Overparameterization of Realistic Quantum Systems

In order for quantum computing devices to accomplish preparation of quantum states, or simulation of other quantum systems, exceptional control of experimental parameters is required. The optimal parameters, such as time dependent magnetic fields for nuclear magnetic resonance, are found via classical simulation and optimization. Such idealized parameterized quantum systems have been shown to exhibit different phases of learning during optimization, such as overparameterization and lazy training, where global optima may potentially be reached exponentially quickly, while parameters negligibly change when the system is evolved for sufficient time (Larocca et al., arXiv:2109.11676, 2021). Here, we study the effects of imposing constraints related to experimental feasibility on the controls, such as bounding or sharing parameters across operators, and relevant noise channels are added after each time step. We observe overparameterization being robust to parameter constraints, however fidelities converge to zero past a critical simulation duration, due to catastrophic accumulation of noise. Compromises arise between numerical and experimental feasibility, suggesting limitations of variational ansatz to account for noise.

Zoom link:  https://pitp.zoom.us/j/98649931693?pwd=Z2s1MlZvSmFVNEFqdjk2dlZNRm9PQT09