Quantum Computers
for
Nuclear/Particle Physicists
Atsushi Nakamura
RCNP, RIKEN and Far Eastern Federal Univ. at Vladivostok
in collaboration withTaizo Sasaki
May, 2023
1

Contents of a recent book, “QuantumComputing: An Applied Approach” J.D. Hidary• I Foundation• 1. Superposition, Entanglement and Reversibility• 2. A Brief History of Quantum Computing• 3. Qubits, Operators and Measurement• 4. Complexity Theory• II Hardware and Applications• 5. Building a Quantum Computer• 6. Development Libraries for Quantum Computer Programming• 7. Teleportation, Superdense Coding and Bell’s Inequality• 8. The Canon: Code Walkthroughs$26.49

Contents of a recent book, “QuantumComputing: An Applied Approach” (cont.)• 9.Quantum Computing Methods• 10. Applications and Quantum Supremacy• III Toolkit
Oh, any physics
department student
knows these !

• 11. Mathematical Tools for Quantum Computing I(Linear Algebra, Complex Numbers and the Inner Product, Matrix, Outer product and Tensor produ
Set Theory, Linear Transformation, Vector space, Linear Independence)• 12. Mathematical Tools for Quantum Computing IISo, we can skip
these,and we attack theessential points now.

(Linear Transformations as Matices, Matirces as Operators, Eigenvectors and Eigenvalues, InnerProducts, Hermitian Operators, Unitary operators, Dirac Sum and Tensor product, Hilbert Space,Qubit as a Hilbert Space• 13. Mathematial Tools for Quantum Computing III(Boolean Functions, Logarithms and Exponentials, Euler’s Formula• 14. Dirac Notation• 15. Table of Quantum Operators and Core Circuits

Table of Contents・References
1. Quantum Computers- Overview 2. Two types of Quantum
Computers
3. Quantum Computers
4. Quantum Algorithms

5. Applications
6. Bleak future of Japan?
7. Big Difficulty
8. What we plan to do
9. Summary
AppendixReferences

Many physicists !

R.P.Feynman, J. Theor Phys 21, 467–488 (1982)
Feynman Lectures On Computation(Frontiers in Physics) (2000),
1984 & 86, Feynman gave a course on computation
at the CalTech“Nature isn’t classical and if you wan’t to makea simulation of nature, you’d better make itquantum mechanical”
5References
One-night
Cramming ?
night 一夜漬け？
cramming

6References (cont.)
Committee on Technical Assessment of the Feasibility and Implicationsof Quantum Computing, Ed. E.Grumbling and M.Horowitz、2020“Quantum Computing: Progress and Prospects”

Course by Andrew Ng
https://www.coursera.org/specializations/deep-learning?
Learn Quantum Computing with Python and IBM Quantum
Experience, A hands-on introduction to quantum computing
and writing your own quantum programs with Python, 2020
Quantum Computing in Practice with Qiskit andIBM Quantum Experience, H.Norlen, 20207

References (cont.)“Dancing with Qubits
How quantum computing works
andhow it can change the world”,
R. S. Sutor (2019)
D-Wave documents
https://dwavejapan.com/
Many tutorials in Youtube.
81. Quantum Computers - Overview 1980 Paul. A. Benioff (young physicist at Argonne National Lab)“The computer as a physical system: A microscopic quantum mechanicalHamiltonian model of computers as represented by Turing machines”,
J. of Statistical Physics 22(5):563, 1980
Quantum Computer can run without energy consumption.

1982 R.P.Feynman“Simulating physics with computers”
J. Theor Phys 21, 467–488 (1982).11,086 citations

Feynman at CalTech

1985 D. Deutsch (British physicist at the University of Oxford)
Quantum Turing machine
1989 D. Deutsch, Quantum circuit, Proc. R. Soc. Lond. A439 553–558
9

Why the factoringis important ?

RSA (Rivest‒Shamir‒Adleman) public-key
cryptosytem uses factorization

1992 D. Deutsch and R.Jozsa,“Rapid solution of problems by quantum computation”
3,627
citations
Proc. R. Soc. Lond. A439 553–558

1993 E. Bernstein and U. Vazirani
1994 P. W. Shor (American mathematician)

Shor“Algorithms for quantum computation:
24=2^3x3,90=2x3^2x5,….
discrete logarithms and factoring”

Store now, decrypt later !

Oh, I can crack crypt-systems!
I will collect public keys, and I willbuy Quantum Computers.
10D-waveIBMThis is the Coolingdevice part.

11The rst made-in-Japan
Quantum computer ?
announced on March 24, 2023

Baidu has released a superconducting
quantum computer “Qian Shi”(乾始)チエン?
Baidu (China) announced their
rst quantum computer

fifi

RIKEN Center for
Quantum Computing

Where are Quantum Computers in Japan
IBM-UTokyo lab. Hongo Campus
Fujitsu and Toshiba proceed Quantum computer studies.
Several companies might have in-house.
Gemini-mini by SpinQ, China, (深圳市)シンセン（1180,000Yen, 118万円)
1. Slower than human-being !
2. Japanese agency sold them(Therst shipment was sold out !)fi13

Where are Quantum Computers in Japan(2)Japan• Osaka university

QIQB (Center for Quantum
Information and Quantum Biology)• RIKEN

RQC (RIKEN Center for Quantum Computing)• IBM-University of Tokyo Laboratory
14

NECFujitsu

Quantum Annealer
Quantum Computer developed by NEC(Quantum Annealing method)（Mock-up）
https://www.nikkei.com/article/
DGXZQOUC235X10T20C22A6000000/
15

Where are Quantum Computers in the World (1)US• BNL Co-Design Center for Quantum Advantage (C2QA), now only design?
• IBM, Argonne National Laboratory (building?)• Tangle Lake (Intel chip for Quantum Computers ?)Tangle Lakein Alaska

49 quantum bit Intel chip16

Where are Quantum Computers in the World (2)Canada• D-Wave
Korea• Quantum Information Institute@Yonsei University (with IBM)

Korea Goes Quantum
17Where are Quantum Computers in the World (3)Russia18

Calculation Speed of Quantum Computer8

1.58 * 10 faster !
Really ?

• Quantum computing is a new generation oftechnology that involves a type of computer
158 million times faster than the most sophisticatedsupercomputer we have in the world today.
https://www.livescience.com/quantum-computing
By Mark Smith published March 18, 202219

2.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 ?

20

3. Quantum computers
What is Quantum computer ?

Quantum computing(Redirected from Quantum computer)
A quantum computer is a computer that exploits quantum
mechanical phenomena. At small scales, physical matter
exhibits properties of both particles and waves, and quantum
computing leverages this behavior using specialized hardware.
Classical physics cannot explain the operation of thesequantum devices, and a scalable quantum computer could
perform some calculations exponentially faster than any
modern "classical" computer. In particular, a large-scalequantum computer could break widely used encryption
schemes and aid physicists in performing physical simulations;however, the current state of the art is still largely experimentaland impractical.

Wiki-pedia
History
Quantum information processing
Communication
Algorithms
Engineering
TheoryToggle Theory subsection
See also
Notes
References
Further reading

The basic unit of information in quantum computing is thequbit, similar to the bit in traditional digital electronics. Unlike a classical bit, a qubit can exist in asuperposition of its two "basis" states, which loosely means that it is in both states simultaneously.
When measuring a qubit, the result is a probabilistic output of a classical bit. If a quantum
computer manipulates the qubit in a particular way, wave interference effects can amplify thedesired measurement results. The design of quantum algorithms involves creating procedures thatallow a quantum computer to perform calculations efficiently.
Physically engineering high-quality qubits has proven challenging. If a physical qubit is not
sufficiently isolated from its environment, it suffers from quantum decoherence, introducing noise
into calculations. National governments have invested heavily in experimental research that aims
to develop scalable qubits with longer coherence times and lower error rates. Two of the mostpromising technologies are superconductors (which isolate an electrical current by eliminating
electrical resistance) and ion traps (which confine a single atomic particle using electromagneticfields).
Any computational problem that can be solved by a classical computer can also be solved by aquantum computer.[2] Conversely, any problem that can be solved by a quantum computer canalso be solved by a classical computer, at least in principle given enough time. In other words,
quantum computers obey the Church–Turing thesis. This means that while quantum computersprovide no additional advantages over classical computers in terms of computability, quantum
algorithms for certain problems have significantly lower time complexities than corresponding
known classical algorithms. Notably, quantum computers are believed to be able to solve certain
problems quickly that no classical computer could solve in any feasible amount of time—a featknown as "quantum supremacy." The study of the computational complexity of problems withrespect to quantum computers is known as quantum complexity theory.

History21

For many years, the fields of quantum mechanics and computer science formed distinct academic
communities.[3] Modern quantum theory developed in the 1920s to explain the wave–particle

Hardware• Superconductivity method• Ion-Trap method (Ion Q etc)
• Many others

35,900 articles !

RCNP can make it !

NISQ era
Often, I see the word NISQ.
What does it mean?
How do I pronounce ?

Until the full-spec Quantum Computer come,NISQ (Noisy Intermediate-Scale Quantum Computer）
plays role.

（ノイズがある中規模の量子コンピュータ）

Quantum computers (cont.)
Quantum bit (Q-bit)States:|ψ> =α|0> + β|1>

Entanglement （もつれ）Superposition24

Entanglement

Past

Entanglement Entropy in Yang-Mills theory: towards a simple model
E. Itou,1, 2 A. Nakamura,3, 4, 5 and V.I. Zakharov6, 4, 7, ∗1

Department of Mathematics and Physics, Kochi University, 2-5-1 Akebono-cho, Kochi 780-8520, Japan
2
Research Center for Nuclear Physics, Osaka University, Osaka, 567-0 047, Japan
3
Research Center for Nuclear Physics, Osaka University, Osaka, 567-0047, Japan
4
School of Biomedicine, Far-East Federal University, Vladivostok, Russia
5
Nishina Center, RIKEN, Wako 351-0198, Japan
6
ITEP, B. Cheremushkinskaya 25, Moscow, 117218 Russia
7Moscow Inst Phys & Technol, Dolgoprudny, Moscow Region, 141700 Russia.
We comment on theoretical implications of recent measurements of entanglement entropy in
SU(3) Yang-Mills theory. We argue that the data represent a clean evidence against the Hagedorn
mechanism of the deconfining phase transition. Holographic models, on the other hand, naturallyaccommodate alternative mechanisms of the phase transition. Next, we (approximately) relate
correlation lengths revealed in measurements of the entanglement entropy and near (and above)the deconfining phase transition. This prediction of holography seems to be in reasonable agreementwith the data.
INTRODUCTION

Dynamics of phase transitions is one of the most
discussed and difficult problems of theories with strong
interactions. One of the earliest and best known models
is due to R. Hagedorn [1] who suggested that density ofstates of hadrons grows exponentially with mass M of
the resonances:such as existence of a finite correlation length.
Moreover, a geometric approach to evaluating
entanglement entropy in relativistic quantum field
theories has been developed [6]. This geometric approach
was generalized to the case of holographic models sothat the geometry of the extra dimensions determines
properties of the entanglement entropy of field theory
living on the boundary [7]. The entanglement entropy isrelated to the minimal value of a geometric volume in
the bulk which has, as its boundary the volume of lowerdimension on which the field theory is defined.
Since the value of the Wilson line is determined bythe minimal area spanned on it in the bulk, holography

Entanglement

States which(1)we cannot write

ρ(m) ∼ exp(βH m) ,as| i = | A i| B i

ff

where βH is a constant. Then, it is straightforward tosee that 1/βH represent a limiting temperature for asystem with spectrum (1). Later, it was recognized thatNow

AMeasure

BActionNo e ect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>26

4. Quantum Algorithms
Coppersmith (1994)
Quantum Fourier TransformShor (1994)
Finding the prime factors

Grover (1996)
Database search

Simon (1994,1997)

Simon wrote a story:
The paper was rejected at a theoretical computerscience conference (STOC 1993), Peter Shor on
the program committee for that conference
realized the value of the paper. but could not
persuade the committee to accept the paper.
He submitted his paper to the next major theoreticalcomputer science conference (FOCS 1993) inparallel with resubmitted paper by Simon.
Shor proposed, if only his paper was accepted, but
not Simon’s, he merged two papers.
At the end, both were accepted and got each credit.

fi

One can determine the periodicity of a function exponentially faster on aquantum computer compared with a classical computer.
(Simon’s algorithm is the rst example of an exponential speedup over thebest known classical algorithm by usingaquantumcomputer.
)27

5. Applications•Quantum Teleportation•Data search•Decryption (暗号解読！)28

6. Bleak future of Japan?
暗雲がNEC: 2020年 筑波研究所は閉鎖「量子ビットを動かすことはできたが、動作する時間は非常に短いものだった」
実用に耐えるレベルまでもっていくには長い年月が必要となった。その過程で、予算規模で勝る米中勢に追い抜かれてしまった
ブルーキャット社
社長

Quantum Computeris a mirage.
The noise problem
is too hard.
Mathematician atHebrew University

7. Big Di culty
Noise problem !
Quantum error correction is inevitable,
but not so easy.

ffi30

8. What we plan to do
1. To use Quantum Computer for lattice QCD
simulations.
2. Application to football trajectories(supervised by Prof. Asai)
Because Quantum Computers run so fast,
before a kicked ball reaches the goal, thecalculation is over !

3. Fluid-Dynamics of Wind instrument
Fluid-Dynamics is clasical, but it requires
huge computational power.

flSasakiʼsuteSummary
Good news:
Quantum physics is our daily tool.
Therefore,
we can easily start quantum computer research.

Bad news:
At this moment,(1) it is unclear whether the quantum computerhas promising future or not.
(2) not so easy to try a real machine.
32

I have a dream:
I use Quantum Computerin lattice QCD simulations.
orWrite down all lattice QCD code
for Quantum Computer !
I hope RCNP introduces a Quantum Computer !
Surely, RCNP high energy group can build
a house maid one.
33

How to use Quantum Computerin High-Energy Physics

Great Sword !
But what isyour Target ?

Molecular Dynamics
in Lattice QCD,
which requires
the computer resource.

Or it is a fun
to write all QCD codeon Quantum Computer.

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

A1• Entanglement Entropy

A2• Quantum Fourier Transform

A3• Quantum Teleportation

A4• Error-tolerable quantum computing

A5(誤り耐性量子計算)

A6• Quantum Random Numbers• Inside of the hardware
35

Backup Slides
A1. Quantum supremacy
A2. Entanglement Entropy in Field Theories
A3. Quantum Fourier Transform using Qiskit
A4. Quantum Teleportation
A5. Error-Tolerable quantum computing
A6. Quantum Random Number Generators

36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」
(Jiu zhang). 九章2号 was announced (2020)

Photo by Kaori Nakamura

A2.Entanglement Entropy in Field Theories
量子コンピュータと何の関係があるの？

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

Famous Example•

EarthMoon38

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

39

Why Interesting
Information for studying the vacuum of eld theories
So farCorrelation functions
Entanglement Entropy may be a new Probe
Interesting to study SU(3), U(1), scalar
Entanglement Entropy may show characteristicfeature at Critical Point
What happens at nite temperature and density
phase transition ?
Entanglement Entropy measures the Degrees ofFreedom.
2
QCD: con nement O(1), Decon nement O(Nc )fifififi40

And many interesting works
Gravity, Black holee.g., Ryu-Takayanagi, 2006
Tensor Network, MERA (Multi-scale
Entanglement Renormalization Ansatz)
Condensed Matter Physics
e.g., Ogawa, Takayanagi, Ugajin - JHEP, 2012etc etc41

A3. 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/Qiskit42

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

43

A4. Quantum Teleportation1. 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 qubit S to Bob

Assist qubit
44？

5. Alice perform a measurement
on her original qubit Q and half of RA5. 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
45

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A7. 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)

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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 …

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