arXiv subjects

Samir Lipovaca

Publications and source records attributed to Samir Lipovaca.

5 recordsLinked to original sources

arXiv2013

The quantal algebra and abstract equations of motion

The quantal algebra combines classical and quantum mechanics into an abstract structurally unified structure. The structure uses two products: one symmetric and one anti-symmetric. The local structure of spacetime is contained in the quantal algebra without having been postulated. We will introduce an abstract derivation concept and generalize classical and quantum mechanics equations of motion to abstract equations of motion in which the anti-symmetric product of the quantal algebra plays a key role. We will express the defining identities of the quantal algebra in terms of the abstract derivation. In this form the first defining identity (the Jacobi identity) is analogous in form to the Bianchi identity in general relativity which is one set of gravitational field equations for the curvature tensor. The identity for the unit element is equivalent to the important property that the metric is covariantly constant. Similarly, the Jacobi identity is analogous in form to the homogeneous Maxwell equations. The anti-symmetric product of the quantal algebra is reflected in the antisymmetry of the electromagnetic tensor.

physics.gen-ph↗

arXiv2010

A Lagrangian for the quantionic field equation

The purpose of this paper is to present a Lagrangian from which we can derive the quantionic field equation written in the Dirac gauge using the principle of stationary action.

physics.gen-ph↗

arXiv2009

Using the Deutsch-Jozsa algorithm to determine parts of an array and apply a specified function to each independent part

Using the Deutsch-Jozsa algorithm, we will develop a method for solving a class of problems in which we need to determine parts of an array and then apply a specified function to each independent part. Since present quantum computers are not robust enough for code writing and execution, we will build a model of a vector quantum computer that implements the Deutsch-Jozsa algorithm from a machine language view using the APL2 programming language. The core of the method is an operator (DJBOX) which allows evaluation of an arbitrary function f by the Deutsch-Jozsa algorithm. Two key functions of the method are GET_PARTITION and CALC_WITH_PARTITIONS. The GET_PARTITION function determines parts of an array based on the function f. The CALC_WITH_PARTITIONS function determines parts of an array based on the function f and then applies another function to each independent part. We will imagine the method is implemented on the above vector quantum computer. We will show that the method can be successfully executed.

quant-ph↗

arXiv2008

Four qubits Hamiltonian of the Rs. molischianum light-harvesting complex II ring

We will construct a simple four qubits Hamiltonian of the Rs. molischianum purple bacteria light harvesting complex II (LH-II) ring which yields energy levels that carry the ring's oscillator strength. In an excitonic representation, these levels are associated with the second and the third lowest electronic excitations of the ring. We will assume that qubits form a closed loop lattice and the interaction between qubits is only due to the exchange effect. As we will show, eigenstates are constructed in a such way that as we subsequently divide qubits of the Rs. molischianum LH-II ring into the subsystem A consisting of only one qubit and the subsystem B consisting of the remaining qubits, respective entropies of entanglement increase until the value of 1 for the maximally entangled state (bipartite system) is reached. Since the Hamiltonian in essence introduces a two-level approximation for the LH-II ring, we will go one step further and assume that interactions between qubits closed loop lattices and an electromagnetic field are described by the Jaynes-Cummings Hamiltonian. This assumption is interesting by itself, since it leads to behavior where the qubits lattice and field oscillate back and fourth exchanging a quantum of energy, at the Rabbi frequency. This opens a challenging opportunity to experimentally study the Rs. molischianum LH-II ring in the regime of cavity QED.

quant-ph↗

arXiv2007

Purple bacteria and quantum Fourier transform

The LH-II of purple bacteria Rhodospirillum (Rs.) molischianum and Rhodopseudomonas (Rps.) acidophila adopts a highly symmetrical ring shape, with a radius of about 7 nm. In the case of Rps. acidophila the ring has a ninefold symmetry axis, and in LH-II from Rs. molischianum the ring has an eightfold symmetry axis. These rings are found to exibit two bands of excitons. A simplified mathematical description of the exciton states is given in Hu, X. & Schulten, K. (1997) Physics Today 50, 28-34. Using this description, we will show, by suitable labeling of the lowest energy (Qy) excited states of individual BChls, that the resulting exciton states are the quantum Fourier transform of the BChls excited states. For Rs. molischianum ring exciton states will be modeled as the four qubit quantum Fourier transform and the explicit circuit will be derived. Exciton states for Rps. acidophila ring cannot be modeled with an integer number of qubits. Both quantum Fourier transforms are instances of the hidden subgroup problem and this opens up a possibility that both purple bacteria implement an efficient quantum circuit for light harvesting.

quant-ph↗