Related papers: Optimal Bounds, Barriers, and Extensions for Non-H…
Long-range (LR) quantum spin systems offer promising advantages for quantum information processing and sensing. Here, we investigate parameter estimation in an long-range XX spin model coupled to a reservoir, which gives rise to an…
Quantum optimization algorithms can be used to recreate unsupervised learning clustering of data by mapping the problem to a graph optimization problem and finding the minimum energy for a MaxCut problem formulation. This research tests the…
Variational Quantum Algorithms are a vital part of quantum computing. It is a blend of quantum and classical methods for tackling tough problems in machine learning, chemistry, and combinatorial optimization. Yet as these algorithms scale…
As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new…
The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical…
Quantum simulation of non-Markovian open quantum dynamics is essential but challenging for standard quantum computers due to their non-Hermitian nature, leading to non-unitary evolution, and the limitations of available quantum resources.…
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…
In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…
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…
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),…
Nonorthogonal quantum state discrimination (QSD) plays an important role in quantum information and quantum communication. In addition, compared to Hermitian quantum systems, parity-time-($\mathcal{PT}$-)symmetric non-Hermitian quantum…
Quantum computing is increasingly offering concrete solutions toward the simulation of nuclear structure, with the potential to overcome the exponential scaling that limits classical diagonalization methods in large spaces. A particularly…
Quantum signal processing (QSP) represents a real scalar polynomial of degree $d$ using a product of unitary matrices of size $2\times 2$, parameterized by $(d+1)$ real numbers called the phase factors. This innovative representation of…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
We propose a natural application of Quantum Linear Systems Problem (QLSP) solvers such as the HHL algorithm to efficiently prepare highly excited interior eigenstates of physical Hamiltonians in a variational and targeted manner. This is…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation. As a…
Quantum computers have long been anticipated to excel in simulating quantum many-body physics. While most previous work has focused on Hermitian physics, we demonstrate the power of variational quantum circuits for resource-efficient…
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…