  One of the most famous problems in mathematics is the Riemann hypothesis:
that the non-trivial zeros of the Riemann zeta function lie on a line in the
complex plane. One way to prove the hypothesis would be to identify the zeros
as eigenvalues of a Hermitian operator, many of whose properties can be derived
through the analogy to quantum chaos. Using this, we construct a set of quantum
graphs that have the same oscillating part of the density of states as the
Riemann zeros, offering an explanation of the overall minus sign. The smooth
part is completely different, and hence also the spectrum, but the graphs pick
out the low-lying zeros.
