ん21世紀の量子情報科学
根本香絵・国立情報学研究所
08.12.2013

−6テクノロジー in 1050!m5cm

微細構造

どのくらい原子のスケールまで近づいているのでしょうか？

−610 から原子レベルへ

１格子単位45ナノメートル

ボーア原子模型
1s

www.jpwikipedia.org

2s

2p

3s

3p

3d

エネルギースペクトルの離散化
http://optoele.ele.tottori-u.ac.jp/~abe/hyd/1s-s.png

重ね合わせ離散化したエネルギー状態| ↑⟩スピンの状態|ψ⟩ = a| ↑⟩ + b| ↓⟩| ↓⟩確率 p|a|2|b|2|a|2 − |b|2
⟨ψ|Sz |ψ⟩ =2
期待値

量子ノイズ
量子ノイズ：原理的に取り除けないノイズ

不確定性原理ノイズとして見える

位置と運動量の両方を正確に測定することはできない

1sx
確率分布
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc2.html

量子的に考えると量子ノイズを制御できる

量子ノイズから量子制御へ|0⟩
最初の状態操作する|1⟩

a|0⟩ + b|1⟩
重ね合わせ状態

測定する|0⟩量子状態を操作する
|0⟩
時間発展

|1⟩

a|0⟩ + b|1⟩

量子測定
|0⟩

0 +12|1⟩ 50%
測定する

0 , 1 へ射影測定|0⟩ 50%

量子測定
|0⟩

0 +12

0 ±1
20 +1へ射影測定

2100%

量子測定
|0⟩

0 +1
0 ±12へ射影測定

20 −12測定によって状態操作ができる
量子計算からみると、量子演算（量子的時間発展）と量子測定は同じ能力をもつ

量子測定
α =e2− α /2α∑ n! nn∞

n0n へ射影測定!
n光子数の期待値： α n α= α ≡n2!

量子リソグラフィー量子相関をもった状態
entangled state

量子相関のない状態
Phys.Rev.Lett., 85, 2773 (2000)

なぜ量子系は複雑なのでしょう

ビット数

α 0 +β 1

10,1200,01,10,11

α1 0 1 + β1 1 1 , α 2 0 2 + β 2 1 23000,001,010,011,100,101,110,111
24=16

α 00 + β 01 + γ 10 + ε 114525=32626=64(α 0 + β 1 )⊗32 n −1n2n∑c j
j=0j7∑c jj=0j

量子系の複雑性
Can a quantum system be probabilistically simulated by aclassical universal computer? ...the answer is certainly, No!
— Richard P. Feynman (1982)

000,…,00!#"#$n qubits

Time evoluation⎯⎯⎯⎯⎯⎯⎯⎯→

2n個の基底状態

2 −1n∑c jj=0j

2n個の係数（指数的な増加）

イオン・原子REVIEWS

NATUREjVol 464j4 March 2010

acbdFigure 3 | Trapped atom qubits. a, Multi-level linear ion trap chip; the inset
displays a linear crystal of several 171Yb1 ions fluorescing when resonant
laser light is applied (the ion–ion spacing is 4 mm in the figure). Other lasers
can provide qubit-state-dependent forces that can entangle the ions throughtheir Coulomb interaction. b, Surface ion trap chip with 200 zones
distributed above the central hexagonal racetrack of width 2.5 mm(photograph courtesy of J. Amini and D. J. Wineland). c, Schematic of
optical lattice of cold atoms formed by multi-dimensional optical standing
wave potentials (graphic courtesy of J. V. Porto). d, Image of individual Rb
atoms from a Bose condensate confined in a two-dimensional optical lattice,with atom–atom spacing of 0.64 mm (photograph courtesy of M. Greiner).
Photo © Oxford Ion trap grouppure quantum state, and are thus favoured in current experiments.
Recently, up to eight trapped ion qubits have been entangled in thisoptical lattices for quantum computing are the controlled initialization, interaction and measurement of the atomic qubits. However,there has been much progress on all of these fronts in recent years.
Optical lattices are typically loaded with 103–106 identical atoms,
usually with non-uniform packing of lattice sites for thermal atoms.
However, when a Bose condensate is loaded in an optical lattice, thecompetition between intrasite tunnelling and the on-site interaction
between multiple atoms can result in a Mott-insulator transition
where approximately the same number of atoms (for example,one) reside in every lattice site34. The interaction between atomic
qubits in optical lattices can be realized in several ways. Adjacentatoms can be brought together depending on their internal qubit
levels with appropriate laser forces, and through contact interactions,entanglement can be formed between the atoms. This approach has
been exploited for the realization of entangling quantum gate operations between atoms and their neighbours35. Another approach
exploits the observation that when atoms are promoted to Rydberg
states, they possess very large electric dipole moments. The Rydberg‘dipole blockade’ mechanism prevents more than one atom frombeing promoted to a Rydberg state, owing to the induced level shiftof the Rydberg state in nearby atoms. Recently, the Rydberg blockade
was used to entangle two atoms confined in two separate optical
dipole traps36,37, and it should be possible to observe this between
many more atoms in an optical lattice.
For trapped atoms and ions, coherence times are many orders ofmagnitude longer than initialization, multi-qubit control, and meaCredit: J. Jost/NIST
surement times. The critical challenge for the future of trapped atom
quantum computers will be to preserve the high-fidelity control
already demonstrated in small systems while scaling to larger, more

ダイヤモンド電子スピンと核スピンの間の量子制御
窒素原子の核スピン

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結晶内の欠陥が作る電子スピン 



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量子情報技術とは✤様々なレベルでの量子制御により、従来の技術原理では原理的に到達できない性能を可能にする。
✤

高精度の測定✤複雑系のシミュレーション✤

高性能の計算✤安全な通信…など

LIGO@US

東京QKDネットワーク@NICT

量子情報技術：従来の方法では原理的に出来ないことを、様々なシーンで可能にする量子コンピュータの中身？

量子情報科学・技術の発展
a

計算の速さ

コンピュータの大きさ

b-2.2-2.2

10-3.0log10 (years)

log10 ( p)

16-3.7-4.5-3.7

0-5-5.2

10億5-4.5-5.2

14log10 (number)

1年-3.0

1210
8
6-6.0

1

162564096

Problem size, L65536

220-10-6.0

1162564096

Problem size, L

768−ビットRSA modulus、数年

65536

2204広がる量子情報領域 ：超伝導素子
Qubit

0.5 mmNV diamond[100]|↓>|R> |L>
Josephson
junctions

DcSQUID

Flux qubit

106ものNVセンターのアンサンブル

２つの巨視的な物理系の間で量子がやりとりできる
これまでは実現出来なかった量子領域へ量子力学系

Nature Nanotechnology 4, 404 - 405 (2009)
doi:10.1038/nnano.2009.169
Science 24 November 2000: vol. 290 no. 5496, 1532-1535

エネルギーレベルの離散化
新しい物理の出現量子情報科学・技術の発展

新しい技術が拓く、新しい科学・技術