Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer

TL;DR

This paper introduces a new quantum circuit approach that significantly reduces the depth needed to prepare fermionic states like Slater determinants, enabling more efficient simulations of larger quantum systems on near-term devices.

Contribution

The authors propose a scalable, shallow circuit design for fermionic state preparation that outperforms existing methods in depth complexity, especially for large systems.

Findings

Achieves ${ m O}(d \log_2^2 N)$ two-qubit gate depth for state preparation.

Provides a subexponential reduction in circuit depth compared to previous approaches.

Enables high-accuracy simulations of larger fermionic systems on near-term quantum hardware.

Abstract

Fermionic ansatz state preparation is a critical subroutine in many quantum algorithms such as Variational Quantum Eigensolver for quantum chemistry and condensed matter applications. The shallowest circuit depth needed to prepare Slater determinants and correlated states to date scale at least linearly with respect to the system size $N$. Inspired by data-loading circuits developed for quantum machine learning, we propose an alternate paradigm that provides shallower, yet scalable ${\mathcal{O}}(d \log_2^2N)$ two-qubit gate depth circuits to prepare such states with d-fermions, offering a subexponential reduction in $N$ over existing approaches in second quantization, enabling high-accuracy studies of $d{\ll}{\mathcal{O}}{\left(N / \log_2^2 N\right)}$ fermionic systems with larger basis sets on near-term quantum devices.