Quantum information:
from the optics laboratory to the “real” world
Kevin Resch
IQC, Dept. of Physics
University of Waterloo
Institute for Quantum Computing
Founded 2001 at
University of
Waterloo
14 faculty
6 post-docs
~50 students
Always looking for more!
Waterloo, Ontario
http://www.iqc.ca/
Optical quantum
Talk Outline
information
Quantum
Information
Quantum
Foundations
Nonlinear
Optics
Quantum
Computation
Measurementinduced
nonlinearity
Interferenceenhanced
nonlinearity
One-way quantum
computation
Linear optics
entangling gates
Quantum
Communication
Free-space
entanglement
distribution
Entanglement
Purification
Quantum
Metrology
Classical
analogues of
quantum
interference
Tomography
Weak
measurement
Multipartite
entanglement
Nonlocality
tests
Quantum information
Quantum bits can be 0 or 1 but also superpositions
bit:
0 or 1
qubit: |0 + |1
|1 = |V
|0 = |H
Photon Polarization
|1
|0
Atomic Levels
Familiar quantum features
Uncertainty principle

 x p 
2
Position
W. Heisenberg
Momentum
No-cloning theorem
 0   
NOPE
Wootters
Zurek
Dieks
…leads to ultimate cryptosystem
“X”
“P”
An
eavesdropper
Attempting
Single
Nor
can
photons
the
must
make
either
strategy
are sent
eavesdropper
in one
measurements
to
will
lead
to
of two
make
identical
learn
about
the
errors
in the
noncommuting
copies
of
the
state,
butsignal
cannot
detected
basis states
state
and
make
do
so without on
measurements
disturbance
them (no-cloning)
(HUP)
C. Bennett, G. Brassard 1984
More quantum features
Superposition

A quantum system can be in
many states at the same time
 

1

N
1

Interference
2

3

 ...
…more powerful computers
ψ
I O
Feynman
Deutsch
Measurement
A computer
Quantum
results
aretakes
takes some
computer
inputa
random,
state to except
superposition
an of
that
interference
output
all
possible
state
(+clever
inputs state to a
algorithms)
can
superposition
of
reduce
wrong
all possible
answers
output states
Entanglement
Separable
An
entangled
states
state
(not entangled)

12


1
  0 1 
0 2 1 1  1 2
1
2
212
“Bell state”
 00  11
Foundation for most quantum information
protocols
Optical photons as qubits
Spatial modes
Polarization
+i
=
|V>
|H>
|D>
|R>
Time-bin
t1
t
Freq. encoding
t2
t
Optical photons as qubits
The Good
Single-qubit
operations
Low decoherence
High speed
Perfect carriers
of quantum
information
The Bad
Easy to lose a
photon
No natural
interactions/weak
nonlinearities
means 2-qubit
operations are
hard
The Ugly
Linear optics
proposals for
scalable quantum
computing are
extremely
complicated
(~50-1000s of
ancillas/elements
per CNOT)
Entangled Photon Source
Parametric Down-conversion
“blue” photon
two “red”
photons
c(2)
wpump = ws + wi
Phase matching:
kpump = ks + ki
Type-II Down-conversion
Entangled Pair
 

1
H 1V
2
2
V
1
H
2
H-Photon
Confused
Correlated V-Photon

Recent source advancements
High-power UV laser diodes (cheap,
easy to use -> UG lab!)
Efficient single-mode coupling (longdistance, low divergence, free-space)
4-, 5-, and 6-photon entanglement

Controllable entanglement – fundamental tests and
quantum computing
State of the art
Source
Brightness
Number
of photons
entangled
Entangled
Pair Detection
Rate (Hz)
Number
of photons
7
10
10
Entangling
Downconversion
measurements
6
10
85
10
4
106
1000
4
100
Year
Year
2010
2010
2005
2005
2000
2000
1995
1995
1990
1990
1985
1985
1980
1980
1975
1975
0
0.1
1970
1970
10 Atomic Cascade
2
1
Long-distance
Entanglement distribution
Quantum source
Zeilinger Group
Not Pictured here:
FS1&2: Michael Taraba
FS2: Bibiane Blauensteiner, Alessandro Fedrizzi, Christian Kurtsiefer,
Tobias Schmitt-Manderbach, Henning Weier, Harald Weinfurter
Distributing Entanglement
Photons are the ideal carriers
Practical quantum communication needs
shared entanglement over long distances
Challenges: High efficiency (no cloning)
and high background rejection (single
photons)
Entanglement takes to the air
500m
150m
Quantum correlations
A “Bell experiment”
+1
+1
-1
Set {A, A’}
Source
Set {B, B’}
Local properties (ex. A=+1, A’=-1, B=+1, B’=+1)
A(B+B’)+A’(B-B’) = ±2
CHSH-Bell inequality (req. 16 measurements)
S = |<AB+AB’+A’B-A’B’>| ≤ 2
QM allows S = 2√2 = 2.83
-1
Freespace 1 Results
Measured S = 2.4 ± 0.1 (larger than 2 indicates
entanglement)
Two links 500m &
100m
~10 coincidences/s
SMF-SMF coupling
Time-stable
channel
Polarization correlations
Science (2003)
The next step
500m to 7.8km (the atmosphere
straight up is 7.3km thick)
No more cable
Light passed over a city – likely realworld scenario
Source telescope
From Source
15cm
Atmospheric fluctuations
Receiver/Movie
Test Range
4 km
Laser source
FS1
Receiver module
H
-45o
45o
PBS
To detector
PBS
λ/2
50/50
V
Practicalities
Absence of good single-photon sources
Can use quantum randomness to select state:
Alice
PBS HWP
BS
45/-45
-45
45
HH  VV
 45,45   45,45
PBS
(HV)
V
H
Triggered single photons, reduced “empty” pulses |0>
and double photons |2>
Laser frequency monitoring unnecessary
Entanglement takes to the air –
again!
Freespace 2
7.8km
ALICE
HWPs
BOB
Pol.
PBS
B
DC
45
HWP PBS
Pol.
45
BS
PBS
BS
PBS
Free-space
(Quantum
Channel)
A
H
Time-tagging
V 135
H
GPS
Rb-clock
Time-tagging
GPS, Rb clock
Public Internet (Classical Channel)
VIENNA
ALICE
V 135
7.8km
BOB
Freespace 2 Results
S = 2.27±0.019 > 2
Quantum Correlations!
Two links 7.8 km and 10-4km
25 ccps found over time tags/internet
Single-mode fibre to spatial-filter coupling
14-σ Bell violation, all 16 meas. taken simultaneously
Optics Express (2005)
Remaining challenges
Longer distances, Higher bit rates
Active components to compensate atmosphere
Long-distance quantum interference
(repeaters)
Full cryptography, different protocols
Moving targets (satellites, airplanes)
IQC free-space experiment
Gregor Weihs
Raymond Laflamme
Chris Erven
One-way quantum computation with
a multi-photon cluster state
“1”
Photonic one-way quantum computation
Philip Walther (ViennaHarvard)
Terry Rudolph (Imperial)
Emmanuel Schenck (ViennaENS)
Vlatko Vedral (Leeds)
Markus Aspelmeyer (Vienna)
Harald Weinfurter (LMU, Munich)
Anton Zeilinger (Vienna)
QC - Circuit vs. One-way model
One-way model
Circuit Model
|0
|0
“1”
Unitary
“0”
|0
|0
“1”
“1”
H
X
Physical qubit
Readout
Algorithm
(dynamics)
Initialization (all
qubits |0)
(classical bits)
Initialization
Readout
Algorithm
(prepare
a “cluster
(measure
finalstate”)
qubits)
(single-qubit
measurements)
Raussendorff & Briegel, PRL 86, 5188 (2001)
Optics: Neilsen; Browne/Rudolph
One-way quantum computing
Cluster states can be represented by graphs
Entanglement “bond”
CPHASE
|+
00|+
01
10
11 |+
|+
00
|+
01
10
|+
-11
0   1
Processing encoded information
How measurement can compute
|ψ>
|+>
Measure
1 in B(α)
Form
If
Qubit
“0”,a2do
cluster
isQubit
nothing
HRz(α)|ψ>
state
iα|1, |0 - eiα|1}
B(α)
= {|0
+ eNOT
“1”,
apply
(bit flip)
2 If
This is an example of Feed-forward
1
Equivalent
0
1 quantum circuit
|ψ>
Rz(α)
H
More general computations
Number of encoded qubits
Number of operations
Readout
Making cluster states
|ψ> = |HHHH>+|HHVV>
+|VVHH>-|VVVV>
Polarizing Beam-splitter
Quantum “parity check”
V polarization
H polarization
The four-photon cluster
Quantum state tomography
Reconstructed density matrix
Fidelity = 63%
Clusters to circuits
Horizontal bond:
Rz(-)
H
Rz(-)
H
Rz(-)
H
1:B()
Vertical bond:
1:B()
2:B()
Clusters to circuits
Multiple circuits
using a single
cluster
One-qubit computations
Different order of
measurements
Two-qubit computations
Single & two-qubit operation
Single-qubit rotations
Fid ~ 83-86%
Two-qubit operations
Separable
Entangled
Fid = 93%
Tangle = 0
Fid = 84%
Tangle = 0.65
Grover’s Algorithm
Hard
Easy
Best Classical: O(N) queries
Quantum: O(√N) queries
Sorted database
Unsorted database
L.K. Grover, Phys. Rev. Lett. 79, 325-328 (1997).
Conclusions and Future directions
First demonstration of one-way quantum
computation using cluster states
Experimental


Larger cluster states = more complex circuits
Feed-forward – two types – easy and hard
Theoretical


Different geometries and measurements
Higher dimensions
Summary
“Real” world

First experiments demonstrating free-space
entanglement distribution
Ideal world

First demonstration of Cluster State Quantum
Computing – including the first algorithm
Clusters/Grover’s Algorithm
90% correct
computational output
First algorithm in the
cluster model
Grover’s algorithm
Interference
Quantum
On
a query
parallelism
to the black box (quantum
database/phonebook),
the
of the
“Inversion
about
mean”
amplifies
GA initializes
thethe
qubits
tosign
equal
amplitude
the
special
element
is
the
correctofelement
and reduces
the
superposition
of all
possible
inputs
flipped
others
Mean
Ampl
000
100
Element
111
THANK YOU!