diff options
Diffstat (limited to 'source/know/concept/toffoli-gate/index.md')
| -rw-r--r-- | source/know/concept/toffoli-gate/index.md | 24 |
1 files changed, 6 insertions, 18 deletions
diff --git a/source/know/concept/toffoli-gate/index.md b/source/know/concept/toffoli-gate/index.md index 7de7600..ba9d3ba 100644 --- a/source/know/concept/toffoli-gate/index.md +++ b/source/know/concept/toffoli-gate/index.md @@ -16,43 +16,31 @@ of which it returns $$A$$ and $$B$$ unchanged, and flips $$C$$ if both $$A$$ and $$B$$ are true. In circuit diagrams, its representation is: -<a href="toffoli.png"> -<img src="toffoli.png" style="width:19%"> -</a> +{% include image.html file="toffoli.png" width="19%" alt="Toffoli gate symbol" %} This gate is reversible, because $$A$$ and $$B$$ are preserved, and are all you need to reconstruct to $$C$$. Moreover, this gate is universal, because we can make a NAND gate from it: -<a href="nand.png"> -<img src="nand.png" style="width:38%"> -</a> +{% include image.html file="nand.png" width="38%" alt="NAND gate made of Toffoli gate" %} A NAND is enough to implement every conceivable circuit. That said, we can efficiently implement NOT, AND, and XOR using a single Toffoli gate too. Note that NOT is a special case of NAND: -<a href="not.png"> -<img src="not.png" style="width:32%"> -</a> +{% include image.html file="not.png" width="32%" alt="NOT gate made of Toffoli gate" %} -<a href="and.png"> -<img src="and.png" style="width:35%"> -</a> +{% include image.html file="and.png" width="35%" alt="AND gate made of Toffoli gate" %} -<a href="xor.png"> -<img src="xor.png" style="width:35%"> -</a> +{% include image.html file="xor.png" width="35%" alt="XOR gate made of Toffoli gate" %} Using these, we can, as an example, make an OR gate from three Toffoli gates, thanks to the fact that $$A \lor B = \neg (\neg A \land \neg B)$$, i.e. OR is NAND of NOT $$A$$ and NOT $$B$$: -<a href="or.png"> -<img src="or.png" style="width:50%"> -</a> +{% include image.html file="or.png" width="50%" alt="OR gate made of Toffoli gates" %} Thanks to its reversibility and universality, the Toffoli gate is interesting for quantum computing. |