0000000000822016
AUTHOR
Janis Iraids
Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection
We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model. In GRAPH-COLLISION we are given free access to a graph $(V,E)$ and access to a function $f:V\rightarrow \{0,1\}$ as a black box. We are asked to determine if there exist $(u,v) \in E$, such that $f(u)=f(v)=1$. In TRIANGLE we have a black box access to an adjacency matrix of a graph and we have to determine if the graph contains a triangle. For both of these problems the known lower bounds are trivial ($\Omega(\sqrt{n})$ and $\Omega(n)$, respectively) and there is no known matching upper …
Saying Hello World with MOLA - A Solution to the TTC 2011 Instructive Case
This paper describes the solution of Hello World transformations in MOLA transformation language. Transformations implementing the task are relatively straightforward and easily inferable from the task specification. The required additional steps related to model import and export are also described.
Optimal one-shot quantum algorithm for EQUALITY and AND
We study the computation complexity of Boolean functions in the quantum black box model. In this model our task is to compute a function $f:\{0,1\}\to\{0,1\}$ on an input $x\in\{0,1\}^n$ that can be accessed by querying the black box. Quantum algorithms are inherently probabilistic; we are interested in the lowest possible probability that the algorithm outputs incorrect answer (the error probability) for a fixed number of queries. We show that the lowest possible error probability for $AND_n$ and $EQUALITY_{n+1}$ is $1/2-n/(n^2+1)$.
Provable Advantage for Quantum Strategies in Random Symmetric XOR Games
Non-local games are widely studied as a model to investigate the properties of quantum mechanics as opposed to classical mechanics. In this paper, we consider a subset of non-local games: symmetric XOR games of $n$ players with 0-1 valued questions. For this class of games, each player receives an input bit and responds with an output bit without communicating to the other players. The winning condition only depends on XOR of output bits and is constant w.r.t. permutation of players. We prove that for almost any $n$-player symmetric XOR game the entangled value of the game is $\Theta (\frac{\sqrt{\ln{n}}}{n^{1/4}})$ adapting an old result by Salem and Zygmund on the asymptotics of random tr…