Potentials and Limitations of Analog Quantum Simulators in Variational Quantum Algorithms

The variational quantum algorithms have a potential to bring about useful applications of near-term quantum devices. While digital gate-based VQAs have been extensively investigated with well-known fundamental results such as barren plateaus, the analog paradigm remains relatively unexplored. In this work, we propose an experimental-friendly ansatz based on analog quench dynamics generated by native Hamiltonian of quantum hardware. By considering a disordered Ising spin chain as an example, we study three fundamental aspects of our ansatz including (i) universality and how (ii) expressivity and (iii) trainability scale with the number of qubits. We show that the ansatz is universal when allowing time within each quench to be parametrized. To study the other two aspects, we operate our ansatz in two different phases of matter namely thermalized and many-body localized (MBL) phases. While maximum expressivity can be achieved in both phases, it is exactly in this regime where the ansatz becomes untrainable with exponentially vanishing variance. Fortunately, since the number of quenches to achieve the maximum expressivity in MBL is much less than in the thermalized phase, this allows a novel strategy with trainability when our anzatz is initialized in MBL. Our results demonstrate the deep connection of quantum many-body phases with expressivity and trainability in analog VQAs.