The Next Project— Moscow, Vladivostok, Osaka —10:00 Moscow
16:00 Japan
17:00 Vladivostok

FEFU

Moscow city

Atsushi Nakamura
May 19,2023

Osaka Castle

Subjects today

Participants
Zakharov
Bornyakov
Molochkov
GoyRagalyov
KudrovWhat shall we do next ?

How aboutEntanglement Entropy !
2

HosakaNakamura
Any newcommers
are welcome

First let us study Entanglement

Study of Quantum Field Theory
by Numerical Simulations
Content
I. Quantum Computer
II. Entanglement
III. What shall we do ?

on Quantum Computers
3

Good paper
I thank Vitaly for
introducing this paper
to me.
Natalie Klco
(U. Washington,Seattle (main))(Oct 26, 2020)

Klco, Calculation Nature Naturally

CLICKI. Quantum Computer
D-waveThis is the Coolingdevice part.

IBM5

How to express |0> and |1>
1. Spin up and down

2. photon polarization(right and left circular polarization)
wiki-pedia

E

3. ground energy level and an excited level|1>

4. etc|0>
6

Two types of Quantum Computers
1. Gate-based quantum computer (IBM, for example)
2. Annealing type (D-wave for example)
They change to the gate method ?

Geordie Rose, the founder of D-Wave Systems7••••••IBM QzIBMDocument
worth reading

Documentation Home
Quantum computing in a nutshell
Getting started
Introduction to Qiskit
Tutorials
API Reference

https://qiskit.org/

IBM Quantum Computing
roadmap

D-wavehttps://docs.dwavesys.com/docs/latest/index.html

What is Leap ?
Look “Introductionto Leap” !

Introduction to Leap…..
…..
Run demos and interactive
coding examples in Resources.

10D-wave (cont.)

11

RIKEN Center for
Quantum
The first made-in-Japan
Quantum computer ?
announced on March 24, 2023

They use Spin-up.down
for “|0> and |1>” ?.
12

ChinaBaidu has released a superconducting
quantum computer “Qian Shi”(乾始)Baidu (China) announced theirfirst quantum computer
13

Russia

When and where ?

Russian scientists have reached the latest
milestone on the country’s quantum
computing road map, having developed
a prototype 4-qubit ion quantum
computer.

Quantum Computing in CERNIs there areal machine?
Can we useit?

Quantum technology is an emerging field of physics and engineeringthat has the potential to revolutionise science and society in the next
five to ten years. Knowledge in this rapidly evolving field has advanced
considerably, yet still, there are resources required that are notmainstream today.
CERN can be at the forefront of this revolution.

II. Entanglement

16V. Chandrasekaran, R. Longo, G. Penington and E. Witten, JHEP 02, 082 (2023)
limit in holography [24, 25], observations outside a black hole horizon were described byan algebra of Type II∞ [26].
The entanglement entropy of a local region in quantum field theory is always ultraviolet
divergent, as discovered long ago [27, 28]. An abstract explanation of why this happens
is that the algebra of observables in a local region in quantum field theory is of Type III[29], and there is no notion of entropy for a state of an algebra of Type III. By contrast,
for states of an algebra of Type II, it is possible to define an entropy, though in physica
lterms this is a sort of renormalized entropy with a state-independent divergent constant
subtracted. Thus, at least for the black hole and de Sitter space, the fact that gravity
converts the algebra of observables from being of Type III to being of Type II gives anabstract explanation of why the entropy of a region of spacetime is better-defined in the~~~~~~~~~~~Witten discussed Entanglement
11,89
全andて Quantum

E. Witten, “Entanglement Properties of Quantum Field Theory,”
Rev. Mod. Phys. 90 (2018), 045003, arXiv:1803.04993.

17

Field Theories already 2018 !

Prog. Theor. Exp. Phys. 2016, 061B01 (8 pages)
DOI: 10.1093/ptep/ptw050

Nakagawa, Nakamura, Motoki and Zakharov
Entanglement entropy of SU(3) Yang-Mills theory
LetterEntanglement in four-dimensional SU(3)gauge theory

PoS LAT2009:188,2009
arXiv:0911.2596 [hep-lat]

Etsuko Itou1,∗ , Keitaro Nagata1,∗ , Yoshiyuki Nakagawa2 , Atsushi Nakamura3,4,5,∗ ,and V. I. Zakharov5,6,7,∗
1

KEK Theory Center, High Energy Accelerator Research Organisation, Tsukuba, 305-0801, Japan
2
RIISE, Hiroshima University, Higashi-Hiroshima, Hiroshima, 739-8521, Japan
3
Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198, Japan
4
Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka, 567-0047, Japan
5
School of Biomedicine, Far Eastern Federal University, Sukhanova 8, Vladivostok 690950, Russia
6
ITEP, B. Cheremushkinskaya 25, Moscow, 117218 Russia
7Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141700 Russia∗E-mail: eitou@post.kek.jp, knagata@post.kek.jp, atsushi@rcnp.osaka-u.ac.jp, vzakharov@itep.ru

Itou, Nagata, Nakagawa, Nakamura and Zakharov
Prog. Theor. Exp. Phys. (2016) 061B01

Received March 28, 2016; Accepted April 4, 2016; Published June 2, 2016...............................................................................

Witten discussed Entanglement 2018?
Zakharov group already 2009.

We investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3)gauge theory. We present the first non-perturbative calculation of the entropic c-function(C(l)) of SU(3) gauge theory in lattice Monte Carlo simulation using the replica method.
For 0 ! l ! 0.7 fm, where l is the length of the subspace, the entropic c-function is almost
constant, indicating conformally invariant dynamics. The value of the constant agrees with that
perturbatively obtained from free gluons, with 20% discrepancy. When l is close to the !−1QCD!
"−1∼ Tc scale, the entropic c-function decreases smoothly, and it is consistent with zero withinerror bars at l " 0.9 fm.

...............................................................................

18

Subject Index

B01, B30

Entanglement Entropy in Field Theories
Past

Quantum entanglement
States which we cannot write as| i = | A i| B ieven A and B are far from each other.

Famous Example•EarthNow

B

MeasureMoon
19

ffAAction

No e ect ?

Quantum entanglement
States which we cannot write as| i = | A i| B ieven A and B are far from each other.

Famous Example•

EarthMoon
20

References
Ryu & Takayanagi• “Aspects of Holographic Entanglement Entropy”• JHEP0608:045,2006 (arXiv:hep-th/0605073)• Phys. Rev. Lett. 96 (2006) 181602
Buividovich & Polikarpov• “Numerical study of entanglement entropy in SU(2) lattice gaugetheory”• Nucl. Phys. B802 p458 (2008) arXiv:0802.4247• SU(2) numerical simulation

21

References
Calabrese & Cardy• “Entanglement Entropy and Quantum Field Theory”• J. Stat. Mech. (2004) P06002 (arXiv:hep-th/0405152)• Entanglement Entropy can be expressed as a path-integral ofregions with cuts.
Ryu & Takayanagi• “Aspects of Holographic Entanglement Entropy”• JHEP0608:045,2006 (arXiv:hep-th/0605073)• Phys. Rev. Lett. 96 (2006) 181602
Buividovich & Polikarpov• “Numerical study of entanglement entropy in SU(2) lattice gauge
theory”• Nucl. Phys. B802 p458 (2008) arXiv:0802.4247• SU(2) numerical simulation

22

III. What shall we do ?
1. Numerical study of the Entanglement Entropy
We have experience.
Very interesting and valuable for studying Quantum Field Theories
2. Study of Hadrons at finite temperature and density
Quantum computer is a good environment for this study
This is valuable for NICA and J-PARC experiments.
3. Problem: At this moment, it is unclear whether we can get GPU timeon any quantum computer.

23

Subjects not discussed today• Quantum supremacy

A1• Quantum Fourier Transform

A2• Quantum Teleportation

A3• Error-tolerable quantum computing

A4• Quantum Random Numbers

A5• Inside of the hardware
24Appendix
Quantum Supremacy
Quantum Fourier transformation
Quantum TeleportationError-tolerable quantum computing
Quantum Random numbers

25

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)26

A2. Quantum Fourier Transformusing Qiskit
https://qiskit.org/textbook/ja/ch-algorithms/quantumfourier-transform.html
目からうろこのWhat is Qiskit ?
Qiskit is an open-source softwaredevelopment kit (SDK) for working
with quantum computers at the levelof circuits, pulses, and algorithms.
Written in： Python (wiki-pedia)

27

フーリエ変換From Fourier toSchroedinger
フーリエからシュレーディンガーま池田 直

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
28

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

A4. Error-tolerable quantum
computing
1995, Shor et al shows that quantum error
correction is possible, in spite of the no-cloning
theorem.
No-cloning theorem:
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
29

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

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

ハードカバー

2023/04/08 19:48

閉じる

ハードカバー:￥20648(税込)

カートに入れる
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_d30

1 / 1ページstableA6.Comparison of R/D among
Japan, US, Europe, China

developpingfrom 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.
ffi36