In this paper, we investigate the optimal decay rate of solutions to the Cauchy problem of the compressible quantum Navier–Stokes–Poisson (QNSP) equations, which had been used in the modelling of semiconductor devices on the nanometre scale. In particular, the quantum effect in the QNSP equations is described by the third-order spacial derivatives of density. Unfortunately the third-order spacial derivatives result in some essential difficulties in the investigation of the optimal decay-in-time rate of solutions by the spectral analysis method. To avoid the essential difficulties, we use the method of pure energy estimates to substitute the spectral analysis method as in [16], and thus establish the decay-in-time rates of the solutions. In particular the decay-in-time rates are optimal, since they are consistent with the ones of the linearized equations.