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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]

Intrigued by the holographic principle, Padmanabhan recently proposed a novel idea, saying that our cosmic space is emergent as cosmic time progresses. In particular, the expansion rate of the Universe is related to the difference between the surface degrees of freedom on the holographic horizon and the bulk degrees of freedom inside. In this note, we generalize this interesting paradigm to brane world, scalartensor gravity, and f(R) theory, respectively, and find that in the cosmological setting the Friedmann equations can be successfully derived. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the growth rates of action for the anti-de Sitter black holes in massive-Einstein gravity models and obtain the universal behaviors of the growth rates of action (the rates of holographic complexity) within the "Wheeler-DeWitt" (WDW) patch at the late limit. Furthermore, we find that, for the static neutral cases, when the same mass of black holes is given, the computational speed of the neutral massive black hole is the same as its Einstein gravity counterpart, which is independent with the effect of the graviton mass terms; nevertheless, for the static charged cases, when the same mass and charge parameters of black holes are given, the growth rates of action for the massive charged black holes are always superior to the growth rates of action without graviton mass terms, which directly shows that the massive charged black holes as computers on the computational speeds are faster than their Einstein gravity counterparts. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a timelike hypersurface, we find that the perturbation effects of massive gravity in bulk can be completely governed by the incompressible Navier-Stokes equation living on the cutoff surface under the near horizon and nonrelativistic limits. Furthermore, we have concisely computed the ratio of dynamical viscosity to entropy density for two massive Einstein gravity theories, and found that they still saturate the Kovtun-Son-Starinets (KSS) bound. [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]

Recently it has been shown that imposing Petrov-like condition on the boundary may reduce the Einstein equation to the Navier-Stokes equation in the nonrelativistic and near-horizon limit. In this paper we extend this framework to a spacetime with a cosmological constant. By explicit construction we show that the Navier-Stokes equation can be derived from both black brane background and spatially curved spacetime. We also conjecture that imposing Petrov-like condition on the boundary should be equivalent to the conventional meühod using the hydrodynamical expansion of the metric in the near-horizon limit. [ABSTRACT FROM AUTHOR]