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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 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…
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…
Programming a quantum computer with quantum instructions
Morten Kjaergaard, Mollie E. Schwartz, Ami Greene +20
The equivalence between the instructions used to define programs and the input data on which the instructions operate is a basic principle of classical computer architectures and p…