Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer
Chong Hian Chee, Daniel Leykam, Adrian Matthew Mak, Dimitris G. Angelakis · Physical Review A · 2023
Fermionic Ansatz state preparation is a critical subroutine in many quantum algorithms such as the variational quantum eigensolver for quantum chemistry and condensed-matter applications. The shallowest circuit depth needed to prepare Slater determinants and correlated states to date scales 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, $O(d{log}_{2}^{2}N)$ 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 $d\ensuremath{\ll}O(N/{log}_{2}^{2}N)$ fermionic systems with larger basis sets on near-term quantum devices.