2,063 research outputs found
Entanglement and complexity of interacting qubits subject to asymmetric noise
The simulation complexity of predicting the time evolution of delocalized
many-body quantum systems has attracted much recent interest, and simulations
of such systems in real quantum hardware are promising routes to demonstrating
a quantum advantage over classical machines. In these proposals, random noise
is an obstacle that must be overcome for a faithful simulation, and a single
error event can be enough to drive the system to a classically trivial state.
We argue that this need not always be the case, and consider a modification to
a leading quantum sampling problem-- time evolution in an interacting
Bose-Hubbard chain of transmon qubits [Neill et al, Science 2018] -- where each
site in the chain has a driven coupling to a lossy resonator and particle
number is no longer conserved. The resulting quantum dynamics are complex and
highly nontrivial. We argue that this problem is harder to simulate than the
isolated chain, and that it can achieve volume-law entanglement even in the
strong noise limit, likely persisting up to system sizes beyond the scope of
classical simulation. Further, we show that the metrics which suggest classical
intractability for the isolated chain point to similar conclusions in the noisy
case. These results suggest that quantum sampling problems including nontrivial
noise could be good candidates for demonstrating a quantum advantage in
near-term hardware.Comment: 20 pages, 15 figure
Efficient computational strategies to learn the structure of probabilistic graphical models of cumulative phenomena
Structural learning of Bayesian Networks (BNs) is a NP-hard problem, which is
further complicated by many theoretical issues, such as the I-equivalence among
different structures. In this work, we focus on a specific subclass of BNs,
named Suppes-Bayes Causal Networks (SBCNs), which include specific structural
constraints based on Suppes' probabilistic causation to efficiently model
cumulative phenomena. Here we compare the performance, via extensive
simulations, of various state-of-the-art search strategies, such as local
search techniques and Genetic Algorithms, as well as of distinct regularization
methods. The assessment is performed on a large number of simulated datasets
from topologies with distinct levels of complexity, various sample size and
different rates of errors in the data. Among the main results, we show that the
introduction of Suppes' constraints dramatically improve the inference
accuracy, by reducing the solution space and providing a temporal ordering on
the variables. We also report on trade-offs among different search techniques
that can be efficiently employed in distinct experimental settings. This
manuscript is an extended version of the paper "Structural Learning of
Probabilistic Graphical Models of Cumulative Phenomena" presented at the 2018
International Conference on Computational Science
Computational astrophysics
Astronomy is an area of applied physics in which unusually beautiful objects challenge the imagination to explain observed phenomena in terms of known laws of physics. It is a field that has stimulated the development of physical laws and of mathematical and computational methods. Current computational applications are discussed in terms of stellar and galactic evolution, galactic dynamics, and particle motions
Nonintegrability, Chaos, and Complexity
Two-dimensional driven dissipative flows are generally integrable via a
conservation law that is singular at equilibria. Nonintegrable dynamical
systems are confined to n*3 dimensions. Even driven-dissipative deterministic
dynamical systems that are critical, chaotic or complex have n-1 local
time-independent conservation laws that can be used to simplify the geometric
picture of the flow over as many consecutive time intervals as one likes. Those
conserevation laws generally have either branch cuts, phase singularities, or
both. The consequence of the existence of singular conservation laws for
experimental data analysis, and also for the search for scale-invariant
critical states via uncontrolled approximations in deterministic dynamical
systems, is discussed. Finally, the expectation of ubiquity of scaling laws and
universality classes in dynamics is contrasted with the possibility that the
most interesting dynamics in nature may be nonscaling, nonuniversal, and to
some degree computationally complex
Making dynamic modelling effective in economics
Mathematics has been extremely effective in physics, but not in economics beyond finance. To establish economics as science we should follow the Galilean method and try to deduce mathematical models of markets from empirical data, as has been done for financial markets. Financial markets are nonstationary. This means that 'value' is subjective. Nonstationarity also means that the form of the noise in a market cannot be postulated a priroi, but must be deduced from the empirical data. I discuss the essence of complexity in a market as unexpected events, and end with a biological speculation about market growth.Economics; fniancial markets; stochastic process; Markov process; complex systems
- …