Quantum computational complexity

J Watrous - arxiv preprint arxiv:0804.3401, 2008 - arxiv.org
This article surveys quantum computational complexity, with a focus on three fundamental
notions: polynomial-time quantum computations, the efficient verification of quantum proofs …

Open problems related to quantum query complexity

S Aaronson - ACM Transactions on Quantum Computing, 2021 - dl.acm.org
I offer a case that quantum query complexity still has loads of enticing and fundamental open
problems—from relativized QMA versus QCMA and BQP versus IP, to time/space tradeoffs …

A survey of quantum property testing

A Montanaro, R de Wolf - arxiv preprint arxiv:1310.2035, 2013 - arxiv.org
The area of property testing tries to design algorithms that can efficiently handle very large
amounts of data: given a large object that either has a certain property or is somehow" far" …

Guest column: the quantum PCP conjecture

D Aharonov, I Arad, T Vidick - Acm sigact news, 2013 - dl.acm.org
The classical PCP theorem is arguably the most important achievement of classical
complexity theory in the past quarter century. In recent years, researchers in quantum …

Faithful squashed entanglement

FGSL Brandao, M Christandl, J Yard - Communications in Mathematical …, 2011 - Springer
Squashed entanglement is a measure for the entanglement of bipartite quantum states. In
this paper we present a lower bound for squashed entanglement in terms of a distance to …

A birthday repetition theorem and complexity of approximating dense CSPs

P Manurangsi, P Raghavendra - arxiv preprint arxiv:1607.02986, 2016 - arxiv.org
A $(k\times l) $-birthday repetition $\mathcal {G}^{k\times l} $ of a two-prover game $\mathcal
{G} $ is a game in which the two provers are sent random sets of questions from $\mathcal …

Testing product states, quantum Merlin-Arthur games and tensor optimization

AW Harrow, A Montanaro - Journal of the ACM (JACM), 2013 - dl.acm.org
We give a test that can distinguish efficiently between product states of n quantum systems
and states that are far from product. If applied to a state| ψ∟ whose maximum overlap with a …

Distillable entanglement under dually non-entangling operations

L Lami, B Regula - Nature Communications, 2024 - nature.com
Computing the exact rate at which entanglement can be distilled from noisy quantum states
is one of the longest-standing questions in quantum information. We give an exact solution …

Quantum proofs

T Vidick, J Watrous - Foundations and Trends® in Theoretical …, 2016 - nowpublishers.com
Quantum information and computation provide a fascinating twist on the notion of proofs in
computational complexity theory. For instance, one may consider a quantum computational …

The power of unentangled quantum proofs with non-negative amplitudes

FG Jeronimo, P Wu - Proceedings of the 55th Annual ACM Symposium …, 2023 - dl.acm.org
Quantum entanglement is a fundamental property of quantum mechanics and it serves as a
basic resource in quantum computation and information. Despite its importance, the power …