Constrained Uniform Polynomial (CUP) and Constrained Adaptive Polynomial (CAP) solvers achieve lower error than standard QSVT and Chebyshev methods in noise-limited regimes by optimizing accuracy versus block-encoding normalization under uniform or moment-based spectral models.
Quantum Realization of the Finite Element Method
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Block encoding of the 3D heterogeneous Poisson matrix enables quantum linear system algorithms to solve discretized fracture flow problems with runtime O(N^{2/3} polylog N log(1/ε)) and exponential memory savings over classical O(N log N log(1/ε)) methods.
A QTT-based solver with Helmholtz-Leray penalization in Fourier space stably computes solutions and gradients for multiscale elliptic PDEs on meshes with up to 10^37 virtual degrees of freedom in 3D.
Schrödingerization-based quantum linear systems solver using LCHS and block preconditioning for near-optimal query complexity.
Unitaria is a new open-source Python library that provides a high-level, composable interface for block encodings in quantum computing, enabling automatic circuit generation and classical simulation-based verification.
citing papers explorer
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Constrained Optimal Polynomials for Quantum Linear System Solvers
Constrained Uniform Polynomial (CUP) and Constrained Adaptive Polynomial (CAP) solvers achieve lower error than standard QSVT and Chebyshev methods in noise-limited regimes by optimizing accuracy versus block-encoding normalization under uniform or moment-based spectral models.
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Block encoding the 3D heterogeneous Poisson equation with application to fracture flow
Block encoding of the 3D heterogeneous Poisson matrix enables quantum linear system algorithms to solve discretized fracture flow problems with runtime O(N^{2/3} polylog N log(1/ε)) and exponential memory savings over classical O(N log N log(1/ε)) methods.
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Stable full-field simulation of a multiscale elliptic equation by means of Quantized Tensor Trains
A QTT-based solver with Helmholtz-Leray penalization in Fourier space stably computes solutions and gradients for multiscale elliptic PDEs on meshes with up to 10^37 virtual degrees of freedom in 3D.
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Schr\"odingerization for quantum linear systems problems with near-optimal dependence on matrix queries
Schrödingerization-based quantum linear systems solver using LCHS and block preconditioning for near-optimal query complexity.
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Unitaria: Quantum Linear Algebra via Block Encodings
Unitaria is a new open-source Python library that provides a high-level, composable interface for block encodings in quantum computing, enabling automatic circuit generation and classical simulation-based verification.