285 research outputs found
Classifying Subset Feedback Vertex Set for H-free graphs
In the FEEDBACK VERTEX SET problem, we aim to find a small set S of vertices in a graph intersecting every cycle. The SUBSET FEEDBACK VERTEX SET problem requires S to intersect only those cycles that include a vertex of some specified set T. We also consider the WEIGHTED SUBSET FEEDBACK VERTEX SET problem, where each vertex u has weight w(u)>0 and we ask that S has small weight. By combining known NP-hardness results with new polynomial-time results we prove full complexity dichotomies for SUBSET FEEDBACK VERTEX SET and WEIGHTED SUBSET FEEDBACK VERTEX SET for H-free graphs, that is, graphs that do not contain a graph H as an induced subgraph
Transition from molecular complex to quantum solvation in OCS(He)_N
We present quantum calculations of the rotational energy levels and
spectroscopic rotational constants of the linear OCS molecule in variable size
clusters of 4He, using spectral evolution quantum Monte Carlo methods that
allow excited states to be accessed without nodal constraints. The rotational
constants of OCS are found to decrease monotonically from the gas phase value
as the number of helium atoms increases to N=6, after which the average
constant increases to saturation at a value in excellent agreement with
experimental measurements made on significantly larger clusters (N>1000). The
minimum is shown to indicate a transition from a molecular complex to a quantum
solvated molecule, with the former characterized by floppy but near rigid
behavior, while the latter is characterized by non-zero permutation exchanges
and a smaller extent of rigid coupling.Comment: 4 pages, 1 figure, submitted to Phys. Rev. Lett. on July 18,200
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
The efficient calculation of Hamiltonian spectra, a problem often intractable
on classical machines, can find application in many fields, from physics to
chemistry. Here, we introduce the concept of an "eigenstate witness" and
through it provide a new quantum approach which combines variational methods
and phase estimation to approximate eigenvalues for both ground and excited
states. This protocol is experimentally verified on a programmable silicon
quantum photonic chip, a mass-manufacturable platform, which embeds entangled
state generation, arbitrary controlled-unitary operations, and projective
measurements. Both ground and excited states are experimentally found with
fidelities >99%, and their eigenvalues are estimated with 32-bits of precision.
We also investigate and discuss the scalability of the approach and study its
performance through numerical simulations of more complex Hamiltonians. This
result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with
minor typos corrected.
Crilin: A CRystal calorImeter with Longitudinal InformatioN for a future Muon Collider
The measurement of physics processes at new energy frontier experiments
requires excellent spatial, time, and energy resolutions to resolve the
structure of collimated high-energy jets. In a future Muon Collider, the
beam-induced backgrounds (BIB) represent the main challenge in the design of
the detectors and of the event reconstruction algorithms. The technology and
the design of the calorimeters should be chosen to reduce the effect of the
BIB, while keeping good physics performance. Several requirements can be
inferred: i) high granularity to reduce the overlap of BIB particles in the
same calorimeter cell; ii) excellent timing (of the order of 100 ps) to reduce
the out-of-time component of the BIB; iii) longitudinal segmentation to
distinguish the signal showers from the fake showers produced by the BIB; iv)
good energy resolution (less than 10%/sqrt(E)) to obtain good physics
performance, as has been already demonstrated for conceptual particle flow
calorimeters. Our proposal consists of a semi-homogeneous electromagnetic
calorimeter based on Lead Fluoride Crystals (PbF2) readout by surface-mount
UV-extended Silicon Photomultipliers (SiPMs): the Crilin calorimeter. In this
paper, the performances of the Crilin calorimeter in the Muon Collider
framework for hadron jets reconstruction have been analyzed. We report the
single components characterizations together with the development of a
small-scale prototype, consisting of 2 layers of 3x3 crystals each
On the price of independence for vertex cover, feedback vertex set and odd cycle transversal.
Let vc(G), fvs(G) and oct(G) denote, respectively, the size of a minimum vertex cover, minimum feedback vertex set and minimum odd cycle transversal in a graph G. One can ask, when looking for these sets in a graph, how much bigger might they be if we require that they are independent; that is, what is the price of independence? If G has a vertex cover, feedback vertex set or odd cycle transversal that is an independent set, then we let, respectively, ivc(G), ifvs(G) or ioct(G) denote the minimum size of such a set. We investigate for which graphs H the values of ivc(G), ifvs(G) and ioct(G) are bounded in terms of vc(G), fvs(G) and oct(G), respectively, when the graph G belongs to the class of H-free graphs. We find complete classifications for vertex cover and feedback vertex set and an almost complete classification for odd cycle transversal (subject to three non-equivalent open cases)
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