892 research outputs found
When are prime formulae characteristic?
In the setting of the modal logic that characterizes modal refinement over modal transition systems, Boudol and Larsen showed that the formulae for which model checking can be reduced to preorder checking, that is, the characteristic formulae, are exactly the consistent and prime ones. This paper presents general, sufficient conditions guaranteeing that characteristic formulae are exactly the consistent and prime ones. It is shown that the given conditions apply to the logics characterizing all the semantics in van Glabbeek's branching-time spectrum
Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
Traditionally, quantum entanglement has played a central role in foundational
discussions of quantum mechanics. The measurement of correlations between
entangled particles can exhibit results at odds with classical behavior. These
discrepancies increase exponentially with the number of entangled particles.
When entanglement is extended from just two quantum bits (qubits) to three, the
incompatibilities between classical and quantum correlation properties can
change from a violation of inequalities involving statistical averages to sign
differences in deterministic observations. With the ample confirmation of
quantum mechanical predictions by experiments, entanglement has evolved from a
philosophical conundrum to a key resource for quantum-based technologies, like
quantum cryptography and computation. In particular, maximal entanglement of
more than two qubits is crucial to the implementation of quantum error
correction protocols. While entanglement of up to 3, 5, and 8 qubits has been
demonstrated among spins, photons, and ions, respectively, entanglement in
engineered solid-state systems has been limited to two qubits. Here, we
demonstrate three-qubit entanglement in a superconducting circuit, creating
Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88%, measured with
quantum state tomography. Several entanglement witnesses show violation of
bi-separable bounds by 830\pm80%. Our entangling sequence realizes the first
step of basic quantum error correction, namely the encoding of a logical qubit
into a manifold of GHZ-like states using a repetition code. The integration of
encoding, decoding and error-correcting steps in a feedback loop will be the
next milestone for quantum computing with integrated circuits.Comment: 7 pages, 4 figures, and Supplementary Information (4 figures)
Computing prime factors with a Josephson phase qubit quantum processor
A quantum processor (QuP) can be used to exploit quantum mechanics to find
the prime factors of composite numbers[1]. Compiled versions of Shor's
algorithm have been demonstrated on ensemble quantum systems[2] and photonic
systems[3-5], however this has yet to be shown using solid state quantum bits
(qubits). Two advantages of superconducting qubit architectures are the use of
conventional microfabrication techniques, which allow straightforward scaling
to large numbers of qubits, and a toolkit of circuit elements that can be used
to engineer a variety of qubit types and interactions[6, 7]. Using a number of
recent qubit control and hardware advances [7-13], here we demonstrate a
nine-quantum-element solid-state QuP and show three experiments to highlight
its capabilities. We begin by characterizing the device with spectroscopy.
Next, we produces coherent interactions between five qubits and verify bi- and
tripartite entanglement via quantum state tomography (QST) [8, 12, 14, 15]. In
the final experiment, we run a three-qubit compiled version of Shor's algorithm
to factor the number 15, and successfully find the prime factors 48% of the
time. Improvements in the superconducting qubit coherence times and more
complex circuits should provide the resources necessary to factor larger
composite numbers and run more intricate quantum algorithms.Comment: 5 pages, 3 figure
Generation of Three-Qubit Entangled States using Superconducting Phase Qubits
Entanglement is one of the key resources required for quantum computation, so
experimentally creating and measuring entangled states is of crucial importance
in the various physical implementations of a quantum computer. In
superconducting qubits, two-qubit entangled states have been demonstrated and
used to show violations of Bell's Inequality and to implement simple quantum
algorithms. Unlike the two-qubit case, however, where all maximally-entangled
two-qubit states are equivalent up to local changes of basis, three qubits can
be entangled in two fundamentally different ways, typified by the states
and . Here we demonstrate the operation of three coupled
superconducting phase qubits and use them to create and measure
and states. The states are fully characterized
using quantum state tomography and are shown to satisfy entanglement witnesses,
confirming that they are indeed examples of three-qubit entanglement and are
not separable into mixtures of two-qubit entanglement.Comment: 9 pages, 5 figures. Version 2: added supplementary information and
fixed image distortion in Figure 2
Planetary Candidates Observed by Kepler. VIII. A Fully Automated Catalog With Measured Completeness and Reliability Based on Data Release 25
We present the Kepler Object of Interest (KOI) catalog of transiting
exoplanets based on searching four years of Kepler time series photometry (Data
Release 25, Q1-Q17). The catalog contains 8054 KOIs of which 4034 are planet
candidates with periods between 0.25 and 632 days. Of these candidates, 219 are
new and include two in multi-planet systems (KOI-82.06 and KOI-2926.05), and
ten high-reliability, terrestrial-size, habitable zone candidates. This catalog
was created using a tool called the Robovetter which automatically vets the
DR25 Threshold Crossing Events (TCEs, Twicken et al. 2016). The Robovetter also
vetted simulated data sets and measured how well it was able to separate TCEs
caused by noise from those caused by low signal-to-noise transits. We discusses
the Robovetter and the metrics it uses to sort TCEs. For orbital periods less
than 100 days the Robovetter completeness (the fraction of simulated transits
that are determined to be planet candidates) across all observed stars is
greater than 85%. For the same period range, the catalog reliability (the
fraction of candidates that are not due to instrumental or stellar noise) is
greater than 98%. However, for low signal-to-noise candidates between 200 and
500 days around FGK dwarf stars, the Robovetter is 76.7% complete and the
catalog is 50.5% reliable. The KOI catalog, the transit fits and all of the
simulated data used to characterize this catalog are available at the NASA
Exoplanet Archive.Comment: 61 pages, 23 Figures, 9 Tables, Accepted to The Astrophysical Journal
Supplement Serie
Characteristics of Kepler Planetary Candidates Based on the First Data Set: The Majority are Found to be Neptune-Size and Smaller
In the spring of 2009, the Kepler Mission commenced high-precision photometry
on nearly 156,000 stars to determine the frequency and characteristics of small
exoplanets, conduct a guest observer program, and obtain asteroseismic data on
a wide variety of stars. On 15 June 2010 the Kepler Mission released data from
the first quarter of observations. At the time of this publication, 706 stars
from this first data set have exoplanet candidates with sizes from as small as
that of the Earth to larger than that of Jupiter. Here we give the identity and
characteristics of 306 released stars with planetary candidates. Data for the
remaining 400 stars with planetary candidates will be released in February
2011. Over half the candidates on the released list have radii less than half
that of Jupiter. The released stars include five possible multi-planet systems.
One of these has two Neptune-size (2.3 and 2.5 Earth-radius) candidates with
near-resonant periods.Comment: Paper to accompany Kepler's June 15, 2010 data release; submitted to
Astrophysical Journal Figures 1,2,& 3 revised. Improved labeling on all
figures. Slight changes to planet frequencies in result
Large-amplitude driving of a superconducting artificial atom: Interferometry, cooling, and amplitude spectroscopy
Superconducting persistent-current qubits are quantum-coherent artificial
atoms with multiple, tunable energy levels. In the presence of large-amplitude
harmonic excitation, the qubit state can be driven through one or more of the
constituent energy-level avoided crossings. The resulting
Landau-Zener-Stueckelberg (LZS) transitions mediate a rich array of
quantum-coherent phenomena. We review here three experimental works based on
LZS transitions: Mach-Zehnder-type interferometry between repeated LZS
transitions, microwave-induced cooling, and amplitude spectroscopy. These
experiments exhibit a remarkable agreement with theory, and are extensible to
other solid-state and atomic qubit modalities. We anticipate they will find
application to qubit state-preparation and control methods for quantum
information science and technology.Comment: 13 pages, 5 figure
Planetary Candidates Observed by Kepler, III: Analysis of the First 16 Months of Data
New transiting planet candidates are identified in sixteen months (May 2009 -
September 2010) of data from the Kepler spacecraft. Nearly five thousand
periodic transit-like signals are vetted against astrophysical and instrumental
false positives yielding 1,091 viable new planet candidates, bringing the total
count up to over 2,300. Improved vetting metrics are employed, contributing to
higher catalog reliability. Most notable is the noise-weighted robust averaging
of multi-quarter photo-center offsets derived from difference image analysis
which identifies likely background eclipsing binaries. Twenty-two months of
photometry are used for the purpose of characterizing each of the new
candidates. Ephemerides (transit epoch, T_0, and orbital period, P) are
tabulated as well as the products of light curve modeling: reduced radius
(Rp/R*), reduced semi-major axis (d/R*), and impact parameter (b). The largest
fractional increases are seen for the smallest planet candidates (197% for
candidates smaller than 2Re compared to 52% for candidates larger than 2Re) and
those at longer orbital periods (123% for candidates outside of 50-day orbits
versus 85% for candidates inside of 50-day orbits). The gains are larger than
expected from increasing the observing window from thirteen months (Quarter 1--
Quarter 5) to sixteen months (Quarter 1 -- Quarter 6). This demonstrates the
benefit of continued development of pipeline analysis software. The fraction of
all host stars with multiple candidates has grown from 17% to 20%, and the
paucity of short-period giant planets in multiple systems is still evident. The
progression toward smaller planets at longer orbital periods with each new
catalog release suggests that Earth-size planets in the Habitable Zone are
forthcoming if, indeed, such planets are abundant.Comment: Submitted to ApJS. Machine-readable tables are available at
http://kepler.nasa.gov, http://archive.stsci.edu/kepler/results.html, and the
NASA Exoplanet Archiv
Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler
We report the distribution of planets as a function of planet radius (R_p),
orbital period (P), and stellar effective temperature (Teff) for P < 50 day
orbits around GK stars. These results are based on the 1,235 planets (formally
"planet candidates") from the Kepler mission that include a nearly complete set
of detected planets as small as 2 Earth radii (Re). For each of the 156,000
target stars we assess the detectability of planets as a function of R_p and P.
We also correct for the geometric probability of transit, R*/a. We consider
first stars within the "solar subset" having Teff = 4100-6100 K, logg =
4.0-4.9, and Kepler magnitude Kp < 15 mag. We include only those stars having
noise low enough to permit detection of planets down to 2 Re. We count planets
in small domains of R_p and P and divide by the included target stars to
calculate planet occurrence in each domain. Occurrence of planets varies by
more than three orders of magnitude and increases substantially down to the
smallest radius (2 Re) and out to the longest orbital period (50 days, ~0.25
AU) in our study. For P < 50 days, the radius distribution is given by a power
law, df/dlogR= k R^\alpha. This rapid increase in planet occurrence with
decreasing planet size agrees with core-accretion, but disagrees with
population synthesis models. We fit occurrence as a function of P to a power
law model with an exponential cutoff below a critical period P_0. For smaller
planets, P_0 has larger values, suggesting that the "parking distance" for
migrating planets moves outward with decreasing planet size. We also measured
planet occurrence over Teff = 3600-7100 K, spanning M0 to F2 dwarfs. The
occurrence of 2-4 Re planets in the Kepler field increases with decreasing
Teff, making these small planets seven times more abundant around cool stars
than the hottest stars in our sample. [abridged]Comment: Submitted to ApJ, 22 pages, 10 figure
- …