Related papers: Superconvergence of High-order Magnus Quantum Algo…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schr\"odingersation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…
Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
In this paper, we propose a quantum algorithm that combines the momentum accelerated gradient method with Schr\"odingerization [S. Jin, N. Liu and Y. Yu, Phys. Rev. Lett, 133 (2024), 230602][S. Jin, N. Liu and Y. Yu, Phys. Rev. A, 108…
This report is concerned with the efficiency of numerical methods for simulating quantum spin systems, with the aim to implement an improved method for simulation of a time-dependent Hamiltonian that displays chirped pulses at a high…
We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hoelder or Sobolev spaces. First we discuss optimal deterministic and randomized algorithms. Then we add a new…
Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here,…
In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of…
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…
We refine a method for finding a canonical form for symmetry operators of arbitrary order for the Schroedinger eigenvalue equation on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal…
In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…
By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…