Editing Quantum computing (section)

=== Challenges ===

There are a number of technical challenges in building a large-scale quantum computer.<ref>{{cite journal |last=Dyakonov |first=Mikhail |url=https://spectrum.ieee.org/the-case-against-quantum-computing |title=The Case Against Quantum Computing |journal=[[IEEE Spectrum]] |date=15 November 2018}}</ref> Physicist [[David P. DiVincenzo|David DiVincenzo]] has listed [[DiVincenzo's criteria|these requirements]] for a practical quantum computer:<ref>{{cite journal| arxiv=quant-ph/0002077 |title=The Physical Implementation of Quantum Computation |last=DiVincenzo |first=David P. |date=13 April 2000 |doi=10.1002/1521-3978(200009)48:9/11<771::AID-PROP771>3.0.CO;2-E |volume=48 |issue=9–11 |journal=Fortschritte der Physik |pages=771–783 |bibcode=2000ForPh..48..771D |s2cid=15439711}}</ref>
* Physically scalable to increase the number of qubits
* Qubits that can be initialized to arbitrary values
* Quantum gates that are faster than [[decoherence]] time
* Universal gate set
* Qubits that can be read easily.

Sourcing parts for quantum computers is also very difficult. [[Superconducting quantum computing|Superconducting quantum computers]], like those constructed by [[Google]] and [[IBM]], need [[helium-3]], a [[Nuclear physics|nuclear]] research byproduct, and special [[superconducting]] cables made only by the Japanese company Coax Co.<ref>{{cite news |last1=Giles |first1=Martin |date=January 17, 2019 |title=We'd have more quantum computers if it weren't so hard to find the damn cables |language=en-US |publisher=MIT Technology Review |url=https://www.technologyreview.com/s/612760/quantum-computers-component-shortage/ |access-date=May 17, 2021}}</ref>

The control of multi-qubit systems requires the generation and coordination of a large number of electrical signals with tight and deterministic timing resolution. This has led to the development of [[quantum controllers]] that enable interfacing with the qubits. Scaling these systems to support a growing number of qubits is an additional challenge.<ref>{{cite journal |vauthors=Pauka SJ, Das K, Kalra B, Moini A, Yang Y, Trainer M, Bousquet A, Cantaloube C, Dick N, Gardner GC, Manfra MJ, Reilly DJ|journal=[[Nature Electronics]]|title=A cryogenic CMOS chip for generating control signals for multiple qubits|year=2021|volume=4|issue=4|pages=64–70 |doi=10.1038/s41928-020-00528-y|url=https://www.nature.com/articles/s41928-020-00528-y|arxiv=1912.01299|s2cid=231715555}}</ref>

==== Decoherence<span class="anchor" id="Quantum decoherence"></span> ====

One of the greatest challenges involved in constructing quantum computers is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time ''T''<sub>2</sub> (for [[Nuclear magnetic resonance|NMR]] and [[MRI]] technology, also called the ''dephasing time''), typically range between nanoseconds and seconds at low temperatures.<ref name="DiVincenzo 1995">{{cite journal |last=DiVincenzo |first=David P. |title=Quantum Computation |journal=Science |year=1995 |volume=270 |issue=5234 |pages=255–261 |doi=10.1126/science.270.5234.255 |bibcode=1995Sci...270..255D |citeseerx=10.1.1.242.2165 |s2cid=220110562}}</ref> Currently, some quantum computers require their qubits to be cooled to 20 millikelvin (usually using a [[dilution refrigerator]]<ref>{{Cite journal |doi=10.1016/j.cryogenics.2021.103390| issn=0011-2275 |title=Development of Dilution refrigerators – A review |journal=Cryogenics| volume=121| year=2022| last1=Zu| first1=H.| last2=Dai| first2=W.| last3=de Waele| first3=A.T.A.M.| s2cid=244005391}}</ref>) in order to prevent significant decoherence.<ref>{{cite journal |last1=Jones |first1=Nicola |title=Computing: The quantum company |journal=Nature |date=19 June 2013 |volume=498 |issue=7454 |pages=286–288 |doi=10.1038/498286a|pmid=23783610|bibcode=2013Natur.498..286J|doi-access=free}}</ref> A 2020 study argues that [[ionizing radiation]] such as [[cosmic rays]] can nevertheless cause certain systems to decohere within milliseconds.<ref>{{cite journal |last1=Vepsäläinen |first1=Antti P. |last2=Karamlou |first2=Amir H. |last3=Orrell |first3=John L. |last4=Dogra |first4=Akshunna S. |last5=Loer |first5=Ben |last6=Vasconcelos |first6=Francisca |last7=Kim |first7=David K. |last8=Melville |first8=Alexander J. |last9=Niedzielski |first9=Bethany M. |last10=Yoder |first10=Jonilyn L. |last11=Gustavsson |first11=Simon |last12=Formaggio |first12=Joseph A. |last13=VanDevender |first13=Brent A. |last14=Oliver |first14=William D. |display-authors=5 |title=Impact of ionizing radiation on superconducting qubit coherence |journal=Nature |date=August 2020 |volume=584 |issue=7822 |pages=551–556 |doi=10.1038/s41586-020-2619-8 |pmid=32848227 |url=https://www.nature.com/articles/s41586-020-2619-8 |language=en |issn=1476-4687|arxiv=2001.09190 |bibcode=2020Natur.584..551V |s2cid=210920566 }}</ref>

As a result, time-consuming tasks may render some quantum algorithms inoperable, as attempting to maintain the state of qubits for a long enough duration will eventually corrupt the superpositions.<ref>{{cite arXiv |last1=Amy |first1=Matthew |last2=Matteo |first2=Olivia |last3=Gheorghiu |first3=Vlad |last4=Mosca |first4=Michele |last5=Parent |first5=Alex |last6=Schanck |first6=John |title=Estimating the cost of generic quantum pre-image attacks on SHA-2 and SHA-3 |date=30 November 2016 |eprint=1603.09383 |class=quant-ph}}</ref>

These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical [[pulse shaping]]. Error rates are typically proportional to the ratio of operating time to decoherence time; hence any operation must be completed much more quickly than the decoherence time.

As described by the [[threshold theorem]], if the error rate is small enough, it is thought to be possible to use [[quantum error correction]] to suppress errors and decoherence. This allows the total calculation time to be longer than the decoherence time if the error correction scheme can correct errors faster than decoherence introduces them. An often-cited figure for the required error rate in each gate for fault-tolerant computation is 10<sup>−3</sup>, assuming the noise is depolarizing.

Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between ''L'' and ''L''<sup>2</sup>, where ''L'' is the number of binary digits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of ''L''. For a 1000-bit number, this implies a need for about 10<sup>4</sup> bits without error correction.<ref>{{cite journal |last=Dyakonov |first=M. I. |date=14 October 2006 |editor2=Xu |editor2-first=J. |editor3=Zaslavsky |editor3-first=A. |title=Is Fault-Tolerant Quantum Computation Really Possible? |journal=Future Trends in Microelectronics. Up the Nano Creek |pages=4–18 |arxiv=quant-ph/0610117 |bibcode=2006quant.ph.10117D |editor1=S. Luryi}}</ref> With error correction, the figure would rise to about 10<sup>7</sup> bits. Computation time is about ''L''<sup>2</sup> or about 10<sup>7</sup> steps and at 1{{nbsp}}MHz, about 10 seconds. However, the encoding and error-correction overheads increase the size of a real fault-tolerant quantum computer by several orders of magnitude. Careful estimates<ref name=":1">{{Cite book |last=Ahsan |first=Muhammad |url=http://worldcat.org/oclc/923881411 |title=Architecture Framework for Trapped-ion Quantum Computer based on Performance Simulation Tool |date=2015 |bibcode=2015PhDT........56A |language=en-US |oclc=923881411}}</ref><ref name=":2">{{Cite journal |last1=Ahsan |first1=Muhammad |last2=Meter |first2=Rodney Van |last3=Kim |first3=Jungsang |date=2016-12-28 |title=Designing a Million-Qubit Quantum Computer Using a Resource Performance Simulator |journal=ACM Journal on Emerging Technologies in Computing Systems |volume=12 |issue=4 |pages=39:1–39:25 |doi=10.1145/2830570 |s2cid=1258374 |issn=1550-4832|doi-access=free |arxiv=1512.00796 }}</ref> show that at least 3{{nbsp}}million physical qubits would factor 2,048-bit integer in 5 months on a fully error-corrected trapped-ion quantum computer. In terms of the number of physical qubits, to date, this remains the lowest estimate<ref>{{Cite journal |last1=Gidney |first1=Craig |last2=Ekerå |first2=Martin |date=2021-04-15 |title=How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits |journal=Quantum |volume=5 |pages=433 |doi=10.22331/q-2021-04-15-433 |arxiv=1905.09749 |bibcode=2021Quant...5..433G |s2cid=162183806 |issn=2521-327X}}</ref> for practically useful integer factorization problem sizing 1,024-bit or larger.

Another approach to the stability-decoherence problem is to create a [[topological quantum computer]] with [[anyon]]s, [[quasi-particle]]s used as threads, and relying on [[braid theory]] to form stable logic gates.<ref>{{cite journal
 | last1 = Freedman | first1 = Michael H. | author1-link = Michael Freedman
 | last2 = Kitaev | first2 = Alexei | author2-link = Alexei Kitaev
 | last3 = Larsen | first3 = Michael J. | author3-link = Michael J. Larsen
 | last4 = Wang | first4 = Zhenghan
 | arxiv = quant-ph/0101025
 | doi = 10.1090/S0273-0979-02-00964-3
 | issue = 1
 | journal = Bulletin of the American Mathematical Society
 | mr = 1943131
 | pages = 31–38
 | title = Topological quantum computation
 | volume = 40
 | year = 2003}}</ref><ref>{{cite journal |last=Monroe |first=Don |url=https://www.newscientist.com/channel/fundamentals/mg20026761.700-anyons-the-breakthrough-quantum-computing-needs.html |title=Anyons: The breakthrough quantum computing needs? |journal=[[New Scientist]] |date=1 October 2008}}</ref>