Closed-Loop Gate Optimisation via Efficient Two-Qubit Tomography for NV Centers

While moving towards the realisation of commercial quantum computers it has become of paramount importance to be able to implement high fidelity quantum gates. As of today, this is a technical challenge for all hardware platforms because of the difficulty to create theoretical models which reach the level of detail required for designing of high precision gates. To overcome this hurdle, closed-loop quan- tum optimal control (QOC) provides an excellent tool for the optimization of con- trol pulses by exploiting experimental feedback which does not require modeling and characterisation. In this work we propose a new protocol for the implementation of an experi- mentally-convenient figure of merit to perform closed-loop QOC for two-qubit gates. We examine its performances on nitrogen vacancy (NV) centers in dia- monds, which have raised as one of the most promising hardware proposals for quantum technologies because of their relatively long decoherence time and their performances at room temperature. In particular, our approach has been tested nu- merically for the realization of entangling gates for a 13C-NV− system, with spe- cial care in the definition of the pulse duration and the control amplitudes accord- ing to typical experimental parameters. Numerical simulations using the dressed Chopped RAndom Basis (dCRAB) algorithm suggest the possibility to build high fidelity CNOT gates within few hundreds of closed-loop optimization iterations, with a significant reduction in the number of required readout operations compared to the state-of-the-art.