Related papers: Quaternionic description of semiconductor position…
We propose a technique for design of quantum Fourier transforms, and ensuing quantum algorithms, in a single interaction step by engineered Hamiltonians of circulant symmetry. The method uses adiabatic evolution and is robust against…
Four electron spin qubits in quantum dots are studied by means of an exchange interaction Hamiltonian. The time-independent Schr\"odinger equation is exactly analytically solved for the symmetric case, that is equal qubit frequencies and…
Exponentiation of Hamiltonians refers to a mathematical operation to a Hamiltonian operator, typically in the form e^(-i.t.H), where H is the Hamiltonian and t is a time parameter. This operation is fundamental in quantum mechanics,…
This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…
In this paper we discuss the use of the transition operator method for the theoretical description of a multi-qubit system in a one-dimensional waveguide. A general calculation has been performed for the N-qubit system, which was then…
In an attempt to better leverage superconducting quantum computers, scaling efforts have become the central concern. These efforts have been further exacerbated by the increased complexity of these circuits. The added complexity can…
We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a…
We describe different strategies for using a semi-classical controller to engineer quantum Hamiltonians to solve control problems such as quantum state or process engineering or optimization of observables.
Quaternions have been used to represent polarization states and polarization operators. But so far, only polarizers, dichroic or non-depolarizing devices have been represented in that way. We propose a quaternionic representation of perfect…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
We compare the behavior of a wave packet in the presence of a complex and a pure quaternionic potential step. This analysis, done for a gaussian convolution function, sheds new light on the possibility to recognize quaternionic deviations…
The transient response of a stationary state of a quantum particle in a step potential to an instantaneous change in the step height (a simplified model for a sudden bias switch in an electronic semiconductor device) is solved exactly by…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…
We analyze a single electron transistor composed of two semi-infinite one dimensional quantum wires and a relatively short segment between them. We describe each wire section by a Luttinger model, and treat tunneling events in the…
The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…
Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via…
Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states - characterized by order in four-electron composite objects, termed electron quadrupling or composite order - can exist…
We present a general, systematic, and efficient method for decomposing any given exponential operator of bosonic mode operators, describing an arbitrary multi-mode Hamiltonian evolution, into a set of universal unitary gates. Although our…