Southwest Quantum Information and Technology

Fourteenth Annual Meeting, February 16-19, 2012
Albuquerque, New Mexico


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SESSION 9: Quantum Measurement - Alvarado "D"
Session Chair:
11:30am-12:00pmAdam Meier, National Institute of Standards and Technology
Randomized Benchmarking of Multiple Qubits

Abstract. Randomized benchmarking is a procedure that extracts a "typical" error probability for an experimental quantum computer. This number describes the failure rate of a typical operation in the middle of a long computation and is a worthwhile figure of merit for quantum control demonstrations. I will present a practical, systematic approach to randomized benchmarking of multiple qubits using a recent two-qubit ion trap experiment at NIST as an example. I will also discuss the ways the basic procedure has been extended to reveal information about individual gates.
12:00pm-12:30pmAlexandre Tacla, University of New Mexico
Entanglement-based perturbation theory for highly anisotropic Bose-Einstein condensates

Abstract. We investigate the emergence of three-dimensional behavior in a reduced-dimension Bose-Einstein condensate trapped by a highly anisotropic potential. We handle the problem analytically by performing a perturbative Schmidt decomposition of the condensate wave function between the tightly confined direction(s) and the loosely confined direction(s). The perturbation theory is valid when the nonlinear scattering energy is small compared to the transverse energy scales. Our approach provides a straightforward way, first, to derive corrections to the transverse and longitudinal wave functions of the reduced-dimension approximation and, second, to calculate the amount of entanglement that arises between the transverse and longitudinal spatial directions. Numerical integration of the three-dimensional Gross-Pitaevskii equation for different cigar-shaped potentials and experimentally accessible parameters reveals good agreement with our analytical model even for relatively high nonlinearities. In particular, we show that even for such stronger nonlinearities the entanglement remains remarkably small, which allows the condensate to be well described by a product wave function that corresponds to a single Schmidt term.