This study considers a virtual multiuser multipleinput multiple-output system with PSK modulation realized via the reconfigurable intelligent surface-based passive transmitter setup. With a discrete phase-shift reconfigurable intelligent surface model the study proposes a power minimization problem under quality-of-service constraints. The problem formulation is divided into two scenarios. First, for the case of QPSK user's data, the symbol-error probability is utilized as the quality-of-service criterion. Then, for the general case of 𝑀-PSK modulation, the union-bound symbol-error probability is utilized for the qualityof-service constraints. Based on the considered formulations a branch-and-bound approach is developed which improves on full branch-and-bound methods in the sense of allowing for favorable complexity performance trade-offs. Finally, for the special case of high-resolution reconfigurable intelligent surfaces, the study proposes a low-complexity approach based on the approximation of the discrete phase shift set by its continuous counterpart. Based on this, the previously proposed power minimization problems are reformulated as constrained optimizations on an oblique manifold, and solved via the proposed bisection method. Numerical results demonstrate the effectiveness of the proposed approaches in minimizing the transmit power for different symbol-error probability requirements.