Kvantecomputeren - hvad er det og hvad kan vi bruge den til?

Future Tech 2024

Jonas Neergaard-Nielsen

DTU Physics

2008

PhD fra Niels Bohr Instituttet

2008-2011

NICT, Tokyo

2011-nu

DTU Fysik

seniorforsker/lektor siden 2018

Hvem er jeg?

Udvikler fotonisk kvanteteknologi, inkl. kvantecomputere, med et fantastisk team
Underviser i Kvanteinformation og Numeriske metoder i kvanteinformation
Stor indsigt i Q. hardware - knap så meget i Q. software og Q. algoritmer

Kvanteteknologi rykker

2022

Investeringer i DK

Novo Nordisk Fondens

Quantum Computing Programme

1.5 milliarder DKK

National strategi

1.0 milliarder + 200 millioner

Investeringer i DK

Hvad er en kvantecomputer?

Hvem er jeg?

0

1 /

001101111110100110001000110011100111001100011001111010101010001001101110100110110000101101001011000010000000110001001100001100110000111000000010000100001001001111110001000110111110100011000100100110111011100101000010000000011100101111100111011111001110110110111010110111000100001011010100111001110011100110011110110000111100101001000101111000000011101110010001110111100001110010110001010011000010100001101101001001001010110011101001111111010001011111001010111100100111011101001010011010001000110011001001011001100110011100100000100010101011101111110110101001011010001110011110000011110101010100101011011011011001100110101000011001111101011010100000011101110101011011100110010111011010001010000010001010111001010010111110001111111000110000000101101101010100000100001000111110111010101011101001101111001001110011011011010111110100110100100101010001010100010111110111010111001100111000101111001100101110011001000000111110101100011001001010101000100100111110111100000100000000100010011111101001111011010111101011010101100111100001000010000100000110101000110000001100001110001100101100110110001011001110111100010011000000110101010011010000100110110010000101100101111111010000100111101101101111110110000000000011110011011011111111111011010110001110000000101001001111001010010010011101001000001111001100000000110111010000011101101111110110010011000010101010001010101100001101001000100110101110010101001110000000000100101101000011110101111111101010011111001101101011100011100100001110010001111101010110001000011001101001010010011000111111110001111000101011110000101010010011101000010100011001101110110110100000001110111011001000110010001101001101111000000000111000111001001110100111001010101100011000010110100010000001000111011001001101001101001011101010011001001101001001001000010010000000111100000110001000001101001111101110010000101110011111110000001000100001010110001100011000101001011001111010110110100000010110010100110011001100001110010011101001111001010110101000011110110110011111100000000000100010000011011111101001100010001100111001110011000110011110101010100010011011101001101100001011010010110000100000001100010011000011001100001110000000100001000010010011111100010001101111101000110001001001101110111001010000100000000111001011111001110111110011101101101110101101110001000010110101001110011100111001100111101100001111001010010001011110000000111011100100011101111000011100101100010100110000101000011011010010010010101100111010011111110100110011001011100110010000001111101011000110010010101010001001001111101111000001000000001000100111111010011110110101111010110101011001111000010000100001000001101010001100000011000011100011001011001101100010110011101111000100110000001101010100110100001001101100100001011001011111110100001001111011011011111101100000000000111100110110111111111110110101100011100000001010010011110010100100100111010010000011110011000000001101110100000111011011111101100100110000101010100010101011000011010010001001101011100101010011100000000001001011010011100100001110010001111101010110001000011001101001010010011000111101011111111010100111110011011010111000111001000011100100011111010101100010000110011010010100100110001111111100011110001010111100

Bit vs. kvantebit

0

1

001101111110100110001000110011100111001100011001111010101010001001101110100110110000101101001011000010000000110001001100001100110000111000000010000100001001001111110001000110111110100011000100100110111011100101000010000000011100101111100111011111001110110110111010110111000100001011010100111001110011100110011110110000111100101001000101111000000011101110010001110111100001110010110001010011000010100001101101001001001010110011101001111111010001011111001010111100100111011101001010011010001000110011001001011001100110011100100000100010101011101111110110101001011010001110011110000011110101010100101011011011011001100110101000011001111101011010100000011101110101011011100110010111011010001010000010001010111001010010111110001111111000110000000101101101010100000100001000111110111010101011101001101111001001110011011011010111110100110100100101010001010100010111110111010111001100111000101111001100101110011001000000111110101100011001001010101000100100111110111100000100000000100010011111101001111011010111101011010101100111100001000010000100000110101000110000001100001110001100101100110110001011001110111100010011000000110101010011010000100110110010000101100101111111010000100111101101101111110110000000000011110011011011111111111011010110001110000000101001001111001010010010011101001000001111001100000000110111010000011101101111110110010011000010101010001010101100001101001000100110101110010101001110000000000100101101000011110101111111101010011111001101101011100011100100001110010001111101010110001000011001101001010010011000111111110001111000101011110000101010010011101000010100011001101110110110100000001110111011001000110010001101001101111000000000111000111001001110100111001010101100011000010110100010000001000111011001001101001101001011101010011001001101001001001000010010000000111100000110001000001101001111101110010000101110011111110000001000100001010110001100011000101001011001111010110110100000010110010100110011001100001110010011101001111001010110101000011110110110011111100000000000100010000011011111101001100010001100111001110011000110011110101010100010011011101001101100001011010010110000100000001100010011000011001100001110000000100001000010010011111100010001101111101000110001001001101110111001010000100000000111001011111001110111110011101101101110101101110001000010110101001110011100111001100111101100001111001010010001011110000000111011100100011101111000011100101100010100110000101000011011010010010010101100111010011111110100110011001011100110010000001111101011000110010010101010001001001111101111000001000000001000100111111010011110110101001100001100110000111000000010000100001001001111110001000110111110100011000100100110111011100101000010000000011100101111100111011111001110110110111010110111000100001011010100111001110011100110011110110000111100101001000101111000000011101110010001110111100001110010110001010011001111010110101011001111000010000100001000001101010001100000011000011100011001011001101100010110011101111000100110000001101010100110100001001101100100001011001011111110100001001111011011011111101100000000000111100110110111111111110110101100011100000001010010011110010100100100111010010000011110011000000001101110100000111011011111101100100110000101010100010101011000011010010001001101011100101010011100000000001001011010011100100001110010001111101010110001000011001101001010010011000111101011111111010100111110011011010111000111001000011100100011111010101100010000110011010010100100110001111111100011110001010111100

P(0)

P(1)

50%

bit

qubit

0

1

001101111110100110001000110011100111001100011001111010101010001001101110100110110000101101001011000010000000110001001100001100110000111000000010000100001001001111110001000110111110100011000100100110111011100101000010000000011100101111100111011111001110110110111010110111000100001011010100111001110011100110011110110000111100101001000101111000000011101110010001110111100001110010110001010011000010100001101101001001001010110011101001111111010001011111001010111100100111011101001010011010001000110011001001011001100110011100100000100010101011101111110110101001011010001110011110000011110101010100101011011011011001100110101000011001111101011010100000011101110101011011100110010111011010001010000010001010111001010010111110001111111000110000000101101101010100000100001000111110111010101011101001101111001001110011011011010111110100110100100101010001010100010111110111010111001100111000101111001100101110011001000000111110101100011001001010101000100100111110111100000100000000100010011111101001111011010111101011010101100111100001000010000100000110101000110000001100001110001100101100110110001011001110111100010011000000110101010011010000100110110010000101100101111111010000100111101101101111110110000000000011110011011011111111111011010110001110000000101001001111001010010010011101001000001111001100000000110111010000011101101111110110010011000010101010001010101100001101001000100110101110010101001110000000000100101101000011110101111111101010011111001101101011100011100100001110010001111101010110001000011001101001010010011000111111110001111000101011110000101010010011101000010100011001101110110110100000001110111011001000110010001101001101111000000000111000111001001110100111001010101100011000010110100010000001000111011001001101001101001011101010011001001101001001001000010010000000111100000110001000001101001111101110010000101110011111110000001000100001010110001100011000101001011001111010110110100000010110010100110011001100001110010011101001111001010110101000011110110110011111100000000000100010000011011111101001100010001100111001110011000110011110101010100010011011101001101100001011010010110000100000001100010011000011001100001110000000100001000010010011111100010001101111101000110001001001101110111001010000100000000111001011111001110111110011101101101110101101110001000010110101001110011100111001100111101100001111001010010001011110000000111011100100011101111000011100101100010100110000101000011011010010010010101100111010011111110100110011001011100110010000001111101011000110010010101010001001001111101111000001000000001000100111111010011110110101001100001100110000111000000010000100001001001111110001000110111110100011000100100110111011100101000010000000011100101111100111011111001110110110111010110111000100001011010100111001110011100110011110110000111100101001000101111000000011101110010001110111100001110010110001010011001111010110101011001111000010000100001000001101010001100000011000011100011001011001101100010110011101111000100110000001101010100110100001001101100100001011001011111110100001001111011011011111101100000000000111100110110111111111110110101100011100000001010010011110010100100100111010010000011110011000000001101110100000111011011111101100100110000101010100010101011000011010010001001101011100101010011100000000001001011010011100100001110010001111101010110001000011001101001010010011000111101011111111010100111110011011010111000111001000011100100011111010101100010000110011010010100100110001111111100011110001010111100

|0⟩

|1⟩

a|0⟩ + b|1⟩

P(0) = |a|²

P(0)

P(1)

P(1) = |b|²

qubit

bit

0

1

001101111110100110001000110011100111001100011001111010101010001001101110100110110000101101001011000010000000110001001100001100110000111000000010000100001001001111110001000110111110100011000100100110111011100101000010000000011100101111100111011111001110110110111010110111000100001011010100111001110011100110011110110000111100101001000101111000000011101110010001110111100001110010110001010011000010100001101101001001001010110011101001111111010001011111001010111100100111011101001010011010001000110011001001011001100110011100100000100010101011101111110110101001011010001110011110000011110101010100101011011011011001100110101000011001111101011010100000011101110101011011100110010111011010001010000010001010111001010010111110001111111000110000000101101101010100000100001000111110111010101011101001101111001001110011011011010111110100110100100101010001010100010111110111010111001100111000101111001100101110011001000000111110101100011001001010101000100100111110111100000100000000100010011111101001111011010111101011010101100111100001000010000100000110101000110000001100001110001100101100110110001011001110111100010011000000110101010011010000100110110010000101100101111111010000100111101101101111110110000000000011110011011011111111111011010110001110000000101001001111001010010010011101001000001111001100000000110111010000011101101111110110010011000010101010001010101100001101001000100110101110010101001110000000000100101101000011110101111111101010011111001101101011100011100100001110010001111101010110001000011001101001010010011000111111110001111000101011110000101010010011101000010100011001101110110110100000001110111011001000110010001101001101111000000000111000111001001110100111001010101100011000010110100010000001000111011001001101001101001011101010011001001101001001001000010010000000111100000110001000001101001111101110010000101110011111110000001000100001010110001100011000101001011001111010110110100000010110010100110011001100001110010011101001111001010110101000011110110110011111100000000000100010000011011111101001100010001100111001110011000110011110101010100010011011101001101100001011010010110000100000001100010011000011001100001110000000100001000010010011111100010001101111101000110001001001101110111001010000100000000111001011111001110111110011101101101110101101110001000010110101001110011100111001100111101100001111001010010001011110000000111011100100011101111000011100101100010100110000101000011011010010010010101100111010011111110100110011001011100110010000001111101011000110010010101010001001001111101111000001000000001000100111111010011110110101001100001100110000111000000010000100001001001111110001000110111110100011000100100110111011100101000010000000011100101111100111011111001110110110111010110111000100001011010100111001110011100110011110110000111100101001000101111000000011101110010001110111100001110010110001010011001111010110101011001111000010000100001000001101010001100000011000011100011001011001101100010110011101111000100110000001101010100110100001001101100100001011001011111110100001001111011011011111101100000000000111100110110111111111110110101100011100000001010010011110010100100100111010010000011110011000000001101110100000111011011111101100100110000101010100010101011000011010010001001101011100101010011100000000001001011010011100100001110010001111101010110001000011001101001010010011000111101011111111010100111110011011010111000111001000011100100011111010101100010000110011010010100100110001111111100011110001010111100

a|0⟩ + b|1⟩

P(0) = |a|²

P(0)

P(1)

P(1) = |b|²

qubit

bit

|0⟩

|1⟩

001101111110100110001000110011100111001100011001111010101010001001101110100110110000101101001011000010000000110001001100001100110000111000000010000100001001001111110001000110111110100011000100100110111011100101000010000000011100101111100111011111001110110110111010110111000100001011010100111001110011100110011110110000111100101001000101111000000011101110010001110111100001110010110001010011000010100001101101001001001010110011101001111111010001011111001010111100100111011101001010011010001000110011001001011001100110011100100000100010101011101111110110101001011010001110011110000011110101010100101011011011011001100110101000011001111101011010100000011101110101011011100110010111011010001010000010001010111001010010111110001111111000110000000101101101010100000100001000111110111010101011101001101111001001110011011011010111110100110100100101010001010100010111110111010111001100111000101111001100101110011001000000111110101100011001001010101000100100111110111100000100000000100010011111101001111011010111101011010101100111100001000010000100000110101000110000001100001110001100101100110110001011001110111100010011000000110101010011010000100110110010000101100101111111010000100111101101101111110110000000000011110011011011111111111011010110001110000000101001001111001010010010011101001000001111001100000000110111010000011101101111110110010011000010101010001010101100001101001000100110101110010101001110000000000100101101000011110101111111101010011111001101101011100011100100001110010001111101010110001000011001101001010010011000111111110001111000101011110000101010010011101000010100011001101110110110100000001110111011001000110010001101001101111000000000111000111001001110100111001010101100011000010110100010000001000111011001001101001101001011101010011001001101001001001000010010000000111100000110001000001101001111101110010000101110011111110000001000100001010110001100011000101001011001111010110110100000010110010100110011001100001110010011101001111001010110101000011110110110011111100000000000100010000011011111101001100010001100111001110011000110011110101010100010011011101001101100001011010010110000100000001100010011000011001100001110000000100001000010010011111100010001101111101000110001001001101110111001010000100000000111001011111001110111110011101101101110101101110001000010110101001110011100111001100111101100001111001010010001011110000000111011100100011101111000011100101100010100110000101000011011010010010010101100111010011111110100110011001011100110010000001111101011000110010010101010001001001111101111000001000000001000100111111010011110110101001100001100110000111000000010000100001001001111110001000110111110100011000100100110111011100101000010000000011100101111100111011111001110110110111010110111000100001011010100111001110011100110011110110000111100101001000101111000000011101110010001110111100001110010110001010011001111010110101011001111000010000100001000001101010001100000011000011100011001011001101100010110011101111000100110000001101010100110100001001101100100001011001011111110100001001111011011011111101100000000000111100110110111111111110110101100011100000001010010011110010100100100111010010000011110011000000001101110100000111011011111101100100110000101010100010101011000011010010001001101011100101010011100000000001001011010011100100001110010001111101010110001000011001101001010010011000111101011111111010100111110011011010111000111001000011100100011111010101100010000110011010010100100110001111111100011110001010111100

qubit

bit

manglende viden

fundamental egenskab

sandsynlighed, tilfældighed

Gates - de elementære operationer

U

Kredsløb - beregningen

Måling - resultatet

1

0

1

Måling - resultatet

1

0

1 U_f

Superposition af flere qubits

U_f

H

|0⟩ + |1⟩

|0⟩

|000⟩

{

|000⟩ + |001⟩ + ... + |110⟩ + |111⟩

{

Vores første kvantealgoritme

U_f

H

Givet en funktion $f: \{0,1,2,\ldots,2^n-1\}\rightarrow\{0,1\}$ der er enten

konstant: $f(x)=0$ eller $f(x)=1$ for alle $x$, eller

balanceret: $f(x)=0$ for præcist halvdelen af alle $x$ og $f(x)=1$ for resten

Hvor mange evalueringer af $f(x)$ for at afgøre:

konstant eller balanceret?

f(3) = 1

f(0) = 1

f(7) = 1

f(4) = 0

Vores første kvantealgoritme

U_f

H

hvis konstant

1

0

1

0

1

hvis balanceret

0

1

0

Deutsch-Jozsa (1992)

Én evaluering!

Hvordan bygger man én?

Intel 80386 (1985)

275 000 transistorer

Apple M2 Ultra (2023)

134 000 000 000 transistorer

Superledende kredsløb

IBM

Google

Intel

AWS

D-Wave (startup)

Rigetti (startup)

IQM (startup)

Alice & Bob (startup)

...

Ionfælder

Quantinuum (Honeywell)

IonQ (startup)

...

Neutrale atomer

QuERA (startup)

Atom Computing (startup)

PASQAL (startup)

Infleqtion (startup)

...

Fotoner

PsiQuantum (startup)

Xanadu (startup)

Quandela (startup)

...

... med mere

Elektronspin i silicium

- Silicon Quantum Computing (startup)

- Diraq (startup)

Farvecenter i diamant

- Quantum Brilliance (startup)

Majorana fermioner

- Microsoft

?

... men hvilken er så bedst?

Hvad kan den?

U_f

H

Unyttige ting...

Er $f(x)$ konstant eller balanceret?

Mere nyttigt...

Kernen i RSA kryptering

523 × 307 =

173 323 = p × q

p

q

200 819

?

Primtals-faktorisering er svært

2140324650240744961264423072839333563008614715144755017797754920881418023447140136643345519095804679610992851872470914587687396261921557363047454770520805119056493106687691590019759405693457452230589325976697471681738069364894699871578494975937497937

64135289477071580278790190170577389084825014742943447208116859632024532344630238623598752668347708737661925585694639798853367

33372027594978156556226010605355114227940760344767554666784520987023841729210037080257448673296881877565718986258036932062711

Eksponentielt svært!

Indtil Peter Shor...

1994: Kvantealgoritme for effektiv faktorisering af heltal

QFT er kernen

Shor vs. bedste klassiske algoritme

Kvantekryptering

Hvor presserende er det?

Hvor langt er vi?

53 qubits slår klassiske computere

(men i en unyttig opgave)

~1000 qubits

- men uklart hvor gode

Shor's algoritme implementeret

2001:
15 = 5 × 3

2007:
15 = 5 × 3

2012:
21 = 7 × 3

2019:
35 = ? × ?...

In 2019, an attempt was made to factor the number $35$ using Shor's algorithm on an IBM Q System One, but the algorithm failed because of accumulating errors.

[Wikipedia]

Problemet...

Fejl i gates

...og i udlæsning

Vores redningsmand

1995: Det er muligt at fejlkorrigere qubits

Kvantefejlkorrektion

Forskningen rykker lige nu

august 2024

september 2024

Hvornår har vi så nok logiske qubits?

?

Lang vej endnu...

Pricing derivatives would require 8K logical qubits, 54 million T gates and a ≈10$^{-8}$ logical qubit error rate.

Option pricing using an amplitude estimation algorithm including an inverse QFT would require a computing depth between 3,927 and 285,204 [...]

Kan vi slet ikke
bruge dem nu?

NISQ

FTQC

Noisy intermediate-scale quantum computers

Fault-tolerant
quantum computers

Potentielle anvendelser i NISQ-æraen

Simulering

Optimering

QML (kvante-maskinlæring)

Hybride kvante-klassiske algoritmer

...

QML

In the near term, Quantum Variational Classifier and Quantum Kernel Estimation algorithms emerge as realistic options for application on Noisy Intermediate-Scale Quantum (NISQ) devices, showing potential for improvements in tasks like credit scoring and risk management.

[...] architectures like the Quantum Compound Transformer show promise for enhancing models used in financial forecasting and decision-making. [...]
However, they should be perhaps looked at as a longer-term investment due to the lack of sufficient research and experiments to demonstrate their real-life applicability which is currently out of reach of current and near-term quantum devices.

Variationelle (hybrid Q-C) metoder

In conclusion, quantum optimization holds vast potential for various applications, but significant challenges remain in demonstrating a practical quantum advantage.
Once a tangible quantum advantage is demonstrated, we expect that quantum optimization would rapidly influence many domains given the widespread relevance of optimization.