Editing Qubit (section)

===Qudits and qutrits===
The term '''qudit''' denotes the unit of quantum information that can be realized in suitable ''d''-level quantum systems.<ref>{{Cite journal|last1=Nisbet-Jones|first1=Peter B. R.|last2=Dilley|first2=Jerome|last3=Holleczek|first3=Annemarie|last4=Barter|first4=Oliver |last5=Kuhn|first5=Axel |date=2013|title=Photonic qubits, qutrits and ququads accurately prepared and delivered on demand|url=http://stacks.iop.org/1367-2630/15/i=5/a=053007|journal=New Journal of Physics|language=en |volume=15|issue=5|pages=053007|doi=10.1088/1367-2630/15/5/053007|issn=1367-2630|arxiv=1203.5614 |bibcode=2013NJPh...15e3007N|s2cid=110606655}}</ref> A qubit register that can be measured to ''N'' states is identical to an ''N''-level qudit. A rarely used<ref>As of June 2022 [https://arxiv.org/search/advanced?advanced=&terms-0-operator=AND&terms-0-term=qudit&terms-0-field=all&classification-physics=True&classification-physics_archives=quant-ph&classification-include_cross_list=include&date-filter_by=all_dates&date-year=&date-from_date=&date-to_date=&date-date_type=submitted_date&abstracts=show&size=50&order=-announced_date_first 1150 uses] versus [https://arxiv.org/search/advanced?advanced=&terms-0-operator=AND&terms-0-term=qunit&terms-0-field=all&classification-physics=True&classification-physics_archives=quant-ph&classification-include_cross_list=include&date-filter_by=all_dates&date-year=&date-from_date=&date-to_date=&date-date_type=submitted_date&abstracts=show&size=50&order=-announced_date_first 31 uses] on in the quant-ph category of [[arxiv.org]].</ref> [[synonym]] for qudit is '''quNit''',<ref>{{Cite journal |last1=Kaszlikowski |first1=Dagomir |last2=Gnaciński |first2=Piotr |last3=Żukowski |first3=Marek |last4=Miklaszewski |first4=Wieslaw |last5=Zeilinger |first5=Anton |year=2000 |title=Violations of Local Realism by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubits |journal=Physical Review Letters |volume=85 |issue=21 |pages=4418–4421 |arxiv=quant-ph/0005028 |bibcode=2000PhRvL..85.4418K |doi=10.1103/PhysRevLett.85.4418 |pmid=11082560 |s2cid=39822693}}</ref> since both ''d'' and ''N'' are frequently used to denote the dimension of a quantum system.

Qudits are similar to the [[Integer (computer science)|integer type]]s in classical computing, and may be mapped to (or realized by) arrays of qubits. Qudits where the ''d''-level system is not an exponent of 2 cannot be mapped to arrays of qubits. It is for example possible to have 5-level qudits.

In 2017, scientists at the [[National Institute of Scientific Research]] constructed a pair of qudits with 10 different states each, giving more computational power than 6 qubits.<ref>{{Cite web |last=Choi |first=Charles Q. |date=2017-06-28 |title=Qudits: The Real Future of Quantum Computing? |url=https://spectrum.ieee.org/qudits-the-real-future-of-quantum-computing |access-date=2017-06-29 |website=IEEE Spectrum |language=en-US}}</ref>

In 2022, researchers at the [[University of Innsbruck]] succeeded in developing a universal qudit quantum processor with trapped ions.<ref>{{cite journal |last1=Ringbauer |first1=Martin |last2=Meth |first2=Michael |last3=Postler |first3=Lukas |last4=Stricker |first4=Roman |last5=Blatt |first5=Rainer |last6=Schindler |first6=Philipp |last7=Monz |first7=Thomas |title=A universal qudit quantum processor with trapped ions |journal=Nature Physics |date=21 July 2022 |volume=18 |issue=9 |pages=1053–1057 |doi=10.1038/s41567-022-01658-0 |arxiv=2109.06903 |bibcode=2022NatPh..18.1053R |s2cid=237513730 |url=https://www.nature.com/articles/s41567-022-01658-0 |access-date=21 July 2022 |language=en |issn=1745-2481}}</ref> In the same year, researchers at [[Tsinghua University]]'s Center for Quantum Information implemented the dual-type qubit scheme in trapped ion quantum computers using the same ion species.<ref>{{cite web|first1=Ingrid|last1=Fardelli|url=https://phys.org/news/2022-08-coherently-qubit-ion-species.amp|title=Researchers realize two coherently convertible qubit types using a single ion species|date=August 18, 2022|publisher=[[Phys.org]]}}</ref> In 2025, the Innsbruck team managed to simulate two-dimensional [[Lattice gauge theory|lattice gauge theories]] on their qudit quantum computer.<ref>{{Cite journal |last=Meth |first=Michael |last2=Zhang |first2=Jinglei |last3=Haase |first3=Jan F. |last4=Edmunds |first4=Claire |last5=Postler |first5=Lukas |last6=Jena |first6=Andrew J. |last7=Steiner |first7=Alex |last8=Dellantonio |first8=Luca |last9=Blatt |first9=Rainer |last10=Zoller |first10=Peter |last11=Monz |first11=Thomas |last12=Schindler |first12=Philipp |last13=Muschik |first13=Christine |last14=Ringbauer |first14=Martin |date=2025-03-25 |title=Simulating two-dimensional lattice gauge theories on a qudit quantum computer |url=https://www.nature.com/articles/s41567-025-02797-w |journal=Nature Physics |language=en |pages=1–7 |doi=10.1038/s41567-025-02797-w |issn=1745-2481|doi-access=free |pmc=11999872 }}</ref>

Also in 2022, researchers at the [[University of California, Berkeley]] developed a technique to dynamically control the cross-Kerr interactions between fixed-frequency qutrits, achieving high two-qutrit gate fidelities.<ref name="Goss Morvan Marinelli Mitchell 2022 p. ">{{cite journal | last1=Goss | first1=Noah | last2=Morvan | first2=Alexis | last3=Marinelli | first3=Brian | last4=Mitchell | first4=Bradley K. | last5=Nguyen | first5=Long B. | last6=Naik | first6=Ravi K. | last7=Chen | first7=Larry | last8=Jünger | first8=Christian | last9=Kreikebaum | first9=John Mark | last10=Santiago | first10=David I. | last11=Wallman | first11=Joel J. | last12=Siddiqi | first12=Irfan | title=High-fidelity qutrit entangling gates for superconducting circuits | journal=Nature Communications | publisher=Springer Science and Business Media LLC | volume=13 | issue=1 | date=2022-12-05 | issn=2041-1723 | doi=10.1038/s41467-022-34851-z | page=7481| pmid=36470858 | pmc=9722686 | arxiv=2206.07216 | bibcode=2022NatCo..13.7481G }}</ref> This was followed by a demonstration of extensible control of superconducting qudits up to <math>d=4</math> in 2024 based on programmable two-photon interactions.<ref name="Nguyen Goss Siva Kim 2023 q896">{{cite journal | last1=Nguyen | first1=Long B. | last2=Goss | first2=Noah | last3=Siva | first3=Karthik | last4=Kim | first4=Yosep | last5=Younis | first5=Ed | last6=Qing | first6=Bingcheng | last7=Hashim | first7=Akel | last8=Santiago | first8=David I. | last9=Siddiqi | first9=Irfan | title=Empowering high-dimensional quantum computing by traversing the dual bosonic ladder | journal=Nature Communications | publisher=Springer Science and Business Media LLC | volume=15 | issue=1 | date=2024-08-19 | issn=2041-1723 | doi=10.1038/s41467-024-51434-2 | page=7117| pmid=39160166 | pmc=11333499 | arxiv=2312.17741 | bibcode=2024NatCo..15.7117N }}</ref>

Similar to the qubit, the [[qutrit]] is the unit of quantum information that can be realized in suitable 3-level quantum systems. This is analogous to the unit of classical information [[trit (computing)|trit]] of [[ternary computer]]s.<ref>{{Cite web |last=Irving |first=Michael |date=2022-10-14 |title="64-dimensional quantum space" drastically boosts quantum computing |url=https://newatlas.com/telecommunications/qudits-64-dimensional-quantum-space/ |access-date=2022-10-14 |website=New Atlas |language=en-US}}</ref> Besides the advantage associated with the enlarged computational space, the third qutrit level can be exploited to implement efficient compilation of multi-qubit gates.<ref name="Nguyen Goss Siva Kim 2023 q896"></ref><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. |date=16 January 2024 |title=Programmable Heisenberg interactions between Floquet qubits |journal=Nature Physics |volume=20 |issue=1 |pages=240–246 |arxiv=2211.10383 |bibcode=2024NatPh..20..240N |doi=10.1038/s41567-023-02326-7 |doi-access=free}}</ref><ref name="Chu He Zhou Yuan 2022 pp. 126–131">{{cite journal | last1=Chu | first1=Ji | last2=He | first2=Xiaoyu | last3=Zhou | first3=Yuxuan | last4=Yuan | first4=Jiahao | last5=Zhang | first5=Libo | last6=Guo | first6=Qihao | last7=Hai | first7=Yongju | last8=Han | first8=Zhikun | last9=Hu | first9=Chang-Kang | last10=Huang | first10=Wenhui | last11=Jia | first11=Hao | last12=Jiao | first12=Dawei | last13=Li | first13=Sai | last14=Liu | first14=Yang | last15=Ni | first15=Zhongchu | last16=Nie | first16=Lifu | last17=Pan | first17=Xianchuang | last18=Qiu | first18=Jiawei | last19=Wei | first19=Weiwei | last20=Nuerbolati | first20=Wuerkaixi | last21=Yang | first21=Zusheng | last22=Zhang | first22=Jiajian | last23=Zhang | first23=Zhida | last24=Zou | first24=Wanjing | last25=Chen | first25=Yuanzhen | last26=Deng | first26=Xiaowei | last27=Deng | first27=Xiuhao | last28=Hu | first28=Ling | last29=Li | first29=Jian | last30=Liu | first30=Song | last31=Lu | first31=Yao | last32=Niu | first32=Jingjing | last33=Tan | first33=Dian | last34=Xu | first34=Yuan | last35=Yan | first35=Tongxing | last36=Zhong | first36=Youpeng | last37=Yan | first37=Fei | last38=Sun | first38=Xiaoming | last39=Yu | first39=Dapeng | title=Scalable algorithm simplification using quantum AND logic | journal=Nature Physics | publisher=Springer Science and Business Media LLC | volume=19 | issue=1 | date=2022-11-14 | issn=1745-2473 | doi=10.1038/s41567-022-01813-7 | pages=126–131| arxiv=2112.14922 }}</ref>