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==Qubit archetypes==
The three primary superconducting qubit archetypes are the [[phase qubit|phase]], [[charge qubit|charge]] and [[flux qubit|flux]] qubit. Many hybridizations of these archetypes exist including the fluxonium,<ref>{{cite journal|last1=Manucharyan|first1=V. E.|last2=Koch|first2=J.|last3=Glazman|first3=L. I.|last4=Devoret|first4=M. H.|title=Fluxonium: Single Cooper-Pair Circuit Free of Charge Offsets|arxiv=0906.0831|journal=Science|date=1 October 2009|volume=326|issue=5949|pages=113–116|doi=10.1126/science.1175552|pmid=19797655 |bibcode=2009Sci...326..113M|s2cid=17645288}}</ref> [[transmon]],<ref>{{cite journal |arxiv=0812.1865 |last1=Houck |first1=A. A. |last2=Koch |first2=Jens |last3=Devoret |first3=M. H. |last4=Girvin |first4=S. M. |last5=Schoelkopf |first5=R. J. |title=Life after charge noise: recent results with transmon qubits |journal=Quantum Information Processing |date=11 February 2009 |volume=8 |issue=2–3 |pages=105–115 |doi=10.1007/s11128-009-0100-6|s2cid=27305073 }}</ref> Xmon,<ref>{{cite journal |last1=Barends |first1=R. |last2=Kelly |first2=J. |last3=Megrant |first3=A. |last4=Sank |first4=D. |last5=Jeffrey |first5=E. |last6=Chen |first6=Y. |last7=Yin |first7=Y. |last8=Chiaro |first8=B. |last9=Mutus |first9=J. |last10=Neill |first10=C. |last11=O’Malley |first11=P. |last12=Roushan |first12=P. |last13=Wenner |first13=J. |last14=White |first14=T. C. |last15=Cleland |first15=A. N. |last16=Martinis |first16=John M. |title=Coherent Josephson Qubit Suitable for Scalable Quantum Integrated Circuits |arxiv=1304.2322 |journal=Physical Review Letters |date=22 August 2013 |volume=111 |issue=8 |pages=080502 |doi=10.1103/PhysRevLett.111.080502|pmid=24010421 |bibcode=2013PhRvL.111h0502B |s2cid=27081288 }}</ref> and quantronium.<ref>{{cite journal |last1=Metcalfe |first1=M. |last2=Boaknin |first2=E. |last3=Manucharyan |first3=V. |last4=Vijay |first4=R. |last5=Siddiqi |first5=I. |last6=Rigetti |first6=C. |last7=Frunzio |first7=L. |last8=Schoelkopf |first8=R. J. |last9=Devoret |first9=M. H. |title=Measuring the decoherence of a quantronium qubit with the cavity bifurcation amplifier |arxiv=0706.0765 |journal=Physical Review B |date=21 November 2007 |volume=76 |issue=17 |pages=174516 |doi=10.1103/PhysRevB.76.174516|bibcode=2007PhRvB..76q4516M |s2cid=19088840 }}</ref> For any qubit implementation the logical [[quantum states]] <math>\{|0\rangle,|1\rangle\}</math> are [[Map (mathematics)|mapped]] to different states of the physical system (typically to discrete [[energy level]]s or their [[quantum superposition]]s). Each of the three archetypes possess a distinct range of Josephson energy to charging energy ratio. Josephson energy refers to the energy stored in Josephson junctions when current passes through, and charging energy is the energy required for one Cooper pair to charge the junction's total capacitance.<ref name="Martinis-2004">{{Cite journal |last1=Martinis |first1=John M. |last2=Osborne |first2=Kevin |date=2004-02-16 |title=Superconducting Qubits and the Physics of Josephson Junctions |arxiv=cond-mat/0402415 |bibcode=2004cond.mat..2415M }}</ref> Josephson energy can be written as [[File:Energy scales for qubits.png|thumb|A graph of various superconducting qubit archetypes by their Josephson energy to charging energy ratio with a legend on the right.<ref name="Hyyppä-2022">{{Cite journal |last1=Hyyppä |first1=Eric |last2=Kundu |first2=Suman |last3=Chan |first3=Chun Fai |last4=Gunyhó |first4=András |last5=Hotari |first5=Juho |last6=Janzso |first6=David |last7=Juliusson |first7=Kristinn |last8=Kiuru |first8=Olavi |last9=Kotilahti |first9=Janne |last10=Landra |first10=Alessandro |last11=Liu |first11=Wei |last12=Marxer |first12=Fabian |last13=Mäkinen |first13=Akseli |last14=Orgiazzi |first14=Jean-Luc |last15=Palma |first15=Mario |date=2022-11-12 |title=Unimon qubit |journal=Nature Communications |language=en |volume=13 |issue=1 |pages=6895 |doi=10.1038/s41467-022-34614-w |pmid=36371435 |pmc=9653402 |arxiv=2203.05896 |bibcode=2022NatCo..13.6895H |issn=2041-1723}}</ref> The top left graphic illustrates a unimon electrical circuit.<ref name="Hyyppä-2022" />]]<math>U_j = - \frac{I_0 \Phi_0}{2 \pi} \cos \delta</math>,
where <math>I_0</math> is the critical current parameter of the Josephson junction, <math>\Phi_0 = \frac{h}{2e}</math> is (superconducting) [[Magnetic flux quantum|flux quantum]], and <math>\delta</math> is the [[Phase (waves)|phase difference]] across the junction.<ref name="Martinis-2004" /> Notice that the term <math>cos \delta</math> indicates nonlinearity of the Josephson junction.<ref name="Martinis-2004" /> Charge energy is written as
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