Adiabatic quantum simulation with a segmented ion trap: Application to long-distance entanglement in quantum spin systems

Abstract

We investigate theoretically systems of ions in segmented linear Paul traps for the quantum simulation of quantum spin models with tunable interactions. The scheme is entirely general and can be applied to the realization of arbitrary spin-spin interactions. As a specific application we discuss in detail the quantum simulation of models that exhibit long-distance entanglement in the ground state. We show how tailoring of the axial trapping potential allows for generating spin-spin coupling patterns that are suitable to create long-distance entanglement. We discuss how suitable sequences of microwave pulses can implement Trotter expansions and realize various kinds of effective spin-spin interactions. The corresponding Hamiltonians can be varied on adjustable time scales, thereby allowing the controlled adiabatic preparation of their ground states

Probing entanglement in adiabatic quantum optimization with trapped ions

“…For the same reason, few theoretical works have considered a site-dependent tunability of couplings [38,[45][46][47] or fields [48]. In contrast, our purpose of engineering NP-complete problems in Hamiltonian Equation (1) requires a certain degree of programmability of the interaction matrix elements J ij and fields h z i (see e.g., Lucas [16]).…”

“…The main challenge is to encode these problems in H final Equation (1), which requires a certain degree of programmability of interactions J ij and fields h z i . Below, we present several models where a local variation of laser power is sufficient to obtain this programmability-as opposed to a much more difficult programming by, e.g., an extensive number of laser frequencies [35] or specially designed trapping potentials [36][37][38][39]. We also describe how engineered noise can be generated in order to study the interplay between decoherence, non-adiabaticity, and entanglement in the well-controlled architecture provided by trapped ions.…”

Optimal quench for distance-independent entanglement and maximal block entropy

“…Alternatively, spin-spin coupling can be generated by laser-induced forces [23,24,67]. An effective XX Hamiltonian can be implemented either with a large transverse magnetic field [23] or via fast sequential applications of Ising evolution in two orthogonal directions [29]. The main sources of error here are long-range interactions and dephasing.…”

“…Entanglement between extremal spins of a chain is currently a topic of active interest because of its linking power [26][27][28][29][30][31][32][33][34]. However, whether fast (non-adiabatic) dynamics following a "global" quench can produce distance-independent entanglement between extremal spins of a chain is an open question.…”

Simulating the Haldane phase in trapped-ion spins using optical fields

“…To date, trapped ions have mostly been used to simulate spin one-half Hamiltonians, showing the phase transition from the (anti)ferromagnetic to paramagnetic phases in the Ising model [19][20][21][22][23][24][25][26][27][28][29][30] and long range correlation functions in the XX model [31,32]. By enlarging the spin's degree and moving into integer spin chains, new and subtle physics can appear [33][34][35][36][37][38][39][40][41]; for example, the local orders vanish and we are left with hidden orders only [42].…”