Editing Adder (electronics) (section)

== Quantum adders ==
[[File:Quantum Full Adder.png|thumb|Quantum full adder, using [[Toffoli gate|Toffoli]] and [[CNOT]] gates. The CNOT-gate that is surrounded by a dotted square in this picture can be omitted if [[uncomputation]] to restore the ''B output'' is not required.]] Using only the [[Toffoli gate|Toffoli]] and [[CNOT]] [[quantum logic gate]]s, it is possible to produce quantum full- and half-adders.<ref>{{cite journal | last=Feynman | first=Richard P. | title=Quantum mechanical computers | journal=Foundations of Physics | publisher=Springer Science and Business Media LLC | volume=16 | issue=6 | year=1986 | issn=0015-9018 | doi=10.1007/bf01886518 | pages=507–531| bibcode=1986FoPh...16..507F | s2cid=122076550 }}</ref><ref>{{cite web|url=https://www.quantum-inspire.com/kbase/full-adder/|title=Code example: Quantum full adder|publisher=QuTech (Delft University of Technology (TU Delft) and the Netherlands Organisation for Applied Scientific Research (TNO))}}</ref><ref>{{cite journal|author=Dibyendu Chatterjee, Arijit Roy|journal=[[Progress of Theoretical and Experimental Physics]]|title=A transmon-based quantum half-adder scheme|year=2015|volume=2015|issue=9|pages=093A02 |doi=10.1093/ptep/ptv122|bibcode=2015PTEP.2015i3A02C|url=https://paperity.org/p/73955611/a-transmon-based-quantum-half-adder-scheme|doi-access=free}}</ref> The same circuits can also be implemented in classical [[reversible computation]], as both CNOT and Toffoli are also classical [[logic gate]]s.

Since the [[quantum Fourier transform]] has a low [[circuit complexity]], it can efficiently be used for adding numbers as well.<ref>{{cite arXiv|last=Draper|first=Thomas G.|eprint=quant-ph/0008033|title=Addition on a Quantum Computer|date=7 Aug 2000}}</ref><ref>{{cite journal|last1=Ruiz-Perez|first1=Lidia|last2=Juan Carlos|first2=Garcia-Escartin|title=Quantum arithmetic with the quantum Fourier transform|journal=Quantum Information Processing|arxiv=1411.5949v2|date=2 May 2017|volume=16|issue=6|page=152 |doi=10.1007/s11128-017-1603-1|bibcode=2017QuIP...16..152R |s2cid=10948948}}</ref><ref>{{cite journal | last=Şahin | first=Engin | title=Quantum arithmetic operations based on quantum Fourier transform on signed integers | year=2020 | journal=International Journal of Quantum Information | volume=18 | issue=6 | pages=2050035 | issn=1793-6918 | doi=10.1142/s0219749920500355 | arxiv=2005.00443v3| bibcode=2020IJQI...1850035S }}</ref>