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

de Clercq LE, Oswald R, Flühmann C, Keitch B, Kienzler D, Lo HY, Marinelli M, Nadlinger D, Negnevitsky V, Home JP - Nat Commun (2016)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.

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.

No MeSH data available.


Parametric bootstrap resampling.Predictions for the effective detuning δ(t) in a, Rabi frequency Ω(t) in b and velocity  in c. Blue and red solid lines show data obtained having the beam centred in zone B and with the beam displaced by a few tens of micron. Dashed lines represent the s.e. on the mean of these estimates obtained using parametric bootstrap resampling, assuming quantum projection noise. This can be compared with the error bounds obtained from the non-parametric method, which are shown in Fig. 3 in the main text. The bounds are tighter for the parametric bootstrapping.
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f7: Parametric bootstrap resampling.Predictions for the effective detuning δ(t) in a, Rabi frequency Ω(t) in b and velocity in c. Blue and red solid lines show data obtained having the beam centred in zone B and with the beam displaced by a few tens of micron. Dashed lines represent the s.e. on the mean of these estimates obtained using parametric bootstrap resampling, assuming quantum projection noise. This can be compared with the error bounds obtained from the non-parametric method, which are shown in Fig. 3 in the main text. The bounds are tighter for the parametric bootstrapping.

Mentions: We have also applied parametric bootstrapping to obtain the error bounds shown in Fig. 7. The difference to the non-parametric case is that in point (2) the samples are created using the solutions obtained from (1) and adding quantum projection noise. For each sample the Hamiltonian is estimated. The estimates from multiple samples are used to construct error bounds in the same manner as for the non-parametric resampling. We have found that the error bounds obtained from parametric bootstrapping are lower compared with that of the non-parametric case as shown in Fig. 3. We think this is due to the latter exploring deviations around a single minimum in the optimization landscape, while the case resampling arrives at different local minima, which are spread over a wider region.


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

de Clercq LE, Oswald R, Flühmann C, Keitch B, Kienzler D, Lo HY, Marinelli M, Nadlinger D, Negnevitsky V, Home JP - Nat Commun (2016)

Parametric bootstrap resampling.Predictions for the effective detuning δ(t) in a, Rabi frequency Ω(t) in b and velocity  in c. Blue and red solid lines show data obtained having the beam centred in zone B and with the beam displaced by a few tens of micron. Dashed lines represent the s.e. on the mean of these estimates obtained using parametric bootstrap resampling, assuming quantum projection noise. This can be compared with the error bounds obtained from the non-parametric method, which are shown in Fig. 3 in the main text. The bounds are tighter for the parametric bootstrapping.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4834628&req=5

f7: Parametric bootstrap resampling.Predictions for the effective detuning δ(t) in a, Rabi frequency Ω(t) in b and velocity in c. Blue and red solid lines show data obtained having the beam centred in zone B and with the beam displaced by a few tens of micron. Dashed lines represent the s.e. on the mean of these estimates obtained using parametric bootstrap resampling, assuming quantum projection noise. This can be compared with the error bounds obtained from the non-parametric method, which are shown in Fig. 3 in the main text. The bounds are tighter for the parametric bootstrapping.
Mentions: We have also applied parametric bootstrapping to obtain the error bounds shown in Fig. 7. The difference to the non-parametric case is that in point (2) the samples are created using the solutions obtained from (1) and adding quantum projection noise. For each sample the Hamiltonian is estimated. The estimates from multiple samples are used to construct error bounds in the same manner as for the non-parametric resampling. We have found that the error bounds obtained from parametric bootstrapping are lower compared with that of the non-parametric case as shown in Fig. 3. We think this is due to the latter exploring deviations around a single minimum in the optimization landscape, while the case resampling arrives at different local minima, which are spread over a wider region.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland.

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.

No MeSH data available.