Universal quantum computing using (Zd)3 symmetry-protected topologically ordered states

Yanzhu Chen, Abhishodh Prakash, and Tzu-Chieh Wei
Phys. Rev. A 97, 022305 – Published 5 February 2018

Abstract

Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically nontrivial, short-ranged entangled states are promising candidates for such a resource. Miller and Miyake [npj Quantum Inf. 2, 16036 (2016)] recently constructed a particular Z2×Z2×Z2 symmetry-protected topological state on the Union Jack lattice and established its quantum-computational universality. However, they suggested that the same construction on the triangular lattice might not lead to a universal resource. Instead of qubits, we generalize the construction to qudits and show that the resulting (d1) qudit nontrivial Zd×Zd×Zd symmetry-protected topological states are universal on the triangular lattice, for d being a prime number greater than 2. The same construction also holds for other 3-colorable lattices, including the Union Jack lattice.

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  • Received 7 November 2017

DOI:https://doi.org/10.1103/PhysRevA.97.022305

©2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Yanzhu Chen, Abhishodh Prakash, and Tzu-Chieh Wei

  • C. N. Yang Institute for Theoretical Physics and Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York 11794-3840, USA

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Issue

Vol. 97, Iss. 2 — February 2018

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