  Dual-unitary circuits are a class of quantum systems for which exact
calculations of various quantities are possible, even for circuits that are
nonintegrable. The array of known exact results paints a compelling picture of
dual-unitary circuits as rapidly thermalizing systems. However, in this Letter,
we present a method to construct dual-unitary circuits for which some simple
initial states fail to thermalize, despite the circuits being "maximally
chaotic," ergodic and mixing. This is achieved by embedding quantum many-body
scars in a circuit of arbitrary size and local Hilbert space dimension. We
support our analytic results with numerical simulations showing the stark
contrast in the rate of entanglement growth from an initial scar state compared
to nonscar initial states. Our results are well suited to an experimental test,
due to the compatibility of the circuit layout with the native structure of
current digital quantum simulators.
