0000000000591303
AUTHOR
Gatis Midrijanis
showing 3 related works from this author
A Polynomial Quantum Query Lower Bound for the Set Equality Problem
2004
The set equality problem is to tell whether two sets A and B are equal or disjoint under the promise that one of these is the case. This problem is related to the Graph Isomorphism problem. It was an open problem to find any ω(1) query lower bound when sets A and B are given by quantum oracles. We will show that any error-bounded quantum query algorithm that solves the set equality problem must evaluate oracles \(\Omega(\sqrt[5]{\frac{n}{\ln n}})\) times, where n=|A|=|B|.
The Complexity of Probabilistic versus Quantum Finite Automata
2002
We present a language Ln which is recognizable by a probabilistic finite automaton (PFA) with probability 1 - ? for all ? > 0 with O(log2 n) states, with a deterministic finite automaton (DFA) with O(n) states, but a quantum finite automaton (QFA) needs at least 2?(n/log n) states.
Quantum lower bounds for the set equality problems
2003
The set equality problem is to decide whether two sets $A$ and $B$ are equal or disjoint, under the promise that one of these is the case. Some other problems, like the Graph Isomorphism problem, is solvable by reduction to the set quality problem. It was an open problem to find any $w(1)$ query lower bound when sets $A$ and $B$ are given by quantum oracles with functions $a$ and $b$. We will prove $\Omega(\frac{n^{1/3}}{\log^{1/3} n})$ lower bound for the set equality problem when the set of the preimages are very small for every element in $A$ and $B$.