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Computing spectral functions in large, non-periodic super-moir\'e systems remains an open problem due to the exceptionally large system size that must be considered. Here, we establish a tensor network methodology that allows computing…
Spectroscopy is the most important method for probing the structure of molecules. However, predicting molecular spectra on classical computers is computationally expensive, with the most accurate methods having a cost that grows…
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…
We compare two recently developed strategies, implemented in open source software packages, for computing linear optical spectra in condensed phase environments in the presence of nonadiabatic effects. Both approaches rely on computing…
The central challenge for describing the dynamics in open quantum systems is that the Hilbert space of typical environments is too large to be treated exactly. In some cases, such as when the environment has a short memory time or only…
Every quantum system is coupled to an environment. Such system-environment interaction leads to temporal correlation between quantum operations at different times, resulting in non-Markovian noise. In principle, a full characterisation of…
The correlated projection superoperator techniques provide a better understanding about how correlations lead to strong non-Markovian effects in open quantum systems. Their superoperators are independent of initial state, which may not be…
Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient…
Dissipative phase transitions in quantum systems have been largely studied under the so-called Markovian approximation, where the environments to which the systems are coupled are memoryless. Here, we present a generalization of the…
Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly…
A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, how to extract the…
Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the…
A general method is discussed to obtain Markovian master equations which describe the interaction with the environment in a microscopic and non-perturbative fashion. It is based on combining time-dependent scattering theory with the concept…
We develop a package of numerical simulations implemented in MATLAB to solve complex many-body quantum systems. We focus on widely used examples that include the calculation of the magnetization dynamics for the closed and open Ising model,…
The combination of chain-mapping and tensor-network techniques provides a powerful tool for the numerically exact simulation of open quantum systems interacting with structured environments. However, these methods suffer from a quadratic…
Spectroscopy is one of the most accurate probes of the molecular world. However, predicting molecular spectra accurately is computationally difficult because of the presence of entanglement between electronic and nuclear degrees of freedom.…
Continuous quantum measurement is the backbone of various methods in quantum control, quantum metrology, and quantum information. Here, we present a generalized formulation of dispersive measurement of a complex quantum systems. We describe…
Estimating the parameters that dictate the dynamics of a quantum system is an important task for quantum information processing and quantum metrology, as well as fundamental physics. In this paper we develop a method for parameter…
We present a formulation of non-Markovian quantum trajectories for open systems from a measurement theory perspective. In our treatment there are three distinct ways in which non-Markovian behavior can arise; a mode dependent coupling…
An approach, called discretized environment method, is introduced to treat exactly non-Markovian effects in open quantum systems. In this approach, a complex environment described by a spectral function is mapped into a finite set of…