Inspired by the direct use of alternating current (AC) for computation, we propose a novel integrated information and energy receiver architecture for simultaneous wireless information and power transfer (SWIPT) networks. In this context, the AC computing method, in which wirelessly harvested AC energy is directly used to supply the computing block of receivers, enhances not only computational ability but also energy efficiency over the conventional direct current (DC) one. Further, we aim to manage the trade-off between the information decoding (ID) and energy harvesting (EH) optimally while taking imperfect channel estimation into account. It results in a worst-case optimization problem of maximizing the data rate under the constraints of an EH requirement, the energy needed for supplying the AC computational logic, and a transmit power budget. Then, we propose a method to derive closed-form optimal solutions. The numerical results demonstrate that the proposed architecture with AC computing significantly improves the rate-energy region.