637 research outputs found
Pathwise super-replication via Vovk's outer measure
Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback
option. In: Finance Stoch. (1998)] the connection between model-independent
pricing and the Skorokhod embedding problem has been a driving force in robust
finance. We establish a general pricing-hedging duality for financial
derivatives which are susceptible to the Skorokhod approach.
Using Vovk's approach to mathematical finance we derive a model-independent
super-replication theorem in continuous time, given information on finitely
many marginals. Our result covers a broad range of exotic derivatives,
including lookback options, discretely monitored Asian options, and options on
realized variance.Comment: 18 page
GALA-n: Generic Architecture of Layout-Aware n-Bit Quantum Operators for Cost-Effective Realization on IBM Quantum Computers
A generic architecture of n-bit quantum operators is proposed for
cost-effective transpilation, based on the layouts and the number of n neighbor
physical qubits for IBM quantum computers, where n >= 3. This proposed
architecture is termed "GALA-n quantum operator". The GALA-n quantum operator
is designed using the visual approach of the Bloch sphere, from the visual
representations of the rotational quantum operations for IBM native gates
(square root of X, X, RZ, and CNOT). In this paper, we also proposed a new
formula for the quantum cost, which calculates the total numbers of native
gates, SWAP gates, and the depth of the final transpiled quantum circuits. This
formula is termed the "transpilation quantum cost". After transpilation, our
proposed GALA-n quantum operator always has a lower transpilation quantum cost
than that of conventional n-bit quantum operators, which are mainly constructed
from costly n-bit Toffoli gates.Comment: 27 pages, 22 figure
Canonical multi-valued input Reed-Muller trees and forms
There is recently an increased interest in logic synthesis using EXOR gates. The paper introduces the fundamental concept of Orthogonal Expansion, which generalizes the ring form of the Shannon expansion to the logic with multiple-valued (mv) inputs. Based on this concept we are able to define a family of canonical tree circuits. Such circuits can be considered for binary and multiple-valued input cases. They can be multi-level (trees and DAG's) or flattened to two-level AND-EXOR circuits. Input decoders similar to those used in Sum of Products (SOP) PLA's are used in realizations of multiple-valued input functions. In the case of the binary logic the family of flattened AND-EXOR circuits includes several forms discussed by Davio and Green. For the case of the logic with multiple-valued inputs, the family of the flattened mv AND-EXOR circuits includes three expansions known from literature and two new expansions
Fault Models for Quantum Mechanical Switching Networks
The difference between faults and errors is that, unlike faults, errors can
be corrected using control codes. In classical test and verification one
develops a test set separating a correct circuit from a circuit containing any
considered fault. Classical faults are modelled at the logical level by fault
models that act on classical states. The stuck fault model, thought of as a
lead connected to a power rail or to a ground, is most typically considered. A
classical test set complete for the stuck fault model propagates both binary
basis states, 0 and 1, through all nodes in a network and is known to detect
many physical faults. A classical test set complete for the stuck fault model
allows all circuit nodes to be completely tested and verifies the function of
many gates. It is natural to ask if one may adapt any of the known classical
methods to test quantum circuits. Of course, classical fault models do not
capture all the logical failures found in quantum circuits. The first obstacle
faced when using methods from classical test is developing a set of realistic
quantum-logical fault models. Developing fault models to abstract the test
problem away from the device level motivated our study. Several results are
established. First, we describe typical modes of failure present in the
physical design of quantum circuits. From this we develop fault models for
quantum binary circuits that enable testing at the logical level. The
application of these fault models is shown by adapting the classical test set
generation technique known as constructing a fault table to generate quantum
test sets. A test set developed using this method is shown to detect each of
the considered faults.Comment: (almost) Forgotten rewrite from 200
Experimental setup and procedure for the measurement of the 7Be(n,p)7Li reaction at n_TOF
Following the completion of the second neutron beam line and the related experimental area (EAR2) at the n_TOF spallation neutron source at CERN, several experiments were planned and performed. The high instantaneous neutron flux available in EAR2 allows to investigate neutron induced reactions with charged particles in the exit channel even employing targets made out of small amounts of short-lived radioactive isotopes. After the successful measurement of the 7Be(n,) cross section, the 7Be(n,p)7Li reaction was studied in order to provide still missing cross section data of relevance for Big Bang Nucleosynthesis (BBN), in an attempt to find a solution to the cosmological Lithium abundance problem. This paper describes the experimental setup employed in such a measurement and its characterization.Séptimo Programa Marco de la Comunidad Europea de la Energía Atómica (Euratom)-Proyecto CHANDA (No. 605203)Narodowe Centrum Nauki (NCN)-UMO-2012/04/M/ST2/00700-UMO-2016/22/M/ST2/00183Croatian Science Foundation-HRZZ 168
Gas electron tracking detector for beta decay experiments
For identification and 3D-tracking of low-energy electrons a new type of
gas-based detector was designed that minimizes scattering and energy loss. The
current version of the detector is a combination of a plastic scintillator,
serving as a trigger source and energy detector, and a hexagonally structured
multi-wire drift chamber (MWDC), filled with a mixture of helium and isobutane
gas. The drift time information is used to track particles in the plane
perpendicular to the wires, while a charge division technique provides spatial
information along the wires. The gas tracker was successfully used in the
miniBETA project as a beta spectrometer for a measurement of the weak magnetism
form factor in nuclear beta decay. The precision of the three-dimensional
electron tracking, in combination with low-mass, low-Z materials and
identification of backscattering from scintillator, facilitated a reduction of
the main systematics effects. At certain conditions, a spatial resolution
better than 0.5 mm was obtained in the plane perpendicular to the wires, while
resolutions of about 6 mm were achieved along wires. Thanks to precise tracking
information, it is possible to eliminate electrons and other particles not
originating from the desired decay with high efficiency. Additionally, using
the coincidence between MWDC and scintillator, background from gamma emission
typically accompanying radioactive decays, was highly suppressed. An overview
of different event topologies is presented together with the tracker's ability
to correctly recognize them. The analysis is supported by Monte Carlo
simulations using Geant4 and Garfield++ packages. Finally, the preliminary
results from the 114In spectrum study are presented.Comment: 5 pages, 3 figures, accepted for publication in JINST - PSD12(2021
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