Entanglement devised barren plateau mitigation

Hybrid quantum-classical variational algorithms are one of the most propitious implementations of quantum computing on near-term devices, offering classical machine-learning support to quantum scale solution spaces. However, numerous studies have demonstrated that the rate at which this space grows in qubit number could preclude learning in deep quantum circuits, a phenomenon known as barren plateaus. In this work, we implicate random entanglement, i.e., entanglement that is formed due to state evolution with random unitaries, as a source of barren plateaus and characterize them in terms of many-body entanglement dynamics, detailing their formation as a function of system size, circuit depth, and circuit connectivity. Using this comprehension of entanglement, we propose and demonstrate a number of barren plateau ameliorating techniques, including initial partitioning of cost function and non-cost function registers, meta-learning of low-entanglement circuit initializations, selective inter-register interaction, entanglement regularization, the addition of Langevin noise, and rotation into preferred cost function eigenbases. We find that entanglement limiting, both automatic and engineered, is a hallmark of high-accuracy training and emphasize that, because learning is an iterative organization process whereas barren plateaus are a consequence of randomization, they are not necessarily unavoidable or inescapable. Our work forms both a theoretical characterization and a practical toolbox; first defining barren plateaus in terms of random entanglement and then employing this expertise to strategically combat them.

Automated summary

This study reveals the role of entanglement in barren plateaus, proposes techniques to ameliorate them, and emphasizes the impact of entanglement on training and the avoidability of barren plateaus in the learning process.