Some Quantum Algorithms
Daniel D. Stancil, Gregory T. Byrd · 2022
In this chapter, the authors present a few selected quantum algorithms that illustrate the promise of quantum computers to provide a computational advantage over classical computers. They briefly discuss computational complexity and how it applies to quantum computing. The authors present the two most famous quantum algorithms which promise quantum advantage: Grover's search algorithm and Shor's algorithm for factoring. They introduce several fundamental building blocks, including amplitude amplification, the Quantum Fourier Transform, and quantum phase estimation. Finally, the authors discuss a class of hybrid classical-quantum algorithms, known as variational algorithms, that are designed to operate within the realm of noisy, intermediate-scale quantum (NISQ) systems that are likely to be prevalent in the early years of quantum applications. Since quantum hardware has become publically available, a major effort has emerged to find algorithms that are suitable for addressing practical problems on near-term NISQ machines.