Optimal training of variational quantum algorithms without barren plateaus
This addresses a critical bottleneck in near-term quantum computing by improving training efficiency and stability for VQAs, though it is incremental as it builds on existing optimization techniques.
The paper tackles the barren plateau problem in variational quantum algorithms (VQAs) by introducing adaptive learning rates and a generalized quantum natural gradient, which together outperform other optimization methods and enable training without vanishing gradients under certain constraints, such as when fidelity is bounded from below.
Variational quantum algorithms (VQAs) promise efficient use of near-term quantum computers. However, training VQAs often requires an extensive amount of time and suffers from the barren plateau problem where the magnitude of the gradients vanishes with increasing number of qubits. Here, we show how to optimally train VQAs for learning quantum states. Parameterized quantum circuits can form Gaussian kernels, which we use to derive adaptive learning rates for gradient ascent. We introduce the generalized quantum natural gradient that features stability and optimized movement in parameter space. Both methods together outperform other optimization routines in training VQAs. Our methods also excel at numerically optimizing driving protocols for quantum control problems. The gradients of the VQA do not vanish when the fidelity between the initial state and the state to be learned is bounded from below. We identify a VQA for quantum simulation with such a constraint that thus can be trained free of barren plateaus. Finally, we propose the application of Gaussian kernels for quantum machine learning.