24 research outputs found
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Performance Evaluation of Classical and Quantum Communication Systems
The Transmission Control Protocol (TCP) is a robust and reliable method used to transport data across a network. Many variants of TCP exist, e.g., Scalable TCP, CUBIC, and H-TCP. While some of them have been studied from empirical and theoretical perspectives, others have been less amenable to a thorough mathematical analysis. Moreover, some of the more popular variants had not been analyzed in the context of the high-speed environments for which they were designed. To address this issue, we develop a generalized modeling technique for TCP congestion control under the assumption of high bandwidth-delay product. In a separate contribution, we develop a versatile fluid model for congestion-window-based and rate-based congestion controllers that can be used to analyze a protocol’s stability. We apply this model to CUBIC – the default implementation of TCP in Linux systems – and discover that under a certain loss probability model, CUBIC is locally asymptotically stable. The contribution of this work is twofold: (i) the first formal stability analysis of CUBIC, and (ii) the fluid model can be easily adapted to other protocols whose window or rate functions are difficult to model. We demonstrate another application of this model by analyzing the stability of H-TCP, another popular variant used in data science networks.
On a different front, a wide range of quantum distributed applications, which either promise to improve on existing classical applications or offer functionality that is entirely unobtainable via classical means, are helping to fuel rapid technological advances in the area of quantum communication. In view of this, it is prudent to model and analyze quantum networks, whose applications range from quantum cryptography to quantum sensing. Several types of quantum distributed applications, such as the E91 protocol for quantum key distribution, make use of entanglement to meet their objectives. Thus, being able to distribute entanglement efficiently is one of the most important and fundamental tasks that must be performed in a quantum network – without this functionality, many quantum distributed applications would be rendered infeasible. Modeling such systems is vital in order to better conceptualize their operation, and more importantly, to discover and address the challenges involved in actualizing them. To this end, we explore the limits of star-topology entanglement switching networks and introduce methods to model the process of entanglement generation, a set of switching policies, memory constraints, link heterogeneity, and quantum state decoherence for a switch that can serve bipartite (and in a specific case, tripartite) entangled states. In one part of this work, we compare two modeling techniques: discrete time Markov chains (DTMCs) and continuous-time Markov chains (CTMCs). We find that while DTMCs are a more accurate way to model the operation of an entanglement distribution switch, they quickly become intractable when one introduces link heterogeneity or state decoherence into the model. In terms of accuracy, we show that not much is lost for the case of homogeneous links, infinite buffer and no decoherence when CTMCs are employed. We then use CTMCs to model more complex systems. In another part of this work, we analyze a switch that can store one or two qubits per link and can serve both bipartite and tripartite entangled states. Through analysis, we discover that randomized policies allow the switch to achieve a better capacity than time-division multiplexing between bipartite and tripartite entangling measurements, but the advantage decreases as the number of links grows
A Control Architecture for Entanglement Generation Switches in Quantum Networks
Entanglement between quantum network nodes is often produced using
intermediary devices - such as heralding stations - as a resource. When scaling
quantum networks to many nodes, requiring a dedicated intermediary device for
every pair of nodes introduces high costs. Here, we propose a cost-effective
architecture to connect many quantum network nodes via a central quantum
network hub called an Entanglement Generation Switch (EGS). The EGS allows
multiple quantum nodes to be connected at a fixed resource cost, by sharing the
resources needed to make entanglement. We propose an algorithm called the Rate
Control Protocol (RCP) which moderates the level of competition for access to
the hub's resources between sets of users. We proceed to prove a convergence
theorem for rates yielded by the algorithm. To derive the algorithm we work in
the framework of Network Utility Maximization (NUM) and make use of the theory
of Lagrange multipliers and Lagrangian duality. Our EGS architecture lays the
groundwork for developing control architectures compatible with other types of
quantum network hubs as well as system models of greater complexity
Towards Stability Analysis of Data Transport Mechanisms: a Fluid Model and an Application
The Transmission Control Protocol (TCP) utilizes congestion avoidance and
control mechanisms as a preventive measure against congestive collapse and as
an adaptive measure in the presence of changing network conditions. The set of
available congestion control algorithms is diverse, and while many have been
studied from empirical and simulation perspectives, there is a notable lack of
analytical work for some variants. To gain more insight into the dynamics of
these algorithms, we: (1) propose a general modeling scheme consisting of a set
of functional differential equations of retarded type (RFDEs) and of the
congestion window as a function of time; (2) apply this scheme to TCP Reno and
demonstrate its equivalence to a previous, well known model for TCP Reno; (3)
show an application of the new framework to the widely-deployed congestion
control algorithm TCP CUBIC, for which analytical models are few and limited;
and (4) validate the model using simulations. Our modeling framework yields a
fluid model for TCP CUBIC. From a theoretical analysis of this model, we
discover that TCP CUBIC is locally uniformly asymptotically stable -- a
property of the algorithm previously unknown.Comment: IEEE INFOCOM 201
On the Quantum Performance Evaluation of Two Distributed Quantum Architectures
Distributed quantum applications impose requirements on the quality of the
quantum states that they consume. When analyzing architecture implementations
of quantum hardware, characterizing this quality forms an important factor in
understanding their performance. Fundamental characteristics of quantum
hardware lead to inherent tradeoffs between the quality of states and
traditional performance metrics such as throughput. Furthermore, any real-world
implementation of quantum hardware exhibits time-dependent noise that degrades
the quality of quantum states over time. Here, we study the performance of two
possible architectures for interfacing a quantum processor with a quantum
network. The first corresponds to the current experimental state of the art in
which the same device functions both as a processor and a network device. The
second corresponds to a future architecture that separates these two functions
over two distinct devices. We model these architectures as Markov chains and
compare their quality of executing quantum operations and producing entangled
quantum states as functions of their memory lifetimes, as well as the time that
it takes to perform various operations within each architecture. As an
illustrative example, we apply our analysis to architectures based on
Nitrogen-Vacancy centers in diamond, where we find that for present-day device
parameters one architecture is more suited to computation-heavy applications,
and the other for network-heavy ones. Besides the detailed study of these
architectures, a novel contribution of our work are several formulas that
connect an understanding of waiting time distributions to the decay of quantum
quality over time for the most common noise models employed in quantum
technologies. This provides a valuable new tool for performance evaluation
experts, and its applications extend beyond the two architectures studied in
this work
Optimal entanglement distribution policies in homogeneous repeater chains with cutoffs
We study the limits of bipartite entanglement distribution using a chain of
quantum repeaters that have quantum memories. To generate end-to-end
entanglement, each node can attempt the generation of an entangled link with a
neighbor, or perform an entanglement swapping measurement. A maximum storage
time, known as cutoff, is enforced on the memories to ensure high-quality
entanglement. Nodes follow a policy that determines when to perform each
operation. Global-knowledge policies take into account all the information
about the entanglement already produced. Here, we find global-knowledge
policies that minimize the expected time to produce end-to-end entanglement.
Our methods are based on Markov decision processes and value and policy
iteration. We compare optimal policies to a policy in which nodes only use
local information. We find that the advantage in expected delivery time
provided by an optimal global-knowledge policy increases with increasing number
of nodes and decreasing probability of successful swapping. Our work sheds
light on how to distribute entangled pairs in large quantum networks using a
chain of intermediate repeaters with cutoffs.Comment: 9 pages, 8 figures, 15 pages appendix with 10 figure
On the Bipartite Entanglement Capacity of Quantum Networks
We consider the problem of multi-path entanglement distribution to a pair of
nodes in a quantum network consisting of devices with non-deterministic
entanglement swapping capabilities. Multi-path entanglement distribution
enables a network to establish end-to-end entangled links across any number of
available paths with pre-established link-level entanglement. Probabilistic
entanglement swapping, on the other hand, limits the amount of entanglement
that is shared between the nodes; this is especially the case when, due to
architectural and other practical constraints, swaps must be performed in
temporal proximity to each other. Limiting our focus to the case where only
bipartite entangled states are generated across the network, we cast the
problem as an instance of generalized flow maximization between two quantum end
nodes wishing to communicate. We propose a mixed-integer quadratically
constrained program (MIQCP) to solve this flow problem for networks with
arbitrary topology. We then compute the overall network capacity, defined as
the maximum number of EPR states distributed to users per time unit, by solving
the flow problem for all possible network states generated by probabilistic
entangled link presence and absence, and subsequently by averaging over all
network state capacities. The MIQCP can also be applied to networks with
multiplexed links. While our approach for computing the overall network
capacity has the undesirable property that the total number of states grows
exponentially with link multiplexing capability, it nevertheless yields an
exact solution that serves as an upper bound comparison basis for the
throughput performance of easily-implementable yet non-optimal entanglement
routing algorithms. We apply our capacity computation method to several
networks, including a topology based on SURFnet -- a backbone network used for
research purposes in the Netherlands
On the Capacity Region of Bipartite and Tripartite Entanglement Switching and Key Distribution
International audienc
Entanglement Routing over Networks with Time Multiplexed Repeaters
Quantum networks will be able to service consumers with long distance
entanglement by use of repeater nodes that can both generate external Bell
pairs with their neighbors, iid with probability , as well as perform
internal Bell State Measurements (BSMs) which succeed with some probability
. The actual values of these probabilities is dependent upon the
experimental parameters of the network in question. While global link state
knowledge is needed to maximize the rate of entanglement generation between any
two consumers, this may be an unreasonable request due to the dynamic nature of
the network. This work evaluates a local link state knowledge, multi-path
routing protocol that works with time multiplexed repeaters that are able to
perform BSMs across different time steps. This study shows that the average
rate increases with the time multiplexing block length, , although the
initial latency also increases. When a step function memory decoherence model
is introduced so that qubits are held in the quantum memory for a time
exponentially distributed with mean , an optimal ()
value appears. As decreases or increases the value of
increases. This value is such that the benefits from time multiplexing are
balanced with the increased risk of losing a previously established entangled
pair.Comment: 11 pages, 15 figure
Designing a Quantum Network Protocol
The second quantum revolution brings with it the promise of a quantum
internet. As the first quantum network hardware prototypes near completion new
challenges emerge. A functional network is more than just the physical
hardware, yet work on scalable quantum network systems is in its infancy. In
this paper we present a quantum network protocol designed to enable end-to-end
quantum communication in the face of the new fundamental and technical
challenges brought by quantum mechanics. We develop a quantum data plane
protocol that enables end-to-end quantum communication and can serve as a
building block for more complex services. One of the key challenges in
near-term quantum technology is decoherence -- the gradual decay of quantum
information -- which imposes extremely stringent limits on storage times. Our
protocol is designed to be efficient in the face of short quantum memory
lifetimes. We demonstrate this using a simulator for quantum networks and show
that the protocol is able to deliver its service even in the face of
significant losses due to decoherence. Finally, we conclude by showing that the
protocol remains functional on the extremely resource limited hardware that is
being developed today underlining the timeliness of this work