>From 85760945ceceff79e0d43156ad428043141c38b0 Mon Sep 17 00:00:00 2001
From: Akira Yokosawa <akiyks@xxxxxxxxx>
Date: Sat, 30 Sep 2017 18:01:14 +0900
Subject: [PATCH 03/10] future/QC: Insert narrow space in front of percent symbol
Signed-off-by: Akira Yokosawa <akiyks@xxxxxxxxx>
---
future/QC.tex | 10 +++++-----
1 file changed, 5 insertions(+), 5 deletions(-)
diff --git a/future/QC.tex b/future/QC.tex
index e5ff74e..437a4d4 100644
--- a/future/QC.tex
+++ b/future/QC.tex
@@ -309,10 +309,10 @@ A qubit is said to:
\item Collapse to a zero ($\ket{0}$) or a one ($\ket{1}$) if measured,
with probability being a function of the relative distance from
$\ket{0}$ and $\ket{1}$, but projected onto the Z-axis.
- Thus, a qubit on the equator of the Bloch sphere has a 50\%
+ 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
- a 14\% chance of being measured as one and 86\% chance
+ a 14\,\% chance of being measured as one and 86\,\% chance
of being measured as zero.
This situation naturally causes developers to prefer a line
segment---or a classic-computing bit---over a sphere.
@@ -335,7 +335,7 @@ are as follows:
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.
+ Either way, we get a qubit that is 50\,\% one and 50\,\% zero.
\item[\qop{S}\,:]
Rotate 90\degree{} ($\frac{\pi}{2}$ radians) about the
Bloch-sphere Z-axis, which has no effect on qubits in the
@@ -1260,9 +1260,9 @@ be extremely valuable in reducing costs (and environmental impacts)
of logistics, but current classic heuristics can find near-optimal
solutions for hundreds of cities~\cite{Martin:1992:LMC:2307953.2308141}
and polynomial-time algorithms that are guaranteed to find routes
-that are no more than 40\% longer than optimal for arbitrarily
+that are no more than 40\,\% longer than optimal for arbitrarily
large numbers of cities~\cite{Sebo:2014:STN:2688265.2688281},
-improving on the 50\% bound located a few decades
+improving on the 50\,\% bound located a few decades
earlier~\cite{NicosChristofides1976TSP-FiftyPercent}.
As of 2006 TSP solvers were finding optimal solutions to
85,900-city problems~\cite{DLApplegate2007TSPtextbook}.
--
2.7.4
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