Hierarchical Learning for Quantum ML: Novel Training Technique for
  Large-Scale Variational Quantum Circuits
We present hierarchical learning, a novel variational architecture for
efficient training of large-scale variational quantum circuits. We test and
benchmark our technique for distribution loading with quantum circuit born
machines (QCBMs). With QCBMs, probability distributions are loaded into the
squared amplitudes of computational basis vectors represented by bitstrings.
Our key insight is to take advantage of the fact that the most significant
(qu)bits have a greater effect on the final distribution and can be learned
first. One can think of it as a generalization of layerwise learning, where
some parameters of the variational circuit are learned first to prevent the
phenomena of barren plateaus. We briefly review adjoint methods for computing
the gradient, in particular for loss functions that are not expectation values
of observables. We first compare the role of connectivity in the variational
ansatz for the task of loading a Gaussian distribution on nine qubits, finding
that 2D connectivity greatly outperforms qubits arranged on a line. Based on
our observations, we then implement this strategy on large-scale numerical
experiments with GPUs, training a QCBM to reproduce a 3-dimensional
multivariate Gaussian distribution on 27 qubits up to $\sim4\%$ total variation
distance. Though barren plateau arguments do not strictly apply here due to the
objective function not being tied to an observable, this is to our knowledge
the first practical demonstration of variational learning on large numbers of
qubits. We also demonstrate hierarchical learning as a resource-efficient way
to load distributions for existing quantum hardware (IBM's 7 and 27 qubit
devices) in tandem with Fire Opal optimizations.
Hrant Gharibyan Vincent Su Hayk Tepanyan