5,216 research outputs found
Process tensor networks for non-Markovian open quantum systems
The advance of quantum technology relies heavily on an accurate understanding of the unavoidable interactions between quantum systems and their environment. While it is often adequate to account for the environment using approximate time-local (i.e. Markovian) equations of motion, in many scenarios such a description fails, and a more general non-Markovian theory becomes necessary. The failure of Markovian descriptions concerns not only quantitative aspects of the reduced dynamics of a quantum system, but also qualitative and conceptual aspects, such as the failure of the quantum regression formula relating the system's dynamics to its multi-time correlations. Despite considerable progress in recent years, the description and simulation of non-Markovian open quantum systems remains a conceptual and computational challenge. In this thesis we develop a versatile set of numerical methods for non-Markovian open quantum systems by combining the so-called process tensor framework with the numerical power of tensor network methods. The recently introduced process tensor is an alternative approach to open quantum systems and is - unlike the canonical approach based on dynamical maps - well suited for a rigorous characterisation of non-Markovian open quantum systems. We construct and apply process tensors in a matrix product operator form (PT-MPO) to yield a numerically exact, yet efficient representation of non-Markovian open quantum systems, which allows for a variety of practical applications. Building on the PT-MPO we introduce general methods to (1) efficiently find optimal control procedures for non-Markovian open quantum systems, (2) compute the dynamics and multi-time correlations of chains of non-Markovian open quantum systems, and (3) construct a time-translational invariant PT-MPO, which allows efficient computation of steady states even in non-equilibrium non-Markovian scenarios
Optimal Control for Open Quantum Systems: Qubits and Quantum Gates
This article provides a review of recent developments in the formulation and
execution of optimal control strategies for the dynamics of quantum systems. A
brief introduction to the concept of optimal control, the dynamics of of open
quantum systems, and quantum information processing is followed by a
presentation of recent developments regarding the two main tasks in this
context: state-specific and state-independent optimal control. For the former,
we present an extension of conventional theory (Pontryagin's principle) to
quantum systems which undergo a non-Markovian time-evolution. Owing to its
importance for the realization of quantum information processing, the main body
of the review, however, is devoted to state-independent optimal control. Here,
we address three different approaches: an approach which treats dissipative
effects from the environment in lowest-order perturbation theory, a general
method based on the time--evolution superoperator concept, as well as one based
on the Kraus representation of the time-evolution superoperator. Applications
which illustrate these new methods focus on single and double qubits (quantum
gates) whereby the environment is modeled either within the Lindblad equation
or a bath of bosons (spin-boson model). While these approaches are widely
applicable, we shall focus our attention to solid-state based physical
realizations, such as semiconductor- and superconductor-based systems. While an
attempt is made to reference relevant and representative work throughout the
community, the exposition will focus mainly on work which has emerged from our
own group.Comment: 27 pages, 18 figure
Non-Markovian dynamics in open quantum systems
The dynamical behavior of open quantum systems plays a key role in many
applications of quantum mechanics, examples ranging from fundamental problems,
such as the environment-induced decay of quantum coherence and relaxation in
many-body systems, to applications in condensed matter theory, quantum
transport, quantum chemistry and quantum information. In close analogy to a
classical Markov process, the interaction of an open quantum system with a
noisy environment is often modelled by a dynamical semigroup with a generator
in Lindblad form, which describes a memoryless dynamics leading to an
irreversible loss of characteristic quantum features. However, in many
applications open systems exhibit pronounced memory effects and a revival of
genuine quantum properties such as quantum coherence and correlations. Here,
recent results on the rich non-Markovian quantum dynamics of open systems are
discussed, paying particular attention to the rigorous mathematical definition,
to the physical interpretation and classification, as well as to the
quantification of memory effects. The general theory is illustrated by a series
of examples. The analysis reveals that memory effects of the open system
dynamics reflect characteristic features of the environment which opens a new
perspective for applications, namely to exploit a small open system as a
quantum probe signifying nontrivial features of the environment it is
interacting with. This article further explores the various physical sources of
non-Markovian quantum dynamics, such as structured spectral densities, nonlocal
correlations between environmental degrees of freedom and correlations in the
initial system-environment state, in addition to developing schemes for their
local detection. Recent experiments on the detection, quantification and
control of non-Markovian quantum dynamics are also discussed.Comment: 26 pages, 10 figure
Quantum control theory and applications: A survey
This paper presents a survey on quantum control theory and applications from
a control systems perspective. Some of the basic concepts and main developments
(including open-loop control and closed-loop control) in quantum control theory
are reviewed. In the area of open-loop quantum control, the paper surveys the
notion of controllability for quantum systems and presents several control
design strategies including optimal control, Lyapunov-based methodologies,
variable structure control and quantum incoherent control. In the area of
closed-loop quantum control, the paper reviews closed-loop learning control and
several important issues related to quantum feedback control including quantum
filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective,
some references are added, published versio
Efficiency of quantum controlled non-Markovian thermalization
We study optimal control strategies to optimize the relaxation rate towards
the fixed point of a quantum system in the presence of a non-Markovian
dissipative bath. Contrary to naive expectations that suggest that memory
effects might be exploited to improve optimal control effectiveness,
non-Markovian effects influence the optimal strategy in a non trivial way: we
present a necessary condition to be satisfied so that the effectiveness of
optimal control is enhanced by non-Markovianity subject to suitable unitary
controls. For illustration, we specialize our findings for the case of the
dynamics of single qubit amplitude damping channels. The optimal control
strategy presented here can be used to implement optimal cooling processes in
quantum technologies and may have implications in quantum thermodynamics when
assessing the efficiency of thermal micro-machines.Comment: 7 pages, 3 figure
Dynamical decoupling efficiency versus quantum non-Markovianity
We investigate the relationship between non-Markovianity and the
effectiveness of a dynamical decoupling protocol for qubits undergoing pure
dephasing. We consider an exact model in which dephasing arises due to a
bosonic environment with a spectral density of the Ohmic class. This is
parametrised by an Ohmicity parameter by changing which we can model both
Markovian and non-Markovian environments. Interestingly, we find that
engineering a non-Markovian environment is detrimental to the efficiency of the
dynamical decoupling scheme, leading to a worse coherence preservation. We show
that each dynamical decoupling pulse reverses the flow of quantum information
and, on this basis, we investigate the connection between dynamical decoupling
efficiency and the reservoir spectral density. Finally, in the spirit of
reservoir engineering, we investigate the optimum system-reservoir parameters
for achieving maximum stationary coherences.Comment: 6 pages, 4 figure
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