FABLE: Fast Approximate Quantum Circuits for Block-Encodings

Understand

Block-encodings of matrices have become an essential element of quantum algorithms derived from the quantum singular value transformation.

• This includes a variety of algorithms ranging from the quantum linear systems problem to quantum walk, Hamiltonian simulation, and quantum machine learning.
• Many of these algorithms achieve optimal complexity in terms of black box matrix oracle queries, but so far the problem of computing quantum circuit implementations for block-encodings of matrices has been under-appreciated.
• In this paper we propose FABLE, a method to generate approximate quantum circuits for block-encodings of matrices in a fast manner.