arXiv subjects

Mikhail Erementchouk

Publications and source records attributed to Mikhail Erementchouk.

At least 19 recordsLinked to original sources

arXiv2026

Self-contained relaxation-based dynamical Ising machines

Dynamical Ising machines are based on continuous dynamical systems evolving from a generic initial state to a state strongly related to the ground state of the classical Ising model on a graph. Reaching the ground state is equivalent to finding the maximum (weighted) cut of the graph, which presents the Ising machines as an alternative way to solving and investigating NP-complete problems. Among the dynamical models, relaxation-based models are distinguished by their relations with guarantees of performance achieved in time scaling polynomially with the problem size. However, the terminal states of such machines are essentially non-binary, necessitating special post-processing relying on disparate computing. We show that an Ising machine implementing a special continuous dynamical system (called the V${}_2$ model) solves the rounding problem dynamically. We prove that the V${}_2$ model, starting from an arbitrary non-binary state, terminates in a state that trivially rounds to a binary state with the cut at least as big as obtained by optimal rounding of the initial state. Besides showing that relaxation-based dynamical Ising machines can be made self-contained, this result presents a non-Boolean realization of solving a non-trivial information processing task on Ising machines. Moreover, we prove that if the initial state of the V${}_2$-machine is a random limited amplitude perturbation of a binary state, the machine progresses to a state with at least as high cut as that of the initial binary state. Since the probability of improving the cut is finite, this shows that the V${}_2$-machine with random agitations converges to a maximum cut state almost surely.

cs.ET↗

arXiv2026

Symmetry-induced quantum-inspired parallelism of classical dynamic systems

Performing multiple computations within the same system, without spatial or temporal separation of tasks, requires encoding multiple data items into a well-defined physical state. The most widely explored mechanism for such encoding is the superposition of physical states representing computational states. However, superposition requires the system to be linear, which significantly limits the set of achievable operations. We show that system symmetries provide an alternative mechanism for encoding multiple computational states. Notably, this mechanism also applies to nonlinear systems and therefore does not impose inherent limits on computed functions. Using the evaluation of Boolean functions as an example, we show that a relaxed spin network driven by the V-2 model supports this mechanism. We relate the resulting simultaneous computations enabled by symmetry-induced parallelism to properties of the evaluated functions. We demonstrate symmetry-induced parallelism for a logical AND/OR gate and an N-bit adder.

cs.ET↗

arXiv2025

Relaxation-based dynamical Ising machines for discrete tomography

Dynamical Ising machines are continuous dynamical systems that evolve from a generic initial state to a state strongly related to the ground state of the classical Ising model. We show that such a machine driven by the V${}_2$ dynamical model can solve exactly discrete tomography problems about reconstructing a binary image from the pixel sums along a discrete set of rays. In contrast to usual applications of Ising machines, targeting approximate solutions to optimization problems, the randomly initialized V${}_2$ model converges with high probability ($P_{\mathrm{succ}} \approx 1$) to an image precisely satisfying the tomographic data. For the problems with at most two rays intersecting at each pixel, the V${}_2$ model converges in internal machine time that depends only weakly on the image size. Our consideration is an example of how specific dynamical systems can produce exact solutions to highly non-trivial data processing tasks. Crucially, this solving capability arises from the dynamical features of the V${}_2$ model itself, in particular its equations of motion that enable non-local transitions of the discrete component of the relaxed spin beyond Hamming-neighborhood constraints, rather than from merely recasting the tomography problem in spin form.

cs.ET↗

arXiv2024

Non-binary dynamical Ising machines for combinatorial optimization

Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous dynamical systems. The main adapted principle of constructing such systems is based on requiring that, on the one hand, the system converges to a binary state and, on the other hand, the system's energy in such states mimics the classical Ising Hamiltonian. The emergence of binary-like states is regarded to be an indispensable feature of dynamical Ising machines as it establishes the relation between the machine's continuous terminal state and the inherently discrete solution of a combinatorial optimization problem. This is emphasized by problems where the unknown quantities are represented by spin complexes, for example, the graph coloring problem. In such cases, an imprecise mapping of the continuous states to spin configurations may lead to invalid solutions requiring intensive post-processing. In contrast to such an approach, we show that there exists a class of non-binary dynamical Ising machines without the incongruity between the continuous character of the machine's states and the discreteness of the spin states. We demonstrate this feature by applying such a machine to the problems of finding proper graph coloring, constructing Latin squares, and solving Sudoku puzzles. Thus, we demonstrate that the information characterizing discrete states can be unambiguously presented in essentially continuous dynamical systems. This opens new opportunities in the realization of scalable electronic accelerators of combinatorial optimization.

cs.ET↗

arXiv2024

Near-field-assisted capacity of spoof-plasmonic channels

Establishing universal features of spoof-plasmonic systems beyond spectral properties is challenging due to the complexity of the specific physical realizations of spoof-plasmonic channels. We introduce a simple 1D scalar model reproducing the key properties of spoof-plasmonic channels and investigate manifestations of plasmonic-like features when only a few local resonances are present. We show that the channel between the source applied to the interior of the structure and the terminal ends (output ports) effectively comprises two subchannels. The activation of one of the subchannels depends on the spatial variation of the source, and therefore, the contribution of this subchannel in conventional systems is small if the source occupies a subwavelength region. We show that, in spoof-plasmonic structures, the activation of this subchannel can enhance significantly in the frequency region where the spoof-plasmonic effects are prominent. This demonstrates that even a few local scattering resonances may strongly impact the flow of wave-carried information.

cond-mat.mtrl-sci↗

arXiv2022

Scalable almost-linear dynamical Ising machines

The past decade has seen the emergence of Ising machines targeting hard combinatorial optimization problems by minimizing the Ising Hamiltonian with spins represented by continuous dynamical variables. However, capabilities of these machines at larger scales are yet to be fully explored. We investigate an Ising machine based on a network of almost-linearly coupled analog spins. We show that such networks leverage the computational resource similar to that of the semidefinite positive relaxation of the Ising model. We estimate the expected performance of the almost-linear machine and benchmark it on a set of {0,1}-weighted graphs. We show that the running time of the investigated machine scales polynomially (linearly with the number of edges in the connectivity graph). As an example of the physical realization of the machine, we present a CMOS-compatible implementation comprising an array of vertices efficiently storing the continuous spins on charged capacitors and communicating externally via analog current.

cs.ET↗

arXiv2022

On computational capabilities of Ising machines based on nonlinear oscillators,

Dynamical Ising machines are actively investigated from the perspective of finding efficient heuristics for NP-hard optimization problems. However, the existing data demonstrate super-polynomial scaling of the running time with the system size, which is incompatible with large NP-hard problems. We show that oscillator networks implementing the Kuramoto model of synchronization are capable of demonstrating polynomial scaling. The dynamics of these networks is related to the semidefinite programming relaxation of the Ising model ground state problem. Consequently, such networks, as we numerically demonstrate, are capable of producing the best possible approximation in polynomial time. To reach such performance, however, the reconstruction of the binary Ising state (rounding) must be specially addressed. We demonstrate that commonly implemented forced collapse to a close-to-Ising state may diminish the computational capabilities up to their complete invalidation. Therefore, consistent treatment of rounding may cardinally improve various operation metrics of already existing and upcoming dynamical Ising machines.

cond-mat.stat-mech↗

arXiv2019

CV QKD with discretized modulations in the strong noise regime

We consider a general family of quantum key distribution (QKD) protocols utilizing displaced thermal states with discretized modulations. Separating the effects of the Gaussian channel and the non-Gaussian distribution, we have studied the dependence of the secret key generation rate on the magnitude of modulations (the strength of the modulated signal). We show that in the limit of strong signal, QKD is impossible: from the perspective of an efficient eavesdropper, the ensemble of transmitted states is effectively classical. This constitutes a quantum correction to performance of finite-length QKD protocols. We demonstrate that two regimes must be distinguished: weak and strong thermal noise. In the case of strong noise, the security boundary is mostly determined by the weak-signal limit. When the noise is weak, however, QKD may become possible only when the signal strength exceeds some critical value.

quant-ph↗

arXiv2018

Weyl fermions in cylindrical wires

The key feature of Weyl semimetals (WSM) is the presence of topologically protected Dirac cones in a 3D material. We consider the effect of restricting geometry on the spectrum of excitations in WSM using as a model a cylindrical WSM wire. For the full manifold of hard boundary conditions, we derive the general form of the dispersion equation relating the energy of the excitations and their momentum along the wire. We show that only the special class of boundary conditions, corresponding to decoupled helicities or, equivalently, to pinned directions of the electron spin on the surface, support massless excitations. For a general boundary condition, these excitations acquire mass inversely proportional to the radius of the wire. This demonstrates that boundary phenomena may play a crucial role in formation of excitations in WSM based structures.

cond-mat.mes-hall↗

arXiv2017

Electronic and Optical Properties of Vacancy Defects in Transition Metal Dichalcogenides

A detailed first-principle study has been performed to evaluate the electronic and optical properties of single-layer (SL) transition metal dichalcogenides (TMDCs) (MX${}_2$; M= transition metal such as Mo, W and X= S, Se, Te), in the presence of vacancy defects (VDs). Defects usually play an important role in tailoring electronic, optical, and magnetic properties of semiconductors. We consider three types of VDs in SL TMDCs i) $X$-vacancy, $X_{2}$-vacancy, and iii) $M$-vacancy. We show that VDs lead to localized defect states (LDS) in the band structure, which in turn give rise to sharp transitions in in-plane and out-of-plane optical susceptibilities, $χ_{\parallel}$ and $χ_{\perp}$. The effects of spin orbit coupling (SOC) are also considered. We find that SOC splitting in LDS is directly related to the atomic number of the transition metal atoms. Apart from electronic and optical properties we also find magnetic signatures (local magnetic moment of $\simμ_{B}$) in MoSe$_{2}$ in the presence of Mo vacancy, which breaks the time reversal symmetry and therefore lifts the Kramers degeneracy. We show that a simple qualitative tight binding model (TBM), involving only the hopping between atoms surrounding the vacancy with an on-site SOC term, is sufficient to capture the essential features of LDS. In addition, the existence of the LDS can be understood from the solution of the 2D Dirac Hamiltonian by employing infinite mass boundary conditions. In order to provide a clear description of the optical absorption spectra, we use group theory to derive the optical selection rules between LDS for both $χ_{\parallel}$ and $χ_{\perp}$.

cond-mat.mes-hall↗

arXiv2016

Dirac electrons in the presence of matrix potential barrier: application to graphene and topological insulators

Scattering of a 2D Dirac electrons on a rectangular matrix potential barrier is considered using the formalism of spinor transfer matrices. It is shown, in particular, that in the absence of the mass term, the Klein tunneling is not necessarily suppressed but occurs at oblique incidence. The formalism is applied to studying waveguiding modes of the barrier, which are supported by the edge and bulk states. The condition of existence of the uni-directionality property is found. We show that the band of edge states is always finite with massless excitations, while the spectrum of the bulk states, depending on parameters of the barrier, may consist of the infinite or finite band with both, massive and massless, low-energy excitations. The effect of the Zeeman term is considered and the condition of appearance of two distinct energy dependent directions corresponding to the Klein tunneling is found.

cond-mat.mes-hall↗

arXiv2015

Optical signatures of states bound to vacancy defects in monolayer MoS$_2$

We show that pristine MoS$_2$ single layer (SL) exhibits two bandgaps $E_{g\parallel}=1.9$ eV and $E_{g\perp}=3.2$ eV for the optical in-plane and out-of-plane susceptibilities $χ_\parallel$ and $χ_\perp$, respectively. In particular, we show that odd states bound to vacancy defects (VDs) lead to resonances in $χ_\perp$ inside $E_{g\perp}$ in MoS$_2$ SL with VDs. We use density functional theory, the tight-binding model, and the Dirac equation to study MoS$_2$ SL with three types of VDs: (i) Mo-vacancy, (ii) S$_2$-vacancy, and (iii) 3$\times$MoS$_2$ quantum antidot. The resulting optical spectra identify and characterize the VDs.

cond-mat.mes-hall↗

arXiv2014

Electrical property tuning via defect engineering of single layer MoS2 by oxygen plasma

We demonstrate that the electrical property of a single layer molybdenum disulfide (MoS2) can be significantly tuned from semiconducting to insulating regime via controlled exposure to oxygen plasma. The mobility, on-current and resistance of single layer MoS2 devices were varied up to four orders of magnitude by controlling the plasma exposure time. Raman spectroscopy, X-ray photoelectron spectroscopy and density functional theory studies suggest that the significant variation of electronic properties is caused by the creation of insulating MoO3-rich disordered domains in the MoS2 sheet upon oxygen plasma exposure, leading to an exponential variation of resistance and mobility as a function of plasma exposure time. The resistance variation calculated using an effective medium model is in excellent agreement with the measurements. The simple approach described here can be used for the fabrication of tunable two dimensional nanodevices on MoS2 and other transition metal dichalcogenides.

cond-mat.mes-hall↗

arXiv2012

Effect of Monolayer Thickness Fluctuations on Coherent Exciton Coupling in Single Quantum Wells

Monolayer fluctuations in the thickness of a semiconductor quantum well (QW) lead to three types of excitons, located in the narrower, average and thicker regions of the QW, which are clearly resolved in optical spectra. Whether or not these excitons are coherently coupled via Coulomb interactions is a long-standing debate. We demonstrate that different types of disorder in QWs distinctly affects the coherent coupling and that the coupling strength can be quantitatively measured using optical two-dimensional Fourier transform spectroscopy. We prove experimentally and theoretically that in narrow quantum wells the coherent coupling occurs predominantly between excitons residing in the disorder-free areas of the QWs and those residing in the plateau-type disorder. In contrast, excitons localized in the fault-type disorder potentials do not coherently couple to other excitons.

cond-mat.mes-hall↗

arXiv2012

Deterministic generation of N00N states using quantum dots in a cavity

Compared to classical light sources, quantum sources based on N00N states consisting of $N$ photons achieve an $N$-times higher phase sensitivity, giving rise to super-resolution. N00N-state creation schemes based on linear optics and projective measurements only have a success probability $p$ that decreases exponentially with $N$, e.g. $p=4.4\times 10^{-14}$ for N=20. Feed-forward improves the scaling but $N$ fluctuates nondeterministically in each attempt. Schemes based on parametric down-conversion suffer from low production efficiency and low fidelity. A recent scheme based on atoms in a cavity combines deterministic time evolution, local unitary operations, and projective measurements. Here we propose a novel scheme based on the off-resonant interaction of $N$ photons with four semiconductor quantum dots (QDs) in a cavity to create N00N states deterministically with $p=1$ and fidelity above 90% for $N\lesssim 60$, without the need of any projective measurement or local unitary operation. Using our measure we obtain maximum $N$-photon entanglement $E_N=1$ for arbitrary $N$. Our method paves the way to the miniaturization of N00N-state sources to the nanoscale regime, with the possibility to integrate them on a computer chip based on semiconductor materials.

cond-mat.mes-hall↗

arXiv2012

Entanglement dynamics of second quantized quantum fields

We study the entanglement dynamics in the system of coupled quantum fields. We prove that if the coupling is linear, that is if the total Hamiltonian is a quadratic form of field operators, entanglement can only be transferred between the fields. We show that entanglement is produced in the model of the two-mode self-interacting boson field with the characteristic Gaussian decay of coherence in the limit of high number of particles. The interesting feature of this system is that the particles in different modes become entangled even if there is no direct interaction between the modes. We apply these results for analysis of the entanglement dynamics in the two-mode Jaynes-Cummings model in the limit of large number of photons. While the photon-atom interaction is assumed to conserve helicity the photons with different polarizations still get entangled due to an effective interaction mediated by the atom with the characteristic entanglement time linearly increasing with the number of photons.

cond-mat.mes-hall↗

arXiv2011

Correlated breakdown of carbon nanotubes in an ultra-high density aligned array

We demonstrate that in a densely packed aligned array of single walled carbon nanotubes, the breakdown of one nanotube leads to a highly correlated breakdown of neighboring nanotubes, thereby producing a nano-fissure. We show that the origin of the correlation is the electrostatic field of the broken nanotubes that produces locally inhomogeneous current and Joule heating distributions in the neighboring intact nanotubes triggering their breakdowns in the vicinity of the broken nanotubes. Our results suggest that the densely aligned array behaves like a correlated solid.

cond-mat.mes-hall↗

arXiv2010

Complex dynamics of photon entanglement in two-mode Jaynes-Cummings model

We study the dynamics of the photon entanglement, $E_{\mathrm{N}}(t)$, for the two-mode Jaynes-Cummings model in the few-photon case. The atomic transitions associated with the photons with different polarizations are assumed to be independent and, hence, the evolution of the "+"- and "-"-polarized photons is formally separable. However, due to the photons indistinguishability such interaction still leads to entanglement of initially disentangled states owing to the non-linear dependence of the characteristic frequencies on the photon population numbers. The time dependence of entanglement is the result of superimposing oscillations with incommensurate frequencies. Therefore, $E_{\mathrm{N}}(t)$ is a quasi-periodic function of time with the complex profile strongly depending on the number of photons.

cond-mat.mes-hall↗