The quantum query complexity of elliptic PDE

DOI10.1016/j.jco.2006.04.005zbMath1110.65130arXivquant-ph/0512241OpenAlexW4206688793MaRDI QIDQ855898

Stefan Heinrich

Publication date: 7 December 2006

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0512241

zbMATH Keywords

Green's functionquantum algorithmweakly singular integralselliptic partial differentialMonte Carlo quadrature

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Boundary value problems for second-order elliptic equations (35J25) Integral representations of solutions to PDEs (35C15) Complexity and performance of numerical algorithms (65Y20) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items

Optimal approximation of elliptic problems by linear and nonlinear mappings. IV: Errors in \(L_{2}\) and other norms, Optimal integration error on anisotropic classes for restricted Monte Carlo and quantum algorithms, Lower bound for quantum integration error on anisotropic Sobolev classes, The randomized information complexity of elliptic PDE, Optimal approximation of elliptic problems by linear and nonlinear mappings. II

Cites Work

• Almost optimal solution of initial-value problems by randomized and quantum algorithms
• Deterministic and stochastic error bounds in numerical analysis
• Quantum integration in Sobolev classes
• Quantum summation with an application to integration.
• From Monte Carlo to quantum computation
• Quantum approximation. I: Embeddings of finite-dimensional \(L_{p}\) spaces
• Quantum approximation. II: Sobolev embeddings
• Quantum complexity of parametric integration
• Worst case complexity of multivariate Feynman--Kac path integration
• The complexity of definite elliptic problems with noisy data
• Monte Carlo approximation of weakly singular integral operators
• The randomized information complexity of elliptic PDE
• Optimal approximation of elliptic problems by linear and nonlinear mappings. I
• Optimal approximation of elliptic problems by linear and nonlinear mappings. II
• A remark on an a really mean p-valent function
• Local polynomial reproduction and moving least squares approximation
• Geometric quantum computation
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• ISOLATION OF SINGULARITIES OF THE GREEN'S FUNCTION
• Quantum complexity of integration
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item