6 papers · 1 filter
Quantum Eigenvalue Transformation via Linear Combination of Hamiltonian Simulation: A Weyl Calculus Approach
Hongkang Ni, Lexing Ying
Linear combination of Hamiltonian simulation (LCHS) provides an efficient method for implementing matrix exponentials on quantum computers. In this paper, we develop LCHS…
Inverse nonlinear fast Fourier transform on SU(2) with applications to quantum signal processing
Hongkang Ni, Rahul Sarkar, Lexing Ying +1
The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on has been widel…
Fast Phase Factor Finding for Quantum Signal Processing
Hongkang Ni, Lexing Ying
This paper presents two efficient and stable algorithms for recovering phase factors in quantum signal processing (QSP), a crucial component of many quantum algorithms. The first a…
Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method
Zhiyan Ding, Haoya Li, Lin Lin +3
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigen…
Quantum wave packet transforms with compact frequency support
Hongkang Ni, Lexing Ying
Different kinds of wave packet transforms are widely used for extracting multi-scale structures in signal processing tasks. This paper introduces the quantum circuit implementation…
Quantum Hamiltonian Learning for the Fermi-Hubbard Model
Hongkang Ni, Haoya Li, Lexing Ying
This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing…