Quantum Reed-Solomon Codes

After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about the position of errors. This error model - the quantum erasure channel - is discussed. Finally, parameters of quantum BCH codes are provided.Comment: Summary only (2 pages), for the full version see: Proceedings Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-13), Lecture Notes in Computer Science 1719, Springer, 199

Quantum secret sharing

Secret sharing is a procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. We show how this procedure can be implemented using GHZ states. In the quantum case the presence of an eavesdropper will introduce errors so that his presence can be detected. We also show how GHZ states can be used to split quantum information into two parts so that both parts are necessary to reconstruct the original qubit.Comment: 6 pages, revtex, revised version, to appear in Phys. Rev.

Perfect quantum error correction coding in 24 laser pulses

An efficient coding circuit is given for the perfect quantum error correction of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The circuit presented employs a double `classical' code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. A further circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary 1-qubit errors. In addition, the performance of two error correction schemes, one based on the quantum Zeno effect and the other using standard methods, is compared. The quantum Zeno error correction scheme is found to fail completely for a model of noise based on phase-diffusion.Comment: Replacement paper: Lost two laser pulses gained one author; added appendix with circuits easily implementable on an ion-trap compute

Experimental realization of the one qubit Deutsch-Jozsa algorithm in a quantum dot

We perform quantum interference experiments on a single self-assembled semiconductor quantum dot. The presence or absence of a single exciton in the dot provides a qubit that we control with femtosecond time resolution. We combine a set of quantum operations to realize the single-qubit Deutsch-Jozsa algorithm. The results show the feasibility of single qubit quantum logic in a semiconductor quantum dot using ultrafast optical control.Comment: REVTex4, 4 pages, 3 figures. Now includes more details about the dephasing in the quantum dots. The introduction has been reworded for clarity. Minor readability fixe

Basic concepts in quantum computation

Section headings: 1 Qubits, gates and networks 2 Quantum arithmetic and function evaluations 3 Algorithms and their complexity 4 From interferometers to computers 5 The first quantum algorithms 6 Quantum search 7 Optimal phase estimation 8 Periodicity and quantum factoring 9 Cryptography 10 Conditional quantum dynamics 11 Decoherence and recoherence 12 Concluding remarksComment: 37 pages, lectures given at les Houches Summer School on "Coherent Matter Waves", July-August 199

Two-Bit Gates are Universal for Quantum Computation

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase breaking (i.e., quantum phase coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.Comment: 21 pages, REVTeX 3.0, two .ps figures available from author upon reques

Mesoscopic superpositions of vibronic collective states of N trapped ions

We propose a scalable procedure to generate entangled superpositions of motional coherent states and electronic states in N trapped ions. Beyond their fundamental importance, these states may be of interest for quantum information processing and may be used in experimental studies of decoherence.Comment: Final version, as published in Physical Review Letters. See also further developments and applications in quant-ph/020207

Extreme Ultraviolet Variability Experiment (EVE) on the Solar Dynamics Observatory (SDO): Overview of Science Objectives, Instrument Design, Data Products, and Model Developments

The highly variable solar extreme ultraviolet (EUV) radiation is the major energy input to the Earth’s upper atmosphere, strongly impacting the geospace environment, affecting satellite operations, communications, and navigation. The Extreme ultraviolet Variability Experiment (EVE) onboard the NASA Solar Dynamics Observatory (SDO) will measure the solar EUV irradiance from 0.1 to 105 nm with unprecedented spectral resolution (0.1 nm), temporal cadence (ten seconds), and accuracy (20%). EVE includes several irradiance instruments: The Multiple EUV Grating Spectrographs (MEGS)-A is a grazing-incidence spectrograph that measures the solar EUV irradiance in the 5 to 37 nm range with 0.1-nm resolution, and the MEGS-B is a normal-incidence, dual-pass spectrograph that measures the solar EUV irradiance in the 35 to 105 nm range with 0.1-nm resolution. To provide MEGS in-flight calibration, the EUV SpectroPhotometer (ESP) measures the solar EUV irradiance in broadbands between 0.1 and 39 nm, and a MEGS-Photometer measures the Sun’s bright hydrogen emission at 121.6 nm. The EVE data products include a near real-time space-weather product (Level 0C), which provides the solar EUV irradiance in specific bands and also spectra in 0.1-nm intervals with a cadence of one minute and with a time delay of less than 15 minutes. The EVE higher-level products are Level 2 with the solar EUV irradiance at higher time cadence (0.25 seconds for photometers and ten seconds for spectrographs) and Level 3 with averages of the solar irradiance over a day and over each one-hour period. The EVE team also plans to advance existing models of solar EUV irradiance and to operationally use the EVE measurements in models of Earth’s ionosphere and thermosphere. Improved understanding of the evolution of solar flares and extending the various models to incorporate solar flare events are high priorities for the EVE team.United States. National Aeronautics and Space Administration (contract NAS5-02140

The Road to Quantum Computational Supremacy

We present an idiosyncratic view of the race for quantum computational supremacy. Google's approach and IBM challenge are examined. An unexpected side-effect of the race is the significant progress in designing fast classical algorithms. Quantum supremacy, if achieved, won't make classical computing obsolete.Comment: 15 pages, 1 figur

Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem

In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in the Communications in Mathematical Physics (http://www.springerlink.com/content/1432-0916/