Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-11-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.3.040315 |
| _version_ | 1811223446223323136 |
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| author | Yu-Jie Liu Kirill Shtengel Adam Smith Frank Pollmann |
| author_facet | Yu-Jie Liu Kirill Shtengel Adam Smith Frank Pollmann |
| author_sort | Yu-Jie Liu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T08:33:07Z |
| format | Article |
| id | doaj.art-97f7128f62f84f4882bce9b368c690ff |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-04-12T08:33:07Z |
| publishDate | 2022-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-97f7128f62f84f4882bce9b368c690ff2022-12-22T03:40:08ZengAmerican Physical SocietyPRX Quantum2691-33992022-11-013404031510.1103/PRXQuantum.3.040315Methods for Simulating String-Net States and Anyons on a Digital Quantum ComputerYu-Jie LiuKirill ShtengelAdam SmithFrank PollmannThe 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.http://doi.org/10.1103/PRXQuantum.3.040315 |
| spellingShingle | Yu-Jie Liu Kirill Shtengel Adam Smith Frank Pollmann Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer PRX Quantum |
| title | Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer |
| title_full | Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer |
| title_fullStr | Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer |
| title_full_unstemmed | Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer |
| title_short | Methods for Simulating String-Net States and Anyons on a Digital Quantum Computer |
| title_sort | methods for simulating string net states and anyons on a digital quantum computer |
| url | http://doi.org/10.1103/PRXQuantum.3.040315 |
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