The paper "Quantum Algorithms Revisited" by R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca explores the common patterns underlying quantum algorithms and their relation to quantum phase estimation. The authors use the concept of multi-particle interference to review and improve existing quantum algorithms, providing an explicit algorithm for generating any prescribed interference pattern with arbitrary precision. They demonstrate that quantum computations can be viewed as multi-particle interferometers, where phase shifts result from operations of quantum logic gates. The paper discusses Deutsch's problem, which shows how interference patterns can lead to computational problems, and generalizes it to more complex scenarios. It also revisits the quantum Fourier transform, explaining its role in phase estimation and its application in algorithms like Shor's order-finding algorithm. The authors provide a universal construction for generating arbitrary interference patterns and conclude by highlighting the significance of estimating eigenvalues in understanding and improving quantum algorithms.The paper "Quantum Algorithms Revisited" by R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca explores the common patterns underlying quantum algorithms and their relation to quantum phase estimation. The authors use the concept of multi-particle interference to review and improve existing quantum algorithms, providing an explicit algorithm for generating any prescribed interference pattern with arbitrary precision. They demonstrate that quantum computations can be viewed as multi-particle interferometers, where phase shifts result from operations of quantum logic gates. The paper discusses Deutsch's problem, which shows how interference patterns can lead to computational problems, and generalizes it to more complex scenarios. It also revisits the quantum Fourier transform, explaining its role in phase estimation and its application in algorithms like Shor's order-finding algorithm. The authors provide a universal construction for generating arbitrary interference patterns and conclude by highlighting the significance of estimating eigenvalues in understanding and improving quantum algorithms.