Bonn 2025 – wissenschaftliches Programm
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QI: Fachverband Quanteninformation
QI 16: Quantum Computing Theory III
QI 16.2: Vortrag
Dienstag, 11. März 2025, 14:15–14:30, HS IV
Preparing ground-states of frustration-free Hamiltonians using measurement-and-feedback algorithms — •Tobias Schmale1, Maria Kalabakov2, and Hendrik Weimer1,2 — 1Institut für Theoretische Physik, Appelstr. 2, 30167 Hannover — 2Institut für Theoretische Physik, Hardenbergstr. 36, 10623 Berlin
Many physically interesting Hamiltonians are frustration-free, meaning that the global ground-state is also a local ground-state. We investigate a measurement-and-feedback scheme for preparing such ground-states on a quantum computer: First partition the (possibly non-commuting) local terms of a given Hamiltonian into sublattices, such that terms of the same sublattice commute. Then, repeatedly iterate through the sublattices and perform simultaneous measurements of commuting terms of the Hamiltonian, and remove excitations by making use of unitary operations and of the classical knowledge about the location of the excitations. Of particular interest here are situations where it can be guaranteed, that these "correction" unitaries do not create new excitations on any sublattice. We present numerical examples of this scheme converging to the ground-state of physically interesting Hamiltonians, as well as some examples where the ground-state is reached in a time independent of system size. We show that in general the runtime is bounded by the Hamiltonian gap, and present further efforts into an analytic understanding of convergence criteria and convergence rates of this scheme.
Keywords: Ground-state preparation; Measurement-and-Feedback; Frustration-free Hamiltonian