Eigen-Spectrum Estimation and Source Detection in a Massive Sensor Array Based on Quantum Assisted Hamiltonian Simulation Framework

In this work, we propose quantum assisted eigenvalue estimation and target detection algorithms for a large sensor array via Hamiltonian simulation. Quantum algorithms provide complexity advantage of a certain class of problems on a quantum computer with fewer physical resources as compared to their classical counterparts. The proposed algorithms make use of the quantum phase estimation (QPE) as its core computing component. We have introduced an analytical quantum framework to map from classical to quantum in the context of target detection. Target detection involves an appropriate choice of threshold based on the probability of detection or false alarm. We exploited the massive sensor array structure and invoked the random matrix theory to propose an optimal threshold. It also takes into account the quantum measurement noise in the framework. Numerical simulations are performed to ascertain the efficacy of the proposed framework. The results suggest near term applications of the quantum algorithm for large-scale linear systems.