Dense arrays of trapped ions provide one way of scaling up ion trap quantum information processing. However, miniaturization of ion traps is currently limited by sharply increasing motional state decoherence at sub-100 µm ion-electrode distances. We characterize heating rates in cryogenically cooled surface-electrode traps, with characteristic sizes in 75 µm to 150 µm range. Upon cooling to 6 K, the measured rates are suppressed by 7 orders of magnitude, two orders of magnitude below previously published data of similarly sized traps operated at room temperature. The observed noise depends strongly on fabrication process, which suggests further improvements are possible.PACS numbers: 32.80. Pj, 39.10.+j, 42.50.Vk Quantum information processing offers a tantalizing possibility of a significant speedup in execution of certain algorithms [1,2], as well as enabling previously unmanageable simulations of large quantum systems [3,4]. One of the most promising avenues towards practical quantum computation uses trapped ions as qubits. Interaction between qubits can be mediated by superconductive wires [5], photons [6,7] or by shared phonon modes [8]. The last scheme has been most successful so far, having demonstrated one and two qubit gates [9], teleportation [10,11], error correction[12] and shuttling [13]. Scaling of these experiments to a large number of ions will require arrays of small traps, on the order of 10 µm, to achieve dense qubit packing, improve the gate speed and reduce the time necessary to shuttle ions between different traps in the array [14,15,16,17]. Micro-fabrication techniques have been successfully used to fabricate a new generation of ion traps, demonstrating trap sizes down to 30 µm [18,19,20]. However, as the trap size is decreased, ion heating and decoherence of the motional quantum state increases rapidly, approximately as the fourth power of the trap size [21,22,23]. At currently observed values, the heating rate in a 10 µm trap would exceed 10 6 quanta/s, precluding ground-state cooling or qubit operations mediated by the motional state.The strong distance dependence of the heating rate suggests that the electric field noise is generated by surface charge fluctuations, which are small compared to the distance to the ion. Charge noise is also observed in condensed matter systems, where device fabrication has proven critical in reducing the problem [24,25]. Similar advances in ion traps are impeded by lack of data and models accurately predicting measured noise [26,27,28]. The charge fluctuations have been demonstrated to be thermally driven, providing another plausible route to reduce the heating. Cooling of the electrodes to 150 K has been shown to significantly decrease the heating rate [23].In this Letter, we present the first measurements of heating rates in ion traps cooled to 6 K. We designed and built a range of surface-electrode traps, in which we are able to cool a single ion to motional ground state with high fidelity and observe heating on a quantum level. Although the traps h...