  Superconducting quantum circuits are promising candidate for building
scalable quantum computers. Here, we use a four-qubit superconducting quantum
processor to solve a two-dimensional system of linear equations based on a
quantum algorithm proposed by Harrow, Hassidim, and Lloyd [Phys. Rev. Lett.
\textbf{103}, 150502 (2009)], which promises an exponential speedup over
classical algorithms under certain circumstances. We benchmark the solver with
quantum inputs and outputs, and characterize it by non-trace-preserving quantum
process tomography, which yields a process fidelity of $0.837\pm0.006$. Our
results highlight the potential of superconducting quantum circuits for
applications in solving large-scale linear systems, a ubiquitous task in
science and engineering.
