M. A. Martin-Delgado

Information and computation: Classical and quantum aspects

Quantum theory has found a new field of application in the realm of information and computation during recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some notable aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as examples of the impact of quanta on the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement made possible in information processing by a quantum computer. Finally the authors provide some examples of current experimental realizations for quantum computers and future prospects.

Topological quantum distillation.

We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits. This allows us to extend their application also to quantum teleportation, dense coding, and computation with magic states.

Diverging entanglement length in gapped quantum spin systems

We prove the existence of gapped quantum Hamiltonians whose ground states exhibit an infinite entanglement length, as opposed to their finite correlation length. Using the concept of entanglement swapping, the localizable entanglement is calculated exactly for valence bond and finitely correlated states, and the existence of the so-called string-order parameter is discussed. We also report on evidence that the ground state of an antiferromagnetic chain can be used as a perfect quantum channel if local measurements on the individual spins can be implemented.

Realistic time-reversal invariant topological insulators with neutral atoms.

We lay out an experiment to realize time-reversal invariant topological insulators in alkali atomic gases. We introduce an original method to synthesize a gauge field in the near field of an atom chip, which effectively mimics the effects of spin-orbit coupling and produces quantum spin-Hall states. We also propose a feasible scheme to engineer sharp boundaries where the hallmark edge states are localized. Our multiband system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Because of their remarkable versatility, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.

Quantum computations on a topologically encoded qubit

Fault-tolerant quantum computing Quantum states can be delicate. Attempts to process and manipulate quantum states can destroy the encoded information. Nigg et al. encoded the quantum state of a single qubit (in this case, a trapped ion) over the global properties of a series of trapped ions. These so-called stabilizers protected the information against noise sources that can degrade the single qubit. The protocol provides a route to fault-tolerant quantum computing. Science, this issue p. 302 A protocol is implemented that allows for fault-tolerant quantum computing. The construction of a quantum computer remains a fundamental scientific and technological challenge because of the influence of unavoidable noise. Quantum states and operations can be protected from errors through the use of protocols for quantum computing with faulty components. We present a quantum error-correcting code in which one qubit is encoded in entangled states distributed over seven trapped-ion qubits. The code can detect one bit flip error, one phase flip error, or a combined error of both, regardless on which of the qubits they occur. We applied sequences of gate operations on the encoded qubit to explore its computational capabilities. This seven-qubit code represents a fully functional instance of a topologically encoded qubit, or color code, and opens a route toward fault-tolerant quantum computing.

Implementation of spin Hamiltonians in optical lattices.

We propose an optical lattice setup to investigate spin chains and ladders. Electric and magnetic fields allow us to vary at will the coupling constants, producing a variety of quantum phases including the Haldane phase, critical phases, quantum dimers, etc. Numerical simulations are presented showing how ground states can be prepared adiabatically. We also propose ways to measure a number of observables, like energy gap, staggered magnetization, end-chain spins effects, spin correlations, and the string-order parameter.

Wave-number spectra and intermittency in the terrestrial foreshock region

We study entanglement distillability of bipartite mixed spin states under Wigner rotations induced by Lorentz transformations. We define weak and strong criteria for relativistic isoentangled and isodistillable states to characterize relative and invariant behavior of entanglement and distillability. We exemplify these criteria in the context of Werner states, where fully analytical methods can be achieved and all relevant cases presented.

EQUIVALENCE OF THE VARIATIONAL MATRIX PRODUCT METHOD AND THE DENSITY MATRIX RENORMALIZATION GROUP APPLIED TO SPIN CHAINS

We study the relationship between the Density Matrix Renormalization Group (DMRG) and the variational matrix product method (MPM). In the latter method one can also define a density matrix whose eigenvalues turn out to be numerically close to those of the DMRG. We illustrate our ideas with the spin-1 Heisenberg chain, where we compute the ground-state energy and the spin correlation length. We also give a rotational invariant formulation of the MPM.

Exact mapping of the 2+1 Dirac oscillator onto the Jaynes-Cummings model: Ion-trap experimental proposal

We study the dynamics of the

Wilson fermions and axion electrodynamics in optical lattices.

2+1