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Joint channel estimation (CE) and multi-user detection (MUD) have become a crucial part of iterative receivers. In this paper, we propose a quantum-assisted repeated weighted boosting search (QRWBS) algorithm for CE and we employ it in the uplink of multiple-input multiple-output orthogonal frequency division multiplexing systems, in conjunction with the maximum a posteriori probability (MAP) MUD and a near-optimal quantum-assisted MUD (QMUD). The performance of the QRWBS-aided CE is evaluated in rank-deficient systems, where the number of receive antenna elements (AEs) at the base station (BS) is lower than the number of supported users. The effect of the channel impulse response prediction filters, of the power delay profile of the channels, and of the Doppler frequency on the attainable system performance is also quantified. The proposed QRWBS-aided CE is shown to outperform the RWBS-aided CE, despite requiring a lower complexity, in systems where iterations are invoked between the MUD, the CE, and the channel decoders at the receiver. In a system, where U = 7 users are supported with the aid of P = 4 receive AEs, the joint QRWBS-aided CE and QMUD achieves a 2-dB gain, when compared with the joint RWBS-aided CE and MAP MUD, despite imposing 43% lower complexity.