no code implementations • 18 Aug 2023 • João F. Doriguello, Alessandro Luongo, Ewin Tang
The time complexity is $O\big(\frac{k^{2}}{\varepsilon^2}(\sqrt{k}d + \log(Nd))\big)$ and maintains the polylogarithmic dependence on $N$ while improving the dependence on most of the other parameters.
1 code implementation • 19 Apr 2021 • Armando Bellante, Alessandro Luongo, Stefano Zanero
This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in machine learning.
no code implementations • 12 Nov 2020 • Alessandro Luongo, Changpeng Shao
We propose and analyze new quantum algorithms for estimating the most common spectral sums of symmetric positive definite (SPD) matrices.
no code implementations • 19 Aug 2019 • Iordanis Kerenidis, Alessandro Luongo, Anupam Prakash
In this work we define and use a quantum version of EM to fit a Gaussian Mixture Model.
2 code implementations • NeurIPS 2019 • Iordanis Kerenidis, Jonas Landman, Alessandro Luongo, Anupam Prakash
For a natural notion of well-clusterable datasets, the running time becomes $\widetilde{O}\left( k^2 d \frac{\eta^{2. 5}}{\delta^3} + k^{2. 5} \frac{\eta^2}{\delta^3} \right)$ per iteration, which is linear in the number of features $d$, and polynomial in the rank $k$, the maximum square norm $\eta$ and the error parameter $\delta$.
no code implementations • 22 May 2018 • Iordanis Kerenidis, Alessandro Luongo
We simulate the quantum classifier (including errors) and show that it can provide classification of the MNIST handwritten digit dataset, a widely used dataset for benchmarking classification algorithms, with $98. 5\%$ accuracy, similar to the classical case.