ROQAM formulates Green's function estimation via orthogonal polynomials to preserve Hessenberg structure under finite precision, enabling lower precision with depth and outperforming QSVD by orders of magnitude in resource estimates for a quantum impurity model.
Approximation Theory and the Design of Fast Algorithms
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abstract
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used to speed up primitives crucial for the design of fast algorithms for problems such as simulating random walks, graph partitioning, solving linear system of equations, computing eigenvalues and combinatorial approaches to solve semi-definite programs.
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quant-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Estimating Green's functions with a robust quantum Arnoldi method
ROQAM formulates Green's function estimation via orthogonal polynomials to preserve Hessenberg structure under finite precision, enabling lower precision with depth and outperforming QSVD by orders of magnitude in resource estimates for a quantum impurity model.