  QCD at finite quark-/baryon-number density, which describes nuclear matter,
has a sign problem which prevents direct application of standard simulation
methods based on importance sampling. When such finite density is implemented
by the introduction of a quark-number chemical potential $\mu$, this manifests
itself as a complex fermion determinant. We apply simulations using the Complex
Langevin Equation (CLE) which can be applied in such cases. However, this is
not guaranteed to give correct results, so that extensive tests are required.
In addition, gauge cooling is required to prevent runaway behaviour. We test
these methods on 2-flavour lattice QCD at zero temperature on a small ($12^4$)
lattice at an intermediate coupling $\beta=6/g^2=5.6$ and relatively small
quark mass $m=0.025$, over a range of $\mu$ values from $0$ to saturation.
While this appears to show the correct phase structure with a phase transition
at $\mu \approx m_N/3$ and a saturation density of $3$ at large $\mu$, the
observables show departures from known values at small $\mu$. We are now
running on a larger lattice ($16^4$) at weaker coupling $\beta=5.7$. At $\mu=0$
this significantly improves agreement between measured observables and known
values, and there is some indication that this continues to small $\mu$s. This
leads one to hope that the CLE might produce correct results in the
weak-coupling -- continuum -- limit.
