  We investigate the continuous-time dynamics of highly-entangling
intermediate-scale quantum circuits in the presence of dissipation and
decoherence. By compressing the Hilbert space to a time-dependent ``corner"
subspace that supports faithful representations of the density matrix, we
simulate a noisy quantum Fourier transform processor with up to 21 qubits. Our
method is efficient to compute with a controllable accuracy the time evolution
of intermediate-scale open quantum systems with moderate entropy, while taking
into account microscopic dissipative processes rather than relying on digital
error models. The circuit size reached in our simulations allows to extract the
scaling behaviour of error propagation with the dissipation rates and the
number of qubits. Moreover, we show that depending on the dissipative
mechanisms at play, the choice of input state has a strong impact on the
performance of the quantum algorithm.
