Journal article 61 views 21 downloads
Robustness of energy landscape control to dephasing
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Frank C. Langbein ,
Edmond Jonckheere,
Sophie Shermer
Research Directions: Quantum Technologies, Volume: 1
Swansea University Author:
Sophie Shermer
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© The Author(s), 2023. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-ShareAlike licence.
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DOI (Published version): 10.1017/qut.2023.6
Abstract
As shown in previous work, in some cases closed quantum systems exhibit a non-conventional absence of trade-off between performance and robustness in the sense that controllers with the highest fidelity can also provide the best robustness to parameter uncertainty. As the dephasing induced by the in...
| Published in: | Research Directions: Quantum Technologies |
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| ISSN: | 2752-9444 |
| Published: |
Cambridge University Press (CUP)
2023
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa68718 |
| Abstract: |
As shown in previous work, in some cases closed quantum systems exhibit a non-conventional absence of trade-off between performance and robustness in the sense that controllers with the highest fidelity can also provide the best robustness to parameter uncertainty. As the dephasing induced by the interaction of the system with the environment guides the evolution to a more classically mixed state, it is worth investigating what effect the introduction of dephasing has on the relationship between performance and robustness. In this paper we analyze the robustness of the fidelity error, as measured by the logarithmic sensitivity function, to dephasing processes. We show that introduction of dephasing as a perturbation to the nominal unitary dynamics requires a modification of the log-sensitivity formulation used to measure robustness about an uncertain parameter with nonzero nominal value used in previous work. We consider controllers optimized for a number of target objectives ranging from fidelity under coherent evolution to fidelity under dephasing dynamics to determine the extent to which optimizing for a specific regime has desirable effects in terms of robustness. Our analysis is based on two independent computations of the log-sensitivity: a statistical Monte Carlo approach and an analytic calculation. We show that despite the different log-sensitivity calculations employed in this study, both demonstrate that the log-sensitivity of the fidelity error to dephasing results in a conventional trade-off between performance and robustness. |
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| Keywords: |
Energy landscape control; spin networks; robust control |
| College: |
Faculty of Science and Engineering |
| Funders: |
Sean O’Neil acknowledges PhD funding through the US Army Advanced Civil Schooling program. |