TY - GEN
T1 - Super-polynomial quantum speed-ups for boolean evaluation trees with hidden structure
AU - Zhan, Bohua
AU - Kimmel, Shelby
AU - Hassidim, Avinatan
N1 - Place of conference:USA
PY - 2012
Y1 - 2012
N2 - We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth n tree using O(n2+logω) queries, where ω is independent of n and depends only on the type of subformulas within the tree. We also prove a classical lower bound of nΩ(log log n) queries, thus showing a (small) super-polynomial speed-up.
AB - We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth n tree using O(n2+logω) queries, where ω is independent of n and depends only on the type of subformulas within the tree. We also prove a classical lower bound of nΩ(log log n) queries, thus showing a (small) super-polynomial speed-up.
KW - NAND tree
KW - span programs
KW - super-polynomial quantum speed-up
UR - https://www.scopus.com/pages/publications/84856479735
U2 - 10.1145/2090236.2090258
DO - 10.1145/2090236.2090258
M3 - Conference contribution
SN - 9781450311151
T3 - ITCS 2012 - Innovations in Theoretical Computer Science Conference
SP - 249
EP - 265
BT - ITCS 2012 - Innovations in Theoretical Computer Science Conference
T2 - 3rd Conference on Innovations in Theoretical Computer Science, ITCS 2012
Y2 - 8 January 2012 through 10 January 2012
ER -