Generative Circuit Design for Quantum-Selected Configuration Interaction

TL;DR

This paper introduces a Transformer-based generative framework for optimizing quantum ansatz circuits in quantum-selected configuration interaction, significantly reducing gate counts while maintaining chemical accuracy.

Contribution

It presents a novel GQE framework that uses a Transformer policy to optimize ansatz structures for QSCI, achieving lower gate counts and compact wavefunctions.

Findings

Optimized circuits reach chemical precision with 98% fewer two-qubit gates than Trotterized methods.

Wavefunctions are competitive with HCI in terms of compactness.

Achieves chemical precision with 50% smaller subspaces in strongly correlated regimes.

Abstract

Quantum-selected configuration interaction (QSCI) has emerged as a feasible approach for approximating electronic ground states on noisy quantum devices toward large-system demonstrations. In QSCI, Slater determinants are sampled from a quantum-prepared state, and the Hamiltonian is then diagonalized in the sampled subspace. To create a high-quality subspace under hardware constraints, the design of the state-preparation circuit is crucial. Here, we present a Generative Quantum Eigensolver (GQE)-based framework that optimizes ansatz structures using a Transformer policy trained on the QSCI subspace energy. We validate the framework on N2 in active spaces of up to 32 qubits. We found that the optimized circuits reach chemical precision with substantially lower gate counts than time-evolved circuits. Quantitatively, this corresponds to an average reduction of 98% in the required two-qubit gate count relative to the single-step first-order Trotterized approximation and 83% relative to the qDRIFT approximation. Furthermore, the resulting wavefunctions are competitive with heat-bath configuration interaction (HCI) in terms of compactness. In stretched-bond, strongly correlated regimes, they achieve chemical precision with subspaces that are 50% smaller than those required by HCI.