MPS energy landscapes lack poor local minima because gauge freedom induces overparametrization that concentrates local minima near the global minimum, with the local minimum distribution proven invariant under orthogonality center moves.
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Coles, Lukasz Cincio, Jarrod R
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Trainable quantum spectral models with an intermediate parameterized mixer (ε ≈ 0.5) outperform standard variational quantum circuits for PDEs by learning in spectral representation, with HHL-inspired architectures showing fastest convergence.
Local tensor-train surrogates approximate quantum machine learning models via Taylor polynomials and tensor networks, delivering polynomial parameter scaling and explicit generalization bounds controlled by patch radius.
Quantum circuits for coherent multilayer neural network inference achieve quadratic to polylogarithmic speedups over classical methods depending on quantum data access models for inputs and weights.
Hybrid QML models trained with classical DP-SGD retain higher accuracy than classical models under fixed privacy budgets on synthetic and image-classification tasks.
Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.
The work constructs a permutation-equivariant quantum GNN that implements message passing at selectable Weisfeiler-Leman levels, supports pre-training on small graphs, and demonstrates readout scalability with simulations up to 56 qubits on synthetic, molecular, and TSP datasets.
Coupling-Grouped XY-QAOA enables joint anomaly-feature selection via a constraint-preserving grouped-angle QAOA variant, achieving 45.9-61.3% circuit depth reduction and larger feasible executions (64 qubits at p=2) on IBM Heron hardware compared to standard approaches.
End-to-end QSP-based quantum circuits solve linear PDEs on IBM hardware with tunable error and handle non-homogeneous Dirichlet boundaries for a plasma Poisson problem.
Meta-learning with 24 classical complexity metrics predicts the optimal quantum encoding circuit among 9 candidates with up to 85.7% top-3 accuracy.
A necessary condition for variational quantum circuits to reach exact ground states requires matching module projection norms between input and solution, enabling classical O(n^5) exact solvers for problems like MaxCut.
JGRA framework extracts geometric descriptors from noise-conditioned Jacobians in QNNs after entropy-matched calibration and noise-aware training, and empirically shows these descriptors predict robustness under unseen noise.
Hybrid quantum-classical model with quantum feature encoding and clustering outperforms classical neural networks for LPBF melt pool prediction.
Introduces a JAX-based framework for pulse-level QML with composable ansatze, end-to-end pulse optimization, and Fourier-analytic diagnostics.
Angle encoding in hybrid quantum logistic regression yields the strongest performance among quantum variants, matching classical baselines in discrimination and achieving the lowest calibration error on pulsar candidate data.
Pauli Correlation Encoding framework achieves competitive or superior solutions on QOPTLib benchmark instances for combinatorial optimization.
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