Recorded 25 January 2022. Seth Lloyd of the Massachusetts Institute of Technology presents "Quantum polar decomposition" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: The polar decomposition decomposes a matrix into the product of a unitary and an Hermitian matrix. This talk presents a quantum algorithm for performing the polar decomposition, applying the unitary, and performing the quantum measurement corresponding to the Hermitian matrix. The algorithm scales as the logarithm of the dimension and can be used for a variety of tasks, including performing pretty good measurements. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/quantum-numerical-linear-algebra/?tab=schedule