Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Joint Conference on Neural Networks (IJCNN)

Quadratic Unconstrained Binary Optimization (QUBO) on neuromorphic computing system

Md Zahangir Alom, Brian Van Essen, Adam T. Moody, David Peter Widemann, Tarek M. Taha

Published May 1, 2017• 38 citations
Publisher

Abstract

The problems of Artificial intelligence (AI) naturally maps to NP-hard optimization problems. This trend has significance to achieve human-level computation capability from machines. This computational ability can be achieved by developing evolutionary algorithms or mapping those evolutionary algorithms onto new generation computing systems: Quantum or Neuromorphic hardware. In this paper, we implemented the NP-hard optimization problem called Quadratic Unconstrained Binary Optimization (QUBO) problem for the solution of graph problems on the IBM's Neurosynaptic TrueNorth System. We have experimented on different types of graph problems with different levels of complexities and achieved encouraging results on IBM's Neuromorphic TrueNorth chip. Moreover, there are a set of potential applications have been discussed based on this proposed QUBO solution. Along with the QUBO on quantum annealing, it is the important first step towards the solutions of QUBO on Neuromorphic computing systems.

DOI
10.1109/ijcnn.2017.7966350

Related papers

A Tutorial on Formulating and Using QUBO Models

Fred Glover, Gary A. Kochenberger, Yu Du

The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and has become a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart of experimentation carried out with quantum computers developed by D-Wave Systems and neuromorphic computers developed by IBM. Computational experience is being amassed by both the classical and the quantum computing communities that highlights not only the potential of the QUBO model but also its effectiveness as an alternative to traditional modeling and solution methodologies. This tutorial discloses the basic features of the QUBO model that give it the power and flexibility to encompass the range of applications that have thrust it onto center stage of the optimization field. We show how many different types of constraining relationships arising in practice can be embodied within the "unconstrained" QUBO formulation in a very natural manner using penalty functions, yielding exact model representations in contrast to the approximate representations produced by customary uses of penalty functions. Each step of generating such models is illustrated in detail by simple numerical examples, to highlight the convenience of using QUBO models in numerous settings. We also describe recent innovations for solving QUBO models that offer a fertile avenue for integrating classical and quantum computing and for applying these models in machine learning.

arXiv:1811.11538•Nov 13, 2018•164 citations

Logical and Inequality Implications for Reducing the Size and Complexity of Quadratic Unconstrained Binary Optimization Problems

Fred Glover, Mark W. Lewis, Gary A. Kochenberger

The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to transform the graph representing the QUBO problem into a smaller equivalent graph is important for improving solution quality and time for both exact and metaheuristic algorithms and is a step towards mapping large scale QUBO to hardware graphs used in quantum annealing computers. In an earlier paper (Lewis and Glover, 2016) a set of rules was introduced that achieved significant QUBO reductions as verified through computational testing. Here this work is extended with additional rules that provide further reductions that succeed in exactly solving 10% of the benchmark QUBO problems. An algorithm and associated data structures to efficiently implement the entire set of rules is detailed and computational experiments are reported that demonstrate their efficacy.

arXiv:1705.09545•May 26, 2017•0 citations

Design and FPGA Realization of QUBO hardware accelerator for MAX-CUT problem

Maciej Lewandowski, Piotr Dudek

Combinatorial optimization problems are fundamental to many industrial and scientific applications, but are often NP-hard, requiring heuristic and probabilistic approaches to find good solutions fast. This paper presents the first hardware implementation of the neuromorphic-inspired NeuroSA algorithm, for accelerating Quadratic Unconstrained Binary Optimization (QUBO) problems. We show that it is possible to run a standard QUBO benchmark problem with 800 variables on a low-cost FPGA with a clock speed of approximately 144 MHz, which converges to the same solution value found by the numerical solver.

IEEE International Symposium on Circuits and Systems proceedings•May 25, 2025•2 citations

Image recognition with an adiabatic quantum computer I. Mapping to quadratic unconstrained binary optimization

Hartmut Neven, Geordie Rose, William G. Macready

Many artificial intelligence (AI) problems naturally map to NP-hard optimization problems. This has the interesting consequence that enabling human-level capability in machines often requires systems that can handle formally intractable problems. This issue can sometimes (but possibly not always) be resolved by building special-purpose heuristic algorithms, tailored to the problem in question. Because of the continued difficulties in automating certain tasks that are natural for humans, there remains a strong motivation for AI researchers to investigate and apply new algorithms and techniques to hard AI problems. Recently a novel class of relevant algorithms that require quantum mechanical hardware have been proposed. These algorithms, referred to as quantum adiabatic algorithms, represent a new approach to designing both complete and heuristic solvers for NP-hard optimization problems. In this work we describe how to formulate image recognition, which is a canonical NP-hard AI problem, as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The QUBO format corresponds to the input format required for D-Wave superconducting adiabatic quantum computing (AQC) processors.

arXiv:0804.4457•Apr 28, 2008•55 citations

Solving QUBO on the Loihi 2 Neuromorphic Processor

A.R. De Pierro, Philipp Stratmann, G. A. Fonseca Guerra +4 more

In this article, we describe an algorithm for solving Quadratic Unconstrained Binary Optimization problems on the Intel Loihi 2 neuromorphic processor. The solver is based on a hardware-aware fine-grained parallel simulated annealing algorithm developed for Intel's neuromorphic research chip Loihi 2. Preliminary results show that our approach can generate feasible solutions in as little as 1 ms and up to 37x more energy efficient compared to two baseline solvers running on a CPU. These advantages could be especially relevant for size-, weight-, and power-constrained edge computing applications.

arXiv:2408.03076•Aug 6, 2024•2 citations

Quantum Artificial Intelligence for Natural Language Processing Applications

Ramin Ayanzadeh

Natural Language Processing and Semantic Web include several NP complete/hard problems that are intractable for classical computing machines. Even though distributed computing has provided remarkable advances (more precisely in dealing with big data), non-decomposable NP problems are still intractable in many real-world applications. And, from quantum computing perspective, solving complex problems with universal quantum gates requires developing of quantum algorithms. Considering commercializing quantum annealing machines by D-Wave, achieving global optimum for discrete optimization problems has been realized. In this study, a novel approach has been introduced to convert symbolic AI problems into quadratic unconstrained binary optimization (QUBO) form. More narrowly, this method represents classification of text documents (fragments) as optimizing a QUBO function. After embedding the train corpus into a QUBO function, D-Wave quantum annealer is used to classify new observations with finding the minimum energy level of the system.

ACM Technical Symposium on Computer Science Education (SIGCSE)•Feb 21, 2018•2 citations
The problems of Artificial intelligence (AI) naturally maps to NP-hard optimization problems. This trend has significance to achieve human-level computation capability from machines. This computational ability can be achieved by developing evolutionary algorithms or mapping those evolutionary algorithms onto new generation computing systems: Quantum or Neuromorphic hardware. In this paper, we implemented the NP-hard optimization problem called Quadratic Unconstrained Binary Optimization (QUBO) problem for the solution of graph problems on the IBM's Neurosynaptic TrueNorth System. We have experimented on different types of graph problems with different levels of complexities and achieved encouraging results on IBM's Neuromorphic TrueNorth chip. Moreover, there are a set of potential applications have been discussed based on this proposed QUBO solution. Along with the QUBO on quantum annealing, it is the important first step towards the solutions of QUBO on Neuromorphic computing systems.
The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and has become a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart of experimentation carried out with quantum computers developed by D-Wave Systems and neuromorphic computers developed by IBM. Computational experience is being amassed by both the classical and the quantum computing communities that highlights not only the potential of the QUBO model but also its effectiveness as an alternative to traditional modeling and solution methodologies. This tutorial discloses the basic features of the QUBO model that give it the power and flexibility to encompass the range of applications that have thrust it onto center stage of the optimization field. We show how many different types of constraining relationships arising in practice can be embodied within the "unconstrained" QUBO formulation in a very natural manner using penalty functions, yielding exact model representations in contrast to the approximate representations produced by customary uses of penalty functions. Each step of generating such models is illustrated in detail by simple numerical examples, to highlight the convenience of using QUBO models in numerous settings. We also describe recent innovations for solving QUBO models that offer a fertile avenue for integrating classical and quantum computing and for applying these models in machine learning.
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to transform the graph representing the QUBO problem into a smaller equivalent graph is important for improving solution quality and time for both exact and metaheuristic algorithms and is a step towards mapping large scale QUBO to hardware graphs used in quantum annealing computers. In an earlier paper (Lewis and Glover, 2016) a set of rules was introduced that achieved significant QUBO reductions as verified through computational testing. Here this work is extended with additional rules that provide further reductions that succeed in exactly solving 10% of the benchmark QUBO problems. An algorithm and associated data structures to efficiently implement the entire set of rules is detailed and computational experiments are reported that demonstrate their efficacy.
Combinatorial optimization problems are fundamental to many industrial and scientific applications, but are often NP-hard, requiring heuristic and probabilistic approaches to find good solutions fast. This paper presents the first hardware implementation of the neuromorphic-inspired NeuroSA algorithm, for accelerating Quadratic Unconstrained Binary Optimization (QUBO) problems. We show that it is possible to run a standard QUBO benchmark problem with 800 variables on a low-cost FPGA with a clock speed of approximately 144 MHz, which converges to the same solution value found by the numerical solver.
Many artificial intelligence (AI) problems naturally map to NP-hard optimization problems. This has the interesting consequence that enabling human-level capability in machines often requires systems that can handle formally intractable problems. This issue can sometimes (but possibly not always) be resolved by building special-purpose heuristic algorithms, tailored to the problem in question. Because of the continued difficulties in automating certain tasks that are natural for humans, there remains a strong motivation for AI researchers to investigate and apply new algorithms and techniques to hard AI problems. Recently a novel class of relevant algorithms that require quantum mechanical hardware have been proposed. These algorithms, referred to as quantum adiabatic algorithms, represent a new approach to designing both complete and heuristic solvers for NP-hard optimization problems. In this work we describe how to formulate image recognition, which is a canonical NP-hard AI problem, as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The QUBO format corresponds to the input format required for D-Wave superconducting adiabatic quantum computing (AQC) processors.
In this article, we describe an algorithm for solving Quadratic Unconstrained Binary Optimization problems on the Intel Loihi 2 neuromorphic processor. The solver is based on a hardware-aware fine-grained parallel simulated annealing algorithm developed for Intel's neuromorphic research chip Loihi 2. Preliminary results show that our approach can generate feasible solutions in as little as 1 ms and up to 37x more energy efficient compared to two baseline solvers running on a CPU. These advantages could be especially relevant for size-, weight-, and power-constrained edge computing applications.
Natural Language Processing and Semantic Web include several NP complete/hard problems that are intractable for classical computing machines. Even though distributed computing has provided remarkable advances (more precisely in dealing with big data), non-decomposable NP problems are still intractable in many real-world applications. And, from quantum computing perspective, solving complex problems with universal quantum gates requires developing of quantum algorithms. Considering commercializing quantum annealing machines by D-Wave, achieving global optimum for discrete optimization problems has been realized. In this study, a novel approach has been introduced to convert symbolic AI problems into quadratic unconstrained binary optimization (QUBO) form. More narrowly, this method represents classification of text documents (fragments) as optimizing a QUBO function. After embedding the train corpus into a QUBO function, D-Wave quantum annealer is used to classify new observations with finding the minimum energy level of the system.