Masih Mozakka

Masih Mozakka, Mohsen Heidari

Feedback-based methods have gained significant attention as an alternative training paradigm for the Quantum Approximate Optimization Algorithm (QAOA) in solving combinatorial optimization problems such as MAX-CUT. In particular, Quantum Lyapunov Control (QLC) employs feedback-driven control laws that guarantee monotonic non-decreasing objective values, can substantially reduce the training overhead of QAOA, and mitigate barren plateaus. However, these methods might require long control sequences, leading to sub-optimal convergence rates. In this work, we propose a hybrid method that incorporates per-layer gradient estimation to accelerate the convergence of QLC while preserving its low training overhead and stability guarantees. By leveraging layer-wise gradient information, the proposed approach selects near-optimal control parameters, resulting in significantly faster convergence and improved robustness. We validate the effectiveness of the method through extensive numerical experiments across a range of problem instances and optimization settings.

Mohsen Heidari, Masih Mozakka, Wojciech Szpankowski

Hybrid quantum-classical optimization and learning strategies are among the most promising approaches to harnessing quantum information or gaining a quantum advantage over classical methods. However, efficient estimation of the gradient of the objective function in such models remains a challenge due to several factors including the exponential dimensionality of the Hilbert spaces, and information loss of quantum measurements. In this work, we developed an efficient framework that makes the Hadamard test efficiently applicable to gradient estimation for a broad range of quantum systems, an advance that had been wanting from the outset. Under certain mild structural assumptions, the gradient is estimated with the measurement shots that scale logarithmically with the number of parameters and with polynomial classical and quantum time. This is an exponential reduction in the measurement cost and polynomial speed up in time compared to existing works. The structural assumptions are (1) the dimension of the dynamical Lie algebra is polynomial in the number of qubits, and (2) the observable has a bounded Hilbert-Schmidt norm.