A team of researchers has realized hybrid quantum algorithm for solving a linear system of equations with exponential speedup that utilizes quantum phase estimation, the algorithm demonstrates quantum supremacy and holds high promise to meet practically relevant challenges.
https://scirate.com/arxiv/2003.12770
There is also a variational hybrid quantum-classical algorithm for solving linear systems, with the aim of reducing the circuit depth and doing much of the computation classically, called VQLS.
https://arxiv.org/abs/1909.05820
https://pennylane.ai/qml/demos/tutorial_vqls.html
How can we compare both algorithms?
In the part of the near-term application of H-HHL paper, they talk about Bayesian deep learning application: "One of the promising applications related to deep neural network training was discussed in[1]in [1]: since the extension of the Bayesian approach to deep architectures is a serious challenge, one can exploit the hybrid quantum HHL algorithm developed for Gaussian processes in order to calculate a model’s predictor" [21][https://arxiv.org/pdf/1806.11463.pdf21].
Which algorithm should be better in the next-gen state-of-art 53-Qubits quantum computer for the Quantum Bayesian deep learning algorithm?
