Related papers: Efficient higher-order matrix product operators fo…
Hyperparameter (HP) optimization of deep learning (DL) is essential for high performance. As DL often requires several hours to days for its training, HP optimization (HPO) of DL is often prohibitively expensive. This boosted the emergence…
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians. Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series…
We propose a new method for simulating certain type of time-dependent Hamiltonian $H(t) = \sum_{i=1}^m \gamma_i(t) H_i$ where $\gamma_i(t)$ (and its higher order derivatives) is bounded, computable function of time $t$, and each $H_i$ is…
We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
Determining the dynamics of the expectation values for operators acting on a quantum many-body (QMB) system is a challenging task. Matrix product states (MPS) have traditionally been the "go-to" models for these systems because calculating…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
Technical indicators use graphic representations of data sets by applying various mathematical formulas to financial time series of prices. These formulas comprise a set of rules and parameters whose values are not necessarily known and…
We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved…
Long Short Term Memory(LSTM) models are the building blocks of many state-of-the-art natural language processing(NLP) and speech enhancement(SE) algorithms. However, there are a large number of parameters in an LSTM model. This usually…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
We present a comparative study of the permutation matrix representation (PMR) method for Hamiltonian simulation alongside other leading quantum algorithms. Our analysis focuses on resource costs for simulating both time-independent and…
Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while…
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…
Hyperparameter optimisation is a crucial process in searching the optimal machine learning model. The efficiency of finding the optimal hyperparameter settings has been a big concern in recent researches since the optimisation process could…
We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a…
Tensor network operators, such as the matrix product operator (MPO) and the projected entangled-pair operator (PEPO), can provide efficient representation of certain linear operators in high dimensional spaces. This paper focuses on the…
Matrix product density operators (MPDOs) are an important class of states with interesting properties. Consequently, it is important to understand how to prepare these states experimentally. One possible way to do this is to design an open…
We propose an approach to factorize the time-evolution operator of a quantum system through a (finite) sequence of elementary operations that are time-ordered. Our proposal borrows from previous approaches based on Lie algebra techniques…