Constrained Quantum Optimization via Iterative Warm-Start XY-Mixers

• URL: http://arxiv.org/abs/2604.02083v1
• Date: Thu, 02 Apr 2026 14:12:04 GMT
• Title: Constrained Quantum Optimization via Iterative Warm-Start XY-Mixers
• Abstract summary: XY-mixers successfully confine quantum state evolution to a feasible subspace.<n>Warm-starting biases the search toward promising regions based on preliminary solutions.<n>We develop a warm-started XY-mixer Hamiltonian for one-hot constraints and prove its ground-state properties.
• Score: 2.848229367557305
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Quantum Approximate Optimization Algorithm (QAOA) is a leading hybrid heuristic for combinatorial optimization, but efficiently handling hard constraints remains a significant challenge. XY-mixers successfully confine quantum state evolution to a feasible subspace, such as the Hamming-weight-1 sector for one-hot constraints. On the contrary, warm-starting biases the search toward promising regions based on preliminary solutions. Combining these two techniques requires maintaining the essential alignment between the initial state and the mixer Hamiltonian to preserve convergence guarantees. Previous work demonstrated warm-starting with XY-mixers via a biased initial state, but relying only on standard mixer Hamiltonians. Consequently, the initial state is no longer a ground state of the mixer. In this work, we overcome these limitations by formulating a warm-started XY-mixer Hamiltonian for one-hot constraints and proving its ground-state properties. Furthermore, we provide a shallow circuit implementation suitable for NISQ implementations. We embed the warm-starting into a classical heuristic that iteratively updates the bias based on previous samples, called Iterative Warm-Starting (IWS). Extensive numerical simulations on Max-$k$-Cut and Traveling Salesperson Problem instances demonstrate that IWS-QAOA significantly accelerates the solution-finding process, increasing the probability of sampling optimal solutions by orders of magnitude compared to standard XY-QAOA. Finally, we validate our approach on the ibm_boston QPU using hardware-tailored 144-qubit problem instances. By coupling IWS-QAOA with a greedy steepest-descent post-processing strategy to repair infeasible measurements caused by hardware noise, we successfully identify optimal solutions on actual quantum devices.

Related papers

• EQE-QAOA: An Equivalence-Preserving Qubit Efficient Framework for Combinatorial Optimization [54.05451096499336]
  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.
  arXiv  Detail & Related papers  (2026-04-20T13:57:49Z)
• Learning Feasible Quantum States for Quadratic Constrained Binary Optimization Problems [41.23247424467223]
  We develop a variational approach that creates an equal superposition of quantum states that satisfy constraints in a QCBO.<n>The resulting equal superposition can be used as an initial state for quantum algorithms that solve QUBOs/QCBOs.
  arXiv  Detail & Related papers  (2025-08-04T16:44:53Z)
• Beyond Ground States: Physics-Inspired Optimization of Excited States of Classical Hamiltonians [0.0]
  ExcLQA is a classical, physics-inspired algorithm that identifies excited states of classical Ising Hamiltonians.<n>We benchmark ExcLQA on the shortest vector problem (SVP), a fundamental lattice problem underlying the security of many postquantum cryptographic schemes.<n>Our results show that ExcLQA manages to solve SVP instances up to rank 46, and outperforms the Metropolis-Hastings algorithm in solved ratio, number of shots, and approximation factor.
  arXiv  Detail & Related papers  (2025-07-16T16:40:49Z)
• A Warm-start QAOA based approach using a swap-based mixer for the TSP: theoretical considerations,implementation and experiments [0.0]
  We introduce a swap-based mixer tailored to the Traveling Salesman Problem (TSP)<n>We propose a warm-start technique that initializes QAOA with a solution generated by any classical solution.<n> Experimental results on a custom TSP instance involving five customers demonstrate the effectiveness of this approach.
  arXiv  Detail & Related papers  (2025-05-02T12:04:46Z)
• Warm-Starting QAOA with XY Mixers: A Novel Approach for Quantum-Enhanced Vehicle Routing Optimization [11.41994899497275]
  Two notable directions include: warm-starting techniques, which incorporate classical approximate solutions to guide the quantum evolution, and custom mixer Hamiltonians, such as XY mixers, which constrain the search to feasible subspaces aligned with the structure of the problem.<n>We propose an approach that integrates these two strategies, enabling constraint-aware quantum evolution toward high-quality classical solutions.<n>We evaluate the approach on 5-city instances of the Traveling Salesperson Problem, a canonical optimization problem frequently encountered as a subroutine in real-world Vehicle Problems.
  arXiv  Detail & Related papers  (2025-04-28T16:08:38Z)
• 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)
• Bayesian Quantum Amplitude Estimation [46.03321798937855]
  We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation.<n>In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically characterize it and self-adapt.<n>We propose a benchmark for amplitude estimation algorithms and use it to test BAE against other approaches.
  arXiv  Detail & Related papers  (2024-12-05T18:09:41Z)
• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• MG-Net: Learn to Customize QAOA with Circuit Depth Awareness [51.78425545377329]
  Quantum Approximate Optimization Algorithm (QAOA) and its variants exhibit immense potential in tackling optimization challenges. The requisite circuit depth for satisfactory performance is problem-specific and often exceeds the maximum capability of current quantum devices. We introduce the Mixer Generator Network (MG-Net), a unified deep learning framework adept at dynamically formulating optimal mixer Hamiltonians.
  arXiv  Detail & Related papers  (2024-09-27T12:28:18Z)
• Alignment between Initial State and Mixer Improves QAOA Performance for Constrained Optimization [11.445200448951072]
  Quantum alternating operator ansatz (QAOA) has a strong connection to the adiabatic algorithm. We demonstrate that the intuition from the adiabatic algorithm applies to the task of choosing the QAOA initial state.
  arXiv  Detail & Related papers  (2023-05-05T21:54:28Z)
• Systematic study on the dependence of the warm-start quantum approximate optimization algorithm on approximate solutions [0.0]
  We study how the accuracy of approximate solutions affect the performance of the warm-start QAOA (WS-QAOA) We find that WS-QAOA tends to outperform QAOA as approximate solutions become closer to the exact solutions in terms of the Hamming distance. We also solve MAX-CUT problems by WS-QAOA with approximate solutions obtained via QAOA, having a better result than QAOA especially when the circuit is relatively shallow.
  arXiv  Detail & Related papers  (2022-09-07T05:26:48Z)
• QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines [81.4597482536073]
  Quantum approximate optimization algorithms (QAOAs) utilize the power of quantum machines and inherit the spirit of adiabatic evolution. We propose QAOA-in-QAOA ($textQAOA2$) to solve arbitrary large-scale MaxCut problems using quantum machines. Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale optimization problems.
  arXiv  Detail & Related papers  (2022-05-24T03:49:10Z)
• 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)

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.