4,277 research outputs found
Quantum field tomography
We introduce the concept of quantum field tomography, the efficient and
reliable reconstruction of unknown quantum fields based on data of correlation
functions. At the basis of the analysis is the concept of continuous matrix
product states, a complete set of variational states grasping states in quantum
field theory. We innovate a practical method, making use of and developing
tools in estimation theory used in the context of compressed sensing such as
Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum
field states based on low-order correlation functions. In the absence of a
phase reference, we highlight how specific higher order correlation functions
can still be predicted. We exemplify the functioning of the approach by
reconstructing randomised continuous matrix product states from their
correlation data and study the robustness of the reconstruction for different
noise models. We also apply the method to data generated by simulations based
on continuous matrix product states and using the time-dependent variational
principle. The presented approach is expected to open up a new window into
experimentally studying continuous quantum systems, such as encountered in
experiments with ultra-cold atoms on top of atom chips. By virtue of the
analogy with the input-output formalism in quantum optics, it also allows for
studying open quantum systems.Comment: 31 pages, 5 figures, minor change
Improved real-time dynamics from imaginary frequency lattice simulations
The computation of real-time properties, such as transport coefficients or
bound state spectra of strongly interacting quantum fields in thermal
equilibrium is a pressing matter. Since the sign problem prevents a direct
evaluation of these quantities, lattice data needs to be analytically continued
from the Euclidean domain of the simulation to Minkowski time, in general an
ill-posed inverse problem. Here we report on a novel approach to improve the
determination of real-time information in the form of spectral functions by
setting up a simulation prescription in imaginary frequencies. By carefully
distinguishing between initial conditions and quantum dynamics one obtains
access to correlation functions also outside the conventional Matsubara
frequencies. In particular the range between and ,
which is most relevant for the inverse problem may be more highly resolved. In
combination with the fact that in imaginary frequencies the kernel of the
inverse problem is not an exponential but only a rational function we observe
significant improvements in the reconstruction of spectral functions,
demonstrated in a simple 0+1 dimensional scalar field theory toy model.Comment: 8 pages, 5 figures, Talk given at the XXXVth International Symposium
on Lattice Field Theory, June 18-24, 2017, Granada, Spai
Can biological quantum networks solve NP-hard problems?
There is a widespread view that the human brain is so complex that it cannot
be efficiently simulated by universal Turing machines. During the last decades
the question has therefore been raised whether we need to consider quantum
effects to explain the imagined cognitive power of a conscious mind.
This paper presents a personal view of several fields of philosophy and
computational neurobiology in an attempt to suggest a realistic picture of how
the brain might work as a basis for perception, consciousness and cognition.
The purpose is to be able to identify and evaluate instances where quantum
effects might play a significant role in cognitive processes.
Not surprisingly, the conclusion is that quantum-enhanced cognition and
intelligence are very unlikely to be found in biological brains. Quantum
effects may certainly influence the functionality of various components and
signalling pathways at the molecular level in the brain network, like ion
ports, synapses, sensors, and enzymes. This might evidently influence the
functionality of some nodes and perhaps even the overall intelligence of the
brain network, but hardly give it any dramatically enhanced functionality. So,
the conclusion is that biological quantum networks can only approximately solve
small instances of NP-hard problems.
On the other hand, artificial intelligence and machine learning implemented
in complex dynamical systems based on genuine quantum networks can certainly be
expected to show enhanced performance and quantum advantage compared with
classical networks. Nevertheless, even quantum networks can only be expected to
efficiently solve NP-hard problems approximately. In the end it is a question
of precision - Nature is approximate.Comment: 38 page
Information field theory
Non-linear image reconstruction and signal analysis deal with complex inverse
problems. To tackle such problems in a systematic way, I present information
field theory (IFT) as a means of Bayesian, data based inference on spatially
distributed signal fields. IFT is a statistical field theory, which permits the
construction of optimal signal recovery algorithms even for non-linear and
non-Gaussian signal inference problems. IFT algorithms exploit spatial
correlations of the signal fields and benefit from techniques developed to
investigate quantum and statistical field theories, such as Feynman diagrams,
re-normalisation calculations, and thermodynamic potentials. The theory can be
used in many areas, and applications in cosmology and numerics are presented.Comment: 8 pages, in-a-nutshell introduction to information field theory (see
http://www.mpa-garching.mpg.de/ift), accepted for the proceedings of MaxEnt
2012, the 32nd International Workshop on Bayesian Inference and Maximum
Entropy Methods in Science and Engineerin
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