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

Chong Hian Chee, Daniel Leykam, Adrian M. Mak, and Dimitris G. Angelakis.

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, \(\mathcal{O} (d {\log}^2_2N) \) 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 \(d≪O(N/\log^2_2N)\) fermionic systems with larger basis sets on near-term quantum devices.

Cite as BibTex
@article{Chee_Leykam_Mak_Angelakis_2023, title={Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer}, volume={108}, DOI={10.1103/physreva.108.022416}, number={2}, journal={Physical Review A}, author={Chee, Chong Hian and Leykam, Daniel and Mak, Adrian M. and Angelakis, Dimitris G.}, year={2023}, month={Aug}} 

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The QCFD (Quantum Computational Fluid Dynamics) project is funded under the European Union’s Horizon Programme (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10), Grant Agreement 101080085 QCFD.