A Caltech Library Service

Pauli Stabilizer Models of Twisted Quantum Doubles

Ellison, Tyler D. and Chen, Yu-An and Dua, Arpit and Shirley, Wilbur and Tantivasadakarn, Nathanan and Williamson, Dominic J. (2022) Pauli Stabilizer Models of Twisted Quantum Doubles. PRX Quantum, 3 (1). Art. No. 010353. ISSN 2691-3399. doi:10.1103/prxquantum.3.010353.

[img] PDF - Published Version
Creative Commons Attribution.

[img] PDF - Accepted Version
See Usage Policy.


Use this Persistent URL to link to this item:


We construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z₄ toric code, where the condensation is implemented at the level of the ground states by two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground-state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes—in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type-I and type-II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain 1-form symmetries of the TQD stabilizer models.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Ellison, Tyler D.0000-0002-1740-6889
Chen, Yu-An0000-0002-8810-9355
Dua, Arpit0000-0001-6348-4135
Tantivasadakarn, Nathanan0000-0001-5295-2124
Williamson, Dominic J.0000-0002-8029-6408
Additional Information:© 2022 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 31 December 2021; accepted 9 March 2022; published 30 March 2022. T.D.E. thanks Lukasz Fidkowski and Meng Cheng for valuable insights on the classification of Abelian topological orders. T.D.E. would also like to acknowledge Timothy H. Hsieh and Zi-Wen Liu for inspirational discussions about the double semion phase. A.D. thanks Bowen Yang for useful discussions on related problems. This work is supported by the JQI fellowship at the University of Maryland (Y.-A.C.), the Simons Foundation through the collaboration on Ultra-Quantum Matter (651438, A.D.; 651444, W.S.), NSERC (N.T.), the It from Qubit collaboration (D.J.W.), and by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center (PHY-1733907, A.D., W.S.).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
University of MarylandUNSPECIFIED
Simons Foundation651438
Simons Foundation651444
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20220427-804972400
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114493
Deposited By: Tony Diaz
Deposited On:27 Apr 2022 23:30
Last Modified:27 Apr 2022 23:30

Repository Staff Only: item control page