Constructing a large scale ion trap quantum processor will require entangling gate operations that are robust in the presence of noise and experimental imperfection. We experimentally demonstrate how a new type of Mølmer-Sørensen gate protects against infidelity caused by heating of the motional mode used during the gate. Furthermore, we show how the same technique simultaneously provides significant protection against slow fluctuations and mis-sets in the secular frequency. Since this parameter sensitivity is worsened in cases where the ions are not ground state cooled, our method provides a path towards relaxing ion cooling requirements in practical realisations of quantum computing and simulation. arXiv:1805.07351v2 [quant-ph]

In this paper, a direct rigorous mathematical proof of the Gregory–Laflamme instability for the five-dimensional Schwarzschild black string is presented. Under a choice of ansatz for the perturbation and a gauge choice, the linearized vacuum Einstein equation reduces to an ordinary differential equation (ODE) problem for a single function. In this work, a suitable rescaling and change of variables is applied, which casts the ODE into a Schrödinger eigenvalue equation to which an energy functional is assigned. It is then shown by direct variational methods that the lowest eigenfunction gives rise to an exponentially growing mode solution, which has admissible behavior at the future event horizon and spacelike infinity. After the addition of a pure gauge solution, this gives rise to a regular exponentially growing mode solution of the linearized vacuum Einstein equation in harmonic/transverse-traceless gauge.

In this paper, a direct rigorous mathematical proof of the Gregory-Laflamme instability [1] for the fivedimensional Schwarzschild black string is presented. Under a choice of ansatz for the perturbation and a gauge choice originally introduced in [2], the linearised vacuum Einstein equation reduces to an ODE problem for a single function. In this work, a suitable rescaling and change of variables is applied which casts the ODE into a Schrödinger eigenvalue equation to which an energy functional is assigned. It is then shown by direct variational methods that the lowest eigenfunction gives rise to an exponentially growing mode solution which has admissible behavior at the future event horizon and spacelike infinity. After the addition of a pure gauge solution, this gives rise to a regular exponentially growing mode solution of the linearised vacuum Einstein equation in harmonic/transverse-traceless gauge.