Noisy intermediate-scale quantum computing algorithm for solving an nn-vertex MaxCut problem with log(nn) qubits

Quantum computers are devices, which allow more efficient solutions of problems as compared to their classical counterparts. As the timeline to developing a quantum-error corrected computer is unclear, the quantum computing community has dedicated much attention to developing algorithms for currently available noisy intermediate-scale quantum computers (NISQ). Thus far, within NISQ, optimization problems are one of the most commonly studied and are quite often tackled with the quantum approximate optimization algorithm (QAOA). This algorithm is best known for computing graph partitions with a maximal separation of edges (MaxCut), but can easily calculate other problems related to graphs. Here, I present a novel quantum optimization algorithm, which uses exponentially less qubits as compared to the QAOA while requiring a significantly reduced number of quantum operations to solve the MaxCut problem. Such an improved performance allowed me to partition graphs with 32 nodes on publicly available 5 qubit gate-based quantum computers without any preprocessing such as division of the graph into smaller subgraphs. These results represent a 40% increase in graph size as compared to state-of-art experiments on gate-based quantum computers such as Google Sycamore. The obtained lower bound is 54.9% on the solution for actual hardware benchmarks and 77.6% on ideal simulators of quantum computers. Furthermore, large-scale optimization problems represented by graphs of a 128 nodes are tackled with simulators of quantum computers, again without any predivision into smaller subproblems and a lower solution bound of 67.9% is achieved. The study presented here paves way to using powerful genetic optimizer in synergy with quantum computersComment: 5 pages, 4 figures, 2 tables + Supplementary materia

Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits

Majorana-zero-modes (MZMs) were predicted to exist as edge states of a physical system called the Kitaev chain. MZMs should host particles that are their own antiparticles and could be used as a basis for a qubit which is robust-to-noise. However, all attempts to prove their existence gave inconclusive results. Here, the Kitaev chain is exactly solved with a quantum computing methodology and properties of MZMs are probed by generating eigenstates of the Kitev Hamiltonian on 3 noisy qubits of a publicly available quantum computer. After an ontological elaboration I show that two eigenstates of the Kitaev Hamiltonian exhibit eight signatures attributed to MZMs. The results presented here are a most comprehensive set of validations of MZMs ever conducted in an actual physical system. Furthermore, the findings of this manuscript are easily reproducible for any user of publicly available quantum computers, solving another important problem of research with MZMs-the result reproducibility crisis

A family of root-finding methods with accelerated convergence

AbstractA parametric family of iterative methods for the simultaneous determination of simple complex zeros of a polynomial is considered. The convergence of the basic method of the fourth order is accelerated using Newton's and Halley's corrections thus generating total-step methods of orders five and six. Further improvements are obtained by applying the Gauss-Seidel approach. Accelerated convergence of all proposed methods is attained at the cost of a negligible number of additional operations. Detailed convergence analysis and two numerical examples are given

Anatomske promene listova Convolvulus arvensis L. prouzrokovane eriofidom Aceria malherbae Nuzz

Anatomical alterations of leaves of weed plant Convolvulus arvensis L. (Convolvulaceae) caused by eriophyoid mite Aceria malherbae Nuzz. are described and quantified. Designated as compatible interaction, they are expressed in dedifferentiation of plant cells, hyperplasia of epidermal layer and their turn to so-called nutritive tissue. Curling of leaf edges emerge as the consequence of mesophyll hypertrophy. It provides protected microhabitat for the huge colony of eriophyoids.U radu su opisane i kvantifikovane promene na listovima korovske vrste Convolvulus arvensis L. (Convolvulaceae) prouzrokovane ishranom eriofidne grinje Aceria malherbae Nuzz.(Acari:Eriophyoi-dea). Simptomi koji se manifestuju uvijanjem listova se mogu uvrstiti u kompatibilne interekcije tipa gala. Biljno tkivo na prisustvo i hranjenje grinja reaguje dediferencijacijom ćelija i hiperplazijom pre svega epidermalnog tkiva, pri čemu nastaje nutritivno tkivo kojim grinje nastavljaju da se hrane. Hipertrofija tkiva mezofila dovodi do uvijanja lista, pa se tako stvara relativno zaštićen prostor na licu lista u kome se razvija populacija grinja velike brojnosti. Dobijeni rezultati doprinose rasvetljavanju interakcije eriofida sa biljkom domaćinom

Frequency domain analysis of lightning protection using four lightning protection rods

In this paper the lightning discharge channel is modeled as a vertical monopole antenna excited by a pulse generator at its base. The lightning electromagnetic field of a nearby lightning discharge in the case of lightning protection using four vertical lightning protection rods was determined in the frequency domain. Unknown current distributions were determined by numerical solving of a system of integral equations of two potentials using the Point Matching Method and polynomial approximation of the current distributions. The influence of the real ground, treated as homogeneous loss half-space of known electrical parameters, expressed through a Sommerfeld integral kernel, was modeled using a new Two-image approximation which gives good results in both near and far fields