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

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 $\mathcal{O}(d{\log }_2^{2}N)$ 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.