High-Fidelity Control and Entanglement of Rydberg-Atom Qubits
Harry Levine, Alexander Keesling, Ahmed Omran, Hannes Bernien, Sylvain Schwartz, Alexander S. Zibrov, Manuel Endres, Markus Greiner, Vladan Vuletić, Mikhail D. Lukin
Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities associated with such Rydberg excitations. We report progress towards high-fidelity quantum control of Rydberg-atom qubits. Enabled by a reduction in laser phase noise, our approach yields a significant improvement in coherence properties of individual qubits. We further show that this high-fidelity control extends to the multi-particle case by preparing a two-atom entangled state with a fidelity exceeding 0.97(3), and extending its lifetime with a two-atom dynamical decoupling protocol. These advances open up new prospects for scalable quantum simulation and quantum computation with neutral atoms.
Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities associated with such Rydberg excitations. We report progress towards high-fidelity quantum control of Rydberg-atom qubits. Enabled by a reduction in laser phase noise, our approach yields a significant improvement in coherence properties of individual qubits. We further show that this high-fidelity control extends to the multi-particle case by preparing a two-atom entangled state with a fidelity exceeding 0.97(3), and extending its lifetime with a two-atom dynamical decoupling protocol. These advances open up new prospects for scalable quantum simulation and quantum computation with neutral atoms.
Abstract The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing 1 . Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits 2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture 4 . The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions 5 . 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 correction 6,7 . Our method uses fast, single-pulse gates based on optimal control 8 , atomic dark states to reduce scattering 9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications 10,11 , 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 gates 12,13 . By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms 14 , error-corrected circuits 7 and digital simulations 15 .
The neutral atom platform has become an attractive choice to study the science of quantum information and quantum simulation, where intense efforts have been devoted to the entangling processes between individual atoms. A two-qubit controlled-phase gate via Rydberg blockade is one of the most essential elements. Recent theoretical studies have suggested the advantages of introducing nontrivial waveform modulation into the gate protocol, which is anticipated to improve its performance towards the next stage. We report our recent experimental results in realizing the two-qubit controlled-phase (CZ) gate via single-modulated-pulse off-resonant modulated driving embedded in a two-photon transition for Rb atoms. It relies on a global driving laser pulse with a carefully calculated smooth waveform to gain the appropriate phase accumulations required by CZ gate. Combining this CZ gate with global microwave pulses, two-atom entanglement is generated with the raw fidelity of 0.945(6). After accounting for state preparation and measurement errors, we extract the entanglement operation fidelity to be 0.980(7). Our work features completing the CZ gate operation within a single pulse to avoid shelved population in the Rydberg levels, thus demonstrating another promising route for realizing a high-fidelity two-qubit gate for the neutral atom platform.
Individually trapped neutral atoms are a promising candidate for use in quantum computing and simulation applications. They are highly scalable, have long coherence times and can be entangled via strong dipole-dipole interactions by driving to highly excited Rydberg states. However, the fidelity of single atom operations as well as two-atom entangling operations is limited by intrinsic sources of decoherence such as atomic motion, as well as technical sources of noise such as laser intensity fluctuations and phase/frequency fluctuations. We study the effect of these factors on single atom Rabi oscillations and two-atom Rydberg blockaded Rabi oscillations, using perturbation theory and numerical simulation. We develop a window function approach which helps us qualitatively understand the significance of the different spectral components of the noise as well as quantitatively understand the dependence of the Rabi oscillation fidelity on Rabi frequency. This allows us to predict the maximum experimentally achievable fidelities using independent measurements of experimental parameters such as noise spectra and atomic temperature. Turning to the question of near-term scalability of the experimental system, we prototype and test a method of generating a ’ladder’ configuration of optical tweezers utilizing two independent lasers. Our setup allows us to fully tune the geometry of the ladder, namely the separation between the two rows, the angle between them, and their relative position along the axis of the ladder. This pseudo-2D configuration enables us to reach larger system sizes in the near future and allows us to access beyond 1D physics.
Individually trapped Rydberg atoms show significant promise as a platform for scalable quantum simulation and for the development of programmable quantum computers. In particular, the Rydberg-blockade effect can be used to facilitate both fast qubit-qubit interactions and long coherence times via low-lying electronic states encoding the physical qubits. To bring existing Rydberg-atom-based platforms a step closer to fault-tolerant quantum computation, we demonstrate high-fidelity state and circuit preparation in a system of five atoms. We specifically show that quantum control can be used to reliably generate fully connected cluster states and to simulate the error-correction encoding circuit based on the ``Perfect Quantum Error Correcting Code'' by Laflamme et al. [Phys. Rev. Lett. 77, 198 (1996)]. Our results make these ideas and their implementation directly accessible to experiments and demonstrate a promising level of noise tolerance with respect to experimental errors. With this approach, we motivate the application of quantum control in small subsystems in combination with the standard gate-based quantum circuits for direct and high-fidelity implementation of few-qubit modules.
A frontier challenge in quantum science and technology is the construction of scalable quantum systems which can operate in regimes beyond classical simulatability. Such systems can be used as tools for simulating and exploring complex phenomena in quantum physics; they can also be used to benchmark and test quantum algorithms. Several experimental platforms, based on a variety of quantum mechanical building blocks, are currently being pursued with these goals in mind, with state-of-the-art systems capable of controlling up to around fifty particles. In this thesis, we present the development of a new platform based on individually controlled neutral atoms. In this approach, hundreds of individual atoms are trapped in an array of optical tweezers, and they are sorted in real-time into programmable geometries in one and two dimensions. After initialization of an array, atom interactions are switched on by coherent excitation to highly excited Rydberg states, resulting in a rich spin Hamiltonian. We experimentally advance several key aspects of this platform, developing new tools for controlling strongly interacting atom arrays and probing novel quantum phases and non-equilibrium dynamics. We additionally utilize Rydberg interactions to entangle atoms, demonstrating high fidelity universal quantum logic gates as well as the preparation of fully entangled Schrödinger cat states. This work highlights the prospects for scalable quantum simulation and quantum information processing beyond the limit of classical computation using neutral atom arrays.
In any physical platform, two ingredients are essential for quantum information processing: single-qubit control, and entangling interactions between qubits. Neutral atoms can be individually controlled with high fidelity and are resilient to environmental noise, making them attractive candidates for implementing quantum information protocols. However, achieving strong interactions remains a major obstacle. One way to increase the interaction strength between neutral atoms is to excite them into high-lying Rydberg states, which exhibit large electric dipole moments (and by extension, strong electric dipole-dipole interactions). By slowly ramping up the Rydberg level coupling in a system, one can "dress'' the atomic ground states with some Rydberg character; this maps the Rydberg dipole interaction to an effective interaction between ground states. Such Rydberg-dressed interaction is the focus of this dissertation. After describing the physics of the Rydberg-dressed interaction, we propose three protocols that demonstrate its versatility and provide a framework for considering some of the details of realistic implementation. In all three cases, Rydberg dressing --- along with some form of single-atom control --- is used to generate highly entangled states of interest. Our first proposal relates to the adiabatic model of quantum computing, in which solutions to problems are encoded in the ground states of carefully engineered Hamiltonians. The Rydberg-dressed interaction can provide nonlinear Hamiltonian terms, allowing us to encode NP-hard and other interesting problems. We model this protocol in the presence of decoherence, and find that computational fidelities of ~0.98 for four atoms should be possible with currently realistic experimental parameters. Our second proposal is also related to quantum computing, this time in the circuit model. The Rydberg-dressed interaction can be used to generate a controlled-NOT logic gate which, when interwoven with single-qubit gates, can perform universal quantum computation. Experimentally, noise due to atomic thermal motion has been a primary limitation on the fidelities of these gates. We show that a Doppler-free setup, with counterpropagating lasers, effectively suppresses this type of noise, allowing simulated fidelities of up to ~0.998 per gate. Such strong suppression is only possible because the Doppler-free configuration can harness the natural robustness of adiabatic dressing; other gate schemes using, e.g., resonant pulses, do not exhibit the same degree of improvement. Finally, we consider exploiting the many-body character of the Rydberg-dressed interaction to generate collective entanglement in mesoscopic ensembles of neutral atoms. An atomic ensemble uniformly illuminated by a single Rydberg-exciting laser is isomorphic to the well-known Jaynes-Cummings model. In addition to adapting generic Jaynes-Cummings entanglement protocols developed in other platforms, one can apply microwaves to drive entanglement in a way that is unique to the atomic platform. We prove that by allowing the microwave phase to vary in time, one can generate arbitrary symmetric states of the ensemble. While this method compares favorably with other entanglement protocols in many ways, the required frequency of phase switching presents a fundamental limitation on its effectiveness. To mitigate this, we propose a variant scheme in which parameters are chosen to only allow excitations within the system's dressed-ground subspace; this effectively cuts phase switching demands in half. All three protocols serve to illustrate the power of the Rydberg-dressed interaction and suggest directions for future study.