Set Reconstruction on the Hypercube

Local distributions and reconstruction of hypercube eigenfunctions

Decomposing the vertex set of a hypercube into isomorphic subgraphs

Let G be an induced subgraph of the hypercube Qk for some k. We show that if |G| is a power of 2 then, for sufficiciently large n, the vertex set of Qn can be partitioned into induced copies of G. This answers a question of Offner. In fact, we prove a stronger statement: if X is a subset of {0, 1} for some k and if |X | is a power of 2, then, for sufficiently large n, {0, 1} can be partitioned ...

Quantum Walks on the Hypercube

Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the n-dimensional hypercube, one in discrete time and one in continuous time. In both cases we show that the quantum walk mixes in (π/4)n steps, faster than the Θ...

Quantum Mechanics on the Hypercube

We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z2n). By construction this representation acts in a natural way on the coordinates of the non-commutative 2torus, T2 and thus is relevant for noncommutative field theories as well as theori...

Randomized Selection on the Hypercube

In this paper we present randomized algorithms for selection on the hypercube. We identify two variants of the hypercube namely, the sequential model and the parallel model. In the sequential model, any node at any time can handle only communication along a single incident edge, whereas in the parallel model a node can communicate along all its incident edges at the same time. We specify three ...