An indispensable part of our personal and working lives, computing has also become
essential to industries and governments. Steady improvements in computer hardware have …

Algorithms in varied fields use the idea of maintaining a distribution over a certain set and
use the multiplicative update rule to iteratively change these weights. Their analyses are …

Semidefinite programs (SDPs) are a fundamental class of optimization problems with
important recent applications in approximation algorithms, quantum complexity, robust …

Recent advances in quantum computers are demonstrating the ability to solve problems at a
scale beyond brute force classical simulation. As such, a widespread interest in quantum …

We give two quantum algorithms for solving semidefinite programs (SDPs) providing
quantum speed-ups. We consider SDP instances with $ m $ constraint matrices, each of …

Semidefinite programming is a fundamental tool in optimization and theoretical computer
science. It has been extensively used as a black-box for solving many problems, such as …

In the classical model of computation, it is well established that one-way functions (OWF) are
minimal for computational cryptography: They are essential for almost any cryptographic …

This paper introduces a new robust interior point method analysis for semidefinite
programming (SDP). This new robust analysis can be combined with either logarithmic …

From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

These are lecture notes from a weeklong course in quantum complexity theory taught at the
Bellairs Research Institute in Barbados, February 21-25, 2016. The focus is quantum circuit …