Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry

Physical Review Letters
Jacob Miller, Akimasa Miyake

Abstract

An emerging insight is that ground states of symmetry-protected topological orders (SPTOs) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the invariance under 3-colorable symmetries of a lattice, we prove that every renormalization fixed-point state of 2D (Z_{2})^{m} SPTO with fractional symmetry can be utilized for universal quantum computation using only Pauli measurements, as long as it belongs to a nontrivial 2D SPTO phase. Our infinite family of fixed-point states may serve as a base model to demonstrate the idea of a "quantum computational phase" of matter, whose states share universal computational complexity ubiquitously.

References

Feb 15, 2001·Physical Review Letters·H J Briegel, R Raussendorf
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Dec 13, 2006·Physical Review Letters·Maarten Van den NestHans J Briegel
Aug 7, 2007·Physical Review Letters·D Gross, J Eisert
Sep 4, 2008·Physical Review Letters·Gavin K Brennen, Akimasa Miyake
Aug 8, 2009·Physical Review Letters·Andrew C Doherty, Stephen D Bartlett
Sep 28, 2010·Physical Review Letters·Stephen D BartlettJoseph M Renes
Sep 28, 2010·Physical Review Letters·Xie ChenBei Zeng
Sep 28, 2010·Physical Review Letters·Akimasa Miyake
Mar 17, 2011·Physical Review Letters·Tzu-Chieh WeiRobert Raussendorf
Sep 26, 2012·Physical Review Letters·Dominic V ElseAndrew C Doherty
Mar 22, 2013·Physical Review Letters·Keisuke FujiiMio Murao
Apr 11, 2015·Physical Review Letters·Jacob Miller, Akimasa Miyake
Jul 22, 2017·Physical Review Letters·David T StephenRobert Raussendorf

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Citations

Apr 2, 2019·Physical Review Letters·Robert RaussendorfHendrik Poulsen Nautrup

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