Superconducting quantum computing: Difference between revisions

Revision as of 03:19, 17 October 2023

Revision as of 21:18, 3 December 2023

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=== Josephson junctions ===

[[File:Single josephson junction.svg|thumb|A single Josephson junction where C is a thin layer of insulator and A & B are (superconducting) currents with nonequivalent wave functions.]]

One distinguishable attribute of superconducting quantum circuits is the use of [[Josephson junction]]s. Josephson junctions are an [[electrical element]] which does not exist in [[Superconductivity#Superconducting phase transition|normal conductors]]. Recall that a [[Electrical junction|junction]] is a weak connection between two leads of wire (in this case a superconductive wire) on either side of a thin layer of [[Insulator (electricity)|insulator]] material only a few [[atom]]s thick, usually implemented using [[Niemeyer–Dolan technique|shadow evaporation]] technique. The resulting Josephson junction device exhibits the [[Josephson effect|Josephson Effect]] whereby the junction produces a [[supercurrent]]. An image of a single Josephson junction is shown to the right. The condensate wave function on the two sides of the junction are weakly correlated, meaning that they are allowed to have different superconducting phases. This distinction of [[Linearity|nonlinearity]] contrasts continuous superconducting wire for which the wave function across the junction must be [[Continuous function|continuous]]. Current flow through the junction occurs by [[quantum tunneling]], seeming to instantaneously "tunnel" from one side of the junction to the other. This tunneling phenomenon is unique to quantum systems. Thus, quantum tunneling is used to create nonlinear inductance, essential for qubit design as it allows a design of [[Anharmonicity|anharmonic oscillators]] for which energy levels are discretized (or [[Virtual memory compression#Compression_using_quantization|quantize]]d) with nonuniform spacing between energy levels, denoted <math>\Delta E</math>.<ref name="docs.pennylane.ai" /> In contrast, the [[quantum harmonic oscillator]] ''cannot'' be used as a qubit as there is no way to address only two of its states.

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=== Charge qubit ===

The charge qubit, also known as the [[Cooper pair box]], possesses a Josephson to charging energy ratio on the order of magnitude <math>< 1</math>. For charge qubits, different energy levels correspond to an integer number of [[Cooper pair]]s on a superconducting island (a small superconducting area with a controllable number of charge carriers).<ref>{{Cite web |date=2019-06-06 |title=Superconducting qubits – on islands, charge qubits and the transmon |url=https://leftasexercise.com/2019/06/06/superconducting-qubits-on-islands-charge-qubits-and-the-transmon/ |access-date=2022-12-12 |website=LeftAsExercise |language=en}}</ref> Indeed, the first experimentally realized qubit was the Cooper pair box, achieved in 1999.<ref>{{Cite journal |last=Wendin |first=G. |date=2017-10-01 |title=Quantum information processing with superconducting circuits: a review |journal=Reports on Progress in Physics |volume=80 |issue=10 |pages=106001 |doi=10.1088/1361-6633/aa7e1a |pmid=28682303 |arxiv=1610.02208 |bibcode=2017RPPh...80j6001W |s2cid=3940479 |issn=0034-4885}}</ref> [[File:4 Qubit, 4 Bus, 4 Resonator IBM Device (Jay M. Gambetta, Jerry M. Chow, and Matthias Steffen, 2017).png|thumb|upright=0.8|A device consisting of four superconducting [[transmon]] qubits, four [[quantum bus|quantum bu]]ses, and four readout [[Resonator#Transmission line resonators|resonators]] fabricated by [[IBM]] and published in [[npj Quantum Information]] in January 2017.<ref>{{cite journal | last1 = Gambetta | first1 = J. M. | author-link2 = J. M. Chow | last2 = Chow | first2 = J. M. | last3 = Steffen | first3 = M. | year = 2017 | title = Building logical qubits in a superconducting quantum computing system | journal = npj Quantum Information | volume = 3 | issue = 1| page = 2 | doi = 10.1038/s41534-016-0004-0 | bibcode = 2017npjQI...3....2G | doi-access = free | arxiv = 1510.04375 }}</ref>|alt=]]

==== Transmon ====

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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>{{Cite journal |title=Fig. 1: Unimon qubit and its measurement setup. {{!}} Nature Communications |url=https://www.nature.com/articles/s41467-022-34614-w/figures/1 |language=en}}</ref>]]

=== Unimon ===

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===Single qubit gates===

[[File:Bloch Sphere.svg|thumb|A depiction of the Bloch sphere.]]

A single qubit gate is achieved by rotation in the [[Bloch sphere]]. Rotations between different energy levels of a single qubit are induced by [[microwave]] pulses sent to an [[Antenna (radio)|antenna]] or [[transmission line]] coupled to the qubit with a [[frequency]] resonant with the energy separation between levels. Individual qubits may be addressed by a dedicated [[transmission line]] or by a shared one if the other qubits are off [[resonance]]. The [[Rotation around a fixed axis|axis of rotation]] is set by [[quadrature amplitude modulation]] of microwave pulse, while pulse length determines the [[angle of rotation]].<ref name="oneQBgate">{{cite journal |last1=Motzoi |first1=F. |last2=Gambetta |first2=J. M. |last3=Rebentrost |first3=P. |last4=Wilhelm |first4=F. K. |title=Simple Pulses for Elimination of Leakage in Weakly Nonlinear Qubits |arxiv=0901.0534 |journal=Physical Review Letters |date=8 September 2009 |volume=103 |issue=11 |pages=110501 |doi=10.1103/PhysRevLett.103.110501|pmid=19792356 |bibcode=2009PhRvL.103k0501M |s2cid=7288207 }}</ref>