scholarly journals A Study of Ising Formulations for Minimizing Setup Cost in the Two-Dimensional Cutting Stock Problem

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 182
Author(s):  
Hiroshi Arai ◽  
Harumi Haraguchi
Keyword(s):  
Ising Model ◽  
Optimal Solution ◽  
Computer Experiments ◽  
Error Rates ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Setup Cost ◽  
Proposed Model ◽  
Acceptance Rates ◽  
Future Work

We proposed the method that translates the two-dimensional CSP for minimizing the number of cuts to the Ising model. After that, we conducted computer experiments of the proposed model using the benchmark problem. From the above, the following results are obtained. (1) The proposed Ising model adequately represents the target problem. (2) Acceptance rates were as low as 0.2% to 9.8% and from 21.8% to 49.4%. (3) Error rates from optimal solution were as broad as 0% to 25.9%. For future work, we propose the following changes: (1) Improve the Hamiltonian for constraints. (2) Improve the proposed model to adjust more complex two-dimensional CSP and reduce the number of spins when it deals with large materials and components. (3) Conduct experiments using a quantum annealer.

scholarly journals POSSIBLE CAUSES OF CHANGE IN THE DIRECTION OF EARTH'S MAGNETIC FIELD

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Dragana Malivuk Gak ◽  
Saša Nježić ◽  
Enes Škrgić ◽  
Zoran Rajilić
Keyword(s):  
Magnetic Field ◽  
Magnetic Properties ◽  
Ising Model ◽  
Computer Experiments ◽  
Ferromagnetic Material ◽  
Two Dimensional ◽  
Earth’S Magnetic Field ◽  
Earth's Magnetic Field ◽  
Properties Of Materials ◽  
Small Change

The study of the magnetic properties of materials have attracted the interest of scientists for ages. Knowing the magnetic properties of materials do their best possible use in industry and technology, as well as better understanding of some yet unexplained phenomena in nature related to the Earth's magnetic field. Several models that describe the given phenomenon are known, such as the domino model, two-dimensional Ising model and model of inversion magnetic Earth's field. In computer experiments whose results are presented in this paper, it is used a simplified two-dimensional Ising model, one version of the model related spins. Computer experiments (simulations) are made in the mathematical software Maple. It has been observed reversing the direction of magnetization in a small change of inhomogeneity energy interactions. Consideration of this issue could be of importance for the study of ferromagnetic material.

scholarly journals Wind Farm Cable Connection Layout Optimization with Several Substations

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3615
Author(s):  
Adelaide Cerveira ◽  
Eduardo J. Solteiro Pires ◽  
José Baptista
Keyword(s):  
Energy Production ◽  
Wind Farm ◽  
Programming Model ◽  
Optimal Solution ◽  
Wind Farms ◽  
Green Energy ◽  
Fossil Energy ◽  
Proposed Model ◽  
Short Time ◽  
Cable Connection

Green energy has become a media issue due to climate changes, and consequently, the population has become more aware of pollution. Wind farms are an essential energy production alternative to fossil energy. The incentive to produce wind energy was a government policy some decades ago to decrease carbon emissions. In recent decades, wind farms were formed by a substation and a couple of turbines. Nowadays, wind farms are designed with hundreds of turbines requiring more than one substation. This paper formulates an integer linear programming model to design wind farms’ cable layout with several turbines. The proposed model obtains the optimal solution considering different cable types, infrastructure costs, and energy losses. An additional constraint was considered to limit the number of cables that cross a walkway, i.e., the number of connections between a set of wind turbines and the remaining wind farm. Furthermore, considering a discrete set of possible turbine locations, the model allows identifying those that should be present in the optimal solution, thereby addressing the optimal location of the substation(s) in the wind farm. The paper illustrates solutions and the associated costs of two wind farms, with up to 102 turbines and three substations in the optimal solution, selected among sixteen possible places. The optimal solutions are obtained in a short time.

scholarly journals Exponential suppression of bit or phase errors with cyclic error correction

Nature ◽  
2021 ◽  
Vol 595 (7867) ◽  
pp. 383-387
Author(s):  
◽  
Zijun Chen ◽  
Kevin J. Satzinger ◽  
Juan Atalaya ◽  
Alexander N. Korotkov ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Rates ◽  
Quantum Error Correction ◽  
Superconducting Qubits ◽  
Two Dimensional ◽  
Logical Error ◽  
Quantum Error ◽  
Logical Qubit

AbstractRealizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

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