  Adaptive quantum circuits employ unitary gates assisted by mid-circuit
measurement, classical computation on the measurement outcome, and the
conditional application of future unitary gates based on the result of the
classical computation. In this paper, we experimentally demonstrate that even a
noisy adaptive quantum circuit of constant depth can achieve a task that is
impossible for any purely unitary quantum circuit of identical depth: the
preparation of long-range entangled topological states with high fidelity. We
prepare a particular toric code ground state with fidelity of at least $76.9\pm
1.3\%$ using a constant depth ($d=4$) adaptive circuit, and rigorously show
that no unitary circuit of the same depth and connectivity could prepare this
state with fidelity greater than $50\%$.
