Unification of quantum algorithm through quantum signal processing

Synopsis

Quantum algorithms demonstrate remarkable speed-ups over classical approaches in addressing diverse computational problems, notably in quantum search, quantum phase estimation, and Hamiltonian simulation. These algorithms, while appearing distinct, have recently been shown to connect under a unified framework through a technique known as quantum signal processing (QSP) and its generalization, quantum singular value transformation (QSVT). QSP, originally rooted in the composite-pulse technique for controlling two-level quantum systems (e.g., in nuclear magnetic resonance), allows for the effective description of these quantum algorithms within a two-level subspace, where they can be formulated through QSP methods.

In this presentation, I will introduce the principles of QSP and QSVT and illustrate their role in linking some foundational quantum algorithms, such as Grover's algorithm and quantum phase estimation. The main reference is the seminal paper, "Grand Unification of Quantum Algorithms," by Isaac L. Chuang et al.

https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.040203