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In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms…

Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and…

Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable…

Discrete Mathematics · Computer Science 2020-02-11 Fred Glover , Gary Kochenberger , Moses Ma , Yu Du

The simulation of quantum dynamics on a digital quantum computer with parameterized circuits has widespread applications in fundamental and applied physics and chemistry. In this context, using the hybrid quantum-classical algorithm,…

Quantum Physics · Physics 2023-07-19 Tangyou Huang , Yongcheng Ding , Léonce Dupays , Yue Ban , Man-Hong Yung , Adolfo del Campo , Xi Chen

Hybrid solvers for combinatorial optimization problems combine the advantages of classical and quantum computing to overcome difficult computational challenges. Although their theoretical performance seems promising, their practical…

Quantum Physics · Physics 2025-07-14 Domenik Eichhorn , Nick Poser , Maximilian Schweikart , Ina Schaefer

Combinatorial optimization is widely regarded as a primary application for near-term quantum processors, although a definitive demonstration of the practical quantum advantage remains elusive. Recent studies have reported that both…

Quantum Physics · Physics 2026-05-21 Xian-Zhe Tao , Pavel Mosharev , Man-Hong Yung

Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…

Quantum Physics · Physics 2026-04-17 Bao Bach , Cameron Ibrahim , Reuben Tate , Jad Salem , Stephan Eidenbenz , Ilya Safro

The Quantum Approximate Optimization Algorithm (QAOA) requires considered optimization problems to be translated into a compatible format. A popular transformation step in this pipeline involves the quadratization of higher-order binary…

Quantum Physics · Physics 2025-11-26 Damian Rovara , Lukas Burgholzer , Robert Wille

We propose and experimentally demonstrate sequential quantum computing (SQC), a paradigm that utilizes multiple homogeneous or heterogeneous quantum processors in hybrid classical-quantum workflows. In this manner, we are able to overcome…

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…

Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…

Quantum Physics · Physics 2022-08-25 Libor Caha , Alexander Kliesch , Robert Koenig

Discrete combinatorial optimization consists in finding the optimal configuration that minimizes a given discrete objective function. An interpretation of such a function as the energy of a classical system allows us to reduce the…

Quantum Physics · Physics 2015-06-22 Sergio Boixo , Gerardo Ortiz , Rolando Somma

The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…

Quantum Physics · Physics 2020-04-21 Edward Farhi , David Gamarnik , Sam Gutmann

Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not…

Optimization and Control · Mathematics 2022-10-11 Byron Tasseff , Tameem Albash , Zachary Morrell , Marc Vuffray , Andrey Y. Lokhov , Sidhant Misra , Carleton Coffrin

Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum…

Recently, quantum computing has gained attention in urban studies as a tool for complex transport planning problems, but its role remains unclear. This paper reviews quantum computing research in urban transport planning and highlights…

Optimization and Control · Mathematics 2026-04-06 Junxiang Xu , Chence Niu , Divya Jayakumar Nair , Vinayak Dixit

In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs.…

Quantum Physics · Physics 2024-05-01 Danylo Lykov , Jonathan Wurtz , Cody Poole , Mark Saffman , Tom Noel , Yuri Alexeev

In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among…

There is a large ongoing research effort towards obtaining a quantum advantage in the solution of combinatorial optimization problems on near-term quantum devices. A particularly promising platform for testing and developing quantum…

Major players in the global aerospace industry are shifting their focus toward achieving net carbon-neutral operations by 2050. A considerable portion of the overall carbon emission reduction is expected to come from new aircraft…

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