Abstract
Quantum computers are a leading platform for the simulation of many-body physics. This task has been recently facilitated by the possibility to program directly the time-dependent pulses sent to the computer. Here, we use this feature to simulate quantum lattice models with long-range hopping. Our approach is based on an exact mapping between periodically driven quantum systems and one-dimensional lattices in the synthetic Floquet direction. By engineering a periodic drive with a power-law spectrum, we simulate a lattice with long-range hopping, whose decay exponent is freely tunable. We propose and realize experimentally two protocols to probe the long tails of the Floquet eigenfunctions and to identify a scaling transition between weak and strong long-range couplings. Our work offers a useful benchmark of pulse engineering and opens the route towards quantum simulations of rich nonequilibrium effects.
Highlights
A common assumption of many-body physics is that particles can interact only with their neighbors
We studied the scaling properties of the Floquet eigenstates and determined the effects of the long tails on the expectation values of physical observables and their time derivatives
By realizing this model on a quantum computer, we demonstrated the experimental capability of controlling and measuring a large number (M = 30) of harmonics
Summary
A common assumption of many-body physics is that particles can interact only with their neighbors. The experimental study of this transition requires a simulator where α is not set by the physical decay of elementary forces and can be tuned continuously This requirement is partially fulfilled by trapped ions, where phonon-mediated interactions can be used to simulate long-range quantum spin models, and α can be tuned within a limited range [19,20]. We propose and realize an alternative approach, based on periodically driven (Floquet) quantum models We use pulse engineering to simulate long-range couplings in the Floquet space
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