2014/10/31 by Abhishodh Prakash, Tzu-Chieh Wei · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Combinatorics #Computation #Ground state #Hamiltonian (control theory) #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum computer #Quantum many-body systems #Quantum mechanics #Qubit #Rotational symmetry #Symmetry operation #Theoretical physics #Topology (electrical circuits) #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physreva.92.022310
published as Phys. Rev. A 92, 022310 (2015) · 16 pages, 1 figure, revised version accepted in PRA
arxiv created 2015/07/20 · openalex publication_date 2015/08/06 · arxiv updated 2015/09/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The program of classifying symmetry-protected topological (SPT) phases in one dimension has been recently completed and has opened the doors to studying closely the properties of systems belonging to these phases. It was recently found that being able to constrain the form of ground states of SPT order based on symmetry properties also makes it possible to explore novel resource states for processing of quantum information. In this paper, we generalize the consideration of Else et al. [Phys. Rev. Lett. 108, 240505 (2012)], where it was shown that the ground-state form of spin-1 chains protected by ℤ2\ifmmode×\else\texttimes\fiℤ2 symmetry supports perfect operation of the identity gate, important also for long-distance transmission of quantum information. We develop a formalism to constrain the ground-state form of SPT phases protected by any arbitrary finite symmetry group and use it to examine examples of ground states of SPT phases protected by various finite groups for similar gate protections. We construct a particular Hamiltonian invariant under A4 symmetry transformation, which is one of the groups that allows protected identity operation, and examine its ground states. We find that there is an extended region where the ground state is the AKLT state, which not only supports the identity gate but also arbitrary single-qubit gates.