Related papers: Simulating Bosonic Baths with Error Bars
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline…
We consider a prototypical system of an infinite range transverse field Ising model coupled to a bosonic bath. By integrating out the bosonic degrees, an effective anisotropic Heisenberg model is obtained for the spin system. The phase…
Many-body physics is one very well suited field for testing quantum algorithms and for finding working heuristics on present quantum computers. We have investigated the non-equilibrium dynamics of one- and two-electron systems, which are…
Reliable quantum technology requires knowledge of the dynamics governing the underlying system. This problem of characterizing and benchmarking quantum devices or experiments in continuous time is referred to as the Hamiltonian learning…
We derive global estimates for the error in solutions of linear hyperbolic systems due to inaccurate boundary geometry. We show that the error is bounded by data and bounded in time when the solutions in the true and approximate domains are…
We study truncations of hierarchical equations of motion (HEOM) for finite-dimensional open quantum systems. We prove that for finite-dimensional approximations constructed with a Schur-complement type of terminator, the spectrum converges…
Given a truncated perturbation expansion of a physical quantity, one can, under certain circumstances, obtain lower or upper bounds (or both) to the sum of the full perturbation series by using the Borel transform and a variational…
Galaxies, dark matter haloes, and star clusters have a finite extent, yet most simple dynamical models have an infinite extent. The default method to generate dynamical models with a finite extent is to apply an energy truncation to the…
We study a harmonic system coupled to chain of first neighbor interacting oscillators. After deriving the exact dynamics of the system, we prove that one can effectively describe the exact dynamics by considering a suitable shorter chain.…
A novel approximation scheme is proposed to describe the dynamics of the spin-boson problem. Being nonperturbative in the coupling strength nor in the tunneling frequency, it gives reliable results over a wide regime of temperatures and…
We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins $S\geq 1/2$. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens…
Within the framework of imaginary-time evolution for matrix product states, we introduce a cluster version of the infinite time-evolving block decimation algorithm for simulating quantum many-body systems, addressing the computational…
A recent promising arena for quantum advantage is simulating exponentially large classical systems. Here, we show how this advantage can be used to calculate the dynamics of open classical systems experiencing dissipation, including the…
We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the…
This paper presents a pseudo-spectral method for Dynamic Optimization Problems (DOPs) that allows for tight polynomial bounds to be achieved via flexible sub-intervals. The proposed method not only rigorously enforces inequality…
Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…
The simulation of long, nonlinear dispersive waves in bounded domains usually requires the use of slip-wall boundary conditions. Boussinesq systems appearing in the literature are generally not well-posed when such boundary conditions are…