Yaoyun Shi

We initiate the study of quantifying the quantumness of

a quantum circuit by the number of gates that do not preserve

the computational basis, as a means to understand the nature

of quantum algorithmic speedups.

Intuitively, a reduction in the quantumness requires

an increase in the amount of classical computation, ...
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Aran Nayebi, Scott Aaronson, Aleksandrs Belovs, Luca Trevisan

Given a random permutation $f: [N] \to [N]$ as a black box and $y \in [N]$, we want to output $x = f^{-1}(y)$. Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on the permutation but \emph{not} on ... more >>>

Paul Beame, Niels Kornerup

We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra problems---including matrix-vector product, matrix inversion, matrix multiplication and powering---existing ... more >>>