Abstract
Controlling the interaction graph between spins or qubits in a quantum simulator allows user-controlled tailoring of native interactions to achieve a target Hamiltonian. Engineering long-ranged phonon-mediated spin–spin interactions in a trapped ion quantum simulator offers such a possibility. Trapped ions, a leading candidate for quantum simulation, are most readily trapped in a linear 1D chain, limiting their utility for readily simulating higher dimensional spin models. In this work, we introduce a hybrid method of analog-digital simulation for simulating 2D spin models which allows for the dynamic changing of interactions to achieve a new graph using a linear 1D chain. We focus this numerical work on engineering 2D rectangular nearest-neighbor spin lattices, demonstrating that the required control parameters scale linearly with ion number. This hybrid approach offers compelling possibilities for the use of 1D chains in the study of Hamiltonian quenches, dynamical phase transitions, and quantum transport in 2D and 3D.
Highlights
Dynamical evolution of interacting quantum many-body systems is often intractable with classical computation
We propose a hybrid quantum simulation that enables the dynamical engineering of a fully connected 1D ion chain to, in principle, an arbitrary 2D lattice
We propose a protocol for time-domain engineering of the interaction graph between trapped ion spins in a quantum simulator
Summary
Dynamical evolution of interacting quantum many-body systems is often intractable with classical computation. Controlled studies are best done in quantum simulators[1,2,3,4] wherein the essential many-body dynamics is manifest but resides in an experimentally manageable configuration. Trapped ions[3] owing to their inherent long-range interactions offer the ability to manipulate individual spin–spin interactions, in principle, arbitrarily.[5] Long-range spin–spin interactions are straightforward to generate in ion trap quantum simulators, and can be controlled in their range, magnitude, and sign.[6,7,8,9,10,11,12,13,14] Leveraging phonon modes to build inter-spin interactions is what makes a trapped ion system fully connected and thereby inherently higher dimensional. The full-connectivity potentially allows the ability to probe a rich variety of physical phenomena, such as quantum transport and localization, topological insulators,[16] the Haldane model,[17] as well as in topological quantum computation following the Kitaev honeycomb model.[18]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
