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<math>\hat{H} = 4 E_C \hat{n}^2 + \frac{1}{2} E_L (\hat{\phi}- \phi_\mathrm{ext})^2 - E_J \cos \hat{\phi} </math>.
One important property of the fluxonium qubit is the longer [[Coherence (physics)#Quantum coherence|qubit lifetime]] at the half flux sweet spot, which can exceed 1 millisecond <ref name="Nguyen-2019">{{Cite journal |last1=Nguyen |first1=Long B. |last2=Lin |first2=Yen-Hsiang |last3=Somoroff |first3=Aaron |last4=Mencia |first4=Raymond |last5=Grabon |first5=Nicholas |last6=Manucharyan |first6=Vladimir E. |date=25 November 2019 |title=High-Coherence Fluxonium Qubit |url=https://link.aps.org/doi/10.1103/PhysRevX.9.041041 |journal=Physical Review X |language=en |volume=9 |issue=4 |pages=041041 |doi=10.1103/PhysRevX.9.041041 |arxiv=1810.11006 |bibcode=2019PhRvX...9d1041N |s2cid=53499609 |issn=2160-3308}} </ref><ref>{{Cite web |last1=Science |first1=The National University of |last2=MISIS |first2=Technology |title=Fluxonium qubits bring the creation of a quantum computer closer |url=https://phys.org/news/2022-11-fluxonium-qubits-creation-quantum-closer.html |access-date=2022-12-12 |website=phys.org |language=en}}</ref>. Another crucial advantage of the fluxonium qubit biased at the sweet spot is the large anharmonicity, which allows fast local microwave control and mitigates spectral crowding problems, leading to better scalability <ref name="Nguyen-2020">{{cite thesis |last1=Nguyen |first1=Long B.|title=Toward the Fluxonium Quantum Processor | url = https://www.proquest.com/dissertations-theses/toward-fluxonium-quantum-processor/docview/2455525166/se-2 | publisher = University of Maryland, College Park |date = 2020 |degree = Ph.D.}}</ref><ref name="Nguyen-2022">{{Cite journal |last1=Nguyen |first1=Long B.|last2=Koolstra |first2=Gerwin|last3=Kim |first3=Yosep|last4=Morvan |first4=Alexis|last5=Chistolini |first5=Trevor|last6=Singh |first6=Shraddha|last7=Nesterov |first7=Konstantin N.|last8=Jünger |first8=Christian|last9=Chen |first9=Larry|last10=Pedramrazi |first10=Zahra|last11=Mitchell |first11=Bradley K.|last12=Kreikebaum |first12=John Mark|last13=Puri |first13=Shruti|last14=Santiago |first14=David I.|last15=Siddiqi |first15=Irfan|title=Blueprint for a High-Performance Fluxonium Quantum Processor |url=https://link.aps.org/doi/10.1103/PRXQuantum.3.037001|journal =PRX Quantum |volume=3 |issue=3 |pages=037001 |doi=10.1103/PRXQuantum.3.037001|date=5 August 2022 |volume=3 |issue= 3 |pages= 037001 |doi=10.1103/PRXQuantum.3.037001 |bibcode=2022PRXQ....3c7001N |doi-access=free |arxiv=2201.09374}} </ref>.
=== Charge qubit ===
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