3.4k citations · 9.6k across the 66 of their papers we have counts for
10 papers · 2 filters
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…
The Quantum Wasserstein Distance of Order 1
Giacomo De Palma, Milad Marvian, Dario Trevisan +1
We propose a generalization of the Wasserstein distance of order 1 to the quantum states of qudits. The proposal recovers the Hamming distance for the vectors of the canonical…
Quantum algorithm for Petz recovery channels and pretty good measurements
András Gilyén, Seth Lloyd, Iman Marvian +2
The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measur…
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…