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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|bibcode=2009QuIP....8..105H |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>\textstyle \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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: <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
=== Charge qubit ===
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==== Transmon ====
Transmons are a special type of qubit with a [[Shunt (electrical)|shunted]] capacitor specifically designed to mitigate [[Quantum noise|noise]]. The transmon qubit model was based on the Cooper pair box<ref>{{Cite journal |last1=Roth |first1=Thomas E. |last2=Ma |first2=Ruichao |last3=Chew |first3=Weng C. |date=
: <math>\hat{H} = \frac{\hbar J}{2} (\sigma_{1}^{x} \sigma_{2}^{x} + \sigma_{1}^{y} \sigma_{2}^{y})</math>,
where <math>J</math> is [[current density]] and <math>\sigma</math> is [[Charge density|surface charge density]].<ref name="docs.pennylane.ai" />
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=== 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 |
=== Heisenberg interactions ===
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<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 |
== 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 |
== DiVincenzo's criteria ==
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== Further reading ==
* {{cite book |title=Principles of Superconducting Quantum Computers |
* {{Cite book |title=Microwave Techniques in Superconducting Quantum Computers |last=Salari |first=Alan |oclc=1405187817 |id=978-1-63081-988-0 (ebook)| publisher=Artech House| year=2024|isbn=978-1-63081-987-3|type=Unabridged edition |___location=Boston}}
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