Differentiable Quantum Programming with Unbounded Loops

TL;DR

This paper introduces the first differentiable quantum programming framework capable of handling unbounded loops, enabling training of quantum applications like quantum walk and unitary implementation that were previously infeasible.

Contribution

The paper presents a novel differentiable quantum programming framework with unbounded loops, including new differentiation rules and code transformation techniques.

Findings

Successfully implemented in Python and Q#

Demonstrated effective parameter optimization in quantum applications

Introduced a randomized estimator for derivatives in unbounded loops

Abstract

The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Recently, Zhu et al. (PLDI 2020) have formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q#, and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications.