Southwest Quantum Information and Technology

Universal Compiling and (No-)Free-Lunch Theorems for Continuous Variable Quantum Learning

Presenting Author: Tyler Volkoff, Los Alamos National Laboratory
Contributing Author(s): Zoe Holmes, Andrew Sornborger

Variational quantum compiling, where a parameterized quantum circuit V(θ) is trained to learn a target unitary U, is a fundamental primitive for quantum computing. It can be used to find optimal circuits to aid the implementation of larger algorithms. In this presentation, we will introduce algorithms for continuous-variable (CV) variational quantum compiling which are motivated by extending the “no-free-lunch” (NFL) theorems of supervised learning theory to the quantum CV setting. These algorithms utilize readily available Gaussian resources, such as coherent states and two-mode squeezed states. In addition to proving quantum NFL theorems for learning linear optical unitaries and general CV unitaries, we will further prove that the corresponding CV compiling algorithms are trainable, and thus do not exhibit obstructions to scalability such as the barren plateau phenomenon that plagues the finite dimensional case. The results show how theorems from statistical learning theory can be used to motivate near-term CV quantum compiling algorithms. We illustrate the wide applicability of our cost functions for CV quantum compiling by numerically demonstrating efficient learning of arbitrary single-mode Gaussian unitaries, two-mode beamsplitters, and Kerr non-linearities. We expect our algorithms to find applications in a broad range of areas including the characterization of nonlinear optical media, entanglement spectroscopy, and optimal CV circuit design.

Read this article online: https://arxiv.org/abs/2105.01049

(Session 5 : Thursday from 12:00pm-2:00 pm)