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

FEFU

Moscow city

Atsushi Nakamura
May 19, 2022

Osaka Castle

Subjects today
What shall we do next ?

How aboutEntanglement Entropy !

Participants
Zakharov
Bornyakov
Molochkov
GoyRagalyov
Kudrov

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

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.

D-wave (cont.)

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>” ?.

ChinaBaidu has released a superconducting
quantum computer “Qian Shi”(乾始)チエン?

Baidu (China) announced theirfirst quantum computer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

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.
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
Letter

PoS LAT2009:188,2009
arXiv:0911.2596 [hep-lat]Entanglement in four-dimensional SU(3)gauge theory
Etsuko Itou1,∗ , Keitaro Nagata1,∗ , Yoshiyuki Nakagawa2 , Atsushi Nakamura3,4,5,∗ ,and V. I. Zakharov5,6,7,∗
1Itou, Nagata, Nakagawa, Nakamura and Zakharov
Prog. Theor. Exp. Phys. (2016) 061B01

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
6ITEP, B. Cheremushkinskaya 25, Moscow, 117218 Russia
7
Moscow 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
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 !−1
QCD!
"−1∼ Tc scale, the entropic c-function decreases smoothly, and it is consistent with zero withinerror bars at l " 0.9 fm.

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

Measure

Moon
19ffA

ActionNo 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 gaugetheory”• 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.

Subjects not discussed today• Quantum supremacy (量子超越性)

A1• Quantum Fourier Transform

A2• Quantum Teleportation

A3• Error-tolerable quantum computing

A4(誤り耐性量子計算)

A5• Quantum Random Numbers• Inside of the hardware
24