Quantum computers can execute algorithms that dramatically outperform classical
computation. As the best-known example, Shor discovered an efficient quantum algorithm …

This concise, accessible text provides a thorough introduction to quantum computing-an
exciting emergent field at the interface of the computer, engineering, mathematical and …

This article surveys the state of the art in quantum computer algorithms, including both black-
box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so …

A thorough exposition of quantum computing and the underlying concepts of quantum
physics, with explanations of the relevant mathematics and numerous examples. The …

A bstract In this paper we discuss quantum computational restrictions on the types of thought
experiments recently used by Almheiri, Marolf, Polchinski, and Sully to argue against the …

Cryptographic group actions are a relaxation of standard cryptographic groups that have
less structure. This lack of structure allows them to be plausibly quantum resistant despite …

In recent years, rapid developments of quantum computer are witnessed in both the
hardware and the algorithm domains, making it necessary to have an updated review of …

Quantum Fourier transformations are an essential component of many quantum algorithms,
from prime factoring to quantum simulation. While the standard abelian QFT is well-studied …

This is a set of lecture notes on quantum algorithms. It is primarily intended for graduate
students who have already taken an introductory course on quantum information. Such a …

It has been known for some time that graph isomorphism reduces to the hidden subgroup
problem (HSP). What is more, most exponential speedups in quantum computation are …