Southwest Quantum Information and Technology

Sixteenth Annual Meeting, February 20-22, 2014
Santa Fe, New Mexico

Full Program | Thursday | Friday | Saturday | All Sessions

10:45am - 11:30am	Richard Cleve, University of Waterloo (invited)
	Simulating Hamiltonian evolution on a quantum computer
	Abstract. I will explain various quantum algorithms that have been proposed for simulating the evolution of a quantum state under a Hamiltonian, including my recent joint work (with Dominic Berry, Andrew Childs, Robin Kothari, and Rolando Somma) that dramatically improves the running time as a function of the precision of the output data.
SESSION 2: Quantum Algorithms
11:30am - 12:00pm	Rolando Somma, Los Alamos National Laboratory
	A quantum fractional Fourier transform
	Abstract. The Fourier transform (FT) is ubiquitous in signal processing, as it can be used to filter noise. The digital version, often named the discrete Fourier transform, when formulated on a basis of quantum states, is the quantum Fourier transform (QFT). The efficiency in the implementation of the QFT is the main reason for several quantum speedups, including the one for factoring and the one in phase estimation at the Heisenberg limit. The fractional FT (frFT) is a generalization of the FT. The frFT has recently gained attention in signal analysis as it can filter noise in scenarios where the FT is not useful. Quantum frFTs (QfrFTs), however, have never been analyzed or applied; We propose a QfrFT and show that a good approximation of this transformation can be implemented on a quantum computer with exponentially less resources than those required for its conventional implementation. We then analyze some problems in signal analysis (parameter estimation) for which our defined QfrFT is useful. Applications of the QfrFT for the simulation of continuous-variable quantum mechanics will also be considered.