62 citations · 281 across the 27 of their papers we have counts for
5 papers · 1 filter
Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance
Dong An, Noah Linden, Jin-Peng Liu +3
Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly…
Quantum algorithms for learning a hidden graph and beyond
Ashley Montanaro, Changpeng Shao
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle re…
Quantum algorithms for spectral sums
Alessandro Luongo, Changpeng Shao
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix , for a function , is defined as $…
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer
Changpeng Shao, Jin-Peng Liu
Many eigenvalue problems arising in practice are often of the generalized form $A\x=λB\x$. One particularly important case is symmetric, namely are Hermitian and is posi…
Quantum vs. classical algorithms for solving the heat equation
Noah Linden, Ashley Montanaro, Changpeng Shao
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equat…