  This paper introduces a new quantum computing framework integrated with a
two-step compressed sensing technique, applied to a joint channel estimation
and user identification problem. We propose a variational quantum circuit (VQC)
design as a new denoising solution. For a practical grant-free communications
system having correlated device activities, variational quantum parameters for
Pauli rotation gates in the proposed VQC system are optimized to facilitate to
the non-linear estimation. Numerical results show that the VQC method can
outperform modern compressed sensing techniques using an element-wise denoiser.
