Rydberg atomic quantum receivers exhibit great potential in assisting classical wireless communications due to their outstanding advantages in detecting radio frequency signals. To realize this potential, we integrate a Rydberg atomic quantum receiver into a classical multi-user multiple-input multiple-output (MIMO) scheme to form a multi-user Rydberg atomic quantum MIMO (RAQ-MIMO) system for the uplink. To study this system, we first construct an equivalent baseband signal model, which facilitates convenient system design, signal processing and optimizations. We then study the ergodic achievable rates under both the maximum ratio combining (MRC) and zero-forcing (ZF) schemes by deriving their tight lower bounds. We next compare the ergodic achievable rates of the RAQ-MIMO and the conventional massive MIMO schemes by offering a closed-form expression for the difference of their ergodic achievable rates, which allows us to directly compare the two systems. Our results show that RAQ-MIMO allows the average transmit power of users to be $> 25$ dBm lower than that of the conventional massive MIMO. Viewed from a different perspective, an extra $\sim 8.8$ bits/s/Hz/user rate becomes achievable by ZF RAQ-MIMO.