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Variational quantum-classical hybrid algorithms are seen as a promisingstrategy for solving practical problems on quantum computers in the near term.While this approach reduces the number of qubits and operations required fromthe quantum machine, it places a heavy load on a classical optimizer. Whileoften under-appreciated, the latter is a computationally hard task due to thebarren plateau phenomenon in parameterized quantum circuits. The absence ofguiding features like gradients renders conventional optimization strategiesineffective as the number of qubits increases. Here, we introduce thefast-and-slow algorithm, which uses Bayesian Learning to identify a promisingregion in parameter space. This is used to initialize a fast local optimizer tofind the global optimum point efficiently. We illustrate the effectiveness ofthis method on the Bars-and-Stripes (BAS) quantum generative model, which hasbeen studied on several quantum hardware platforms. Our results movevariational quantum algorithms closer to their envisioned applications inquantum chemistry, combinatorial optimization, and quantum simulation problems.

Surviving The Barren Plateau in Variational Quantum Circuits with Bayesian Learning Initialization