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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 Society2025 

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_{\mu }$in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to $a_{\mu }$, respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong-isospin breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark-connected contribution, we obtain $a_{\mu }^{ll,\mathrm{SD}}\left(\mathrm{conn}\right)=48.139\left(11{)}_{\mathrm{stat}}\right(91{)}_{\mathrm{syst}}[92{]}_{\text{total}}\times {10}^{-10}$and $a_{\mu }^{ll,\mathrm{W}}\left(\mathrm{conn}\right)=206.90\left(14{)}_{\mathrm{stat}}\right(61{)}_{\mathrm{syst}}[63{]}_{\text{total}}\times {10}^{-10}$. We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a_{\mu }^{\mathrm{SD}}=69.05\left(1{)}_{\mathrm{stat}}\right(21{)}_{\mathrm{syst}}[21{]}_{\text{total}}\times {10}^{-10}$and $a_{\mu }^{\mathrm{W}}=236.45\left(17{)}_{\mathrm{stat}}\right(83{)}_{\mathrm{syst}}[85{]}_{\text{total}}\times {10}^{-10}$. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few-permille level. Published by the American Physical Society2025