Post on 10-Aug-2020
Shuntaro Takeda1The University of Tokyo
2JST PRESTO
An Introduction to Quantum
Computing: From Basic
Concepts to Hardware
@shuntaro_takeda
~20 people in total
Self-introduction
Professor
A. Furusawa
Project Lecturer
S. Takeda
- Department of Applied Physics, The Univ. of Tokyo
- Research on optical quantum information processing
Oct. 1st, 2019
Became Associate Professor
and started my own group!
An Introduction to Quantum
Computing: From Basic
Concepts to Hardware
1. Introduction
2. Basic principles of quantum computing
3. Quantum algorithms
4. Hardware implementations
What is a quantum computer?
Quantum computers are quantum mechanical
devices that enable us to perform certain
computational tasks more efficiently than what
is possible on classical (existing) computers.
Simulation of
quantum systems
Optimization Machine learning
Applications:
IBM’s commercial QCs
QC is now an exceptionally hot topic!
Heavy investment in USA/Europe/China
Japan started a big project
Much attention
from industry
History of quantum computing
1980’s Proposal of quantum computingD. Deutsch
R. Feynman
2010’s Companies join quantum computer race
・Small-scale QCs with tens of qubits have emerged
1990’s Quantum algorithm discovered
・Integer factorization(Shor, 1994)・Quantum error correction(Shor,1995)・Database search(Grover, 1996)
2000’s Development of basic technologies
・Basic experiments with spins, ions, photons, etc.
There’s still a long way to go to build a practical QC
・Formalization of QC (Deutsch, 1985)
An Introduction to Quantum
Computing: From Basic
Concepts to Hardware
1. Introduction
2. Basic principles of quantum computing
3. Quantum algorithms
4. Hardware implementations
Double-slit experiment
Classical mechanics
Quantum mechanics
Two slits
Electron, atom,
photon, etc.
Interference
“Left” or “Right”
Superposition
RightLeft
Measurement
Wall
Introduce these principles
into computing!
Principle of quantum computing
Classical computer’s information unit
0 1or
Bit
Quantum computer’s information unit
01
Qubit
Superposition10 10 cc
12
1
2
0 cc
0
1x
z
y
12
sin02
cos ie
“Bloch sphere”Real
Principle of quantum computing
Classical computer’s information unit
0 1or
Bit
Quantum computer’s information unit
01
Qubit
Superposition10 10 cc
12
1
2
0 cc
0
1
2
00 cP
2
11 cP
Measure
Principle of quantum computing
Classical computer’s information unit
Quantum computer’s information unit
Two bits
or or or
01
Two qubits
0111100100 11100100 cccc
Superposition
12
11
2
10
2
01
2
00 cccc
n qubits can be any superposition of 2n states
n bits can be only one of 2n states
Classical computer’s logic gates
Quantum computer’s logic gates
0 1
Principle of quantum computing
1
11
01 01
1-bit NOT 2-bit AND
R̂
1-qubit rotation
1 0
10 10 cc 10 10 cc
otherwise 0
Classical computer’s logic gates
Quantum computer’s logic gates
0 1
Principle of quantum computing
1
11
1-bit NOT 2-bit AND
R̂
1-qubit rotation 2-qubit Controlled-NOT
1 0
otherwise 0
0 01 1
0 11
11
R̂
1 0
0 01 1
101 0
01 01
01 01
1-bit NOT 2-bit AND
Classical computer’s logic gates
2-qubit Controlled-NOT1-qubit rotation
Quantum computer’s logic gates
otherwise 0
Principle of quantum computing
11100100 11100100 cccc
10110100 11100100 cccc
R̂ R̂
R̂
R̂
Classical computer’s calculation
Quantum computer’s calculation
01
01
01
01
01
01
01
01
0
1
1
0 0
0
1
Perform multiple
calculations
in parallel
Perform only
one calculation
at a time
NOT
AND
C-NOT
Rotation
Principle of quantum computing
111100010000 111100010000 ccc
R̂ R̂
R̂
R̂
Classical computer’s calculation
Quantum computer’s calculation
01
01
01
01
0
1
1
0 0
0
1 Perform only
one calculation
at a time
NOT
AND
Principle of quantum computing
111100010000 111100010000 ccc
Quantum algorithm
needed
Meas.
Meas.
Meas.
Meas.Only one
outcome can
be read out
An Introduction to Quantum
Computing: From Basic
Concepts to Hardware
1. Introduction
2. Basic principles of quantum computing
3. Quantum algorithms
4. Hardware implementations
Quantum algorithm
- Quantum computers are only better than
classical computers at specific computational tasks
- What problems will we use quantum computers to
solve? What algorithms will solve them?
VS
・Database search
・Integer factorization
・Quantum simulation
Examples
Database search
https://slideplayer.com/slide/3169508/
Search space size N
Num
ber
of opera
tions
Grover’s algorithm (Grover, 1996)
- Searching through a database for a specific item
- Application: optimization, NP-complete problems, etc.
- Quadratic speedup over classical algorithm
Yamada 2359
Suzuki 8723
Hayashi 3850
Sato 1123
Tanaka 5678
Database
N
Enter PINQuantum
Database search
Classical algorithm
- Sequentially try all N possibilities
- Average search takes N/2 steps
Grover’s algorithm
- Simultaneously try all possibilities
- Average search takes N1/2 steps
Enter PIN
1 2 3 4Wrong!
Correct!or
×N/2
2 5 9 1Correct PIN
×N1/2
0 0 0 00 0 0 10 0 0 2
9 9 9 9
Superposition
01
01
01
Database searchGrover’s algorithm’s circuit (3-qubit case)
1. Equal superposition of all states
2. Selectively invert the solution state
Inter-
ference
3. Invert all states about the mean
111001000 111001000 ccc
Am
plit
ude
0mean
Inter-
ference
Database searchGrover’s algorithm’s circuit (3-qubit case)
01
01
01
Inter-
ference
111001000 111001000 ccc
Am
plit
ude
0
1. Equal superposition of all states
2. Selectively invert the solution state
3. Invert all states about the mean
Repeat
~N1/2
times
Inter-
ference
Database searchGrover’s algorithm’s circuit (3-qubit case)
01
01
01
Inter-
ference
111001000 111001000 ccc
Am
plit
ude
0
1. Equal superposition of all states
2. Selectively invert the solution state Repeat
~N1/2
times3. Invert all states about the mean
0
1
1
Meas.
Meas.
Meas.
Inter-
ference
Database searchGrover’s algorithm’s circuit (3-qubit case)
01
01
01
Inter-
ference
1. Equal superposition of all states
2. Selectively invert the solution state Repeat
~N1/2
times3. Invert all states about the mean
0
1
1
Meas.
Meas.
Meas.
Simultaneously investigate all patterns by superposition
Increase the amplitude of the solution by interference
Quadratic speedup!
Quantum algorithm
・Database search
・Integer factorization
・Quantum simulation
- Quantum computers are only better than
classical computers at specific computational tasks
- What problems will we use quantum computers to
solve? What algorithms will solve them?
VS
Examples
Integer factorizationShor’s Factoring algorithm(Shor, 1994)
- Factoring integers efficiently (e.g. 191207=367×521)
https://github.com/mett29/Shor-s-Algorithm
1010
1020
1030
Num
be
r of op
era
tion
s
100
0 50 100 150 200 250
Number of digits d
exp(const×d1/3)
Best classical
algorithm
const×d3
Shor’s algorithm
- Exponential speedup over classical algorithm
- Application: breaking RSA encryption
speedup
Quantum simulation
Quantum simulation
- Application: material & chemical engineering
“Nature isn't classical, dammit, and if you
want to make a simulation of nature, you'd
better make it quantum mechanical, and by
golly it's a wonderful problem, because it
doesn't look so easy.” (1982)
R. Feynman
Shown to be correct! Science 273, 1073 (1996)
- Classical simulation of quantum systems
(such as molecules) is hard
- QCs can simulate dynamics or find ground states of
a Hamiltonian Science 309, 5741 (2005)
Quantum algorithm
・Database search
・Integer factorization
・Quantum simulation
- Quantum computers are only better than
classical computers at specific computational tasks
- What problems will we use quantum computers to
solve? What algorithms will solve them?
VS
Examples
Quantum algorithm
About 60 kinds of quantum algorithms
An Introduction to Quantum
Computing: From Basic
Concepts to Hardware
1. Introduction
2. Basic principles of quantum computing
3. Quantum algorithms
4. Hardware implementations
0
1
1
0 0
0
1
Hardware of classical computer
Vth
Time
VoltageControl of
voltages by
transistors
Bit Logic gates
Hardware of quantum computer
R̂ R̂
R̂
R̂
01
01
01
01
Meas.
Meas.
Meas.
Meas.
Qubit
Any system that obeys
quantum mechanics
Quantum logic gates
Control of quantum states
of the system
atom
electron
photon
Hardware of quantum computer
R̂ R̂
R̂
R̂
01
01
01
01
Meas.
Meas.
Meas.
Meas.
atom
electron
photon
111100010000 111100010000 ccc
Small change = error
Error is accumulated
Qubit
Any system that obeys
quantum mechanics
Quantum logic gates
Control of quantum states
of the system
Hardware of quantum computer
Building a quantum computer is super difficult!
atom
electron
photon
Qubit
Any system that obeys
quantum mechanics
Quantum logic gates
Control of quantum states
of the system
Hardware of quantum computer
Various systems to build a quantum computer
- Superconducting circuits
- Trapped ions
- Semiconductor quantum dots
- Photonics
- Neutral atoms
- Diamond vacancies
- Topological qubits
・・・
Tens of qubits
>99% gate accuracy
A few qubits
Low gate accuracy
All approaches have pros & cons!
Superconducting circuits
Refrigerator
Superconducting
chip (10~20mK)
Superconducting chip
Device
Superconducting circuits
etc.
qubit
Electric
wiring
0 1
ElectrodesJosephson
junction
Qubit
High gate accuracy>99%
Scalable fabrication
×Short lifetime of qubits
×Requires cryogenic temperature
Device
Electrodes
Trapped ions
Vacuum
chamber
Ions
Ion
0
1
Qubit
High gate accuracy>99%
Long lifetime of qubits
×Low gate speed
×Requires vacuum
Semiconductor quantum dots
DeviceElectrodes
Electrons2DEGelectron
spin
0 1
Qubit
Small footprint
×Gate accuracy is still low
×Requires cryogenic temperature
Photonics
Optical
circuit
Device
V-pol H-pol
Photon
Qubit
0 1crystal Photon
Room temperature/ in Air
High gate speed
×Probabilistic operation
×Gate accuracy is still low My tomorrow’s talk!
100 101 102 103 104 105 106 107 108
10%
1%
0.1%
0.01%
0.001%
Number of qubits
Gate
err
or
Roadmap to practical QC
Practical
QC
Current state-of-the-art
Improve quantity & quality
Introduce error correction
Factoring/Database search
NISQ=Noisy Intermediate-Scale Quantum computer
Recent trend: Developing useful algorithms that run
on NISQ computers (without error correction)
An Introduction to Quantum
Computing: From Basic
Concepts to Hardware
1. Introduction
2. Basic principles of quantum computing
3. Quantum algorithms
4. Hardware implementations
Summary of quantum computing
Basic principles Algorithm
Hardware
・Database search
・Integer factorization
・Quantum simulation
- All approaches have pros & cons
- There’s still a long way to go to build a practical QC
Qubit & quantum logic gates
& measurement
etc.