Disordered Complex Systems Using Cold Gases and Trapped Ions (original) (raw)

Quantum-information processing in disordered and complex quantum systems

Physical Review A, 2006

We investigate quantum information processing and manipulations in disordered systems of ultracold atoms and trapped ions. First, we demonstrate generation of entanglement and local realization of quantum gates in a quantum spin glass system. Entanglement in such systems attains significantly high values, after quenched averaging, and has a stable positive value for arbitrary times. Complex systems with long range interactions, such as ion chains or dipolar atomic gases, can be modeled by neural network Hamiltonians. In such systems, we find the characteristic time of persistence of quenched averaged entanglement, and also find the time of its revival.

Cold trapped ions as quantum information processors

Journal of Modern Optics, 2002

In this tutorial we review physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multi-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on off-resonant transitions associated with a qualitative estimation of the weak coupling regime and of the Lamb-Dicke regime is included in Appendix.

Tutorial review Cold trapped ions as quantum information processors

In this tutorial we review the physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and con®ning of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travellingwave and standing-wave con®guration for dipole and quadrupole transitions. We review di erent types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb± Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multiple-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on o -resonance transitions associated with a qualitative estimation of the weak-coupling regime is included in Appendix A and of the Lamb±Dicke regime in Appendix B.

Quantum simulations with cold trapped ions

Journal of Physics B: Atomic, Molecular and Optical Physics, 2009

The control of internal and motional quantum degrees of freedom of laser cooled trapped ions has been subject to intense theoretical and experimental research for about three decades. In the realm of quantum information science the ability to deterministically prepare and measure quantum states of trapped ions is unprecedented. This expertise may be employed to investigate physical models conceived to describe systems that are not directly accessible for experimental investigations. Here, we give an overview of current theoretical proposals and experiments for such quantum simulations with trapped ions. This includes various spin models (e.g., the quantum transverse Ising model, or a neural network), the Bose-Hubbard Hamiltonian, the Frenkel-Kontorova model, and quantum fields and relativistic effects.

A quantum information processor with trapped ions

New Journal of Physics, 2013

Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40 Ca + ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm.

Trapped Ion Chain as a Neural Network: Error Resistant Quantum Computation

Physical Review Letters, 2007

We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit one to store information distributed over the whole system. The storage capacity of such a network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. We analyze the implementation of error resistant universal quantum information processing in such systems.

Quantum information processing with trapped ions

2003

Experiments directed towards the development of a quantum computer based on trapped atomic ions are described briefly. We discuss the implementation of single qubit operations and gates between qubits. A geometric phase gate between two ion qubits is described. Limitations of the trapped-ion method such as those caused by Stark shifts and spontaneous emission are addressed. Finally, we describe a strategy to realize a large-scale device.

Cold Atomic Gases in Optical Lattices with Disorder

2007

Cold atomic gases placed in optical lattices enable studies of simple condensed matter theory models with parameters that may be tuned relatively easily. When the optical potential is randomized (e.g. using laser speckle to create a random intensity distribution) one may be able to observe Anderson localization of matter waves for non-interacting bosons, the so-called Bose glass in the presence of interactions, as well as the Fermi glass or quantum spin glass for mixtures of fermions and bosons.

Trapped Ion Quantum Computing and the Principles of Logic

An experimental realization of quantum computers is composed of two or more calcium ions trapped in a magnetic quadripole. Information is transferred to and read from the ions by means of structured lasers that interact with the ions' vibration pattern, causing changes of energy distribution in their electronic structure. Departing from an initial state when the ions are cooled, the use of lasers modifies the internal state of one ion that is entangled with the others, then changing the collective states. In such quantum computers, some of the physically possible electronic states are avoided or not taken into consideration, to force the system to work as a binary device. In this essay, we discuss the dynamics that the ions could spontaneously display and its possible implications for the principles of computational logics.

Quantum simulation of frustrated Ising spins with trapped ions

Nature, 2010

A network is frustrated when competing interactions between nodes prevent each bond from being satisfied. This compromise is central to the behaviour of many complex systems, from social 1 and neural 2 networks to protein folding 3 and magnetism 4,5 . Frustrated networks have highly degenerate ground states, with excess entropy and disorder even at zero temperature. In the case of quantum networks, frustration can lead to massively entangled ground states, underpinning exotic materials such as quantum spin liquids and spin glasses 6-9 . Here we realize a quantum simulation of frustrated Ising spins in a system of three trapped atomic ions 10-12 , whose interactions are precisely controlled using optical forces 13 . We study the ground state of this system as it adiabatically evolves from a transverse polarized state, and observe that frustration induces extra degeneracy. We also measure the entanglement in the system, finding a link between frustration and ground-state entanglement. This experimental system can be scaled to simulate larger numbers of spins, the ground states of which (for frustrated interactions) cannot be simulated on a classical computer.