Affiliation:
1. QuOne Lab, Phanous Research and Innovation Centre, Tehran, Iran
Abstract
It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity
O(
√
GT
where
T
is the query complexity of the classical algorithm (depth of the decision tree) and
G
is the maximum number of wrong answers by the guessing algorithm [
3
,
14
]. In this article, we show that, given some constraints on the classical algorithms, this quantum algorithm can be implemented in time
Õ
(√
GT
). Our algorithm is based on non-binary span programs and their efficient implementation. We conclude that various graph-theoretic problems including bipartiteness, cycle detection, and topological sort can be solved in time
O(n
3/2
log
2
n
) and with
O(n
3/2
) quantum queries. Moreover, finding a maximal matching can be solved with
O(n
3/2
) quantum queries in time
O(n
3/2
log
2
n
), and maximum bipartite matching can be solved in time
O(n
2
log
2
n
).
Publisher
Association for Computing Machinery (ACM)