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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 dimensional linear equation in O(log N) 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. [ABSTRACT FROM AUTHOR]

A set of stabilizer operations augmented by some special initial states known as "magic states" gives the possibility of universal fault-tolerant quantum computation. However, magic state preparation inevitably involves nonideal operations that introduce noise. The most common method to eliminate the noise is magic state distillation (MSD) by stabilizer operations. Here we propose a hybrid MSD protocol by connecting a four-qubit H-type MSD with a five-qubit 7'-type MSD in order to overcome the shortcomings of the previous MSD protocols. The hybrid MSD protocol further integrates distillable ranges of different existing MSD protocols and provides considerable improvement in qubit cost. Moreover, we experimentally demonstrate the four-qubit H-type MSD protocol using nuclear magnetic resonance technology, together with the previous five-qubit MSD experiment, to show the feasibility of the hybrid MSD protocol. [ABSTRACT FROM AUTHOR]