arXiv subjects

Pinaki Mazumder

Publications and source records attributed to Pinaki Mazumder.

11 recordsLinked to original sources

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↗

arXiv2023

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↗

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↗

arXiv2020

Terahertz Quantum Cryptography

A well-known empirical rule for the demand of wireless communication systems is that of Edholm's law of bandwidth. It states that the demand for bandwidth in wireless short-range communications doubles every 18 months. With the growing demand for bandwidth and the decreasing cell size of wireless systems, terahertz (THz) communication systems are expected to become increasingly important in modern day applications. With this expectation comes the need for protecting users' privacy and security in the best way possible. With that in mind, we show that quantum key distribution can operate in the THz regime and we derive the relevant secret key rates against realistic collective attacks. In the extended THz range (from 0.1 to 50 THz), we find that below 1 THz, the main detrimental factor is thermal noise, while at higher frequencies it is atmospheric absorption. Our results show that high-rate THz quantum cryptography is possible over distances varying from a few meters using direct reconciliation, to about 220m via reverse reconciliation. We also give a specific example of the physical hardware and architecture that could be used to realize our THz quantum key distribution scheme.

quant-ph↗

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↗

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↗