Improving quantum clocks via
semidefinite programming
(pp0553-0574)
Michael
Mullan and Emanuel Knill
doi:
https://doi.org/10.26421/QIC12.7-8-2
Abstracts:
The accuracies of modern quantum logic clocks have surpassed those of
standard atomic fountain clocks. These clocks also provide a greater
degree of control, because before and after clock queries, we are able
to apply chosen unitary operations and measurements. Here, we take
advantage of these choices and present a numerical technique designed to
increase the accuracy of these clocks. We use a greedy approach,
minimizing the phase variance of a noisy classical oscillator with
respect to a perfect frequency standard after an interrogation step; we
do not optimize over successive interrogations or the probe times. We
consider arbitrary prior frequency knowledge and compare clocks with
varying numbers of ions and queries interlaced with unitary control. Our
technique is based on the semidefinite programming formulation of
quantum query complexity, a method first developed in the context of
deriving algorithmic lower bounds. The application of semidefinite
programming to an inherently continuous problem like that considered
here requires discretization; we derive bounds on the error introduced
and show that it can be made suitably small.
Key words:
Quantum Query Algorithms, Quantum Logic Clocks,
Semidefinite Programming |