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

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

arXiv:2301.07477

Preparing quantum ansatzes is a necessary prerequisite in many quantum algorithms for quantum chemistry such as the variational quantum eigensolver. Widely-used ansatzes including the Slater determinants and Unitary Coupled Cluster, employ parameterized fermionic excitation gates, with the latter resulting in deep quantum circuits that scale at least polynomially with the system size N. Here we propose an alternate paradigm for fermionic ansatz state preparation inspired by data-loading circuits methods developed for quantum machine learning. Our approach provides a shallower, yet scalable O(dlog2^N) two-qubit gate depth preparation of d-fermion Slater determinants and correlated states, a subexponential improvement in gate depth over existing approaches. This is particularly important as it can be implemented on planar architectures without qubit swapping overheads, thereby enabling the use of larger basis sets needed for high-precision quantum chemistry studies on near-term quantum devices.