arXiv subjects

Gayane Vardoyan

Publications and source records attributed to Gayane Vardoyan.

28 records · Page 2Linked to original sources

arXiv2023

Mapping quantum circuits to modular architectures with QUBO

Modular quantum computing architectures are a promising alternative to monolithic QPU (Quantum Processing Unit) designs for scaling up quantum devices. They refer to a set of interconnected QPUs or cores consisting of tightly coupled quantum bits that can communicate via quantum-coherent and classical links. In multi-core architectures, it is crucial to minimize the amount of communication between cores when executing an algorithm. Therefore, mapping a quantum circuit onto a modular architecture involves finding an optimal assignment of logical qubits (qubits in the quantum circuit) to different cores with the aim to minimize the number of expensive inter-core operations while adhering to given hardware constraints. In this paper, we propose for the first time a Quadratic Unconstrained Binary Optimization (QUBO) technique to encode the problem and the solution for both qubit allocation and inter-core communication costs in binary decision variables. To this end, the quantum circuit is split into slices, and qubit assignment is formulated as a graph partitioning problem for each circuit slice. The costly inter-core communication is reduced by penalizing inter-core qubit communications. The final solution is obtained by minimizing the overall cost across all circuit slices. To evaluate the effectiveness of our approach, we conduct a detailed analysis using a representative set of benchmarks having a high number of qubits on two different multi-core architectures. Our method showed promising results and performed exceptionally well with very dense and highly-parallelized circuits that require on average 0.78 inter-core communications per two-qubit gate.

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arXiv2023

Quantum Internet: The Future of Internetworking

Quantum information, computation and communication, will have a great impact on our world. One important subfield will be quantum networking and the quantum Internet. The purpose of a quantum Internet is to enable applications that are fundamentally out of reach for the classical Internet. Quantum networks enable new capabilities to communication systems. This allows the parties to generate long distance quantum entanglement, which serves a number of tasks including the generation of multiparty shared secrets whose security relies only on the laws of physics, distributed quantum computing, improved sensing, quantum computing on encrypted data, and secure private-bid auctions. However, quantum signals are fragile, and, in general, cannot be copied or amplified. In order to enable widespread use and application development, it is essential to develop methods that allow quantum protocols to connect to the underlying hardware implementation transparently and to make fast and reactive decisions for generating entanglement in the network to mitigate limited qubit lifetimes. Architectures for large-scale quantum internetworking are in development, paralleling theoretical and experimental work on physical layers and low-level error management and connection technologies. This chapter aims to present the main concepts, challenges, and opportunities for research in quantum information, quantum computing and quantum networking.

cs.NI↗

arXiv2023

Tools for the analysis of quantum protocols requiring state generation within a time window

Quantum protocols commonly require a certain number of quantum resource states to be available simultaneously. An important class of examples is quantum network protocols that require a certain number of entangled pairs. Here, we consider a setting in which a process generates a quantum resource state with some probability $p$ in each time step, and stores it in a quantum memory that is subject to time-dependent noise. To maintain sufficient quality for an application, each resource state is discarded from the memory after $w$ time steps. Let $s$ be the number of desired resource states required by a protocol. We characterise the probability distribution $X_{(w,s)}$ of the ages of the quantum resource states, once $s$ states have been generated in a window $w$. Combined with a time-dependent noise model, the knowledge of this distribution allows for the calculation of fidelity statistics of the $s$ quantum resources. We also give exact solutions for the first and second moments of the waiting time $τ_{(w,s)}$ until $s$ resources are produced within a window $w$, which provides information about the rate of the protocol. Since it is difficult to obtain general closed-form expressions for statistical quantities describing the expected waiting time $\mathbb{E}(τ_{(w,s)})$ and the distribution $X_{(w,s)}$, we present two novel results that aid their computation in certain parameter regimes. The methods presented in this work can be used to analyse and optimise the execution of quantum protocols. Specifically, with an example of a Blind Quantum Computing (BQC) protocol, we illustrate how they may be used to infer $w$ and $p$ to optimise the rate of successful protocol execution.

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arXiv2023

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.

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arXiv2022

On the Analysis of a Multipartite Entanglement Distribution Switch

We study a quantum switch that distributes maximally entangled multipartite states to sets of users. The entanglement switching process requires two steps: first, each user attempts to generate bipartite entanglement between itself and the switch; and second, the switch performs local operations and a measurement to create multipartite entanglement for a set of users. In this work, we study a simple variant of this system, wherein the switch has infinite memory and the links that connect the users to the switch are identical. Further, we assume that all quantum states, if generated successfully, have perfect fidelity and that decoherence is negligible. This problem formulation is of interest to several distributed quantum applications, while the technical aspects of this work result in new contributions within queueing theory. Via extensive use of Lyapunov functions, we derive necessary and sufficient conditions for the stability of the system and closed-form expressions for the switch capacity and the expected number of qubits in memory.

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arXiv2022

Quantum Network Utility Maximization

Network Utility Maximization (NUM) is a mathematical framework that has endowed researchers with powerful methods for designing and analyzing classical communication protocols. NUM has also enabled the development of distributed algorithms for solving the resource allocation problem, while at the same time providing certain guarantees, e.g., that of fair treatment, to the users of a network. We extend here the notion of NUM to quantum networks, and propose three quantum utility functions -- each incorporating a different entanglement measure. We aim both to gain an understanding of some of the ways in which quantum users may perceive utility, as well as to explore structured and theoretically-motivated methods of simultaneously servicing multiple users in distributed quantum systems. Using our quantum NUM constructions, we develop an optimization framework for networks that use the single-photon scheme for entanglement generation, which enables us to solve the resource allocation problem while exploring rate-fidelity tradeoffs within the network topologies that we consider. We learn that two of our utility functions, which are based on distillable entanglement and secret key fraction, are in close agreement with each other and produce similar solutions to the optimization problems we study. Our third utility, based on entanglement negativity, has more favorable mathematical properties, and tends to place a higher value on the rate at which users receive entangled resources, compared to the two previous utilities, which put a higher emphasis on end-to-end fidelity. These contrasting behaviors thus provide ideas regarding the suitability of quantum network utility definitions to different quantum applications.

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arXiv2022

On the Capacity Region of Bipartite and Tripartite Entanglement Switching

We study a quantum entanglement distribution switch serving a set of users in a star topology with equal-length links. The quantum switch, much like a quantum repeater, can perform entanglement swapping to extend entanglement across longer distances. Additionally, the switch is equipped with entanglement switching logic, enabling it to implement switching policies to better serve the needs of the network. In this work, the function of the switch is to create bipartite or tripartite entangled states among users at the highest possible rates at a fixed ratio. Using Markov chains, we model a set of randomized switching policies. Discovering that some are better than others, we present analytical results for the case where the switch stores one qubit per user, and find that the best policies outperform a time division multiplexing (TDM) policy for sharing the switch between bipartite and tripartite state generation. This performance improvement decreases as the number of users grows. The model is easily augmented to study the capacity region in the presence of quantum state decoherence and associated cut-off times for qubit storage, obtaining similar results. Moreover, decoherence-associated quantum storage cut-off times appear to have little effect on capacity in our identical-link system. We also study a smaller class of policies when the switch stores two qubits per user.

cs.NI↗

arXiv2021

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.

cs.PF↗

arXiv2019

On the Stochastic Analysis of a Quantum Entanglement Switch

We study a quantum entanglement switch that serves $k$ users in a star topology. We model variants of the system using Markov chains and standard queueing theory and obtain expressions for switch capacity and the expected number of qubits stored in memory at the switch. While it is more accurate to use a discrete-time Markov chain (DTMC) to model such systems, we quickly encounter practical constraints of using this technique and switch to using continuous-time Markov chains (CTMCs). Using CTMCs allows us to obtain a number of analytic results for systems in which the links are homogeneous or heterogeneous and for switches that have infinite or finite buffer sizes. In addition, we can model the effects of decoherence of quantum states fairly easily using CTMCs. We also compare the results we obtain from the DTMC against the CTMC in the case of homogeneous links and infinite buffer, and learn that the CTMC is a reasonable approximation of the DTMC. From numerical observations, we discover that decoherence has little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating close to stability constraints, buffer size and decoherence can have significant effects on performance metrics. We also learn that in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, while increasing the buffer size further yields diminishing returns.

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arXiv2018

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.

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