Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer

• URL: http://arxiv.org/abs/2302.01917v3
• Date: Wed, 30 Aug 2023 18:03:25 GMT
• Title: Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
• Authors: Mohsin Iqbal, Nathanan Tantivasadakarn, Thomas M. Gatterman, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Aaron Hankin, Nathan Hewitt, Chandler V. Horst, Mitchell Matheny, Tanner Mengle, Brian Neyenhuis, Ashvin Vishwanath, Michael Foss-Feig, Ruben Verresen, and Henrik Dreyer
• Abstract summary: We show for the first time a constant-depth procedure for creating a toric code ground state in real-time. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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