Topological order from measurements and feed-forward on a trapped ion quantum computer
Abstract
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.
Copyright and License
© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Acknowledgement
This work was made possible by a large group of people, and the authors would like to thank the entire Quantinuum team for their many contributions. We are grateful for helpful discussions and feedback from Ciaran Ryan-Anderson, Konstantinos Meichanetzidis, Ben Criger, Eli Chertkov, Kevin Hemery, Ramil Nigmatullin, Reza Haghshenas, Khaldoon Ghanem, Alexander Schuckert, Ella Crane, David Hayes, and Natalie Brown. N.T. is supported by the Walter Burke Institute for Theoretical Physics at Caltech. R.V. is supported by the Harvard Quantum Initiative Postdoctoral Fellowship in Science and Engineering. A.V. is supported by NSF-DMR 2220703 and A.V. and R.V. are supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (618615, A.V.). The experimental data in this work was produced by the Quantinuum H1-1 trapped ion quantum computer, Powered by Honeywell. H.D. acknowledges support by the German Federal Ministry of Education and Research (BMBF) through the project EQUAHUMO (grant number 13N16069) within the funding program quantum technologies—from basic research to market.
Data Availability
The numerical data that support the findings of this study, including a full list of shots is available on the Zenodo repository63.
Code Availability
The code used for quantum circuit construction, submission and data analysis is available on the Zenodo repository63.
Conflict of Interest
H.D. is a shareholder of a subsidiary of Quantinuum. All other authors declare no competing interests.
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Additional details
- California Institute of Technology
- Walter Burke Institute for Theoretical Physics
- Harvard University
- National Science Foundation
- DMR-2220703
- Simons Foundation
- 618615
- Federal Ministry of Education and Research
- 13N16069
- Caltech groups
- Walter Burke Institute for Theoretical Physics