A Probability-Based Optimization Approach for Entanglement Distribution and Source Position in Quantum Networks

Quantum Internet (QI) is a system of interconnected quantum computers able to exchange information encoded in the so called quantum bits (qubits). Differently from the classical counterpart, qubits benefit from a manifold properties guaranteed by quantum mechanics, such as superposition and entanglement. Despite the fact that quantum networks bring significant advantages, several phenomena can negatively impact the overall system, potentially hindering communication. In order to evaluate the network performance, a comprehensive probability expression is derived in this work to ultimately determine how many qubits are expected to be successfully received by nodes. On this basis, a Mixed-Integer Non-Linear Programming (MINLP) problem is formulated to fairly maximize the qubits exchanged between node pairs and jointly optimize 1) the position of the quantum source, and 2) the entanglement distribution plan. To cope with the non-convexity of the problem, an iterative optimization algorithm, leveraging Block Coordinate Descendent (BCD) and Successive Convex Approximation (SCA) techniques, is proposed. A thorough simulation campaign is conducted to corroborate the theoretical findings. Numerical results demonstrates, under different parameter setups, that the proposed algorithm provides superior performance with respect to a baseline approach.

I. Introduction

Quantum computing [1] is widely considered an emerging paradigm that holds the potential to solve specific challenging problems more efficiently than classical computers [2]. The basic unit of quantum information is the quantum bit (qubit), which is a two-level quantum system, representing the foundation of quantum devices and hence of quantum computing. Qubits can be physically represented as single atoms, photons or a cold superconducting circuits with moving electrons [3]. Unlike classical bits, a qubit has the unique ability to simultaneously exist in two states until a measurement is performed. This property, namely superposition, is granted by quantum mechanics and allows quantum computers to exponentially increase their computational power with the number of qubits [4].