AltGraph: Redesigning Quantum Circuits Using Generative Graph Models for Efficient Optimization

Quantum circuit transformation aims to produce equivalent circuits while optimizing for various aspects such as circuit depth, gate count, and compatibility with modern Noisy Intermediate Scale Quantum (NISQ) devices. There are two techniques for circuit transformation. The first is a rule-based approach that greedily cancels out pairs of gates that equate to the identity unitary operation. Rule-based approaches are used in quantum compilers such as Qiskit, tket, and Quilc. The second is a search-based approach that tries to find an equivalent quantum circuit by exploring the quantum circuits search space. Search-based approaches typically rely on machine learning techniques such as generative models and Reinforcement Learning (RL). In this work, we propose AltGraph, a novel search-based circuit transformation approach that generates equivalent quantum circuits using existing generative graph models. We use three main graph models: DAG Variational Autoencoder (D-VAE) with two variants: Gated Recurrent Unit (GRU) and Graph Convolutional Network (GCN), and Deep Generative Model for Graphs (DeepGMG) that take a Direct Acyclic Graph (DAG) of the quantum circuit as input and output a new DAG from which we reconstruct the equivalent quantum circuit. Next, we perturb the latent space to generate equivalent quantum circuits some of which may be more compatible with the hardware coupling map and/or enable better optimization leading to reduced gate count and circuit depth. AltGraph achieves on average a 37.55 reduction in the number of gates and a 37.75 post-transpiling compared to the original transpiled circuit with only 0.0074 Mean Squared Error (MSE) in the density matrix.