Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

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