Classical step-size extrapolation reduces the maximum single-run circuit depth of a one-ancilla quantum ODE solver from O(1/ε) to O(polylog(1/ε)) without adding ancillae.
Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are well studied, eigenvalue transformations are distinct, especially for non-normal matrices. We propose an efficient quantum algorithm for performing a class of eigenvalue transformations that can be expressed as a certain type of matrix Laplace transformation. This allows us to significantly extend the recently developed linear combination of Hamiltonian simulation (LCHS) method [An, Liu, Lin, Phys. Rev. Lett. 131, 150603, 2023; An, Childs, Lin, arXiv:2312.03916] to represent a wider class of eigenvalue transformations, such as powers of the matrix inverse, $A^{-k}$, and the exponential of the matrix inverse, $e^{-A^{-1}}$. The latter can be interpreted as the solution of a mass-matrix differential equation of the form $A u'(t)=-u(t)$. We demonstrate that our eigenvalue transformation approach can solve this problem without explicitly inverting $A$, reducing the computational complexity.
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quant-ph 3years
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A dual Fourier-PSF and contour-PSF framework resolves the smoothness-sparsity trade-off for efficient quantum simulation of singular and holomorphic matrix functions.
Using multi-product formulas in LCHS produces commutator-sensitive error bounds and better quadrature scaling than norm-based analyses for dissipative dynamics.
citing papers explorer
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Circuit Depth Reduction of One-Ancilla Quantum Differential Equation Solver via Extrapolation
Classical step-size extrapolation reduces the maximum single-run circuit depth of a one-ancilla quantum ODE solver from O(1/ε) to O(polylog(1/ε)) without adding ancillae.
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A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations
A dual Fourier-PSF and contour-PSF framework resolves the smoothness-sparsity trade-off for efficient quantum simulation of singular and holomorphic matrix functions.
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Linear Combination of Hamiltonian Simulation with Commutator Scaling
Using multi-product formulas in LCHS produces commutator-sensitive error bounds and better quadrature scaling than norm-based analyses for dissipative dynamics.