Simulating open quantum systems: from many-body interactions to stabilizer pumping

In a recent experiment, Barreiro et al. demonstrated the fundamental building blocks of an open-system quantum simulator with trapped ions [Nature 470, 486 (2011)]. Using up to five ions, single- and multi-qubit entangling gate operations were combined with optical pumping in stroboscopic sequences. This enabled the implementation of both coherent many-body dynamics as well as dissipative processes by controlling the coupling of the system to an artificial, suitably tailored environment. This engineering was illustrated by the dissipative preparation of entangled two- and four-qubit states, the simulation of coherent four-body spin interactions and the quantum non-demolition measurement of a multi-qubit stabilizer operator. In the present paper, we present the theoretical framework of this gate-based ("digital") simulation approach for open-system dynamics with trapped ions. In addition, we discuss how within this simulation approach minimal instances of spin models of interest in the context of topological quantum computing and condensed matter physics can be realized in state-of-the-art linear ion-trap quantum computing architectures. We outline concrete simulation schemes for Kitaev's toric code Hamiltonian and a recently suggested color code model. The presented simulation protocols can be adapted to scalable and two-dimensional ion-trap architectures, which are currently under development.Comment: 27 pages, 9 figures, submitted to NJP Focus on Topological Quantum Computatio

The dynamics of quantum vortices in a toroidal trap

The dynamics of quantum vortices in a two-dimensional annular condensate are considered by numerically simulating the Gross-Pitaevskii equation. Families of solitary wave sequences are reported, both without and with a persistent flow, for various values of interaction strength. It is shown that in the toroidal geometry the dispersion curve of solutions is much richer than in the cases of a semi-infinite channel or uniform condensate studied previously. In particular, the toroidal condensate is found to have states of single vortices at the same position and circulation that move with different velocities. The stability of the solitary wave sequences for the annular condensate without a persistent flow are also investigated by numerically evolving the solutions in time. In addition, the interaction of vortex-vortex pairs and vortex-antivortex pairs is considered and it is demonstrated that the collisions are either elastic or inelastic depending on the magnitude of the angular velocity. The similarities and differences between numerically simulating the Gross-Pitaevskii equation and using a point vortex model for these collisions are elucidated.Comment: Submitted to Phys. Rev. A. 18 pages, 22 figure

Identifying and decoupling many-body interactions in spin ensembles in diamond

We simulate the dynamics of varying density quasi-two-dimensional spin ensembles in solid-state systems, focusing on the nitrogen-vacancy centers in diamond. We consider the effects of various control sequences on the averaged dynamics of large ensembles of spins, under a realistic "spin-bath" environment. We reveal that spin locking is efficient for decoupling spins initialized along the driving axis, both from coherent dipolar interactions and from the external spin-bath environment, when the driving is two orders of magnitude stronger than the relevant coupling energies. Since the application of standard pulsed dynamical decoupling sequences leads to strong decoupling from the environment, while other specialized pulse sequences can decouple coherent dipolar interactions, such sequences can be used to identify the dominant interaction type. Moreover, a proper combination of pulsed decoupling sequences could lead to the suppression of both interaction types, allowing additional spin manipulations. Finally, we consider the effect of finite-width pulses on these control protocols and identify improved decoupling efficiency with increased pulse duration, resulting from the interplay of dephasing and coherent dynamics