Hybrid quantum linear equation algorithm and its experimental test on
  IBM Quantum Experience
We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd
(HHL) algorithm for solving a system of linear equations. In our hybrid scheme,
a classical information feed-forward is required from the quantum phase
estimation algorithm to reduce a circuit depth from the original HHL algorithm.
In this paper, we show that this hybrid algorithm is functionally identical to
the HHL algorithm under the assumption that the number of qubits used in
algorithms is large enough. In addition, it is experimentally examined with
four qubits in the IBM Quantum Experience setups, and the experimental results
of our algorithm show higher accurate performance on specific systems of linear
equations than that of the HHL algorithm.
Yonghae Lee Jaewoo Joo Soojoon Lee