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serves as the basis for analog quantum simulation of spin systems and the primitive for an expressive set of quantum gates, sometimes referred to as ''fermionic simulation'' (or ''fSim'') gates. In superconducting circuits, this interaction model has been implemented using flux-tunable qubits with flux-tunable coupling <ref name="Foxen Neill Dunsworth Roushan 2020 p. ">{{cite journal | last=Foxen | first=B. | last2=Neill | first2=C. | last3=Dunsworth | first3=A. | last4=Roushan | first4=P. | last5=Chiaro | first5=B. | last6=Megrant | first6=A. | last7=Kelly | first7=J. | last8=Chen | first8=Zijun | last9=Satzinger | first9=K. | last10=Barends | first10=R. | last11=Arute | first11=F. | last12=Arya | first12=K. | last13=Babbush | first13=R. | last14=Bacon | first14=D. | last15=Bardin | first15=J. C. | last16=Boixo | first16=S. | last17=Buell | first17=D. | last18=Burkett | first18=B. | last19=Chen | first19=Yu | last20=Collins | first20=R. | last21=Farhi | first21=E. | last22=Fowler | first22=A. | last23=Gidney | first23=C. | last24=Giustina | first24=M. | last25=Graff | first25=R. | last26=Harrigan | first26=M. | last27=Huang | first27=T. | last28=Isakov | first28=S. V. | last29=Jeffrey | first29=E. | last30=Jiang | first30=Z. | last31=Kafri | first31=D. | last32=Kechedzhi | first32=K. | last33=Klimov | first33=P. | last34=Korotkov | first34=A. | last35=Kostritsa | first35=F. | last36=Landhuis | first36=D. | last37=Lucero | first37=E. | last38=McClean | first38=J. | last39=McEwen | first39=M. | last40=Mi | first40=X. | last41=Mohseni | first41=M. | last42=Mutus | first42=J. Y. | last43=Naaman | first43=O. | last44=Neeley | first44=M. | last45=Niu | first45=M. | last46=Petukhov | first46=A. | last47=Quintana | first47=C. | last48=Rubin | first48=N. | last49=Sank | first49=D. | last50=Smelyanskiy | first50=V. | last51=Vainsencher | first51=A. | last52=White | first52=T. C. | last53=Yao | first53=Z. | last54=Yeh | first54=P. | last55=Zalcman | first55=A. | last56=Neven | first56=H. | last57=Martinis | first57=J. M. | author58=Google AI Quantum | title=Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms | journal=Physical Review Letters | volume=125 | issue=12 | date=2020-09-15 | issn=0031-9007 | doi=10.1103/PhysRevLett.125.120504 | page=}}</ref>, allowing the demonstration of quantum supremacy <ref name="Arute Arya Babbush Bacon 2019 pp. 505–510">{{cite journal | last=Arute | first=Frank | last2=Arya | first2=Kunal | last3=Babbush | first3=Ryan | last4=Bacon | first4=Dave | last5=Bardin | first5=Joseph C. | last6=Barends | first6=Rami | last7=Biswas | first7=Rupak | last8=Boixo | first8=Sergio | last9=Brandao | first9=Fernando G. S. L. | last10=Buell | first10=David A. | last11=Burkett | first11=Brian | last12=Chen | first12=Yu | last13=Chen | first13=Zijun | last14=Chiaro | first14=Ben | last15=Collins | first15=Roberto | last16=Courtney | first16=William | last17=Dunsworth | first17=Andrew | last18=Farhi | first18=Edward | last19=Foxen | first19=Brooks | last20=Fowler | first20=Austin | last21=Gidney | first21=Craig | last22=Giustina | first22=Marissa | last23=Graff | first23=Rob | last24=Guerin | first24=Keith | last25=Habegger | first25=Steve | last26=Harrigan | first26=Matthew P. | last27=Hartmann | first27=Michael J. | last28=Ho | first28=Alan | last29=Hoffmann | first29=Markus | last30=Huang | first30=Trent | last31=Humble | first31=Travis S. | last32=Isakov | first32=Sergei V. | last33=Jeffrey | first33=Evan | last34=Jiang | first34=Zhang | last35=Kafri | first35=Dvir | last36=Kechedzhi | first36=Kostyantyn | last37=Kelly | first37=Julian | last38=Klimov | first38=Paul V. | last39=Knysh | first39=Sergey | last40=Korotkov | first40=Alexander | last41=Kostritsa | first41=Fedor | last42=Landhuis | first42=David | last43=Lindmark | first43=Mike | last44=Lucero | first44=Erik | last45=Lyakh | first45=Dmitry | last46=Mandrà | first46=Salvatore | last47=McClean | first47=Jarrod R. | last48=McEwen | first48=Matthew | last49=Megrant | first49=Anthony | last50=Mi | first50=Xiao | last51=Michielsen | first51=Kristel | last52=Mohseni | first52=Masoud | last53=Mutus | first53=Josh | last54=Naaman | first54=Ofer | last55=Neeley | first55=Matthew | last56=Neill | first56=Charles | last57=Niu | first57=Murphy Yuezhen | last58=Ostby | first58=Eric | last59=Petukhov | first59=Andre | last60=Platt | first60=John C. | last61=Quintana | first61=Chris | last62=Rieffel | first62=Eleanor G. | last63=Roushan | first63=Pedram | last64=Rubin | first64=Nicholas C. | last65=Sank | first65=Daniel | last66=Satzinger | first66=Kevin J. | last67=Smelyanskiy | first67=Vadim | last68=Sung | first68=Kevin J. | last69=Trevithick | first69=Matthew D. | last70=Vainsencher | first70=Amit | last71=Villalonga | first71=Benjamin | last72=White | first72=Theodore | last73=Yao | first73=Z. Jamie | last74=Yeh | first74=Ping | last75=Zalcman | first75=Adam | last76=Neven | first76=Hartmut | last77=Martinis | first77=John M. | title=Quantum supremacy using a programmable superconducting processor | journal=Nature | publisher=Springer Science and Business Media LLC | volume=574 | issue=7779 | date=2019-10-23 | issn=0028-0836 | doi=10.1038/s41586-019-1666-5 | pages=505–510}}</ref>. In addition, it can also be realized in fixed-frequency qubits with fixed-coupling using microwave drives <ref>{{cite journal |last1=Nguyen |first1=L.B. |last2=Kim |first2=Y. |last3=Hashim |first3=A. |last4=Goss |first4=N.|last5=Marinelli |first5=B.|last6=Bhandari |first6=B.|last7=Das |first7=D.|last8=Naik |first8=R.K.|last9=Kreikebaum |first9=J.M.|last10=Jordan |first10=A.|last11=Santiago |first11=D.I.|last12=Siddiqi |first12=I. |title=Programmable Heisenberg interactions between Floquet qubits
|journal=Nature Physics |date=16 January 2024 |volume=20 |issue=1 |pages=240-246 |doi=10.1038/s41567-023-02326-7 |bibcode=2024NatPh..20..240N |doi-access=free |arxiv=2211.10383}}
</ref>. The fSim gate family encompasses arbitrary XY and ZZ two-qubit unitaries, including the iSWAP, the CZ, and the SWAP gates (see [[Quantum logic gate]]).
==Qubit readout==
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