  We construct an infinite family of microstates with geometric interiors for
eternal black holes in general relativity with negative cosmological constant
in any dimension. Wormholes in the Euclidean path integral for gravity cause
these states to have small, but non-zero, quantum mechanical overlaps that have
a universal form. The overlaps have a dramatic consequence: the microstates
span a Hilbert space of log dimension equal to the Bekenstein-Hawking entropy.
The semiclassical microstates we construct contain Einstein-Rosen bridges of
arbitrary size behind their horizons. Our results imply that all these bridges
can be interpreted as quantum superpositions of wormholes of size at most
exponential in the entropy.
