Quantum Error Mitigation Strategies for Variational PDE-Constrained Circuits on Noisy Hardware

• URL: http://arxiv.org/abs/2604.10099v1
• Date: Sat, 11 Apr 2026 08:45:08 GMT
• Title: Quantum Error Mitigation Strategies for Variational PDE-Constrained Circuits on Noisy Hardware
• Abstract summary: Variational circuits (VQCs) solving partial differential equations (PDEs) on near-term quantum hardware face a critical challenge: hardware noise degrades solution fidelity and disrupts convergence.<n>We present a systematic study of three noise channels; depolarizing, damping, and bit-flip on VQCs constrained by PDE residual loss functions for the heat equation Burgers' equation.<n>We benchmark three error mitigation strategies: zero-noise extrapolation (ZNE), probabilistic error cancellation (PEC), and measurement error mitigation through inverse confusion matrices.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Variational quantum circuits (VQCs) solving partial differential equations (PDEs) on near-term quantum hardware face a critical challenge: hardware noise degrades solution fidelity and disrupts convergence. We present a systematic study of three noise channels; depolarizing, amplitude damping, and bit-flip on VQCs constrained by PDE residual loss functions for the heat equation, Burgers' equation, and the Saint-Venant shallow water equations. We benchmark three error mitigation strategies: zero-noise extrapolation (ZNE) via Richardson polynomial fitting, probabilistic error cancellation (PEC), and measurement error mitigation through inverse confusion matrices. Our numerical experiments on 6-qubit, 4-layer circuits demonstrate that ZNE reduces absolute error by 82-96% at low noise (p = 0.001), with effectiveness degrading gracefully at higher noise strengths. We prove analytically and confirm numerically that physics-constrained circuits exhibit inherent noise resilience: at p = 0.01, constrained circuits maintain 25-47% higher fidelity than unconstrained counterparts, with the advantage scaling with PDE complexity. PEC provides near-exact correction at low gate counts but incurs exponential sampling overhead, rendering it impractical beyond ~60 gates at p >= 0.02. Error budget decomposition reveals that systematic errors dominate at all noise levels (43-58%), while the PDE residual component grows from ~10% to ~31% as noise increases, indicating that physics constraints absorb noise through structured gradient information. These results establish practical guidelines for deploying variational PDE solvers on NISQ hardware.

Related papers

• Physics-Guided Linear Mapper for Quantum Error Mitigation [0.0]
  We introduce a novel physics-guided linear mapper (PGLM) for quantum error mitigation.<n>The goal is to provide a data-efficient, interpretable, and low-latency alternative to the black-box machine learning for quantum error mitigation.
  arXiv  Detail & Related papers  (2026-08-24T11:19:10Z)
• Quantum Noise Mitigation with Adaptive Zero-Noise Extrapolation: A Contextual Multi-Armed Bandits Approach [8.98664000532717]
  Variational quantum circuits (VQCs) are central to near-term quantum computing, yet their practical deployment is severely hindered by noise.<n>Our work introduces a novel adaptive noise mitigation framework for VQCs that integrates zero-noise extrapolation (ZNE) with contextual multi-armed bandits (CMAB)<n>Unlike fixed-fold ZNE, our approach uses online adaptation to improve the accuracy of ZNE and reduce quantum circuit executions.
  arXiv  Detail & Related papers  (2026-08-05T19:07:26Z)
• Accelerating Noisy Variational Quantum Algorithms with Physics-Informed Denoising Networks [8.108113752089812]
  Variational quantum algorithms are promising for near-term quantum computing, but are severely limited by hardware noise and the substantial circuit overhead required for error mitigation methods such as Zero-Noise Extrapolation (ZNE)<n>We propose a Physics-Informed Denoising Network (PIDN) that reduces the cost of ZNE by learning a surrogate model of its optimization dynamics.<n>Across all tasks, PIDN attains performance comparable to ZNE, while reducing the number of circuit executions by a factor of approximately 4 to 6.
  arXiv  Detail & Related papers  (2026-05-03T21:32:31Z)
• Noise-Induced Landscape Distortion in QAOA for Constrained Binary Optimization: Empirical Characterization on IBM Quantum Hardware [0.0]
  We introduce and empirically validate Landscape Span Compression (LSC)<n>LSC measures how much noise flattens the energy landscape, approaching 1 as the landscape collapses toward a barren plateau.<n>We report an experience study of applying QAOA with LSC-based noise characterization on IBM's ibm_fez for three constrained QUBO portfolio instances.
  arXiv  Detail & Related papers  (2026-04-21T12:55:50Z)
• Mitigating Barren Plateaus in Variational Quantum Circuits through PDE-Constrained Loss Functions [0.0]
  We show that partial differential equation (PDE) constraints into the VQC loss function provide a natural and effective mitigation mechanism against barren plateaus.<n>We find that PDE-constrained circuits exhibit favorable gradient variance scaling with system size, with the physics constraints creating a stabilizing effect that resists exponential gradient vanishing.<n>These results establish PDE constraints as a principled, physically motivated strategy for designing trainable variational quantum circuits.
  arXiv  Detail & Related papers  (2026-04-10T23:36:59Z)
• Q-Drift: Quantization-Aware Drift Correction for Diffusion Model Sampling [45.88028371034407]
  Post-training quantization (PTQ) is a practical path to deploy large diffusion models.<n>We propose Q-Drift, a principled sampler-side correction that treats quantization error as an implicit perturbation.<n>Q-Drift estimates a time-wise variance statistic from calibration, in practice requiring as few as 5 full-precision/quantized calibration runs.
  arXiv  Detail & Related papers  (2026-03-18T10:19:36Z)
• Folding-Free Zero-Noise Extrapolation by Layout-induced Noise Diversity [3.1941554288428193]
  Zero Noise Extrapolation (ZNE) is a widely used but biased error mitigation method that lacks rigorous error bounds.<n>We introduce Folding Free Zero Noise Extrapolation (FF-ZNE), a method that removes the need for noise factor selection.<n>Experiments on a 133 qubit IBM Quantum device demonstrate that FF-ZNE yields mitigated expectation values with average deviations of 6% and 4.5%.
  arXiv  Detail & Related papers  (2026-03-14T13:54:42Z)
• An exploration of the noise sensitivity of the Shor's algorithm [7.668628159028283]
  This paper proposes that quantum algorithms may possess inherent noise resilience characteristics that could reduce implementation barriers.<n>We investigate Shor's algorithm by applying circuit-level noise models directly to the original circuit.
  arXiv  Detail & Related papers  (2025-08-30T08:54:35Z)
• 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)
• Emergence of noise-induced barren plateaus in arbitrary layered noise models [44.99833362998488]
  In variational quantum algorithms the parameters of a parameterized quantum circuit are optimized in order to minimize a cost function that encodes the solution of the problem. We discuss how, and in which sense, the phenomenon of noise-induced barren plateaus emerges in parameterized quantum circuits with a layered noise model.
  arXiv  Detail & Related papers  (2023-10-12T15:18:27Z)
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits [37.84307089310829]
  Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit. Despite their promise, the trainability of these algorithms is hindered by barren plateaus. We present a general Lie algebra that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits.
  arXiv  Detail & Related papers  (2023-09-17T18:14:10Z)
• Error-aware Quantization through Noise Tempering [43.049102196902844]
  Quantization-aware training (QAT) optimize model parameters with respect to the end task while simulating quantization error. In this work, we incorporate exponentially decaying quantization-error-aware noise together with a learnable scale of task loss gradient to approximate the effect of a quantization operator. Our method obtains state-of-the-art top-1 classification accuracy for uniform (non mixed-precision) quantization, out-performing previous methods by 0.5-1.2% absolute.
  arXiv  Detail & Related papers  (2022-12-11T20:37:50Z)
• 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)
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits [58.720142291102135]
  We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) We prove that the detection of entanglement in a linear number of bipartitions by a number of measurements scales linearly, suffices to certify GME. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version.
  arXiv  Detail & Related papers  (2020-10-06T18:00:07Z)

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.