Hostetler, Leon (ORCID:0000000274161443)

DOE OSTI2025

Efficient state preparation for the Schwinger model with a theta term

We present a comparison of different quantum state preparation algorithms and their overall efficiency for the Schwinger model with a theta term. While adiabatic state preparation is proved to be effective, in practice it leads to large gate counts to prepare the ground state. The quantum approximate optimization algorithm (QAOA) provides excellent results while keeping the counts small by design, at the cost of an expensive classical minimization process. We introduce a “blocked” modification of the Schwinger Hamiltonian to be used in the QAOA that further decreases the length of the algorithms as the size of the problem is increased. The rodeo algorithm (RA) provides a powerful tool to efficiently prepare any eigenstate of the Hamiltonian, as long as its overlap with the initial guess is large enough. We obtain the best results when combining the blocked QAOA ansatz and the RA, as this provides an excellent initial state with a relatively short algorithm without the need to perform any classical steps for large problem sizes. Published by the American Physical Society 2025

Bazavov, Alexei (ORCID:0000000321411901)↗

DOE OSTI2024

Symmetry breaking in an extended O(2) model

Motivated by attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we study an extended-O(2) model in two dimensions that differs from the ordinary O(2) model by the addition of an explicit symmetry breaking term − h q cos ( q φ ) . Its coupling h q allows to smoothly interpolate between the O(2) model ( h q = 0 ) and a q -state clock model ( h q → ∞ ). In the latter case, a q -state clock model can also be defined for noninteger values of q . Thus, such a limit can also be considered as an analytic continuation of an ordinary q -state clock model to noninteger q . In previous work, we established the phase diagram for noninteger q in the infinite coupling limit ( h q → ∞ ). We showed that there is a second-order phase transition at low temperature and a crossover at high temperature. In this work, we seek to establish the phase diagram at finite values of the coupling using Monte Carlo and tensor methods. We show that for noninteger q , the second-order phase transition at low temperature and crossover at high temperature persist to finite coupling. For integer q = 2 , 3, 4, we know there is a second-order phase transition at infinite coupling (i.e. the well-known clock models). At finite coupling, we find that the critical exponents for q = 3 , 4 vary with the coupling, and for q = 4 the transition may turn into a Berezinskii-Kosterlitz-Thouless transition at small coupling. We comment on the similarities and differences of the phase diagrams with those of quantum simulators of the Abelian-Higgs model based on ladder-shaped arrays of Rydberg atoms. Published by the American Physical Society 2024

Astronomy & Astrophysics↗