Related papers: Provably Efficient Simulation of 1D Long-Range Int…
The density matrix renormalization group (DMRG) method allows an efficient computation of the properties of interacting 1D quantum systems. Two-dimensional (2D) systems, capable of displaying much richer quantum behavior, generally lie…
Competition between short- and long-range interactions underpins many emergent phenomena in nature. Despite rapid progress in their experimental control, computational methods capable of accurately simulating open quantum many-body systems…
This chapter gives a self-contained review of the how standard open quantum system Hamiltonians can be mapped analytically onto representations in which the environments appear as one dimensional harmonic chains with nearest neighbour…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the…
Many-body systems of quantum interacting particles in which time-reversal symmetry is broken give rise to a variety of rich collective behaviors, and are therefore a major target of research in modern physics. Quantum simulators can…
While recent advances have established efficient quantum algorithms for preparing Gibbs states of finite-dimensional systems, comparable complexity results for bosonic and other infinite-dimensional models remain unexplored. We introduce…
A linearized tensor renormalization group (LTRG) algorithm is proposed to calculate the thermodynamic properties of one-dimensional quantum lattice models, that is incorporated with the infinite time-evolving block decimation technique, and…
We develop a method for studying the real time dynamics of Heisenberg operators in strongly-interacting nonequilibrium quantum impurity models. Our method is applicable to a wide range of interaction strengths and to bias voltages beyond…
The Fokker-Planck equation models rare events across sciences, but its high-dimensional nature challenges classical computers. Quantum algorithms for such non-unitary dynamics often suffer from exponential {decay in} success probability. We…
We present and analyze the fermionic time evolving density matrix using orthogonal polynomials algorithm (fTEDOPA), which enables the numerically exact simulation of open quantum systems coupled to a fermionic environment. The method allows…
Quantum systems typically reach thermal equilibrium rather quickly when coupled to a thermal environment. The usual way of bounding the speed of this process is by estimating the spectral gap of the dissipative generator. However the gap,…
In this paper recent substantial progress in applying the density-matrix renormalization-group (DMRG) to the simulation of the time-evolution of strongly correlated quantum systems in one dimension is reviewed. Various approaches to…
We show that coupling ultracold atoms in optical lattices to quantized modes of an optical cavity leads to quantum phases of matter, which at the same time posses properties of systems with both short- and long-range interactions. This…
The fabrication, utilisation, and efficiency of quantum technologies rely on a good understanding of quantum thermodynamic properties. Many-body systems are often used as hardware for these quantum devices, but interactions between…
While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
Quantum simulation is one of the most promising scientific applications of quantum computers. Due to decoherence and noise in current devices, it is however challenging to perform digital quantum simulation in a regime that is intractable…
Calculations at finite temperatures are fundamental in different scientific fields, from nuclear physics to condensed matter. Evolution in imaginary time is a prominent classical technique for preparing thermal states of quantum systems. We…