233 citations · 531 across the 32 of their papers we have counts for
6 papers · 1 filter
Quantum algorithm for nonlinear differential equations
Seth Lloyd, Giacomo De Palma, Can Gokler +5
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we pres…
Quantum advantage for differential equation analysis
Bobak T. Kiani, Giacomo De Palma, Dirk Englund +3
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also…
Quantum polar decomposition algorithm
Seth Lloyd, Samuel Bosch, Giacomo De Palma +5
The polar decomposition for a matrix is , where is a positive Hermitian matrix and is unitary (or, if is not square, an isometry). This paper shows that the a…
Quantum Medical Imaging Algorithms
Bobak Toussi Kiani, Agnes Villanyi, Seth Lloyd
A central task in medical imaging is the reconstruction of an image or function from data collected by medical devices (e.g., CT, MRI, and PET scanners). We provide quantum algorit…
Adversarial Robustness Guarantees for Random Deep Neural Networks
Giacomo De Palma, Bobak T. Kiani, Seth Lloyd
The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close t…
Learning Unitaries by Gradient Descent
Bobak Toussi Kiani, Seth Lloyd, Reevu Maity
We study the hardness of learning unitary transformations in via gradient descent on time parameters of alternating operator sequences. We provide numerical evidence that, d…