Ernesto Campos

I am Ernesto Campos, a researcher and adjunct professor of computer science at the Monterrey Institute of Technology (ITESM).

I study the intersection of quantum and classical machine learning, with research subjects including variational quantum algorithms, quantum approximate optimization, analog-digital algorithms, quantum walks, and tensor networks.

Much of my work on variational quantum algorithms has focused on a simple question: when, and why, does training succeed? In 2021, we identified several mechanisms that explain failure modes in shallow circuits. We showed that cost landscapes can undergo abrupt training transitions,¹ where shallow models become trapped in trivial minima and require substantially greater depth to reach meaningful solutions. We also introduced the notion of training saturation,² demonstrating that layerwise-optimized circuits hit a structural ceiling beyond which performance cannot improve. In parallel, we proved parameter concentration effects,³ showing that optimal parameters cluster across problem instances.

These results helped shift attention away from barren plateaus as the only obstacle, toward a broader landscape of structural training limits. In response, we proposed hardware-native, problem-tailored ansatz constructions.⁴ These models not only improved performance on combinatorial optimization problems, but also exhibited markedly better training behavior than generic circuit templates. More recently, we proved that QAOA achieves the same depth scaling as Grover search for unstructured problems,⁵ formally establishing a quantum speedup in that setting.

Together, this line of work has helped shape modern strategies such as warm-start initialization and dynamically constructed ansatz circuits. The central challenge now is sharper: to identify trainable quantum models that cannot be efficiently dequantized, and that deliver a provable advantage on meaningful problems.