Simulating quantum circuits with sparse output distributions

M Schwarz, MV Nest - arxiv preprint arxiv:1310.6749, 2013 - arxiv.org
We show that several quantum circuit families can be simulated efficiently classically if it is
promised that their output distribution is approximately sparse ie the distribution is close to …

Abelian hypergroups and quantum computation

J Bermejo-Vega, KC Zatloukal - arxiv preprint arxiv:1509.05806, 2015 - arxiv.org
Motivated by a connection, described here for the first time, between the hidden normal
subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions …

Normalizer circuits and quantum computation

J Bermejo-Vega - arxiv preprint arxiv:1611.09274, 2016 - arxiv.org
(Abridged abstract.) In this thesis we introduce new models of quantum computation to study
the emergence of quantum speed-up in quantum computer algorithms. Our first contribution …

The computational power of normalizer circuits over black-box groups

J Bermejo-Vega, CYY Lin, MV Nest - arxiv preprint arxiv:1409.4800, 2014 - arxiv.org
This work presents a precise connection between Clifford circuits, Shor's factoring algorithm
and several other famous quantum algorithms with exponential quantum speed-ups for …

[PDF][PDF] On the Computational Power of Quantum Computers

DIM Schwarz - phaidra.univie.ac.at
In this thesis we make progress in our understanding of the computational power made
available by quantum computers. While answering this question in full generality in the …