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Quantum circuit complexity of one-dimensional topological phases

Huang, Yichen and Chen, Xie (2015) Quantum circuit complexity of one-dimensional topological phases. Physical Review B, 91 (19). Art. No. 195143. ISSN 1098-0121. doi:10.1103/PhysRevB.91.195143.

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Topological quantum states cannot be created from product states with local quantum circuits of constant depth and are in this sense more entangled than topologically trivial states, but how entangled are they? Here we quantify the entanglement in one-dimensional topological states by showing that local quantum circuits of linear depth are necessary to generate them from product states. We establish this linear lower bound for both bosonic and fermionic one-dimensional topological phases and use symmetric circuits for phases with symmetry. We also show that the linear lower bound can be saturated by explicitly constructing circuits generating these topological states. The same results hold for local quantum circuits connecting topological states in different phases.

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Additional Information:© 2015 American Physical Society. Received 5 August 2014; revised manuscript received 8 April 2015; published 26 May 2015. We would like to thank Isaac H. Kim, Spyridon Michalakis, Joel E. Moore, John Preskill, Frank Pollmann, and Ashvin Vishwanath for helpful discussions. In particular, I.H.K. pointed out that a variant of Proposition 2 can be proved using his entropic topological invariant [32]. This work was supported by the Miller Institute for Basic Research in Science at the University of California, Berkeley, the Caltech Institute for Quantum Information and Matter, the Walter Burke Institute for Theoretical Physics (X.C.), and DARPA OLE (Y.H.).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
University of California, BerkeleyUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Walter Burke Institute for Theoretical PhysicsUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Issue or Number:19
Classification Code:PACS: 03.67.Ac, 71.10.Fd, 75.10.Pq, 89.70.Eg
Record Number:CaltechAUTHORS:20150618-130311270
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58346
Deposited By: Tony Diaz
Deposited On:19 Jun 2015 00:57
Last Modified:10 Nov 2021 22:03

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