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Diffstat (limited to 'source/know/concept/deutsch-jozsa-algorithm')
| -rw-r--r-- | source/know/concept/deutsch-jozsa-algorithm/deutsch-circuit.avif | bin | 0 -> 2028 bytes | |||
| -rw-r--r-- | source/know/concept/deutsch-jozsa-algorithm/deutsch-jozsa-circuit.avif | bin | 0 -> 3311 bytes | |||
| -rw-r--r-- | source/know/concept/deutsch-jozsa-algorithm/index.md | 12 |
3 files changed, 5 insertions, 7 deletions
diff --git a/source/know/concept/deutsch-jozsa-algorithm/deutsch-circuit.avif b/source/know/concept/deutsch-jozsa-algorithm/deutsch-circuit.avif Binary files differnew file mode 100644 index 0000000..c498cd9 --- /dev/null +++ b/source/know/concept/deutsch-jozsa-algorithm/deutsch-circuit.avif diff --git a/source/know/concept/deutsch-jozsa-algorithm/deutsch-jozsa-circuit.avif b/source/know/concept/deutsch-jozsa-algorithm/deutsch-jozsa-circuit.avif Binary files differnew file mode 100644 index 0000000..2312ff3 --- /dev/null +++ b/source/know/concept/deutsch-jozsa-algorithm/deutsch-jozsa-circuit.avif diff --git a/source/know/concept/deutsch-jozsa-algorithm/index.md b/source/know/concept/deutsch-jozsa-algorithm/index.md index bbdd58d..5f2f268 100644 --- a/source/know/concept/deutsch-jozsa-algorithm/index.md +++ b/source/know/concept/deutsch-jozsa-algorithm/index.md @@ -27,6 +27,7 @@ while classical computers need up to $$2^{N - 1} + 1$$ queries for an $$N$$-bit $$x$$. + ## Deutsch algorithm The Deutsch algorithm handles the simplest case, @@ -40,9 +41,7 @@ In other words, we only need to determine if $$f(0) = f(1)$$ or $$f(0) \neq f(1) To do this, we use the following quantum circuit, where $$U_f$$ is the oracle we query: -<a href="deutsch-circuit.png"> -<img src="deutsch-circuit.png" style="width:48%"> -</a> +{% include image.html file="deutsch-circuit.png" width="48%" alt="Deutsch circuit" %} Due to unitarity constraints, the action of $$U_f$$ is defined to be as follows, @@ -134,16 +133,15 @@ A classical computer would need to query it twice, once with input $$x = 0$$, and again with $$x = 1$$. -## Full Deutsch-Jozsa algorithm + +## Deutsch-Jozsa algorithm The Deutsch-Jozsa algorithm generalizes the above to $$N$$-bit inputs $$x$$. We are promised that $$f(x)$$ is either constant or balanced; other possibilities are assumed to be impossible. This algorithm is then implemented by the following quantum circuit: -<a href="deutsch-jozsa-circuit.png"> -<img src="deutsch-jozsa-circuit.png" style="width:52%"> -</a> +{% include image.html file="deutsch-jozsa-circuit.png" width="52%" alt="Deutsch-Jozsa circuit" %} There are $$N$$ qubits in initial state $$\Ket{0}$$, and one in $$\Ket{1}$$. For clarity, the oracle $$U_f$$ works like so: |
