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.

Artificial Higher Order Neural Networks for Modeling Combinatorial Optimization Problems

2013 ◽  
pp. 44-57
Author(s):  
Yuxin Ding
Keyword(s):  
Neural Networks ◽  
Combinatorial Optimization ◽  
Convergence Rates ◽  
Optimization Problems ◽  
High Order ◽  
Hopfield Network ◽  
Hopfield Networks ◽  
Combinatorial Optimization Problems ◽  
Complete Problems ◽  
Higher Order Neural Networks

Traditional Hopfield networking has been widely used to solve combinatorial optimization problems. However, high order Hopfiled networks, as an expansion of traditional Hopfield networks, are seldom used to solve combinatorial optimization problems. In theory, compared with low order networks, high order networks have better properties, such as stronger approximations and faster convergence rates. In this chapter, the authors focus on how to use high order networks to model combinatorial optimization problems. Firstly, the high order discrete Hopfield Network is introduced, then the authors discuss how to find the high order inputs of a neuron. Finally, the construction method of energy function and the neural computing algorithm are presented. In this chapter, the N queens problem and the crossbar switch problem, which are NP-complete problems, are used as examples to illustrate how to model practical problems using high order neural networks. The authors also discuss the performance of high order networks for modeling the two combinatorial optimization problems.

scholarly journals Combinatorial optimization by weight annealing in memristive hopfield networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Z. Fahimi ◽  
M. R. Mahmoodi ◽  
H. Nili ◽  
Valentin Polishchuk ◽  
D. B. Strukov
Keyword(s):  
Neural Network ◽  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Main Idea ◽  
Hopfield Neural Network ◽  
Combinatorial Problems ◽  
Hopfield Network ◽  
Global Minima ◽  
Mixed Signal ◽  
Combinatorial Optimization Problems

AbstractThe increasing utility of specialized circuits and growing applications of optimization call for the development of efficient hardware accelerator for solving optimization problems. Hopfield neural network is a promising approach for solving combinatorial optimization problems due to the recent demonstrations of efficient mixed-signal implementation based on emerging non-volatile memory devices. Such mixed-signal accelerators also enable very efficient implementation of various annealing techniques, which are essential for finding optimal solutions. Here we propose a “weight annealing” approach, whose main idea is to ease convergence to the global minima by keeping the network close to its ground state. This is achieved by initially setting all synaptic weights to zero, thus ensuring a quick transition of the Hopfield network to its trivial global minima state and then gradually introducing weights during the annealing process. The extensive numerical simulations show that our approach leads to a better, on average, solutions for several representative combinatorial problems compared to prior Hopfield neural network solvers with chaotic or stochastic annealing. As a proof of concept, a 13-node graph partitioning problem and a 7-node maximum-weight independent set problem are solved experimentally using mixed-signal circuits based on, correspondingly, a 20 × 20 analog-grade TiO2 memristive crossbar and a 12 × 10 eFlash memory array.

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.

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