419 research outputs found
Faster quantum mixing for slowly evolving sequences of Markov chains
Markov chain methods are remarkably successful in computational physics,
machine learning, and combinatorial optimization. The cost of such methods
often reduces to the mixing time, i.e., the time required to reach the steady
state of the Markov chain, which scales as , the inverse of the
spectral gap. It has long been conjectured that quantum computers offer nearly
generic quadratic improvements for mixing problems. However, except in special
cases, quantum algorithms achieve a run-time of , which introduces a costly dependence on the Markov chain size
not present in the classical case. Here, we re-address the problem of mixing of
Markov chains when these form a slowly evolving sequence. This setting is akin
to the simulated annealing setting and is commonly encountered in physics,
material sciences and machine learning. We provide a quantum memory-efficient
algorithm with a run-time of ,
neglecting logarithmic terms, which is an important improvement for large state
spaces. Moreover, our algorithms output quantum encodings of distributions,
which has advantages over classical outputs. Finally, we discuss the run-time
bounds of mixing algorithms and show that, under certain assumptions, our
algorithms are optimal.Comment: 20 pages, 2 figure
The Power Of Quantum Walk Insights, Implementation, And Applications
In this thesis, I investigate quantum walks in quantum computing from three aspects: the insights, the implementation, and the applications. Quantum walks are the quantum analogue of classical random walks. For the insights of quantum walks, I list and explain the required components for quantizing a classical random walk into a quantum walk. The components are, for instance, Markov chains, quantum phase estimation, and quantum spectrum theorem. I then demonstrate how the product of two reflections in the walk operator provides a quadratic speed-up, in comparison to the classical counterpart. For the implementation of quantum walks, I show the construction of an efficient circuit for realizing one single step of the quantum walk operator. Furthermore, I devise a more succinct circuit to approximately implement quantum phase estimation with constant precision controlled phase shift operators. From an implementation perspective, efficient circuits are always desirable because the realization of a phase shift operator with high precision would be a costly task and a critical obstacle. For the applications of quantum walks, I apply the quantum walk technique along with other fundamental quantum techniques, such as phase estimation, to solve the partition function problem. However, there might be some scenario in which the speed-up of spectral gap is insignificant. In a situation like that that, I provide an amplitude amplification-based iii approach to prepare the thermal Gibbs state. Such an approach is useful when the spectral gap is extremely small. Finally, I further investigate and explore the effect of noise (perturbation) on the performance of quantum walk
Parametric Sensitivity Analysis for Biochemical Reaction Networks based on Pathwise Information Theory
Stochastic modeling and simulation provide powerful predictive methods for
the intrinsic understanding of fundamental mechanisms in complex biochemical
networks. Typically, such mathematical models involve networks of coupled jump
stochastic processes with a large number of parameters that need to be suitably
calibrated against experimental data. In this direction, the parameter
sensitivity analysis of reaction networks is an essential mathematical and
computational tool, yielding information regarding the robustness and the
identifiability of model parameters. However, existing sensitivity analysis
approaches such as variants of the finite difference method can have an
overwhelming computational cost in models with a high-dimensional parameter
space. We develop a sensitivity analysis methodology suitable for complex
stochastic reaction networks with a large number of parameters. The proposed
approach is based on Information Theory methods and relies on the
quantification of information loss due to parameter perturbations between
time-series distributions. For this reason, we need to work on path-space,
i.e., the set consisting of all stochastic trajectories, hence the proposed
approach is referred to as "pathwise". The pathwise sensitivity analysis method
is realized by employing the rigorously-derived Relative Entropy Rate (RER),
which is directly computable from the propensity functions. A key aspect of the
method is that an associated pathwise Fisher Information Matrix (FIM) is
defined, which in turn constitutes a gradient-free approach to quantifying
parameter sensitivities. The structure of the FIM turns out to be
block-diagonal, revealing hidden parameter dependencies and sensitivities in
reaction networks
On delay-sensitive communication over wireless systems
This dissertation addresses some of the most important issues in delay-sensitive
communication over wireless systems and networks. Traditionally, the design of communication
networks adopts a layered framework where each layer serves as a “black
box” abstraction for higher layers. However, in the context of wireless networks with
delay-sensitive applications such as Voice over Internet Protocol (VoIP), on-line gaming,
and video conferencing, this layered architecture does not offer a complete picture.
For example, an information theoretic perspective on the physical layer typically ignores
the bursty nature of practical sources and often overlooks the role of delay in
service quality. The purpose of this dissertation is to take on a cross-disciplinary
approach to derive new fundamental limits on the performance, in terms of capacity
and delay, of wireless systems and to apply these limits to the design of practical
wireless systems that support delay-sensitive applications. To realize this goal, we
consider a number of objectives.
1. Develop an integrated methodology for the analysis of wireless systems that
support delay-sensitive applications based, in part, on large deviation theory.
2. Use this methodology to identify fundamental performance limits and to design
systems which allocate resources efficiently under stringent service requirements.
3. Analyze the performance of wireless communication networks that takes advantage of novel paradigms such as user cooperation, and multi-antenna systems.
Based on the proposed framework, we find that delay constraints significantly
influence how system resources should be allocated. Channel correlation has a major
impact on the performance of wireless communication systems. Sophisticated power
control based on the joint space of channel and buffer states are essential for delaysensitive
communications
Noisy channels with synchronization errors : information rates and code design
Master'sMASTER OF ENGINEERIN
Proceedings of the Eighth Workshop on Information Theoretic Methods in Science and Engineering
Proceedings of the Eighth Workshop on Information Theoretic Methods in Science and Engineering (WITMSE 2015) held in Copenhagen, Denmark, 24-26 June 2015; published in the series of the Department of Computer Science, University of Helsinki.Peer reviewe
- …