Abstract: Harrow-Hassidim-Lloyd (HHL) quantum algorithm has basically realized the function of solving linear equation Ax = b, and it is also the essential ingredient of many complex quantum algorithms. Although HHL quantum algorithm achieves exponential speedup over its classical counterpart, most of the current HHL quantum algorithms are abstract algorithm descriptions or their analyses. Especially, the HHL quantum circuits developed so far are small in scale and not general. By analyzing the basic units of HHL quantum algorithm, the key modules of HHL algorithm, including a unitary matrix decomposition module by general quantum gates, a quantum phase estimation module, a quantum full adder and multiplier module, and a conditional rotation module of quantum state, etc, were designed from top to down using general quantum gates, thus achieving a general quantum circuit for solving linear equations. Quantum simulations on the IBM qiskit quantum computation development platform show that the designed quantum circuits are suitable for solving more general linear equations and can be easily extended to medium or large-scale quantum circuits.

Key words: quantum computation, HHL quantum algorithm, quantum circuit, quantum phase estimation; IBM qiskit platform