Abstract
In a recent experiment, Barreiro et al (2011 Nature 470 486) demonstrated the fundamental building blocks of an open-system quantum simulator with trapped ions. Using up to five ions, dynamics were realized by sequences that combined single- and multi-qubit entangling gate operations with optical pumping. This enabled the implementation of both coherent many-body dynamics and 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 this 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.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. The development of quantum simulators offers the opportunity to simulate the dynamics of interacting many-particle quantum systems, which are inherently difficult to treat on classical computers. Ultimately, such a device would allow one to simulate both the coherent, complex Hamiltonian dynamics of the system as well as the dissipative processes, which result from the coupling of the many-body system to its environment. Today, trapped ions are one of the most promising candidate systems for a physical realization of a general-purpose quantum simulator. In a recent experiment with up to five ions, Barreiro et al demonstrated the elementary building blocks of such an open-system quantum simulator (2011 Nature 470 486). In particular, they employed a so-called 'digital' simulation technique, which is based on the sequential application of coherent gates and dissipative steps via optical pumping.
Main results. In this paper, we present the theoretical framework of this gate-based simulation approach and provide a general toolbox for the simulation of coherent and dissipative n-particle dynamics. In addition, we show that the developed techniques are particularly suited to simulating small instances of complex spin models, which are of interest in the field of topological quantum computing.
Wider implications. The possibility of simulating coherent Hamiltonian time evolution in combination with dissipative dynamics allows one to explore novel physics such as non-equilibrium phase transitions in driven dissipative many-body systems. This work also opens up perspectives on the realization of a recently suggested new paradigm of quantum computation, which is solely based on controlled dissipation.