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IEEE International Conference on Quantum Computing and Engineering (QCE)

Virtual Network Function Embedding with Quantum Annealing

Pietro Chiavassa, Andrea Marchesin, Ignazio Pedone, Maurizio Ferrari Dacrema, Paolo Cremonesi

Published Sep 1, 2022• 3 citations
Publisher

Abstract

In recent years, the growing number of devices connected to the internet led network operators to continuously expand their own infrastructures. In order to simplify this scaling process, the research community is currently investigating the opportunity to move the complexity from a hardware to a software domain, through the introduction of a new paradigm, called Network Functions Virtualisation (NFV). It considers standard hardware platforms where many virtual instances are allocated to implement specific network services. However, despite the theoretical benefits, the mapping of the different virtual instances to the available physical resources represents a complex problem, difficult to be solved classically. The present work proposes a Quadratic Unconstrained Binary Optimisation (QUBO) formulation of this embedding process, exploring the implementation possibilities on D-Wave’s Quantum Annealers. Many test cases, with realistic constraints, have been considered to validate and characterise the potential of the model, and the promising results achieved are discussed throughout the document. The technical discussion is enriched with comparisons of the results obtained through heuristic algorithms, highlighting the strengths and the limitations in the resolution of the QUBO formulation proposed on current quantum machines.

DOI
10.1109/qce53715.2022.00048

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In recent years, the growing number of devices connected to the internet led network operators to continuously expand their own infrastructures. In order to simplify this scaling process, the research community is currently investigating the opportunity to move the complexity from a hardware to a software domain, through the introduction of a new paradigm, called Network Functions Virtualisation (NFV). It considers standard hardware platforms where many virtual instances are allocated to implement specific network services. However, despite the theoretical benefits, the mapping of the different virtual instances to the available physical resources represents a complex problem, difficult to be solved classically. The present work proposes a Quadratic Unconstrained Binary Optimisation (QUBO) formulation of this embedding process, exploring the implementation possibilities on D-Wave’s Quantum Annealers. Many test cases, with realistic constraints, have been considered to validate and characterise the potential of the model, and the promising results achieved are discussed throughout the document. The technical discussion is enriched with comparisons of the results obtained through heuristic algorithms, highlighting the strengths and the limitations in the resolution of the QUBO formulation proposed on current quantum machines.
Network function virtualization (NFV) is a crucial technology for the 5G network development because it can improve the flexibility of employing hardware and reduce the construction of base stations. There are vast service chains in NFV to meet users’ requests, which are composed of a sequence of network functions. These virtual network functions (VNFs) are implemented in virtual machines by software and virtual environment. How to deploy VMs to process VNFs of the service chains as soon as possible when users’ requests are received is very challenging to solve by traditional algorithms on a large scale. Compared with traditional algorithms, quantum computing has better computational performance because of quantum parallelism. We build an integer linear programming model of the VNF scheduling problem with the objective of minimizing delays, and transfer it into the quadratic unconstrained binary optimization (QUBO) model. Our proposed heuristic algorithm employs a quantum annealer to solve the model. Finally, we evaluate the computational results and explore the feasibility of leveraging quantum computing to solve the VNF scheduling problem.
Quantum annealing algorithms were introduced to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes typical of NP - hard problems. In this work, we propose using quantum annealing for the theory of cuts, a field of paramount importance in theoretical computer science. We have proposed a method to formulate the Minimum Multicut Problem into the QUBO representation, and the technical difficulties faced when embedding and submitting a problem to the quantum annealer processor. We show two constructions of the quadratic unconstrained binary optimization functions for the Minimum Multicut Problem and we review several tradeoffs between the two mappings and provide numerical scaling analysis results from several classical approaches. Furthermore, we discuss some of the expected challenges and tradeoffs in the implementation of our mapping in the current generation of D-Wave machines.
This paper explores the application of quantum annealing to the challenging domain of combinatorial optimization within large-scale networks. Specifically, it investigates the feasibility of utilizing quantum annealing for problems such as network routing and scheduling, where traditional classical algorithms often struggle due to computational complexity. The core approach involves formulating the network optimization problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem. This transformation enables the mapping of the problem onto the quantum annealing hardware, leveraging the quantum annealing process – characterized by its adiabatic evolution – to discover the optimal solution. We argue that this method presents a potential advantage over conventional algorithms for large-scale network scenarios, offering a pathway to tackling problems previously considered intractable. The theoretical framework and underlying principles are thoroughly discussed, outlining the methodology and highlighting the anticipated benefits.
Quantum annealers such as the D-Wave 2X computer are designed to natively solve Quadratic Unconstrained Binary Optimization (QUBO) problems to optimality or near optimality. Most NP-hard problems, which are hard for classical computers, can be naturally described as quadratic binary problems that contain a quadratic binary objective function and one or more constraints. Since a QUBO cannot have constraints, each such constraint has to be added to the objective function as a penalty, in order to solve on D-Wave. For a minimization problem, for instance, such penalty can be a quadratic term that gets a value zero, if the constraint is satisfied, and a large value, if it is not. In many cases, however, the penalty can significantly increase the number of quadratic terms in the resulting QUBO and make it too large to embed into the D-Wave hardware. In this paper, we develop an alternative method for formulating and embedding constraints of the type Σi=1sxi=1, which is much more scalable than the existing ones, and analyze the properties of the resulting embeddings.
Cybersecurity in telecommunication networks often leads to hard combinatorial optimization problems that are challenging to solve with classical methods. This work investigates the practical feasibility of using quantum annealing to address the Restricted Vertex Minimum Multicut Problem. The problem is formulated as a Quadratic Unconstrained Binary Optimization model and implemented on D-Wave s quantum annealer. Rather than focusing on solution quality alone, we analyze key aspects of the quantum workflow including minor embedding techniques, chain length, topology constraints, chain strength selection, unembedding procedures, and postprocessing. Our results show that quantum annealing faces substantial hardware-level constraints limitations in embedding and scalability, especially for large instances, while hybrid quantum-classical solvers provide improved feasibility. This study offers a realistic assessment of the D-Wave system s current capabilities and identifies crucial parameters that govern the success of quantum optimization in cybersecurity-related network problems.
Quantum annealing is a metaheuristic method aimed at finding the global minimum of a pseudo-Boolean quadratic function. To solve a problem by a quantum annealer, it must be restated as a QUBO (quadratic unconstrained binary optimization) problem, the standard format acceptable to an annealer. However, there are many natural problems that turn out be of cubic or higher order, yet promising solutions can be obtained for many instances using quantum annealers, after converting to the QUBO format, using order reduction criteria. Accordingly, quadratization becomes a crucial preprocessing step in order to make use of present-day quantum annealing hardware that relies on coupling technology, which can only process interactions of at most degree two. A critical challenge is that quadratization methods often require many additional variables, degrading the performance of the annealers. A number of algorithmic and heuristic quadratization techniques have been proposed and used for annealing in the literature, affecting the performance of the annealers differently. We examine a number of such quadratization techniques, focusing on their efficiency, compactness, and applicability. We analyze the approaches motivated by diverse goals and highlight the transition from foundational approaches to more recent compact approaches. An evaluation of the current usage of different quadratization methods in the literature is carried out at the end of the survey. Further, we comment on the limitations on usage and show possible opportunities to enhance the performance of annealers.