arXiv subjects

Dawit Hiluf Hailu

Publications and source records attributed to Dawit Hiluf Hailu.

4 recordsLinked to original sources

arXiv2026

Implementation of Finite state logic machines via the dynamics of atomic systems

Following the success of Moore's predictions, we are approaching a limit in the miniaturization of semiconductors for computing materials. This has led to the exploration of various research paths to develop alternative computing paradigms, such as quantum computing, 3D transistors, molecular logic, and continuous logic. In this context, we propose a novel approach in which the dynamics of a two-level atom is used to execute classical Boolean logic operations. Unlike traditional combinational logic circuits, where the output depends solely on the input, we suggest a finite-state machine-like computing model, where the output is influenced by both the input and the system's initial state. The proposed mechanism leverages the dynamics of a two-level quantum state, with information encoded in observable quantities. These observables, the density matrix's population (diagonal) and coherence (off-diagonal) elements, were analyzed using the Liouville equation. The selection of observables within the Liouville space allows us to encode more variables. Although environmental noise may cause some loss of encoded information, fast computations can still be performed before it dissipates. In addition, logic operations can be read in parallel, enabling complex computations. This system can also be scaled to an N-level configuration.

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arXiv2020

On Sylvester solution for degenerate eigenvalues

In this paper we introduce the use of Sylvester's formula for systems with degenerate eigenvalues in relation to obtaining their analytical solutions. To appreciate the use we include two other forms of analytical solutions namely adiabatic and Magnus approximations. In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the evolution over time of a physical system in which quantum effects, such as wave--particle duality, are significant. The equation is a mathematical formulation for studying quantum mechanical systems. Just like Newtons's laws govern the motion of objects, Schrödinger equations of motion also govern the motion of quantum objects. Unlike the classical motion of objects the equation of motions of quantum phenomenon deals with the likelihood of the trajectories.

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arXiv2019

$SU(2)$ Dynamics and Logic machines -- part II

In this second part about dynamics of atomic system we revisit the logic application of $SU(2)$ dynamics. We reiterate that solution of quantum dynamics systems can be represented geometrically. Such geometric representations of solutions provides intuitive physical insights. To which end studying dynamics of Quantum systems via $su (2)$ Lie algebra proves to be convenient way of obtaining geometric solution for two level systems. In this paper link is established between two formalisms that made use of Lie algebra to describe equation of motion for quantum system. In both approaches the Hamiltonian and the density matrix are expressed as a linear combination of the Lie group. To exemplify the approach we consider a very well studied two level system whose coupling laser pulse have area of $\fracπ{2}$. Beyond establishing link between these two formalism we provide analytical solutions using Magnus expansion by exploiting the Sylvester formula where knowledge of eigenvalues suffice to obtain solution. Furthermore we also obtained two constants of motion by assuming time dependent detuning whose time. Consequently we have shown how one can have two disjoint subspaces whose evolution vector is independent of each other. As an application we present two classical binary logic machines, namely CNOT- gate and parity checker, that the two level system's dynamics mimics.

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arXiv2016

Solution of two level system using $3^{rd}$ order Magnus expansion

The solution of a two level system driven by a Laser in the adiabatic limit is determined using third order Magnus expansion. We made the assumption that the laser is on resonance or close to resonance with the Bohr transition. As a consequence of which we are able to obtain a Hamiltonian which commute with itself at different times. We solve the problem using the Sylvester Formula where we make use of the eigenvalues.

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