Universal measurement-based quantum computation in two-dimensional SPT phases

Abstract

Recent progress in characterization for gapped quantum phases has also triggered the search of universal resource for quantum computation in symmetric gapped phases. Prior works in one dimension suggest that it is a feature more common than previously thought that nontrivial 1D symmetry-protected topological (SPT) phases provide quantum computational power characterized by the algebraic structure defining these phases. Progress in two and higher dimensions so far has been limited to special fixed points in SPT phases. Here we provide two families of 2D $Z_2$ symmetric wave functions such that there exists a finite region of the parameter in the SPT phases that supports universal quantum computation. The quantum computational power loses its universality at the boundary between the SPT and symmetry-breaking phases.

13 pages, 9 figures

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum algorithm for solving linear systems of equations
• Universal computation by quantum walk
• Exponential algorithmic speedup by quantum walk
• Valence Bond Solids for Quantum Computation
• Novel schemes for measurement-based quantum computation
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Quantum computational capability of a 2D valence bond solid phase
• Classical simulation versus universality in measurement based quantum computation
• Fundamentals of universality in one-way quantum computation
• Computation by measurements: a unifying picture
• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• Quantum computation by local measurement