Ansatz
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Related Articles from SNS
Expressibility, Noise, and Error Mitigation in VQE Ansatz Selection
arXiv:2606.04955v1 Announce Type: cross Abstract: The variational quantum eigensolver (VQE) is a promising algorithm for near-term quantum chemistry applications, but selecting optimal ansatz circuits remains challenging. Expressibility, a metric quantifying a circuit's ability to explore the Hilbert space, has been proposed as a guide for ansatz selection, but recent work showed it inconsistently predicts VQE performance under realistic noise for $H_2$. We extend this investigation to cover...
Enhancing Neural-Network Variational Monte Carlo through Basis Transformation
arXiv:2604.15888v2 Announce Type: replace-cross Abstract: Neural-network variational Monte Carlo (NNVMC) has emerged as a powerful tool for solving quantum many-body problems, yet systematic pathways for improving its accuracy remain largely heuristic. Here, we introduce a physically motivated basis transformation for NNVMC that enhances variational expressivity without increasing the complexity of the neural-network ansatz itself. By formulating the many-body wave function in a Gaussian...
The Coercivity Gap in Neural PDE Solvers: Parameter Escape and Functional Convergence
arXiv:2606.04018v1 Announce Type: new Abstract: We study neural approximation of elliptic PDE solutions from a variational perspective. The central point is the distinction between the geometry of neural parameters and the convergence of the corresponding physical states. Even when the original elliptic energy is coercive and strictly convex in the natural energy space, its restriction to a nonlinear neural ansatz may fail to be coercive in parameter space.
ND-TNN: Tensor-Neural-Network Approximation for High-Dimensional Nonlocal Diffusion Models
arXiv:2606.08685v1 Announce Type: new Abstract: We study a numerical method, built on the tensor neural network (TNN) architecture introduced in \cite{wang2022tensor}, for solving nonlocal diffusion models in high-dimensional spaces. The tensor-product structure of the TNN ansatz, combined with the separability of the Gaussian kernel, reduces the high-dimensional integrals in the nonlocal energy to products of low-dimensional integrals, which are evaluated by Gauss--Legendre quadrature;...
Generative Quantum Data Embeddings for Supervised Learning
Announce Type: cross Abstract: Many practically relevant applications of quantum machine learning involve classical data, for which performance depends critically on how inputs are embedded into quantum states. Yet the use of a fixed embedding circuit ansatz remains standard practice.
Self-focusing of helicity drives finite-time singularities in inviscid flows
arXiv:2605.17569v2 Announce Type: replace Abstract: This paper deals with the longstanding quest of the possible existence of finite-time singularities in the equations governing the dynamics of inviscid fluids, namely, Euler equations. Here, two contributions are brought for the case of perfect fluids with finite initial energy. First, a self-similar velocity field inspired by Leray Ansatz is proposed which allows for a separation of variables that transforms the original partial...
Kernel Methods in the Deep Ritz framework: Theory and practice
Announce Type: replace Abstract: In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential equations with weak enforcement of boundary conditions using Nitsche's method. A priori error estimates are proven in different norms leveraging both standard results for weak solutions of elliptic equations and well-established convergence results for kernel methods.
Resource-efficient energy-based operator selection in fermionic ADAPT-VQE via exact Hamiltonian transformation
arXiv:2606.04786v1 Announce Type: cross Abstract: The energy-based approach to operator selection in ADAPT-VQE relies on reconstructing the one-parameter energy landscape for each operator in the pool. In fermionic implementations, the cost of reconstructing this energy landscape often becomes a bottleneck. We address this issue through an exact Hamiltonian transformation that reformulates the one-parameter energy landscape according to a generator-dependent fragmentation of the transformed...
Accurate, full-dimensional computations of thousands of complex vibrational eigenstates with tree tensor network states
arXiv:2605.00998v2 Announce Type: replace Abstract: Tree tensor network states (TTNSs) combined with the density matrix renormalization group (DMRG) are emerging as powerful tools for vibrational and vibronic structure simulations in molecules with strong coupling and fluxionality. In this Perspective, we discuss how TTNS methods enable accurate, full-dimensional computations of thousands of eigenstates for molecular systems ranging from quartic-force-field benchmarks to molecules with...
Quantum feature-map learning with reduced resource overhead
Announce Type: replace-cross Abstract: Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature-maps, which embed classical data into the state space of qubits. We introduce Quantum Feature-Map Learning via Analytic Iterative Reconstructions (Q-FLAIR), an algorithm that reduces quantum resource overhead in iterative feature-map circuit construction.