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We show that a deep-learning neural network potential (DP) based on density functional theory (DFT) calculations can well describe Cu-Zr materials, an example of a binary alloy system that can coexist in several ordered intermetallics and as an amorphous phase. The complex phase diagram for Cu-Zr makes it a challenging system for traditional atomistic force-fields that fail to describe well the different properties and phases. Instead, we show that a DP approach using a large database with ~300k configurations can render results generally on par with DFT. The training set includes configurations of pristine and bulk elementary metals and intermetallics in the liquid and solid phases in addition to slab and amorphous configurations. The DP model was validated by comparing bulk properties such as lattice constants, elastic constants, bulk moduli, phonon spectra, surface energies to DFT values for identical structures. Further, we contrast the DP results with values obtained using well-established two embedded atom method potentials. Overall, our DP potential provides near DFT accuracy for the different Cu-Zr phases but with a fraction of its computational cost, thus enabling accurate computations of realistic atomistic models especially for the amorphous phase.