Realization of a scalable Shor algorithm.

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%.

Undoing a quantum measurement.

In general, a quantum measurement yields an undetermined answer and alters the system to be consistent with the measurement result. This process maps multiple initial states into a single state and thus cannot be reversed. This has important implications in quantum information processing, where errors can be interpreted as measurements. Therefore, it seems that it is impossible to correct errors in a quantum information processor, but protocols exist that are capable of eliminating them if they affect only part of the system. In this work we present the deterministic reversal of a fully projective measurement on a single particle, enabled by a quantum error-correction protocol in a trapped ion quantum information processor. We further introduce an in-sequence, single-species recooling procedure to counteract the motional heating of the ion string due to the measurement.

Narrow-linewidth chirped frequency comb from a frequency-shifted feedback Ti:sapphire laser seeded by a phase-modulated single-frequency fiber laser.

Frequency-shifted feedback (FSF) lasers have emerged as powerful tools for precision distance metrology. At the output of a Michelson interferometer, the detected rf spectra of the FSF laser light contain a length-dependent heterodyne beat signal whose linewidth ultimately limits the achievable accuracy of length measurements. Here, we demonstrate a narrow-linewidth chirped frequency comb from an FSF Ti:sapphire ring laser seeded by a phase-modulated, ultra-low-phase-noise, single-frequency fiber laser. We experimentally investigate the influence of the seed laser linewidth on the resulting width and shape of the length-dependent rf beat signal. An ultranarrow heterodyne beat linewidth of <20 Hz is observed.