Southwest Quantum Information and Technology

Eleventh Annual Meeting, February 19-22, 2009
Seattle, Washington

Full Program | Thursday | Friday | Saturday | Sunday

SESSION 11: Quantum Algorithms
Session Chair:
8:30-9:15	Andrew Childs, University of Waterloo (invited)
	The relationship between continuous- and discrete-time quantum walk
	Abstract. Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. However, whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this talk, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. This provides a description of continuous-time quantum walk as a certain limit of discrete-time quantum walks, and also leads to improved methods for simulating Hamiltonian dynamics. In particular, there is a simulation whose complexity grows linearly with the total evolution time and that does not necessarily require the Hamiltonian to be sparse.
9:15-9:45	Alan Aspuru-Guzik, Harvard University
	The Role of Coherence in Photosynthetic Energy Transfer
	Abstract. Recently, direct evidence of long-lived coherence has been experimentally demonstrated for the dynamics of the Fenna-Matthews-Olson (FMO) protein complex at 77K [Engel et al., Nature 446, 782 (2007)]. It was suggested that quantum coherence was important for exploring many relaxation pathways simultaneously. I will talk about our recent work in developing methods for exploring that question and analyzing the different contributions of the different processes to the efficiency of energy transfer in the complex. We generalized the concept of continuous-time quantum walks to a Liouville space formalism. This helped us analyze these contributions and report that at room temperature, this complex has contribution of coherent dynamics of about 10%. Relaxation processes are responsible for 80% of the efficiency. The quantum transport efficiency can actually be enhanced by the dynamical interplay of the system Hamiltonian with the pure dephasing dynamics induced by a fluctuating environment. This occurs in an intermediate regime between fully coherent hopping and highly incoherent transport. I will finalize with a short discussion of this environment-assisted quantum transport regime.
9:45-10:15	Robert Koenig, California Institute of Technology
	Simplifying quantum double Hamitonians using perturbative gadgets
	Abstract. Perturbative gadgets were originally introduced to generate effective k-local interactions in the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgets which are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonic excitations. At the core of our construction is a perturbative analysis of a widely used hopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian can be approximated by a certain ordered product of operators. In particular, this provides a simplified realization of Kitaev's quantum double Hamiltonians.