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Quantum Natural Gradient
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Quantum Natural Gradient
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A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of the Quantum Geometric Tensor (QGT), also known as the Fubini-Study metric tensor. An efficient algorithm is presented for computing a block-diagonal approximation to the Fubini-Study metric tensor for parametrized quantum circuits, which may be of independent interest.
Forward citations
Cited by 9 Pith papers
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Loss-aware state space geometry for quantum variational algorithms
Loss-aware natural gradient variants are introduced by embedding the loss hypersurface in a statistical manifold or using quantum state overlaps, yielding conformal updates that adjust effective step size.
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Variational Thermal State Preparation on Digital Quantum Processors Assisted by Matrix Product States
A variational framework assisted by matrix product states prepares approximate thermal Gibbs states for 1D lattices up to 30 sites and 2D lattices up to 6x6 using up to 44 qubits, with a demonstration on IBM Heron hardware.
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PennyLane: Automatic differentiation of hybrid quantum-classical computations
PennyLane is a software library extending automatic differentiation to hybrid quantum-classical systems for variational quantum algorithms.
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Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning
Learning-induced spectral structure in hybrid quantum models is diagnosed by edge-resolved two-boson interference correlated with Fiedler cuts and by absolute Bloch drift that separates anomalies from benign states.
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Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning
Training in graph-regularized quantum networks increases spectral dimension by 0.23 and enables anomaly detection via Bloch drift (ROC-AUC ≥0.9) while bosonic enhancement correlates with Fiedler splits (r=-0.50).
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Quantum encodings that preserve persistent homology
Investigates which quantum encodings of classical datasets preserve persistent homology so that quantum algorithms can extract topological features directly from the data.
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Evaluating quantum circuits in the reservoir computing paradigm
Brickwall quantum circuits with Haar-random, dual-unitary, and solvable two-qubit gates serve as effective reservoirs for temporal processing tasks, with performance correlated to circuit dynamics and validated on syn...
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Evaluating quantum circuits in the reservoir computing paradigm
Brickwall circuits from Haar-random, dual-unitary, and solvable two-qubit gates are tested as quantum reservoirs, showing effective fading memory and prediction accuracy on synthetic time-series data.
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Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning
Training reorganizes output similarity graphs in quantum networks, increasing spectral dimension by 0.23, with bosonic interference correlations and Bloch drift enabling high-ROC-AUC anomaly detection via a proposed s...
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