A. S. Sørensen

We present an architecture for remotely connecting cavity-coupled trapped ions via a quantum repeater based on rare-earth-doped crystals. The main challenge for its realization lies in interfacing these two physical platforms, which produce photons with a typical temporal mismatch of one or two orders of magnitude. To address this, we propose an efficient protocol that enables custom temporal reshaping of single-photon pulses whilst preserving purity. Our approach is to modify a commonly used memory protocol, called atomic frequency comb, for systems exhibiting inhomogeneous broadening like rare-earth-doped crystals. Our results offer a viable solution for uniting quantum processing nodes with a quantum repeater backbone.

Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin- or phase flips. Our dissipative error correction scheme operates in a fully autonomous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.

Entangled states are a crucial resource for quantum-based technologies such as quantum computers and quantum communication systems (1,2). Exploring new methods for entanglement generation is important for diversifying and eventually improving current approaches. Here, we create entanglement in atomic ions by applying laser fields to constrain the evolution to a restricted number of states, in an approach that has become known as "quantum Zeno dynamics" (3-5). With two trapped $^9\rm{Be}^+$ ions, we obtain Bell state fidelities up to $0.990^{+2}_{-5}$, with three ions, a W-state (6) fidelity of $0.910^{+4}_{-7}$ is obtained. Compared to other methods of producing entanglement in trapped ions, this procedure is relatively insensitive to certain imperfections such as fluctuations in laser intensity, laser frequency, and ion-motion frequencies.

Entangled states are a key resource in fundamental quantum physics, quantum cryp-tography, and quantum computation [1].To date, controlled unitary interactions applied to a quantum system, so-called "quantum gates", have been the most widely used method to deterministically create entanglement [2]. These processes require high-fidelity state preparation as well as minimizing the decoherence that inevitably arises from coupling between the system and the environment and imperfect control of the system parameters. Here, on the contrary, we combine unitary processes with engineered dissipation to deterministically produce and stabilize an approximate Bell state of two trapped-ion qubits independent of their initial state. While previous works along this line involved the application of sequences of multiple time-dependent gates [3] or generated entanglement of atomic ensembles dissipatively but relied on a measurement record for steady-state entanglement [4], we implement the process in a continuous time-independent fashion, analogous to optical pumping of atomic states. By continuously driving the system towards steady-state, the entanglement is stabilized even in the presence of experimental noise and decoherence. Our demonstration of an entangled steady state of two qubits represents a step towards dissipative state engineering, dissipative quantum computation, and dissipative phase transitions [5-7]. Following this approach, engineered coupling to the environment may be applied to a broad range of experimental systems to achieve desired quantum dynamics or steady states. Indeed, concurrently with this work, an entangled steady state of two superconducting qubits was demonstrated using dissipation [8].

We describe a method to enhance the sensitivity of precision measurements that takes advantage of a quantum sensor's environment to amplify its response to weak external perturbations. An individual qubit is used to sense the dynamics of surrounding ancillary qubits, which are in turn affected by the external field to be measured. The resulting sensitivity enhancement is determined by the number of ancillas that are coupled strongly to the sensor qubit; it does not depend on the exact values of the coupling strengths and is resilient to many forms of decoherence. The method achieves nearly Heisenberg-limited precision measurement, using a novel class of entangled states. We discuss specific applications to improve clock sensitivity using trapped ions and magnetic sensing based on electronic spins in diamond.