3,454 research outputs found
A Monte-Carlo simulation of the equilibrium beam polarization in ultra-high energy electron (positron) storage rings
With the recently emerging global interest in building a next generation of
circular electron-positron colliders to study the properties of the Higgs
boson, and other important topics in particle physics at ultra-high beam
energies, it is also important to pursue the possibility of implementing
polarized beams at this energy scale. It is therefore necessary to set up
simulation tools to evaluate the beam polarization at these ultra-high beam
energies. In this paper, a Monte-Carlo simulation of the equilibrium beam
polarization based on the Polymorphic Tracking Code(PTC) (Schmidt et al., 2002
[1]) is described. The simulations are for a model storage ring with parameters
similar to those of proposed circular colliders in this energy range, and they
are compared with the suggestion (Derbenev et al., 1978 [2]) that there are
different regimes for the spin dynamics underlying the polarization of a beam
in the presence of synchrotron radiation at ultra-high beam energies. In
particular, it has been suggested that the so-called "correlated" crossing of
spin resonances during synchrotron oscillations at current energies, evolves
into "uncorrelated" crossing of spin resonances at ultra-high energies.Comment: submitted to and accepted by Nucl. Instrum. Meth.
Enhanced Feedback Iterative Decoding of Sparse Quantum Codes
Decoding sparse quantum codes can be accomplished by syndrome-based decoding
using a belief propagation (BP) algorithm.We significantly improve this
decoding scheme by developing a new feedback adjustment strategy for the
standard BP algorithm. In our feedback procedure, we exploit much of the
information from stabilizers, not just the syndrome but also the values of the
frustrated checks on individual qubits of the code and the channel model.
Furthermore we show that our decoding algorithm is superior to belief
propagation algorithms using only the syndrome in the feedback procedure for
all cases of the depolarizing channel. Our algorithm does not increase the
measurement overhead compared to the previous method, as the extra information
comes for free from the requisite stabilizer measurements.Comment: 10 pages, 11 figures, Second version, To be appeared in IEEE
Transactions on Information Theor
Unified Algorithms for RL with Decision-Estimation Coefficients: No-Regret, PAC, and Reward-Free Learning
Finding unified complexity measures and algorithms for sample-efficient
learning is a central topic of research in reinforcement learning (RL). The
Decision-Estimation Coefficient (DEC) is recently proposed by Foster et al.
(2021) as a necessary and sufficient complexity measure for sample-efficient
no-regret RL. This paper makes progress towards a unified theory for RL with
the DEC framework. First, we propose two new DEC-type complexity measures:
Explorative DEC (EDEC), and Reward-Free DEC (RFDEC). We show that they are
necessary and sufficient for sample-efficient PAC learning and reward-free
learning, thereby extending the original DEC which only captures no-regret
learning. Next, we design new unified sample-efficient algorithms for all three
learning goals. Our algorithms instantiate variants of the
Estimation-To-Decisions (E2D) meta-algorithm with a strong and general model
estimation subroutine. Even in the no-regret setting, our algorithm E2D-TA
improves upon the algorithms of Foster et al. (2021) which require either
bounding a variant of the DEC which may be prohibitively large, or designing
problem-specific estimation subroutines. As applications, we recover existing
and obtain new sample-efficient learning results for a wide range of tractable
RL problems using essentially a single algorithm. We also generalize the DEC to
give sample-efficient algorithms for all-policy model estimation, with
applications for learning equilibria in Markov Games. Finally, as a connection,
we re-analyze two existing optimistic model-based algorithms based on Posterior
Sampling or Maximum Likelihood Estimation, showing that they enjoy similar
regret bounds as E2D-TA under similar structural conditions as the DEC
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