Controlled phase (CPHASE) gates can in principle be realized with trapped neutral atoms by making use of the Rydberg blockade. Achieving the ultra-high fidelities required for quantum computation with such Rydberg gates is however compromised by experimental inaccuracies in pulse amplitudes and timings, as well as by stray fields that cause fluctuations of the Rydberg levels. We report here a comparative study of analytic and numerical pulse sequences for the Rydberg CPHASE gate that specifically examines the robustness of the gate fidelity with respect to such experimental perturbations. Analytical pulse sequences of both simultaneous and stimulated Raman adiabatic passage (STIRAP) are found to be at best moderately robust under these perturbations. In contrast, optimal control theory is seen to allow generation of numerical pulses that are inherently robust within a predefined tolerance window. The resulting numerical pulse shapes display simple modulation patterns and their spectra contain only one additional frequency beyond the basic resonant Rydberg gate frequencies. Pulses of such low complexity should be experimentally feasible, allowing gate fidelities of order 99.90 -99.99% to be achievable under realistic experimental conditions.

We present a scheme for generating robust and persistent entanglement between qubits that do not interact and that are separated by a long and lossy transmission channel, using Markovian reservoir engineering. The proposal uses only the correlated decay into the common channel of remotely separated, driven single-photon qubit transitions. This simple scheme is generic and applicable to various experimental implementations, including circuit and cavity QED, with little experimental overhead compared with methods requiring dynamic control, initialization, measurement, or feedback. In addition to avoiding these inefficiencies, the simple protocol is highly robust against noise, miscalibration, and loss in the channel. We find high quality solutions over a wide range of parameters and show that the optimal strategy reflects a transition from ballistic to diffusive photon transmission, going from symmetrically and coherently driving a common steady state to asymmetrically absorbing photons that are emitted from one qubit by the second. Detailed analysis of the role of the transmission channel shows that allowing bi-directional decay drastically increases indistinguishability and thereby quadratically suppresses infidelity. Deterministically generating remote steady-state entanglement is of fundamental interest for ongoing developments of quantum technologies. Applications include quantum cryptography, quantum networks, entanglement distillation, scalable quantum computation, and distributed quantum computing [1][2][3][4][5][6]. Much akin to how operational amplifiers have removed many of the timing, calibration, and variability issues in classical circuit technology, offering stabilised entanglement on-demand can serve a similar purpose for quantum technologies, alleviating the need for complex and often inefficient measurement, initialization, photon creation, photon collection, or travel-time synchronization processes. In this work we propose a scheme for on-demand deterministic generation of remote entanglement that employs reservoir engineering to autonomously arrive at a high-fidelity entangled steady-state solution of qubits in distinct cavities. Perturbation away from the desired steady-state is self-healing due to the nonlocal relaxation back-action, and therefore naturally robust against noise in ways that pulse and measurement-based generation of entanglement cannot be.A number of theoretical schemes have been proposed for realizing deterministic steady-state entanglement over short distances, e.g., within a single cavity [7][8][9][10][11] or between spatially separated qubits assuming zero or minimal losses in communication [12][13][14][15], and several recent experimental demonstrations have realized above threshold steady-state entanglement, although with limited fidelities [16][17][18]. Medium-distance entanglement has also been studied theoretically [19][20][21][22] and realized experimentally in [23][24][25][26]. However, achieving even postselected, transient entanglement over truly long distances is...