2022/07/04 by Troy J. Sewell, Sewell, Troy, Aniruddha Bapat +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2207.01692
openalex publication_date 2022/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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'' 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. > 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.