Quantum Algorithms Without Coherent Quantum Access

Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint on the implementability of these quantum algorithms. It has even been shown that without such an access, the quantum computer cannot be stronger than the classical counterparts. Thus, whether a quantum computer can be useful for practical applications is still open. In this work, we develop several variants of quantum algorithms. Our key framework employs a classical preprocessing step and a quantum procedure to perform gradient descent. We then translate such algorithm into an algorithm for solving linear systems, performing least-square fitting, building a support vector machine, performing supervised cluster assignment, training neural network, and solving for ground-state/excited-state energy, performing principle component analysis, with end-to-end applications of quantum algorithms. The classical preprocessing and the quantum procedure of our framework are shown to have logarithmic complexity in the dimension of input data, and quantum coherent access to input data is not required. Thus, our framework suggests an alternatively efficient route for quantum computers to handle real-world problems.