  Random quantum circuit is a minimally structured model to study the
entanglement dynamics of many-body quantum systems. In this paper, we
considered a one-dimensional quantum circuit with noisy Haar-random unitary
gates using density matrix operator and tensor contraction methods. It is shown
that the entanglement evolution of the random quantum circuits is properly
characterized by the logarithmic entanglement negativity. By performing exact
numerical calculations, we found that, as the physical error rate is decreased
below a critical value $p_c\approx 0.056$, the logarithmic entanglement
negativity changes from the area law to the volume law, giving rise to an
entanglement transition. The critical exponent of the correlation length can be
determined from the finite-size scaling analysis, revealing the universal
dynamic property of the noisy intermediate-scale quantum devices.
