Measurement-Based Quantum Computation in Symmetry-Enriched Topological Phases
Creators
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1.
Leibniz University Hannover
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2.
University of British Columbia
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3.
Rice University
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4.
National University of Singapore
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University of Colorado Boulder
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6.
California Institute of Technology
Abstract
We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation (MBQC). This is possible due to a new framework for analyzing the computational properties of phases of matter that is more general than previous constructions, which have been limited to short-range entangled phases in one dimension. We show that ground states of the toric code in an anisotropic magnetic field yield a natural, albeit noncomputationally universal, application of our framework. We then present a new model with topological order the ground states of which are universal resources for MBQC. Both topological models are enriched by subsystem symmetries and these symmetries protect their computational power. Our framework greatly expands the range of physical models that can be analyzed from the computational perspective.
Copyright and License
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.
Acknowledgement
We thank Arnab Adhikary, Ehud Altman, Michael Knap, Tobias J. Osborne, and Frank Pollmann for helpful discussions. P.H. is funded by the National Science and Engineering Research Council of Canada (NSERC). This work was done in part while V.B.B. was visiting the Simons Institute for the Theory of Computing, supported by U.S. Department of Energy (DOE) Quantum Systems Accelerator (QSA) Grant No. #FP00010905. Y.J. acknowledges funding by the Ministry of Science and Culture of Lower Saxony through Quantum Valley Lower Saxony Q1 (QVLS-Q1). D.T.S. acknowledges support from the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (Grant No. 651440). R.R. is funded by the Humboldt Foundation.
Data Availability
The data that support the findings of this paper are openly available [72].
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Additional details
Additional titles
- Alternative title
- Duality between string and computational order in symmetry-enriched topological phases
Related works
- Is new version of
- Discussion Paper: arXiv:2410.02716 (arXiv)
- Is supplemented by
- Dataset: 10.5281/zenodo.17175550 (DOI)
Funding
- Natural Sciences and Engineering Research Council
- United States Department of Energy
- FP00010905
- Ministry of Science and Culture of Lower Saxony
- Simons Foundation
- 651440
- Alexander von Humboldt Foundation
Dates
- Accepted
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2025-08-13