Experimental simulation and limitations of quantum walks with trapped ions

Abstract

We examine the prospects of discrete quantum walks (QWs) with trapped ions. In particular, we analyze in detail the limitations of the protocol of Travaglione and Milburn (2002 Phys. Rev. A 65 032310) that has been implemented by several experimental groups in recent years. Based on the first realization in our group (Schmitz et al 2009 Phys. Rev. Lett. 103 090504), we investigate the consequences of leaving the scope of the approximations originally made, such as the Lamb-Dicke approximation. We explain the consequential deviations from the idealized QW for different experimental realizations and an increasing number of steps by taking into account higherorder terms of the quantum evolution. It turns out that these already become significant after a few steps, which is confirmed by experimental results and is currently limiting the scalability of this approach. Finally, we propose a new scheme using short laser pulses, derived from a protocol from the field of quantum computation. We show that this scheme is not subject to the abovementioned restrictions and analytically and numerically evaluate its limitations, based on a realistic implementation with our specific setup. Implementing

Experimental quantum simulations of many-body physics with trapped ions

“…The types of qubits can be divided into two classes: in optical qubits, the states are encoded in two states with a dipole-forbidden transition at an optical frequency. An example is 40 Ca + with |↓ := |S 1/2 and |↑ := |D 5/2 . The lifetime of |↑ is on the order of 1 s, which defines the upper bound for its coherence time.…”

“…Examples for the first category are emanating from the fields of cosmology [26][27][28], relativistic dynamics [29][30][31][32][33][34], quantum field theory [35], quantum optics [36] including quantum walks as a potential tool for QSs [15,[37][38][39][40], chemistry [41], and biology [42,43]. For the second category, quantum spin Hamiltonians [21], Bose-Hubbard [22] and spin-boson [44] models were proposed to describe solid-state systems and their simulation would allow the observation and investigation of a rich variety of QPTs [45].…”

Control of the conformations of ion Coulomb crystals in a Penning trap

“…Many further proposals have been made for the use of ICCs in direct quantum simulation of a wide variety of physical systems and processes, from quantum spin systems7 to Hawking radiation8. A few such ideas have been implemented experimentally, including the simulation of a quantum magnet9 and simulations of quantum walks10. Of particular interest to the work presented here is a body of theoretical work that considers quantum mechanical aspects of linear-to-zigzag transitions in ion chains11.…”

Implementation of multidimensional quantum walks using linear optics and classical light

“…Despite all these advantages, so far, only one-dimensional quantum walks have been implemented [21,[23][24][25][26][27][28]. There have been a few attempts to realize two-dimensional quantum walks experimentally [22].…”