Content deleted Content added
m Open access bot: arxiv updated in citation with #oabot. |
|||
Line 168:
===Geometric phase gate===
Higher levels (outside of the computational subspace) of a pair of coupled superconducting circuits can be used to induce a geometric phase on one of the computational states of the qubits. This leads to an entangling conditional phase shift of the relevant qubit states. This effect has been implemented by flux-tuning the qubit spectra <ref name="DiCarlo Chow Gambetta Bishop 2009 pp. 240–244">{{cite journal | last=DiCarlo | first=L. | last2=Chow | first2=J. M. | last3=Gambetta | first3=J. M. | last4=Bishop | first4=Lev S. | last5=Johnson | first5=B. R. | last6=Schuster | first6=D. I. | last7=Majer | first7=J. | last8=Blais | first8=A. | last9=Frunzio | first9=L. | last10=Girvin | first10=S. M. | last11=Schoelkopf | first11=R. J. | title=Demonstration of two-qubit algorithms with a superconducting quantum processor | journal=Nature | publisher=Springer Science and Business Media LLC | volume=460 | issue=7252 | date=2009-06-28 | issn=0028-0836 | doi=10.1038/nature08121 | pages=240–244}}</ref> and by using selective microwave driving.<ref name="Ficheux Nguyen Somoroff Xiong 2021 p. ">{{cite journal | last=Ficheux | first=Quentin | last2=Nguyen | first2=Long B. | last3=Somoroff | first3=Aaron | last4=Xiong | first4=Haonan | last5=Nesterov | first5=Konstantin N. | last6=Vavilov | first6=Maxim G. | last7=Manucharyan | first7=Vladimir E. | title=Fast Logic with Slow Qubits: Microwave-Activated Controlled-Z Gate on Low-Frequency Fluxoniums | journal=Physical Review X | volume=11 | issue=2 | date=2021-05-03 | issn=2160-3308 | doi=10.1103/PhysRevX.11.021026 | page=| arxiv=2011.02634 }}</ref> Off-resonant driving can be used to induce differential ac-Stark shift, allowing the implementation of all-microwave controlled-phase gates.<ref name="Xiong Ficheux Somoroff Nguyen 2022 p. ">{{cite journal | last=Xiong | first=Haonan | last2=Ficheux | first2=Quentin | last3=Somoroff | first3=Aaron | last4=Nguyen | first4=Long B. | last5=Dogan | first5=Ebru | last6=Rosenstock | first6=Dario | last7=Wang | first7=Chen | last8=Nesterov | first8=Konstantin N. | last9=Vavilov | first9=Maxim G. | last10=Manucharyan | first10=Vladimir E. | title=Arbitrary controlled-phase gate on fluxonium qubits using differential ac Stark shifts | journal=Physical Review Research | volume=4 | issue=2 | date=2022-04-15 | issn=2643-1564 | doi=10.1103/PhysRevResearch.4.023040 | page=| arxiv=2103.04491 }}</ref>
===Heisenberg interactions===
Line 175:
<math>\hat{\mathcal{H}}_\mathrm{XXZ}/\hbar =\sum_{ i,j} J_\mathrm{XY}(\hat{\sigma}_\text{x}^{i}\hat{\sigma}_\text{x}^{j} + \hat{\sigma}_\text{y}^{i}\hat{\sigma}_\text{y}^{j}) + J_\mathrm{ZZ}\hat{\sigma}_\text{z}^{i}\hat{\sigma}_\text{z}^{j}</math>,
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=| arxiv=2001.08343 }}</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| arxiv=1910.11333 }}</ref> In addition, it can also be realized in fixed-frequency qubits with fixed-coupling using microwave drives.<ref name="Nguyen-2024"/> 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==
Architecture-specific readout, or [[Quantum measurement|measurement]], mechanisms exist. Readout of a phase qubit is explained in the [[#Qubit archetypes|qubit archetypes table]] above. A flux qubit state is often read using an adjustable DC-[[SQUID]] [[magnetometer]]. States may also be measured using an [[electrometer]].<ref name="docs.pennylane.ai">{{Cite web |title=PennyLane Documentation — PennyLane |url=https://docs.pennylane.ai/en/stable/index.html |access-date=2022-12-11 |website=docs.pennylane.ai |language=en}}</ref> A more general readout scheme includes a coupling to a microwave [[resonator]], where resonance frequency of the resonator is dispersively shifted by the qubit state.<ref name=NatRev2017>{{cite journal |last1=Gambetta |first1=Jay M. |last2=Chow |first2=Jerry M. |last3=Steffen |first3=Matthias |title=Building logical qubits in a superconducting quantum computing system |journal=[[npj Quantum Information]] |date=13 January 2017 |volume=3 |issue=1 |pages=2 |doi=10.1038/s41534-016-0004-0 |doi-access=free |bibcode=2017npjQI...3....2G |arxiv=1510.04375 }}
</ref><ref name="Dispersive Readout">{{cite journal |last1=Blais |first1=Alexandre |last2=Huang |first2=Ren-Shou |last3=Wallraff |first3=Andreas |last4=Girvin |first4=Steven |last5=Schoelkopf |first5=Robert |title=Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation |journal=Phys. Rev. A |date=2004 |volume=69 |issue=6 |pages=062320 |doi=10.1103/PhysRevA.69.062320 |url=https://link.aps.org/doi/10.1103/PhysRevA.69.062320|arxiv=cond-mat/0402216 |bibcode=2004PhRvA..69f2320B |s2cid=20427333 }}</ref> Multi-level systems (qudits) can be readout using electron shelving.<ref name="Cottet Xiong Nguyen Lin 2021 p. ">{{cite journal | last=Cottet | first=Nathanaël | last2=Xiong | first2=Haonan | last3=Nguyen | first3=Long B. | last4=Lin | first4=Yen-Hsiang | last5=Manucharyan | first5=Vladimir E. | title=Electron shelving of a superconducting artificial atom | journal=Nature Communications | publisher=Springer Science and Business Media LLC | volume=12 | issue=1 | date=2021-11-04 | issn=2041-1723 | doi=10.1038/s41467-021-26686-x | page=| arxiv=2008.02423 }}</ref>
==DiVincenzo's criteria==
| |||