15,142 research outputs found
How Quantum Computers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation
The feasibility of computationally superior quantum computers is one of the
most exciting and clear-cut scientific questions of our time. The question
touches on fundamental issues regarding probability, physics, and
computability, as well as on exciting problems in experimental physics,
engineering, computer science, and mathematics. We propose three related
directions towards a negative answer. The first is a conjecture about physical
realizations of quantum codes, the second has to do with correlations in
stochastic physical systems, and the third proposes a model for quantum
evolutions when noise accumulates. The paper is dedicated to the memory of
Itamar Pitowsky.Comment: 16 page
Synchronization Strings: Explicit Constructions, Local Decoding, and Applications
This paper gives new results for synchronization strings, a powerful
combinatorial object that allows to efficiently deal with insertions and
deletions in various communication settings:
We give a deterministic, linear time synchronization string
construction, improving over an time randomized construction.
Independently of this work, a deterministic time
construction was just put on arXiv by Cheng, Li, and Wu. We also give a
deterministic linear time construction of an infinite synchronization string,
which was not known to be computable before. Both constructions are highly
explicit, i.e., the symbol can be computed in time.
This paper also introduces a generalized notion we call
long-distance synchronization strings that allow for local and very fast
decoding. In particular, only time and access to logarithmically
many symbols is required to decode any index.
We give several applications for these results:
For any we provide an insdel correcting
code with rate which can correct any fraction
of insdel errors in time. This near linear computational
efficiency is surprising given that we do not even know how to compute the
(edit) distance between the decoding input and output in sub-quadratic time. We
show that such codes can not only efficiently recover from fraction of
insdel errors but, similar to [Schulman, Zuckerman; TransInf'99], also from any
fraction of block transpositions and replications.
We show that highly explicitness and local decoding allow for
infinite channel simulations with exponentially smaller memory and decoding
time requirements. These simulations can be used to give the first near linear
time interactive coding scheme for insdel errors
Limit Synchronization in Markov Decision Processes
Markov decision processes (MDP) are finite-state systems with both strategic
and probabilistic choices. After fixing a strategy, an MDP produces a sequence
of probability distributions over states. The sequence is eventually
synchronizing if the probability mass accumulates in a single state, possibly
in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a
probability distribution in the sequence assigns probability at least p to some
state, and we distinguish three synchronization modes: (i) sure winning if
there exists a strategy that produces a 1-synchronizing sequence; (ii)
almost-sure winning if there exists a strategy that produces a sequence that
is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure
winning if for all epsilon > 0, there exists a strategy that produces a
(1-epsilon)-synchronizing sequence.
We consider the problem of deciding whether an MDP is sure, almost-sure,
limit-sure winning, and we establish the decidability and optimal complexity
for all modes, as well as the memory requirements for winning strategies. Our
main contributions are as follows: (a) for each winning modes we present
characterizations that give a PSPACE complexity for the decision problems, and
we establish matching PSPACE lower bounds; (b) we show that for sure winning
strategies, exponential memory is sufficient and may be necessary, and that in
general infinite memory is necessary for almost-sure winning, and unbounded
memory is necessary for limit-sure winning; (c) along with our results, we
establish new complexity results for alternating finite automata over a
one-letter alphabet
A Complexity-Based Hierarchy for Multiprocessor Synchronization
For many years, Herlihy's elegant computability based Consensus Hierarchy has
been our best explanation of the relative power of various types of
multiprocessor synchronization objects when used in deterministic algorithms.
However, key to this hierarchy is treating synchronization instructions as
distinct objects, an approach that is far from the real-world, where
multiprocessor programs apply synchronization instructions to collections of
arbitrary memory locations. We were surprised to realize that, when considering
instructions applied to memory locations, the computability based hierarchy
collapses. This leaves open the question of how to better capture the power of
various synchronization instructions.
In this paper, we provide an approach to answering this question. We present
a hierarchy of synchronization instructions, classified by their space
complexity in solving obstruction-free consensus. Our hierarchy provides a
classification of combinations of known instructions that seems to fit with our
intuition of how useful some are in practice, while questioning the
effectiveness of others. We prove an essentially tight characterization of the
power of buffered read and write instructions.Interestingly, we show a similar
result for multi-location atomic assignments
Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption
Optical chaos is a topic of current research characterized by
high-dimensional nonlinearity which is attributed to the delay-induced
dynamics, high bandwidth and easy modular implementation of optical feedback.
In light of these facts, which adds enough confusion and diffusion properties
for secure communications, we explore the synchronization phenomena in
spatiotemporal semiconductor laser systems. The novel system is used in a
two-phase colored image encryption process. The high-dimensional chaotic
attractor generated by the system produces a completely randomized chaotic time
series, which is ideal in the secure encoding of messages. The scheme thus
illustrated is a two-phase encryption method, which provides sufficiently high
confusion and diffusion properties of chaotic cryptosystem employed with unique
data sets of processed chaotic sequences. In this novel method of cryptography,
the chaotic phase masks are represented as images using the chaotic sequences
as the elements of the image. The scheme drastically permutes the positions of
the picture elements. The next additional layer of security further alters the
statistical information of the original image to a great extent along the
three-color planes. The intermediate results during encryption demonstrate the
infeasibility for an unauthorized user to decipher the cipher image. Exhaustive
statistical tests conducted validate that the scheme is robust against noise
and resistant to common attacks due to the double shield of encryption and the
infinite dimensionality of the relevant system of partial differential
equations.Comment: 20 pages, 11 figures; Article in press, Optics Communications (2011
- …