



01880nas a2200133   4500008004100000245008500041210006900126260001500195520144100210100001701651700002101668700002001689856003701709       2022                        eng d00aEstimating gate complexities for the site-by-site preparation of fermionic vacua0 aEstimating gate complexities for the sitebysite preparation of f  c07/04/20223 a<p>An important aspect of quantum simulation is the preparation of physically interesting states on a quantum computer, and this task can often be costly or challenging to implement. A digital, ``site-by-site&#39;&#39; scheme of state preparation was introduced in arXiv:1911.03505 as a way to prepare the vacuum state of certain fermionic field theory Hamiltonians with a mass gap. More generally, this algorithm may be used to prepare ground states of Hamiltonians by adding one site at a time as long as successive intermediate ground states share a non-zero overlap and the Hamiltonian has a non-vanishing spectral gap at finite lattice size. In this paper, we study the ground state overlap as a function of the number of sites for a range of quadratic fermionic Hamiltonians. Using analytical formulas known for free fermions, we are able to explore the large-N behavior and draw conclusions about the state overlap. For all models studied, we find that the overlap remains large (e.g. &gt;0.1) up to large lattice sizes (N=64,72) except near quantum phase transitions or in the presence of gapless edge modes. For one-dimensional systems, we further find that two N/2-site ground states also share a large overlap with the N-site ground state everywhere except a region near the phase boundary. Based on these numerical results, we additionally propose a recursive alternative to the site-by-site state preparation algorithm.</p>1 aSewell, Troy1 aBapat, Aniruddha1 aJordan, Stephen  uhttps://arxiv.org/abs/2207.01692