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Fortschritte der Physik

Ensemble quantum computation and algorithmic cooling in optical lattices

M. Popp, K. G. H. Vollbrecht, J. I. Cirac

Published Aug 1, 2006• 4 citations
Publisher

Abstract

Abstract We show how to perform universal quantum computation with atoms confined in optical lattices which works both in the presence of defects and without individual addressing. We further present a scheme for cooling atoms close to the ground state of the Mott‐insulator regime. This method is based on a similar set of operations as for ensemble quantum computation and aims at cooling to temperatures which are low enough for the experimental realization of quantum simulation in present setups.

DOI
10.1002/prop.200610316

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Abstract We show how to perform universal quantum computation with atoms confined in optical lattices which works both in the presence of defects and without individual addressing. We further present a scheme for cooling atoms close to the ground state of the Mott‐insulator regime. This method is based on a similar set of operations as for ensemble quantum computation and aims at cooling to temperatures which are low enough for the experimental realization of quantum simulation in present setups.
We propose and analyse several schemes for cooling bosonic and fermionic atoms in an optical lattice potential close to the ground state of the no-tunnelling regime. Some of the protocols rely on the concept of algorithmic cooling, which combines occupation number filtering with ideas from ensemble quantum computation. We also design algorithms that create an ensemble of defect-free quantum registers. We study the efficiency of our protocols for realistic temperatures and in the presence of a harmonic confinement. We also propose an incoherent physical implementation of filtering which can be operated in a continuous way.
Scalable, coherent many-body systems can enable the realization of previously unexplored quantum phases and have the potential to exponentially speed up information processing. Thermal fluctuations are negligible and quantum effects govern the behavior of such systems with extremely low temperature. We report the cooling of a quantum simulator with 10,000 atoms and mass production of high-fidelity entangled pairs. In a two-dimensional plane, we cool Mott insulator samples by immersing them into removable superfluid reservoirs, achieving an entropy per particle of [Formula: see text] The atoms are then rearranged into a two-dimensional lattice free of defects. We further demonstrate a two-qubit gate with a fidelity of 0.993 ± 0.001 for entangling 1250 atom pairs. Our results offer a setting for exploring low-energy many-body phases and may enable the creation of large-scale entanglement.
Quantum computer that is composed of Mott insulator atoms trapped in an optical lattice and a control atom(s) that moves with an independent optical lattice is discussed. A three-dimensional array of Mott insulator atoms functions as memory qubits. The control atom that moves with the second lattice mediates one and two qubit operations among memory qubits with the help of resonant optical beams. Explicit examples of general quantum computational operations are described. In this system all memory qubits are equivalent, and the system is scalable. It is also not necessary to address individual memory qubits by optical means.
A scheme for globally addressing a quantum computer is presented along with its realization in an optical lattice set-up of one, two or three dimensions. The required resources are mainly those necessary for performing quantum simulations of spin systems with optical lattices, circumventing the necessity for single qubit addressing. We present the control procedures, in terms of laser manipulations, required to realize universal quantum computation. Error avoidance with the help of the quantum Zeno effect is presented and a scheme for globally addressed error correction is given. The latter does not require measurements during the computation, facilitating its experimental implementation. As an illustrative example, the pulse sequence for the factorization of the number 15 is given.
Cold atoms in optical lattices offer an exciting new laboratory where quantum many-body phenomena can be realized in a highly controlled way. They can even serve as quantum simulators for notoriously difficult problems like high-temperature superconductivity. This review is focussed on the recent developments and new results in multi-component systems. Fermionic atoms with SU(N) symmetry have exotic superfluid and flavor-ordered ground states. We discuss symmetry breaking, collective modes, and detection issues, e.g. in Bragg scattering. On the other hand, bosonic multiflavor ensembles allow for engineering of spin Hamiltonians which are interesting from a quantum computation point of view. Finally, we address the role of disorder in optical lattices. Fermionic atoms experience Anderson localization at sufficiently strong disorder. Interactions among the atoms induce a competing tendency towards delocalization. We present a complete phase diagram obtained within dynamical mean-field theory and discuss experimental observability of the Mott and Anderson phases.