  Conformal field theory, describing systems with scaling symmetry, plays a
crucial role throughout physics. We describe a quantum algorithm to simulate
the dynamics of conformal field theories, including the action of local
conformal transformations. A full analysis of the approximation errors suggests
near-term applicability of our algorithm: promising results for conformal field
theories with central charge c=1/2 are obtained already with 128 logical
qubits.
