The Implementation of Quantum Computing Operations with Phase Modulated Microwave Pulses and High-Spin Ions at Zero Magnetic Fields

New physical implementations of quantum computing elementary operations by pulse manipulations with electron spins of paramagnetic ions having two electrons and spin S=1 in a zero magnetic field are proposed. New type of microwave pulses with variable phases and different polarizations are able to induce different transitions between ion spin states, and those transitions are described by quantum computing operators. To describe the effects of such pulses, a new way to present exponential operators as polynomials of Pauli matrices is proposed.