  Quantum systems evolve in time in one of two ways: through the Schr\"odinger
equation or wavefunction collapse. So far, deterministic control of quantum
many-body systems in the lab has focused on the former, due to the
probabilistic nature of measurements. This imposes serious limitations:
preparing long-range entangled states, for example, requires extensive circuit
depth if restricted to unitary dynamics. In this work, we use mid-circuit
measurement and feed-forward to implement deterministic non-unitary dynamics on
Quantinuum's H1 programmable ion-trap quantum computer. Enabled by these
capabilities, we demonstrate for the first time a constant-depth procedure for
creating a toric code ground state in real-time. In addition to reaching high
stabilizer fidelities, we create a non-Abelian defect whose presence is
confirmed by transmuting anyons via braiding. This work clears the way towards
creating complex topological orders in the lab and exploring deterministic
non-unitary dynamics via measurement and feed-forward.
