scholarly journals Assessment of image generation by quantum annealer

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Takehito Sato ◽  
Masayuki Ohzeki ◽  
Kazuyuki Tanaka
Keyword(s):  
Machine Learning ◽  
Optimization Problems ◽  
A Priori ◽  
Monte Carlo Sampling ◽  
Boltzmann Distribution ◽  
Generative Model ◽  
Production Model ◽  
Boltzmann Machine ◽  
Quantum Annealing ◽  
Combinatorial Optimization Problems

AbstractQuantum annealing was originally proposed as an approach for solving combinatorial optimization problems using quantum effects. D-Wave Systems has released a production model of quantum annealing hardware. However, the inherent noise and various environmental factors in the hardware hamper the determination of optimal solutions. In addition, the freezing effect in regions with weak quantum fluctuations generates outputs approximately following a Gibbs–Boltzmann distribution at an extremely low temperature. Thus, a quantum annealer may also serve as a fast sampler for the Ising spin-glass problem, and several studies have investigated Boltzmann machine learning using a quantum annealer. Previous developments have focused on comparing the performance in the standard distance of the resulting distributions between conventional methods in classical computers and sampling by a quantum annealer. In this study, we focused on the performance of a quantum annealer as a generative model from a different aspect. To evaluate its performance, we prepared a discriminator given by a neural network trained on an a priori dataset. The evaluation results show a higher performance of quantum annealer compared with the classical approach for Boltzmann machine learning in training of the generative model. However the generation of the data suffers from the remanent quantum fluctuation in the quantum annealer. The quality of the generated images from the quantum annealer gets worse than the ideal case of the quantum annealing and the classical Monte-Carlo sampling.

scholarly journals A QUBO Formulation of Minimum Multicut Problem Instances in Trees for D-Wave Quantum Annealers

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
William Cruz-Santos ◽  
Salvador E. Venegas-Andraca ◽  
Marco Lanzagorta
Keyword(s):  
Optimization Problems ◽  
Theoretical Computer Science ◽  
Scaling Analysis ◽  
Quantum Annealing ◽  
Theoretical Computer ◽  
Combinatorial Optimization Problems ◽  
Hard Problems ◽  
Problem Instances ◽  
Annealing Algorithms ◽  
D Wave

AbstractQuantum annealing algorithms were introduced to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes typical of NP − hard problems. In this work, we propose using quantum annealing for the theory of cuts, a field of paramount importance in theoretical computer science. We have proposed a method to formulate the Minimum Multicut Problem into the QUBO representation, and the technical difficulties faced when embedding and submitting a problem to the quantum annealer processor. We show two constructions of the quadratic unconstrained binary optimization functions for the Minimum Multicut Problem and we review several tradeoffs between the two mappings and provide numerical scaling analysis results from several classical approaches. Furthermore, we discuss some of the expected challenges and tradeoffs in the implementation of our mapping in the current generation of D-Wave machines.

scholarly journals Reconfigurable Stochastic neurons based on tin oxide/MoS2 hetero-memristors for simulated annealing and the Boltzmann machine

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiaodong Yan ◽  
Jiahui Ma ◽  
Tong Wu ◽  
Aoyang Zhang ◽  
Jiangbin Wu ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Combinatorial Optimization ◽  
Tin Oxide ◽  
Optimization Problems ◽  
Process Efficiency ◽  
Np Hard ◽  
Boltzmann Machine ◽  
Combinatorial Optimization Problems ◽  
Cooling Strategies ◽  
Neuromorphic Hardware

AbstractNeuromorphic hardware implementation of Boltzmann Machine using a network of stochastic neurons can allow non-deterministic polynomial-time (NP) hard combinatorial optimization problems to be efficiently solved. Efficient implementation of such Boltzmann Machine with simulated annealing desires the statistical parameters of the stochastic neurons to be dynamically tunable, however, there has been limited research on stochastic semiconductor devices with controllable statistical distributions. Here, we demonstrate a reconfigurable tin oxide (SnOx)/molybdenum disulfide (MoS2) heterogeneous memristive device that can realize tunable stochastic dynamics in its output sampling characteristics. The device can sample exponential-class sigmoidal distributions analogous to the Fermi-Dirac distribution of physical systems with quantitatively defined tunable “temperature” effect. A BM composed of these tunable stochastic neuron devices, which can enable simulated annealing with designed “cooling” strategies, is conducted to solve the MAX-SAT, a representative in NP-hard combinatorial optimization problems. Quantitative insights into the effect of different “cooling” strategies on improving the BM optimization process efficiency are also provided.

scholarly journals Ising Model Optimization Problems on a FPGA Accelerated Restricted Boltzmann Machine

2020 ◽  
Author(s):  
Saavan Patel ◽  
Lili Chen ◽  
Philip Canoza ◽  
Sayeef Salahuddin
Keyword(s):  
Optimization Problems ◽  
Restricted Boltzmann Machine ◽  
Model Optimization ◽  
Boltzmann Machine ◽  
Stochastic Sampling ◽  
Combinatorial Optimization Problems ◽  
Field Programmable ◽  
Max Cut Problem ◽  
Asymptotic Scaling ◽  
Better Than

Abstract In this work we demonstrate usage of the Restricted Boltzmann Machine (RBM) as a stochastic neural network capable of solving NP-Hard Combinatorial Optimization problems efficiently. By mapping the RBM onto a reconfigurable Field Programmable Gate Array (FPGA), we can effectively hardware accelerate the RBM's stochastic sampling algorithm. We benchmark the RBM against the DWave 2000Q Quantum Adiabatic Computer and the Optical Coherent Ising Machine on two such optimization problems: the MAX-CUT problem and the Sherrington-Kirkpatrick (SK) spin glass. The hardware accelerated RBM shows asymptotic scaling either similar or better than these other accelerators. This leads to 107x and 105x time to solution improvement compared to the DWave 2000Q on the MAX-CUT and SK problems respectively, along with a 150x and 1000x improvement compared to the Coherent Ising Machine annealer on those problems. By utilizing commodity hardware running at room temperature, the RBM shows potential for immediate and scalable use.

scholarly journals New Directions in Streaming Algorithms

2020 ◽  
Author(s):  
Ali Vakilian
Keyword(s):  
Machine Learning ◽  
Combinatorial Optimization ◽  
Design Theory ◽  
Large Scale ◽  
Computational Models ◽  
Optimization Problems ◽  
Low Rank ◽  
Set Cover ◽  
Streaming Algorithms ◽  
Combinatorial Optimization Problems

Large volumes of available data have led to the emergence of new computational models for data analysis. One such model is captured by the notion of streaming algorithms: given a sequence of N items, the goal is to compute the value of a given function of the input items by a small number of passes and using a sublinear amount of space in N. Streaming algorithms have applications in many areas such as networking and large scale machine learning. Despite a huge amount of work on this area over the last two decades, there are multiple aspects of streaming algorithms that remained poorly understood, such as (a) streaming algorithms for combinatorial optimization problems and (b) incorporating modern machine learningtechniques in the design of streaming algorithms. In the first part of this thesis, we will describe (essentially) optimal streaming algorithms for set cover and maximum coverage, two classic problems in combinatorial optimization. Next, in the second part, we will show how to augment classic streaming algorithms of the frequency estimation and low-rank approximation problems with machine learning oracles in order to improve their space-accuracy tradeoffs. The new algorithms combine the benefits of machine learning with the formal guarantees available through algorithm design theory.

The Two Step Mutation Evolutionary Programming Using in Image Segmentation

2012 ◽  
Vol 433-440 ◽  
pp. 5459-5462
Author(s):  
Fang Liu
Keyword(s):  
Image Segmentation ◽  
Convergence Rates ◽  
Optimization Problems ◽  
A Priori ◽  
Algorithm Design ◽  
Evolutionary Programming ◽  
Image Resolution ◽  
Function Optimization ◽  
Combinatorial Optimization Problems ◽  
Whole Space

Image segmentation is an important task in image analysis and processing. Many of the existing methods for segmenting a multi-component image (satellite or aerial) are very slow and require a priori knowledge of the image that could be difficult to obtain. Furthermore, the success of each of these methods depends on several factors, such as the characteristics of the acquired image, resolution limitations, intensity in-homogeneities and the percentage of imperfections induced by the process of image acquisition. Evolutionary programming(EP) has been applied with success to many numerical and combinatorial optimization problems in recent years. EP has rather slow convergence rates, however, on some function optimization problems. In this paper the new evolutionary programming is proposed to overcome the premature convergence. There are two step mutation in the new evolutionary programming. The first step is responsible for searching the whole space. The second is responsible for searching the local part in detail. The cooperation and specialization between different two step mutation are considered during the algorithm design. The new evolutionary programming can use in image segmentation and the experimental results show the new evolutionary programming is efficient.

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