Quantum Algorithms - An Overview of Techniques

Explore quantum algorithms in this comprehensive lecture from the Quantum Wave in Computing Boot Camp. Delve into key techniques including Discrete and Quantum Fourier Transform, the Deutsch-Jozsa and Bernstein-Vazirani algorithms, and Jordan's quantum algorithm for gradients. Examine generalizations and applications, including a simpler algorithm for graph isomorphism and approaches to approximating the Jones polynomial. Investigate Hamiltonian simulation techniques, ground state preparation, and continuous-time quantum walks. Gain insights into the exponential speedup potential of quantum algorithms through this in-depth overview presented by András Gilyén from Caltech.

Intro
Outline
Discrete & Quantum Fourier Transform (QFT)
The Deutsch-Jozsa algorithm (1992)
The Bernstein-Vazirani algorithm (1992)
Jordan's quantum algorithm for gradients (2004)
Generalizations and applications of Jordan's algorithm
The non-Abelian HSP
A simpler algorithm for graph isomorphism
Towards approximating the Jones polynomial
(Dynamical) Hamiltonian simulation
Product formula approach (Lloyd 1996)
Ground state preparation of frustration-free Hamiltonian
Continuous-time quantum / random walks
Exponential speedup by a quantum walk