Estimation of a general time-dependent Hamiltonian for a single qubit

L. E. de Clercq, R. Oswald, C. Flühmann, B. Keitch, D. Kienzler, H. -Y. Lo, M. Marinelli, D. Nadlinger, V. Negnevitsky and J. P. Home ()
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L. E. de Clercq: Institute for Quantum Electronics, ETH Zürich
R. Oswald: Institute for Quantum Electronics, ETH Zürich
C. Flühmann: Institute for Quantum Electronics, ETH Zürich
B. Keitch: Institute for Quantum Electronics, ETH Zürich
D. Kienzler: Institute for Quantum Electronics, ETH Zürich
H. -Y. Lo: Institute for Quantum Electronics, ETH Zürich
M. Marinelli: Institute for Quantum Electronics, ETH Zürich
D. Nadlinger: Institute for Quantum Electronics, ETH Zürich
V. Negnevitsky: Institute for Quantum Electronics, ETH Zürich
J. P. Home: Institute for Quantum Electronics, ETH Zürich

Nature Communications, 2016, vol. 7, issue 1, 1-8

Abstract: Abstract The Hamiltonian of a closed quantum system governs its complete time evolution. While Hamiltonians with time-variation in a single basis can be recovered using a variety of methods, for more general Hamiltonians the presence of non-commuting terms complicates the reconstruction. Here using a single trapped ion, we propose and experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. We measure the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. The initially unknown Hamiltonian arises from transporting an ion through a static laser beam. Hamiltonian estimation allows us to estimate the spatial beam intensity profile and the ion velocity as a function of time. The estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high-operational fidelities in quantum control.

Date: 2016
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DOI: 10.1038/ncomms11218

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