Mapping between Morita-equivalent string-net states with a constant depth quantum circuit

Laurens Lootens; Bram Vancraeynest-De Cuiper; Norbert Schuch; Frank Verstraete

doi:10.1103/PhysRevB.105.085130

Mapping between Morita-equivalent string-net states with a constant depth quantum circuit

Laurens Lootens (Corresponding author)
, Bram Vancraeynest-De Cuiper
, Norbert Schuch
, Frank Verstraete

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We construct a constant depth quantum circuit that maps between Morita-equivalent string-net models. Due to its constant depth and unitarity, the circuit cannot alter the topological order, which demonstrates that Morita-equivalent string nets are in the same phase. The circuit is constructed from an invertible bimodule category connecting the two input fusion categories of the relevant string-net models, acting as a generalized Fourier transform for fusion categories. The circuit not only acts on the ground state subspace but also acts unitarily on the full Hilbert space when supplemented with ancillas.

Original language	English
Article number	085130
Number of pages	12
Journal	Physical Review B
Volume	105
Issue number	8
DOIs	https://doi.org/10.1103/PhysRevB.105.085130
Publication status	Published - 17 Feb 2022

Funding

We are grateful to Nick Bultinck for inspiring discussions and to Jacob Bridgeman for insightful comments on invertible bimodule categories and tube algebras. This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [Grant Agreements No. 647905 (QUTE) and No. 863476 (SEQUAM)], and the Research Foundation Flanders via Grants No. G087918N and No. G0E1820N. L.L. is supported by a Ph.D. fellowship from the Research Foundation Flanders (FWO). B.V.-D.C. is supported by a Ph.D. fellowship from Bijzonder Onderzoeksfonds (BOF).

Austrian Fields of Science 2012

103025 Quantum mechanics
103015 Condensed matter

Access to Document

10.1103/PhysRevB.105.085130

https://arxiv.org/abs/2112.12757v2Licence: Other

Cite this

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title = "Mapping between Morita-equivalent string-net states with a constant depth quantum circuit",

abstract = "We construct a constant depth quantum circuit that maps between Morita-equivalent string-net models. Due to its constant depth and unitarity, the circuit cannot alter the topological order, which demonstrates that Morita-equivalent string nets are in the same phase. The circuit is constructed from an invertible bimodule category connecting the two input fusion categories of the relevant string-net models, acting as a generalized Fourier transform for fusion categories. The circuit not only acts on the ground state subspace but also acts unitarily on the full Hilbert space when supplemented with ancillas. ",

author = "Laurens Lootens and \{Vancraeynest-De Cuiper\}, Bram and Norbert Schuch and Frank Verstraete",

note = "Funding Information: We are grateful to Nick Bultinck for inspiring discussions and to Jacob Bridgeman for insightful comments on invertible bimodule categories and tube algebras. This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [Grant Agreements No. 647905 (QUTE) and No. 863476 (SEQUAM)], and the Research Foundation Flanders via Grants No. G087918N and No. G0E1820N. L.L. is supported by a Ph.D. fellowship from the Research Foundation Flanders (FWO). B.V.-D.C. is supported by a Ph.D. fellowship from Bijzonder Onderzoeksfonds (BOF). Publisher Copyright: {\textcopyright} 2022 American Physical Society. Copyright: Copyright 2022 Elsevier B.V., All rights reserved.",

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doi = "10.1103/PhysRevB.105.085130",

language = "English",

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AU - Vancraeynest-De Cuiper, Bram

AU - Schuch, Norbert

AU - Verstraete, Frank

N1 - Funding Information: We are grateful to Nick Bultinck for inspiring discussions and to Jacob Bridgeman for insightful comments on invertible bimodule categories and tube algebras. This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [Grant Agreements No. 647905 (QUTE) and No. 863476 (SEQUAM)], and the Research Foundation Flanders via Grants No. G087918N and No. G0E1820N. L.L. is supported by a Ph.D. fellowship from the Research Foundation Flanders (FWO). B.V.-D.C. is supported by a Ph.D. fellowship from Bijzonder Onderzoeksfonds (BOF). Publisher Copyright: © 2022 American Physical Society. Copyright: Copyright 2022 Elsevier B.V., All rights reserved.

PY - 2022/2/17

Y1 - 2022/2/17

N2 - We construct a constant depth quantum circuit that maps between Morita-equivalent string-net models. Due to its constant depth and unitarity, the circuit cannot alter the topological order, which demonstrates that Morita-equivalent string nets are in the same phase. The circuit is constructed from an invertible bimodule category connecting the two input fusion categories of the relevant string-net models, acting as a generalized Fourier transform for fusion categories. The circuit not only acts on the ground state subspace but also acts unitarily on the full Hilbert space when supplemented with ancillas.

AB - We construct a constant depth quantum circuit that maps between Morita-equivalent string-net models. Due to its constant depth and unitarity, the circuit cannot alter the topological order, which demonstrates that Morita-equivalent string nets are in the same phase. The circuit is constructed from an invertible bimodule category connecting the two input fusion categories of the relevant string-net models, acting as a generalized Fourier transform for fusion categories. The circuit not only acts on the ground state subspace but also acts unitarily on the full Hilbert space when supplemented with ancillas.

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Mapping between Morita-equivalent string-net states with a constant depth quantum circuit

Abstract

Funding

Austrian Fields of Science 2012

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Other files and links

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SEQUAM: Symmetries and Entanglement in Quantum Matter

Cite this

Mapping between Morita-equivalent string-net states with a constant depth quantum circuit

Abstract

Funding

Austrian Fields of Science 2012

Access to Document

Other files and links

Fingerprint

Projects

SEQUAM: Symmetries and Entanglement in Quantum Matter

Cite this