Tag - Quantum computing

Ronald de Wolf: Quantum computing

31st January, 2022

The field of quantum computing studies computers based on quantum-mechanical effects such as superposition, interference, and entanglement. We will give an overview of this field, first describing in some detail what quantum computers are and then focusing on computational tasks where we know they could be much better (faster, safer, …) than classical computers, in particular in the areas of cryptography, optimization, and simulation of quantum systems. This talk is mostly from the perspective of theoretical computer science, but we will also briefly discuss the current state of the art in physically realizing such computers in the lab.

Ori Parzanchevski: Golden Gates, Ramanujan Complexes and Ramanujan Digraphs

31st January, 2017

Some thirty years ago, Lubotzky, Phillips and Sarnak used deep number-theoretic insights to construct the first Ramanujan graphs, as well as optimal pseudo-random generators for the rotation group SO(3). In the last decade their work has seen several developments: On the discrete side, in the study of Ramanujan complexes, which are finite simplicial complexes with the spectral behaviour of infinite buildings. On the continuous side, in the study of pseudo-random generators for U(n), motivated by the problem of constructing optimal gates for fault-tolerant quantum computation. Results on both the continuous and discrete sides draw on the study of Ramanujan digraphs, which seem to be of independent interest. Based on joint works with Eyal Lubetzky, Alex Lubotzky and Peter Sarnak.

Naser Talebizadeh Sardari: Discrete Log Problem with respect to the LPS generators on PGL_2

31st January, 2017

We discuss our p-adic version of the best known quantum compiling algorithm on a single qubit that is developed by Ross and Selinger. Two main applications of our algorithm are computing optimally the discrete log of diagonal matrices of PGL2(ℤ/qℤ) with respect to Lubotzky, Phillips and Sarnak generators and navigation problem for diagonal vertices of LPS Ramanujan graphs. My algorithm and Ross and Selinger's algorithm are conditional on assuming one can factor quickly, and a natural conjecture on the distribution of integers representable as a sum of two squares.