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{{Short description|Quantum computing implementation}}
'''Superconducting quantum computing''' is a branch of [[Solid-state physics|solid state]] physics and quantum computing that implements [[superconductivity|superconducting]] [[electronic circuit]]s using superconducting qubits as artificial atoms, or [[quantum dot]]s. For superconducting qubits, the two logic states are the [[ground state]] and the [[excited state]], denoted <math>|g\rangle \text{ and } |e\rangle</math> respectively.<ref name="docs.pennylane.ai" /> Research in superconducting quantum computing is conducted by companies such as [[Google]],<ref>{{cite journal |last1=Castelvecchi |first1=Davide |title=Quantum computers ready to leap out of the lab in 2017 |journal=Nature |date=5 January 2017 |volume=541 |issue=7635 |pages=9–10 |doi=10.1038/541009a|pmid=28054624 |bibcode=2017Natur.541....9C |s2cid=4447373 |doi-access=free }}</ref> [[IBM]],<ref name="IBM">{{cite web |title=IBM Makes Quantum Computing Available on IBM Cloud |url=https://www-03.ibm.com/press/us/en/pressrelease/49661.wss |archive-url=https://web.archive.org/web/20160504214945/http://www-03.ibm.com/press/us/en/pressrelease/49661.wss |url-status=dead |archive-date=May 4, 2016 |website=www-03.ibm.com |date=4 May 2016}}</ref> [[IMEC]],<ref>{{Cite web|url=https://www.imec-int.com/en/articles/imec-enters-the-race-to-unleash-quantum-computing-with-silicon-qubits|title=Imec enters the race to unleash quantum computing with silicon qubits|website=www.imec-int.com|language=en|access-date=2019-11-10}}</ref> [[BBN Technologies]],<ref>{{cite journal | arxiv=1704.08314 | doi=10.1063/1.5006525 | title=Hardware for dynamic quantum computing | date=2017 | last1=Ryan | first1=Colm A.
{{As of|2016|May|df=US}}, up to 9 fully controllable [[qubit]]s are demonstrated in the 1D [[Array programming|array]],<ref>{{cite journal |last1=Kelly |first1=J. |last2=Barends |first2=R. |last3=Fowler |first3=A. G. |last4=Megrant |first4=A. |last5=Jeffrey |first5=E. |last6=White |first6=T. C. |last7=Sank |first7=D. |last8=Mutus |first8=J. Y. |last9=Campbell |first9=B. |last10=Chen |first10=Yu |last11=Chen |first11=Z. |last12=Chiaro |first12=B. |last13=Dunsworth |first13=A. |last14=Hoi |first14=I.-C. |last15=Neill |first15=C. |last16=O’Malley |first16=P. J. J. |last17=Quintana |first17=C. |last18=Roushan |first18=P. |last19=Vainsencher |first19=A. |last20=Wenner |first20=J. |last21=Cleland |first21=A. N. |last22=Martinis |first22=John M. |title=State preservation by repetitive error detection in a superconducting quantum circuit |arxiv=1411.7403 |journal=Nature |date=4 March 2015 |volume=519 |issue=7541 |pages=66–69 |doi=10.1038/nature14270|pmid=25739628 |bibcode=2015Natur.519...66K |s2cid=3032369 }}</ref> and up to 16 in 2D architecture.<ref name="IBM" /> In October 2019, the [[John M. Martinis|Martinis]] group, partnered with [[Google]], published an article demonstrating novel [[quantum supremacy]], using a chip composed of 53 superconducting qubits.<ref>{{cite journal |last1=Arute |first1=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 |date=October 2019 |volume=574 |issue=7779 |pages=505–510 |doi=10.1038/s41586-019-1666-5 |pmid=31645734 | arxiv=1910.11333|bibcode=2019Natur.574..505A |doi-access=free }}</ref>
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=== Superconductors ===
Unlike typical conductors, superconductors possess a [[critical temperature]] at which resistivity plummets to
==== Bose–Einstein condensates ====
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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
: <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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==== Gatemon ====
Another variation of the transmon qubit is the Gatemon. Like the Xmon, the Gatemon is a tunable variation of the transmon. The Gatemon is tunable via [[Threshold voltage|gate voltage]]. [[File:Chip unimon.png|thumb|Superconducting circuit consisting of 3 Unimons (blue), each connected to resonators (red), drive lines (green), and joint probe lines (yellow)<ref>
=== Unimon ===
In 2022 researchers from [[IQM
{| class="wikitable"
|+Superconducting Qubit Archetypes
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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 ==
[[DiVincenzo's criteria]] is a list describing the requirements for a physical system to be capable of implementing a logical qubit. DiVincenzo's criteria is satisfied by superconducting quantum computing implementation. Much of the current development effort in superconducting quantum computing aim to achieve interconnect, control, and [[Readout integrated circuit|readout]] in the 3rd dimension with additional [[lithography]] layers.The list of DiVincenzo's criteria for a physical system to implement a logical qubit is satisfied by the implementation of superconducting qubits. Although DiVincenzo's criteria as originally proposed consists of five criteria required for physically implementing a quantum computer, the more complete list consists of seven criteria as it takes into account communication over a computer network capable of transmitting quantum information between computers, known as the “quantum internet”. Therefore, the first five criteria ensure successful quantum computing, while the final two criteria allow for quantum communication.
# '''A scalable physical system with well characterized qubits.''' "Well characterized implies that that [[Hamiltonian mechanics|Hamiltonian function]] must be well-defined i.e. the energy eigenstates of the qubit should be able to be quantified.. A scalable system is self-explanatory, it indicates that this ability to regulate a qubit should be augmentable for multiple more qubits. Herein lies the major issue Quantum Computers face, as more qubits are implemented it leads to
# '''Ability to initialize the state of qubits to a simple fiducial state.'''<ref name="DiVincenzo-2008">{{Cite journal |last=DiVincenzo |first=David |date=February 1, 2008 |title=The Physical Implementation of Quantum Computation |journal=IBM T.J. Watson Research Center|volume=48 |issue=9–11 |pages=771–783 |doi=10.1002/1521-3978(200009)48:9/11<771::AID-PROP771>3.0.CO;2-E |arxiv=quant-ph/0002077 |bibcode=2000ForPh..48..771D |s2cid=15439711 }}</ref> A fiducial state is one that is easily and consistently replicable and is useful in quantum computing as it may be used to guarantee the initial state of qubits. One simple way to initialize a superconducting qubit is to wait long enough for the qubits to relax to the ground state. Controlling qubit potential with tuning knobs allows faster initialization mechanisms.
# '''Long relevant decoherence times'''<ref name="DiVincenzo-2008" />'''.''' Decoherence of superconducting qubits is affected by multiple factors. Most decoherence is attributed to the quality of the Josephson junction and imperfections in the chip substrate. Due to their mesoscopic scale, superconducting qubits are relatively short lived. Nevertheless, thousands of gate operations have been demonstrated in these many-qubit systems.<ref>{{cite journal |last1=Devoret |first1=M. H. |last2=Schoelkopf |first2=R. J. |title=Superconducting Circuits for Quantum Information: An Outlook |journal=Science |date=7 March 2013 |volume=339 |issue=6124 |pages=1169–1174 |doi=10.1126/science.1231930|pmid=23471399 |bibcode=2013Sci...339.1169D |s2cid=10123022 }}</ref> Recent strategies to improve device coherence include purifying the circuit materials and designing qubits with decreased sensitivity to noise sources.<ref name="Nguyen-2019" />
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The journey has been long, arduous and full of breakthroughs but has seen significant advancements in the recent history and has massive potential for revolutionizing computing.
'''Recent Advances in Josephson Junction–Based QPUs'''
A recent paper by Mohebi and Mohseni provides additional insight into the engineering challenges and innovations necessary for advancing superconducting quantum processing units (QPUs):
# '''Decoherence and Noise Mitigation:''' The paper emphasizes that decoherence—primarily due to quasiparticle tunneling—is a major obstacle that limits qubit performance. Improved material innovations and optimized control techniques are essential to reduce noise and enhance qubit coherence.<ref name="MohebiMohseni2025">{{Cite arXiv |title=An Overview of Josephson Junctions Based QPUs |date=3 April 2025 |eprint=2504.02500 |last1=Mohebi |first1=Omid |author2=Alireza Hesam Mohseni |class=cond-mat.supr-con }}</ref>
# '''Fabrication and Reproducibility:''' Achieving consistent and reproducible Josephson junctions is crucial for scaling up superconducting QPUs. The study discusses advanced lithography techniques and control of junction geometry as methods to minimize fluctuations in critical current, thereby enhancing qubit fidelity.<ref name="MohebiMohseni2025" />
# '''Balancing Qubit Parameters:''' The authors highlight the trade-offs between achieving large anharmonicity (to suppress charge noise) and maintaining the nonlinearity required for effective qubit operation. Striking the optimal balance between these factors is pivotal for the development of robust, scalable quantum processors.<ref name="MohebiMohseni2025" />
'''Future of superconducting quantum computing:'''
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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}}
* {{Cite book |title=Single Flux Quantum Integrated Circuit Design |last1=Krylov |first1=Gleb |publisher=Springer |year=2024 |isbn=978-3-031-47474-3 |type=Second Edition|___location=Cham |last2=Jabbari |first2=Tahereh |last3=Friedman |first3=Eby G. |doi=10.1007/978-3-031-47475-0 |oclc=1430662174}}
* {{Cite book |title=Design and Applications of Emerging Computer Systems |last1=Absar |first1=Rubaya |publisher=Springer |year=2024|chapter=Cryogenic CMOS for Quantum Computing |isbn=978-3-031-42478-6 |edition=1st |___location=Cham |last2=Elgabra |first2=Hazem |last3=Ma |first3=Dylan |last4=Zhao |first4=Yiju |last5=Wei |first5=Lan |editor-last=Liu |editor-first=Weiqiang |pages=591–621 |doi=10.1007/978-3-031-42478-6_22 |oclc=1418721165 |editor-last2=Han |editor-first2=Jie |editor-last3=Lombardi |editor-first3=Fabrizio}}
*{{cite book|last1=Awan|first1=Shakil|last2=Kibble|first2=Bryan P.|last3=Schurr|first3=Jürgen|year=2011|title=Coaxial Electrical Circuits for Interference-Free Measurements|series=Electrical Measurement Series 13|___location=Stevenage|publisher=The Institution of Engineering and Technology (IET)|isbn=978-1-84919-069-5|doi=10.1049/PBEL013E |oclc=761013886
}}
*{{cite book|last1=Jordan|first1=Andrew N.|last2=Siddiqi|first2=Irfan A.|title=Quantum Measurement: Theory and Practice|edition=1st|publisher=Cambridge University Press
|year=2024|isbn=9781009100069 |oclc=1435711501}}
* {{cite book|last=Zagoskin|first=Alexandre M.
|title=Quantum Engineering: Theory and Design of Quantum Coherent Structures|publisher=Cambridge University Press|year=2011|isbn=978-0-521-11369-4|oclc=768771210}}
*{{cite book|last1=Van Duzer|first1=Theodore|last2=Turner|first2=Charles W.|title=Principles of Superconductive Devices and Circuits|edition=2nd|publisher=Prentice Hall
|year=1999|isbn=9780132627429|oclc=40251418}}
*{{cite book|last=Solymar|first=Lazlo|title=Superconductive Tunnelling and Applications|publisher=Chapman and Hall
|___location=London|year=1972|isbn=0-412-10210-2|oclc=488903}}
== External links ==
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