Constraint-Aware Quantum Optimization via Hamming Weight Operators

• URL: http://arxiv.org/abs/2601.01516v1
• Date: Sun, 04 Jan 2026 12:58:04 GMT
• Title: Constraint-Aware Quantum Optimization via Hamming Weight Operators
• Authors: Yajie Hao, Qiming Ding, Xiao Yuan, Xiaoting Wang,
• Abstract summary: Constrained optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance.<n>We introduce Hamming Weight Operators, a new class of constraint-aware operators that confine quantum evolution strictly within the feasible subspace.<n>We validate our approach on benchmark tasks from both finance and high-energy physics, specifically portfolio optimization and two-jet clustering with energy balance.
• Score: 1.1463843149836523
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales. The Quantum Approximate Optimization Algorithm (QAOA) offers a promising quantum framework, but conventional penalty-based formulations distort optimization landscapes and demand deep circuits, undermining scalability on near-term hardware. In this work, we introduce Hamming Weight Operators, a new class of constraint-aware operators that confine quantum evolution strictly within the feasible subspace. Building on this idea, we develop Adaptive Hamming Weight Operator QAOA, which dynamically selects the most effective operators to construct shallow, problem-tailored circuits. We validate our approach on benchmark tasks from both finance and high-energy physics, specifically portfolio optimization and two-jet clustering with energy balance. Across these problems, our method inherently satisfies all constraints by construction, converges faster, and achieves higher Approximation Ratios than penalty-based QAOA, while requiring roughly half as many gates. By embedding constraint-aware operators into an adaptive variational framework, our approach establishes a scalable and hardware-efficient pathway for solving practical constrained optimization problems on near-term quantum devices.

Related papers

• Quantum Annealing for Combinatorial Optimization: Foundations, Architectures, Benchmarks, and Emerging Directions [0.0]
  Critical decision-making issues in science, engineering, and industry are based on optimization.<n>We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers.<n>We find that overhead in embedding and encoding is the largest of the scalability and performance.
  arXiv  Detail & Related papers  (2026-02-03T04:51:26Z)
• Feedback-Based Quantum Strategies for Constrained Combinatorial Optimization Problems [0.6554326244334868]
  We extend the feedback-based quantum algorithms framework to address a broader class of constraints known as invalid configuration (IC) constraints.<n>We propose an alternative method tailored for feedback-based quantum algorithms that directly tackles IC constraints without requiring slack variables.<n>These methods eliminate the need for slack variables, significantly reducing the quantum circuit depth and the number of qubits required.
  arXiv  Detail & Related papers  (2025-02-20T08:57:28Z)
• Multiobjective variational quantum optimization for constrained problems: an application to Cash Management [45.82374977939355]
  We introduce a new method for solving optimization problems with challenging constraints using variational quantum algorithms. We test our proposal on a real-world problem with great relevance in finance: the Cash Management problem. Our empirical results show a significant improvement in terms of the cost of the achieved solutions, but especially in the avoidance of local minima.
  arXiv  Detail & Related papers  (2023-02-08T17:09:20Z)
• Fermionic Quantum Approximate Optimization Algorithm [11.00442581946026]
  We propose fermionic quantum approximate optimization algorithm (FQAOA) for solving optimization problems with constraints. FQAOA tackle the constrains issue by using fermion particle number preservation to intrinsically impose them throughout QAOA. We provide a systematic guideline for designing the driver Hamiltonian for a given problem Hamiltonian with constraints.
  arXiv  Detail & Related papers  (2023-01-25T18:36:58Z)
• Exploiting In-Constraint Energy in Constrained Variational Quantum Optimization [7.541345730271882]
  In general, such constraints cannot be easily encoded in the circuit, and the quantum circuit measurement outcomes are not guaranteed to respect the constraints. We propose a new approach for solving constrained optimization problems with unimplement, easy-to-constrained quantum ansatze. We implement our method in QVoice, a Python package that interfaces with Qiskit for quick prototyping in simulators and on quantum hardware.
  arXiv  Detail & Related papers  (2022-11-13T20:58:00Z)
• 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)
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage [43.3054117987806]
  We introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for quantum circuits. We show this method significantly improves the trainability and performance of PQCs on a variety of problems. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing.
  arXiv  Detail & Related papers  (2022-08-29T15:24:03Z)
• 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)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• 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.