Related papers: Sample-based Hamiltonian and Lindbladian simulatio…

We establish improved sample-complexity bounds for sample-based Lindbladian simulation based on the Wave Matrix Lindbladization (WML) algorithm. For a jump operator $L$ with dimension $d$, we derive an explicit non-asymptotic sample…

Density matrix exponentiation (DME) is a general procedure that converts an unknown quantum state into the Hamiltonian evolution. This enables state-dependent operations and can reveal nontrivial properties of the state, among other…

Since precisely controlling dissipation in realistic environments is challenging, digital simulation of the Lindblad master equation (LME) is of great significance for understanding nonequilibrium dynamics in open quantum systems. However,…

Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian…

We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd,…

In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum…

The reduced density matrix (RDM) plays a key role in quantum entanglement and measurement, as it allows the extraction of almost all physical quantities related to the reduced degrees of freedom. However, restricted by the degrees of…

Diffusion Probabilistic Models (DPMs) are generative models showing competitive performance in various domains, including image synthesis and 3D point cloud generation. Sampling from pre-trained DPMs involves multiple neural function…

SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…

Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…

Score-based diffusion models have achieved remarkable empirical success in generating high-quality samples from target data distributions. Among them, the Denoising Diffusion Probabilistic Model (DDPM) is one of the most widely used…

We study infinite-horizon Discounted Markov Decision Processes (DMDPs) under a generative model. Motivated by the Algorithm with Advice framework Mitzenmacher and Vassilvitskii 2022, we propose a novel framework to investigate how a…

Distance metric learning (DML) is to learn the embeddings where examples from the same class are closer than examples from different classes. It can be cast as an optimization problem with triplet constraints. Due to the vast number of…

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…

Quantum phase estimation (QPE) and Lindbladian dynamics are both foundational in quantum information science and central to quantum algorithm design. In this work, we bridge these two concepts: certain simple Lindbladian processes can be…

The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these…

Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…

Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a powerful family of generative models that can yield high-fidelity samples and competitive log-likelihoods across a range of domains, including image and speech synthesis.…

Deep Metric Learning (DML) is a group of techniques that aim to measure the similarity between objects through the neural network. Although the number of DML methods has rapidly increased in recent years, most previous studies cannot…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…