Bang-bang shortcut to adiabaticity in trapped-ion quantum simulators

Abstract

We model the bang-bang optimization protocol as a shortcut to adiabaticity in the ground-state preparation of an ion-trap-based quantum simulator. Compared to a locally adiabatic evolution, the bang-bang protocol produces a somewhat lower ground-state probability, but its implementation is so much simpler than the locally adiabatic approach, that it remains an excellent choice to use for maximizing ground-state preparation in systems that cannot be solved with conventional computers. We describe how one can optimize the shortcut and provide specific details for how it can be implemented with current ion-trap-based quantum simulators. Introduction. There has been much recent progress in ion-trap-based quantum simulation. Original experiments focused on adiabatic state preparation [1-3] of the transverse-field Ising model by initially orienting all of the spins along the field axis (in a large initial field) and then ramping the field to zero to create the ground state of the Ising model. But when the system size was increased, and frustrated antiferromagnetic systems were examined, it became clear that these experiments would have a large amount of diabatic excitation [4], which led to the study of excited states [4][5][6][7] and to a protocol that optimizes the field ramp with a locally adiabatic criterion [8]. In addition, other experimental situations were examined, such as Lieb-Robinson bounds [9, 10] and higher-spin cases [11]. Currently, there are two foci for adiabatic state preparation: (i) find shortcuts which will allow the original protocol to be achieved or (ii) use the diabatic excitations as a means to study low-energy excitations. Within the first category, recent work has found an exact shortcut for adiabatic state preparation [12,13] (at least for the nearest-neighbor transverse field Ising model), but the multiple-spin interactions needed to accomplish this goal are too complicated to implement in the current generation of quantum simulators. In the second category, we already mentioned experimental [4,5,7] and theoretical [6] methods to produce or measure specific excitations. It also is possible, in some cases, for the diabatic excitations to resemble an equilibrium thermal state, especially for ferromagnetic systems [14].

Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment

“…The procedure involves optimizing two parameters: the external parameter for the intermediate Hamiltonian and the holding time. In earlier work, the protocol was shown to work better for longer-range interactions [12].…”

Smooth bang-bang shortcuts to adiabaticity for atomic transport in a moving harmonic trap

“…Finally, we should emphasize that the analytical and numerical methods proposed for smooth bang-bang control are useful in the field of quantum control, since the time-optimal bang-bang control are ubiquitous, for instance, in the atom cooling [49][50][51] and ground-state preparation [52,53]. Moreover, our results can be supplemented by machine learning [23,24,59] for the rapid transport with a harmonic trap [43][44][45] and optical lattice [60][61][62] in presence of noise or spinorbit coupling [63], and will be extended to other problems, including the load manipulation by cranes in classical system [64], and Brownian motion in statistical physics as well [65].…”

“…The smoother control input makes the experiments more feasible, and improve the overall performance of STA. Finally, we shall emphasize that our results can be easily extended to other different scenarios [49][50][51][52][53], although the smooth bang-bang control is applied here to atomic transport on a heuristic basis.…”

Quantum Simulation of Non‐Perturbative Cavity QED with Trapped Ions

“…Figure 4 shows the numerically simulated result of such an experiment for the case of ions but otherwise similar parameters as discussed in Section 3.3.1. Since from these simulations we found that a fully adiabatic preparation of the ground state requires a too long time of hundreds of milliseconds, we use a non‐adiabatic bang‐bang scheme, similar to what has been used previously . With this procedure detailed in App.…”