4 research outputs found
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
Can One Trust Quantum Simulators?
Various fundamental phenomena of strongly-correlated quantum systems such as
high- superconductivity, the fractional quantum-Hall effect, and quark
confinement are still awaiting a universally accepted explanation. The main
obstacle is the computational complexity of solving even the most simplified
theoretical models that are designed to capture the relevant quantum
correlations of the many-body system of interest. In his seminal 1982 paper
[Int. J. Theor. Phys. 21, 467], Richard Feynman suggested that such models
might be solved by "simulation" with a new type of computer whose constituent
parts are effectively governed by a desired quantum many-body dynamics.
Measurements on this engineered machine, now known as a "quantum simulator,"
would reveal some unknown or difficult to compute properties of a model of
interest. We argue that a useful quantum simulator must satisfy four
conditions: relevance, controllability, reliability, and efficiency. We review
the current state of the art of digital and analog quantum simulators. Whereas
so far the majority of the focus, both theoretically and experimentally, has
been on controllability of relevant models, we emphasize here the need for a
careful analysis of reliability and efficiency in the presence of
imperfections. We discuss how disorder and noise can impact these conditions,
and illustrate our concerns with novel numerical simulations of a paradigmatic
example: a disordered quantum spin chain governed by the Ising model in a
transverse magnetic field. We find that disorder can decrease the reliability
of an analog quantum simulator of this model, although large errors in local
observables are introduced only for strong levels of disorder. We conclude that
the answer to the question "Can we trust quantum simulators?" is... to some
extent.Comment: 20 pages. Minor changes with respect to version 2 (some additional
explanations, added references...
Quantum simulation of the transverse Ising model with trapped ions
10.1088/1367-2630/13/10/105003New Journal of Physics13