Related papers: Exponential quantum advantages for practical non-H…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
The motivation for studying non-Hermitian systems and the role of $\mathcal{PT}$-symmetry is discussed. We investigate the use of a quantum algorithm to find the eigenvalues and eigenvectors of non-Hermitian Hamiltonians, with applications…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
Quantum mechanics features a variety of distinct properties such as coherence and entanglement, which could be explored to showcase potential advantages over classical counterparts in information processing. In general, legitimate quantum…
We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…
Non-Hermitian quantum systems exhibit fascinating characteristics such as non-Hermitian topological phenomena and skin effect, yet their studies are limited by the intrinsic difficulties associated with their eigenvalue problems, especially…
Quantum computing's potential for exponential speedup is fundamentally limited by decoherence, a phenomenon arising from environmental interactions. Non-Hermitian quantum mechanics, particularly $PT$-symmetric systems, offers a novel…
We establish a connection between quantum mechanics and computation, revealing fundamental limitations for algorithms computing spectra, especially in non-Hermitian settings. Introducing the concept of locally trivial pseudospectra (LTP),…
Non-Hermitian physics predicts open quantum system dynamics with unique topological features such as exceptional points and the non-Hermitian skin effect. We show that this new paradigm of topological systems can serve as probes for bulk…
Quantum sensing utilizing unique quantum properties of non-Hermitian systems to realize ultra-precision measurements has been attracting increasing attention. However, the debate on whether non-Hermitian systems are superior to Hermitian…
Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, based on energy variance, we propose a variational method for solving the…
A numerical algorithm is proposed to deal with parametric eigenvalue problems involving non-Hermitian matrices and is exploited to find location of defective eigenvalues in the parameter space of non-Hermitian parametric eigenvalue…
We study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the so-called non-Hermitian skin effect does not provide any distinct advantage,…
Exceptional points (EPs), the degeneracy point of non-Hermitian systems, have recently attracted great attention after its ability to greatly enhance the sensitivity of micro-cavities is demonstrated experimentally. Unlike the usual…
Time symmetry in quantum mechanics, where the current quantum state is determined jointly by both the past and the future, offers a more comprehensive description of physical phenomena. This symmetry facilitates both forward and backward…