Principles of Control for Decoherence-Free Subsystems

Decoherence-Free Subsystems (DFS) are a powerful means of protecting quantum information against noise with known symmetry properties. Although Hamiltonians theoretically exist that can implement a universal set of logic gates on DFS encoded qubits without ever leaving the protected subsystem, the natural Hamiltonians that are available in specific implementations do not necessarily have this property. Here we describe some of the principles that can be used in such cases to operate on encoded qubits without losing the protection offered by the DFS. In particular, we show how dynamical decoupling can be used to control decoherence during the unavoidable excursions outside of the DFS. By means of cumulant expansions, we show how the fidelity of quantum gates implemented by this method on a simple two-physical-qubit DFS depends on the correlation time of the noise responsible for decoherence. We further show by means of numerical simulations how our previously introduced "strongly modulating pulses" for NMR quantum information processing can permit high-fidelity operations on multiple DFS encoded qubits in practice, provided that the rate at which the system can be modulated is fast compared to the correlation time of the noise. The principles thereby illustrated are expected to be broadly applicable to many implementations of quantum information processors based on DFS encoded qubits.Comment: 12 pages, 7 figure

A Note on the correspondence between Qubit Quantum Operations and Special Relativity

We exploit a well-known isomorphism between complex hermitian $2\times 2$ matrices and $\mathbb{R}^4$, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map onto a Minkowskian future cone in $\mathbb{E}^{1,3}$, whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with a discussion of the equivalence and some of its possible consequences.Comment: 6 pages, revtex, v3: revised discussio

Experimental Implementation of Logical Bell State Encoding

Liquid phase NMR is a general purpose test-bed for developing methods of coherent control relevant to quantum information processing. Here we extend these studies to the coherent control of logical qubits and in particular to the unitary gates necessary to create entanglement between logical qubits. We report an experimental implementation of a conditional logical gate between two logical qubits that are each in decoherence free subspaces that protect the quantum information from fully correlated dephasing.Comment: 9 Pages, 5 Figure

A Method for Modeling Decoherence on a Quantum Information Processor

We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an $N^2$-dimensional quantum environment and random classical fields. This model offers the advantage that it may be implemented on small quantum information processors in order to explore the intermediate regime between semiclassical and fully quantum models. We consider in particular $\sigma_z\sigma_z$ system-environment couplings which induce coherence (phase) damping, though the model is directly extendable to other coupling Hamiltonians. Effective, irreversible phase-damping of the system is obtained by applying an additional stochastic Hamiltonian on the environment alone, periodically redressing it and thereby irreversibliy randomizing the system phase information that has leaked into the environment as a result of the coupling. This model is exactly solvable in the case of phase-damping, and we use this solution to describe the model's behavior in some limiting cases. In the limit of small stochastic phase kicks the system's coherence decays exponentially at a rate which increases linearly with the kick frequency. In the case of strong kicks we observe an effective decoupling of the system from the environment. We present a detailed implementation of the method on an nuclear magnetic resonance quantum information processor.Comment: 12 pages, 9 figure

SOPHIE velocimetry of Kepler transit candidates. XV. KOI-614b, KOI-206b, and KOI-680b: a massive warm Jupiter orbiting a G0 metallic dwarf and two highly inflated planets with a distant companion around evolved F-type stars

We report the validation and characterization of three new transiting exoplanets using SOPHIE radial velocities: KOI-614b, KOI-206b, and KOI-680b. KOI-614b has a mass of $2.86\pm0.35~{\rm M_{Jup}}$ and a radius of $1.13^{+0.26}_{-0.18}~{\rm R_{Jup}}$, and it orbits a G0, metallic ([Fe/H]=$0.35\pm0.15$) dwarf in 12.9 days. Its mass and radius are familiar and compatible with standard planetary evolution models, so it is one of the few known transiting planets in this mass range to have an orbital period over ten days. With an equilibrium temperature of $T_{eq}=1000 \pm 45$ K, this places KOI-614b at the transition between what is usually referred to as "hot" and "warm" Jupiters. KOI-206b has a mass of $2.82\pm 0.52~{\rm M_{Jup}}$ and a radius of $1.45\pm0.16~{\rm R_{Jup}}$, and it orbits a slightly evolved F7-type star in a 5.3-day orbit. It is a massive inflated hot Jupiter that is particularly challenging for planetary models because it requires unusually large amounts of additional dissipated energy in the planet. On the other hand, KOI-680b has a much lower mass of $0.84\pm0.15~{\rm M_{Jup}}$ and requires less extra-dissipation to explain its uncommonly large radius of $1.99\pm0.18~{\rm R_{Jup}}$. It is one of the biggest transiting planets characterized so far, and it orbits a subgiant F9-star well on its way to the red giant stage, with an orbital period of 8.6 days. With host stars of masses of $1.46\pm0.17~M_{\odot}$ and $1.54 \pm 0.09~M_{\odot}$, respectively, KOI-206b, and KOI-680b are interesting objects for theories of formation and survival of short-period planets around stars more massive than the Sun. For those two targets, we also find signs of a possible distant additional companion in the system

Artificial Neural Networks for Classification in Metabolomic Studies of Whole Cells Using 1H Nuclear Magnetic Resonance

We report the successful classification, by artificial neural networks (ANNs), of 1H NMR spectroscopic data recorded on whole-cell culture samples of four different lung carcinoma cell lines, which display different drug resistance patterns. The robustness of the approach was demonstrated by its ability to classify the cell line correctly in 100% of cases, despite the demonstrated presence of operator-induced sources of variation, and irrespective of which spectra are used for training and for validation. The study demonstrates the potential of ANN for lung carcinoma classification in realistic situations

Characterization of the four new transiting planets KOI-188b, KOI-195b, KOI-192b, and KOI-830b

The characterization of four new transiting extrasolar planets is presented here. KOI-188b and KOI-195b are bloated hot Saturns, with orbital periods of 3.8 and 3.2 days, and masses of 0.25 and 0.34 M_Jup. They are located in the low-mass range of known transiting, giant planets. KOI-192b has a similar mass (0.29 M_Jup) but a longer orbital period of 10.3 days. This places it in a domain where only a few planets are known. KOI-830b, finally, with a mass of 1.27 M_Jup and a period of 3.5 days, is a typical hot Jupiter. The four planets have radii of 0.98, 1.09, 1.2, and 1.08 R_Jup, respectively. We detected no significant eccentricity in any of the systems, while the accuracy of our data does not rule out possible moderate eccentricities. The four objects were first identified by the Kepler Team as promising candidates from the photometry of the Kepler satellite. We establish here their planetary nature thanks to the radial velocity follow-up we secured with the HARPS-N spectrograph at the Telescopio Nazionale Galileo. The combined analyses of the datasets allow us to fully characterize the four planetary systems. These new objects increase the number of well-characterized exoplanets for statistics, and provide new targets for individual follow-up studies. The pre-screening we performed with the SOPHIE spectrograph at the Observatoire de Haute-Provence as part of that study also allowed us to conclude that a fifth candidate, KOI-219.01, is not a planet but is instead a false positive.Comment: 13 pages, 4 figures, 6 tables, final version accepted for publication in A&

A Study of Quantum Error Correction by Geometric Algebra and Liquid-State NMR Spectroscopy

Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the state of a ``data'' spin into multiple quantum coherences involving additional ancilla spins. These multiple quantum coherences relax at differing rates, thus permitting the original state of the data to be approximately reconstructed by mixing them together in an appropriate fashion. This paper describes the operation of a simple, three-bit quantum code in the product operator formalism, and uses geometric algebra methods to obtain the error-corrected decay curve in the presence of arbitrary correlations in the external random fields. These predictions are confirmed in both the totally correlated and uncorrelated cases by liquid-state NMR experiments on 13C-labeled alanine, using gradient-diffusion methods to implement these idealized decoherence models. Quantum error correction in weakly polarized systems requires that the ancilla spins be prepared in a pseudo-pure state relative to the data spin, which entails a loss of signal that exceeds any potential gain through error correction. Nevertheless, this study shows that quantum coding can be used to validate theoretical decoherence mechanisms, and to provide detailed information on correlations in the underlying NMR relaxation dynamics.Comment: 33 pages plus 6 figures, LaTeX article class with amsmath & graphicx package

SOPHIE velocimetry of Kepler transit candidates XI. Kepler-412 system: probing the properties of a new inflated hot Jupiter

We confirm the planetary nature of Kepler-412b, listed as planet candidate KOI-202 in the Kepler catalog, thanks to our radial velocity follow-up program of Kepler-released planet candidates, which is on going with the SOPHIE spectrograph. We performed a complete analysis of the system by combining the Kepler observations from Q1 to Q15, to ground-based spectroscopic observations that allowed us to derive radial velocity measurements, together with the host star parameters and properties. We also analyzed the light curve to derive the star's rotation period and the phase function of the planet, including the secondary eclipse. We found the planet has a mass of 0.939 $\pm$ 0.085 M$_{Jup}$ and a radius of 1.325 $\pm$ 0.043 R$_{Jup}$ which makes it a member of the bloated giant subgroup. It orbits its G3 V host star in 1.72 days. The system has an isochronal age of 5.1 Gyr, consistent with its moderate stellar activity as observed in the Kepler light curve and the rotation of the star of 17.2 $\pm$ 1.6 days. From the detected secondary, we derived the day side temperature as a function of the geometric albedo and estimated the geometrical albedo, Ag, is in the range 0.094 to 0.013. The measured night side flux corresponds to a night side brightness temperature of 2154 $\pm$ 83 K, much greater than what is expected for a planet with homogeneous heat redistribution. From the comparison to star and planet evolution models, we found that dissipation should operate in the deep interior of the planet. This modeling also shows that despite its inflated radius, the planet presents a noticeable amount of heavy elements, which accounts for a mass fraction of 0.11 $\pm$ 0.04.Comment: 11 pages, 9 figure