Related papers: Solving oscillations problems through affine quant…
We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite…
Using a quantumlike description for light propagation in nonhomogeneous optical fibers, quantum information processing can be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and…
We numerically investigate the role of quantum fluctuations in superresolution of optical objects. First, we confirm that when quantum fluctuations are not taken into account, one can easily improve the resolution by one order of magnitude…
The utility of satisfiability (SAT) as an application focused hard computational problem is well established. We explore the potential of quantum annealing to enhance classical SAT solving, especially where sampling from the space of all…
By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…
An ultralocal form of any classical field theory eliminates all spatial derivatives in its action functional, e.g., in its Hamiltonian functional density. It has been applied to covariant scalar field theories and even to Einstein's general…
Quantum annealing aims at solving hard computational problems through adiabatic state preparation. Here, I propose to use inhomogeneous longitudinal magnetic fields to enhance the efficiency of the annealing. Such fields are able to bias…
I propose a superoscillation measurement method for subdiffraction incoherent optical sources, with potential applications in astronomy, remote sensing, fluorescence microscopy, and spectroscopy. The proposal, based on coherent optical…
Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation,…
When training neural networks with simulated quantization, we observe that quantized weights can, rather unexpectedly, oscillate between two grid-points. The importance of this effect and its impact on quantization-aware training (QAT) are…
In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in the real Hilbert space, both in the analytic method and in the algebraic method. The quaternionic solutions have many…
The main obstacle for practical quantum technology is the noise, which can induce the decoherence and destroy the potential quantum advantages. The fluctuation of a field, which induces the dephasing of the system, is one of the most common…
Quantum annealing is a powerful alternative model for quantum computing, which can succeed in the presence of environmental noise even without error correction. However, despite great effort, no conclusive proof of a quantum speedup…
We present a quantum solution to coordination problems that can be implemented with present technologies. It provides an alternative to existing approaches, which rely on explicit communication, prior commitment or trusted third parties.…
The problem of initializing phase in a quantum computing system is considered. The initialization of phases is a problem when the system is initially present in an entangled state and also in the application of the quantum gate…
We consider the application of the theory of vibrational control to H_infinity-problems. We study the possibility of introduction of high-frequency parametric vibrations in order to decrease the minimal attainable value of the…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
We consider a range of unconventional modifications to Quantum Annealing (QA), applied to an artificial trial problem with continuously tunable difficulty. In this problem, inspired by "transverse field chaos" in larger systems, classical…
A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly oscillatory behavior and slow decay in time. This extends…
The recently proposed Holography-inspired approach to quantum gravity is reviewed and expanded. The approach is based on the foliation of the background spacetime and reduction of the offshell states to the physical states. Careful…