Gradient Estimation with Constant Scaling for Hybrid Quantum Machine Learning

Understand

We present a novel method for determining gradients of parameterised quantum circuits (PQCs) in hybrid quantum-classical machine learning models by applying the multivariate version of the simultaneous perturbation stochastic approximation (SPSA) algorithm.

• The gradients of PQC layers can be calculated with an overhead of two evaluations per circuit per forward-pass independent of the number of circuit parameters, compared to the linear scaling of the parameter shift rule.
• These are then used in the backpropagation algorithm by applying the chain rule.
• We compare our method to the parameter shift rule for different circuit widths and batch sizes, and for a range of learning rates.