Details
| Original language | English |
|---|---|
| Article number | 012310 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 92 |
| Issue number | 1 |
| Publication status | Published - 9 Jul 2015 |
| Externally published | Yes |
Abstract
We demonstrate that the spin-2 Affleck-Kennedy-Lieb-Tasaki (AKLT) state on a square lattice is a universal resource for measurement-based quantum computation. Our proof is done by locally converting the AKLT to two-dimensional random planar graph states and by certifying that with a high probability the resulting random graphs are in the supercritical phase of percolation using Monte Carlo simulations. One key enabling point is the exact weight formula that we derive for arbitrary measurement outcomes according to a spin-2 positive operator-valued measure on all spins. We also argue that the spin-2 AKLT state on a three-dimensional diamond lattice is a universal resource, the advantage of which would be the possibility of implementing fault-tolerant quantum computation with topological protection. In addition, as we deform the AKLT Hamiltonian, there is a finite region in which the ground state can still support a universal resource before making a transition in its quantum computational power.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
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In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 92, No. 1, 012310, 09.07.2015.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
AU - Wei, Tzu Chieh
AU - Raussendorf, Robert
PY - 2015/7/9
Y1 - 2015/7/9
N2 - We demonstrate that the spin-2 Affleck-Kennedy-Lieb-Tasaki (AKLT) state on a square lattice is a universal resource for measurement-based quantum computation. Our proof is done by locally converting the AKLT to two-dimensional random planar graph states and by certifying that with a high probability the resulting random graphs are in the supercritical phase of percolation using Monte Carlo simulations. One key enabling point is the exact weight formula that we derive for arbitrary measurement outcomes according to a spin-2 positive operator-valued measure on all spins. We also argue that the spin-2 AKLT state on a three-dimensional diamond lattice is a universal resource, the advantage of which would be the possibility of implementing fault-tolerant quantum computation with topological protection. In addition, as we deform the AKLT Hamiltonian, there is a finite region in which the ground state can still support a universal resource before making a transition in its quantum computational power.
AB - We demonstrate that the spin-2 Affleck-Kennedy-Lieb-Tasaki (AKLT) state on a square lattice is a universal resource for measurement-based quantum computation. Our proof is done by locally converting the AKLT to two-dimensional random planar graph states and by certifying that with a high probability the resulting random graphs are in the supercritical phase of percolation using Monte Carlo simulations. One key enabling point is the exact weight formula that we derive for arbitrary measurement outcomes according to a spin-2 positive operator-valued measure on all spins. We also argue that the spin-2 AKLT state on a three-dimensional diamond lattice is a universal resource, the advantage of which would be the possibility of implementing fault-tolerant quantum computation with topological protection. In addition, as we deform the AKLT Hamiltonian, there is a finite region in which the ground state can still support a universal resource before making a transition in its quantum computational power.
UR - http://www.scopus.com/inward/record.url?scp=84936972624&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.92.012310
DO - 10.1103/PhysRevA.92.012310
M3 - Article
AN - SCOPUS:84936972624
VL - 92
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 1
M1 - 012310
ER -