Optimum Resource Allocation in Secure Quantum Networks: Survey of Enabling Technology

Due to its complexity, resource allocation in complex communication networks has been always designed with great deal of approximations and restrictions. With the availability of quantum computing, quantum optimization and quantum search algorithms, we are able to overcome these limitations significantly and come up with more precise and efficient “quantum era” algorithms. The main objective of this paper is to provide the future network designers with a new optimization framework for resource (capacity and secrete key rate) allocation in quantum networks. The analysis is general to include: the classical capacity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i>, for transmitting classical information; the quantum capacity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i>, for reliably transmitting intact quantum states; the two-way classical-assisted quantum capacity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>, for transmitting quantum states with the help of a two-way classical side channel; and the entanglement-assisted classical capacity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_E</i> , which we define as the classical capacity of a quantum channel enabled by prior shared entanglement between two nodes. Once the optimization framework is introduced the rest of the paper discusses the optimization constraints, by surveying some examples of the relevant work on achievable network resources (capacity and secrete key rate) and relaxation of the optimization constraints by increasing these parameters using the quantum coding schemes. These constraints are an integral part of the optimization algorithms and full understanding of their nature and limits is essential for system optimization. The achievable secret key rates/capacity of quantum channels are limited, so our optimization framework for resource allocation enables maximization of the overall resources allocated to all users, or maximization of the number of users accessing the network, or minimization of the number of hopes on the routes or maximization of remaining resources in the most critical node in the network. The optimization problems have combinatorial form, and the most efficient execution of these algorithms can be achieved by using quantum search algorithms like Grover’s algorithm or quantum approximative optimization algorithms (QAOA) which are extensively discussed in the paper.Regarding the scope of the technology survey in Section VIII we summarize the coverage of our targeted survey and the coverage of other relevant works.