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High-performance numerical methods are essential not only for advancing quantum many-body physics but also for enabling integration with emerging quantum computing platforms. We present a scalable and general-purpose parallel algorithm for…
We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
We formulate an effective-description framework for the dynamics of open quantum systems by extending the time-coarse-graining formalism to open systems. Our coarse-graining procedure efficiently removes high-frequency processes which are…
We introduce Quantum Index Algebra (QIA) as a finite, index-based algebraic framework for representing and manipulating quantum operators on Hilbert spaces of dimension $2^m$. In QIA, operators are expressed as structured combinations of…
In numerical studies of the dynamics of unbound quantum mechanical systems, absorbing boundary conditions are frequently applied. Although this certainly provides a useful tool in facilitating the description of the system, its applications…
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and…
We propose a framework for computing the structure and dynamics for second-quantized many-nucleon Hamiltonians on quantum computers. We develop an oracle-based Hamiltonian input model that computes the many-nucleon states and nonzero…
An algorithm for simulation of quantum many-body dynamics having su(2) spectrum-generating algebra is developed. The algorithm is based on the idea of dynamical coarse-graining. The original unitary dynamics of the target observables, the…
We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers, addressing key challenges in the field. In contrast to existing approaches, our method achieves…
We discuss the possibility to modify many-body Hilbert quantum formalism that is necessary for the representation of quantum systems dynamics. The notion of effective classical algorithm and visualization of quantum dynamics play the key…
Non-commutative algebras and entanglement are two of the most important hallmarks of many-body quantum systems. Dynamical perturbation methods are the most widely used approaches for quantum many-body systems. While study of…
Encoding combinatorial optimization problems into physically meaningful Hamiltonians with tractable energy landscapes forms the foundation of quantum optimization. Numerous works have studied such efficient encodings for the class of…
Due to the exponential growth of the state space of coupled quantum systems it is not possible, in general, to numerically store the state of a very large number of quantum systems within a classical computer. We demonstrate a method for…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…
A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the…
Simulating open quantum systems is an essential technique for understanding complex physical phenomena and advancing quantum technologies. Some quantum algorithms simulate Lindblad dynamics exponentially accurately, i.e., they achieve…
The formation, dissolution, and dynamics of multi-particle complexes is of fundamental interest in the study of stochastic chemical systems. In 1976, Masao Doi introduced a Fock space formalism for modeling classical particles. Doi's…
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…