>From 1d0506d2cc0dcfc983a2aedcc011cf9f9cc9be1f Mon Sep 17 00:00:00 2001
From: Akira Yokosawa <akiyks@xxxxxxxxx>
Date: Thu, 15 Jun 2017 00:23:16 +0900
Subject: [PATCH 7/8] future/QC: Use \ket{} macro for |0> and |1>
|0> and |1> can be typeset properly by using \ket{} macro of
"braket" package. Note that \ket{} can only be used in math mode.
Signed-off-by: Akira Yokosawa <akiyks@xxxxxxxxx>
---
future/QC.tex | 28 ++++++++++++++--------------
perfbook.tex | 1 +
2 files changed, 15 insertions(+), 14 deletions(-)
diff --git a/future/QC.tex b/future/QC.tex
index 701c086..fa4084e 100644
--- a/future/QC.tex
+++ b/future/QC.tex
@@ -306,9 +306,9 @@ A qubit is said to:
\begin{enumerate}
\item Be represented by a Bloch sphere, as shown in
Figure~\ref{fig:future:Qubit as Bloch Sphere}.
-\item Collapse to a zero (\co{|0>}) or a one (\co{|1>}) if measured,
+\item Collapse to a zero ($\ket{0}$) or a one ($\ket{1}$) if measured,
with probability being a function of the relative distance from
- \co{|0>} and \co{|1>}, but projected onto the Z-axis.
+ $\ket{0}$ and $\ket{1}$, but projected onto the Z-axis.
Thus, a qubit on the equator of the Bloch sphere has a 50\%
probability of being measured as a one or as a zero, while
a qubit on the 45\textdegree-north latitude would have
@@ -331,39 +331,39 @@ are as follows:
\item[H:]
Rotate 180\degree{} ($\pi$ radians) about the Bloch-sphere
X-Z axis, that is, about the 45\degree{} line on the
- X-Z plane. This rotates \co{|0>} to the point at which the
- positive X-axis intersects the Bloch sphere, and rotates \co{|1>}
+ X-Z plane. This rotates $\ket{0}$ to the point at which the
+ positive X-axis intersects the Bloch sphere, and rotates $\ket{1}$
to the point at which the negative X-axis intersects the Bloch
sphere.
Either way, we get a qubit that is 50\% one and 50\% zero.
\item[S:]
Rotate 90\degree{} ($\frac{\pi}{2}$ radians) about the
Bloch-sphere Z-axis, which has no effect on qubits in the
- \co{|0>} or \co{|1>} states.
+ $\ket{0}$ or $\ket{1}$ states.
\item[S\textsuperscript{$\dagger$}:]
Rotate $-90\degree$ ($-\frac{\pi}{2}$ radians) about the
Bloch-sphere Z-axis, which has no effect on qubits in the
- \co{|0>} or \co{|1>} states.
+ $\ket{0}$ or $\ket{1}$ states.
This operator is the inverse of \co{S}.
\item[T:]
Rotate 45\degree{} ($\frac{\pi}{4}$ radians) about the
Bloch-sphere Z-axis, which has no effect on qubits in the
- \co{|0>} or \co{|1>} states.
+ $\ket{0}$ or $\ket{1}$ states.
\item[T\textsuperscript{$\dagger$}:]
Rotate $-45\degree$ ($-\frac{\pi}{4}$ radians) about the
Bloch-sphere Z-axis, which has no effect on qubits in the
- \co{|0>} or \co{|1>} states.
+ $\ket{0}$ or $\ket{1}$ states.
This operator is the inverse of \co{T}.
\item[X:]
Rotate 180\degree{} ($\pi$ radians) about the Bloch-sphere
- X-axis, which takes \co{|0>} to \co{|1>} and vice versa.
+ X-axis, which takes $\ket{0}$ to $\ket{1}$ and vice versa.
\item[Y:]
Rotate 180\degree{} ($\pi$ radians) about the Bloch-sphere
- Y-axis, which also takes \co{|0>} to \co{|1>} and vice versa.
+ Y-axis, which also takes $\ket{0}$ to $\ket{1}$ and vice versa.
\item[Z:]
Rotate 180\degree{} ($\pi$ radians) about the Bloch-sphere
- Z-axis, which has no effect on qubits in the \co{|0>} or
- \co{|1>} states.
+ Z-axis, which has no effect on qubits in the $\ket{0}$ or
+ $\ket{1}$ states.
\end{description}
\begin{figure}[tb]
@@ -390,11 +390,11 @@ Similarly, the probability of collapse to one is:
Thus, one (limited) way to think of a qubit is as a fixed-point number
ranging between zero and one, inclusive, based on these probabilities
of collapse.
-Constants may be formed by starting with (say) a \co{|0>} qubit and
+Constants may be formed by starting with (say) a $\ket{0}$ qubit and
applying sequences of \co{H}, \co{S}, and \co{T} operations.
For example, the constant $0.14$ can be formed by applying an
\co{H}, \co{T}\textsuperscript{$\dagger$}, and another \co{H}
-operation on a \co{|0>} qubit as shown in
+operation on a $\ket{0}$ qubit as shown in
Figure~\ref{fig:future:QC Program as Quantum Experience Score},
in a manner not entirely unlike constant formation on classic
computers with small immediate fields.
diff --git a/perfbook.tex b/perfbook.tex
index b4458f2..0b7cff1 100644
--- a/perfbook.tex
+++ b/perfbook.tex
@@ -46,6 +46,7 @@
\usepackage{epigraph}
\setlength{\epigraphwidth}{2.6in}
\usepackage[xspace]{ellipsis}
+\usepackage{braket} % for \ket{} macro in QC section
% custom packages
--
2.7.4
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