Twodimensional AffleckKennedyLiebTasaki state on the honeycomb lattice is a universal resource for quantum computation
Abstract
Universal quantum computation can be achieved by simply performing singlequbit measurements on a highly entangled resource state. Resource states can arise from ground states of carefully designed twobody interacting Hamiltonians. This opens up an appealing possibility of creating them by cooling. The family of AffleckKennedyLiebTasaki (AKLT) states are the ground states of particularly simple Hamiltonians with high symmetry, and their potential use in quantum computation gives rise to a new research direction. Expanding on our prior work [T.C. Wei, I. Affleck, and R. Raussendorf, Phys. Rev. Lett.PRLTAO0031900710.1103/PhysRevLett.106.070501 106, 070501 (2011)], we give a detailed analysis to explain why the spin3/2 AKLT state on a twodimensional honeycomb lattice is a universal resource for measurementbased quantum computation. Along the way, we also provide an alternative proof that the 1D spin1 AKLT state can be used to simulate arbitrary onequbit unitary gates. Moreover, we connect the quantum computational universality of 2D random graph states to their percolation property and show that these states whose graphs are in the supercritical (i.e., percolated) phase are also universal resources for measurementbased quantum computation.
 Publication:

Physical Review A
 Pub Date:
 September 2012
 DOI:
 10.1103/PhysRevA.86.032328
 Bibcode:
 2012PhRvA..86c2328W
 Keywords:

 03.67.Lx;
 03.67.Ac;
 64.60.ah;
 75.10.Jm;
 Quantum computation;
 Quantum algorithms protocols and simulations;
 Percolation;
 Quantized spin models