Topological order from measurements and feed-forward on a trapped ion quantum computer

Quantum systems evolve in time in one of two ways: through the Schrödinger 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 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. Topological quantum states are essential resources in quantum error correction and quantum simulation but unitary quantum circuits for their preparation require extensive circuit depth. The authors demonstrate a constant-depth protocol to prepare topologically ordered states on a trapped-ion quantum computer using non-unitary operations.