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)