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We investigate the feasibility of integrating quantum algorithms as subroutines of simulation-based optimisation problems with relevance to and potential applications in mathematical finance. To this end, we conduct a thorough analysis of all systematic errors arising in the formulation of quantum Monte Carlo integration in order to better understand the resources required to encode various distributions such as a Gaussian, and to evaluate statistical quantities such as the Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) of an asset. Finally, we study the applicability of quantum Monte Carlo integration for fundamental financial use cases in terms of simulation-based optimisations, notably Mean-Conditional-Value-at-Risk (Mean-CVaR) and (risky) Mean-Variance (Mean-Var) optimisation problems. In particular, we study the Mean-Var optimisation problem in the presence of noise on a quantum device, and benchmark a quantum error mitigation method that applies to quantum amplitude estimation -- a key subroutine of quantum Monte Carlo integration -- showcasing the utility of such an approach.

The quantum approximate optimization algorithm (QAOA) conceived for solving combinatorial optimization problems has attracted significant interest since it can be run on the existing noisy intermediate-scale quantum (NISQ) devices. A primary step of using the QAOA is the efficient Hamiltonian construction based on different problem instances. Hence, we solve the maximum likelihood (ML) detection problem for general constellations by appropriately adapting the QAOA, which gives rise to a new paradigm in communication systems. We first transform the ML detection problem into a weighted minimum $N$-satisfiability (WMIN-$N$-SAT) problem, where we formulate the objective function of the WMIN-$N$-SAT as a pseudo Boolean function. Furthermore, we formalize the connection between the degree of the objective function and the Gray-labelled modulation constellations. Explicitly, we show a series of results exploring the connection between the coefficients of the monomials and the patterns of the associated constellation points, which substantially simplifies the objective function with respect to the problem Hamiltonian of the QAOA. In particular, for an M-ary Gray-mapped quadrature amplitude modulation (MQAM) constellation, we show that the specific qubits encoding the in-phase components and those encoding the quadrature components are independent in the quantum system of interest, which allows the in-phase and quadrature components to be detected separately using the QAOA. Furthermore, we characterize the degree of the objective function in the WMIN-$N$-SAT problem corresponding to the ML detection of multiple-input and multiple-output (MIMO) channels. Finally, we evaluate the approximation ratio of the QAOA for the ML detection problem of quadrature phase shift keying (QPSK) relying on QAOA circuits of different depths.

Data packet routing in aeronautical ad-hoc networks (AANETs) is challenging due to their high-dynamic topology. In this paper, we invoke deep learning (DL) to assist routing in AANETs. We set out from the single objective of minimizing the end-to-end (E2E) delay. Specifically, a deep neural network (DNN) is conceived for mapping the local geographic information observed by the forwarding node into the information required for determining the optimal next hop. The DNN is trained by exploiting the regular mobility pattern of commercial passenger airplanes from historical flight data. After training, the DNN is stored by each airplane for assisting their routing decisions during flight relying solely on local geographic information. Furthermore, we extend the DL-aided routing algorithm to a multi-objective scenario, where we aim for simultaneously minimizing the delay, maximizing the path capacity, and maximizing the path lifetime. Our simulation results based on real flight data show that the proposed DL-aided routing outperforms existing position-based routing protocols in terms of its E2E delay, path capacity as well as path lifetime, and it is capable of approaching the Pareto front that is obtained using global link information., Comment: Published in IEEE Internet of Things Journal

Data packet routing in aeronautical ad-hoc networks (AANETs) is challenging due to their high-dynamic topology. In this paper, we invoke deep reinforcement learning for routing in AANETs aiming at minimizing the end-to-end (E2E) delay. Specifically, a deep Q-network (DQN) is conceived for capturing the relationship between the optimal routing decision and the local geographic information observed by the forwarding node. The DQN is trained in an offline manner based on historical flight data and then stored by each airplane for assisting their routing decisions during flight. To boost the learning efficiency and the online adaptability of the proposed DQN-routing, we further exploit the knowledge concerning the system's dynamics by using a deep value network (DVN) conceived with a feedback mechanism. Our simulation results show that both DQN-routing and DVN-routing achieve lower E2E delay than the benchmark protocol, and DVN-routing performs similarly to the optimal routing that relies on perfect global information.

Current maritime communications mainly rely on satellites having meager transmission resources, hence suffering from poorer performance than modern terrestrial wireless networks. With the growth of transcontinental air traffic, the promising concept of aeronautical ad hoc networking relying on commercial passenger airplanes is potentially capable of enhancing satellite-based maritime communications via air-to-ground and multi-hop air-to-air links. In this article, we conceive space-air-ground integrated networks (SAGINs) for supporting ubiquitous maritime communications, where the low-earth-orbit satellite constellations, passenger airplanes, terrestrial base stations, ships, respectively, serve as the space-, air-, ground- and sea-layer. To meet heterogeneous service requirements, and accommodate the time-varying and self-organizing nature of SAGINs, we propose a deep learning (DL) aided multi-objective routing algorithm, which exploits the quasi-predictable network topology and operates in a distributed manner. Our simulation results based on real satellite, flight, and shipping data in the North Atlantic region show that the integrated network enhances the coverage quality by reducing the end-to-end (E2E) delay and by boosting the E2E throughput as well as improving the path-lifetime. The results demonstrate that our DL-aided multi-objective routing algorithm is capable of achieving near Pareto-optimal performance., Comment: Accepted by IEEE Wireless Communications

Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where quantum approximation optimization algorithms (QAOAs) constitute promising candidates for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider the maximum likelihood (ML) detection problem of binary symbols transmitted over a multiple-input and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers. Here, we apply the QAOA for the ML detection by encoding the problem of interest into a level-p QAOA circuit having 2p variational parameters, which can be optimized by classical optimizers. This level-p QAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately in p consecutive rounds. More explicitly, we first encode the optimal solution of the ML detection problem into the ground state of a problem Hamiltonian. Using the quantum adiabatic evolution technique, we provide both analytical and numerical results for characterizing the evolution of the eigenvalues of the quantum system used for ML detection. Then, for level-1 QAOA circuits, we derive the analytical expressions of the expectation values of the QAOA and discuss the complexity of the QAOA based ML detector. Explicitly, we evaluate the computational complexity of the classical optimizer used and the storage requirement of simulating the QAOA. Finally, we evaluate the bit error rate (BER) of the QAOA based ML detector and compare it both to the classical ML detector and to the classical MMSE detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector. This paves the way for a host of large-scale classical optimization problems to be solved by NISQ computers., Comment: 30 pages

Relying on multi-hop communication techniques, aeronautical ad hoc networks (AANETs) seamlessly integrate ground base stations (BSs) and satellites into aircraft communications for enhancing the on-demand connectivity of planes in the air. In this integrated AANET context we investigate the shortest-path routing problem with the objective of minimizing the total delay of the in-flight connection from the ground BS subject to certain minimum-rate constraints for all selected links in support of low-latency and high-speed services. Inspired by the best-first search and priority queue concepts, we model the problem formulated by a weighted digraph and find the optimal route based on the shortest-path algorithm. Our simulation results demonstrate that aircraft-aided multi-hop communications are capable of reducing the total delay of satellite communications, when relying on real historical flight data., Comment: 13 pages