Southwest Quantum Information and Technology

Quantifying expressibility of variational quantum circuits

Presenting Author: Yash Chitgopekar, Oak Ridge National Laboratory
Contributing Author(s): Kathleen Hamilton

Deep learning methods have become constrained by available computational power, and new platforms are required. As quantum hardware has progressed into the Noisy Intermediate-Scale Quantum (NISQ) era, variational quantum circuits have been proposed as models for feed-forward networks. For them to be successful in supervised learning tasks, they must be capable of representing a variety of quantum states. Shallow circuits are unsuitable for this, yet similar to difficulties with deep neural networks, as the length of a quantum circuit increases, gradient-based training loses its efficacy. To combat this phenomenon, shorter circuit ansatze with greater expressibility must be identified. The expressibility of quantum circuits for quantum state preparation tasks has previously been quantified in terms of coverage of the Bloch sphere. Adapting this analysis for quantum circuits that are trained to prepare classical distributions, we propose a novel method based on Löwner-John ellipsoids that directly quantifies the circuits' ability to explore the probability simplex. We execute noiseless simulations of one, two, and three-qubit circuits of varying depth over randomly sampled parameter sets to compare different circuit topologies. In our studies on circuits with up to three quits and thirty parameters, we observe that increases in expressibility arrive in abrupt, step-like increments. Using this characteristic, we suggest guidelines on circuit design in quantum circuit learning.

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