scholarly journals Petri Net Modeling for Ising Model Formulation in Quantum Annealing

2021 ◽  
Vol 11 (16) ◽  
pp. 7574
Author(s):  
Morikazu Nakamura ◽  
Kohei Kaneshima ◽  
Takeo Yoshida
Keyword(s):  
Combinatorial Optimization ◽  
Ising Model ◽  
Petri Net ◽  
Optimization Problems ◽  
Ising Models ◽  
Objective Functions ◽  
Quantum Annealing ◽  
Model Formulation ◽  
Target Problem ◽  
Straightforward Manner

Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas of everyday life. Our research is aimed at the proposal of a Petri net modeling approach for an Ising model formulation. Although the proposed method requires users to model their optimization problems with Petri nets, this process can be carried out in a relatively straightforward manner if we know the target problem and the simple Petri net modeling rules. With our method, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models, extracted systematically from Petri net models, and then converted into binary quadratic nets, equivalent to Ising models. The proposed method can drastically reduce the difficulty of the Ising model formulation.

scholarly journals A Quantum Adiabatic Algorithm for Multiobjective Combinatorial Optimization

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 32 ◽  
Author(s):  
Benjamín Barán ◽  
Marcos Villagra
Keyword(s):  
Combinatorial Optimization ◽  
Multiobjective Optimization ◽  
Theorem Proving ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Quantum Annealing ◽  
Multiobjective Optimization Problems ◽  
First Time

In this work we show how to use a quantum adiabatic algorithm to solve multiobjective optimization problems. For the first time, we demonstrate a theorem proving that the quantum adiabatic algorithm can find Pareto-optimal solutions in finite-time, provided some restrictions to the problem are met. A numerical example illustrates an application of the theorem to a well-known problem in multiobjective optimization. This result opens the door to solve multiobjective optimization problems using current technology based on quantum annealing.

scholarly journals Charged particle tracking with quantum annealing optimization

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Alexander Zlokapa ◽  
Abhishek Anand ◽  
Jean-Roch Vlimant ◽  
Javier M. Duarte ◽  
Joshua Job ◽  
...  
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Hadron Collider ◽  
Hopfield Network ◽  
Quantum Annealing ◽  
Track Reconstruction ◽  
Combinatorial Optimization Problems ◽  
Charged Particle Tracking ◽  
Near Term ◽  
Quantum Speedup

AbstractAt the High Luminosity Large Hadron Collider (HL-LHC), traditional track reconstruction techniques that are critical for physics analysis will need to be upgraded to scale with track density. Quantum annealing has shown promise in its ability to solve combinatorial optimization problems amidst an ongoing effort to establish evidence of a quantum speedup. As a step towards exploiting such potential speedup, we investigate a track reconstruction approach by adapting the existing geometric Denby-Peterson (Hopfield) network method to the quantum annealing framework for HL-LHC conditions. We develop additional techniques to embed the problem onto existing and near-term quantum annealing hardware. Results using simulated annealing and quantum annealing with the D-Wave 2X system on the TrackML open dataset are presented, demonstrating the successful application of a quantum annealing algorithm to the track reconstruction challenge. We find that combinatorial optimization problems can effectively reconstruct tracks, suggesting possible applications for fast hardware-specific implementations at the HL-LHC while leaving open the possibility of a quantum speedup for tracking.

scholarly journals Enhancing quantum annealing performance by a degenerate two-level system

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Shohei Watabe ◽  
Yuya Seki ◽  
Shiro Kawabata
Keyword(s):  
Magnetic Field ◽  
Combinatorial Optimization ◽  
Longitudinal Magnetic Field ◽  
Energy Gap ◽  
Optimization Problems ◽  
Success Probability ◽  
Level System ◽  
Quantum Annealing ◽  
Combinatorial Optimization Problems ◽  
High Success Probability

AbstractQuantum annealing is an innovative idea and method for avoiding the increase of the calculation cost of the combinatorial optimization problem. Since the combinatorial optimization problems are ubiquitous, quantum annealing machine with high efficiency and scalability will give an immeasurable impact on many fields. However, the conventional quantum annealing machine may not have a high success probability for finding the solution because the energy gap closes exponentially as a function of the system size. To propose an idea for finding high success probability is one of the most important issues. Here we show that a degenerate two-level system provides the higher success probability than the conventional spin-1/2 model in a weak longitudinal magnetic field region. The physics behind this is that the quantum annealing in this model can be reduced into that in the spin-1/2 model, where the effective longitudinal magnetic field may open the energy gap, which suppresses the Landau–Zener tunneling providing leakage of the ground state. We also present the success probability of the Λ-type system, which may show the higher success probability than the conventional spin-1/2 model.

scholarly journals Maximizing gerrymandering through ising model optimization

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yasuharu Okamoto
Keyword(s):  
Combinatorial Optimization ◽  
Ising Model ◽  
Model Optimization ◽  
Model Formulation ◽  
Binary Variables ◽  
Electoral District

AbstractBy using the Ising model formulation for combinatorial optimization with 0–1 binary variables, we investigated the extent to which partisan gerrymandering is possible from a random but even distribution of supporters. Assuming that an electoral district consists of square subareas and that each subarea shares at least one edge with other subareas in the district, it was possible to find the most tilted assignment of seats in most cases. However, in cases where supporters' distribution included many enclaves, the maximum tilted assignment was usually found to fail. We also discussed the proposed algorithm is applicable to other fields such as the redistribution of delivery destinations.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

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