Auxiliary-Qubit-Free Quantum Approximate Optimization Algorithm for the Minimum Dominating Set Problem

• URL: http://arxiv.org/abs/2509.16653v1
• Date: Sat, 20 Sep 2025 12:01:57 GMT
• Title: Auxiliary-Qubit-Free Quantum Approximate Optimization Algorithm for the Minimum Dominating Set Problem
• Authors: Guanghui Li, Xiaohui Ni, Junjian Su, Sujuan Qin, Fenzhuo Guo, Bingjie Xu, Wei Huang, Fei Gao,
• Abstract summary: We present an auxiliary-qubit-free Quantum Approximate Optimization Algorithm (QAOA) for the Minimum Dominating Set (MDS) problem.<n>Our algorithm achieves comparable performance to the existing best QAOA for this problem while using fewer qubits.<n>An ablation study based on multi-angle QAOA reveals that the solution quality of the algorithm can be further improved by replacing shared circuit parameters with independent ones.
• Score: 6.467872637658972
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum Approximate Optimization Algorithm (QAOA) is a promising framework for solving combinatorial optimization problems on near-term quantum devices. One such problem is the Minimum Dominating Set (MDS), which is NP-hard in graph theory. Existing QAOA studies for the MDS problem typically require a large number of auxiliary qubits, which increases hardware demands and hinders scalability on Noisy Intermediate-Scale Quantum (NISQ) devices. In this paper, we propose an auxiliary-qubit-free QAOA for the MDS problem. Unlike previous studies that introduce auxiliary variables to convert inequality constraints into equalities, our algorithm utilizes Boolean algebra to perform this transformation, eliminating the need for auxiliary qubits. Numerical experiments demonstrate that our algorithm achieves comparable performance to the existing best QAOA for this problem while using fewer qubits. Additionally, an ablation study based on multi-angle QAOA reveals that the solution quality of the algorithm can be further improved by replacing shared circuit parameters with independent ones.

Related papers

• A Non-Variational Quantum Approach to the Job Shop Scheduling Problem [0.3078691410268859]
  We introduce Iterative-QAOA, a variant of QAOA designed to mitigate near-term hardware limitations.<n>We benchmark the algorithm on Just-in-Time Job Shop Scheduling Problem (JIT-JSSP) instances on IonQ Forte Generation QPUs.<n>We find that Iterative-QAOA robustly converges to find optimal solutions as well as high-quality, near-optimal solutions for all problem instances evaluated.
  arXiv  Detail & Related papers  (2025-10-30T16:14:13Z)
• Quantum Approximate Optimization Algorithm for MIMO with Quantized b-bit Beamforming [47.98440449939344]
  Multiple-input multiple-output (MIMO) is critical for 6G communication, offering improved spectral efficiency and reliability.<n>This paper explores the use of the Quantum Approximate Optimization Algorithm (QAOA) and alternating optimization to address the problem of b-bit quantized phase shifters both at the transmitter and the receiver.<n>We demonstrate that the structure of this quantized beamforming problem aligns naturally with hybrid-classical methods like QAOA, as the phase shifts used in beamforming can be directly mapped to rotation gates in a quantum circuit.
  arXiv  Detail & Related papers  (2025-10-07T17:53:02Z)
• On the role of overparametrization in Quantum Approximate Optimization [0.0]
  Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research.<n>Our study focuses on the quantum approximate optimization algorithm (QAOA) -- a prominent variational quantum algorithm designed to solve optimization problems.<n>We investigate if circuit overparametrization is necessary and sufficient to solve such problems in QAOA, considering two representative problems -- MAX-CUT and MAX-2-SAT.
  arXiv  Detail & Related papers  (2025-08-13T18:00:00Z)
• Variational quantum algorithm-preserving feasible space for solving the uncapacitated facility location problem [3.3682090109106446]
  We propose the Variational Quantum Algorithm-Preserving Feasible Space (VQA-PFS) ansatz. This ansatz applies mixed operators on constrained variables while employing Hardware-Efficient Ansatz (HEA) on unconstrained variables. The numerical results demonstrate that VQA-PFS significantly enhances the success probability and exhibits faster convergence.
  arXiv  Detail & Related papers  (2023-12-12T01:36:49Z)
• Multi-sequence alignment using the Quantum Approximate Optimization Algorithm [0.0]
  We present a Hamiltonian formulation and implementation of the Multiple Sequence Alignment problem with the variational Quantum Approximate Optimization Algorithm (QAOA)<n>We consider a small instance of our QAOA-MSA algorithm in both a quantum simulator and its performance on an actual quantum computer.<n>While the ideal solution to the instance of MSA investigated is shown to be the most probable state sampled for a shallow p5 quantum circuit, the level of noise in current devices is still a formidable challenge.
  arXiv  Detail & Related papers  (2023-08-23T12:46:24Z)
• A Review on Quantum Approximate Optimization Algorithm and its Variants [47.89542334125886]
  The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve intractable optimization problems. This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios. We conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm.
  arXiv  Detail & Related papers  (2023-06-15T15:28:12Z)
• Unbalanced penalization: A new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms [42.29248343585333]
  We present an alternative method that does not require extra slack variables. We evaluate our approach on the traveling salesman problem, the bin packing problem, and the knapsack problem. This new approach can be used to solve problems with inequality constraints with a reduced number of resources.
  arXiv  Detail & Related papers  (2022-11-25T06:05:18Z)
• General Hamiltonian Representation of ML Detection Relying on the Quantum Approximate Optimization Algorithm [74.6114458993128]
  The quantum approximate optimization algorithm (QAOA) conceived for solving optimization problems can be run on the existing noisy intermediate-scale quantum (NISQ) devices. We solve the maximum likelihood (ML) detection problem for general constellations by appropriately adapting the QAOA. In particular, for an M-ary Gray-mapped quadrature amplitude modulation (MQAM) constellation, we show that the specific qubits encoding the in-phase components and those encoding the quadrature components are independent in the quantum system of interest.
  arXiv  Detail & Related papers  (2022-04-11T14:11:24Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Scaling Quantum Approximate Optimization on Near-term Hardware [49.94954584453379]
  We quantify scaling of the expected resource requirements by optimized circuits for hardware architectures with varying levels of connectivity. We show the number of measurements, and hence total time to synthesizing solution, grows exponentially in problem size and problem graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.
  arXiv  Detail & Related papers  (2022-01-06T21:02:30Z)
• Quantum constraint learning for quantum approximate optimization algorithm [0.0]
  This paper introduces a quantum machine learning approach to learn the mixer Hamiltonian required to hard constrain the search subspace. One can directly plug the learnt unitary into the QAOA framework using an adaptable ansatz. We also develop an intuitive metric that uses Wasserstein distance to assess the performance of general approximate optimization algorithms with/without constraints.
  arXiv  Detail & Related papers  (2021-05-14T11:31:14Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer [0.0]
  The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves optimization problems. We develop an iterative version of QAOA that is problem-tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the standard QAOA.
  arXiv  Detail & Related papers  (2020-05-20T18:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.