Speaker
Description
Quantum algorithms for basic numerical linear algebraic tasks have proven essential for translating diverse problems to a unified quantum computational context. Many of these tasks—e.g., applying a function to the spectrum of a matrix embedded in a unitary process (a so-called block encoding)—are well-addressed by techniques like quantum singular value transformation (QSVT). However, there exist useful matrix transforms whose realization by quantum algorithms is unclear or inefficient. In this work we construct improved quantum algorithms for some of these transforms, the simplest of which is a scalar function applied element-wise. We show the auxiliary space required to compute quantum element-wise transforms can be reduced exponentially in the degree of the applied function compared to prior work, and raise and rectify errors in previous constructions. We present these algorithms alongside applications to machine learning, simulation, and signal processing.
| Topic | Quantum algorithms for machine learning applications |
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| Additional Topic | Encoding and processing of data in quantum systems |