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

Bulletin of the American Physical Society

An Approach for Combinatorial Optimization on Noisy Quantum Computers

Xiaoyuan Liu, Anthony Angone, Ruslan Shaydulin, Ilya Safro, Yuri Alexeev, Łukasz Cincio

Published Mar 16, 2021• 0 citations
OpenAlex

Related papers

Combinatorial Optimization and Quantum Computers

Alexandre Gondran, Michel Gondran

•Feb 7, 2020•0 citations

Combinatorial optimization with variational approaches on noisy quantum devices

Tsukasa Miki, Ryo Okita, Moe Shimada +1 more

Variational quantum eigensolver (VQE), a kind of quantum-classical hybrid method, has latent powers to leverage noisy quantum devices by effectively managing a limited number of qubits with finite coherent times. We implemented VQE with real quantum processors through IBM Quantum Experience and applied it to combinatorial optimizations. Notably, a short-depth quantum circuit consisting of a lower number of quantum gate than that in the quantum approximate optimization algorithm can search the ground states of diagonal Hamiltonians encoding the problems. Since the simplest case of the quantum circuit for VQE requires only single-qubit gates, it can be realized using current quantum computers.

IEEE International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale (3M-NANO)•Aug 2, 2021•1 citation

A Review on Quantum Circuit Optimization using ZX-Calculus

Tobias Fischbach, Talbot, Pierre, Pascal Bouvry

Quantum computing promises significant speed-ups for certain algorithms but the practical use of current noisy intermediate-scale quantum (NISQ) era computers remains limited by resources constraints (e.g., noise, qubits, gates, and circuit depth). Quantum circuit optimization is a key mitigation strategy. In this context, ZX-calculus has emerged as an alternative framework that allows for semantics-preserving quantum circuit optimization. We review ZX-based optimization of quantum circuits, categorizing them by optimization techniques, target metrics and intended quantum computing architecture. In addition, we outline critical challenges and future research directions, such as multi-objective optimization, scalable algorithms, and enhanced circuit extraction methods. This survey is valuable for researchers in both combinatorial optimization and quantum computing. For researchers in combinatorial optimization, we provide the background to understand a new challenging combinatorial problem: ZX-based quantum circuit optimization. For researchers in quantum computing, we classify and explain existing circuit optimization techniques.

arXiv:2509.20663•Sep 25, 2025•0 citations

Toward Quantum Combinatorial Optimization

Yunpyo Hong, Jaejoon Gill, Daeyeun Kim +3 more

IEEE Nanotechnology Magazine•Jan 1, 2026•0 citations

Variational Quantum Algorithms for Combinatorial Optimization

Daniel F. Pérez-Ramírez

The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of quantum computing, denominated Noisy Intermediate-Scale Quantum (NISQ) era, has introduced algorithms and methods that are able to harness the computational power of current quantum computers with advantages over classical computers (referred to as quantum advantage). Achieving quantum advantage is of particular relevance for the combinatorial optimization domain, since it often implies solving an NP-Hard optimization problem. Moreover, combinatorial problems are highly relevant for practical application areas, such as operations research, or resource allocation problems. Among quantum computing methods, Variational Quantum Algorithms (VQA) have emerged as one of the strongest candidates towards reaching practical applicability of NISQ systems. This paper explores the current state and recent developments of VQAs, emphasizing their applicability to combinatorial optimization. We identify the Quantum Approximate Optimization Algorithm (QAOA) as the leading candidate for these problems. Furthermore, we implement QAOA circuits with varying depths to solve the MaxCut problem on graphs with 10 and 20 nodes, demonstrating the potential and challenges of using VQAs in practical optimization tasks. We release our code, dataset and optimized circuit parameters under https://github.com/DanielFPerez/VQA-for-MaxCut.

arXiv:2407.06421•Jul 8, 2024•3 citations

Quantum approximate optimization for combinatorial problems with constraints

Yue Ruan, Zhiqiang Yuan, Xiling Xue +1 more

Information Sciences•Nov 11, 2022•24 citations
Variational quantum eigensolver (VQE), a kind of quantum-classical hybrid method, has latent powers to leverage noisy quantum devices by effectively managing a limited number of qubits with finite coherent times. We implemented VQE with real quantum processors through IBM Quantum Experience and applied it to combinatorial optimizations. Notably, a short-depth quantum circuit consisting of a lower number of quantum gate than that in the quantum approximate optimization algorithm can search the ground states of diagonal Hamiltonians encoding the problems. Since the simplest case of the quantum circuit for VQE requires only single-qubit gates, it can be realized using current quantum computers.
Quantum computing promises significant speed-ups for certain algorithms but the practical use of current noisy intermediate-scale quantum (NISQ) era computers remains limited by resources constraints (e.g., noise, qubits, gates, and circuit depth). Quantum circuit optimization is a key mitigation strategy. In this context, ZX-calculus has emerged as an alternative framework that allows for semantics-preserving quantum circuit optimization. We review ZX-based optimization of quantum circuits, categorizing them by optimization techniques, target metrics and intended quantum computing architecture. In addition, we outline critical challenges and future research directions, such as multi-objective optimization, scalable algorithms, and enhanced circuit extraction methods. This survey is valuable for researchers in both combinatorial optimization and quantum computing. For researchers in combinatorial optimization, we provide the background to understand a new challenging combinatorial problem: ZX-based quantum circuit optimization. For researchers in quantum computing, we classify and explain existing circuit optimization techniques.
The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of quantum computing, denominated Noisy Intermediate-Scale Quantum (NISQ) era, has introduced algorithms and methods that are able to harness the computational power of current quantum computers with advantages over classical computers (referred to as quantum advantage). Achieving quantum advantage is of particular relevance for the combinatorial optimization domain, since it often implies solving an NP-Hard optimization problem. Moreover, combinatorial problems are highly relevant for practical application areas, such as operations research, or resource allocation problems. Among quantum computing methods, Variational Quantum Algorithms (VQA) have emerged as one of the strongest candidates towards reaching practical applicability of NISQ systems. This paper explores the current state and recent developments of VQAs, emphasizing their applicability to combinatorial optimization. We identify the Quantum Approximate Optimization Algorithm (QAOA) as the leading candidate for these problems. Furthermore, we implement QAOA circuits with varying depths to solve the MaxCut problem on graphs with 10 and 20 nodes, demonstrating the potential and challenges of using VQAs in practical optimization tasks. We release our code, dataset and optimized circuit parameters under https://github.com/DanielFPerez/VQA-for-MaxCut.