Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.

Open quantum systems can have exceptional points (EPs), degeneracies where both eigenvalues and eigenvectors coalesce. Recently, it has been proposed and demonstrated that EPs can enhance the performance of sensors in terms of amplification of a detected signal. However, typically amplification of signals also increases the system noise, and it has not yet been shown that an EP sensor can have improved signal to noise performance. We develop a quantum noise theory to calculate the signal-to-noise performance of an EP sensor. We use the quantum Fisher information to extract a lower bound for the signal-to-noise ratio(SNR) and show that parametrically improved SNR is possible. Finally, we construct a specific experimental protocol for sensing using an EP amplifier near its lasing threshold and heterodyne signal detection to achieves the optimal scaling predicted by the Fisher bound. Our results can be generalized to higher order EPs for any bosonic non-Hermitian system with linear interactions.

Modular quantum computing architectures require fast and efficient distribution of quantum information through propagating signals. Here we report rapid, on-demand quantum state transfer between two remote superconducting cavity quantum memories through traveling microwave photons. We demonstrate a quantum communication channel by deterministic transfer of quantum bits with 76% fidelity. Heralding on errors induced by experimental imperfection can improve this to 87% with a success probability of 0.87. By partial transfer of a microwave photon, we generate remote entanglement at a rate that exceeds photon loss in either memory by more than a factor of three. We further show the transfer of quantum error correction code words that will allow deterministic mitigation of photon loss. These results pave the way for scaling superconducting quantum devices through modular quantum networks.The assembly of large-scale quantum machines hinges on the ability to coherently connect individually controlled quantum storage elements. Quantum networkswherein small, highly coherent modules can exchange quantum information via propagating photons-present a promising approach to achieve this connectivity [1]. Such networks allow for bottom-up construction of reconfigurable quantum systems, forming a backbone for fault-tolerant modular quantum computers [2][3][4]. A crucial challenge, however, is presented by inefficiencies in the mapping of stored quantum information onto traveling signals as well as those during the subsequent photon transfer. Primarily because these inefficiencies have so far been large, quantum communication between remote memories has only been achieved probabilistically [5][6][7][8][9][10][11], requiring local storage of quantum information on long time scales in order for a network to be scalable [12]. Even simple protocols, such as transferring a single quantum bit in a network, have been executed at rates that are orders of magnitude slower than available coherence times [13,14].Direct quantum state transfer, which can be rapid and deterministic, is a desirable scheme for quantum communication within a scalable network [15]. In this protocol, a sending system emits a quantum state as a shaped photonic wavepacket that is then absorbed by a receiving system. This requires strong, tunable coupling between light and matter, as well as efficient transfer of photons at a shared communication frequency; so far, state transfer in optical networks has been highly probabilistic due to inefficiencies in photon coupling and transfer [7].can combine low loss with strong coupling. This platform is well-suited to realize on-demand state transfer, and thus to scale quantum devices in a modular fashion. To this end, superconducting microwave memories and propagating modes have successfully been interfaced to realize controlled photon emission [16][17][18][19] and absorption [20][21][22] independently. Due to the difficulty posed by the need for efficient, frequency-matched photon transfer, however, the goal of deterministic...