title: Estimation of a general time-dependent Hamiltonian for a single qubit.
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.
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: L E
authors.initials: LE
authors.lastname: de Clercq
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: R
authors.initials: R
authors.lastname: Oswald
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: C
authors.initials: C
authors.lastname: Flühmann
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: B
authors.initials: B
authors.lastname: Keitch
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: D
authors.initials: D
authors.lastname: Kienzler
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: H-Y
authors.initials: HY
authors.lastname: Lo
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: M
authors.initials: M
authors.lastname: Marinelli
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: D
authors.identifier: http://orcid.org/0000-0003-0219-274X
authors.initials: D
authors.lastname: Nadlinger
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: V
authors.initials: V
authors.lastname: Negnevitsky
authors.affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.
authors.forename: J P
authors.initials: JP
authors.lastname: Home