Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer

Liu, Yu-Jie; Shtengel, Kirill; Smith, Adam; Pollmann, Frank

Abstract

The finding of physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. We show how to realize a large class of topologically ordered states and simulate their quasiparticle excitations on a digital quantum computer. To achieve this, we design a set of linear-depth quantum circuits to generate ground states of general string-net models together with unitary open-string operators to simulate the creation and braiding of Abelian and non-Abelian anyons. We show that the Abelian (non-Abelian) unitary string operators can be implemented with a constant- (linear-) depth quantum circuit. Our scheme allows us to directly probe characteristic topological properties, including topological entanglement entropy, braiding statistics, and fusion channels of anyons. Moreover, this set of efficiently prepared topologically ordered states has potential applications in the development of fault-tolerant quantum computers.

Citation

Liu, Y., Shtengel, K., Smith, A., & Pollmann, F. (2022). Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer. PRX Quantum, 3(4), Article 040315. https://doi.org/10.1103/prxquantum.3.040315

• Journal Article Type: Article
• Acceptance Date: Oct 6, 2022
• Online Publication Date: Nov 7, 2022
• Publication Date: Nov 7, 2022
• Deposit Date: Nov 30, 2022
• Publicly Available Date: Dec 20, 2022
• Journal: PRX Quantum
• Print ISSN: 2691-3399
• Electronic ISSN: 2691-3399
• Publisher: American Physical Society (APS)
• Peer Reviewed: Peer Reviewed
• Volume: 3
• Issue: 4
• Article Number: 040315
• DOI: https://doi.org/10.1103/prxquantum.3.040315
• Keywords: General Medicine
• Public URL: https://nottingham-repository.worktribe.com/output/13465394
• Publisher URL: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.040315