# Exploring the tradeoff between fidelity and time optimal control of quantum unitary transformations

## Author(s): Moore Tibbetts, Katharine. W.; Brif, Constantin; Grace, Matthew D.; Donovan, Ashley; Hocker, David L.; et al

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr10z3k
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dc.contributor.authorMoore Tibbetts, Katharine. W.-
dc.contributor.authorBrif, Constantin-
dc.contributor.authorGrace, Matthew D.-
dc.contributor.authorDonovan, Ashley-
dc.contributor.authorHocker, David L.-
dc.contributor.authorHo, Tak-San-
dc.contributor.authorWu, Re-Bing-
dc.contributor.authorRabitz, Herschel-
dc.date.accessioned2020-10-30T18:35:27Z-
dc.date.available2020-10-30T18:35:27Z-
dc.date.issued2012-12-12en_US
dc.identifier.citationTibbetts, Katharine W Moore, Brif, Constantin, Grace, Matthew D, Donovan, Ashley, Hocker, David L, Ho, Tak-San, Wu, Re-Bing, Rabitz, Herschel. (2012). Exploring the tradeoff between fidelity and time optimal control of quantum unitary transformations. PHYSICAL REVIEW A, 86 (10.1103/PhysRevA.86.062309en_US
dc.identifier.issn1050-2947-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr10z3k-
dc.description.abstractGenerating a unitary transformation in the shortest possible time is of practical importance to quantum information processing because it helps to reduce decoherence effects and improve robustness to additive control field noise. Many analytical and numerical studies have identified the minimum time necessary to implement a variety of quantum gates on coupled-spin qubit systems. This work focuses on exploring the Pareto front that quantifies the tradeoff between the competitive objectives of maximizing the gate fidelity F and minimizing the control time T. In order to identify the critical time T* below which the target transformation is not reachable, as well as to determine the associated Pareto front, we introduce a numerical method of Pareto front tracking (PFT). We consider closed two- and multiqubit systems with constant interqubit coupling strengths and each individual qubit controlled by a separate time-dependent external field. Our analysis demonstrates that unit fidelity (to a desired numerical accuracy) can be achieved at any T >= T* in most cases. However, the optimization search effort rises superexponentially as T decreases and approaches T*. Furthermore, a small decrease in control time incurs a significant penalty in fidelity for T < T*, indicating that it is generally undesirable to operate below the critical time. We investigate the dependence of the critical time T* on the coupling strength between qubits and the target gate transformation. Practical consequences of these findings for laboratory implementation of quantum gates are discussed. DOI: 10.1103/PhysRevA.86.062309en_US
dc.format.extent062309-1 - 062309-16en_US
dc.language.isoen_USen_US
dc.relation.ispartofPHYSICAL REVIEW Aen_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleExploring the tradeoff between fidelity and time optimal control of quantum unitary transformationsen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1103/PhysRevA.86.062309-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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