SciPost Submission Page
Optimal control of a quantum sensor: A fast algorithm based on an analytic solution
by Santiago Hern{\'a}ndez-G{\'o}mez, Federico Balducci, Giovanni Fasiolo, Paola Cappellaro, Nicole Fabbri, Antonello Scardicchio
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Santiago Hernández-Gómez |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202401_00041v1 (pdf) |
| Date submitted: | Jan. 31, 2024, 10:47 a.m. |
| Submitted by: | Santiago Hernández-Gómez |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Experimental |
Abstract
Quantum sensors can show unprecedented sensitivities, provided they are controlled in a very specific, optimal way. Here, we consider a spin sensor of time-varying fields in the presence of dephasing noise, and we show that the problem of finding the optimal pulsed control field can be mapped to the determination of the ground state of a spin chain. We find an approximate but analytic solution of this problem, which provides a lower bound for the sensor sensitivity, and a pulsed control very close to optimal, which we further use as initial guess for realizing a fast simulated annealing algorithm. We experimentally demonstrate the sensitivity improvement for a spin-qubit magnetometer based on a nitrogen-vacancy center in diamond.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2024-3-25 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202401_00041v1, delivered 2024-03-25, doi: 10.21468/SciPost.Report.8764
Strengths
2 - Detailed implementation of the optimisation routines
3 - Experimental confirmation already implemented
Weaknesses
Report
Requested changes
1 - The overall clarity of the manuscript would be much increased if the abstract already specified the usage of the word "optimal", with a sentence to the effect of "in the sense that it optimises the sensitivity, i.e., the smallest detectable signal". It would also be beneficial to explicitly state in the introduction that the minimisation of the sensitivity is analogous to the classical Hamiltonian minimisation (upon time discretisation).
2 - In deriving (A.4), why is it that C can be set to 1?
3 - In Eqs.(2,4), I take it Phi(T)=Phi(T,b)/b ? (Since Phi(T,b) is proportional to b?) This shouldbe clarified.
4 - Eq.(4): absolutely explain the opernational significance of the sensitivity
Report #1 by Anonymous (Referee 1) on 2024-2-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202401_00041v1, delivered 2024-02-29, doi: 10.21468/SciPost.Report.8637
Strengths
1- relevant physics issue addressed 2- original mapping to a known model 3- helpful discussion of approximations 4- experimental verification
Weaknesses
1- clarity of some formulations should be improved 2- final measurement of field strength not or insufficiently presented 3- not all sentences are in idiomatic English
Report
optimize the measurement sensitivity in presence of noise by
bang-bang control. The line or argument is theoretically appealing
since it eventually resorts to a frustrated 1D Ising model
and a mean field treatment known from spin glass theory.
Another great asset consists in the experimental verification
which the authors carried out as well. Thus, I am
voting for publication, once the points below will have been
addressed.
Requested changes
1) It must be emphasized early on that h(t) must be known beforehand. Only the amplitude can be detected. Please discuss whether this is a realistic situation occurring in practice! Me, being a theorist, am a bit skeptical whether the by far more relevant goal would not be to detect b(t) including its time dependence.
Similarly, please state clearly, that the power spectrum S(\omega) of the noise needs to be known a priori.
2) Emphasize early on that you are dealing with dephasing only, omitting other decoherence processes. Justify that "dephasing only" is still a relevant issue.
3) What is meant by the "overlap" between noise and target field between Eq. (3) and (4)? Please be a bit more precise.
4) The quantity \eta is called "sensitivity", but later minimized. From the sense of the word, however, the sensitivity should be large - so I would rather call 1/\eta sensitivity.
5) In Eq. (11) the inverse of a delta-function is used in the continuum. Please comment on what this really means and how one can define it mathematically.
6) After Eq. (15) please state that you take lambda to be constant. The notation lambda(t)=lambda is not unambiguous.
7) Fig. 2 should be rendered much larger, including the fonts, to reach a decent readability.
8) An important point needs to be elucidated in the experimental part: How can the "true" value of b read off and with which error? This must be elucidated, at best by a figure.
9) Fig. 6, panel b) the tick labels on the y-axis should start at 0.
10) Why does the rightmost panel of Fig. 7 not contain data for Sph.?
11) Finally, a careful reading by an English native speaker can improve the manuscript by leading to more idiomatic sentences at several occasions. "A minima" should read "A minimum", on page 9.