Benchmarking and Resource Analysis for Augmented-Lagrangian Quantum Hamiltonian Descent

• URL: http://arxiv.org/abs/2605.12066v1
• Date: Tue, 12 May 2026 12:54:59 GMT
• Title: Benchmarking and Resource Analysis for Augmented-Lagrangian Quantum Hamiltonian Descent
• Abstract summary: Quantum Hamiltonian Descent (QHD) is a continuous optimization algorithm based on simulating a time-dependent quantum Hamiltonian.<n>While it is useful for constrained nontolerant optimization with QHD, it would likely require large-scale fault quantum hardware.
• Score: 20.262110626069653
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Quantum Hamiltonian Descent (QHD) is a continuous optimization algorithm based on simulating a time-dependent quantum Hamiltonian whose potential energy encodes the objective function and whose kinetic energy promotes exploration through quantum interference and tunneling. While QHD is formulated for unconstrained optimization, many real-world optimization problems are constrained and highly nonconvex. In this paper, we benchmark AL-QHD, a hybrid framework that embeds QHD within the Augmented Lagrangian Method (ALM), thereby solving a sequence of unconstrained subproblems while using ALM to enforce constraints. We evaluate AL-QHD on standard nonconvex test functions and use iterative refinement to improve solution accuracy at fixed per-run qubit cost. We also perform a gate-based resource analysis on ACOPF-derived power system subproblems constructed from power-network data to estimate the quantum-computer scale required for practical applications. Resource estimates on Texas7k-derived ACOPF instances show steep hard-gate scaling, reaching $\sim 4.46 \times 10^7$ entangling gates in a NISQ-oriented model and $\sim 9.42 \times 10^8$ T gates in a fault-tolerant model at $\sim 5.3 \times 10^2$ active variables. These results suggest that AL-QHD is a useful framework for studying constrained nonconvex optimization with QHD, but that practical ACOPF-scale applications would likely require large-scale fault-tolerant quantum hardware.

Related papers

• Benchmarking Quantum Algorithmic Resilience for CVaR Portfolio Optimization: The Expressibility-Coherence Trade-off [0.0]
  Quantum optimization offers theoretical advantages for complex financial modeling.<n>Physical implementation on Noisy Intermediate Scale Quantum (NISQ) devices is severely constrained by hardware topology.<n>This study presents a benchmarking analysis between a Hardware Efficient Variational Quantum Neural Network (HE-VQNN) and the Warm Start Quantum Approximate Optimization Algorithm (WS-QAOA)
  arXiv  Detail & Related papers  (2026-06-05T17:07:59Z)
• 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)
• SpinGQE: A Generative Quantum Eigensolver for Spin Hamiltonians [42.007194397302825]
  Ground state search is central to quantum computing.<n>We present SpinGQE, an extension of the Generative Quantum Eigensolver framework to spin Hamiltonians.<n>We employ a transformer-based decoder to learn over quantum circuits that produce low-energy states.
  arXiv  Detail & Related papers  (2026-03-25T13:38:15Z)
• AQER: a scalable and efficient data loader for digital quantum computers [62.40228216126285]
  We develop AQER, a scalable AQL method that constructs the loading circuit by systematically reducing entanglement in target states.<n>We conduct systematic experiments to evaluate the effectiveness of AQER, using synthetic datasets, classical image and language datasets, and a quantum many-body state datasets with up to 50 qubits.
  arXiv  Detail & Related papers  (2026-02-02T14:39:42Z)
• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• TensorHyper-VQC: A Tensor-Train-Guided Hypernetwork for Robust and Scalable Variational Quantum Computing [50.95799256262098]
  We introduceHyper-VQC, a novel tensor-train (TT)-guided hypernetwork framework for quantum machine learning.<n>Our framework delegates the generation of quantum circuit parameters to a classical TT network, effectively decoupling optimization from quantum hardware.<n>These results positionHyper-VQC as a scalable and noise-resilient framework for advancing practical quantum machine learning on near-term devices.
  arXiv  Detail & Related papers  (2025-08-01T23:37:55Z)
• RhoDARTS: Differentiable Quantum Architecture Search with Density Matrix Simulations [44.13836547616739]
  Variational Quantum Algorithms (VQAs) are a promising approach to leverage Noisy Intermediate-Scale Quantum (NISQ) computers.<n> choosing optimal quantum circuits that efficiently solve a given VQA problem is a non-trivial task.<n>Quantum Architecture Search (QAS) algorithms enable automatic generation of quantum circuits tailored to the provided problem.
  arXiv  Detail & Related papers  (2025-06-04T08:30:35Z)
• Practical Application of the Quantum Carleman Lattice Boltzmann Method in Industrial CFD Simulations [44.99833362998488]
  This work presents a practical numerical assessment of a hybrid quantum-classical approach to CFD based on the Lattice Boltzmann Method (LBM)<n>We evaluate this method on three benchmark cases featuring different boundary conditions, periodic, bounceback, and moving wall.<n>Our results confirm the validity of the approach, achieving median error fidelities on the order of $10-3$ and success probabilities sufficient for practical quantum state sampling.
  arXiv  Detail & Related papers  (2025-04-17T15:41:48Z)
• Performance Evaluation of Variational Quantum Eigensolver and Quantum Dynamics Algorithms on the Advection-Diffusion Equation [0.0]
  This study benchmarks a ground-state algorithm, Variational Quantum Eigensolver (VQE), against three leading quantum dynamics algorithms.<n>VQE can reach final-time infidelities as low as $O(10-9)$ with $N=4$ qubits and moderate circuit depths.
  arXiv  Detail & Related papers  (2025-03-31T13:09:59Z)
• Large-scale quantum annealing simulation with tensor networks and belief propagation [0.0]
  We show that quantum annealing for 3-regular graphs can be classically simulated even at scales of 1000 qubits and 5000000qubit gates. For non-degenerate instances, the unique solution can be read out from the final reduced single-qubit states. For degenerate problems, such as MaxCut, we introduce an approximate measurement simulation algorithm for graph tensor-network states.
  arXiv  Detail & Related papers  (2024-09-18T18:00:08Z)
• Subspace-Based Local Compilation of Variational Quantum Circuits for Large-Scale Quantum Many-Body Simulation [0.0]
  This paper proposes a hybrid quantum-classical algorithm for compiling the time-evolution operator. It achieves a 95% reduction in circuit depth compared to Trotterization while maintaining accuracy. We estimate the gate count needed to execute the quantum simulations using the LSVQC on near-term quantum computing architectures.
  arXiv  Detail & Related papers  (2024-07-19T09:50:01Z)
• Connecting the Hamiltonian structure to the QAOA performance and energy landscape [0.0]
  Quantum Alternating Operator Ansatz (QAOA) is effective for solving Quadratic Unconstrained Binary Optimization problems. This study emphasizes the algorithm's robustness and potential for optimization tasks on near-term quantum devices.
  arXiv  Detail & Related papers  (2024-07-05T11:32:46Z)
• 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)
• 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)

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.