Last Update
Oct 23, 2022

Quantum Generative Adversarial Network for k-Forrelation Dataset

This is a currently a work in progress.

This project investigates whether Quantum Generative Adversarial Network (QuGAN) can be used to generate the k-Forrelation Dataset.

Classically generate the k-Forrelation is challenging:

• The positive class is exponentially rare at larger problem sizes, making it prohibitively difficult to sample a balanced dataset

• Random sampling in the function space is incapable of generating examples with high positive thresholds, which requires the development of a novel sampling algorithm

Each k-Forrelation instance can be represented as a quantum circuit with Hadamard layers alternating with encoding layers that describe each discrete Boolean function (Aaronson, 2014), as shown below:

It is natural to ask whether QuGAN can be used to generate the k-Forrelation datasets more easily. I.e., can the Generator in QuGAN learn the distribution of k-Forrelation instances with high $\Phi$ values?

Note: Generation of the k-Forrelation dataset using classical GAN is yet to be attempted. So far, the project is simply motivated by the theoretical formulation of k-Forrelation as quantum circuits

The QuGAN architecture is based on the paper by Dallaire-Demers & Killoran (2018)