Quantum computational universality of Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
Abstract
Universal quantum computation can be achieved by simply performing single-spin measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki (AKLT) states has recently been explored; for example, the spin-1 AKLT chain can be used to simulate single-qubit gate operations on a single qubit, and the spin-3/2 two-dimensional AKLT state on the honeycomb lattice can be used as a universal resource. However, it is unclear whether such universality is a coincidence for the specific state or a shared feature in all two-dimensional AKLT states. Here we consider the family of spin-3/2 AKLT states on various trivalent Archimedean lattices and show that in addition to the honeycomb lattice, the spin-3/2 AKLT states on the square octagon (4,82) and the “cross” (4,6,12) lattices are also universal resource, whereas the AKLT state on the “star” (3,122) lattice is likely not due to geometric frustration.
- Publication:
-
Physical Review A
- Pub Date:
- December 2013
- DOI:
- 10.1103/PhysRevA.88.062307
- arXiv:
- arXiv:1306.1420
- Bibcode:
- 2013PhRvA..88f2307W
- Keywords:
-
- 03.67.Lx;
- 03.67.Ac;
- 64.60.ah;
- 75.10.Jm;
- Quantum computation;
- Quantum algorithms protocols and simulations;
- Percolation;
- Quantized spin models;
- Quantum Physics;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 10 pages, 11 figures, title changed, close to published version