiating atoms spontaneously organize to produce spatially coherent light. The reason for this coherence is collective-coupling of the individual emitters via Dicke superradiance and subradiance (as opposed to amplification through stimulated emission)., Comment: 12 pages, 11 figures

Variational quantum algorithms such as the quantum approximate optimization algorithm (QAOA) are particularly attractive candidates for implementation on near-term quantum processors. As hardware realities such as error and qubit connectivity will constrain achievable circuit depth in the near future, new ways to achieve high-performance at low depth are of great interest. In this work, we present a modification to QAOA that adds additional variational parameters in the form of freedom of the rotation-axis in the $XY$-plane of the mixer Hamiltonian. Via numerical simulation, we show that this leads to a drastic performance improvement over standard QAOA at finding solutions to the MAXCUT problem on graphs of up to 7 qubits. Furthermore, we explore the Z-phase error mitigation properties of our modified ansatz, its performance under a realistic error model for a neutral atom quantum processor, and the class of problems it can solve in a single round., Comment: 8 pages, 4 figures, 3 pages and 5 figures supplementary

Limits to Rydberg gate fidelity that arise from the entanglement of internal states of neutral atoms with the motional degrees of freedom due to the momentum kick from photon absorption and re-emission is quantified. This occurs when the atom is in a superposition of internal states but only one of these states is manipulated by visible or UV photons. The Schr\"odinger equation that describes this situation is presented and two cases are explored. In the first case, the entanglement arises because the spatial wave function shifts due to the separation in time between excitation and stimulated emission. For neutral atoms in a harmonic trap, the decoherence can be expressed within a sudden approximation when the duration of the laser pulses are shorter than the harmonic oscillator period. In this limit, the decoherence is given by simple analytic formulas that account for the momentum of the photon, the temperature of the atoms, the harmonic oscillator frequency, and atomic mass. In the second case, there is a reduction in gate fidelity because the photons causing absorption and stimulated emission are in focused beam modes. This leads to a dependence of the optically induced changes in the internal states on the center of mass atomic position. In the limit where the time between pulses is short, the decoherence can be expressed as a simple analytic formula involving the laser waist, temperature of the atoms, the trap frequency and the atomic mass. These limits on gate fidelity are studied for the standard $\pi-2\pi-\pi$ Rydberg gate and a new protocol based on a single adiabatic pulse with Gaussian envelope., Comment: 8 figures

Atomic nuclei are important laboratories for exploring and testing new insights into the universe, such as experiments to directly detect dark matter or explore properties of neutrinos. The targets of interest are often heavy, complex nuclei that challenge our ability to reliably model them (as well as quantify the uncertainty of those models) with classical computers. Hence there is great interest in applying quantum computation to nuclear structure for these applications. As an early step in this direction, especially with regards to the uncertainties in the relevant quantum calculations, we develop circuits to implement variational quantum eigensolver (VQE) algorithms for the Lipkin-Meshkov-Glick model, which is often used in the nuclear physics community as a testbed for many-body methods. We present quantum circuits for VQE for two and three particles and discuss the construction of circuits for more particles. Implementing the VQE for a two-particle system on the IBM Quantum Experience, we identify initialization and two-qubit gates as the largest sources of error. We find that error mitigation procedures reduce the errors in the results significantly, but additional quantum hardware improvements are needed for quantum calculations to be sufficiently accurate to be competitive with the best current classical methods., Comment: 11 pages of RevTeX, 8 figures

The problem of high-speed transport for cold atoms with minimal heating has received considerable attention in theory and experiment. Much theoretical work has focused on solutions of general problems, often assuming a harmonic trapping potential or a 1D geometry. However in the case of optical conveyor belts these assumptions are not always valid. Here we present experimental and numerical studies of the effects of various motional parameters on heating and retention of atoms transported in an optical conveyor. Our numerical model is specialized to the geometry of a moving optical lattice and uses dephasing in the density matrix formalism to account for effects of motion in the transverse plane. We verify the model by a comparison with experimental measurements, and use it to gain further insight into the relationship between the conveyor's performance and the various parameters of the system., Comment: 10 pages, 6 figures, references corrected

We review methods for coherently controlling Rydberg quantum states of atomic ensembles using Adiabatic Rapid Passage and Stimulated Raman Adiabatic Passage. These methods are commonly used for population inversion in simple two-level and three-level systems. We show that adiabatic techniques allow us to control population and phase dynamics of complex entangled states of mesoscopic atomic ensembles for quantum information processing with Rydberg atoms. We also propose several schemes of single-qubit and two-qubit gates based on adiabatic passage, Rydberg blockade and F\"{o}rster resonances in Rydberg atoms., Comment: 13 pages, 15 figures. This is a tutorial, submitted to Journal of Physics B. arXiv admin note: text overlap with arXiv:1606.08198, arXiv:1310.3921

We analyze neutral atom Rydberg $C_Z$ gates based on adiabatic pulses applied symmetrically to both atoms. Analysis with smooth pulse shapes and Cs atom parameters predicts the gates can create Bell states with fidelity ${\mathcal F}>0.999$ using adiabatic rapid passage (ARP) pulses. With globally optimized adiabatic pulse shapes, in a two-photon excitation process, we generate Bell states with fidelity ${\mathcal F}=0.997$. The analysis fully accounts for spontaneous emission from intermediate and Rydberg states, including the Rydberg lifetime in a room temperature environment, but does not include errors arising from laser noise. The gate protocols do not require individual addressing and are shown to be robust against Doppler shifts due to atomic motion., Comment: 10 figures, added robustness analysis with respect to laser intensity and frequency

We demonstrate high fidelity two-qubit Rydberg blockade and entanglement in a two-dimensional qubit array. The qubit array is defined by a grid of blue detuned lines of light with 121 sites for trapping atomic qubits. Improved experimental methods have increased the observed Bell state fidelity to $F_{\rm Bell}=0.86(2)$. Accounting for errors in state preparation and measurement (SPAM) we infer a fidelity of $F_{\rm Bell}^{\rm -SPAM}=0.88$. Accounting for errors in single qubit operations we infer that a Bell state created with the Rydberg mediated $C_Z$ gate has a fidelity of $F_{\rm Bell}^{C_Z}=0.89$. Comparison with a detailed error model based on quantum process matrices indicates that finite atom temperature and laser noise are the dominant error sources contributing to the observed gate infidelity., Comment: includes supplemental material, error analysis revised to use process matrices

We propose a scheme of fast three-qubit Toffoli quantum gate for ultracold neutral-atom qubits. The scheme is based on the Stark-tuned three-body F\"{o}rster resonances, which we have observed in our recent experiment [D.B.Tretyakov et al., Phys.Rev.Lett. 119, 173402 (2017)]. The three-body resonance corresponds to a transition when the three interacting atoms change their states simultaneously, and it occurs at a different dc electric field with respect to the two-body F\"{o}rster resonance. A combined effect of three-body and two-body F\"{o}rster interactions in external electric and magnetic fields near the three-body resonance results in complex coherent behavior of the populations and phases of collective states of a three-atom system. We have found that it is possible to obtain experimental conditions suitable to implement three-qubit Toffoli gate with 96.8\% fidelity and less than 3~$\mu$s duration., Comment: 7 pages, 5 figures, Version 2 revised according to referee's comments. Typo in Eq.(2) corrected in Version 3

The theory is developed for one and two atom interactions when the atom has a Rydberg electron attached to a hyperfine split core state. This situation is relevant for some of the rare earth and alkaline earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare earth atoms, the core electrons can have a very substantial total angular momentum, $J$, and a non-zero nuclear spin, $I$. In the alkaline earth atoms there is a single, $s$, core electron whose spin can couple to a non-zero nuclear spin for odd isotopes. The resulting hyperfine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the unperturbed Rydberg series of the alkali atoms, the series perturbations and near degeneracies from the different parity states could lead to qualitatively different behavior for single atom Rydberg properties (polarizability, Zeeman mixing and splitting, etc) as well as Rydberg-Rydberg interactions ($C_5$ and $C_6$ matrices).

We propose a method for reducing the sensitivity of atomic ground to Rydberg transitions to stray dc electric fields, using microwave-induced dressing of Rydberg states. Calculations are presented for the Cs $\state{90S}{1/2}$ and $\state{90P}{3/2}$ states. With zero dc bias electric field, a two-frequency ac field is used to simultaneously reduce the sensitivity of both states to dc field variations. The sensitivity reduction is a factor of 95 for the $\state{90S}{1/2}$ state and a factor of 1600 for the $\state{90P}{3/2}, m_J=3/2$ state. We also show how the two-frequency ac field can be used to cancel both second- and fourth-order terms in the polarizability of a single Rydberg state. These results are relevant to improving the stability of experiments that seek to excite Rydberg atoms in the proximity of charged surfaces., Comment: 9 figures, minor revisions

We demonstrate low-loss measurement of the hyperfine ground state of Rubidium atoms in a dipole trap array of five sites by state dependent fluorescence detection. The presence of atoms and their internal states are minimally altered by utilizing circularly polarized probe light and a strictly controlled quantization axis. We achieve mean state detection fidelity of \(97\%\) without correcting for imperfect state preparation or background losses, and \(98.7\%\) when corrected. After state detection and correction for background losses, the probability of atom loss due to the state measurement is \(<2\%\) and the initial hyperfine state is preserved with \(>98\%\) probability., Comment: includes supplemental material

A candidate for converting quantum information from microwave to optical frequencies is the use of a single atom that interacts with a superconducting microwave resonator on one hand and an optical cavity on the other. The large electric dipole moments and microwave transition frequencies possessed by Rydberg states allow them to couple strongly to superconducting devices. Lasers can then be used to connect a Rydberg transition to an optical transition to realize the conversion. Since the fundamental source of noise in this process is spontaneous emission from the atomic levels, the resulting control problem involves choosing the pulse shapes of the driving lasers so as to maximize the transfer rate while minimizing this loss. Here we consider the concrete example of a cesium atom, along with two specific choices for the levels to be used in the conversion cycle. Under the assumption that spontaneous emission is the only significant source of errors, we use numerical optimization to determine the likely rates for reliable quantum communication that could be achieved with this device. These rates are on the order of a few Mega-qubits per second., Comment: 11 pages, 4 pdf figures, 2 png figures, Revtex4-1. v2: correction to metadata only

We propose schemes of controlled-Z and controlled-NOT gates with ultracold neutral atoms based on deterministic phase accumulation during double adiabatic passage of the Stark-tuned F\"{o}rster resonance of Rydberg states. The effect of deterministic phase accumulation during double adiabatic passage in a two-level quantum system has been analyzed in detail. Adiabatic rapid passage using nonlinearly chirped pulses with rectangle intensity profile has been discussed. Nonlinear time dependence of the energy detuning from the F\"{o}rster resonance is used to achieve a high fidelity of population transfer between Rydberg states. Fidelity of two-qubit gates has been studied with an example of the $90S+96S\to 90P+95P$ Stark-tuned F\"{o}rster resonance in Cs Rydberg atoms., Comment: 10 pages, 7 figures. Version 2 revised according to the referees' comments. Fig.1 replaced in Version 3. Accepted to PRA

We present a pair of optimized objective lenses with long working distances of 117~mm and 65~mm respectively that offer diffraction limited performance for both Cs and Rb wavelengths when imaging through standard vacuum windows. The designs utilise standard catalog lens elements to provide a simple and cost-effective solution. Objective 1 provides $\mathrm{NA}=0.175$ offering 3~$\mu$m resolution whilst objective 2 is optimized for high collection efficiency with $\mathrm{NA}=0.29$ and 1.8~$\mu$m resolution. This flexible design can be further extended for use at shorter wavelengths by simply re-optimising the lens separations., Comment: 4 pages, 5 figures

We show that the use of shaped pulses improves the fidelity of a Rydberg blockade two-qubit entangling gate by several orders of magnitude compared to previous protocols based on square pulses or optimal control pulses. Using analytical Derivative Removal by Adiabatic Gate (DRAG) pulses that reduce excitation of primary leakage states and an analytical method of finding the optimal Rydberg blockade we generate Bell states with a fidelity of $F>0.9999$ in a 300 K environment for a gate time of only $50\;{\rm ns}$, which is an order of magnitude faster than previous protocols. These results establish the potential of neutral atom qubits with Rydberg blockade gates for scalable quantum computation., Comment: 6 pages, 5 figures

We present a review of quantum computation with neutral atom qubits. After an overview of architectural options and approaches to preparing large qubit arrays we examine Rydberg mediated gate protocols and fidelity for two- and multi-qubit interactions. Quantum simulation and Rydberg dressing are alternatives to circuit based quantum computing for exploring many body quantum dynamics. We review the properties of the dressing interaction and provide a quantitative figure of merit for the complexity of the coherent dynamics that can be accessed with dressing. We conclude with a summary of the current status and an outlook for future progress., Comment: updated references, additional material on Rydberg dressing, 10 figures

We describe the design and characterization of superconducting coplanar waveguide cavities tailored to facilitate strong coupling between superconducting quantum circuits and single trapped Rydberg atoms. For initial superconductor-atom experiments at 4.2 K, we show that resonator quality factors above $10^4$ can be readily achieved. Furthermore, we demonstrate that the incorporation of thick-film copper electrodes at a voltage antinode of the resonator provides a route to enhance the zero-point electric fields of the resonator in a trapping region that is 40 $\mu$m above the chip surface, thereby minimizing chip heating from scattered trap light. The combination of high resonator quality factor and strong electric dipole coupling between the resonator and the atom should make it possible to achieve the strong coupling limit of cavity quantum electrodynamics with this system., Comment: 4 pages, 4 figures

We have numerically simulated quantum tomography of single-qubit and two-qubit quantum gates with qubits represented by mesoscopic ensembles containing random numbers of atoms. Such ensembles of strongly interacting atoms in the regime of Rydberg blockade are known as Rydberg superatoms. The Stimulated Raman Adiabatic Passage (STIRAP) in the regime of Rydberg blockade is used for deterministic Rydberg excitation in the ensemble, required for storage of quantum information in the collective state of the atomic ensemble and implementation of two-qubit gates. The optimized shapes of the STIRAP pulses are used to achieve high fidelity of the population transfer. Our simulations confirm validity and high fidelity of single-qubit and two-qubit gates with Rydberg superatoms., Comment: 12 pages, 7 figures, to appear in Special issue on Rydberg atomic physics of Journal of Physics B. Typos in Table 2 corrected in version 3

We study the fidelity of single qubit quantum gates performed with two-frequency laser fields that have a Gaussian or super Gaussian spatial mode. Numerical simulations are used to account for imperfections arising from atomic motion in an optical trap, spatially varying Stark shifts of the trapping and control beams, and transverse and axial misalignment of the control beams. Numerical results that account for the three dimensional distribution of control light show that a super Gaussian mode with intensity $I\sim e^{-2(r/w_0)^n}$ provides reduced sensitivity to atomic motion and beam misalignment. Choosing a super Gaussian with $n=6$ the decay time of finite temperature Rabi oscillations can be increased by a factor of 60 compared to an $n=2$ Gaussian beam, while reducing crosstalk to neighboring qubit sites., Comment: 11 figures, added material on sensitivity to super Gaussian order

We calculate interspecies Rydberg-Rydberg interaction strengths for the heavy alkalis Rb and Cs. The presence of strong F\"orster resonances makes interspecies coupling a promising approach for long range entanglement generation. We also provide an overview of the strongest F\"orster resonances for Rb-Rb and Cs-Cs using different principal quantum numbers for the two atoms. We show how interspecies coupling can be used for high fidelity quantum non demolition state measurements with low crosstalk in qubit arrays., Comment: v2 angular dependence corrected, 10 figures

We present experimental results on two-qubit Rydberg blockade quantum gates and entanglement in a two-dimensional qubit array. Without post selection against atom loss we achieve a Bell state fidelity of $0.73\pm 0.05$, the highest value reported to date. The experiments are performed in an array of single Cs atom qubits with a site to site spacing of $3.8 ~ \mu\rm m$. Using the standard protocol for a Rydberg blockade C$_Z$ gate together with single qubit operations we create Bell states and measure their fidelity using parity oscillations. We analyze the role of AC Stark shifts that occur when using two-photon Rydberg excitation and show how to tune experimental conditions for optimal gate fidelity., Comment: 9 figures, corrected notation for C_X gates

We demonstrate $|W\rangle$ state encoding of multi-atom ensemble qubits. Using optically trapped Rb atoms the $T_2$ coherence time is 2.6(3) ms for $\bar N=7.6$ atoms and scales approximately inversely with the number of atoms. Strong Rydberg blockade between two ensemble qubits is demonstrated with a fidelity of $0.89(1)$ and a fidelity of $\sim \hspace{-.05cm}1.0$ when postselected on control ensemble excitation. These results are a significant step towards deterministic entanglement of atomic ensembles., Comment: 5 figures, v4: citations updated

We characterize single qubit Clifford gate operations with randomized benchmarking in a 2D array of neutral atom qubits, and demonstrate global and site selected gates with high fidelity. An average fidelity of $F^2=0.9983(14)$ is measured for global microwave driven gates applied to a 49 qubit array. Single site gates are implemented with a focused laser beam to Stark shift the microwaves into resonance at a selected site. At Stark selected single sites we observe $F^2=0.9923(7)$ and an average spin flip crosstalk error at other sites of $0.002(9)$., Comment: 5 figures, supplemental material, minor revisions to text regarding fault tolerance

We report measurements of the absolute excitation frequencies of $^{165}$Ho $4f^{11}6sns$ and $4f^{11}6snd$ odd-parity Rydberg series. The states are detected through depletion of a magneto-optical trap via a two-photon excitation scheme. Measurements of 162 Rydberg levels in the range $n=40-101$ yield quantum defects well described by the Rydberg-Ritz formula. We observe a strong perturbation in the $ns$ series around $n=51$ due to an unidentified interloper at 48515.47(4) cm$^{-1}$. From the series convergence, we determine the first ionization potential $E_\mathrm{IP}=48565.939(4)$ cm$^{-1}$, which is three orders of magnitude more accurate than previous work. This work represents the first time such spectroscopy has been done in Holmium and is an important step towards using Ho atoms for collective encoding of a quantum register., Comment: 6 figures

We analyze doubly magic trapping of Cs hyperfine transitions including previously neglected contributions from the ground state hyperpolarizability and the interaction of the laser light and a static magnetic field. Extensive numerical searches do not reveal any doubly magic trapping conditions for any pair of hyperfine states. However, including the hyperpolarizability reveals light intensity insensitive traps for a wide range of wavelengths at specific intensities. We then investigate the possibility of using bichromatic trapping light fields. Deploying a bichromatic scheme, we demonstrate doubly magic red and blue detuned traps for pairs of states separated by one or two single photon transitions., Comment: additional rewording for clarity

We demonstrate sub-Doppler laser cooling and magneto-optical trapping of the rare earth element Holmium. Atoms are loaded from an atomic beam source and captured in six-beam $\sigma_+ - \sigma_-$ molasses using a strong $J=15/2 \leftrightarrow J=17/2$ cycling transition at $\lambda=410.5 \rm nm$. Due to the small difference in hyperfine splittings and Land\'e $g$-factors in the lower and upper levels of the cooling transition the MOT is self-repumped without additional repump light, and deep sub-Doppler cooling is achieved with the magnetic trap turned on. We measure the leakage out of the cycling transition to metastable states and find a branching ratio $\sim 10^{-5}$ which is adequate for state resolved measurements on hyperfine encoded qubits., Comment: 5 figures, v2: numerical values in Table I corrected, v3: metastable decay rate value revised, v4: minor changes and eq. (2) corrected for Holmium

We propose and analyze the implementation of a two qubit quantum gate using circular Rydberg states with maximum orbital angular momentum. The intrinsic quantum gate error is limited by the finite Rydberg lifetime and finite Rydberg blockade shift. Circular states have much longer radiative lifetimes than low orbital angular momentum states and are therefore candidates for high fidelity gate operations. We analyze the dipole-dipole interaction of two circular state Rydberg atoms and present numerical simulations of quantum process tomography to find the intrinsic fidelity of a Rydberg blockade controlled phase gate. Our analysis shows that the intrinsic gate error can be less than $9 \times10^{-6}$ for circular Cs atoms in a cryogenic environment., Comment: 6 figures

We discuss methods for coherently controlling mesoscopic atomic ensembles where the number of atoms varies randomly from one experimental run to the next. The proposed schemes are based on adiabatic passage and Rydberg blockade and can be used for implementation of a scalable quantum register formed by an array of randomly loaded optical dipole traps., Comment: 14 pages, 7 figures, to be published in Proceedings of the 6th International Symposium on Modern Problems of Laser Physics (MPLP-2013)

We propose a novel hybrid quantum gate between an atom and a microwave photon in a superconducting coplanar waveguide cavity by exploiting the strong resonant microwave coupling between adjacent Rydberg states. Using experimentally achievable parameters gate fidelities $> 0.99$ are possible on sub-$\mu$s timescales for waveguide temperatures below 40 mK. This provides a mechanism for generating entanglement between two disparate quantum systems and represents an important step in the creation of a hybrid quantum interface applicable for both quantum simulation and quantum information processing., Comment: 4 pages, 4 figures

We describe a new type of blue detuned optical lattice for atom trapping which is intrinsically two dimensional, while providing three-dimensional atom localization. The lattice is insensitive to optical phase fluctuations since it does not depend on field interference between distinct optical beams. The array is created using a novel arrangement of weakly overlapping Gaussian beams that creates a two-dimensional array of dark traps which are suitable for magic trapping of ground and Rydberg states. We analyze the spatial localization that can be achieved and demonstrate trapping and detection of single Cs atoms in 6 and 49 site two-dimensional arrays., Comment: Fig. 1 caption extended, to appear Phys. Rev. A

A diffractive optical element (DOE) has been fabricated for creating blue detuned atomic bottle beam traps. The DOE integrates several diffractive lenses for trap creation and imaging of atomic fluorescence. We characterize the performance of the DOE and demonstrate trapping of cold Cesium atoms inside a bottle beam., Comment: 13 figures, submitted to Appl. Phys. B