8 research outputs found
Crossover between ballistic and diffusive transport: The Quantum Exclusion Process
We study the evolution of a system of free fermions in one dimension under
the simultaneous effects of coherent tunneling and stochastic Markovian noise.
We identify a class of noise terms where a hierarchy of decoupled equations for
the correlation functions emerges. In the special case of incoherent,
nearest-neighbour hopping the equation for the two-point functions is solved
explicitly. The Green's function for the particle density is obtained
analytically and a timescale is identified where a crossover from ballistic to
diffusive behaviour takes place. The result can be interpreted as a competition
between the two types of conduction channels where diffusion dominates on large
timescales.Comment: 20 pages, 5 figure
The - divergence and Mixing times of quantum Markov processes
We introduce quantum versions of the -divergence, provide a detailed
analysis of their properties, and apply them in the investigation of mixing
times of quantum Markov processes. An approach similar to the one presented in
[1-3] for classical Markov chains is taken to bound the trace-distance from the
steady state of a quantum processes. A strict spectral bound to the convergence
rate can be given for time-discrete as well as for time-continuous quantum
Markov processes. Furthermore the contractive behavior of the
-divergence under the action of a completely positive map is
investigated and contrasted to the contraction of the trace norm. In this
context we analyse different versions of quantum detailed balance and, finally,
give a geometric conductance bound to the convergence rate for unital quantum
Markov processes
Quantum kinetic Ising models
We introduce a quantum generalization of classical kinetic Ising models,
described by a certain class of quantum many body master equations. Similarly
to kinetic Ising models with detailed balance that are equivalent to certain
Hamiltonian systems, our models reduce to a set of Hamiltonian systems
determining the dynamics of the elements of the many body density matrix. The
ground states of these Hamiltonians are well described by matrix product, or
pair entangled projected states. We discuss critical properties of such
Hamiltonians, as well as entanglement properties of their low energy states.Comment: 20 pages, 4 figures, minor improvements, accepted in New Journal of
Physic
Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
We calculate a nonequilibrium steady state of a quantum XX chain in the
presence of dephasing and driving due to baths at chain ends. The obtained
state is exact in the limit of weak driving while the expressions for one- and
two-point correlations are exact for an arbitrary driving strength. In the
steady state the magnetization profile and the spin current display diffusive
behavior. Spin-spin correlation function on the other hand has long-range
correlations which though decay to zero in either the thermodynamical limit or
for equilibrium driving. At zero dephasing a nonequilibrium phase transition
occurs from a ballistic transport having short-range correlations to a
diffusive transport with long-range correlations.Comment: 5 page
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...
A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
We study quantum transport properties of an open Heisenberg XXZ spin 1/2
chain driven by a pair of Lindblad jump operators satisfying a global
`microcanonical' constraint, i.e. conserving the total magnetization. We will
show that this system has an additional discrete symmetry which is particular
to the Liouvillean description of the problem. Such symmetry reduces the
dynamics even more than what would be expected in the standard Hilbert space
formalism and establishes existence of multiple steady states. Interestingly,
numerical simulations of the XXZ model suggest that a pair of distinct
non-equilibrium steady states becomes indistinguishable in the thermodynamic
limit, and exhibit sub-diffusive spin transport in the easy-axis regime of
anisotropy Delta > 1.Comment: 14 pages with 5 pdf figures, revised version, as accepted by New
Journal of Physic
Rank-based model selection for multiple ions quantum tomography
The statistical analysis of measurement data has become a key component of
many quantum engineering experiments. As standard full state tomography becomes
unfeasible for large dimensional quantum systems, one needs to exploit prior
information and the "sparsity" properties of the experimental state in order to
reduce the dimensionality of the estimation problem. In this paper we propose
model selection as a general principle for finding the simplest, or most
parsimonious explanation of the data, by fitting different models and choosing
the estimator with the best trade-off between likelihood fit and model
complexity. We apply two well established model selection methods -- the Akaike
information criterion (AIC) and the Bayesian information criterion (BIC) -- to
models consising of states of fixed rank and datasets such as are currently
produced in multiple ions experiments. We test the performance of AIC and BIC
on randomly chosen low rank states of 4 ions, and study the dependence of the
selected rank with the number of measurement repetitions for one ion states. We
then apply the methods to real data from a 4 ions experiment aimed at creating
a Smolin state of rank 4. The two methods indicate that the optimal model for
describing the data lies between ranks 6 and 9, and the Pearson test
is applied to validate this conclusion. Additionally we find that the mean
square error of the maximum likelihood estimator for pure states is close to
that of the optimal over all possible measurements.Comment: 24 pages, 6 figures, 3 table