Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40 Ca + ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire

Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four "cache qubits" and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%.

Electric field noise from fluctuating patch potentials is a significant problem for a broad range of precision experiments, including trapped ion quantum computation and single spin detection. Recent results demonstrated strong suppression of this noise by cryogenic cooling, suggesting an underlying thermal process. We present measurements characterizing the temperature and frequency dependence of the noise from 7 to 100 K, using a single Sr+ ion trapped 75 mum above the surface of a gold plated surface electrode ion trap. The noise amplitude is observed to have an approximate 1/f spectrum around 1 MHz, and grows rapidly with temperature as T;{beta} for beta from 2 to 4. The data are consistent with microfabricated cantilever measurements of noncontact friction but do not extrapolate to the dc measurements with neutral atoms or contact potential probes.