EQE-QAOA: An Equivalence-Preserving Qubit Efficient Framework for Combinatorial Optimization

• URL: http://arxiv.org/abs/2604.18285v1
• Date: Mon, 20 Apr 2026 13:57:49 GMT
• Title: EQE-QAOA: An Equivalence-Preserving Qubit Efficient Framework for Combinatorial Optimization
• Abstract summary: Existing techniques rely on qubit reduction at the cost of information loss, leading to degraded computational performance.<n>We propose the Equivalence-preserving Qubit Efficient QAOA, which significantly reduces the required number of qubits without degrading performance.<n>We show that it is broadly applicable to large-scale optimization problems, excluding only unconstrained problems with completely independent variables.
• Score: 54.05451096499336
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The limited number of qubits is a major bottleneck in Quantum Approximate Optimization Algorithm (QAOA) for large-scale combinatorial optimization in the Noisy Intermediate-Scale Quantum (NISQ) era. To make progress, existing techniques rely on qubit reduction at the cost of information loss, hence leading to degraded computational performance. As a remedy, we propose the Equivalence-preserving Qubit Efficient QAOA (EQE-QAOA), which significantly reduces the required number of qubits without degrading the performance of QAOA. By exploiting intrinsic symmetries and conserved quantities, we first demonstrate that the QAOA dynamics are strictly confined to an invariant subspace of the Hilbert space. We subsequently prove that the evolution within this subspace is exactly equivalent to that of the full-scale system, achieving the same optimal solution as the original QAOA. Moreover, to reduce the number of qubits, we propose an isometric mapping that re-encodes the subspace into a space relying on fewer qubits. Furthermore, we derive the applicability conditions of EQE-QAOA and show that it is broadly applicable to large-scale combinatorial optimization problems, excluding only unconstrained problems with completely independent variables. Numerical simulations based on Max-Cut instances validate that EQE-QAOA significantly reduces qubit requirements and computational resources, while preserving exact optimization performance.

Related papers

• Design and Analysis of an Improved Constrained Hypercube Mixer in Quantum Approximate Optimization Algorithm [0.0]
  In the Noisy Intermediate-Scale Quantum (NISQ) era, QAOA is not suited for constrained problems.<n>One way to incorporate certain types of constraints is to restrict the mixing operator to the feasible subspace.<n>We present a modification that generates circuits with fewer gates for a broad class of constrained problems.
  arXiv  Detail & Related papers  (2026-03-05T13:57:15Z)
• Tensor Network Assisted Distributed Variational Quantum Algorithm for Large Scale Combinatorial Optimization Problem [19.046113542182436]
  We propose the Distributed Variational Quantum Algorithm (DVQA) for solving Combinatorial Optimization Problems (COPs)<n>A key innovation of DVQA is its use of the truncated higher-order singular value decomposition to preserve inter-variable dependencies without relying on complex long-range entanglement.<n> Empirically, DVQA achieves state-of-the-art performance in simulations and has been experimentally validated on the Wu Kong quantum computer for portfolio optimization.
  arXiv  Detail & Related papers  (2026-01-20T13:31:02Z)
• Auxiliary-Qubit-Free Quantum Approximate Optimization Algorithm for the Minimum Dominating Set Problem [6.467872637658972]
  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.
  arXiv  Detail & Related papers  (2025-09-20T12:01:57Z)
• End-to-End On-Device Quantization-Aware Training for LLMs at Inference Cost [53.25965863436039]
  Quantization-aware training (QAT) provides a more principled solution, but its reliance on backpropagation incurs prohibitive memory costs.<n>We propose ZeroQAT, a zeroth-order optimization-based QAT framework that supports both weight and activation quantization.<n>Experiments show that ZeroQAT consistently outperforms representative PTQ and QAT baselines while requiring significantly less memory.
  arXiv  Detail & Related papers  (2025-08-21T01:18:27Z)
• MPQ-DMv2: Flexible Residual Mixed Precision Quantization for Low-Bit Diffusion Models with Temporal Distillation [74.34220141721231]
  We present MPQ-DMv2, an improved textbfMixed textbfPrecision textbfQuantization framework for extremely low-bit textbfDiffusion textbfModels.
  arXiv  Detail & Related papers  (2025-07-06T08:16:50Z)
• Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking [45.147301546565316]
  This paper considers the problem of decentralized optimization on compact submanifolds.<n>We propose an algorithm where agents update variables using quantized variables.<n>To the best of our knowledge, this is the first algorithm to achieve an $mathcalO (1/K)$ convergence rate in the presence of quantization.
  arXiv  Detail & Related papers  (2025-06-09T01:57:25Z)
• Solving Constrained Combinatorial Optimization Problems with Variational Quantum Imaginary Time Evolution [4.266376725904727]
  We show that VarQITE achieves significantly lower mean optimality gaps compared to other conventional methods.<n>We demonstrate that scaling the Hamiltonian can further reduce optimization costs and accelerate convergence.
  arXiv  Detail & Related papers  (2025-04-17T03:09:37Z)
• 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)
• Error Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis [42.275148861039895]
  Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy processors. gate noise due to imperfections and decoherence affects the gradient estimates by introducing a bias. Quantum error mitigation (QEM) techniques can reduce the estimation bias without requiring any increase in the number of qubits. QEM can reduce the number of required iterations, but only as long as the quantum noise level is sufficiently small.
  arXiv  Detail & Related papers  (2022-09-23T10:48:04Z)
• Prog-QAOA: Framework for resource-efficient quantum optimization through classical programs [0.0]
  Current quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent cost Hamiltonian suitable for the quantum device.<n>We propose to design classical programs for computing the objective function and certifying the constraints, and later compile them to quantum circuits.<n>We exploit this idea for optimization tasks like the Travelling Salesman Problem and Max-$K$-Cut and obtain circuits that are near-optimal with respect to all relevant cost measures.
  arXiv  Detail & Related papers  (2022-09-07T18:01:01Z)
• 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)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• 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)

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.