Quantum Error Mitigation with Attention Graph Transformers for Burgers Equation Solvers on NISQ Hardware

• URL: http://arxiv.org/abs/2512.23817v1
• Date: Mon, 29 Dec 2025 19:23:20 GMT
• Title: Quantum Error Mitigation with Attention Graph Transformers for Burgers Equation Solvers on NISQ Hardware
• Abstract summary: We present a hybrid quantum-classical framework augmented with learned error mitigation for solving the viscous Burgers equation.<n>Quantum simulations are executed on noisy Aer backends and IBM superconducting quantum devices.<n>We train an attention-based graph neural network that incorporates circuit structure, light-cone information, global circuit parameters, and noisy quantum outputs to predict error-mitigated solutions.
• Score: 6.082976940335597
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a hybrid quantum-classical framework augmented with learned error mitigation for solving the viscous Burgers equation on noisy intermediate-scale quantum (NISQ) hardware. Using the Cole-Hopf transformation, the nonlinear Burgers equation is mapped to a diffusion equation, discretized on uniform grids, and encoded into a quantum state whose time evolution is approximated via Trotterized nearest-neighbor circuits implemented in Qiskit. Quantum simulations are executed on noisy Aer backends and IBM superconducting quantum devices and are benchmarked against high-accuracy classical solutions obtained using a Krylov-based solver applied to the corresponding discretized Hamiltonian. From measured quantum amplitudes, we reconstruct the velocity field and evaluate physical and numerical diagnostics, including the L2 error, shock location, and dissipation rate, both with and without zero-noise extrapolation (ZNE). To enable data-driven error mitigation, we construct a large parametric dataset by sweeping viscosity, time step, grid resolution, and boundary conditions, producing matched tuples of noisy, ZNE-corrected, hardware, and classical solutions together with detailed circuit metadata. Leveraging this dataset, we train an attention-based graph neural network that incorporates circuit structure, light-cone information, global circuit parameters, and noisy quantum outputs to predict error-mitigated solutions. Across a wide range of parameters, the learned model consistently reduces the discrepancy between quantum and classical solutions beyond what is achieved by ZNE alone. We discuss extensions of this approach to higher-dimensional Burgers systems and more general quantum partial differential equation solvers, highlighting learned error mitigation as a promising complement to physics-based noise reduction techniques on NISQ devices.

Related papers

• Physics-Informed Quantum Machine Learning with Hard Constraint Embedding for Nonlinear Differential Equations of the First Order [14.324339765884053]
  This work proposes a physics-informed quantum machine learning (PIQML) framework with hard constraint embedding.<n>Within this framework, parameterized quantum circuits serve as machine learning models, where the input variable is encoded into a high-dimensional feature space.<n>Results demonstrate that our quantum model successfully learns the solution, showing close agreement with a high-precision classical numerical benchmark.
  arXiv  Detail & Related papers  (2026-08-04T02:17:21Z)
• Fault-Tolerant Logical Operations and Efficient State Preparation in Modular Quantum Architectures with Noisy Interfaces [0.12314765641075438]
  We show that interfaces can tolerate noise up to an order of magnitude higher than intra-QPU noise, with only a minor reduction in the fault-tolerance threshold.<n>We develop a protocol for preparing fault-tolerant logical GHZ states, reducing overhead, time, and nonlocal Bellpair consumption.<n>Our results provide quantitative evidence that distributed quantum error can enable scalable, fault-tolerant quantum computation in modular architectures.
  arXiv  Detail & Related papers  (2026-07-29T17:59:57Z)
• 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)
• Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks [4.542801731045077]
  This work establishes a mapping from discretised physical equations to logarithmic-scale quantum circuits.<n>It provides a new and exploratory path to exponential memory compression and computational acceleration for PDE solvers on future fault-tolerant quantum computers.
  arXiv  Detail & Related papers  (2026-03-25T11:19:56Z)
• Digital Quantum Simulation of the Holstein-Primakoff Transformation on Noisy Qubits [40.8066152850216]
  We study the digital quantum simulation of bosonic modes on a cloud-based superconducting quantum processor.<n>We examine the interplay between algorithmic and hardware-induced errors to identify optimal simulation parameters.
  arXiv  Detail & Related papers  (2026-02-19T20:14:04Z)
• 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)
• Ensemble-Based Quantum Signal Processing for Error Mitigation [3.5659159991711618]
  Noise remains a central obstacle to deploying quantum algorithms on near-term devices.<n>In particular, random coherent errors that accumulate during circuit execution constitute a dominant and fundamentally challenging noise source.<n>We introduce a noise-resilient framework for Quantum Signal Processing that mitigates such coherent errors without increasing circuit depth or ancillary qubit requirements.
  arXiv  Detail & Related papers  (2026-01-27T21:35:06Z)
• Crosstalk-Resilient Quantum MIMO for Scalable Quantum Communications [40.44880302154388]
  Crosstalk arises when physically coupled quantum modes interfere, degrading signal fidelity.<n>We propose a mitigation strategy based on encoding discrete-variable quantum information into continuous-variable modes.<n>We prove the existence of a gauge-fixing decoder enabling recovery of the logical information.
  arXiv  Detail & Related papers  (2025-06-26T18:40:26Z)
• 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)
• EnQode: Fast Amplitude Embedding for Quantum Machine Learning Using Classical Data [4.329112531155235]
  Amplitude embedding (AE) is essential in quantum machine learning (QML) for encoding classical data onto quantum circuits.<n>We introduce EnQode, a fast AE technique based on symbolic representation that addresses limitations by clustering dataset samples.<n>With over 90% fidelity in data mapping, EnQode enables robust, high-performance QML on noisy intermediate-scale quantum (NISQ) devices.
  arXiv  Detail & Related papers  (2025-03-18T17:48:03Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application.<n>We analyse the generation of random states in PQCs under restrictions on the qubits connectivities.<n>We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• Quantum time dynamics mediated by the Yang-Baxter equation and artificial neural networks [3.9079297720687536]
  This study explores new strategies for mitigating quantum errors using artificial neural networks (ANN) and the Yang-Baxter equation (YBE)<n>We developed a novel method that combines ANN for noise mitigation combined with the YBE to generate noisy data.<n>This approach effectively reduces noise in quantum simulations, enhancing the accuracy of the results.
  arXiv  Detail & Related papers  (2024-01-30T15:50:06Z)
• Quantum benefit of the quantum equation of motion for the strongly coupled many-body problem [0.0]
  The quantum equation of motion (qEOM) is a hybrid quantum-classical algorithm for computing excitation properties of a fermionic many-body system. We demonstrate explicitly that the qEOM exhibits a quantum benefit due to the independence of the number of required quantum measurements.
  arXiv  Detail & Related papers  (2023-09-18T22:10:26Z)
• Quantum Federated Learning with Entanglement Controlled Circuits and Superposition Coding [44.89303833148191]
  We develop a depth-controllable architecture of entangled slimmable quantum neural networks (eSQNNs) We propose an entangled slimmable QFL (eSQFL) that communicates the superposition-coded parameters of eS-QNNs. In an image classification task, extensive simulations corroborate the effectiveness of eSQFL.
  arXiv  Detail & Related papers  (2022-12-04T03:18:03Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Model-Independent Error Mitigation in Parametric Quantum Circuits and Depolarizing Projection of Quantum Noise [1.5162649964542718]
  Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the prospect to efficiently perform such computations. Current quantum devices still suffer from inherent quantum noise.
  arXiv  Detail & Related papers  (2021-11-30T16:08:01Z)
• Towards the real-time evolution of gauge-invariant $\mathbb{Z}_2$ and $U(1)$ quantum link models on NISQ Hardware with error-mitigation [0.0]
  We benchmark the real-time dynamics of $mathbbZ$ and $U(1)$ gauge in plaquette models using noisy intermediate scale quantum (NISQ) hardware. We design quantum circuits for models of increasing complexity and measure physical observables such as the return probability to the initial state, and locally conserved charges.
  arXiv  Detail & Related papers  (2021-09-30T12:22:21Z)
• Fusion-based quantum computation [43.642915252379815]
  Fusion-based quantum computing (FBQC) is a model of universal quantum computation in which entangling measurements, called fusions, are performed on qubits of small constant-sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems for quantum computing, such as photonics.
  arXiv  Detail & Related papers  (2021-01-22T20:00:22Z)

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.