With the research on implementing a universal quantum computer being under the technological spotlight, new possibilities appear for their employment in wireless communications systems for reducing their complexity and improving their performance. In this treatise, we consider the downlink of a rank-deficient, multi-user system and we propose the discrete-valued and continuous-valued Quantum-assisted Particle Swarm Optimization (QPSO) algorithms for performing Vector Perturbation (VP) precoding, as well as for lowering the required transmission power at the Base Station (BS), while minimizing the expected average Bit Error Ratio (BER) at the mobile terminals. We use the Minimum BER (MBER) criterion. We show that the novel quantum-assisted precoding methodology results in an enhanced BER performance, when compared to that of a classical methodology employing the PSO algorithm, while requiring the same computational complexity in the challenging rank-deficient scenarios, where the number of transmit antenna elements at the BS is lower than the number of users. Moreover, when there is limited Channel State Information (CSI) feedback from the users to the BS, due to the necessary quantization of the channel states, the proposed quantum-assisted precoder outperforms the classical precoder.
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