  In this note we investigate the role of Lloyd's computational bound in
holographic complexity. Our goal is to translate the assumptions behind Lloyd's
proof into the bulk language. In particular, we discuss the distinction between
orthogonalizing and `simple' gates and argue that these notions are useful for
diagnosing holographic complexity. We show that large black holes constructed
from series circuits necessarily employ simple gates, and thus do not satisfy
Lloyd's assumptions. We also estimate the degree of parallel processing
required in this case for elementary gates to orthogonalize. Finally, we show
that for small black holes at fixed chemical potential, the orthogonalization
condition is satisfied near the phase transition, supporting a possible
argument for the Weak Gravity Conjecture first advocated in Brown et al.
