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Solid-state qubits hold the promise to achieve unmatched combination of sensitivity and spatial resolution. To achieve their potential, the qubits need however to be shielded from the deleterious effects of the environment. While dynamical decoupling techniques can improve the coherence time, they impose a compromise between sensitivity and bandwidth, since to higher decoupling power correspond higher frequencies of the field to be measured. Moreover, the performance of pulse sequences is ultimately limited by control bounds and errors. Here we analyze a versatile alternative based on continuous driving. We find that continuous dynamical decoupling schemes can be used for AC magnetometry, providing similar frequency constraints on the AC field and improved sensitivity for some noise regimes. In addition, the exibility of phase and amplitude modulation could yield superior robustness to driving errors and a better adaptability to external experimental scenarios

The sensitivity of quantum magnetometer is challenged by control errors and, especially in the solid state, by their short coherence times. Refocusing techniques can overcome these limitations and improve the sensitivity to periodic fields, but they come at the cost of reduced bandwidth and cannot be applied to sense static or aperiodic fields. Here we experimentally demonstrate that continuous driving of the sensor spin by a composite pulse known as rotary-echo yields a flexible magnetometry scheme, mitigating both driving power imperfections and decoherence. A suitable choice of rotary-echo parameters compensates for different scenarios of noise strength and origin. The method can be applied to nanoscale sensing in variable environments or to realize noise spectroscopy. In a room-temperature implementation, based on a single electronic spin in diamond, composite-pulse magnetometry provides a tunable trade-off between sensitivities in the mTHz À 1/2 range, comparable with those obtained with Ramsey spectroscopy, and coherence times approaching T 1 .

Engineering desired operations on qubits subjected to the deleterious effects of their environment is a critical task in quantum information processing, quantum simulation and sensing. The most common approach is to rely on open-loop quantum control techniques, including optimal control algorithms, based on analytical [1] or numerical [2] solutions, Lyapunov design [3] and Hamiltonian engineering [4]. An alternative strategy, inspired by the success of classical control, is feedback control [5]. Because of the complications introduced by quantum measurement [6], closed-loop control is less pervasive in the quantum settings and, with exceptions [7,8], its experimental implementations have been mainly limited to quantum optics experiments. Here we implement a feedback control algorithm with a solid-state spin qubit system associated with the Nitrogen Vacancy (NV) centre in diamond, using coherent feedback [9] to overcome limitations of measurement-based feedback, and show that it can protect the qubit against intrinsic dephasing noise for milliseconds. In coherent feedback, the quantum system is connected to an auxiliary quantum controller (ancilla) that acquires information about the system's output state (by an entangling operation) and performs an appropriate feedback action (by a conditional gate). In contrast to open-loop dynamical decoupling (DD) techniques [10], feedback control can protect the qubit even against Markovian noise and for an arbitrary period of time (limited only by the ancilla coherence time), while allowing gate operations. It is thus more closely related to Quantum Error Correction schemes [11][12][13][14], which however require larger and increasing qubit overheads. Increasing the number of fresh ancillas allows protection even beyond their coherence time. We can further evaluate the robustness of the feedback protocol, which could be applied to quantum computation and sensing, by exploring an interesting tradeoff between information gain and decoherence protection, as measurement of the ancilla-qubit correlation after the feedback algorithm voids the protection, even if the rest of the dynamics is unchanged.To demonstrate coherent feedback with spin qubits, we choose two of the most common tasks for qubits, implementing the no-operation (NOOP) and NOT gates, while cancelling the effects of noise. A simple, measurementbased feedback scheme, exploiting one ancillary qubit, was proposed in [16]. The correction protocol (Fig. 1a) works by entangling the qubit-ancilla system before the desired gate operation. By selecting an entangling operation U c appropriate for the type of bath acting on the system, information about the noise action is encoded in the ancilla state. After undoing the entangling operation, the qubit coherence can be restored by a feedback action, Hadamard gates prepare and read out a superposition state of the qubit, |φ q = 1 √ 2 (|0 + |1 ). Amid entangling gates between qubit and ancilla, the qubit is subjected to noise (and possibly unitary gates U ). We assume the ancil...

Precise characterization of a system's Hamiltonian is crucial to its high-fidelity control that would enable many quantum technologies, ranging from quantum computation to communication and sensing. In particular, non-secular parts of the Hamiltonian are usually more difficult to characterize, even if they can give rise to subtle but non-negligible effects. Here we present a strategy for the precise estimation of the transverse hyperfine coupling between an electronic and a nuclear spin, exploiting effects due to forbidden transitions during the Rabi driving of the nuclear spin. We applied the method to precisely determine the transverse coupling between a Nitrogen-Vacancy center electronic spin and its Nitrogen nuclear spin. In addition, we show how this transverse hyperfine, that has been often neglected in experiments, is crucial to achieving large enhancements of the nuclear Rabi driving