From b1a9b1b9b2f04efd6dc39bd2a02c544d34d1259c Mon Sep 17 00:00:00 2001 From: Prefetch Date: Sun, 1 Jan 2023 16:40:56 +0100 Subject: Change license, add Makefile, add image caching control --- source/know/concept/repetition-code/index.md | 15 ++++++++++----- 1 file changed, 10 insertions(+), 5 deletions(-) (limited to 'source/know/concept/repetition-code/index.md') 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. -- cgit v1.2.3