Intelligent transportation systems (ITS) are a critical component of Industry 4.0 and 5.0, particularly having applications in logistic management. One of their crucial utilization is in supply-chain management and scheduling for optimally routing transportation of goods by vehicles at a given set of locations. This paper discusses the broader problem of vehicle traffic management, more popularly known as the Vehicle Routing Problem (VRP), and investigates the possible use of near-term quantum devices for solving it. For this purpose, we give the Ising formulation for VRP and some of its constrained variants. Then, we present a detailed procedure to solve VRP by minimizing its corresponding Ising Hamiltonian using a hybrid quantum-classical heuristic called Quantum Approximate Optimization Algorithm (QAOA), implemented on the IBM Qiskit platform. We compare the performance of QAOA with classical solvers such as CPLEX on problem instances of up to 15 qubits. We find that performance of QAOA has a multifaceted dependence on the classical optimization routine used, the depth of the ansatz parameterized by p, initialization of variational parameters, and problem instance itself.

Precise measurements of the anisotropies in the cosmic microwave background enable us to do an accurate study on the form of the primordial power spectrum for a given set of cosmological parameters. In a previous paper [A. Shafieloo and T. Souradeep, Phys. Rev. D 70, 043523 (2004).], we implemented an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the first year of WMAP data to determine the primordial power spectrum assuming a concordance cosmological model. This recovered spectrum has a likelihood far better than a scale invariant, or, “best fit” scale free spectra ($\Delta \ln \mathcal{L}\approx 25$ with respect to the Harrison-Zeldovich spectrum, and, $\Delta \ln \mathcal{L}\approx 11$ with respect to the power law spectrum with $n_s=0.95$). In this paper we use the discrete wavelet transform (DWT) to decompose the local features of the recovered spectrum individually to study their effect and significance on the recovered angular power spectrum and hence the likelihood. We show that besides the infrared cutoff at the horizon scale, the associated features of the primordial power spectrum around the horizon have a significant effect on improving the likelihood. The strong features are localized at the horizon scale.

We show the existence of self-similar giant rogue waves in a tapered graded-index nonlinear fiber and analytically illustrate their amplification in a rather small spatiotemporal domain by controlled manipulation of the phase. Our exact analysis takes recourse to the large manifold of available tapering profiles in conjunction with appropriate gain functions, which are allowed by the dynamical equation governing the tapered graded-index nonlinear fiber. The fact that these profiles and gain functions provide a wide class of boundary conditions makes them particularly relevant for transient rogue waves, which manifest rather rarely.