6 research outputs found
Assessing non-Markovian dynamics
We investigate what a snapshot of a quantum evolution - a quantum channel
reflecting open system dynamics - reveals about the underlying continuous time
evolution. Remarkably, from such a snapshot, and without imposing additional
assumptions, it can be decided whether or not a channel is consistent with a
time (in)dependent Markovian evolution, for which we provide computable
necessary and sufficient criteria. Based on these, a computable measure of
`Markovianity' is introduced. We discuss how the consistency with Markovian
dynamics can be checked in quantum process tomography. The results also clarify
the geometry of the set of quantum channels with respect to being solutions of
time (in)dependent master equations.Comment: 5 pages, RevTex, 2 figures. (Except from typesetting) version to be
published in the Physical Review Letter
Third quantization: a general method to solve master equations for quadratic open Fermi systems
The Lindblad master equation for an arbitrary quadratic system of n fermions
is solved explicitly in terms of diagonalization of a 4n x 4n matrix, provided
that all Lindblad bath operators are linear in the fermionic variables. The
method is applied to the explicit construction of non-equilibrium steady states
and the calculation of asymptotic relaxation rates in the far from equilibrium
problem of heat and spin transport in a nearest neighbor Heisenberg XY spin 1/2
chain in a transverse magnetic field.Comment: 24 pages, with 8 eps figures - few minor corrections to the published
version, e.g. anti-symmetrizing the matrix given by eq. (27
Entanglement and correlation functions following a local quench: a conformal field theory approach
We show that the dynamics resulting from preparing a one-dimensional quantum
system in the ground state of two decoupled parts, then joined together and
left to evolve unitarily with a translational invariant Hamiltonian (a local
quench), can be described by means of quantum field theory. In the case when
the corresponding theory is conformal, we study the evolution of the
entanglement entropy for different bi-partitions of the line. We also consider
the behavior of one- and two-point correlation functions. All our findings may
be explained in terms of a picture, that we believe to be valid more generally,
whereby quasiparticles emitted from the joining point at the initial time
propagate semiclassically through the system.Comment: 19 pages, 4 figures, v2 typos corrected and refs adde
Optimal Control for Generating Quantum Gates in Open Dissipative Systems
Optimal control methods for implementing quantum modules with least amount of
relaxative loss are devised to give best approximations to unitary gates under
relaxation. The potential gain by optimal control using relaxation parameters
against time-optimal control is explored and exemplified in numerical and in
algebraic terms: it is the method of choice to govern quantum systems within
subspaces of weak relaxation whenever the drift Hamiltonian would otherwise
drive the system through fast decaying modes. In a standard model system
generalising decoherence-free subspaces to more realistic scenarios,
openGRAPE-derived controls realise a CNOT with fidelities beyond 95% instead of
at most 15% for a standard Trotter expansion. As additional benefit it requires
control fields orders of magnitude lower than the bang-bang decouplings in the
latter.Comment: largely expanded version, superseedes v1: 10 pages, 5 figure
Can One Trust Quantum Simulators?
Various fundamental phenomena of strongly-correlated quantum systems such as
high- superconductivity, the fractional quantum-Hall effect, and quark
confinement are still awaiting a universally accepted explanation. The main
obstacle is the computational complexity of solving even the most simplified
theoretical models that are designed to capture the relevant quantum
correlations of the many-body system of interest. In his seminal 1982 paper
[Int. J. Theor. Phys. 21, 467], Richard Feynman suggested that such models
might be solved by "simulation" with a new type of computer whose constituent
parts are effectively governed by a desired quantum many-body dynamics.
Measurements on this engineered machine, now known as a "quantum simulator,"
would reveal some unknown or difficult to compute properties of a model of
interest. We argue that a useful quantum simulator must satisfy four
conditions: relevance, controllability, reliability, and efficiency. We review
the current state of the art of digital and analog quantum simulators. Whereas
so far the majority of the focus, both theoretically and experimentally, has
been on controllability of relevant models, we emphasize here the need for a
careful analysis of reliability and efficiency in the presence of
imperfections. We discuss how disorder and noise can impact these conditions,
and illustrate our concerns with novel numerical simulations of a paradigmatic
example: a disordered quantum spin chain governed by the Ising model in a
transverse magnetic field. We find that disorder can decrease the reliability
of an analog quantum simulator of this model, although large errors in local
observables are introduced only for strong levels of disorder. We conclude that
the answer to the question "Can we trust quantum simulators?" is... to some
extent.Comment: 20 pages. Minor changes with respect to version 2 (some additional
explanations, added references...