Fig. 1: Content overview.
From: Large-scale simulations of Floquet physics on near-term quantum computers
(a) QHiFFS Algorithm Concept. To realize a time-dependent periodic time evolution, we transform from the standard basis to a (periodically) rotating frame using \({e}^{+i\hat{K}({t}_{0})}\). Evolution in this frame from t0 to t is governed by the time-independent effective Hamiltonian \({\hat{H}}_{{\rm{eff}}}\). The adjoint of the kick operator \({e}^{-i\hat{K}(t)}\) is applied at the final simulation time t to kick back into the original frame. (b) Benchmark system. To demonstrate the advantage of QHiFFS, as compared to standard Trotterization, we implement the 20-qubit transversely driven 2D biaxial next-nearest neighbor Ising (BNNNI) model with periodic boundary conditions on Quantinuum’s H1 trapped ion quantum hardware (see Fig. 3). The BNNNI model, Eq. (6), consists of nearest-neighbor coupling with strength J and next-nearest-neighbor coupling with strength κJ. We suppose a 4 by 5 qubit lattice is periodically driven with strength h and at frequency ω.
