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arXiv:quant-ph/0507172 · Physical Review A

Quantum-information processing in disordered and complex quantum systems

Aditi Sen, Ujjwal Sen, V. Ahufinger, Hans J. Briegel, Anna Sanpera, Maciej Lewenstein

Published Dec 18, 2006• 10 citations
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Abstract

We study quantum information processing in complex disordered many body systems that can be implemented by using lattices of ultracold atomic gases and trapped ions. We demonstrate, first in the short range case, the generation of entanglement and the local realization of quantum gates in a disordered magnetic model describing a quantum spin glass. We show that in this case it is possible to achieve fidelities of quantum gates higher than in the classical case. Complex systems with long range interactions, such as ions chains or dipolar atomic gases, can be used to model neural network Hamiltonians. For such systems, where both long range interactions and disorder appear, it is possible to generate long range bipartite entanglement. We provide an efficient analytical method to calculate the time evolution of a given initial state, which in turn allows us to calculate its quantum correlations.

DOI
10.1103/physreva.74.062309

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We study quantum information processing in complex disordered many body systems that can be implemented by using lattices of ultracold atomic gases and trapped ions. We demonstrate, first in the short range case, the generation of entanglement and the local realization of quantum gates in a disordered magnetic model describing a quantum spin glass. We show that in this case it is possible to achieve fidelities of quantum gates higher than in the classical case. Complex systems with long range interactions, such as ions chains or dipolar atomic gases, can be used to model neural network Hamiltonians. For such systems, where both long range interactions and disorder appear, it is possible to generate long range bipartite entanglement. We provide an efficient analytical method to calculate the time evolution of a given initial state, which in turn allows us to calculate its quantum correlations.
We report our research on disordered complex systems using cold gases and trapped ions, and address the possibility of using complex systems for quantum information processing. Two simple paradigmatic models of disordered complex systems are revisited here. The first one corresponds to a short range disordered Ising Hamiltonian (spin glasses), which can be implemented with a Bose-Fermi (Bose-Bose) mixture in a disordered optical lattice. The second model we address here is a long range disordered Hamiltonian, characteristic of neural networks (Hopfield model), which can be implemented in a chain of trapped ions with appropriately designed interactions.
Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information.In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations.In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t = 0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Foss-Feig et al (2013 Phys.Rev. A 87 042101).Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g.Bloch vector and spin-squeezing dynamics.In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence 5
In this thesis we address relevant problems of the physics of quantum disordered systems from a numerical and theoretical point of view, with specific attention to the connection of our findings with ultracold atomic gases experiments. We concentrate on two main issues: the interplay between localization and interaction in disordered systems and the problem of localization in correlated random potentials. The first problem is investigated considering the expansion of a weakly interacting Bose gas in a bichromtic optical lattice. We observe that interaction has a destructive effect on the disorder-induced localization and leads to a subdiffusive expansion of the atomic gas. By comparing three characteristic energy scales of the system one can identify three different spreading regimes: weak chaos, strong chaos and self-trapping. The spreading behaviour in these regimes is predicted theoretically and verified numerically. We also interpreted existing experimental data on the basis of our findings and showed that there is a qualitative agreement between our numerical simulations and experiments. The second problem is investigated proposing a new model of correlated disorder that can be implemented experimentally using ultracold dipolar gases. We show that this model is characterized by the presence of both short and long range correlations. We study the localization properties of the model and highlight the role played by short and long range correlations in the determination of those properties. In particular we show that when short-range correlations are dominant, extended states can appear in the spectrum. The effect of long-range correlations is instead to restore localization over the whole spectrum and lead to counterintuitive behaviours of the localization length. More precisely, depending on the localization regime they can enhance or reduce the localization length at the centre of the band.
Disorder is ubiquitous in condensed matter systems, but a thorough understanding of these systems is hindered by poor control over the nature of disorder and competing interactions. Ultracold gases trapped in optical lattices, on the other hand, offer an unprecedented level of control over interactions and disorder, and are ideal candidates to test theoretical predictions and study fascinating phenomena resulting from the interplay between disorder, interaction, and quantum degeneracy. In this dissertation, I present my research on strongly correlated many-body lattice bosons in the presence of disordered potentials. My results are based on quantum Monte Carlo simulations by the Worm algorithm. Experimentally, lattice bosons can be realized by ultracold gases in optical lattices. I studied the ground state phase diagram of the above systems in the presence of diagonal (quasi-periodic disordered potential or random disordered potential) and off-diagonal disorder (in the form of site dilution). First, I will discuss the ground state phase diagram of two-dimensional bosons in quasi-periodic lattices. Then, I will discuss the phase diagram as well as finite temperature thermodynamic properties of two-dimensional dipolar lattice bosons in the presence of random diagonal disordered potentials. Finally, I will discuss the phase diagram of two-dimensional hard-core lattice bosons system in the presence of long-range hopping and long-range two-body interactions both in the absence of disorder and in the presence of site dilution (equivalent to off-diagonal disorder). This system is equivalent to the long-range XXZ model as realized by polar molecules trapped in a deep optical lattice. These results provide theoretical guidance for experimentalists to find quantum phase transitions as well as exotic quantum phases in strongly correlated bosonic lattice systems.
Quantum technology with atomic, molecular and optical systems has advanced to a stage that single particles can be manipulated precisely so that quantum information processing is no longer elusive. In fact, a great number of quantum information protocols have been demonstrated with small scaled systems. The remaining task is to build large scale practical devices. However it turns out that scaling up is highly nontrivial in the quantum world. A protocol valid in principle could face enormous technical challenges when the system size is increased. Therefore new ideas and smart designs that bypass the technical obstacles are extremely useful in this field. In this dissertation we tackle several specific problems in quantum information processing with trapped ions and cold atomics gases. For ions, we first present a scalable implementation scheme for the recently proposed concept of Boson sampling, which holds the promise of outperforming classical computers in the near future. The scheme is based on the technically mature linear Paul trap and the transverse motional phonons of the ions are manipulated with laser to perform sampling. A complete recipe is provided and the technical requirements are discussed. Then we go back to the conventional circuit model for computation and discuss a method to perform individual ion addressing quantum gates with Gaussian beams. We describe the so-called spatial refocusing technique to significantly narrow down the beams with coherent interference. We also extend the original quantum gate formalism to include the effect of micromotion. We demonstrate high fidelity gates in the presence of significant micromotion. This paves the way to the development of a two dimensional ion crystal quantum processor with hundreds of ions inside a single trap. On the other hand, we explore precision measurement with a cold atom interferometer. Combining a spin-spin interaction Hamiltonian and coherent spin rotation pulses, we construct optimized pulse sequences for spin squeezing to approach the Heisenberg limit of noise. Finally we investigate the general problem of state detection with faulty detectors. We develop a statistical procedure to recover the true correlation from noisy data.