  Quantum complexity is emerging as a key property of many-body systems,
including black holes, topological materials, and early quantum computers. A
state's complexity quantifies the number of computational gates required to
prepare the state from a simple tensor product. The greater a state's distance
from maximal complexity, or "uncomplexity," the more useful the state is as
input to a quantum computation. Separately, resource theories -- simple models
for agents subject to constraints -- are burgeoning in quantum information
theory. We unite the two domains, confirming Brown and Susskind's conjecture
that a resource theory of uncomplexity can be defined. The allowed operations,
fuzzy operations, are slightly random implementations of two-qubit gates chosen
by an agent. We formalize two operational tasks, uncomplexity extraction and
expenditure. Their optimal efficiencies depend on an entropy that we engineer
to reflect complexity. We also present two monotones, uncomplexity measures
that decline monotonically under fuzzy operations, in certain regimes. This
work unleashes on many-body complexity the resource-theory toolkit from quantum
information theory.
