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About 1,241 papers for “Quadratic unconstrained binary optimization”

Goal seeking Quadratic Unconstrained Binary Optimization

Amit Verma, Mark A. Lewis · Results in Control and Optimization · 2022

The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In order to incorporate the problem-specific insights, a diverse set of solutions meeting an acceptable target metric or goal is the preference in high level decision making. In this paper, we present two alternatives for goal-seeking QUBO for minimizing the deviation from a given target as well as a range of values around a target. Experimental results illustrate the efficacy of the proposed approach over Constraint Programming for quickly finding a satisficing set of solutions.

Cited by 7Open access

Extremal Optimization for Quadratic Unconstrained Binary Problems

Stefan Boettcher · Physics Procedia · 2015

We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.

Cited by 3Open access

Quadratic Unconstrained Binary Optimization via Quantum-Inspired Annealing

Joseph Bowles, Alexandre Dauphin, Patrick Huembeli et al. · Physical Review Applied · 2022

We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimization. The algorithm can be seen as an analog of quantum annealing under the restriction of a product-state space, where the dynamical evolution in quantum annealing is replaced with a gradient-descent-based method. This formulation is able to quickly find high-quality solutions to large-scale problem instances and can naturally be accelerated by dedicated hardware such as graphics processing units. We benchmark our approach for large-scale problem instances with tunable hardness and planted solutions. We find that our algorithm offers a similar performance to current state-of-the-art approaches within a comparably simple gradient-based and nonstochastic setting.

Cited by 17

A Collaborative Neurodynamic Algorithm for Quadratic Unconstrained Binary Optimization

Hongzong Li, Jun Wang · IEEE Transactions on Emerging Topics in Computational Intelligence · 2024

Quadratic unconstrained binary optimization (QUBO) is a typical combinatorial optimization problem with widespread applications in science, engineering, and business. As QUBO problems are usually NP-hard, conventional QUBO algorithms are very time-consuming for solving large-scale QUBO problems. In this paper, we present a collaborative neurodynamic optimization algorithm for QUBO. In the proposed algorithm, multiple discrete Hopfield networks, Boltzmann machines, or their variants are employed for scattered searches, and a particle swarm optimization rule is used to re-initialize neuronal states repeatedly toward global optima. With extensive experimental results on four classic combinatorial optimization problems, we demonstrate the efficacy and potency of the algorithm against several prevailing exact and meta-heuristic algorithms.

Cited by 10

On the hardness of quadratic unconstrained binary optimization problems

Vrinda Mehta, Fengping Jin, Kristel Michielsen et al. · Frontiers in Physics · 2022

We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments with the D-Wave Advantage 5.1 quantum annealer, solving many instances of up to 170-variable, quadratic unconstrained binary optimization problems. Our results demonstrate that the exponents characterizing the success probability of a D-Wave annealer to solve a quadratic unconstrained binary optimization correlate very well with the predictions based on the Hamming distance distributions computed for small problem instances.

Cited by 8Open access

On the hardness of quadratic unconstrained binary optimization problems

Vrinda Mehta, Fengping Jin, Kristel Michielsen et al. · arXiv (Cornell University) · 2022

We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments with the D-Wave Advantage 5.1 quantum annealer, solving many instances of up to 170-variable, quadratic unconstrained binary optimization problems. Our results demonstrate that the exponents characterizing the success probability of a D-Wave annealer to solve a QUBO correlate very well with the predictions based on the Hamming distance distributions computed for small problem instances.

Cited by 0Open access

A Multilevel Algorithm for Large Unconstrained Binary Quadratic Optimization

Yang Wang, Fred Glover, Jin‐Kao Hao · 2016

Abstract. The unconstrained binary quadratic programming (UBQP) problem is a general NP-hard problem with various applications. In this paper, we present a multilevel algorithm designed to approximate large UBQP instances. The proposed multilevel algorithm is composed of a backbone-based coarsening phase, an asymmetric uncoarsening phase and a memetic refinement phase, where the backbone-based procedure and the memetic refinement procedure make use of tabu search to obtain improved solutions. Evaluated on a set of 11 largest instances from the literature (with 5000 to 7000 variables), the proposed algorithm proves to be able to attain all the best known values with a computing effort less than any existing approach.

Cited by 1

Rydberg-atom graphs for quadratic unconstrained binary optimization problems

Andrew Byun, Junwoo Jung, Kangheun Kim et al. · Figshare · 2023

The result of adiabatic quantum computation of the Rydberg-atom graph which represents quadratic unbounded binary optimization(QUBO).The ordering of the atoms follows the figures in the paper.Each .csv file contains the N-by-M matrix: the number of qubits(N) and the number of experiments(M).

Cited by 0Open access

A Quadratic Unconstrained Binary Optimization Approach for Qubit Mapping

Prielinger, Luise · reposiTUm (TU Wien) · 2023

Logische Bitoperationen sind die Grundbausteine von Computer Software. Hierbei werden Bits manipuliert, um verschiedene Aufgaben auszuführen, beispielsweise bitweise AND-, OR-, XOR- und NOT-Operationen. Dies ist der Quantensoftware sehr ähnlich. Hier werden sogenannte Quantum Gates - die Quantengegenstücke von klassischen Bitoperationen - zur Manipulation von Quantenbits, der kleinsten Einheit der Quanteninformation, verwendet.Die Zuordnung von logischen Qubits in einem Quantenprogramm zu den physischen Qubits eines Quantencomputers wird als Qubit-Mapping bezeichnet. Dieser Schritt ist Teil der Kompilierung eines Quantenprogramms und daher Vorraussetung für die Ausführbarkeit jedes Quantenprogramms auf einem Quantencomputer. Während dieses Mapping-Schritts werden zusätzliche Operationen in das Programm eingebaut, die für die Ausführbarkeit des Programms notwendig sind. Da Quantencomputer aktuell eine sehr begrenzte Rechenleistung haben, ist das Ziel so wenig zusätzliche Operationen wie möglich in das Quantenprogramm durch das Mapping einzubauen. Das Qubit-Mapping Problem beschreibt das Optimierungsproblem, welches diese notwendigen zusätzlichen Operationen minimiert.Es wird in dieser Arbeit eine neue Methode zur Lösung des Qubit-Mapping Problems vorgestellt, die auf quadratischer unbeschränkter binärer Optimierung und einem evolutionären Algorithmus basiert. Der Ansatz erzielt für eine Reihe von Quantenprogrammen signifikant bessere Lösungen zu aktuellen Mapping-Algorithmen.

Cited by 0Open access

Quadratic Unconstrained Binary Optimization (QUBO) on neuromorphic computing system

Md Zahangir Alom, Brian Van Essen, Adam Moody et al. · 2017

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.

Cited by 39

High‐throughput FPGA implementation for quadratic unconstrained binary optimization

Hiroshi Kagawa, Yasuaki Ito, Koji Nakano et al. · Concurrency and Computation Practice and Experience · 2021

Abstract Quadratic unconstrained binary optimization (QUBO) is a combinatorial optimization problem. Since various NP‐hard problems such as the traveling salesman problem can be formulated as a QUBO instance, QUBO is used with a wide range of applications. The main contribution of this article is to propose high‐throughput FPGA implementations for the QUBO solver. We perform the local search using different bit‐selection strategies based on the simulated annealing in the proposed implementation. The hardware is a pipeline structure with no pipeline hazards using multiple instances, where the bit‐flip operation is always performed every clock cycle. We implemented the proposed circuit on Xilinx UltraScale+ FPGA VU9P. The implementation result shows that the circuit can search solutions per second. Besides, by sharing the block RAM that stores a weight matrix, we implemented a dual annealer architecture that has two QUBO solvers into the FPGA. As a result, the dual annealer architecture can search solutions per second.

Cited by 13

Decoding of Polar Codes Using Quadratic Unconstrained Binary Optimization

Huayi Zhou, Ryan Seah, Marwan Jalaleddine et al. · IEEE Journal on Selected Areas in Communications · 2024

Polar codes encounter challenges in decoder complexity while preserving good error-correction properties. Instead of conventional decoders, a quantum annealer (QA) decoder has been proposed to explore untapped possibilities. For future QA applications, a crucial prerequisite is transforming the optimization problem into quadratic unconstrained binary optimization (QUBO) form. However, existing QUBO forms for polar decoding result in suboptimal frame error rate (FER) performance for codes exceeding 8 bits. This paper redesigns the QUBO form for polar decoding. We first introduce a novel receiver constraint modeled by the binary cross-entropy (BCE) function. Utilizing a simulated annealing (SA) solver with the proposed QUBO form with BCE (QUBO-BCE) achieves maximum-likelihood (ML) performance for a code length of 32 bits. Next, to reduce the number of variables, we remove the frozen variables and introduce a simplified QUBO-BCE form (SQUBO-BCE). Additionally, CRC polynomials are modelled into constraints in QUBO form, resulting in a CRC-aided SQUBO-BCE (CA-SQUBO-BCE) form for polar decoding to further enhance the FER. Numerical results demonstrate that SQUBO-BCE achieves ML performance and reduces up to 61.5% of variables compared to QUBO-BCE. Furthermore, the proposed CA-SQUBO-BCE achieves near CRC-aided ML performance. The proposed SQUBO-BCE requires the lowest number of SA processes to reach a specific FER.

Cited by 0

Rydberg-atom graphs for quadratic unconstrained binary optimization problems

Byun, Andrew, Jung, Junwoo, Kim, Kangheun et al. · Figshare · 2023

The result of adiabatic quantum computation of the Rydberg-atom graph which represents quadratic unbounded binary optimization(QUBO).The ordering of the atoms follows the figures in the paper.Each .csv file contains the N-by-M matrix: the number of qubits(N) and the number of experiments(M).

Cited by 0Open access

Rydberg‐Atom Graphs for Quadratic Unconstrained Binary Optimization Problems

Andrew Byun, Junwoo Jung, Kangheun Kim et al. · Advanced Quantum Technologies · 2024

Abstract There is a growing interest in harnessing the potential of the Rydberg‐atom system to address complex combinatorial optimization challenges. Here an experimental demonstration of how the quadratic unconstrained binary optimization (QUBO) problem can be effectively addressed using Rydberg‐atom graphs is presented. The Rydberg‐atom graphs are configurations of neutral atoms organized into mathematical graphs, facilitated by programmable optical tweezers, and designed to exhibit many‐body ground states that correspond to the maximum independent set (MIS) of their respective graphs. Four elementary Rydberg‐atom subgraph components are developed, not only to eliminate the need of local control but also to be robust against interatomic distance errors, while serving as the building blocks sufficient for formulating generic QUBO graphs. To validate the feasibility of the approach, a series of Rydberg‐atom experiments selected to demonstrate proof‐of‐concept operations of these building blocks are conducted. These experiments illustrate how these components can be used to programmatically encode the QUBO problems to Rydberg‐atom graphs and, by measuring their many‐body ground states, how their QUBO solutions are determined subsequently.

Cited by 13Open access