Related papers: $TimeEvolver$: A Program for Time Evolution With I…

We study the problem of learning an unknown quantum many-body Hamiltonian $H$ from black-box queries to its time evolution $e^{-\mathrm{i} H t}$. Prior proposals for solving this task either impose some assumptions on $H$, such as its…

Simulating vibrational dynamics is essential for understanding molecular structure, unlocking useful applications such as vibrational spectroscopy for high-fidelity chemical detection. Quantum algorithms for vibrational dynamics are…

We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given…

First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…

From weather to neural networks, modeling is not only useful for understanding various phenomena, but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their…

We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for…

This paper proposes and analyzes an a posteriori error estimator for the finite element multi-scale discretization approximation of the Steklov eigenvalue problem. Based on the a posteriori error estimates, an adaptive algorithm of shifted…

We examine the time evolution of an asymmetric Hubbard dimer, which has a different on-site interaction on the two sites. The Hamiltonian has a time-dependent hopping term, which can be employed to describe an electric field (which creates…

We propose an iterative variational quantum algorithm to simulate the time evolution of arbitrary initial states within a given subspace. The algorithm compresses the Trotter circuit into a shorter-depth parameterized circuit, which is…

Simulation of open quantum systems is an area of active research in quantum algorithms. In this work, we revisit the connection between Markovian open-system dynamics and averages of Hamiltonian real-time evolutions, which we refer to as…

There exists the well known approximate expression describing the large time behaviour of matrix elements of the evolution operator in quantum theory: <U(t)>=exp(at)+... This expression plays the crucial role in considerations of problems…

Quantum Krylov subspace methods can extract ground and excited states by diagonalizing the Hamiltonian in a compact variational space. In practice, these spaces are almost always generated by real or imaginary time evolution, forcing a…

In this paper a new restarting method for Krylov subspace matrix exponential evaluations is proposed. Since our restarting technique essentially employs the residual, some convergence results for the residual are given. We also discuss how…

Simulating physical systems has been an important application of classical and quantum computers. In this article we present an efficient classical algorithm for simulating time-dependent quantum mechanical Hamiltonians over constant…

During the training phase of machine learning (ML) models, it is usually necessary to configure several hyperparameters. This process is computationally intensive and requires an extensive search to infer the best hyperparameter set for the…

We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior…

Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…

Most machine learning methods assume fixed probability distributions, limiting their applicability in nonstationary real-world scenarios. While continual learning methods address this issue, current approaches often rely on black-box models…

Recent advances in LLM-guided evolutionary computation, particularly AlphaEvolve, have demonstrated remarkable success in discovering novel mathematical constructions and solving challenging optimization problems. In this article, we…

We introduce CodeEvolve, an open-source framework that couples large language models with island-based evolutionary search for end-to-end algorithmic discovery. CodeEvolve integrates inspiration-based crossover, meta-prompting, and…