Editing Quantum logic gate (section)

=== Deutsch gate ===
A single-gate set of universal quantum gates can also be formulated using the parametrized three-qubit Deutsch gate <math>D(\theta)</math>,<ref>{{Citation |last=Deutsch |first=David |title=Quantum computational networks |date=September 8, 1989 |journal=[[Proc. R. Soc. Lond. A]] |volume=425 |issue=1989 |pages=73–90 |bibcode=1989RSPSA.425...73D |doi=10.1098/rspa.1989.0099 |author-link=David Deutsch |s2cid=123073680}}</ref> named after physicist [[David Deutsch]]. It is a general case of ''CC-U'', or ''controlled-controlled-unitary'' gate, and is defined as

: <math>|a, b, c\rangle \mapsto \begin{cases}
 i \cos(\theta) |a, b , c\rangle + \sin(\theta) |a, b, 1 - c\rangle & \text{for}\ a = b = 1, \\
 |a, b, c\rangle & \text{otherwise}.
\end{cases}</math>

Unfortunately, a working Deutsch gate has remained out of reach, due to lack of a protocol. There are some proposals to realize a Deutsch gate with dipole–dipole interaction in neutral atoms.<ref>{{Cite journal |last=Shi |first=Xiao-Feng |date=2018-05-22 |title=Deutsch, Toffoli, and cnot Gates via Rydberg Blockade of Neutral Atoms |url=https://link.aps.org/doi/10.1103/PhysRevApplied.9.051001 |journal=Physical Review Applied |language=en |volume=9 |issue=5 |pages=051001 |arxiv=1710.01859 |bibcode=2018PhRvP...9e1001S |doi=10.1103/PhysRevApplied.9.051001 |issn=2331-7019 |s2cid=118909059}}</ref>

{{anchor|Universal gates|Deutsch gate}}

A universal logic gate for reversible classical computing, the Toffoli gate, is reducible to the Deutsch gate <math>D(\pi/2)</math>, thus showing that all reversible classical logic operations can be performed on a universal quantum computer.

There also exist single two-qubit gates sufficient for universality. In 1996, Adriano Barenco showed that the Deutsch gate can be decomposed using only a single two-qubit gate ([[List of quantum logic gates#Barenco|Barenco gate]]), but it is hard to realize experimentally.{{r|Williams|pages=93}} This feature is exclusive to quantum circuits, as there is no classical two-bit gate that is both reversible and universal.{{r|Williams|pages=93}} Universal two-qubit gates could be implemented to improve classical reversible circuits in fast low-power microprocessors.{{r|Williams|pages=93}}