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authorPrefetch2023-01-01 16:40:56 +0100
committerPrefetch2023-01-01 17:02:29 +0100
commitb1a9b1b9b2f04efd6dc39bd2a02c544d34d1259c (patch)
tree1fd87919deee17e58f8ad19c09abd54bd4a70886 /source/know/concept/repetition-code/index.md
parent1d700ab734aa9b6711eb31796beb25cb7659d8e0 (diff)
Change license, add Makefile, add image caching control
Diffstat (limited to 'source/know/concept/repetition-code/index.md')
-rw-r--r--source/know/concept/repetition-code/index.md15
1 files changed, 10 insertions, 5 deletions
diff --git a/source/know/concept/repetition-code/index.md b/source/know/concept/repetition-code/index.md
index 89e6f4d..fa039a3 100644
--- a/source/know/concept/repetition-code/index.md
+++ b/source/know/concept/repetition-code/index.md
@@ -77,7 +77,8 @@ $$\begin{aligned}
Such a transformation is easy to achieve with the following sequence
of [quantum gates](/know/concept/quantum-gate/):
-{% include image.html file="bit-flip-encode.png" width="32%" alt="Bit flip code encoder" %}
+{% include image.html file="bit-flip-encode.png" width="32%"
+ alt="Bit flip code encoder" %}
So, a little while after encoding the state $$\Ket{\psi}$$ like that,
a bit flip occurs on the 2nd qubit:
@@ -180,7 +181,8 @@ without affecting $$\ket{\overline{\psi}}$$ itself,
by applying $$\mathrm{CNOT}$$s to some ancillary qubits
and then measuring those:
-{% include image.html file="bit-flip-detect.png" width="62%" alt="Bit flip code decoder" %}
+{% include image.html file="bit-flip-detect.png" width="62%"
+ alt="Bit flip code decoder" %}
The two measurements, respectively representing $$ZZI$$ and $$IZZ$$,
yield $$\Ket{1}$$ if a bit flip definitely occurred,
@@ -231,14 +233,16 @@ $$\begin{aligned}
= \alpha \Ket{+\!+\!+} + \beta \Ket{-\!-\!-}
\end{aligned}$$
-{% include image.html file="phase-flip-encode.png" width="40%" alt="Phase flip code encoder" %}
+{% include image.html file="phase-flip-encode.png" width="40%"
+ alt="Phase flip code encoder" %}
A phase flip along the $$Z$$-axis
corresponds to a bit flip along the $$X$$-axis $$\Ket{+} \to \Ket{-}$$.
In this case, the stabilizers are $$XXI$$ and $$IXX$$,
and the error detection circuit is as follows:
-{% include image.html file="phase-flip-detect.png" width="70%" alt="Phase flip code decoder" %}
+{% include image.html file="phase-flip-detect.png" width="70%"
+ alt="Phase flip code decoder" %}
This system protects us against all single-qubit phase flips,
but not against bit flips.
@@ -281,7 +285,8 @@ This encoding is achieved by the following quantum circuit,
which simply consists of the phase flip encoder,
followed by 3 copies of the bit flip encoder:
-{% include image.html file="shor-code-encode.png" width="55%" alt="Shor code encoder" %}
+{% include image.html file="shor-code-encode.png" width="55%"
+ alt="Shor code encoder" %}
We thus use 9 physical qubits to store 1 logical qubit.
Fortunately, more efficient schemes exist.