Experimental realization of quantum algorithm for solving linear systems of equations

Many important problems in science and engineering can be reduced to the problem of solving linear equations. The quantum algorithm discovered recently indicates that one can solve an N-dimensional linear equation in $O(logN)$ time, which provides an exponential speedup over the classical counterpart. Here we report an experimental demonstration of the quantum algorithm when the scale of the linear equation is 2×2 using a nuclear magnetic resonance quantum information processor. For all sets of experiments, the fidelities of the final four-qubit states are all above 96%. This experiment gives the possibility of solving a series of practical problems related to linear systems of equations and can serve as the basis to realize many potential quantum algorithms.