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

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


Yu-Jie Liu

Kirill Shtengel

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Assistant Professor

Frank Pollmann


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.


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.

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
Peer Reviewed Peer Reviewed
Volume 3
Issue 4
Article Number 040315
Keywords General Medicine
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