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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.


Time-dependent detuning and spatial Rabi frequency.(a) The estimated δ(t) obtained from the second pair of data sets (Fig. 8 in Methods). (b) The estimated Rabi frequency Ω(t) for the same two data sets. In each part, the blue and red solid lines show data obtained using different velocity profiles. Dashed lines indicate the s.e. on the mean of these estimates, which are obtained using resampling.
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f4: Time-dependent detuning and spatial Rabi frequency.(a) The estimated δ(t) obtained from the second pair of data sets (Fig. 8 in Methods). (b) The estimated Rabi frequency Ω(t) for the same two data sets. In each part, the blue and red solid lines show data obtained using different velocity profiles. Dashed lines indicate the s.e. on the mean of these estimates, which are obtained using resampling.

Mentions: Our second comparison involves using two different velocity profiles but with a common beam position. The resolution in both time and detuning were lower in this case than for the data shown in Fig. 2 (see Methods for the data). Figure 4 shows the results of the reconstruction. We observe that the estimated Rabi frequency profiles agree to within the error bars of the reconstruction. One interesting feature of this plot is that the error bars produced from the resampled data sets increase near the peak. We believe that this happens because the sampling time of the data is 0.5 μs, which starts to become comparable to the Rabi frequency (the Nyquist frequency is 1 MHz). To optimize the efficiency of our method, it would be advantageous to run the reconstruction method in parallel with data taking, thus allowing updating of the sampling time and frequency resolution based on the current estimates of parameter values.


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)

Time-dependent detuning and spatial Rabi frequency.(a) The estimated δ(t) obtained from the second pair of data sets (Fig. 8 in Methods). (b) The estimated Rabi frequency Ω(t) for the same two data sets. In each part, the blue and red solid lines show data obtained using different velocity profiles. Dashed lines indicate the s.e. on the mean of these estimates, which are obtained using resampling.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Time-dependent detuning and spatial Rabi frequency.(a) The estimated δ(t) obtained from the second pair of data sets (Fig. 8 in Methods). (b) The estimated Rabi frequency Ω(t) for the same two data sets. In each part, the blue and red solid lines show data obtained using different velocity profiles. Dashed lines indicate the s.e. on the mean of these estimates, which are obtained using resampling.
Mentions: Our second comparison involves using two different velocity profiles but with a common beam position. The resolution in both time and detuning were lower in this case than for the data shown in Fig. 2 (see Methods for the data). Figure 4 shows the results of the reconstruction. We observe that the estimated Rabi frequency profiles agree to within the error bars of the reconstruction. One interesting feature of this plot is that the error bars produced from the resampled data sets increase near the peak. We believe that this happens because the sampling time of the data is 0.5 μs, which starts to become comparable to the Rabi frequency (the Nyquist frequency is 1 MHz). To optimize the efficiency of our method, it would be advantageous to run the reconstruction method in parallel with data taking, thus allowing updating of the sampling time and frequency resolution based on the current estimates of parameter values.

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.