This paper describes a general method for the manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclear gyromagnetic ratios and spin-spin couplings. For spin-$\frac{1}{2}$ nuclei with different gyromagnetic ratios (i.e., different species) in zero magnetic field, we describe the scheme to realize a set of universal quantum logic gates, e.g., arbitrary single-qubit gates and a two-qubit controlled-not gate. This method allows for universal quantum control in systems which might provide promising applications in materials science, chemistry, biology, quantum information processing, and fundamental physics.

• Received 21 January 2017

DOI:https://doi.org/10.1103/PhysRevA.95.052342