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

This article surveys quantum computational complexity, with a focus on three fundamental
notions: polynomial-time quantum computations, the efficient verification of quantum proofs …

We present a new methodology to efficiently realize recursive composition of succinct non-
interactive arguments of knowledge (SNARKs). Prior to this work, the only known …

The quantum random oracle model (QROM) has become the standard model in which to
prove the post-quantum security of random-oracle-based constructions. Unfortunately, none …

We show the following hold, unconditionally unless otherwise stated, relative to a random
oracle:—There are NP search problems solvable by quantum polynomial-time (QPT) …

This is a textbook about quantum walks and quantum search algorithms. The readers will
take advantage of the pedagogical aspects and learn the topics faster and make less effort …

The interest in post-quantum cryptography—classical systems that remain secure in the
presence of a quantum adversary—has generated elegant proposals for new cryptosystems …

We use quantum walks to construct a new quantum algorithm for element distinctness and
its generalization. For element distinctness (the problem of finding two equal items among N …

The key cryptographic protocols used to secure the internet and financial transactions of
today are all susceptible to attack by the development of a sufficiently large quantum …

In the near future, there will likely be special-purpose quantum computers with 40-50 high-
quality qubits. This paper lays general theoretical foundations for how to use such devices to …