Multi-qubit entanglement and algorithms on a neutral-atom quantum computer.

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 owing to their identical characteristics, long coherence times and ability to be trapped in dense, multidimensional arrays1. Combined with the strong entangling interactions provided by Rydberg states2-4, 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) states5 with up to six qubits, quantum phase estimation for a chemistry problem6 and the quantum approximate optimization algorithm (QAOA)7 for the maximum cut (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.

Multiscale architecture for fast optical addressing and control of large-scale qubit arrays.

This paper presents a technique for rapid site-selective control of the quantum state of particles in a large array using the combination of a fast deflector (e.g., an acousto-optic deflector) and a relatively slow spatial light modulator (SLM). The use of SLMs for site-selective quantum state manipulation has been limited due to slow transition times that prevent rapid, consecutive quantum gates. By partitioning the SLM 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 SLM full-frame setting. We analyzed the performance of this device in two different configurations: In configuration 1, each SLM segment addresses the full qubit array; in configuration 2, each SLM segment addresses a subarray and an additional fast deflector positions that subarray with respect to the full qubit array. With these hybrid scanners, we calculated qubit addressing rates that are tens to hundreds of times faster than using an SLM alone.

Rydberg-Mediated Entanglement in a Two-Dimensional Neutral Atom Qubit Array.

We demonstrate high fidelity two-qubit Rydberg blockade and entanglement on a pair of sites in a large 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_{Bell}=0.86(2). Accounting for errors in state preparation and measurement we infer a fidelity of F_{Bell}^{-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_{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.

Parallel Low-Loss Measurement of Multiple Atomic Qubits.

We demonstrate low-loss measurement of the hyperfine ground state of rubidium atoms by state dependent fluorescence detection in a dipole trap array of five sites. 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.

Improved Error Thresholds for Measurement-Free Error Correction.

Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information, giving our procedure extra fault tolerance and eliminating the need for ancilla verification. The procedure is particularly favorable when multiqubit gates are available for the correction step. Simulations of the bit-flip, Bacon-Shor, and Steane codes indicate that coherent error correction can produce threshold error rates that are on the order of 10^{-3} to 10^{-4}-comparable with or better than measurement-based values, and much better than previous results for other coherent error correction schemes. This indicates that coherent error correction is worthy of serious consideration for achieving protected logical qubits.

Doubly Magic Optical Trapping for Cs Atom Hyperfine Clock Transitions.

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 use of 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.

Coherence and Rydberg Blockade of Atomic Ensemble Qubits.

We demonstrate |W⟩ state encoding of multiatom ensemble qubits. Using optically trapped Rb atoms, the T_{2} coherence time is 2.6(3) ms for N[over ¯]=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 with a fidelity of ∼1.0 when postselected on a control ensemble excitation. These results are a significant step towards deterministic entanglement of atomic ensembles.

Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits.

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 F2=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 F2=0.9923(7) and an average spin-flip crosstalk error at other sites of 0.002(9).

Preparation of entangled and antiferromagnetic states by dissipative Rydberg pumping.

We propose and analyze an approach for preparation of high fidelity entanglement and antiferromagnetic states using Rydberg mediated interactions with dissipation. Using asymmetric Rydberg interactions the two-atom Bell singlet is a dark state of the Rydberg pumping process. Master equation simulations demonstrate Bell singlet preparation fidelity F=0.998. Antiferromagnetic states are generated on a four-spin plaquette in agreement with results found from diagonalization of the transverse field Ising Hamiltonian.

Crossed vortex bottle beam trap for single-atom qubits.

We demonstrate trapping and quantum state control of single cesium atoms in a 532 nm wavelength bottle beam trap. The three-dimensional trap is formed by crossing two unit charge vortex beams. Single atoms are loaded with 50% probability directly from a magneto-optical trap. We achieve a trapping lifetime of up to 6 s and demonstrate fast Rabi oscillations with a coherence time of T(2)~43±9 ms.

Rydberg-induced solitons: three-dimensional self-trapping of matter waves.

We propose a scheme for the creation of stable three-dimensional bright solitons in Bose-Einstein condensates, i.e., the matter-wave analog of so-called spatiotemporal "light bullets." Off-resonant dressing to Rydberg nD states is shown to provide nonlocal attractive interactions, leading to self-trapping of mesoscopic atomic clouds by a collective excitation of a Rydberg atom pair. We present detailed potential calculations and demonstrate the existence of stable solitons under realistic experimental conditions by means of numerical simulations.

Demonstration of a neutral atom controlled-NOT quantum gate.

We present the first demonstration of a CNOT gate between two individually addressed neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by >8 microm. Using two different gate protocols we measure CNOT fidelities of F=0.73 and 0.72 based on truth table probabilities. The gate was used to generate Bell states with fidelity F=0.48+/-0.06. After correcting for atom loss we obtain an a posteriori entanglement fidelity of F=0.58.

Long working distance objective lenses for single atom trapping and imaging.

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 NA = 0.175 offering 3 µm resolution whilst objective 2 is optimized for high collection efficiency with NA = 0.29 and 1.8 µm resolution. This flexible design can be further extended for use at shorter wavelengths by simply re-optimising the lens separations.

Spiral intensity patterns in the internally pumped optical parametric oscillator

We describe a nonlinear optical system that supports spiral pattern solutions in the field intensity. This new spatial structure is found to bifurcate above a secondary instability in the internally pumped optical parametric oscillator. The analytical predictions of threshold and spatial scale for the instability are supplemented by detailed numerical investigations of the formation of spiral patterns.

Efficient multiparticle entanglement via asymmetric Rydberg blockade.

We present an efficient method for producing N particle entangled states using Rydberg blockade interactions. Optical excitation of Rydberg states that interact weakly, yet have a strong coupling to a second control state is used to achieve state dependent qubit rotations in small ensembles. On the basis of quantitative calculations, we predict that an entangled quantum superposition state of eight atoms can be produced with a fidelity of 84% in cold Rb atoms.

Atom trapping in an interferometrically generated bottle beam trap.

We demonstrate an optical bottle beam trap created by interfering two fundamental Gaussian beams with different waists. The beams are derived from a single laser source using a Mach-Zehnder interferometer whose arms have unequal magnifications. Destructive interference of the two beams from the Mach-Zehnder leads to a three-dimensional intensity null at the mutual focus of the beams. We demonstrate trapping of cold cesium atoms in a blue detuned bottle beam trap.

Doppler-free, multiwavelength acousto-optic deflector for two-photon addressing arrays of Rb atoms in a quantum information processor.

We demonstrate a dual wavelength acousto-optic deflector (AOD) designed to deflect two wavelengths to the same angles by driving with two RF frequencies. The AOD is designed as a beam scanner to address two-photon transitions in a two-dimensional array of trapped neutral Rb87 atoms in a quantum computer. Momentum space is used to design AODs that have the same diffraction angles for two wavelengths (780 and 480 nm) and have nonoverlapping Bragg-matched frequency response at these wavelengths, so that there will be no cross talk when proportional frequencies are applied to diffract the two wavelengths. The appropriate crystal orientation, crystal shape, transducer size, and transducer height are determined for an AOD made with a tellurium dioxide crystal (TeO(2)). The designed and fabricated AOD has more than 100 resolvable spots, widely separated band shapes for the two wavelengths within an overall octave bandwidth, spatially overlapping diffraction angles for both wavelengths (780 and 480 nm), and a 4 micros or less access time. Cascaded AODs in which the first device upshifts and the second downshifts allow Doppler-free scanning as required for addressing the narrow atomic resonance without detuning. We experimentally show the diffraction-limited Doppler-free scanning performance and spatial resolution of the designed AOD.