We give a comprehensive characterisation of the computational power of shallow quantum
circuits combined with classical computation. Specifically, for classes of search problems …

It is a long-standing open question in quantum complexity theory whether the definition of $
non-deterministic $ quantum computation requires quantum witnesses (QMA) or if classical …

Collision-resistant hashing, a fundamental primitive in modern cryptography, ensures that
there is no efficient way to find distinct inputs that produce the same hash value. This …

We study tradeoffs between quantum and classical queries for hybrid algorithms that have
black-box access to a random oracle. Although there are several established techniques for …

Recently, Chia, Chung and Lai (STOC 2020) and Coudron and Menda (STOC 2020) have
shown that there exists an oracle $\mathcal {O} $ such that $\mathsf {BQP}^\mathcal {O}\neq …

We study how the choices made when designing an oracle affect the complexity of quantum
property testing problems defined relative to this oracle. We encode a regular graph of even …

The problem of phase estimation (or amplitude estimation) admits a quadratic quantum
speedup. Wang, Higgott, and Brierley [Wang, Higgott, and Brierley, Phys. Rev. Lett. 122 …

Low-depth quantum circuits are a well-suited model for near-term quantum devices, given
short coherence times and noisy gate operations, making it pivotal to examine their …