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The presence of stochastic elements in combinatorial optimization problems makes them particularly challenging, as such problems quickly become intractable for classical computers even at relatively small sizes. In this work, we propose a…

The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…

Recent advances in the development of commercial quantum annealers such as the D-Wave 2X allow solving NP-hard optimization problems that can be expressed as quadratic unconstrained binary programs. However, the relatively small number of…

Quantum Physics · Physics 2018-02-01 Georg Hahn , Hristo N. Djidjev

Quadratic Unconstrained Binary Optimization (QUBO) is recognized as a unifying framework for modeling a wide range of problems. Problems can be solved with commercial solvers customized for solving QUBO and since QUBO have degree two, it is…

Optimization and Control · Mathematics 2021-07-27 Amit Verma , Mark Lewis , Gary Kochenberger

We present a novel quantum optimization-based route compression technique that significantly reduces storage requirements compared to conventional methods. Route optimization systems face critical challenges in efficiently storing selected…

Quantum Physics · Physics 2025-04-07 Shunsuke Sotobayashi , Yuichiro Minato , Takao Tomono

A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…

NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp's 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers…

Quantum Physics · Physics 2022-03-01 Elijah Pelofske , Georg Hahn , Hristo Djidjev

We propose an approach suitable for solving NP-complete problems via adiabatic quantum computation with an architecture based on a lattice of interacting spins (qubits) driven by locally adjustable effective magnetic fields. Interactions…

Quantum Physics · Physics 2007-05-23 S. Knysh , V. N. Smelyanskiy

Digital Annealer (DA) is a computer architecture designed for tackling combinatorial optimization problems formulated as quadratic unconstrained binary optimization (QUBO) models. In this paper, we present the results of an extensive…

Optimization and Control · Mathematics 2020-12-24 Oylum Şeker , Neda Tanoumand , Merve Bodur

We demonstrate that the search space of the quadratic assignment problem (QAP), known as an NP-hard combinatorial optimization problem, can be reduced using Grover adaptive search (GAS) with permutation preparation operator (PPO). To that…

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian…

Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that…

Quantum Physics · Physics 2026-01-01 Sascha Mücke , Thore Gerlach , Nico Piatkowski

Many computational problems involve optimization over discrete variables with quadratic interactions. Known as discrete quadratic models (DQMs), these problems in general are NP-hard. Accordingly, there is increasing interest in encoding…

Quantum Physics · Physics 2024-02-16 Tristan Zaborniak , Ulrike Stege

Demonstrating quantum advantage for combinatorial optimization requires more than standalone algorithmic results; it calls for end-to-end case studies that integrate problem modelling, quantum execution, and classical refinement into…

Ising machines, including quantum annealing machines, are promising next-generation computers for combinatorial optimization problems. However, due to hardware limitations, most Ising-type hardware can only solve objective functions…

Statistical Mechanics · Physics 2025-10-29 Kazuki Ikeuchi , Yoshiki Matsuda , Shu Tanaka

Understanding NP-complete problems is a central topic in computer science. This is why adiabatic quantum optimization has attracted so much attention, as it provided a new approach to tackle NP-complete problems using a quantum computer.…

Quantum Physics · Physics 2010-12-13 Boris Altshuler , Hari Krovi , Jeremie Roland

Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To…

Quantum Physics · Physics 2015-10-14 Walter Vinci , Tameem Albash , Gerardo Paz-Silva , Itay Hen , Daniel A. Lidar

In this paper, we present a brief review and introduction to Quadratic Unconstrained D-ary Optimization (QUDO), Tensor Quadratic Unconstrained D-ary Optimization (T-QUDO) and Higher-Order Unconstrained Binary Optimization (HOBO)…

Emerging Technologies · Computer Science 2026-05-04 Alejandro Mata Ali

We propose a scalable encoding of combinatorial optimization problems with arbitrary connectivity, including higher-order terms, on arrays of trapped neutral atoms requiring only a global laser drive. Our approach relies on modular…

Quantum Physics · Physics 2024-10-08 Martin Lanthaler , Kilian Ender , Clemens Dlaska , Wolfgang Lechner

We discuss several mappings from well-known NP-hard problems to Quadratic Unconstrained Binary Optimisation problems which are treated incorrectly by Lucas. We provide counterexamples and correct the mappings. We also extend the body of…

Data Structures and Algorithms · Computer Science 2020-08-04 Bas Lodewijks