Download The First Quantum Revolution

The Future of Quantum Computing
Dr. Matthew Broome
University of New South Wales
Sydney, Australia
QSceptics2013.pptx
1. What’s weird about quantum?
2. The First Quantum Revolution
– wave-particle duality
– entanglement
3. The Second Quantum Revolution
4. Are Quantum Computers Useful?
5. Challenges For Optical Quantum
Computers
Art vs Physics, Sydney, 2016
Quantum Weirdness:
The First Quantum Revolution
quantum.info
The First Quantum Revolution
Two weird things
Entanglement
Wave-particle duality
Richard Feynman
Nobel
Prize
1965
“…a phenomena which is impossible,
absolutely impossible, to explain in any
classical way, and which has in it the
heart of quantum mechanics. In reality, it
contains the only mystery.”
Erwin Schrödinger
Nobel
Prize
1933
“I would not call that one, but rather
the characteristic trait of quantum
mechanics, the one that enforces its
entire departure from classical lines
of thought.”
quantum.info
The First Quantum Revolution
Two weird things
Entanglement
Wave-particle duality
Richard Feynman
Nobel
Prize
1965
“…a phenomena which is impossible,
absolutely impossible, to explain in any
classical way, and which has in it the
heart of quantum mechanics. In reality, it
contains the only mystery.”
Erwin Schrödinger
Nobel
Prize
1933
“I would not call that one, but rather
the characteristic trait of quantum
mechanics, the one that enforces its
entire departure from classical lines
of thought.”
quantum.info
Waves
Particles
Things, stuff … atoms, planets, frogs…
Discrete – can count them
know where
things go
know where
things are
waves interfere
choppy
calm
quantum.info
What is light?
Particle
1670 Light travels in straight lines
Newton
Wave
1800 Light has interference fringes.
Young
quantum.info
What is light?
Particle
1670 Light travels in straight lines
Newton
Wave
1800 Light has interference fringes.
Young
1880 Light is alternating electric
and magnetic fields.
Maxwell
quantum.info
Who is correct?
quantum.info
Who is correct?
1909 Even feeble light sources cause interference fringes
“a candle burning at a distance slightly exceeding a mile”
G I Taylor
quantum.info
A real single photon experiment
Look at screen...
quantum.info
10 Seconds
quantum.info
100 Seconds
quantum.info
1,000 Seconds
quantum.info
10,000 Seconds
quantum.info
100,000 Seconds
quantum.info
A real single photon experiment
A. Both
Look at screen...
What is light?
quantum.info
Particle
Wave
Look at screen...
What is light?
quantum.info
Particle
Newton
Wave
Young
Look at screen...
What is light?
quantum.info
Particle
Newton
Wave
Young
Look at screen...
What is light?
quantum.info
Particle
Newton
Wave
Young
Look at screen...
quantum.info
What is light?
What is light?
quantum.info
Particle
and
Wave
What is light?
quantum.info
Particle
and
Wave
Depending on what is being measured
What is light?
quantum.info
50%
“click”
“click”
50%
half-silvered
mirror
light acts like it is a particle
What is light?
quantum.info
25%
25%
50%
half-silvered
mirror
block
half-silvered
mirror
full-silvered
mirror
light acts like it is a particle
What is light?
quantum.info
0%
full-silvered
mirror
100%
half-silvered
mirror
half-silvered
mirror
full-silvered
mirror
How can a particle do this?
Particles can’t … waves can
What is light?
quantum.info
0%
full-silvered
mirror
100%
+
half-silvered
mirror
full-silvered
mirror
What is light?
quantum.info
0%
full-silvered
mirror
half-silvered
mirror
100%
full-silvered
mirror
light acts like it is a wave
Maybe we can trick the photon?
What is light?
quantum.info
full-silvered
mirror
half-silvered
mirror
half-silvered
mirror
full-silvered
mirror
What is light?
quantum.info
25%
full-silvered
mirror
25%
half-silvered
mirror
block
half-silvered
mirror
full-silvered
mirror
Wave/particle duality
quantum.info
0%
full-silvered
mirror
100%
half-silvered
mirror
block
half-silvered
mirror
full-silvered
mirror
everything
light can act as a particle or a wave
…it depends on the experiment
electrons
neutrons
atoms
molecules, Na2
bucky ball molecules, C60, C70
viruses…
I lied....
quantum.info
Not photons....
I lied....
quantum.info
Not photons....
actually electrons.... particles with mass!
quantum.info
The Quantum Revolution
Two weird things
Entanglement
Wave-particle duality
Richard Feynman
Nobel
Prize
1965
“…a phenomena which is impossible,
absolutely impossible, to explain in any
classical way, and which has in it the
heart of quantum mechanics. In reality, it
contains the only mystery.”
Erwin Schrödinger
Nobel
Prize
1933
“I would not call that one, but rather
the characteristic trait of quantum
mechanics, the one that enforces its
entire departure from classical lines
of thought.”
quantum.info
Entanglement: a culinary analogy
• Cakes prepared in pairs
• Baked on trips down
two conveyor belts
Q
Cakes
Inc.
• Lucy measures Left conveyor
• Ricky measures Right conveyor
Kwiat and Hardy, American Journal of Physics 68, 33, (2000)
quantum.info
Entanglement: a culinary analogy
• Cakes prepared in pairs
• Baked on trips down
two conveyor belts
Q
Cakes
Inc.
• Lucy measures Left conveyor
• Ricky measures Right conveyor
• For each cake-pair they each randomly choose to measure
EITHER at half-way, the state of the cake
Risen / Flat
quantum.info
Entanglement: a culinary analogy
• Cakes prepared in pairs
• Baked on trips down
two conveyor belts
Q
Cakes
Inc.
• Lucy measures Left conveyor
• Ricky measures Right conveyor
• For each cake-pair they each randomly choose to measure
EITHER at half-way, the state of the cake
Risen / Flat
at end, the taste of the cake
Good / Bad
• So they measure:
state / state (25%)
state / taste (25%)
taste / state (25%)
taste / taste (25%)
quantum.info
Entanglement: a culinary analogy
• Cakes prepared in pairs
• Baked on trips down
two conveyor belts
Q
Cakes
Inc.
• Lucy and Ricky find that 10% of the time both cakes are Risen (RR)
quantum.info
Entanglement: a culinary analogy
• Cakes prepared in pairs
• Baked on trips down
two conveyor belts
Q
Cakes
Inc.
• Lucy and Ricky find that 10% of the time both cakes are Risen (RR)
• Whenever Lucy’s cake is Risen, Ricky’s cake tastes Good (RG)
quantum.info
Entanglement: a culinary analogy
• Cakes prepared in pairs
• Baked on trips down
two conveyor belts
Q
Cakes
Inc.
• Lucy and Ricky find that 10% of the time both cakes are Risen (RR)
• Whenever Lucy’s cake is Risen, Ricky’s cake tastes Good (RG)
• Whenever Ricky’s cake is Risen, Lucy’s cake tastes Good (GR)
quantum.info
Entanglement: a culinary analogy
• Cakes prepared in pairs
• Baked on trips down
two conveyor belts
Q
Cakes
Inc.
• Lucy and Ricky find that 10% of the time both cakes are Risen (RR)
• Whenever Lucy’s cake is Risen, Ricky’s cake tastes Good (RG)
• Whenever Ricky’s cake is Risen, Lucy’s cake tastes Good (GR)
• How often do both Lucy and Ricky find that both cakes taste Good? (GG)
Measure taste / taste 25% of time
Therefore expect both Good = 25% x 10% = 2.5% (at least)
If the cakes are entangled, then quantum mechanics predicts
both cakes never taste Good! = 0%
Einstein had major problems with this!
quantum.info
Entanglement: the cake experiment
• Photons entangled in polarisation
US
Patent
6424665
We found that both cakes
never tasted good
Pretty sure…
with 2 reasonable physical assumptions,
probability of error is 0.0000…00006%
3,233 zeroes
If there is a hidden variable theory
that describes the world, then it requires
some faster-than-light aspects…
R = -50.9˚ G = 0˚ (horizontal)
F = 39.2˚ B = 90˚ (vertical)
quantum.info
weird?
useful…
Quantum technologies use the wave/particle duality
quantum.info
Great... but what is all this good for?
quantum.info
Great... but what is all this good for?
The First Quantum Revolution:
Using quantum mechanics to predict interesting physical behaviour
- Wave/particle duality
- Entanglement
quantum.info
Great... but what is all this good for?
The First Quantum Revolution:
Using quantum mechanics to predict interesting physical behaviour
- Wave/particle duality
- Entanglement
“...there is a Second Quantum Revolution coming —
which will be responsible for most of the key physical
technological advances for the 21st Century”
Dowling & Milburn, Philosophical Transactions of the Royal Society of London A 361, 1655 (2003)
quantum.info
Great... but what is all this good for?
The First Quantum Revolution:
Using quantum mechanics to predict interesting physical behaviour
- Wave/particle duality
- Entanglement
“...there is a Second Quantum Revolution coming —
which will be responsible for most of the key physical
technological advances for the 21st Century”
Dowling & Milburn, Philosophical Transactions of the Royal Society of London A 361, 1655 (2003)
The Second Quantum Revolution:
Engineered quantum systems
- Quantum technologies
- Quantum computers
- Quantum communications
quantum.info
Great... but what is all this good for?
The First Quantum Revolution:
Using quantum mechanics to predict interesting physical behaviour
- Wave/particle duality
- Entanglement
“...there is a Second Quantum Revolution coming —
which will be responsible for most of the key physical
technological advances for the 21st Century”
Dowling & Milburn, Philosophical Transactions of the Royal Society of London A 361, 1655 (2003)
The Second Quantum Revolution:
Engineered quantum systems
- Quantum technologies
- Quantum computers
- Quantum communication
Entanglement
Wave-particle duality
In the last 10 years, >10,000 papers on Quantum Information Science
Quantum Computing:
The Second Quantum Revolution
Classical computing
quantum.info
insoluble
insoluble
hard
soluble
factoring
travelling
salesman
easy
Nomenclature
easy = “tractable” = “efficiently computable”
hard = “intractable” = “not efficiently computable”
Quantum computing
quantum.info
insoluble
insoluble
hard
soluble
travelling
salesman
factoring
easy
Nomenclature
easy = “tractable” = “efficiently computable”
hard = “intractable” = “not efficiently computable”
Quantum computers are interesting physical systems in their own right
quantum.info
Quantum computing everywhere?
• To build a quantum computer, need 2-level quantum systems — qubits
• Over 20 physical systems currently being experimentally investigated
Computing
quantum.info
Classical
Quantum
Bits, binary digits
Qubits
0
1
0
0+1
Gates
0+i1
Toffoli
1
NAND
Gates
INPUT
A
B
0
0
0
1
1
0
1
1
OUTPUT
A AND B
1
1
1
0
can be
irreversible
A
0
0
0
0
1
1
1
1
INPUT OUTPUT
B
C
A
B
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
CNOT
C
0
1
0
1
0
1
1
0
can be reversible
INPUT
A
B
0
0
0
1
1
0
1
1
OUTPUT
A
B
0
0
0
1
1
1
1
0
0+1 0
00+11
must be reversible
quantum.info
Where are we with quantum
computers?
quantum.info
- Single photons
Where are we with quantum
computers now?
quantum.info
- Single photons
- Trapped ions
Where are we with quantum
computers now?
quantum.info
Where are we with quantum
computers now?
- Single photons
- Trapped ions
- Superconducting circuits
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
Factoring numbers into primes - Shor’s Algorithm
insoluble
hard
travelling
salesman
factoring
easy
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
Factoring numbers into primes - Shor’s Algorithm
3x5 = 15
insoluble
hard
travelling
salesman
factoring
easy
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
Factoring numbers into primes - Shor’s Algorithm
3x5 = 15
3x7 = 21
insoluble
hard
travelling
salesman
factoring
easy
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
Factoring numbers into primes - Shor’s Algorithm
3x5 = 15
3x7 = 21
Simulating quantum systems
insoluble
hard
travelling
salesman
factoring
easy
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
Factoring numbers into primes - Shor’s Algorithm
3x5 = 15
3x7 = 21
Simulating quantum systems
Lanyon, et al., Nature Chemistry 2, 106 (2010)
insoluble
hard
travelling
salesman
factoring
easy
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
Factoring numbers into primes - Shor’s Algorithm
3x5 = 15
3x7 = 21
Simulating quantum systems
Shors algorithm
Quantum chemistry
Simulating quantum systems...
Are quantum computers actually useful?
insoluble
hard
travelling
salesman
factoring
easy
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
Factoring numbers into primes - Shor’s Algorithm
3x5 = 15
3x7 = 21
Simulating quantum systems
Shors algorithm
Quantum chemistry
Simulating quantum systems...
Are quantum computers actually useful? YES!
insoluble
hard
travelling
salesman
factoring
easy
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
Factoring numbers into primes - Shor’s Algorithm
3x5 = 15
3x7 = 21
Simulating quantum systems
Shors algorithm
Quantum chemistry
Simulating quantum systems...
Are quantum computers actually useful? YES!
PROVE IT!
insoluble
hard
travelling
salesman
factoring
easy
quantum.info
Where are we with quantum
computers now?
- Solving small scale problems
insoluble
Factoring numbers into primes - Shor’s Algorithm
travelling
salesman
factoring
easy
3x5 = 15
3x7 = 21
Simulating quantum systems
Shors algorithm
Quantum chemistry
Simulating quantum systems...
Are quantum computers actually useful? YES!
PROVE IT!
hard
OK.
Small scale
^
Experimental
BosonSampling
qt
lab
quantum.info
:
AUSTRALIAN RESEARCH COUNCIL
CENTRE OF EXCELLENCE FOR
ENGINEERED QUANTUM SYSTEMS
Unsolved Problem in
Computer Science
The Extended Church-Turing Thesis (ECT)
Statement:
“All computational problems that are efficiently solvable by
realistic physical devices, are efficiently solvable by a
probabilistic Turing machine”
Why bother building a quantum computer?
Including quantum computers
qt
lab
The Extended Church-Turing Thesis (ECT)
Lots of head scratching....
No widely accepted proof FOR or AGAINST the ECT
- Dershowitz and Falkovich (2012). “A formalisation and proof of the
Extended Church-Turing thesis”, arXiv:1207.7148v1
&
Experience tells us that simulating quantum systems is HARD
- Feynman, (1982). “Simulating Physics with Computers”,
International Journal of Theoretical Physics 21 (6–7): 467–488
- Lloyd, (1996). “Universal Quantum Simulators”,
Science 273 (5278)
&
Shor’s algorithm is faster than any known classical counterpart
qt
lab
- Shor (1994), Proc. 35th Ann. Symp. Found. Comp. Sci.,
IEEE Comp. Soc. Press, Los Alamitos, California p. 124
Problem?
Existence of Shors algorithm poses a Trilemma
- Aaronson, (2004), Limits on Efficient Computation in the Physical World
Fast quantum algorithm
arXiv:quant-ph/0412143
for factoring numbers
into primes
1. The Extended Church-Turing thesis is incorrect
- cannot efficiently simulate quantum systems using classical computers
2. Quantum mechanics is wrong
- # qubits >> quantum mechanics breaks -> can’t factor large numbers
3. There is a fast classical factoring algorithm
- RSA key encryption breaks down
qt
lab
1. The Extended Church-Turing thesis is incorrect
- cannot efficiently simulate quantum systems using classical computers
How do we show this?
One way to do this:
Build a physical device that computes something KNOWN or STRONGLY BELIEVED to
be classically intractable...
Shor’s Algorithm?
Building scalable
Factoring NOT KNOWN
qt
lab
to be classically
intractable
quantum computers is
Fast quantum algorithm
for factoring numbers
HARD!
Computing With Optical Networks
Complexity of linear optical networks
Can we use linear optical networks to calculate HARD problems?
YES! BosonSampling
m bosons
⎧ ●●
⎪ ●
⎨
⎪
⎩ ●●●
1
2
3
⋮
n
Network
⋮
?
?
?
?
We measure
Aaronson, S., and Arkhipov, A., (2011), The Computational Complexity of Linear
Optical Networks, Proc. of the 43rd annual ACM symp. on theory of comp., p. 333342
would make
lot toofcalculate
us really
However, optical networks This
output distributions
that are a
HARD
on classical
computers → BosonSampling
unhappy!
Main Results
If a classical computer can do the same in efficiently the polynomial hierarchy collapses!
Large Scale Demonstration would be Strongest empirical evidence for
qt
lab
1. The Extended Church-Turing thesis is incorrect
- cannot efficiently simulate quantum systems using classical computers
Remarks on BosonSampling
Large scale demonstration would be Strongest empirical evidence against ECT
Universal Quantum Computer
1.
BosonSampling is a model of intermediate quantum computation
Classical Computer
2.
Unlike factoring large primes, BosonSampling is KNOWN to be
classically HARD
3.
Ultimate goal: Large scale BosonSampling --> Quantum Wins
m = 20-30 photons
2
n = m ~ 400-900
modes
Can verify fast quantum
experiment
using a slow classical simulation
qt
lab
Demonstrates that at least ECT is incorrect up to this limit
Experimental BosonSampling
6x6 mode linear optics network
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Quantum Computer Scientist
6x6 mode linear optics network
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Photons
6x6 mode linear optics network
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Quantum Computer Scientist
Beam-Splitter Network
Photons
6x6 mode linear optics network
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Photon Detectors
Beam-Splitter Network
Photons
2 Photons in 6 Modes
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Quantum Computer Scientist
2 Photons in 6 Modes
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Classical Computer Scientist
U
6
2 Photons in 6 Modes
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Classical Computer Scientist
U
6
Quantum Computer Scientist
2 Photons in 6 Modes
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2 Photons in 6 Modes
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3 Photons in 6 Modes
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How do we know we’re sampling
the quantum distribution?
3 classical states in 6 Modes
Similar interference experiment using classical states (lasers)
don’t produce the same outputs as single photons
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Strong evidence to suggest using classical states is EASY to predict
Rohde, Ralph, PRA, (2012)
Experimental imperfections
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Experimental imperfections
Not a perfect single photon source...
... higher order photon emission reduces number state purity
Challenges for
Photonic Quantum Computing
The Challenges
Photons
True
single photons
Large scale BosonSampling
m = 20-30 photons
2
n = m ~ 400-900 modes
Detectors
fast,
efficient,
quiet,
numberresolving...
Large
Scale
Photonic
QC
Linear optics
Low loss
Large networks
The Challenges
Detectors
Photon-number resolving
Efficient
Large
Scale
Photonic
QC
Fast
Quiet
✓
⩽ 99±1%
150-250 ps jitter, 1 ns rise ...
≪1 photon dark noise @ 800
nm
Broadband 0.4-5.0 µm
Smith, Devin H., et al. "Conclusive quantum steering with superconducting transition-edge
The Challenges
Linear optics
Low loss
MONDAY
Sciarrino
✓
Compact
Robust
Large
Scale
Photonic
QC
Maskless fabrication
Reconfigurable
Ensure U is
HARD
To sample
Peruzzo, A., et al., (2010), Quantum walks of correlated photons, Science 389, 5998
Shadbolt, P. J., et al., (2011), Generating, manipulating and measuring entanglement and
The Challenges
Photons
Current best photon source:
spontaneous downconversion
~
Excellent spatio-temporal modes, entanglement T<99.9%
BUT
Low event probability <10-4% ... eight-fold events 10/day
Large
Scale
Photonic
QC
Higher-order terms:
2-4% 4-photon events
lead to 20% gate errors
M. Barbieri, et. al.,
JMO, (2011)
Dousse et al., Nature 466, 217–220 (2010)
MUCH better
sources are
required
High event probability 40%
BUT Higher-order spatial modes...
~
The Challenges
Photons
True
single photons
✓
Detectors
fast,
efficient,
quiet,
numberresolving...
Large
Scale
Photonic
QC
~
Theory
Fault tolerance
Imperfect Experiments
✓
Linear optics
Large
Low Loss
Outlook for Quantum Computing
QIT industry strategy?
QKD
Banks, government
QC
Simulation: semiconductors, …
QC
Factoring, searching
2005
2010
2015
2020
2025
2030
2035
Courtesy of R. Beausoleil, HP Labs, Palo Alto
38
QIT industry strategy!
QKD
Banks, government
Few-qubit QIP
Distributed algorithms & entanglement, economics, …
QC
Simulation: semiconductors, …
QC
Factoring, searching
2005
2010
2015
2020
2025
2030
2035
Courtesy of R. Beausoleil, HP Labs, Palo Alto
39
Where to next?
quantum.info
Today
The Future