6533b81ffe1ef96bd1278426
RESEARCH PRODUCT
A Polynomial Quantum Query Lower Bound for the Set Equality Problem
Gatis Midrijanissubject
Discrete mathematicsPolynomial (hyperelastic model)CombinatoricsOpen problemGraph isomorphism problemTheoryofComputation_GENERALCollision problemQuantum algorithmDisjoint setsIsomorphismUpper and lower boundsMathematicsdescription
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|.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-01-01 |