Rydberg atomic quantum receivers (RAQRs) are capable of receiving multi-band radio-frequency (RF) signals simultaneously, which are expected to break Chu's limit for classical electronic antennas. However, signals from different users will interfere with each other in the optical intermediate frequency (IF) domain of the multi-band quantum receiver, which is termed the IF interference (IFI) problem. To address this problem, in this paper, we propose a multi-input multi-output (MIMO) architecture for Rydberg atomic quantum receiver (RAQ-MIMO) by exploiting the additional spatial diversity of MIMO receivers. Specifically, by applying the dynamic signal model of RAQRs, we clarify the physical relationship between the quantum local oscillator (LO) configurations and the multi-band gains with the concept of quantum transconductance. Then, with the quantum transconductance-based signal model, we formulate the spectral efficiency (SE) maximization problem and further propose the quantum weighted minimum mean square error (qWMMSE) algorithm, which jointly optimizes the quantum LO configurations and the classical precoder/combiner matrices. Furthermore, we test the qWMMSE algorithm within the standard space division multiple access (SDMA) scheme and the frequency division multiple access (FDMA) scheme. Simulation results demonstrate that the qWMMSE optimization framework can significantly improve the SE of RAQ-MIMO systems for both multiple access schemes, and that RAQ-MIMO systems can outperform classical electronic receiver-based multi-user MIMO systems by eliminating the mutual coupling effect between classical antennas.