Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms

Rydberg-Atom Manipulation through Strong Interaction with Free Electrons

Optically trapped Rydberg atoms are a suitable platform to explore quantum many-body physics mediated by long-range atom-atom interactions that can be engineered through externally applied light fields. However, this approach is limited to dipole-allowed transitions and a spatial resolution of the order of the optical wavelength. Here, we theoretically investigate the interaction between free electrons and individual Rydberg atoms as an approach to induce nondipolar transitions with subnanometer spatial precision and a substantial degree of control over the final atomic states. We observe unity-order excitation probabilities produced by a single electron for suitably chosen combinations of electron energies and electron-beam distance to the atom. We further discuss free-electron-atom entanglement and atom-atom entanglement in combination with lateral shaping of the electron followed by postselection. Our results support free electrons as powerful tools to manipulate Rydberg atoms in previously inaccessible ways.

High-rate quantum LDPC codes for long-range-connected neutral atom registers

High-rate quantum error correcting (QEC) codes with moderate overheads in qubit number and control complexity are highly desirable for achieving fault-tolerant quantum computing. Recently, quantum error correction has experienced significant progress both in code development and experimental realizations, with neutral atom qubit architecture rapidly establishing itself as a leading platform in the field. Scalable quantum computing will require processing with QEC codes that have low qubit overhead and large error suppression, and while such codes do exist, they involve a degree of non-locality that has yet to be integrated into experimental platforms. In this work, we analyze a family of high-rate Low-Density Parity-Check (LDPC) codes with limited long-range interactions and outline a near-term implementation in neutral atom registers. By means of circuit-level simulations, we find that these codes outperform surface codes in all respects when the two-qubit nearest neighbour gate error probability is below  ~ 0.1%. By using multiple laser colors, we show how these codes can be natively integrated in two-dimensional static neutral atom qubit architectures with open boundaries, where the desired long-range connectivity can be targeted via the Rydberg blockade interaction.

Polarization and Orbital Angular Momentum Encoded Quantum Toffoli Gate Enabled by Diffractive Neural Networks

Controlled quantum gates play a crucial role in enabling quantum universal operations by facilitating interactions between qubits. Direct implementation of three-qubit gates simplifies the design of quantum circuits, thereby being conducive to performing complex quantum algorithms. Here, we propose and present an experimental demonstration of a quantum Toffoli gate fully exploiting the polarization and orbital angular momentum of a single photon. The Toffoli gate is implemented using the polarized diffractive neural networks scheme, achieving a mean truth table visibility of 97.27±0.20%. We characterize the gate's performance through quantum state tomography on 216 different input states and quantum process tomography, which yields a process fidelity of 94.05±0.02%. Our method offers a novel approach for realizing the Toffoli gate without requiring exponential optical elements while maintaining extensibility to the implementation of other three-qubit gates.

Multi-qubit gates and Schrödinger cat states in an optical clock

Many-particle entanglement is a key resource for achieving the fundamental precision limits of a quantum sensor1. Optical atomic clocks2, the current state of the art in frequency precision, are a rapidly emerging area of focus for entanglement-enhanced metrology3-6. Augmenting tweezer-based clocks featuring microscopic control and detection7-10 with the high-fidelity entangling gates developed for atom-array information processing11,12 offers a promising route towards making use of highly entangled quantum states for improved optical clocks. Here we develop and use a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger-Horne-Zeilinger (GHZ) type with up to nine optical clock qubits in a programmable atom array. In an atom-laser comparison at sufficiently short dark times, we demonstrate a fractional frequency instability below the standard quantum limit (SQL) using GHZ states of up to four qubits. However, because of their reduced dynamic range, GHZ states of a single size fail to improve the achievable clock precision at the optimal dark time compared with unentangled atoms13. Towards overcoming this hurdle, we simultaneously prepare a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval14-17. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision.

Universal quantum operations and ancilla-based read-out for tweezer clocks

Enhancing the precision of measurements by harnessing entanglement is a long-sought goal in quantum metrology1,2. Yet attaining the best sensitivity allowed by quantum theory in the presence of noise is an outstanding challenge, requiring optimal probe-state generation and read-out strategies3-7. Neutral-atom optical clocks8, which are the leading systems for measuring time, have shown recent progress in terms of entanglement generation9-11 but at present lack the control capabilities for realizing such schemes. Here we show universal quantum operations and ancilla-based read-out for ultranarrow optical transitions of neutral atoms. Our demonstration in a tweezer clock platform9,12-16 enables a circuit-based approach to quantum metrology with neutral-atom optical clocks. To this end, we demonstrate two-qubit entangling gates with 99.62(3)% fidelity-averaged over symmetric input states-through Rydberg interactions15,17,18 and dynamical connectivity19 for optical clock qubits, which we combine with local addressing16 to implement universally programmable quantum circuits. Using this approach, we generate a near-optimal entangled probe state1,4, a cascade of Greenberger-Horne-Zeilinger states of different sizes, and perform a dual-quadrature5 Greenberger-Horne-Zeilinger read-out. We also show repeated fast phase detection with non-destructive conditional reset of clock qubits and minimal dead time between repetitions by implementing ancilla-based quantum logic spectroscopy20 for neutral atoms. Finally, we extend this to multi-qubit parity checks and measurement-based, heralded, Bell-state preparation21-24. Our work lays the foundation for hybrid processor-clock devices with neutral atoms and more generally points to a future of practical applications for quantum processors linked with quantum sensors25.

High-Fidelity Detection of Large-Scale Atom Arrays in an Optical Lattice

Recent advances in quantum simulation based on neutral atoms have largely benefited from high-resolution, single-atom sensitive imaging techniques. A variety of approaches have been developed to achieve such local detection of atoms in optical lattices or optical tweezers. For alkaline-earth and alkaline-earth-like atoms, the presence of narrow optical transitions opens up the possibility of performing novel types of Sisyphus cooling, where the cooling mechanism originates from the capability to spatially resolve the differential optical level shifts in the trap potential. Up to now, it has been an open question whether high-fidelity imaging could be achieved in a "repulsive Sisyphus" configuration, where the trap depth of the ground state exceeds that of the excited state involved in cooling. Here, we demonstrate high-fidelity (99.971(1)%) and high-survival (99.80(5)%) imaging of strontium atoms using repulsive Sisyphus cooling. We use an optical lattice as a pinning potential for atoms in a large-scale tweezer array with up to 399 tweezers and show repeated, high-fidelity lattice-tweezer-lattice transfers. We furthermore demonstrate loading the lattice with approximately 10 000 atoms directly from the MOT and scalable imaging over >10 000 lattice sites with a combined survival probability and classification fidelity better than 99.2%. Our lattice thus serves as a locally addressable and sortable reservoir for continuous refilling of optical tweezer arrays in the future.

A Perspective on Protein Structure Prediction Using Quantum Computers

Despite the recent advancements by deep learning methods such as AlphaFold2, in silico protein structure prediction remains a challenging problem in biomedical research. With the rapid evolution of quantum computing, it is natural to ask whether quantum computers can offer some meaningful benefits for approaching this problem. Yet, identifying specific problem instances amenable to quantum advantage and estimating the quantum resources required are equally challenging tasks. Here, we share our perspective on how to create a framework for systematically selecting protein structure prediction problems that are amenable for quantum advantage, and estimate quantum resources for such problems on a utility-scale quantum computer. As a proof-of-concept, we validate our problem selection framework by accurately predicting the structure of a catalytic loop of the Zika Virus NS3 Helicase, on quantum hardware.

An optical tweezer array of ultracold polyatomic molecules

Polyatomic molecules have rich structural features that make them uniquely suited to applications in quantum information science1-3, quantum simulation4-6, ultracold chemistry7 and searches for physics beyond the standard model8-10. However, a key challenge is fully controlling both the internal quantum state and the motional degrees of freedom of the molecules. Here we demonstrate the creation of an optical tweezer array of individual polyatomic molecules, CaOH, with quantum control of their internal quantum state. The complex quantum structure of CaOH results in a non-trivial dependence of the molecules' behaviour on the tweezer light wavelength. We control this interaction and directly and non-destructively image individual molecules in the tweezer array with a fidelity greater than 90%. The molecules are manipulated at the single internal quantum state level, thus demonstrating coherent state control in a tweezer array. The platform demonstrated here will enable a variety of experiments using individual polyatomic molecules with arbitrary spatial arrangement.

Logical quantum processor based on reconfigurable atom arrays

Suppressing errors is the central challenge for useful quantum computing1, requiring quantum error correction (QEC)2-6 for large-scale processing. However, the overhead in the realization of error-corrected 'logical' qubits, in which information is encoded across many physical qubits for redundancy2-4, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays7, our system combines high two-qubit gate fidelities8, arbitrary connectivity7,9, as well as fully programmable single-qubit rotations and mid-circuit readout10-15. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code6 distance from d = 3 to d = 7, preparation of colour-code qubits with break-even fidelities5, fault-tolerant creation of logical Greenberger-Horne-Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks16,17, we realize computationally complex sampling circuits18 with up to 48 logical qubits entangled with hypercube connectivity19 with 228 logical two-qubit gates and 48 logical CCZ gates20. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.

Superposed Quantum Error Mitigation

Overcoming the influence of noise and imperfections is a major challenge in quantum computing. Here, we present an approach based on applying a desired unitary computation in superposition between the system of interest and some auxiliary states. We demonstrate, numerically and on the IBM Quantum Platform, that parallel applications of the same operation lead to significant noise mitigation when arbitrary noise processes are considered. We first design probabilistic implementations of our scheme that are plug and play, independent of the noise characteristic and require no postprocessing. We then enhance the success probability (up to deterministic) using adaptive corrections. We provide an analysis of our protocol performance and demonstrate that unit fidelity can be achieved asymptotically. Our approaches are suitable to both standard gate-based and measurement-based computational models.

Floquet-tailored Rydberg interactions

The Rydberg blockade is a key ingredient for entangling atoms in arrays. However, it requires atoms to be spaced well within the blockade radius, which limits the range of local quantum gates. Here we break this constraint using Floquet frequency modulation, with which we demonstrate Rydberg-blockade entanglement beyond the traditional blockade radius and show how the enlarged entanglement range improves qubit connectivity in a neutral atom array. Further, we find that the coherence of entangled states can be extended under Floquet frequency modulation. Finally, we realize Rydberg anti-blockade states for two sodium Rydberg atoms within the blockade radius. Such Rydberg anti-blockade states for atoms at close range enables the robust preparation of strongly-interacting, long-lived Rydberg states, yet their steady-state population cannot be achieved with only the conventional static drive. Our work transforms between the paradigmatic regimes of Rydberg blockade versus anti-blockade and paves the way for realizing more connected, coherent, and tunable neutral atom quantum processors with a single approach.

Universal Quantum Computation in Globally Driven Rydberg Atom Arrays

We develop a model for quantum computation with Rydberg atom arrays, which only relies on global driving, without the need of local addressing of the qubits: any circuit is executed by a sequence of global, resonant laser pulses on a static atomic arrangement. We present two constructions: for the first, the circuit is imprinted in the trap positions of the atoms and executed by the pulses; for the second, the atom arrangement is circuit-independent, and the algorithm is entirely encoded in the global driving sequence. Our results show in particular that a quadratic overhead in atom number is sufficient to eliminate the need for local control to realize a universal quantum processor. We give explicit protocols for all steps of an arbitrary quantum computation, and discuss strategies for error suppression specific to our model. Our scheme is based on dual-species processors with atoms subjected to Rydberg blockade constraints, but it might be transposed to other setups as well.

High-fidelity gates and mid-circuit erasure conversion in an atomic qubit

The development of scalable, high-fidelity qubits is a key challenge in quantum information science. Neutral atom qubits have progressed rapidly in recent years, demonstrating programmable processors1,2 and quantum simulators with scaling to hundreds of atoms3,4. Exploring new atomic species, such as alkaline earth atoms5-7, or combining multiple species8 can provide new paths to improving coherence, control and scalability. For example, for eventual application in quantum error correction, it is advantageous to realize qubits with structured error models, such as biased Pauli errors9 or conversion of errors into detectable erasures10. Here we demonstrate a new neutral atom qubit using the nuclear spin of a long-lived metastable state in 171Yb. The long coherence time and fast excitation to the Rydberg state allow one- and two-qubit gates with fidelities of 0.9990(1) and 0.980(1), respectively. Importantly, a large fraction of all gate errors result in decays out of the qubit subspace to the ground state. By performing fast, mid-circuit detection of these errors, we convert them into erasure errors; during detection, the induced error probability on qubits remaining in the computational space is less than 10-5. This work establishes metastable 171Yb as a promising platform for realizing fault-tolerant quantum computing.

High-fidelity parallel entangling gates on a neutral-atom quantum computer

The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing1. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture4. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions5. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction6,7. Our method uses fast, single-pulse gates based on optimal control8, atomic dark states to reduce scattering9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms14, error-corrected circuits7 and digital simulations15.

Erasure conversion in a high-fidelity Rydberg quantum simulator

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices1 and for the quest towards fault-tolerant quantum computation2,3. Rydberg arrays have emerged as a prominent platform in this context4 with impressive system sizes5,6 and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution7,8, a form of erasure error conversion9-12. However, two-qubit entanglement fidelities in Rydberg atom arrays13,14 have lagged behind competitors15,16 and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator5,6,17,18. When excising data with erasure errors observed via fast imaging of alkaline-earth atoms19-22, we achieve a Bell state fidelity of [Formula: see text], which improves to [Formula: see text] when correcting for remaining state-preparation errors. We further apply erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, and reveal the otherwise hidden impact of these errors on the simulation outcome. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the 0.999 regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices. These techniques could be translated directly to quantum-error-correction codes with the addition of long-lived qubits7,22-24.

A Survey of Universal Quantum von Neumann Architecture

The existence of universal quantum computers has been theoretically well established. However, building up a real quantum computer system not only relies on the theory of universality, but also needs methods to satisfy requirements on other features, such as programmability, modularity, scalability, etc. To this end, here we study the recently proposed model of quantum von Neumann architecture by putting it in a practical and broader setting, namely, the hierarchical design of a computer system. We analyze the structures of quantum CPU and quantum control units and draw their connections with computational advantages. We also point out that a recent demonstration of our model would require less than 20 qubits.

Bichromatic Imaging of Single Molecules in an Optical Tweezer Array

We report on a novel bichromatic fluorescent imaging scheme for background-free detection of single CaF molecules trapped in an optical tweezer array. By collecting fluorescence on one optical transition while using another for laser cooling, we achieve an imaging fidelity of 97.7(2)% and a nondestructive detection fidelity of 95.5(6)%. Notably, these fidelities are achieved with a modest photon budget, suggesting that the method could be extended to more complex laser-coolable molecules with less favorable optical cycling properties. We also report on a framework and new methods to characterize various loss mechanisms that occur generally during fluorescent detection of trapped molecules, including two-photon decay and admixtures of higher excited states that are induced by the trapping light. In particular, we develop a novel method to dispersively measure transition matrix elements between electronically excited states. The method could also be used to measure arbitrarily small Franck-Condon factors between electronically excited states, which could significantly aid in ongoing efforts to laser cool complex polyatomic molecules.

Randomized Benchmarking Using Nondestructive Readout in a Two-Dimensional Atom Array

Neutral atoms are a promising platform for scalable quantum computing, however, prior demonstration of high fidelity gates or low-loss readout methods have employed restricted numbers of qubits. Using randomized benchmarking of microwave-driven single-qubit gates, we demonstrate average gate errors of 7(2)×10^{-5} on a 225 site atom array using conventional, destructive readout. We further demonstrate a factor of 1.7 suppression of the primary measurement errors via low-loss, nondestructive, and state-selective readout on 49 sites while achieving gate errors of 2(9)×10^{-4}.

Observation of Rydberg Blockade Due to the Charge-Dipole Interaction between an Atom and a Polar Molecule

We demonstrate Rydberg blockade due to the charge-dipole interaction between a single Rb atom and a single RbCs molecule confined in optical tweezers. The molecule is formed by magnetoassociation of a Rb+Cs atom pair and subsequently transferred to the rovibrational ground state with an efficiency of 91(1)%. Species-specific tweezers are used to control the separation between the atom and molecule. The charge-dipole interaction causes blockade of the transition to the Rb(52s) Rydberg state, when the atom-molecule separation is set to 310(40) nm. The observed excitation dynamics are in good agreement with simulations using calculated interaction potentials. Our results open up the prospect of a hybrid platform where quantum information is transferred between individually trapped molecules using Rydberg atoms.

Mid-circuit correction of correlated phase errors using an array of spectator qubits

Scaling up invariably error-prone quantum processors is a formidable challenge. Although quantum error correction ultimately promises fault-tolerant operation, the required qubit overhead and error thresholds are daunting. In a complementary proposal, co-located, auxiliary 'spectator' qubits act as in-situ probes of noise, and enable real-time, coherent corrections of data qubit errors. We use an array of cesium spectator qubits to correct correlated phase errors on an array of rubidium data qubits. By combining in-sequence readout, data processing, and feed-forward operations, these correlated errors are suppressed within the execution of the quantum circuit. The protocol is broadly applicable to quantum information platforms, and establishes key tools for scaling neutral-atom quantum processors: mid-circuit readout of atom arrays, real-time processing and feed-forward, and coherent mid-circuit reloading of atomic qubits.

Dark-State Enhanced Loading of an Optical Tweezer Array

Neutral atoms and molecules trapped in optical tweezers have become a prevalent resource for quantum simulation, computation, and metrology. However, the maximum achievable system sizes of such arrays are often limited by the stochastic nature of loading into optical tweezers, with a typical loading probability of only 50%. Here we present a species-agnostic method for dark-state enhanced loading (DSEL) based on real-time feedback, long-lived shelving states, and iterated array reloading. We demonstrate this technique with a 95-tweezer array of ^{88}Sr atoms, achieving a maximum loading probability of 84.02(4)% and a maximum array size of 91 atoms in one dimension. Our protocol is complementary to, and compatible with, existing schemes for enhanced loading based on direct control over light-assisted collisions, and we predict it can enable close-to-unity filling for arrays of atoms or molecules.

Rydberg Macrodimers: Diatomic Molecules on the Micrometer Scale

Controlling molecular binding at the level of single atoms is one of the holy grails of quantum chemistry. Rydberg macrodimers─bound states between highly excited Rydberg atoms─provide a novel perspective in this direction. Resulting from binding potentials formed by the strong, long-range interactions of Rydberg states, Rydberg macrodimers feature bond lengths in the micrometer regime, exceeding those of conventional molecules by orders of magnitude. Using single-atom control in quantum gas microscopes, the unique properties of these exotic states can be studied with unprecedented control, including the response to magnetic fields or the polarization of light in their photoassociation. The high accuracy achieved in spectroscopic studies of macrodimers makes them an ideal testbed to benchmark Rydberg interactions, with direct relevance to quantum computing and information protocols where these are employed. This review provides a historic overview and summarizes the recent findings in the field of Rydberg macrodimers. Furthermore, it presents new data on interactions between macrodimers, leading to a phenomenon analogous to Rydberg blockade at the level of molecules, opening the path toward studying many-body systems of ultralong-range Rydberg molecules.

All-optical quantum information processing via a single-step Rydberg blockade gate

One of the critical elements in the realization of the quantum internet are deterministic two-photon gates. This CZ photonic gate also completes a set of universal gates for all-optical quantum information processing. This article discusses an approach to realize a high fidelity CZ photonic gate by storing both control and target photons within an atomic ensemble using non-Rydberg electromagnetically induced transparency (EIT) followed by a fast, single-step Rydberg excitation with global lasers. The proposed scheme operates by relative intensity modulation of two lasers used in Rydberg excitation. Circumventing the conventional π-gap-π schemes, the proposed operation features continuous laser protection of the Rydberg atoms from the environment noise. The complete spatial overlap of stored photons inside the blockade radius optimizes the optical depth and simplifies the experiment. The coherent operation here is performed in the region that was dissipative in the previous Rydberg EIT schemes. Encountering the main imperfection sources, i.e., the spontaneous emission of the Rydberg and intermediate levels, population rotation errors, Doppler broadening of the transition lines, storage/retrieval efficiency, and atomic thermal motion induced decoherence, this article concludes that with realistic experimental parameters 99.7% fidelity is achievable.

Optical Trapping of a Polyatomic Molecule in an ℓ-Type Parity Doublet State

We report optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). CaOH molecules from a magneto-optical trap are sub-Doppler laser cooled to 20(3)  μK in free space and loaded into an optical dipole trap. We attain an in-trap molecule number density of 3(1)×10^{9}  cm^{-3} at a temperature of 57(8)  μK. Trapped CaOH molecules are optically pumped into an excited vibrational bending mode, whose ℓ-type parity doublet structure is a potential resource for a wide range of proposed quantum science applications with polyatomic molecules. We measure the spontaneous, radiative lifetime of this bending mode state to be ∼0.7  s.

Scalable quantum processors empowered by the Fermi scattering of Rydberg electrons

Quantum computing promises exponential speed-up compared to its classical counterpart. While the neutral atom processors are the pioneering platform in terms of scalability, the dipolar Rydberg gates impose the main bottlenecks on the scaling of these devices. This article presents an alternative scheme for neutral atom quantum processing, based on the Fermi scattering of a Rydberg electron from ground-state atoms in spin-dependent lattice geometries. Instead of relying on Rydberg pair-potentials, the interaction is controlled by engineering the electron cloud of a sole Rydberg atom. The present scheme addresses the scaling obstacles in Rydberg processors by exponentially suppressing the population of short-lived states and by operating in ultra-dense atomic lattices. The restoring forces in molecule type Rydberg-Fermi potential preserve the trapping over a long interaction period. Furthermore, the proposed scheme mitigates different competing infidelity criteria, eliminates unwanted cross-talks, and significantly suppresses the operation depth in running complicated quantum algorithms.

Two-qubit atomic gates: spatio-temporal control of Rydberg interaction

By controlling the temporal and spatial features of light, we propose a novel protocol to prepare two-qubit entangling gates on atoms trapped at close distance, which could potentially speed up the operation of the gate from the sub-micro to the nanosecond scale. The protocol is robust to variations in the pulse areas and the position of the atoms, by virtue of the coherent properties of a dark state, which is used to drive the population through Rydberg states. From the time-domain perspective, the protocol generalizes the one proposed by Jaksch and coworkers [Jaksch et al., Phys. Rev. Lett., 2000, 85, 2208], with three pulses that operate symmetrically in time, but with different pulse areas. From the spatial-domain perspective, it uses structured light. We analyze the map of the gate fidelity, which forms rotated and distorted lattices in the solution space. Finally, we study the effect of an additional qubit to the gate performance and propose generalizations that operate with multi-pulse sequences.

Off-resonant modulated driving gate protocols for two-photon ground-Rydberg transition and finite Rydberg blockade strength

Recently, the concept of two-qubit controlled phase gate via off-resonant modulated driving has been introduced into the neutral atom qubit platform, with respect to both single-photon and two-photon ground-Rydberg transitions. In order to reach a better performance practically, further developments are in need to overcome a few known limitations in previous discussions. Here, we thoroughly analyze a variety of modulation styles for two-photon transitions, demonstrating the versatility of off-resonant modulated driving protocols. Furthermore, we show that it is possible to refine the designing process for improved performances for specific finite Rydberg blockade strength values. In particular, a reduced requirement on the blockade strength can be directly linked to an improvement of connectivity in qubit array of neutral atoms. These progress are closely related to the core feature that the atomic wave function acquires a geometric phase from the time evolution, which begins and finishes at the same quantum state. Under reasonable experimental conditions readily available nowadays, we anticipate that the fidelity of such protocols can reach as high as the essential requirement of NISQ even if the effects of technical errors and cold atoms' nonzero temperatures are considered.

Mid-Circuit Cavity Measurement in a Neutral Atom Array

Subsystem readout during a quantum process, or mid-circuit measurement, is crucial for error correction in quantum computation, simulation, and metrology. Ideal mid-circuit measurement should be faster than the decoherence of the system, high-fidelity, and nondestructive to the unmeasured qubits. Here, we use a strongly coupled optical cavity to read out the state of a single tweezer-trapped ^{87}Rb atom within a small tweezer array. Measuring either atomic fluorescence or the transmission of light through the cavity, we detect both the presence and the state of an atom in the tweezer, within only tens of microseconds, with state preparation and measurement infidelities of roughly 0.5% and atom loss probabilities of around 1%. Using a two-tweezer system, we find measurement on one atom within the cavity causes no observable hyperfine-state decoherence on a second atom located tens of microns from the cavity volume. This high-fidelity mid-circuit readout method is a substantial step toward quantum error correction in neutral atom arrays.

Demonstration of a Quantum Gate Using Electromagnetically Induced Transparency

We demonstrate a native CNOT gate between two individually addressed neutral atoms based on electromagnetically induced transparency. This protocol utilizes the strong long-range interactions of Rydberg states to enable conditional state transfer on the target qubit when operated in the blockade regime. An advantage of this scheme is it enables implementation of multiqubit CNOT^{k} gates using a pulse sequence independent of qubit number, providing a simple gate for efficient implementation of digital quantum algorithms and stabilizer measurements for quantum error correction. We achieve a loss corrected gate fidelity of F_{CNOT}^{cor}=0.82(6), and prepare an entangled Bell state with F_{Bell}^{cor}=0.66(5), limited at present by laser power. We present a number of technical improvements to advance this to a level required for fault-tolerant scaling.

Hardware Efficient Quantum Simulation of Non-Abelian Gauge Theories with Qudits on Rydberg Platforms

Non-Abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. Here we take an approach where gauge fields, discretized in spacetime, are represented by qudits and are time evolved in Trotter steps with multiqudit quantum gates. This maps naturally and hardware efficiently to an architecture based on Rydberg tweezer arrays, where long-lived internal atomic states represent qudits, and the required quantum gates are performed as holonomic operations supported by a Rydberg blockade mechanism. We illustrate our proposal for a minimal digitization of SU(2) gauge fields, demonstrating a significant reduction in circuit depth and gate errors in comparison to a traditional qubit-based approach, which puts simulations of non-Abelian gauge theories within reach of NISQ devices.

Implementation of Quantum Algorithms via Fast Three-Rydberg-Atom CCZ Gates

Multiqubit CCZ gates form one of the building blocks of quantum algorithms and have been involved in achieving many theoretical and experimental triumphs. Designing a simple and efficient multiqubit gate for quantum algorithms is still by no means trivial as the number of qubits increases. Here, by virtue of the Rydberg blockade effect, we propose a scheme to rapidly implement a three-Rydberg-atom CCZ gate via a single Rydberg pulse, and successfully apply the gate to realize the three-qubit refined Deutsch-Jozsa algorithm and three-qubit Grover search. The logical states of the three-qubit gate are encoded to the same ground states to avoid an adverse effect of the atomic spontaneous emission. Furthermore, there is no requirement for individual addressing of atoms in our protocol.

Two-Dimensional Programmable Tweezer Arrays of Fermions

We prepare high-filling two-component arrays of tens of fermionic ^{6}Li atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. A full spin- and density-resolved readout of individual sites allows us to postselect near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator.

Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice

Quantum walks provide a framework for designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a walker traverses while maintaining coherence. We do this by combining the fast, programmable control provided by optical tweezers with the scalable, homogeneous environment of an optical lattice. With these tools we study continuous-time quantum walks of single atoms on a square lattice and perform proof-of-principle demonstrations of spatial search with these walks. When scaled to more particles, the capabilities demonstrated can be extended to study a variety of problems in quantum information science, including performing more effective versions of spatial search using a larger graph with increased connectivity.

Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays

Executing quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. In this work, we propose a qubit encoding and gate protocol for ¹⁷¹Yb neutral atom qubits that converts the dominant physical errors into erasures, that is, errors in known locations. The key idea is to encode qubits in a metastable electronic level, such that gate errors predominantly result in transitions to disjoint subspaces whose populations can be continuously monitored via fluorescence. We estimate that 98% of errors can be converted into erasures. We quantify the benefit of this approach via circuit-level simulations of the surface code, finding a threshold increase from 0.937% to 4.15%. We also observe a larger code distance near the threshold, leading to a faster decrease in the logical error rate for the same number of physical qubits, which is important for near-term implementations. Erasure conversion should benefit any error correcting code, and may also be applied to design new gates and encodings in other qubit platforms.

In quantum computing, realistic error models can allow tailored correction schemes for specific platforms. Here, while considering the case of qubits encoded in metastable electronic levels of atomic arrays, the authors propose a way to convert a large fraction of occurring errors into detectable leakages, or erasure errors, which are vastly easier to correct.

N-Body Interactions between Trapped Ion Qubits via Spin-Dependent Squeezing

We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows for the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.

Optimal Control of Families of Quantum Gates

Quantum optimal control (QOC) enables the realization of accurate operations, such as quantum gates, and supports the development of quantum technologies. To date, many QOC frameworks have been developed, but those remain only naturally suited to optimize a single targeted operation at a time. We extend this concept to optimal control with a continuous family of targets, and demonstrate that an optimization based on neural networks can find families of time-dependent Hamiltonians realizing desired classes of quantum gates in minimal time.

Realization of a Fermi-Hubbard Optical Tweezer Array

We use lithium-6 atoms in an optical tweezer array to realize an eight-site Fermi-Hubbard chain near half filling. We achieve single site detection by combining the tweezer array with a quantum gas microscope. By reducing disorder in the energy offsets to less than the tunneling energy, we observe Mott insulators with strong antiferromagnetic correlations. The measured spin correlations allow us to put an upper bound on the entropy of 0.26(4)k_{B} per atom, comparable to the lowest entropies achieved with optical lattices. Additionally, we establish the flexibility of the tweezer platform by initializing atoms on one tweezer and observing tunneling dynamics across the array for uniform and staggered 1D geometries.

Magneto-optical trapping and sub-Doppler cooling of a polyatomic molecule

Laser cooling and trapping^1,2, and magneto-optical trapping methods in particular², have enabled groundbreaking advances in science, including Bose-Einstein condensation^3-5, quantum computation with neutral atoms^6,7 and high-precision optical clocks⁸. Recently, magneto-optical traps (MOTs) of diatomic molecules have been demonstrated^9-12, providing access to research in quantum simulation¹³ and searches for physics beyond the standard model¹⁴. Compared with diatomic molecules, polyatomic molecules have distinct rotational and vibrational degrees of freedom that promise a variety of transformational possibilities. For example, ultracold polyatomic molecules would be uniquely suited to applications in quantum computation and simulation^15-17, ultracold collisions¹⁸, quantum chemistry¹⁹ and beyond-the-standard-model searches^20,21. However, the complexity of these molecules has so far precluded the realization of MOTs for polyatomic species. Here we demonstrate magneto-optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). After trapping, the molecules are laser cooled in a blue-detuned optical molasses to a temperature of 110 μK, which is below the Doppler cooling limit. The temperatures and densities achieved here make CaOH a viable candidate for a wide variety of quantum science applications, including quantum simulation and computation using optical tweezer arrays^15,17,22,23. This work also suggests that laser cooling and magneto-optical trapping of many other polyatomic species^24-27 will be both feasible and practical.

A quantum processor based on coherent transport of entangled atom arrays

The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems^1,2. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation^3–5. We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state^6,7. Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits⁸ and a toric code state on a torus with sixteen data and eight ancillary qubits⁹. Finally, we use this architecture to realize a hybrid analogue–digital evolution² and use it for measuring entanglement entropy in quantum simulations^10–12, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars^13,14. Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology.

A quantum processer is realized using arrays of neutral atoms that are transported in a parallel manner by optical tweezers during computations, and used for quantum error correction and simulations.

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 states^2-4, 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.

Quantum Optimization via Four-Body Rydberg Gates

A large ongoing research effort focuses on obtaining a quantum advantage in the solution of combinatorial optimization problems on near-term quantum devices. A particularly promising platform implementing quantum optimization algorithms are arrays of trapped neutral atoms, laser coupled to highly excited Rydberg states. However, encoding combinatorial optimization problems in atomic arrays is challenging due to limited interqubit connectivity of the native finite-range interactions. Here, we present a four-body Rydberg parity gate, enabling a direct and straightforward implementation of the parity architecture, a scalable architecture for encoding arbitrarily connected interaction graphs. Our gate relies on adiabatic laser pulses and is fully programmable by adjusting two hold times during operation. We numerically demonstrate implementations of the quantum approximate optimization algorithm (QAOA) for small-scale test problems. Variational optimization steps can be implemented with a constant number of system manipulations, paving the way for experimental investigations of QAOA beyond the reach of numerical simulations.

Realizing Distance-Selective Interactions in a Rydberg-Dressed Atom Array

Measurement-based quantum computing relies on the rapid creation of large-scale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highly-excited Rydberg states. Typically, isolating pairs during gate operation is difficult because Rydberg interactions feature long tails at large distances. Here, we engineer distance-selective interactions that are strongly peaked in distance through off-resonant laser coupling of molecular potentials between Rydberg atom pairs. Employing quantum gas microscopy, we verify the dressed interactions by observing correlated phase evolution using many-body Ramsey interferometry. We identify atom loss and coupling to continuum modes as a limitation of our present scheme and outline paths to mitigate these effects, paving the way towards the creation of large-scale entanglement.

Defect-Free Arbitrary-Geometry Assembly of Mixed-Species Atom Arrays

Optically trapped mixed-species single atom arrays with arbitrary geometry are an attractive and promising platform for various applications, because tunable quantum systems with multiple components provide extra degrees of freedom for experimental control. Here, we report the first demonstration of two-dimensional 6×4 dual-species atom assembly of ^{85}Rb (^{87}Rb) atoms with a filling fraction of 0.88 (0.89). This mixed-species atomic synthesis is achieved via rearranging initially randomly distributed atoms by a sorting algorithm (heuristic heteronuclear algorithm) which is designed for bottom-up atom assembly with both user-defined geometries and two-species atom number ratios. Our fully tunable hybrid-atom systems with scalable advantages are a good starting point for high-fidelity quantum logic, many-body quantum simulation, and single molecule array formation.

Superresolution Microscopy of Optical Fields Using Tweezer-Trapped Single Atoms

We realize a scanning probe microscope using single trapped ^{87}Rb atoms to measure optical fields with subwavelength spatial resolution. Our microscope operates by detecting fluorescence from a single atom driven by near-resonant light and determining the ac Stark shift of an atomic transition from other local optical fields via the change in the fluorescence rate. We benchmark the microscope by measuring two standing-wave Gaussian modes of a Fabry-Pérot resonator with optical wavelengths of 1560 and 781 nm. We attain a spatial resolution of 300 nm, which is superresolving compared to the limit set by the 780 nm wavelength of the detected light. Sensitivity to short length scale features is enhanced by adapting the sensor to characterize an optical field via the force it exerts on the atom.

Quantum register of fermion pairs

Quantum control of motion is central for modern atomic clocks¹ and interferometers². It enables protocols to process and distribute quantum information^3,4, and allows the probing of entanglement in correlated states of matter⁵. However, the motional coherence of individual particles can be fragile to maintain, as external degrees of freedom couple strongly to the environment. Systems in nature with robust motional coherence instead often involve pairs of particles, from the electrons in helium, to atom pairs⁶, molecules⁷ and Cooper pairs. Here we demonstrate long-lived motional coherence and entanglement of pairs of fermionic atoms in an optical lattice array. The common and relative motion of each pair realize a robust qubit, protected by exchange symmetry. The energy difference between the two motional states is set by the atomic recoil energy, is dependent on only the mass and the lattice wavelength, and is insensitive to the noise of the confining potential. We observe quantum coherence beyond ten seconds. Modulation of the interactions between the atoms provides universal control of the motional qubit. The methods presented here will enable coherently programmable quantum simulators of many-fermion systems⁸, precision metrology based on atom pairs and molecules^9,10 and, by implementing further advances^11-13, digital quantum computation using fermion pairs¹⁴.

Trapping Alkaline Earth Rydberg Atoms Optical Tweezer Arrays

Neutral atom qubits with Rydberg-mediated interactions are a leading platform for developing large-scale coherent quantum systems. In the majority of experiments to date, the Rydberg states are not trapped by the same potential that confines ground state atoms, resulting in atom loss and constraints on the achievable interaction time. In this Letter, we demonstrate that the Rydberg states of an alkaline earth atom, ytterbium, can be stably trapped by the same red-detuned optical tweezer that also confines the ground state, by leveraging the polarizability of the Yb^{+} ion core. Using the previously unobserved ^{3}S_{1} series, we demonstrate trapped Rydberg atom lifetimes exceeding 100  μs, and observe no evidence of auto- or photoionization from the trap light for these states. We measure a coherence time of T_{2}=59  μs between two Rydberg levels, exceeding the 28  μs lifetime of untrapped Rydberg atoms under the same conditions. These results are promising for extending the interaction time of Rydberg atom arrays for quantum simulation and computing, and are vital to capitalize on the extended Rydberg lifetimes in circular states or cryogenic environments.

Localization and Criticality in Antiblockaded Two-Dimensional Rydberg Atom Arrays

Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under antiblockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.

Super-resolved Imaging of a Single Cold Atom on a Nanosecond Timescale

In cold atomic systems, fast and high-resolution microscopy of individual atoms is crucial, since it can provide direct information on the dynamics and correlations of the system. Here, we demonstrate nanosecond-scale two-dimensional stroboscopic pictures of a single trapped ion beyond the optical diffraction limit, by combining the main idea of ground-state depletion microscopy with quantum-state transition control in cold atoms. We achieve a spatial resolution up to 175 nm using a NA=0.1 objective in the experiment, which represents a more than tenfold improvement compared with direct fluorescence imaging. To show the potential of this method, we apply it to observe the secular motion of the trapped ion; we demonstrate a temporal resolution up to 50 ns with a displacement detection sensitivity of 10 nm. Our method provides a powerful tool for probing particle positions, momenta, and correlations, as well as their dynamics in cold atomic systems.

Asymmetric Blockade and Multiqubit Gates via Dipole-Dipole Interactions

Because of their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multiqubit Rydberg-blockade gates that involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multiqubit gates can drastically simplify both quantum algorithms and state preparation. To illustrate this, we show that a 25-atom Greenberger-Horne-Zeilinger state can be created using only three gates with an error of 5.8%.