Sculpting Quantum Landscapes: Fubini-Study Metric Conditioning for Geometry Aware Learning in Parameterized Quantum Circuits

• URL: http://arxiv.org/abs/2506.21940v3
• Date: Fri, 11 Jul 2025 10:21:05 GMT
• Title: Sculpting Quantum Landscapes: Fubini-Study Metric Conditioning for Geometry Aware Learning in Parameterized Quantum Circuits
• Authors: Marwan Ait Haddou, Mohamed Bennai,
• Abstract summary: We present a novel meta learning framework called Sculpture that explicitly conditions the Fubini Study metric tensor to mitigate barren plateaus in variational quantum algorithms.<n>Our theoretical analysis identifies the logarithmic condition number of the Fubini Study metric as a critical geometric quantity governing trainability, optimization dynamics, and generalization.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We present a novel meta learning framework called Sculpture that explicitly conditions the Fubini Study metric tensor of parameterized quantum circuits to mitigate barren plateaus in variational quantum algorithms. Our theoretical analysis identifies the logarithmic condition number of the Fubini Study metric as a critical geometric quantity governing trainability, optimization dynamics, and generalization. Sculpture uses a classical meta model trained to generate data dependent quantum circuit initializations that minimize the logarithmic condition number, thereby promoting an isotropic and well conditioned parameter space. Empirical results show that meta training reduces the logarithmic condition number from approximately 1.47 to 0.64 by significantly increasing the minimum eigenvalue and slightly decreasing the maximum eigenvalue of the metric, effectively alleviating barren plateaus. This improved conditioning generalizes well to unseen data, consistently producing well conditioned quantum circuit initializations. In a downstream hybrid quantum classical classification task on the Kaggle diabetes dataset, increasing the meta scaling coefficient accelerates convergence, reduces training loss and gradient norms, and crucially improves generalization, with test accuracy increasing from about 0.68 to over 0.78. These findings demonstrate that sculpting the quantum landscape via meta learning serves as a principled geometric regularizer, substantially enhancing trainability, optimization, and generalization of parameterized quantum circuits and enabling more robust and efficient variational quantum algorithms.

Related papers

• Variational quantum algorithms with exact geodesic transport [0.0]
  Variational quantum algorithms (VQAs) are promising candidates for near-term applications of quantum computers.<n>We introduce exact-geodesic VQAs, a curvature-aware framework that enables analytic Riemannian optimization of variational quantum circuits.
  arXiv  Detail & Related papers  (2025-06-20T18:00:10Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [60.996803677584424]
  Variational Quantum Circuits (VQCs) offer a novel pathway for quantum machine learning.<n>Their practical application is hindered by inherent limitations such as constrained linear expressivity, optimization challenges, and acute sensitivity to quantum hardware noise.<n>This work introduces VQC-MLPNet, a scalable and robust hybrid quantum-classical architecture designed to overcome these obstacles.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum [78.27945336558987]
  Decentralized server (DFL) eliminates reliance on client-client architecture.<n>Non-smooth regularization is often incorporated into machine learning tasks.<n>We propose a novel novel DNCFL algorithm to solve these problems.
  arXiv  Detail & Related papers  (2025-04-17T08:32:25Z)
• GAQAT: gradient-adaptive quantization-aware training for domain generalization [54.31450550793485]
  We propose a novel Gradient-Adaptive Quantization-Aware Training (GAQAT) framework for DG.<n>Our approach begins by identifying the scale-gradient conflict problem in low-precision quantization.<n>Extensive experiments validate the effectiveness of the proposed GAQAT framework.
  arXiv  Detail & Related papers  (2024-12-07T06:07:21Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Guided-SPSA: Simultaneous Perturbation Stochastic Approximation assisted by the Parameter Shift Rule [4.943277284710129]
  We introduce a novel gradient estimation approach called Guided-SPSA, which meaningfully combines the parameter-shift rule and SPSA-based gradient approximation.<n>The Guided-SPSA results in a 15% to 25% reduction in the number of circuit evaluations required during training for a similar or better optimality of the solution found.<n>We demonstrate the performance of Guided-SPSA on different paradigms of quantum machine learning, such as regression, classification, and reinforcement learning.
  arXiv  Detail & Related papers  (2024-04-24T09:13:39Z)
• Efficient Gradient Estimation of Variational Quantum Circuits with Lie Algebraic Symmetries [16.4882269584049]
  We develop an efficient framework that makes the Hadamard test efficiently applicable to gradient estimation for a broad range of quantum systems. This is an exponential reduction in the measurement cost and up in time compared to existing works.
  arXiv  Detail & Related papers  (2024-04-07T23:34:51Z)
• Identifying overparameterization in Quantum Circuit Born Machines [1.7259898169307613]
  We study the onset of over parameterization transitions for quantum circuit Born machines, generative models that are trained using non-adversarial gradient methods. Our results indicate that fully understanding the trainability of these models remains an open question.
  arXiv  Detail & Related papers  (2023-07-06T21:05:22Z)
• Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization [3.031137751464259]
  We show that by reducing the initial domain of each parameter proportional to the square root of circuit depth, the magnitude of the cost gradient decays at most inversely to qubit count and circuit depth. This strategy can protect specific quantum neural networks from exponentially many spurious local minima.
  arXiv  Detail & Related papers  (2023-02-14T06:41:37Z)
• Improving Convergence for Quantum Variational Classifiers using Weight Re-Mapping [60.086820254217336]
  In recent years, quantum machine learning has seen a substantial increase in the use of variational quantum circuits (VQCs) We introduce weight re-mapping for VQCs, to unambiguously map the weights to an interval of length $2pi$. We demonstrate that weight re-mapping increased test accuracy for the Wine dataset by $10%$ over using unmodified weights.
  arXiv  Detail & Related papers  (2022-12-22T13:23:19Z)
• 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)
• Mode connectivity in the loss landscape of parameterized quantum circuits [1.7546369508217283]
  Variational training of parameterized quantum circuits (PQCs) underpins many employed on near-term noisy intermediate scale quantum (NISQ) devices. We adapt the qualitative loss landscape characterization for neural networks introduced in citegoodfellowqualitatively,li 2017visualizing and tests for connectivity used in citedraxler 2018essentially to study the loss landscape features in PQC training.
  arXiv  Detail & Related papers  (2021-11-09T18:28:46Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• 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)
• Quantum Optimization for Training Quantum Neural Networks [16.780058676633914]
  We devise a framework for leveraging quantum optimisation algorithms to find optimal parameters of QNNs for certain tasks. We coherently encode the cost function of QNNs onto relative phases of a superposition state in the Hilbert space of the network parameters.
  arXiv  Detail & Related papers  (2021-03-31T13:06:30Z)
• FLIP: A flexible initializer for arbitrarily-sized parametrized quantum circuits [105.54048699217668]
  We propose a FLexible Initializer for arbitrarily-sized Parametrized quantum circuits. FLIP can be applied to any family of PQCs, and instead of relying on a generic set of initial parameters, it is tailored to learn the structure of successful parameters. We illustrate the advantage of using FLIP in three scenarios: a family of problems with proven barren plateaus, PQC training to solve max-cut problem instances, and PQC training for finding the ground state energies of 1D Fermi-Hubbard models.
  arXiv  Detail & Related papers  (2021-03-15T17:38:33Z)
• GradInit: Learning to Initialize Neural Networks for Stable and Efficient Training [59.160154997555956]
  We present GradInit, an automated and architecture method for initializing neural networks. It is based on a simple agnostic; the variance of each network layer is adjusted so that a single step of SGD or Adam results in the smallest possible loss value. It also enables training the original Post-LN Transformer for machine translation without learning rate warmup.
  arXiv  Detail & Related papers  (2021-02-16T11:45:35Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• 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)
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule [0.0]
  We study the problem of estimating the gradient of the function to be optimized directly from quantum measurements. We derive a mathematically exact formula that provides an algorithm for estimating the gradient of any multi-qubit parametric quantum evolution. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy.
  arXiv  Detail & Related papers  (2020-05-20T18:24:11Z)

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.