Numerical optimal control of spin systems at zero magnetic field

Zero-field nuclear magnetic resonance (NMR) has been recently developed as a complementary tool for nondestructive structural investigations of matter. However, precise and efficient control in such systems is still at the beginning. Based on the controllability of spin systems, we theoretically study the issue of quantum control in zero-field NMR by using a numerical optimization method based on the gradient ascent pulse engineering (GRAPE) algorithm. A set of quantum gates, including single-qubit and two-qubit gates, are achieved as examples. In particular, we show that homonuclear spins can be individually manipulated in zero-field NMR by the GRAPE method, which extends the ability to manipulate spin systems at zero magnetic field. Quantum control realized by the numerical GRAPE method features the properties of high fidelity, robustness, and hardware-friendly characteristics. High-fidelity quantum control in zero-field NMR systems might provide promising applications in material science, chemical analysis, quantum information processing, and fundamental physics.