Details
| Original language | English |
|---|---|
| Title of host publication | 10th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2015 |
| Editors | Salman Beigi, Robert Konig |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| Pages | 48-63 |
| Number of pages | 16 |
| ISBN (electronic) | 9783939897965 |
| Publication status | Published - 1 Nov 2015 |
| Externally published | Yes |
| Event | 10th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2015 - Brussels, Belgium Duration: 20 May 2015 → 22 May 2015 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
|---|---|
| Volume | 44 |
| ISSN (Print) | 1868-8969 |
Abstract
One-way quantum computation was first invented using the cluster state. Since then graph states, the generalization of the cluster state, were investigated and understood when they would enable such a measurement-based approach for quantum computation. Are there any other family of states, i.e., states with different entanglement structures, that can also serve as the universal resource for quantum computation? Recent study shows that the Affleck-Kennedy-Lieb-Tasaki (AKLT) states also provide a useful source. Here, we show that the spin-2 state on the square lattice is a universal resource for measurement-based quantum computation. We employ a POVM on all sites that convert the local 5-level system to 2-level, and the post-POVM state is a graph state, whose graph is in general non-planar. We then follow with another round of measurement to recover the planarity of the graphs by thinning. The resultant typical graphs are shown to reside in the supercritical phase of percolation via Monte Carlo simulations and the associated graph states are universal, implying the AKLT state is also universal.
Keywords
- AKLT state, Graph state, Measurement-based quantum computation, Percolation
ASJC Scopus subject areas
- Computer Science(all)
- Software
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
10th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2015. ed. / Salman Beigi; Robert Konig. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2015. p. 48-63 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 44).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - The Spin-2 AKLT State on the Square Lattice is Universal for Measurement-based Quantum Computation
AU - Wei, Tzu Chieh
AU - Raussendorf, Robert
PY - 2015/11/1
Y1 - 2015/11/1
N2 - One-way quantum computation was first invented using the cluster state. Since then graph states, the generalization of the cluster state, were investigated and understood when they would enable such a measurement-based approach for quantum computation. Are there any other family of states, i.e., states with different entanglement structures, that can also serve as the universal resource for quantum computation? Recent study shows that the Affleck-Kennedy-Lieb-Tasaki (AKLT) states also provide a useful source. Here, we show that the spin-2 state on the square lattice is a universal resource for measurement-based quantum computation. We employ a POVM on all sites that convert the local 5-level system to 2-level, and the post-POVM state is a graph state, whose graph is in general non-planar. We then follow with another round of measurement to recover the planarity of the graphs by thinning. The resultant typical graphs are shown to reside in the supercritical phase of percolation via Monte Carlo simulations and the associated graph states are universal, implying the AKLT state is also universal.
AB - One-way quantum computation was first invented using the cluster state. Since then graph states, the generalization of the cluster state, were investigated and understood when they would enable such a measurement-based approach for quantum computation. Are there any other family of states, i.e., states with different entanglement structures, that can also serve as the universal resource for quantum computation? Recent study shows that the Affleck-Kennedy-Lieb-Tasaki (AKLT) states also provide a useful source. Here, we show that the spin-2 state on the square lattice is a universal resource for measurement-based quantum computation. We employ a POVM on all sites that convert the local 5-level system to 2-level, and the post-POVM state is a graph state, whose graph is in general non-planar. We then follow with another round of measurement to recover the planarity of the graphs by thinning. The resultant typical graphs are shown to reside in the supercritical phase of percolation via Monte Carlo simulations and the associated graph states are universal, implying the AKLT state is also universal.
KW - AKLT state
KW - Graph state
KW - Measurement-based quantum computation
KW - Percolation
UR - http://www.scopus.com/inward/record.url?scp=84959049954&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.TQC.2015.48
DO - 10.4230/LIPIcs.TQC.2015.48
M3 - Conference contribution
AN - SCOPUS:84959049954
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 48
EP - 63
BT - 10th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2015
A2 - Beigi, Salman
A2 - Konig, Robert
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 10th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2015
Y2 - 20 May 2015 through 22 May 2015
ER -