Abstract
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 $2\ifmmode\times\else\texttimes\fi{}2$ 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.
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