Appendix
Quantum Supremacy
Quantum Fourier transformation
Quantum Teleportation
Error-tolerable quantum computing
Quantum Random numbers

A1. Quantum supremacy
Speed of Computation
Quantum computer >> Ordinary computer
In 2015, Google and NASA reported that D-Wave quantum
computer works 10^6 faster than a regular computer chip !
In 2019, Google publishes the quantum supremacy claim.
Nature, vol. 574, no. 7779, Oct. 2019, pp. 461+
In 2020, University of Science and Technologyof China (中国科学技術大学) announced theyrealized Quantum supremacy by 「九章」
(Jiuzhang). 九章2号 was announced (2020)

A2. Quantum Fourier Transformusing Qiskit
https://qiskit.org/textbook/ja/ch-algorithms/quantumfourier-transform.html

目からうろこのフーリエ変換

フーリエからシュレーディンガーまで

What is Qiskit？

https://ja.wikipedia.org/wiki/Qiskit

3池田 直量子フーリエ変換
このチュートリアルでは、量子フーリエ変換（QFT）の紹介と、回路の導出、Qiskitを使用した実装を紹介します。
実装においては、シミュレーターと5量子ビットデバイスでQFTを実行する方法を示します。
目次
1.はじめに
2.直感的解釈https://qiskit.org/textbook/ja/ch-algorithms/
quantum-fourier-transform.html

2.1 フーリエ基底での計算
3.例 1: 1量子ビットQFT
4.量子フーリエ変換
5.QFTを実装する回路
6.例 2: 3量子ビットQFT
7.QFT回路の形式に関する注意
8.Qiskitでの実装
8.1 3量子ビットでの例
8.2 一般的なQFT関数
8.3 実量子デバイスでのQFTの実行
9.問題
10.参考文献

4A3. Quantum Teleportation
1. Alice has a qubit, Q with state | Ψ>.
Alice wishes to transmit the state Ψ| >to Bob

AliceBob 2. Alice starts with two additional qubits,

Alice will transmit
the state of a qubit,Q
Alice’s qubit

which we label R and S.
S will be sent to Bob, and the otherwill stay with Alice.

Receiver3. Alice prepares an entangle state withqubits R and S.

Bob’s qubit 4. Alice sends quibit S to Bob

Assist qubit
5

5. Alice perform a measurement
on her original qubit Q and half of R

A4. Error-tolerable quantum computing(誤り耐性量子計算)
1995, Shor et al shows that quantum error
correction is possible, in spite of the no-cloningtheorem.
No-cloning theorem: (量子複製不可能定理)
The theorem forbids the creation of identical copies
of an arbitrary unknown quantum state.
W. Wootters and W. Zurek,"A Single Quantum Cannot be Cloned” Nature 299: 802‒803.
D. Dieks,"Communication by EPR devices” Physics Letters A 92: 271
6

A5. Quantum Random Number Generators
Kindleご利用いただけるサンプル:• Important for Monte Carlo simulationsKindle

Quantum Random Number
Generation: Theory and Practic…
(Quantum Scienceand1 評価Technology)

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発送・販売元: SuperBookDeals_。

その他の購入オプションを表示する• But old pseudo-random number such as“Linear congruential method”, “Mersennetwister” are not enough ?

• If Quantum computers run very fast, we needlots of Random numbers …

https://read.amazon.co.jp/sample/3319725947?f=4&l=ja_JP&rid=XBNGG3JM8KXH4NQZNZR3&sid=356-3879328-3928547&ref_=litb_d7

1 / 1ページ

A6.Comparison of R/D among
Japan, US, Europe, China
from JST CRDS “R/D and industry trends”
Hardware
Basic research
Application
research
Software
Basic research
Application
researchJapanUSEurope

ChinaEntropy
Entropy is important quantity.
S A= -Tr ρAln ρA
But it is non-trivial to calculate it on the Lattice.

In the previous analysis, we got reasonable results.
But we suffered from large errors especially near the phase transition point.
Simulations with the renormalization-group improved action will improve
this situation.

Quantum annealing
Developped by D-W ve Systems

1. Backgroud・In 2013 IT consumed around 10 % of the world power generation
Big IT companied construct their data-center at cool areas, for reducing
power for the cooling・Quantum anneaaling machines using the super-conductivity quantum bits isaround 20kW:
corresponding ca. 50 houses in Japana(in case of Super computer, K, around 300,000 houses)

What is Quantum Annealing（D-Wave System Documentation documentation.pdf）

What is Quantum Annealing (contin.)
Intuitive explanation by D-Wave in youtube
https://youtu.be/zvfkXjzzYOo

D-Wave company page:Big Di culty of Quantum Computers
Quantum Computers will run much fasterthan super-computers.

But

Noise problem !

Noise due to decoherence and other quantum noise
For the perfect coherence,the system should be perfectlyisolated.

Noise from disturbances in Earth’s magnetic field,
local radiation from Wi-Fi or mobile phones, cosmic rays,
and even the influence that neighboring qubits

Quantum error correction is inevitable, but not so easy.
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