Physics – Quantum Physics
Scientific paper
2006-08-07
Phys. Rev. A 75, 012337 (2007)
Physics
Quantum Physics
16 pages, 4 figures
Scientific paper
10.1103/PhysRevA.75.012337
We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidt--rank width, a measure recently introduced to assess universality of resource states, plays a crucial role in also this context. We relate Schmidt--rank width to the optimal description of states in terms of tree tensor networks and show that an efficient classical simulation of measurement based quantum computation is possible for all states with logarithmically bounded Schmidt--rank width (with respect to the system size). For graph states where the Schmidt--rank width scales in this way, we efficiently construct the optimal tree tensor network descriptions, and provide several examples. We highlight parallels in the efficient description of complex systems in quantum information theory and graph theory.
Briegel Hans J.
den Nest Maarten Van
Dür Wolfgang
Vidal German
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