K. Birgitta Whaley

Quantum random-walk search algorithm

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speedup over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random-walk architecture that provides such a speedup. It will be shown that this algorithm performs an oracle search on a database of N items with

Quantum entanglement in photosynthetic light-harvesting complexes

O(\sqrt{N})

Quantum solvation and molecular rotations in superfluid helium clusters

calls to the oracle, yielding a speedup similar to other quantum search algorithms. It appears that the quantum random-walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms.

Decoherence-Free Subspaces and Subsystems

Recently, coherent quantum beating has been observed in photosynthetic complexes. Theoretical work now shows how quantum correlations in biological systems can be quantified, and establishes that quantum entanglement exists in light-harvesting complexes, even at physiological temperatures.

Geometric theory of nonlocal two-qubit operations

Spectroscopic experiments on molecules embedded in free clusters of liquid helium reveal a number of unusual features deriving from the unique quantum behavior of this nanoscale matrix environment. The apparent free rotation of small molecules in bosonic 4He clusters is one of the experimentally most well documented of these features. In this Focus article, we set this phenomenon in the context of experimental and theoretical advances in this field over the last ten years, and describe the microscopic insight which it has provided into the nature and dynamic consequences of quantum solvation in a superfluid. We provide a comprehensive theoretical analysis which is based on a unification of conclusions drawn from diffusion and path integral Monte Carlo calculations. These microscopic quantum calculations elucidate the origin of the empirical free rotor spectrum, and its relation to the boson character and superfluid nature of the quantum nanosolvent. The free rotor behavior of the molecular rotation is pre...

Superfluid Helium Droplets: An Ultracold Nanolaboratory

Decoherence is the phenomenon of non-unitary dynamics that arises as a consequence of coupling between a system and its environment. It has important harmful implications for quantum information processing, and various solutions to the problem have been proposed. Here we provide a detailed a review of the theory of decoherence-free subspaces and subsystems, focusing on their usefulness for preservation of quantum information.

Structure and dynamics of quantum clusters

We study nonlocal two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of nonlocal gates is a 3-torus. We derive the invariants for local transformations, and connect these local invariants to the coordinates of the 3-torus. Since different points on the 3-torus may correspond to the same local equivalence class, we use the Weyl group theory to reduce the symmetry. We show that the local equivalence classes of two-qubit gates are in one-to-one correspondence with the points in a tetrahedron except on the base. We then study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some initially separable states. We provide criteria to determine whether a given two-qubit gate is a perfect entangler and establish a geometric description of perfect entanglers by making use of the tetrahedral representation of nonlocal gates. We find that exactly half the nonlocal gates are perfect entanglers. We also investigate the nonlocal operations generated by a given Hamiltonian. We first study the gates that can be directly generated by a Hamiltonian. Then we explicitly construct a quantum circuit that contains at most three nonlocal gates generated by a two-body interaction Hamiltonian, together with at most four local gates generated by single-qubit terms. We prove that such a quantum circuit can simulate any arbitrary two-qubit gate exactly, and hence it provides an efficient implementation of universal quantum computation and simulation.

Limits of quantum speedup in photosynthetic light harvesting

The unique environment in liquid helium droplets opens up new opportunities for molecular spectroscopy and for probing superfluid phenomena on the atomic scale.

Using coherence to enhance function in chemical and biophysical systems

Abstract Quantum clusters are van der Waals aggregates of light atomic and molecular species whose behaviour is dominated by quantum delocalization and exchange effects. We summarize here recent theoretical and experimental studies of helium and molecular hydrogen clusters, focusing primarily on techniques developed to address the quantum nature of these systems. Indicators of superfluid behaviour are discussed, as well as the use of molecular probe species to study structural and dynamical properties.

Path integral Monte Carlo study of SF6-doped helium clusters

It has been suggested that excitation transport in photosynthetic light-harvesting complexes features speedups analogous to those found in quantum algorithms. Here we compare the dynamics in these light-harvesting systems to the dynamics of quantum walks, in order to elucidate the limits of such quantum speedups. For the Fenna–Matthews–Olson complex of green sulfur bacteria, we show that while there is indeed speedup at short times, this is short lived (70 fs) despite longer-lived (ps) quantum coherence. Remarkably, this timescale is independent of the details of the decoherence model. More generally, we show that the distinguishing features of light-harvesting complexes not only limit the extent of quantum speedup but also reduce the rates of diffusive transport. These results suggest that quantum coherent effects in biological systems are optimized for efficiency or robustness rather than the more elusive goal of quantum speedup.