42. function ^s3
z
s6
z
&c in the high-temperature side. At low
ratures, on the other hand, the spins 4 and 5 tend to be
n some definite direction and consequently the effec-
. 5. The frustrated model where the solid lines denote ferro-
ic interactions and the broken line is for an antiferromag-
nteraction.
PRE 58TADASHI KADOWAKI AND HIDETOSHI NISHIMORI h/J = 0.1 N = 8
時刻
T(t) =
3
t
(t) =
3
t
(t)
i
x
iH =
i,j
Jij
z
i
z
j h
i
z
i
43. The cities are located on a square with the side length N to make the
length of the tour extensive for “random”, “semi-random” and “H-character”.
For “ulysses16”, we re-scale dij and set the average to 2.2. The average,
the dispersion and the ratio of the dispersion and the average are shown in
Table 4.1.
58. D-Wave のプログラミング
例題:4色問題をD-Wave の量子ビットネットワーク上にマップ
1 2 3 4
5
6
7
8
1
2
3
4
5
6
7
8
D-Wave Systems Inc. webサイト掲載 whitepaper
WHITEPAPER
WHITEPAPER
WHITEPAPER
1. Introduction
Quantum computers utilize quantum bits (qubits) to hold information. The behavior of each qubit is governed by the laws of
quantum mechanics, enabling qubits to be in a “superposition” state – that is, both a 0 and a 1 at the same time, until an out-
side event causes it to “collapse” into either a 0 or a 1. This property is foreign to our everyday experiences in the macroscopic
world, but it is the basis upon which a quantum computer is constructed. Exploiting this property gives a quantum computer the
ability to quickly solve certain classes of complex problems such as optimization, machine learning and sampling problems.
Programming a quantum computer is very different than programming a traditional computer. To program the system a user
maps a problem into a search for the “lowest point in a vast landscape” which corresponds to the best possible outcome. The
processor considers all the possibilities simultaneously to determine the lowest energy required to form those relationships.
Because a quantum computer is probabilistic rather than deterministic, the computer returns many very good answers in a
short amount of time - 10,000 answers in one second. This gives the user not only the optimal solution or a single answer,
but also other alternatives to choose from.
This paper describes the set of transformations to turn a map coloring problem into a single quantum machine instruction
(QMI) using the “direct embedding” programming model, one of a few different methods to program a D-Wave system. Map
coloring represents a large class of combinatorial optimization problems and is thus a good model problem for the D-Wave
system. While finding a valid coloring of the map of Canada is not a hard exercise (even by hand), our focus is on the transla-
tion from the problem to the programming model.
Maps of Canada display ten provinces and three territories. Typical maps (see figure 1) assign a color to each of the thirteen
regions subject to a simple constraint: two regions that share a border receive different colors. (Regions touching at one or
more isolated points, for example Nunavut and Saskatchewan, are not considered to share a border.) The point of such a
coloring is obvious: it allows our eyes to easily distinguish geographic areas that belong to a given region.
Figure 1: Map of Canada’s ten provinces and three territories
隣り合う州を別の色で塗り分ける。
使える色は4色。
62. D-Wave のプログラミング
例題:4色問題をD-Wave の量子ビットネットワーク上にマップ
D-Wave Systems Inc. webサイト掲載 whitepaper
WHITEPAPER
WHITEPAPER
WHITEPAPER
1. Introduction
Quantum computers utilize quantum bits (qubits) to hold information. The behavior of each qubit is governed by the laws of
quantum mechanics, enabling qubits to be in a “superposition” state – that is, both a 0 and a 1 at the same time, until an out-
side event causes it to “collapse” into either a 0 or a 1. This property is foreign to our everyday experiences in the macroscopic
world, but it is the basis upon which a quantum computer is constructed. Exploiting this property gives a quantum computer the
ability to quickly solve certain classes of complex problems such as optimization, machine learning and sampling problems.
Programming a quantum computer is very different than programming a traditional computer. To program the system a user
maps a problem into a search for the “lowest point in a vast landscape” which corresponds to the best possible outcome. The
processor considers all the possibilities simultaneously to determine the lowest energy required to form those relationships.
Because a quantum computer is probabilistic rather than deterministic, the computer returns many very good answers in a
short amount of time - 10,000 answers in one second. This gives the user not only the optimal solution or a single answer,
but also other alternatives to choose from.
This paper describes the set of transformations to turn a map coloring problem into a single quantum machine instruction
(QMI) using the “direct embedding” programming model, one of a few different methods to program a D-Wave system. Map
coloring represents a large class of combinatorial optimization problems and is thus a good model problem for the D-Wave
system. While finding a valid coloring of the map of Canada is not a hard exercise (even by hand), our focus is on the transla-
tion from the problem to the programming model.
Maps of Canada display ten provinces and three territories. Typical maps (see figure 1) assign a color to each of the thirteen
regions subject to a simple constraint: two regions that share a border receive different colors. (Regions touching at one or
more isolated points, for example Nunavut and Saskatchewan, are not considered to share a border.) The point of such a
coloring is obvious: it allows our eyes to easily distinguish geographic areas that belong to a given region.
Figure 1: Map of Canada’s ten provinces and three territories
BC
AB
SK
NT
YT
MB
NU
NS
ON
QC
NB
NL
PE
6つの州に隣接している
ユニットコピーを用いる
64. N is the number of qubits and Twor
date a wordline. We average Tworl
in the quantum annealing schedu
of Twordline depends on the partic
As explained above for SA, we repo
tional e↵ort of QMC in standard u
core. For the annealing schedule u
Wave 2X processor, we find
Twordline = ⇥ 87
using an Intel(R) Xeon(R) CPU E
This study is designed to explor
as a classical optimization routine
timize QMC by running at a low
We also observe that QMC with o
tions (OBC) performs better than
periodic boundary conditions in th