Limits...
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.


Extending the horizon estimation.The steps performed when extending the time horizon from Tn to Tn+1 are illustrated. We first predict in the old basis, then move to the new basis, and finally optimize again. The figure also shows the B-splines Bi,k(t).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4834628&req=5

f5: Extending the horizon estimation.The steps performed when extending the time horizon from Tn to Tn+1 are illustrated. We first predict in the old basis, then move to the new basis, and finally optimize again. The figure also shows the B-splines Bi,k(t).

Mentions: Figure 5 gives a visualization of the B-splines Bi,k(t) and a B-spline curve. The B-spline construction ensures that any linear combination of the B-splines is continuous and has (k−2) continuous derivatives. The knot vector K determines how the basis functions are positioned within the interval [t0, tn+k]. We notice that for our Hamiltonian the spacing of the B-splines is not critical, which we think is due to the smoothness of the variations in our Hamiltonian parameters δ(t) and Ω(t). We therefore used the Matlab function spap2 to automatically choose a suitable knot vector and restricted ourselves to optimizing the coefficients αi. We collect all coefficients αi for δ(t) and Ω(t) and store them in a single vector α.


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)

Extending the horizon estimation.The steps performed when extending the time horizon from Tn to Tn+1 are illustrated. We first predict in the old basis, then move to the new basis, and finally optimize again. The figure also shows the B-splines Bi,k(t).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: Extending the horizon estimation.The steps performed when extending the time horizon from Tn to Tn+1 are illustrated. We first predict in the old basis, then move to the new basis, and finally optimize again. The figure also shows the B-splines Bi,k(t).
Mentions: Figure 5 gives a visualization of the B-splines Bi,k(t) and a B-spline curve. The B-spline construction ensures that any linear combination of the B-splines is continuous and has (k−2) continuous derivatives. The knot vector K determines how the basis functions are positioned within the interval [t0, tn+k]. We notice that for our Hamiltonian the spacing of the B-splines is not critical, which we think is due to the smoothness of the variations in our Hamiltonian parameters δ(t) and Ω(t). We therefore used the Matlab function spap2 to automatically choose a suitable knot vector and restricted ourselves to optimizing the coefficients αi. We collect all coefficients αi for δ(t) and Ω(t) and store them in a single vector α.

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.